Sloan Andrew

The Role of Non-Ferritic Phase in the

Micro-Void Damage Accumulation and Failure

of Dual-Phase Steels

by

Andrew D.C. Sloan

A thesis submitted to the

Department of Mechanical and Materials Engineering

in conformity with the requirements for

the degree of Master of Applied Science

Queen’s University

Kingston, Ontario, Canada

September 2011

Copyright c© Andrew D.C. Sloan, 2011

For Sarah

There’s no question, you’re the answer.

i

Abstract

Dual-phase (DP) sheet steels are a class of advanced high strength steels which boast a

desirable combination of properties for the forming of automotive components, includ-

ing: high strength, continuous yielding behaviour, and a high initial work hardening

rate. The higher strength of DP steels relative to predecessors used to form automo-

tive components allows for a reduction in part gauge, translating to the potential for

reduced automobile weight, emissions, and fuel consumption.

However, a form of premature failure during component forming known as ‘shear

fracture’ has become a prominent challenge to manufacturers’ adoption of DP steels.

Martensite particles in DP steel microstructures act as nucleation sites for the de-

velopment of void damage during deformation, resulting in a deleterious effect upon

formability and thought to contribute to the observed shear fractures.

This dissertation contributes to the overall goal of offering guidance for the im-

provement of DP steel microstructures for more desirable fracture behaviour. Specif-

ically, the role of non-ferritic phase/constituent (NFP) volume percent and spatial

distribution in the accumulation of void damage in DP steels was investigated. Void

damage accumulation in ten DP steel microstructural variants tested to failure under

near plane-strain deformation was qualified and quantified in three dimensions using

an X-ray micro-computed tomography technique. These results were correlated to the

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microstructural parameters of the variants, which clearly indicated the detrimental

effects of NFP banding in DP steels.

It was observed that DP microstructures with increased severity of NFP banding

(generally aligned in the sheet rolling direction) incurred a reduced strain to failure.

Often, microstructural variants with NFP bands aligned transverse to the major

loading direction incurred a reduced strain to failure, accumulated a greater number

of voids, and exhibited a larger void volume percent than a specimen with oppositely

oriented NFP bands. Void damage spatial distribution was generally reflective of

the spatial distribution of the most coarse NFP bands through the sheet thickness.

In microstructural variants with NFP bands aligned transverse to the major loading

direction, accumulated void damage was often observed to be highly elongated in the

direction of NFP banding.

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Acknowledgments

I would like to extend my sincerest thanks to my supervisors Dr. Keith Pilkey and

Dr. Doug Boyd. Your genorosity, candor, and genuine interest in the success of my

graduate studies at Queen’s University have made this journey a most enjoyable one.

Thank you for all of your guidance, the independence you have granted me, and the

Tuesday afternoon shinny.

I am grateful for all of the assistance of Charlie Cooney; he is a true MacGyver

of materials science problems. His resourcefulness and extensive practical knowledge

prevented many hours of fruitless experimentation. The McLaughlin Hall machine

laboratory technicians, particularly Andy Bryson, deserve my thanks for all of their

assistance in mechanical testing specimen preparation.

Many thanks are extended to Dr. Brent Lievers for his expertise in the use of

Linux and Tesselation3DSuite. Hossein Seyedrezai has been an excellent colleague

for discussing the minutiae of dual-phase steels with. Of course, thanks go to Eric

Tulk too for his friendship and comic relief; especially the SSMB and the materials

engineering puns.

Luke Hunter and Tiffany Fong of Xradia Inc. were most helpful in tackling tomo-

graphic issues. The work of Drew Marshall, Sean Cunningham, and Brandon Haw,

NSERC Undergraduate Summer Research Award (USRA) students, was invaluable

iv

to the completion of this thesis.

I acknowledge the financial support of Queen’s University, the AUTO21 Network

of Centres of Excellence, and the U.S. Steel Canada graduate fellowship. Thank you

to U.S. Steel and Jian Wang for supplying the sheet steel used in this study.

Sarah, this thesis is dedicated to you for enduring the endless hours of materials

banter between Eric and I, the nights and weekends at the lab, and for your unwaver-

ing encouragement. Most of all, thank you to my family. Without your love, support,

and teachings, I would not be half the man I am today.

v

List of Abbreviations

AHSS Advanced high-strength steelAT Austempering/AustemperedBCC Body-centered cubicBCT Body-centered tetragonalCCD Charge-coupled deviceCCT Continuous cooling transformationCR Cold-rolledDP Dual-phaseFCC Face-centered cubicFEM Finite element methodFLC Forming limit curveFLD Forming limit diagramFOV Field of viewfps Frames per secondGA GalvannealedHSLA High-strength low-alloyHSS High-strength steelIC IntercriticalIPPS In-plane plane-strainIR InfraredLAC Linear absorption coefficientMSE Mean squared errorND Through-thickness direction of sheetNDT Non-destructive testingNFP Non-ferritic phase(s) and/or constituent(s)NL-means Non-local meansRD Rolling direction of sheetROI Region of interestSEM Scanning electron microscopeSMB Sodium MetabisulfiteSNR Signal-to-noise ratioTD Transverse direction of sheetUTS Ultimate tensile strengthXµCT X-ray micro-computed tomography

vi

Nomenclature

Ac1 Eutectoid temperature

Ac3 Minimum austenitizing temperature

Ar3 Austenite to ferrite start temperature

Ms Martensite start temperature

Mf Martensite finish temperature

φ Spherical coordinate azimuth orientation of a void.

θ Quasi-spherical coordinate inclination orientation. See Table 4.8

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Contents

Abstract ii

Acknowledgments iv

List of Abbreviations vi

Nomenclature vii

List of Tables xvi

List of Figures xviii

Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Chapter 2: Literature Review . . . . . . . . . . . . . . . . . . . . . . . 9

2.1 DP Steel Microstructures . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.2 Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2.1 Commercial DP Steel Processing . . . . . . . . . . . 12

viii

2.1.2.2 Austenite Formation during IC Annealing . . . . . . 14

2.1.2.3 Transformation of Austenite to Martensite . . . . . . 15

2.1.2.4 Evolution of Microstructural Banding . . . . . . . . 16

2.2 DP Steel Mechanical Properties . . . . . . . . . . . . . . . . . . . . . 21

2.2.1 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.2 Constituent Strain Incompatibility . . . . . . . . . . . . . . . 22

2.2.3 Work Hardening . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.4 Ductility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.5 Sheet Metal Formability . . . . . . . . . . . . . . . . . . . . . 24

2.2.6 In-Plane Plane-Strain Tensile Testing . . . . . . . . . . . . . . 24

2.3 Ductile Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3.1 Void Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.1.1 Void Nucleation Mechanisms . . . . . . . . . . . . . 27

Effect of Martensite Particle Size . . . . . . . . . . . . 29

Effect of Martensite Particle Shape . . . . . . . . . . . 31

Effect of Martensite Spatial Distribution . . . . . . . . 32

Effect of Martensite Carbon Content . . . . . . . . . . 34

2.3.1.2 Critical Nucleation Strain . . . . . . . . . . . . . . . 35

2.3.2 Void Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.3.3 Void Coalescence . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.3.4 Fracture Surface Orientation . . . . . . . . . . . . . . . . . . . 37

2.4 Damage Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.4.1 X-ray Micro-computed Tomography . . . . . . . . . . . . . . . 39

2.4.1.1 Micro-focus X-ray Sources . . . . . . . . . . . . . . . 39

ix

2.4.1.2 X-ray attenuation . . . . . . . . . . . . . . . . . . . 40

2.4.1.3 Tomography Fundamentals . . . . . . . . . . . . . . 42

2.4.1.4 Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . 44

Beam Hardening . . . . . . . . . . . . . . . . . . . . . 44

Ring Artifacts . . . . . . . . . . . . . . . . . . . . . . . 45

Streak Artifacts . . . . . . . . . . . . . . . . . . . . . . 47

2.4.2 Previous XµCT Experimentation . . . . . . . . . . . . . . . . 48

2.5 Digital Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.5.1 Image Denoising . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.5.2 Image Segmentation . . . . . . . . . . . . . . . . . . . . . . . 56

Chapter 3: Experimental Methods and Materials . . . . . . . . . . . 58

3.1 Received Material Characteristics . . . . . . . . . . . . . . . . . . . . 58

3.2 DP Steel Microstructural Variant Design . . . . . . . . . . . . . . . . 59

3.2.1 Thermal Path One . . . . . . . . . . . . . . . . . . . . . . . . 60

3.2.2 Thermal Path Two . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2.3 Heat Treatment Procedures and Apparatus . . . . . . . . . . . 61

3.2.4 IPPS Specimen Heat Treatment Schedule . . . . . . . . . . . . 65

3.2.4.1 Austempering Apparatus . . . . . . . . . . . . . . . 69

Tube Furnace Preparation . . . . . . . . . . . . . . . . 69

Custom Salt Bath Preparation . . . . . . . . . . . . . . 70

3.2.4.2 Austempering Procedure . . . . . . . . . . . . . . . . 70

3.2.4.3 IC Annealing Apparatus . . . . . . . . . . . . . . . . 71

Salt Bath Preparation . . . . . . . . . . . . . . . . . . 72

3.2.4.4 IC Annealing Procedure . . . . . . . . . . . . . . . . 72

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3.3 Metallography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.3.1 Specimen Preparation . . . . . . . . . . . . . . . . . . . . . . 75

3.3.1.1 Grinding and Polishing . . . . . . . . . . . . . . . . . 75

Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Polishing . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.3.1.2 Etching . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.3.2 Microstructure Characterization Methods . . . . . . . . . . . . 79

3.3.2.1 Volume Percent Measurement . . . . . . . . . . . . . 79

3.3.2.2 Particle Size Measurement . . . . . . . . . . . . . . . 81

3.4 In-Plane Plane-Strain Mechanical Testing . . . . . . . . . . . . . . . . 81

3.4.1 Sample Geometry and Preparation . . . . . . . . . . . . . . . 82

3.4.1.1 Specimen Cleaning . . . . . . . . . . . . . . . . . . . 83

3.4.2 IPPS Testing Methodology . . . . . . . . . . . . . . . . . . . . 85

3.4.2.1 IPPS Testing Procedure . . . . . . . . . . . . . . . . 86

3.4.3 Image Processing and Strain Analysis . . . . . . . . . . . . . . 90

3.4.4 Experimental Error Analysis . . . . . . . . . . . . . . . . . . . 93

3.5 X-ray Micro-computed Tomography Damage Analysis . . . . . . . . . 95

3.5.1 Sample Preparation and Geometry . . . . . . . . . . . . . . . 97

3.5.2 Tomography Acquisition . . . . . . . . . . . . . . . . . . . . . 101

3.5.2.1 Tomography Acquisition Procedure . . . . . . . . . . 101

3.5.2.2 Projections . . . . . . . . . . . . . . . . . . . . . . . 103

3.5.2.3 Exposure Time . . . . . . . . . . . . . . . . . . . . . 104

3.5.2.4 Source Power . . . . . . . . . . . . . . . . . . . . . . 104

3.5.2.5 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . 104

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3.5.2.6 Binning . . . . . . . . . . . . . . . . . . . . . . . . . 105

3.5.2.7 Dynamic Ring Removal . . . . . . . . . . . . . . . . 105

3.5.2.8 Multiple Reference Imaging . . . . . . . . . . . . . . 106

3.5.3 3-D Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 106

3.5.3.1 Projection Post-processing . . . . . . . . . . . . . . . 106

3.5.3.2 Reconstruction Procedure . . . . . . . . . . . . . . . 108

Center Shift Correction . . . . . . . . . . . . . . . . . . 108

Beam Hardening Correction . . . . . . . . . . . . . . . 109

Other Reconstruction Parameters . . . . . . . . . . . . 110

3.5.4 Slice Post-processing . . . . . . . . . . . . . . . . . . . . . . . 110

3.5.4.1 Segmentation . . . . . . . . . . . . . . . . . . . . . . 112

3.5.4.2 Quantitative and Qualitative Volume Analysis . . . . 118

3.6 Fractography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

3.7 Metallographic Damage Analysis . . . . . . . . . . . . . . . . . . . . 122

Chapter 4: Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4.1 Microstructure Characterization . . . . . . . . . . . . . . . . . . . . . 123

4.1.1 Cold-rolled DP Steels . . . . . . . . . . . . . . . . . . . . . . . 124

4.1.2 Galvannealed DP Steels . . . . . . . . . . . . . . . . . . . . . 124

4.1.3 TP1-treated DP Steels . . . . . . . . . . . . . . . . . . . . . . 126


4.1.5 Summary of Microstructures . . . . . . . . . . . . . . . . . . . 131

4.2 IPPS Mechanical Testing . . . . . . . . . . . . . . . . . . . . . . . . . 133

4.3 Void Damage Accumulation and Failure . . . . . . . . . . . . . . . . 139

4.3.1 Galvannealed DP Steels . . . . . . . . . . . . . . . . . . . . . 142

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4.3.1.1 Degree of Damage . . . . . . . . . . . . . . . . . . . 142

4.3.1.2 Damage Distribution . . . . . . . . . . . . . . . . . . 143

4.3.1.3 Void Orientations . . . . . . . . . . . . . . . . . . . . 143

4.3.1.4 Failure Mechanism . . . . . . . . . . . . . . . . . . . 143


4.3.2.1 Degree of Damage . . . . . . . . . . . . . . . . . . . 164





4.3.3.1 Degree of Damage . . . . . . . . . . . . . . . . . . . 226




Chapter 5: Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

5.1 Microstructural Variants . . . . . . . . . . . . . . . . . . . . . . . . . 246

5.1.1 TP1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

5.1.2 TP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

5.1.2.1 Explanation of Residual Banding for TP2 . . . . . . 248

5.2 IPPS Variant Ductility and Failure . . . . . . . . . . . . . . . . . . . 248

5.2.1 Effect of NFP Content on Ductility . . . . . . . . . . . . . . . 248

5.2.2 DP Steel Variant Failure Behaviour . . . . . . . . . . . . . . . 249

5.3 XµCT for Characterization of Damage . . . . . . . . . . . . . . . . . 250

5.4 DP Steel Damage Accumulation in Plane-Strain Fracture . . . . . . . 251

xiii

5.4.1 Void Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . 251

5.4.2 Failure Behaviour Variation with Degree of NFP Banding . . . 252

5.4.3 Explanation for Reduced Ductility with Increased NFP Banding 253

5.5 Effects of Microstructure on Damage Accumulation . . . . . . . . . . 259

5.5.1 Effect of NFP Volume Percent . . . . . . . . . . . . . . . . . . 259

5.5.2 Effect of NFP Morphology . . . . . . . . . . . . . . . . . . . . 260

5.5.3 Effect of NFP Spatial Distribution . . . . . . . . . . . . . . . 261

5.5.4 Importance of NFP Banding to Damage . . . . . . . . . . . . 263

Chapter 6: Conclusions and Recommendations . . . . . . . . . . . . . 264

6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

6.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

Appendix A: Preliminary IC Annealing Experiments . . . . . . . . . 281

A.1 Preliminary Heat Treatment Experiment . . . . . . . . . . . . . . . . 281

A.1.1 Alloy Intercritical Temperature Ranges . . . . . . . . . . . . . 282

A.1.2 IC-Annealing Calibration Curves for NFP Content . . . . . . 283

A.1.2.1 Optical Microscopy Procedure . . . . . . . . . . . . . 284

A.2 Optical vs. SE Quantitative Metallography . . . . . . . . . . . . . . . 285

Appendix B: IPPS Blanks - Time to Heat to IC Temperature . . . . 291

Appendix C: IPPS Specimen Cleaning Procedure . . . . . . . . . . . 295

Appendix D: NL-Means Denoising Parametric Study . . . . . . . . . 298

xiv

Appendix E: Complete IPPS Testing Results . . . . . . . . . . . . . . 304

xv

List of Tables

2.1 DP steel typical alloying elements . . . . . . . . . . . . . . . . . . . . 10

3.1 Experimental sheet steel elemental compositions . . . . . . . . . . . . 59

3.2 Experimental sheet steel thicknesses . . . . . . . . . . . . . . . . . . . 59

3.3 IPPS specimen production schedule . . . . . . . . . . . . . . . . . . . 68

3.4 Metallographic specimen preparation grinding stages . . . . . . . . . 76

3.5 Metallographic specimen preparation polishing stages . . . . . . . . . 78

3.6 Metallographic specimen etchants . . . . . . . . . . . . . . . . . . . . 79

3.7 Micro-XCT 400 Specifications . . . . . . . . . . . . . . . . . . . . . . 95

3.8 X-ray micro-computed tomography acquisition parameters . . . . . . 101

4.1 Cold-rolled sheet steel constituent volume percents . . . . . . . . . . 124

4.2 NFP particle characteristics of the galvannealed DP steels . . . . . . 126

4.3 NFP particle characteristics of the TP1-treated DP steels . . . . . . . 128

4.4 NFP particle characteristics of the TP2-treated DP steels . . . . . . . 131

4.5 NFP microstructural characteristics summary for all DP steel variants 134

4.6 IPPS specimen failure strains . . . . . . . . . . . . . . . . . . . . . . 136

4.7 IPPS match-head specimen void accumulation quantitative measures 140

4.8 IPPS match-head specimen void accumulation quantitative measures(2)141

4.9 Galvannealed specimen damage observations . . . . . . . . . . . . . . 144

xvi

4.10 7TP1-treated specimen damage observations . . . . . . . . . . . . . . 166

4.11 9TP1-treated specimen damage observations . . . . . . . . . . . . . . 167

4.12 TP2-treated specimen damage observations . . . . . . . . . . . . . . . 227

A.1 Approximated alloy solid state transformation temperatures . . . . . 283

A.2 NFP content - galvannealed and preliminary heat-treatment specimens 285

E.1 Complete IPPS failure strain results. . . . . . . . . . . . . . . . . . . 305




xvii

List of Figures

1.1 Historical view of DP steel use in automobiles . . . . . . . . . . . . . 4

1.2 Elongation vs. strength ranges for several classes of steel . . . . . . . 5

1.3 Example automotive component forming shear fracture . . . . . . . . 5

2.1 Effect of manganese alloying on austenite hardenability . . . . . . . . 11

2.2 Typical industrial continuous annealing schedule . . . . . . . . . . . . 13

2.3 Microstructural banding in 1020 steel hot-rolled plate . . . . . . . . . 17

2.4 As-solidified crystal morphologies of a section of steel . . . . . . . . . 18

2.5 Schematic of dendritic solidification . . . . . . . . . . . . . . . . . . . 19

2.6 Manganese segregation in 4140 steel . . . . . . . . . . . . . . . . . . . 20

2.7 DP steel tensile stress-strain behaviour . . . . . . . . . . . . . . . . . 22

2.8 General categories of fracture processes in metals . . . . . . . . . . . 27

2.9 Void nucleation with respect to local strain . . . . . . . . . . . . . . . 28

2.10 Void damage in DP steels of differing banded microstructures . . . . 34

2.11 XµCT beam and detector geometries . . . . . . . . . . . . . . . . . . 40

2.12 Bremsstrahlung and characteristic radiation . . . . . . . . . . . . . . 41

2.13 Lab-scale XµCT schematic . . . . . . . . . . . . . . . . . . . . . . . . 43

2.14 Beam hardening artifact . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.15 Ring artifact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

xviii

2.16 Streak artifact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.17 Damage anisotropy in steel due to inclusion orientation . . . . . . . . 49

2.18 Damage distribution evolution in DP600 steel tension specimen . . . 51

2.19 NL-means denoising scheme . . . . . . . . . . . . . . . . . . . . . . . 53

2.20 Effectiveness of various denoising methods on a natural image . . . . 54

2.21 Method noise produced by various denoising methods . . . . . . . . . 55

2.22 Effectiveness of various denoising methods on a periodic image . . . . 56

3.1 Heat treatment path representations . . . . . . . . . . . . . . . . . . 62

3.2 Tube furnace used for austenitization . . . . . . . . . . . . . . . . . . 63

3.3 Salt bath used for bainite hold portion of austempering . . . . . . . . 63

3.4 Salt bath used for IC annealing . . . . . . . . . . . . . . . . . . . . . 64

3.5 IC annealing IPPS rectangular blank holder . . . . . . . . . . . . . . 74

3.6 IPPS metallographic specimen extraction location . . . . . . . . . . . 75

3.7 IPPS tension test specimen geometry . . . . . . . . . . . . . . . . . . 82

3.8 Custom paint plotting press for IPPS grid application . . . . . . . . . 84

3.9 Inter-dot spacing for the grid applied to IPPS specimens. . . . . . . . 84

3.10 Alignment of IPPS specimens in bottom grip . . . . . . . . . . . . . . 87

3.11 Alignment of IPPS specimens in top grip . . . . . . . . . . . . . . . . 88

3.12 IPPS testing experimental setup . . . . . . . . . . . . . . . . . . . . . 89

3.13 IPPS grid image segmentation process Fig. 1/2 . . . . . . . . . . . . 91

3.14 IPPS grid image segmentation process Fig. 2/2 . . . . . . . . . . . . 92

3.15 Example IPPS specimen strain path . . . . . . . . . . . . . . . . . . 94

3.16 Micro-XCT 400 instrument . . . . . . . . . . . . . . . . . . . . . . . . 96

3.17 Schematic of match-head extraction location . . . . . . . . . . . . . . 98

xix

3.18 Micro-XCT 400 interior components . . . . . . . . . . . . . . . . . . . 99

3.19 X-ray source to specimen and detector distances . . . . . . . . . . . . 100

3.20 Reconstructed XµCT slice greyscale intensity mapping variation . . . 113

3.21 Poor preliminary reconstructed slice thresholding results . . . . . . . 114

3.22 Poor reconstructed slice thresholding results due to noise . . . . . . . 115

3.23 Poor thresholding results for uncropped reconstructed slices . . . . . 116

3.24 Locally adaptive thresholding of uncropped reconstructed slice . . . . 119

3.25 Custom threshold mask overlay software . . . . . . . . . . . . . . . . 120

4.1 Cold-rolled DP steel microstructures . . . . . . . . . . . . . . . . . . 125

4.2 Galvannealed DP steel microstructures . . . . . . . . . . . . . . . . . 127

4.3 DP780CR-TP1-treated DP steel microstructures . . . . . . . . . . . . 129

4.4 DP980CR-TP1-treated DP steel microstructures . . . . . . . . . . . . 130

4.5 TP2-treated DP steel microstructures . . . . . . . . . . . . . . . . . . 132

4.6 7-series IPPS specimen failure strain vs. NFP volume percent . . . . 137

4.7 9-series IPPS specimen failure strain vs. NFP volume percent . . . . 138

4.8 7GA-R4 void accumulation 3-D rendering . . . . . . . . . . . . . . . 145

4.9 7GA-R4 through-thickness void accumulation 3-D rendering . . . . . 146

4.10 Optical micrographs of 7GA-R4 match-head specimen . . . . . . . . . 147

4.11 SEM fractographs of 7GA-R4 match-head specimen . . . . . . . . . . 148

4.12 7GA-T2 void accumulation 3-D rendering . . . . . . . . . . . . . . . . 149

4.13 7GA-T2 through-thickness void accumulation 3-D rendering . . . . . 150

4.14 Optical micrographs of 7GA-T2 match-head specimen . . . . . . . . . 151

4.15 SEM fractographs of 7GA-T2 match-head specimen . . . . . . . . . . 152

4.16 9GA-R3 void accumulation 3-D rendering . . . . . . . . . . . . . . . 153

xx

4.17 9GA-R3 through-thickness void accumulation 3-D rendering . . . . . 154

4.18 Optical micrographs of 9GA-R3 match-head specimen . . . . . . . . . 155

4.19 SEM fractographs of 9GA-R3 match-head specimen . . . . . . . . . . 156

4.20 9GA-T4 void accumulation 3-D rendering . . . . . . . . . . . . . . . . 157

4.21 9GA-T4 through-thickness void accumulation 3-D rendering . . . . . 158

4.22 Optical micrographs of 9GA-T4 match-head specimen . . . . . . . . . 159

4.23 SEM fractographs of 9GA-T4 match-head specimen . . . . . . . . . . 160

4.24 Galvannealed DP steel variant void size histograms . . . . . . . . . . 161

4.25 Galvannealed DP steel variant void spatial distribution histograms . . 162

4.26 Galvannealed DP steel variant void volume profiles in ND . . . . . . 163

4.27 Effect of NFP volume percent on void volume % in 7TP1 variants . . 168

4.28 Effect of NFP volume percent on void volume % in 9TP1 variants . . 169

4.29 Effect of NFP volume percent on # of voids in 7TP1 variants . . . . 170

4.30 Effect of NFP volume percent on # of voids in 9TP1 variants . . . . 171

4.31 7TP1-15-R4 void accumulation 3-D rendering . . . . . . . . . . . . . 172

4.32 7TP1-15-R4 through-thickness void accumulation 3-D rendering . . . 173

4.33 Optical micrographs of 7TP1-15-R4 match-head specimen . . . . . . 174

4.34 SEM fractographs of 7TP1-15-R4 match-head specimen . . . . . . . . 175

4.35 7TP1-15-T11 void accumulation 3-D rendering . . . . . . . . . . . . . 176

4.36 7TP1-15-T11 through-thickness void accumulation 3-D rendering . . 177

4.37 Optical micrographs of 7TP1-15-T11 match-head specimen . . . . . . 178

4.38 SEM fractographs of 7TP1-15-T11 match-head specimen . . . . . . . 179


4.40 7TP1-33-R11 through-thickness void accumulation 3-D rendering . . 181

xxi


4.42 SEM fractographs of 7TP1-33-R11 match-head specimen . . . . . . . 183










4.52 7TP1-43-T5 through-thickness void accumulation 3-D rendering . . . 193


4.54 SEM fractographs of 7TP1-43-T5 match-head specimen . . . . . . . . 195











xxii















4.79 TP1-treated DP steel variant void size histograms . . . . . . . . . . . 220

4.80 TP1-treated DP steel variant void size histograms . . . . . . . . . . . 221

4.81 TP1-treated DP steel variant void spatial distribution histograms . . 222

4.82 TP1-treated DP steel variant void spatial distribution histograms . . 223

4.83 TP1-treated DP steel variant void volume profiles in ND . . . . . . . 224

4.84 TP1-treated DP steel variant void volume profiles in ND . . . . . . . 225





xxiii












4.100TP2-treated DP steel variant void size histograms . . . . . . . . . . . 243

4.101TP2-treated DP steel variant void spatial distribution histograms . . 244

4.102TP2-treated DP steel variant void volume profiles in ND . . . . . . . 245

5.1 Schematic proposing failure sequences dependent upon NFP banding 255

5.2 Galvannealed DP steel failure schematic . . . . . . . . . . . . . . . . 256

5.3 TP1- and TP2-treated DP steel failure schematic . . . . . . . . . . . 257

A.1 DP780 preliminary heat treatment microstructures . . . . . . . . . . 286

A.2 DP980 preliminary heat treatment microstructures . . . . . . . . . . 287

A.3 IPPS rectangular blank metallographic specimen extraction . . . . . . 288

A.4 IC annealing NFP content calibration curve for CR alloys . . . . . . . 289

A.5 Example optical micrograph and grid for volume percent counting . . 290

B.1 IPPS rectangular blank heating rates . . . . . . . . . . . . . . . . . . 293

xxiv

B.2 Salt bath transient temperature response to IC annealing . . . . . . . 294

C.1 Acid cleaning of IPPS specimens; “before” and “after” photographs . 297

D.1 Test images for NL-means denoising parametric study . . . . . . . . . 300

D.2 NL-means denoising parametric study results . . . . . . . . . . . . . . 301

D.3 NL-means denoising algorithm filtering parameter testing . . . . . . . 303

xxv

Chapter 1

Introduction

This thesis focuses on the detection and quantification of void damage accumulated in

dual-phase steels under near plane-strain loading using X-ray micro-computed tomog-

raphy, working towards developing an increased understanding of the microstructural

features and mechanisms which contribute to the failure of this family of steels.

1.1 Motivation

At the forefront of current trends influencing automobile design worldwide are ris-

ing oil prices, increasingly stringent emissions regulations, stronger safety legislation,

and the heightened environmental consciousness of consumers. This new industry

trajectory has necessitated rapid innovation and product mix turnover on the part of

steel producers and auto parts manufacturers to maintain market share in response to

consumer desires for lightweight, fuel-efficient vehicles with reduced greenhouse gas

emissions. A cost-effective and straightforward means to producing automobiles that

meet these desires is a reduction in vehicle weight via the implementation of thinner

1

CHAPTER 1. INTRODUCTION 2

gauge, higher strength sheet steels for the manufacture of structural components.

Steel remains the material of choice for structural component weight reduction

despite the availability of many other lower density material choices such as aluminum

and magnesium. Some keys to this distinction are the relatively low cost and volatility

in the price of steels, their high level of recyclability, and the weldability and re-

workability of steels necessary to repair defects and in-service damage [1]. Dual-

phase (DP) steels, a grade of advanced high-strength steels (AHSS), have emerged as

a frontrunner for vehicle light-weighting, with many steel producers having invested

in continuous annealing facilities and further development of these sheet steels.

DP sheet steels boast a desirable combination of properties for the forming of auto-

motive components: high strengths, continuous yielding behaviour, and a high initial

work hardening rate. The higher strengths of DP steels relative to high-strength steel

(HSS) predecessors allow for a reduction in sheet thickness necessary for component

weight reduction. It follows that reduced automobile structural weight leads to re-

duced emissions and fuel consumption. Also, the reduction in structural weight allows

for power-train downsizing to further improve fuel efficiency. It has been estimated

that an overall vehicle weight reduction of 9% can be made in a typical five-passenger

automobile by replacing the main frame structure with an optimized blend of AHSS

products [2]. This weight savings translates into a decrease in fuel consumption of ap-

proximately 0.4 L per 100 km and an elimination of approximately 1800 kg of carbon

dioxide emissions over a 200 000 km vehicle lifetime [3]. One other important benefit

of DP steels for structural automotive components is their positive strain rate sensi-

tivity, which elicits a high level of energy absorption during crash scenarios, thereby

enhancing vehicle crashworthiness.


Research of DP steels began as early as the 1960s [4], but intensified research

interest in DP steels first began in 1975-76 after the 1973 world oil crisis produced

a strong demand for lightweight, fuel-efficient transport [5, 6]. It is only recently,

however, that widespread adoption of DP steels has occurred amongst automotive

parts manufacturers, as shown in Fig. 1.1. This rapid introduction of DP steels to

parts manufacturing regimes has not been without challenges. While a reduction in

ductility with increased steel strength is generally to be expected (as illustrated in

Fig. 1.2), many premature component forming failures have been reported within the

predicted formability limits of DP steels by automotive manufacturers.

Until about two decades ago, stamping of newly designed steel components from

sheet required months to years of experimental die tryout and modifications [11].

With the emergence of improved processing power for computers and non-linear finite

element software, these arduous trial periods have been all but eliminated [11]. Today,

dies for a part forming operation are designed and tested in a virtual environment

using finite element models tied to experimentally determined forming limit diagrams,

which delineate in principal strain space the limit strains within which a material can

be deformed without the occurrence of local necking. Such a method has been highly

successful for the relatively ductile alloys for which dies have been designed in the

past. However, the method has failed to predict so-called ‘shear fractures’ of DP steels

in high-curvature regions of dies (Fig. 1.3) when used with DP steels. Shear fracture

is typically associated with a lack of significant sheet thinning near the failure region

and occurs most frequently in die regions of low bending ratio, i.e. the ratio of the

bend radius to the sheet thickness [11].

The constant applied strain path inherent to the creation of experimental forming


(a)

(b)

(c)

Figure 1.1: Demonstration of the rapid implementation of DPsteels in automobile structures in the early 21st century: a)Typical steel mix for automobile bodies in 1980 and 2000 [1]; b)Steel grades used in the body of a small-size vehicle introducedin Japan in 2002, adapted from [7]; c) Steel grades used in astate of the art automobile body as of 2004 [8].


Figure 1.2: Typical ultimate tensile strength and total elon-gation ranges for several classes of steel, demonstrating thegeneral decline in ductility with increasing strength [9].

Figure 1.3: Shear fracture of a stamped DP600 automotive railpart in a region of near plane-strain bending [10].


limit curve (FLC) locii can result in situations where the formability for a more

complex strain path is over-predicted. However, the far more likely contributors

to the unpredicted shear fractures are the nucleation and growth of void damage

at martensite particles in DP steel microstructures [10, 12, 13] and the deleterious

softening effect of deformation induced heating [11]. The latter concern is typically

unaccounted for in an FEM + FLC approach, where FLCs that are experimentally-

determined under low-rate, near-isothermal conditions are used to predict failure

during quasi-adiabatic, high-rate commercial forming operations [11]. Developing an

improved understanding of how the two aforementioned mechanisms contribute to the

premature failure of DP steels is imperative to the realization of their full potential

for automobile light-weighting through both improved prediction of low and high-rate

failures (forming and in-service) and new DP microstructures that are less prone to

damage.

1.2 Research Objectives

In this thesis, focus is placed upon studying the role of void damage in the fail-

ure of DP steels subject to a near plane-strain path. Particularly, developing an

improved understanding of the interaction between martensite particles, voids, and

shear bands in the failure of DP steels is a milestone target of this research, looking

towards the greater goal of modeling these interactions. In the past, investigations

into these relationships have been undertaken using two-dimensional metallographic

methods [14–19]. However, the data collected using such techniques tend to lack

a robustness due to the sampling of 2-D planes at large finite spacings relative to

void size. Recently, it has been shown that the most reliable method for obtaining


quantitative 3-D information concerning damage in materials is through X-ray ab-

sorption microtomography [20, 21]. Three known studies to date have made use of

the technique to examine damage in DP steels, including its evolution in the case of

Maire et al. [22], but none have provided insight into the role of the microstructural

parameters of the martensitic phase in the accumulation of void damage [22–24].

The unique contribution of this thesis is the quantitative and qualitative study

of void damage in ten DP steel microstructural variants using lab-scale X-ray micro-

computed tomography (XµCT) to acquire reliable 3-D measurements. To date, such

use of a lab-scale X-ray source to image damage in steel has only been reported once

by Gupta et al. [23]. The primary goal of the present study is to employ mechanical

testing of the DP steel variants to failure under a critical strain path representative of

typical automotive forming failures and observe the damage accumulation produced

using XµCT. DP steel microstructural variants were selected and designed to: a)

be representative of current microstructures used commercially to form automotive

components (i.e. commercially available sheet); b) be of varied martensite volume

percent while maintaining morphology; and c) be of varied martensite morphology

and distribution while maintaining volume percent. These variants were selected to

provide useful insight into how non-martensitic second phases in commercial DP steels

affect damage accumulation and the significance of variation in the volume percent

and morphology of martensite in a DP steel microstructure to damage and failure.


1.3 Organization

The remainder of this thesis is divided into five chapters as outlined below:

Chapter 2 provides a pertinent review of the literature and explains the

principles underlying X-ray absorption micro-computed tomography.

Chapter 3 details the DP steel alloys used in this study, outlines the heat

treatment methods used to produce DP steel microstructural variants,

chronicles the microstructural characterization methods employed, doc-

uments the procedures of the mechanical testing protocol, and describes

the experimental and analytical procedures of the XµCT examination

of failed mechanical testing specimens.

Chapter 4 presents the results of the experiments outlined in Chapter

3.

Chapter 5 provides a discussion of the results and methodologies and

their significance with respect to the existing literature.

Chapter 6 draws the primary conclusions of this study and offers guid-

ance for future work in this particular field.

Chapter 2

Literature Review

2.1 DP Steel Microstructures

The microstructure of dual-phase steels consists mainly of ferrite and martensite.

Small amounts of bainite, pearlite, and retained austenite may also be present. A typi-

cal microstructure consists of a matrix of 70-95% ferrite with 5-30% dispersed marten-

site islands [8]. The unique tensile behaviour of DP steels, examined in Sec. 2.2, is a

direct result of the use of a hard second phase dispersed in a soft matrix.

2.1.1 Chemistry

Many alloying elements are used in DP steels to assist in their production and final

properties. These elements and their functions are summarized in Table 2.1. Carbon

content of DP steels is generally kept low to improve weldability. By weight percent,

the largest elemental alloying additions in many DP steels for strengthening purposes

are manganese, silicon, and molybdenum. The remainder of the alloying content of

9

CHAPTER 2. LITERATURE REVIEW 10

the steel is carefully tweaked to provide a hardenability which allows for a martensitic

transformation to occur through carefully controlled cooling. Manganese content is

a particular point of interest as it has been demonstrated in many studies to be the

alloying element most responsible for the development of microstructural banding

during the production of low alloy steels [25–27]. A poignant example of the effect

of manganese content on hardenability is provided in the continuous cooling trans-

formation (CCT) diagrams of Fig. 2.1, displaying transformation differences between

low- and high-Mn 5140 steels. The addition of manganese is shown to push austen-

ite decomposition to bainite, pearlite, and ferrite to longer times under continuous

cooling.

Table 2.1: Typical alloying elements in DP steels and theirfunction. Adapted from [28].

Element Function

C, Mn, Si, Ni, Cr, MoIncreases solid-solution strength and hardnessIncreases hardenability

V, Cb, NbIncreases strength and hardness through grain refinementIncreases hardenability

Al, Ti Increases strength and hardness through grain refinement

B Increases hardenability

N Increases amount of nitrides, required for strengthening or grain refinement

2.1.2 Processing

At its most basic, the process for producing a DP steel microstructure is as follows. A

steel of appropriately low carbon content is intercritically heat treated (heating to the

ferrite + austenite region of the iron-carbon phase diagram). Following a short hold in

the intercritical region to produce a ferrite-austenite mixture, the steel is put through

accelerated cooling to cause a diffusionless transformation of the FCC austenite to

BCT martensite, resulting in a dual phase microstructure completely composed of


(a)

(b)

Figure 2.1: CCT diagrams for 5140 steel containing: a) 1.83pct Mn and b) 0.82 pct Mn [29].


ferrite and martensite. Carbon atoms in the austenite remain as interstitial alloying

elements in the martensite, resulting in a metastable supersaturated solid solution.

2.1.2.1 Commercial DP Steel Processing

To produce DP steel sheet in an economical manner at high volumes, a complex

thermomechanical procedure is necessary. Cast steel slab is taken through a hot

rolling process involving several roughing and finishing stages to produce sheet of

uniform thickness (typically 2-3 mm) and properties. Cold rolling is applied to the

sheet to further reduce its thickness to a gauge which is appropriate for the forming

of automotive components (∼1 mm). At this stage, the steel typically consists of

ferrite and pearlite elongated in the rolling direction, but may also contain bainite

and martensite. Commercial DP steel sheets are typically produced on a continuous

annealing line + hot dip galvanizing/galvannealing line, which provides a protective

surface layer to the sheet to guard against corrosion. A typical industrial continuous

annealing schedule for DP steel sheet which includes constituent evolution is provided

in Fig. 2.2.

The design of an economical physical facility line for implementing a galvanneal-

ing schedule limits cooling rates to levels that are often too low to produce a purely

dual-phase microstructure, such that epitaxial ferrite, bainite, or pearlite may form

in some small portion from intercritical austenite. These transformations are not as

desirable because these constituents do not provide the high strength of martensite

and do not result in the production of a highly mobile dislocation network in sur-

rounding ferrite grains (as is the case for the martensitic transformation). As such,


Figure 2.2: Schematic of a typical industrial continuous anneal-ing schedule for the production of dual-phase steel. Neitherthe time nor the temperature axis is scaled due to the minorvariations in scheduling from producer to producer. ‘F’ repre-sents ferrite, ‘B’ represents bainite, ‘P’ represents pearlite, ‘A’represents austenite, and ‘M’ represents martensite. Adaptedfrom the work of [30].


partitioning a greater amount of carbon into austenite during intercritical (IC) an-

nealing is advantageous to increase the hardenability of the austenite and thus shift

pearlite and bainite transformation to lower temperatures and slower cooling rates.

Utilizing lower IC annealing temperatures produces a greater concentration of carbon

in austenite for a given IC annealing hold time. As well, further carbon enrichment

of the austenite phase occurs during slow cooling from IC temperature as carbon

is redistributed from “new ferrite” to austenite grains [30]. As shown in Table 2.1,

manganese, silicon, nickel, chromium, and molybdenum also serve the purposes of

increasing austenite hardenability.

2.1.2.2 Austenite Formation during IC Annealing

It is well known that austenite forms by a nucleation and growth mechanism upon

heating. Speich et al. [6] have shown that the formation of austenite in low-carbon

1.5 weight percent Mn steels during IC annealing can be broken into three steps:

(1) nearly instantaneous nucleation of austenite in pearlite, followed by rapid growth

until complete pearlite dissolution, (2) slow growth of austenite into ferrite primarily

controlled by carbon diffusion in austenite, and (3) very slow equilibration of ferrite

and austenite controlled by manganese diffusion in austenite. Step (1) is completed on

the order of seconds due to the short range diffusion of carbon atoms, step (2) requires

hours to fully complete, and step (3) is never completed under normal annealing times

[6]. It should be noted that other microstructural regions of high carbon concentration

may also act as austenite nucleation sites, such as martensite particles and ferrite grain

boundaries [31, 32].

The preceding generally accepted mechanisms of austenite formation are largely


drawn from isothermal studies using hot-rolled or fully annealed steels [31]. As such,

they pay no heed to the effects of the cold rolling which is performed prior to IC

annealing during DP steel production, or to the effect of heating rate to IC annealing

temperature. Huang et al. [31] demonstrated that heating rate is a very important

variable affecting the nucleation and growth of austenite, especially in cold-rolled DP

steel. For a high heating rate (∼100◦C/s), it is purported that concurrent ferrite

recrystallization and austenite nucleation during IC annealing of cold-rolled ferrite-

pearlite steel allows for unabated growth of pearlite-nucleated austenite due to a lack

of any ferrite-nucleated austenite presenting any competition [31]. For high heating

rates to IC temperature, this results in a higher austenite transformation rate and

coarser austenite grains elongated in a continuous fashion in the rolling direction [31].

2.1.2.3 Transformation of Austenite to Martensite

Rapid cooling below the martensite start temperature from the IC temperature range

causes a diffusionless transformation of FCC austenite to BCT martensite. All carbon

atoms in the austenite remain as interstitial impurities in the martensite, resulting in

a metastable supersaturated solid solution. Depending upon the carbon content of the

parent austenite, martensite morphology can vary from lath substructure, typical of

low-carbon martensite, to internally twinned substructure plate martensite, typical of

high-carbon martensite. The former is associated with high toughness and ductility,

but low strength; the latter with high strength, but low ductility and toughness. It

should be mentioned that the low- and high-carbon terms used in this section refer

to the relative changes that may be made to the carbon content of parent austenite

by varying IC annealing temperature, i.e. on the order of 0.5%.


A small fraction of austenite that has been sufficiently stabilized with carbon

and other solid-solution alloying elements may remain after cooling in the form of

retained austenite in DP steels due to a resultant shift of the martensite start and

finish temperatures to lower levels. For steels with low- or medium-carbon martensite,

austenite is believed to be retained as interlath films within martensite [33]. For

steels with high-carbon martensite, austenite is believed to be retained as isolated

particles [34, 35].

The final microstructure of a DP steel post-IC annealing is heavily dependent

upon the microstructure of the input steel prior to the annealing treatment. It has

been demonstrated that the resultant size, morphology, and distribution of marten-

site in DP steels is dependent upon the IC annealing heating rate, temperature, hold

time, cooling rate, and the distribution of carbon and manganese prior to IC an-

nealing [6, 31, 36–38]. Thermomechanical processing may be used to influence the

latter via alteration of the size, spatial distribution, morphology, and composition of

microstructural constituents.

2.1.2.4 Evolution of Microstructural Banding

In hot rolled low alloy steels, it is well known that ferrite and pearlite are normally

arranged in layers [39]. In an etched metallographic section showing a plane defined

by the sheet rolling direction and through-thickness direction (RD-ND), this arrange-

ment is visually apparent as a banded microstructure [25, 29] such as in Fig. 2.3.

Some degree of banding is present in all types of steel [29]. The root cause of this

banding is known to be the segregation of alloying elements, both macroscopically

and microscopically, in cast steel products.


Figure 2.3: Ferrite (light) and pearlite (dark) bands in 1020steel hot-rolled plate. Nital etch, light micrograph. [29].

The typical crystal morphologies of a transverse section in an as-cast steel shape

are shown in Fig. 2.4. The columnar and interior equiaxed grains form by a dendritic

solidification mechanism due to constitutional supercooling and preferred crystallo-

graphic growth [29]. Partitioning of alloying elements between parent liquid and the

solidifying secondary dendritic arms produces a non-uniform distribution of these

elements through the thickness of sheet steel [29], exemplified in Fig. 2.5. As so-

lidification proceeds, the concentration of solutes in the remaining liquid increases,

translating into the highest solute content of the steel being partitioned into the last

liquid to freeze [29], i.e. at the sheet centerline. Secondary dendrite arm spacing

grows with increasing section size, increasing distance from the slab surface, and with

decreasing cooling rate [29]. Therefore, segregation in sheet steel may be minimized


through the casting of thinner gauges [29]. Hot rolling aligns the inter-dendritic seg-

regation of alloying elements into bands along the rolling direction [29]. Due to the

low diffusion coefficients of substitutional alloying elements, the homogenizing effects

of hot-rolling are minimal [29].

Figure 2.4: Schematic diagram of zones of crystal morphologiesin an as-solidified section of steel [40]. Shown are the outerchill zone, the columnar zone, and the interior equiaxed zone.

Solute elements with a lower equilibrium partition ratio have the greatest tendency

to segregate, but the amount of element present in the steel is another important

factor [29]. Manganese, generally present in very high concentrations relative to other

alloying additions in DP steels, is generally accepted to play a more important role in

segregation and banding [29,39]. An example of this concentration of manganese into


Figure 2.5: Schematic of dendritic solidification [41]. The darkshading in liquid adjacent to dendrites represents concentra-tions of solute atoms rejected from solid. Due to the thin gaugeof sheet product, primary dendritic arms would predominantlybe aligned along the through-thickness direction.


bands is provided in Fig. 2.6 for a quench and tempered 4140 steel bar, containing

by heat analysis 1.00 pct. Mn. The longitudinal banding of ferrite and pearlite in

hypoeutectoid steels, such as in Fig. 2.3, is explained by the banded distribution of

manganese. Manganese acts to stabilize austenite and thus reduces Ar3 temperature.

Upon cooling, ferrite forms first in austenite with a low concentration of manganese,

i.e. along low-Mn bands, and rejects carbon into high-Mn bands as it grows [29]. Thus,

the austenite in these high-Mn, high-C bands eventually transforms into pearlite [29].

It is worth noting that with austenite grain sizes greater than the wavelength of

chemical segregation, microstructural constituent banding upon cooling is eliminated

[29].

Figure 2.6: Variations in Mn and C concentrations across aquench and tempered 4140 steel bar, 95.25 mm in diameterand containing by heat analysis 1.00 pct. Mn [42]. Electronmicroprobe analysis.


2.2 DP Steel Mechanical Properties

The mechanical properties of a DP steel are highly dependent upon the volume

fraction, carbon concentration, and spatial distribution of non-ferritic phases and

constituents (NFP) in the microstructure [31]. The transformation of austenite to

martensite requires a volume expansion of approximately 2 to 4 percent [43,44]. Sur-

rounding ferrite grains must plastically accommodate this volume expansion, which

produces a high dislocation density in the ferrite near the ferrite-martensite interface

and produces residual stresses. The highly mobile dislocations and residual stresses

result in a low yield stress for DP steels [34, 44, 45]. Plastic flow generally begins

simultaneously at many sites throughout a DP steel tensile specimen, suppressing

discontinuous yielding [46]. These characteristics are clearly evident when compared

to the higher yield stress and yield point phenomena of a microalloyed steel shown

in Fig. 2.7. The naming of DP steels follows the convention of DP-UTS, where UTS

is the ultimate tensile strength of the steel quoted in MPa. For instance, a steel

classified as DP780 is expected to have a UTS of 780 MPa.

2.2.1 Strength

The relatively high strength of DP steels is a result of a composite strengthening

effect contributed by hard martensite in a ductile ferrite matrix. The yield and

tensile strengths of DP steels have been reported to increase in a linear [45, 47, 48]

and a non-linear [49–52] manner with increasing martensite volume fraction by many

researchers. It has been proposed that the non-linear relationship, deviating from the

rule of mixtures, is a result of changing martensite strengths due to differing carbon

content in the martensite; a result of the range of IC annealing temperatures used


Figure 2.7: Tensile stress-strain behaviour of a DP steel and amicroalloyed steel [8].

to vary martensite volume fraction. The cause of the differences in these findings is

unclear, but may be related to scatter in experimental data and testing of DP steels

with a limited range of martensite volume fractions [6]. Changes in the strength of

the ferrite phase, resultant from grain size, solid solution hardening, and precipitation

hardening can also affect the strength of the mixture.

2.2.2 Constituent Strain Incompatibility

Despite DP steels exhibiting macroscopically homogeneous and uniform deformation,

the microscopic plastic deformation is inherently heterogeneous due to the differing

strength levels of martensite and ferrite [53]. Shen et al. [54] used a scanning electron

microscope (SEM) equipped with an in-situ tensile straining stage to demonstrate the

inhomogeneous strain distributions between ferrite grains and martensite particles in


DP steels. The group observed that, in general, ferrite grains deformed immediately

and at a much higher rate than martensite particles, whose deformation was delayed.

These results have been confirmed via in-situ SEM testing by Ghadbeigi et al. and

Tasan et al. [55, 56].

2.2.3 Work Hardening

During deformation of a DP steel, strain is not distributed evenly between ferrite

and martensite; a plastic incompatibility exists between the two. This leads to a

rapid buildup of back stresses in ferrite and coincident with this is the elimination of

residual stresses caused by the martensitic transformation, contributing to the very

high initial work hardening rate of DP steels [6]. Work hardening of DP steels can

be simplified to three stages [34,57,58], with the aforementioned classified as stage 1

between 0.1-0.5% strain. Stage 2, from approximately 0.5-4.0% strain, consists of a

reduced work hardening rate of ferrite due to strain incompatibility constraining the

plastic flow of ferrite. Stage 3 involves the formation of dislocation cell structures,

cross slip and dynamic recovery of ferrite, and eventual yielding of martensite.

2.2.4 Ductility

Many factors are known to influence the ductility of DP steels [6]: volume fraction of

martensite, carbon content of martensite, plasticity of martensite, spatial distribution

of martensite, alloy content of ferrite, amount of epitaxial ferrite, and the amount

of retained austenite. Uniform elongation is known to decrease non-linearly with

increasing martensite volume fraction [47,49] and to increase slightly with decreasing

martensite carbon content [49]. The former effect is presumably produced by an


increase in the number of voids nucleated with increasing martensite volume fraction.

The latter effect may be due to reduced strain incompatibility between martensite

and ferrite, leading to a reduction in the ease with which void damage may form [49].

A uniform spatial distribution of widely-spaced small martensite particles is desirable

for increased ductility [6]. A banded martensite distribution offers an easy crack

propagation path (stress-state dependent), thus adversely affecting ductility [6, 27].

2.2.5 Sheet Metal Formability

The history, construction, and use of forming limit diagrams (FLDs), created to

delimit the maximal safe deformation in strain space for sheet product, is clearly

described in the works of Pilkey, Valletta, Kilfoil, and Lawrence [59–62]. For the sake

of brevity, the reader is referred to these resources for detailed information on the

subject matter.

2.2.6 In-Plane Plane-Strain Tensile Testing

The formability limits, i.e. the occurrence of local necking, of sheet material are

typically lower in plane-strain than any other proportional forming path. As men-

tioned previously, DP steel components have been known to fail prematurely via

shear fracture during forming in plane-strain bending areas. In-plane plane-strain

(IPPS) tensile testing is advantageous in that it may be performed on sheet material

to produce an approximate plane-strain forming path using typical tensile testing

equipment. The wide geometry of the tensile IPPS specimens used and their notch

geometry produce a condition of near full constraint of strain in the minor direc-

tion at the center of specimens, with deformation occurring mainly in the major and


through-thickness directions. Again, for the sake of brevity, the reader is referred to

the works of Valletta, Kilfoil, and Lawrence [60–62] for detailed information concern-

ing the history and development of IPPS tensile testing. The methods corresponding

to this mechanical testing protocol are clearly outlined in Sec. 3.4.

2.3 Ductile Failure

The failure of DP steels has been reported by many researchers to take place through

ductile failure [49, 53, 58, 63–78], i.e. microscopic deformation behaviour leading to

plastic strain localization. Critically, plastic strain localization is preceded by diffuse

necking. Deformation of a metal prior to the occurrence of diffuse necking is re-

soundingly believed to be controlled by elemental plastic properties; crystallographic

texture being the most dominant of these [79]. The development of plastic strain

localization, also referred to as local necking, is believed to be controlled by mi-

crostructural inhomogeneities [79]. For DP steels, hard NFP particles plus inclusions

and the voids formed in association with each represent the inhomogeneities critical

to plastic localization.

For a high purity BCC or FCC polycrystalline metal with negligible second phase

or impurity content, final failure under tensile load occurs through nearly 100% area

reduction of the external neck [80, 81]. This form of ductile failure is termed plastic

failure [82]. However, practical engineering alloys, such as DP steels, contain large

numbers of microstructural inhomogeneities in the form of second phase particles

and inclusions among others. As such, DP steels fail in a ductile manner not through

plastic failure, but via two other mechanisms described according to Ashby et al. [82]

as ductile fracture and shear fracture; both of which are the focus of this study. These


mechanisms, along with plastic failure, are illustrated in Fig. 2.8.

Ductile fracture takes place by three non-mutually exclusive [59] component mech-

anisms; namely void nucleation, void growth, and void coalescence [83]. During plastic

flow, voids nucleate at microstructural inhomogeneities and continuously grow due to

the externally applied stress and strain-rate field [83]. Eventually, these voids become

numerous and large enough to cause localization of strain and increased void-void in-

teractions; resulting in the breaking or necking-down of inter-void ligaments. This

interplay of void nucleation, growth, and coalescence continues until a critically-sized

flaw activates final fracture [59].

Shear fracture, in the sense of a ductile failure, is produced by the formation of a

macroscopic shear band across a developing neck [59]. Often this process is facilitated

in part by the production of planar sheets of microvoids in regions of intense plastic

flow [59]. This form of failure typically exhibits reduced degrees of through-thickness

thinning compared to ductile fracture.

2.3.1 Void Nucleation

It has generally been assumed throughout a great portion of literature that all damage

nucleates solely at the onset of plastic deformation, followed purely by growth and

no further nucleation [85–89]. It has been verified through experimentation that this

assumption is invalid; damage nucleation in ductile materials is progressive [20,90,91].

Maire et al. [22] found two distinct regimes of void nucleation with respect to local

strain during XµCT in-situ tensile testing of a DP600 steel: a linear void nucleation

rate with local strain up until the point of necking, at which time voids began to

nucleate at an exponential rate due to increased stress triaxiality (Fig. 2.9). Poruks


(a) Plastic failure (b) Ductile fracture (c) Shear fracture

Figure 2.8: General categories of fracture processes in metals[84]. Note that final failure in ductile and shear fracture maybe transgranular as shown or intergranular.

et al. [92] and Avramovic-Cingara et al. [14] have confirmed this void nucleation trend

for a bainitic and DP600 steel respectively. Void density has been shown throughout

the literature to increase towards the fracture surface and to be greater in samples

which exhibit localized necking [14,22,72]. This is of course explained by an increasing

strain gradient with increasing proximity to the fracture surface.

2.3.1.1 Void Nucleation Mechanisms

Void nucleation occurs at material discontinuities such as second phase particles,

inclusions, and grain boundary triple points [59, 83]. In the case of DP steels, void

nucleation has been reported by many investigators to occur as a result of both

martensite particle fracture and ferrite-martensite interfacial decohesion [22, 66, 68–

72,93,94]. It has been pointed out by Balliger [70], Gladman [69], and Koo [71] that


Figure 2.9: The evolution of void nucleation in a DP600 tensilespecimen with a clear linear regime prior to necking and anexponential regime post-necking [22]. Data captured in 3-Dusing synchrotron XµCT.

the largest voids are nucleated via martensite particle fracture. Speich and Miller [49]

observed void nucleation to occur only via ferrite-martensite interfacial decohesion for

low martensite volume fractions, while martensite cracking also operated for higher

martensite volume fractions. Szewczyk and Gurland [75] echoed these results by

failing to observe any martensite particle cracking for martensite volume fractions in

the range of 15-20%. Avramovic-Cingara et al. and Poruks et al. [15, 92] reported

that void nucleation via ferrite-martensite interfacial decohesion occurs generally on

the interface perpendicular to the tensile axis.

Many other researchers have reported that void nucleation occurs primarily due

to ferrite-martensite interfacial decohesion [49,58,67,75,76]. Nam and Bae [76] stated

that overwhelming reports find the majority of voids which lead to fracture are nucle-

ated via ferrite-martensite interfacial decohesion, rather than via martensite particle


cracking.

Steinbrunner and Krauss [72] observed void nucleation to occur via the aforemen-

tioned mechanisms plus the separation of deformed martensite particles. Ahmed et

al. [77] reported a unique mechanism of void nucleation via decohesion at ferrite-ferrite

interfaces with minimum plastic deformation. They reported that for low to interme-

diate martensite volume fraction, void formation was due to ferrite-martensite inter-

facial decohesion. Otherwise for martensite volume fractions above 32%, martensite

particle cracking and ferrite-ferrite decohesion mechanisms also operated. Avramovic-

Cingara et al. observed a small number of voids to have nucleated at inclusions [15].

These voids were relatively large and non-negligible in terms of their contribution to

void volume fraction [15].

The variation reported for the aforementioned void nucleation mechanisms ap-

pears to be a function of DP steel chemical compositions, heat treatment histories,

and microstructural differences [15]. Some of these characteristics and their potential

effects on void damage nucleation in DP steels under uniaxial tension are outlined in

the following subsections.

Effect of Martensite Particle Size

Martensite particle size has been shown in the literature to have a significant effect on

the strength and damage behaviour of DP steels [14,15,19]. It has been emphasized by

many research workers that the probability of fracture of martensite increases with

increasing martensite grain size [95–97]. For a Fe-2Si-0.1C DP steel with a coarse

martensite structure, Kim and Thomas [74] have reported uniaxial tensile failure

via ferrite cleavage due to maximum localized stress concentrations in these grains.


For both fine fibrous and fine globular martensite microstructures of the DP steel

chemistry used, it was reported that failure occurred via void nucleation, growth,

and coalescence after large degrees of straining. These voids formed at the ferrite-

martensite interfaces.

He et al. [19] studied the evolution of damage in Fe-Mn-C DP600 steels with 17%

volume fraction of martensite; one with coarse martensite particles and the other

with fine martensite. Under uniaxial tension it was reported that coarse structures

of martensite tend to initiate voids due to cracking of the martensite at very low

strain levels, i.e. in the uniformly elongated region [19]. This was followed by interfa-

cial decohesion at ferrite-martensite interfaces for higher strain levels; the dominant

mechanism in the necked region. Cracks that initiated within martensite particles

always traversed the entire particle and were always arrested by ferrite grains [19].

For the material with finer martensite grains, the majority of voids were observed

to form via decohesion of the ferrite-martensite interfaces, attributed to the strain

incompatibility between the two phases [19]. Most of this decohesion was observed

in the non-uniformly elongated region. The size of voids in the strained material was

reported to be directly related to the size of martensite islands, for both modes of void

nucleation. It should be mentioned that the coarse martensite material failed via void

nucleation and coalescence at the center of the sample (via both martensite cracking

and ferrite-martensite decohesion), with ferrite cleavage at the sample edges due to

sharp rises in the stress level as damage accumulated in the center of the sample. The

fine-grained martensite material failed purely in a ductile manner.

The work of Erdogan [98] agreed with the aforementioned void nucleation mecha-

nism observations. Coarse martensite that was interconnected and distributed along


ferrite grain boundaries cracked easily. Finer martensite that was not as intercon-

nected, but still distributed along ferrite grain boundaries, cracked less easily. Kad-

khodapour et al. [53] also observed that the interfacial decohesion of ferrite grains

mainly occurs in regions where two ferrite grains have a long contact surface with

the martensite. This was explained by the strain incompatibility between ferrite and

martensite.

Effect of Martensite Particle Shape

The shape of martensite particles is an important factor to consider. Elongated

particles experience a stress similar to that of fibers in a composite material [19].

That is, the stress in elongated second phase particles is thought to be proportional

to the ratio of the length to the width of the particle [19]. As well, martensite particles

elongated in the tensile direction are thought by Han et al. [99] to produce multiple,

sequential nucleation of voids which join by coalescence. This sentiment is echoed by

Avramovic et al. [14], reporting that elongated martensite particles with the major

axis aligned with the tensile axis of the sample will fracture preferentially. This is

in contrast to the work of Nam and Bae [76] who reported that unlike martensite

particles aligned nearly parallel with the drawing axis, which are thinned to fibrous

shape, those particles aligned transverse to the drawing axis are severely bent and

even fractured with increasing drawing strain.

Sun and Pugh [66] reported that void nucleation occurs by both ferrite-martensite

decohesion and martensite cracking, depending upon the martensite morphology.

Elongated martensite ribbons were observed to be most prone to martensite cracking.


Effect of Martensite Spatial Distribution

Distribution of martensite particles carries strong implications for the strength and

damage behaviour of dual phase steels. In terms of the spatial distribution of marten-

site with respect to ferrite grains, martensite grains located close together produce rel-

atively undesirable damage properties. The strain incompatibility between the closely

situated martensite particles and ferrite grains results in a condition that prevents

deformation of ferrite due to a need to maintain grain boundary coherence between

the two phases [19]. Being that martensite is very brittle, cracking typically occurs

for these clustered particles, firstly those with quenching flaws, with the subsequent

nucleation and growth of a void to geometrically allow for ferrite deformation [19].

Such a process quickly leads to an increase in the volume fraction of voids present,

resulting in the rapid formation of a neck. Decohesion of ferrite-martensite interfaces

within the necked region nucleates further voids which grow and coalesce to produce

a central cavity in the sample. This results in a high stress level in the tensile sample

that the microstructure is incapable of supporting, resulting in rapid cleavage failure.

A microstructure that contains well dispersed martensite islands provides much

more desirable mechanical properties and delayed nucleation of void damage. This

is because plastic flow of ferrite grains is not as restricted due to reduced interfacial

constraints at the ferrite grain boundaries [19]. Plastic deformation of ferrite grains

reduces stress concentrations in the microstructure and prevents cracking of marten-

site particles [19]. As plastic deformation of the ferrite grains increases, voids form

via ferrite-martensite decohesion as a result of the strain incompatibility between the

two phases [19]. However, these voids form progressively with strain and result in a

ductile fracture that occurs after a large elongation [19].


Avramovic et al. [14] performed a uniaxial tension study on two galvannealed

DP600 steels with differing chemistry, both with roughly 20% martensite volume

fraction, and both with differing banded microstructures. DP600A exhibited strong

banding of martensite along the sheet centerline in the rolling direction, whereas

DP600B exhibited martensite bands aligned in the rolling direction dispersed rela-

tively uniformly throughout the sheet thickness. Void damage in the DP600A steel

was highly concentrated at the sheet centerline where a coarse martensite band was

located, as seen in Fig. 2.10(a). The largest voids were also located at the sheet

centerline, nucleated by martensite cracking. Away from this band, voids nucleated

typically by ferrite-martensite decohesion. In the DP600B steel, void damage was

distributed relatively uniformly throughout the thickness as in Fig. 2.10(b), reflect-

ing the distribution of martensite bands throughout the thickness. The steel with a

more uniform distribution of martensite, DP600B, showed a slower rate of damage

growth and a continuous void nucleation during the deformation process, which re-

sulted in a higher void density before fracture. The steel with coarse sheet centerline

banding of martensite through the thickness exhibited accelerated void growth and

catastrophic coalescence in the transverse orientation to the applied load. Interest-

ingly, void growth and coalescence was observed preferentially along the plane normal

to applied load in DP600A, the opposite of DP600B for which void growth occurred

preferentially along ferrite grain boundaries parallel to applied load. As well, the

ductile dimples of the fracture surfaces of both steels closely reflected the distribution

of martensite in the microstructures.


(a) (b)

Figure 2.10: Voids revealed by light microscopy in a polishedthrough-thickness longitudinal cross-section of (a) DP600A and(b) DP600B steels. Strong concentration of voids at the sheetcenterline is visible in DP600A. [14]

Effect of Martensite Carbon Content

Mazinani and Poole [100] have reported that martensite plasticity is capable of re-

ducing strain incompatibility between ferrite and martensite particles and thus makes

decohesion of these interfaces and subsequent void nucleation more difficult, resulting

in both higher fracture stresses and strains. For martensite particles to be capable of

significant plastic deformation, their strength must be reduced via decreased carbon

content [100]. This can be achieved through tempering or through an increase of the

martensite volume fraction due to a mass balance [100]. Szewczyk and Gurland [75]

have also reported this martensite plasticity effect for DP steels, particularly in the

neck of tensile specimens. Speich and Miller [49] observed that low volume fractions

and high carbon contents of martensite resulted in easier ferrite-martensite decohesion

than in microstructures of high volume fractions and low carbon contents of marten-

site. Avramovic-Cingara et al. [14] observed in two DP600 steels of similar martensite


volume fraction but differing carbon content that the higher carbon martensite pro-

duced a higher tendency for void nucleation via ferrite-martensite decohesion.

In contrast, Kang and Kwon [73] identified void nucleation to occur predominantly

by ferrite-martensite interfacial decohesion for lath-type martensite, i.e. low-carbon

martensite. Plate martensite, typically of higher carbon content, was observed to

nucleate voids predominantly via cleavage cracking.

2.3.1.2 Critical Nucleation Strain

A critical stress/strain must be achieved prior to nucleation of a microvoid by in-

terfacial decohesion or particle cracking. Avramovic-Cingara et al. [15] calculated a

critical nucleation thickness strain for a banded DP600 steel of 0.15. Steinbrunner et

al. [72] observed void nucleation via fractured martensite particles at global strains

as low as 0.05 for DP steel of a similar chemical composition. For another banded

DP600 steel of the same NFP volume fraction, but different chemical composition and

significantly coarser banding at the sheet centerline, Avramovic-Cingara et al. [14] re-

ported a critical local true void nucleation strain of 0.029 for martensite cracking and

0.09 for ferrite-martensite decohesion.

2.3.2 Void Growth

Subsequent to the nucleation of microvoids, an externally applied stress and plastic

strain-rate field results in the continuous plastic growth of microvoids [83]. Experi-

mental studies have shown that void growth is primarily extensional in nature along

the tensile axis in the central regions of necked tension specimens where the maxi-

mum mean normal stress was approximately 0.7 times that of the yield strength [83].


Work with DP steels under uniaxial tension has confirmed this observation, with

Avramovic-Cingara et al. [15] reporting that nucleated microvoids grew longitudi-

nally along ferrite grain boundaries parallel to the tensile loading direction.

Factors experimentally determined to influence void growth behaviour include

stress state and strain hardening rate [59]. It has been demonstrated that a state of

increased stress triaxiality increases both dilational void growth [101] and void growth

rates [85,101]. This dependance of void growth rate upon tensile stress triaxiality has

been shown to be exponential in nature [102–107]. Rationally, the application of a

hydrostatic pressure upon deforming tensile specimens reduces tensile stress triaxiality

and thus dilational void growth [108]. The rate of void growth has been demonstrated

in maraging steels to depend upon yield strength, with increasing yield strength

resulting in increased growth rates [109,110]. This effect has been explained by a lower

strain-hardening rate and higher applied stresses in steels of greater strength [59].

2.3.3 Void Coalescence

Void coalescence is the least understood portion of ductile failure due to the ra-

pidity with which it typically precipitates final failure [59]. Two prevailing forms

of coalescence behaviour have been experimentally observed [59]. The first is the

formation of a shear band between closely-spaced voids which ultimately severs the

inter-void ligament [111,112]. As well, this intense plastic shear can nucleate a plane

of voids, known as void sheeting, which assist in the severing of the inter-void liga-

ment. The other form of void coalescence simply involves stable void growth until

the inter-void ligament has necked down entirely, impinging the two voids upon one

another [112–114].


2.3.4 Fracture Surface Orientation

The orientation(s) of a ductile fracture surface for a mechanical testing specimen is

heavily dependent upon the volume fraction of second phase present, the specimen

geometry, and the loading of the specimen. For instance, to elicit the typical cup-

cone ductile fracture surface of uniaxial tensile testing of round bar, clearly a critical

condition must precipitate intervention from void coalescence across the plane normal

to the tensile direction in a macroscopically homogeneous state of plastic flow to

a localized mode of internal microscopic necking across a sheet of microvoids [83].

This intervention is mathematically equivalent to the development of a stationary

velocity-discontinuity in the plastic velocity-field [83]. The work of Hill [115] provides

an invariant formulation of the conditions necessary for determining the location of

characteristic surfaces on which fracture surfaces can develop in a plastic velocity

field. Applying Hill’s formulated condition to a state of plane-strain plastic velocity-

fields, it has been shown that the characteristic surfaces upon which fractures tend to

form along are oriented 45◦ with respect to the major strain direction [83]. However,

despite this tendency for final ductile fracture under plane-strain to occur on a plane

45◦ with respect to the major strain direction, this is not always the case. Final

ductile fracture surfaces are not confined to their respective characteristic surfaces of

a particular plastic field and can develop on other surfaces under certain circumstances

[83]. As pointed out by Thomason [116], this is because the internal necking form of

microvoid coalescence differs to first order from the previous stable, macroscopically

homogeneous state of plastic flow.


2.4 Damage Characterization

Typically, investigation into the process of ductile failure of steels via void nucle-

ation, growth, and coalescence has been undertaken with scanning electron or light

microscopy of strained and failed mechanical testing samples [14–19]. This technique

is beset with many drawbacks, including the need to use a sectioning technique that

accurately preserves the integrity of the void structure developed during deformation,

such as electric discharge machining or the use of a focused ion beam. This act of

sectioning irreversibly destroys the integrity of the original failed specimen. As well,

SEM analysis provides only two-dimensional data at the discrete planes of sectioning

concerning the morphology of voids. As such, extracting robust 3-D data concerning

void morphology and spatial distribution requires a time-intensive serial-sectioning

technique whereby a small layer of material is removed between subsequent 2-D im-

age captures, which can later be stacked to form a 3-D reconstruction of the volume

sampled.

These limitations, and recent advancements in the resolution of synchrotron beam-

lines have led to the use of synchrotron X-ray micro-computed tomography (XµCT)

to characterize damage evolution in materials as dense as automotive structural steels.

The advantages of such a technique include that it is non-destructive, relatively fast,

and provides 3-D information on the morphology of voids. However, unlike SEM

study, phases of similar density cannot be differentiated by greyscale contrast using

XµCT. This limitation prevents simultaneous analysis of the microscopic features

and mechanisms that can lead to premature failures during typical forming opera-

tions for DP steels due to the very similar densities of ferrite and martensite phases.

Thus, it is necessary to couple light or scanning electron microscopy analysis of failed


or interrupted mechanical samples with XµCT results. It has been demonstrated

that X-ray absorption micro-computed tomography is the most reliable method for

obtaining three-dimensional quantitative information about void damage in mate-

rials [20, 21]. The following subsection presents the basic theory encompassing the

XµCT technique.

2.4.1 X-ray Micro-computed Tomography

XµCT makes use of an X-ray source to image materials in three dimensions at high

spatial (below 1 µm) resolutions [117]. The technique is based upon X-ray radiogra-

phy: X-ray photons are directed at a sample for a defined period of time and those

photons that are transmitted through or around the sample are counted/recorded by a

detector. For X-ray tomography, charge-coupled device (CCD) detectors are typically

used. Detectors may be 1-D (linear) or 2-D as shown in Fig. 2.11, the latter providing

faster acquisition times by eliminating the need for sample vertical translation.

2.4.1.1 Micro-focus X-ray Sources

Lab X-ray sources, also known as micro-focus sources, produce polychromatic, conical

X-ray beams. High potential differences on the order of tens of kV are produced be-

tween the cathode and anode (target) of an X-ray tube. This large potential difference

causes electrons to travel from the cathode to the anode, impacting the atoms of the

target. When these incident electrons interact with shell electrons of the target atoms,

it is possible that a shell electron may be ejected and the incident electron scattered.

This results in an electron vacancy in said shell that will be filled by an electron

dropping from a higher-energy shell, producing an x-ray photon (of discrete energy


Figure 2.11: XµCT beam and detector geometries. (a) Fanbeam geometry: micro-focus X-ray source with 1D detector.The sample requires vertical translation to be scanned. (b)Cone-beam geometry: micro-focus source with 2D detector.The sample is magnified on the detector. (c) Parallel beamgeometry: synchrotron source ensures nearly parallel X-raybeams. The sample is negligibly magnified on the detector.Not shown are a scintillating material that is used to convertthe wavelength of the radiation from X-ray to visible light andan optical objective for image magnification [118].

level) with the latent energy; i.e. characteristic X-ray generation. Bremsstrahlung

radiation, carrying a continuum of photon energy levels, is also produced in lab X-ray

sources due to incident electron path changes resulting from interactions with tar-

get atom electrons. Both characteristic and Bremsstrahlung radiation are shown in

Fig. 2.12.

2.4.1.2 X-ray attenuation

X-ray beams produced from a synchrotron source are typically monochromated. This

is useful in X-ray tomography as it eliminates artifacts due to beam hardening and

can allow for quantitative phase analysis due to a direct relationship between the grey

level of projections and the absorption coefficient of phases [118]. This absorption

coefficient is linked to the density and the atomic number of materials, plus the energy


Figure 2.12: X-ray spectrum of a molybdenum target asa function of applied voltage. Shown are the continuousBremsstrahlung radiation and the discretely peaked character-istic radiation produced. [119]

of impinging X-rays. Thus, when a beam is monochromated to a single energy, E,

grey levels in projections become purely a function of the material density, ρ, and

atomic number, Z, plus a constant K as in Eq. 2.1 [117]. Monochromators for lab-

scale tomography, i.e. micro-focus X-ray sources, are currently prohibitively costly for

many research groups. In the case of a polychromatic beam, grey levels in projections

are not purely a function of material density and thus reconstructions from these

projections are inherently subject to slightly increased noise.

µ(x, y, z) = KρZ4

E3(2.1)

The probability of X-ray attenuation in a material is a function of the probability

of photoelectric absorption and the probability of Compton scattering, both of which


are related to the density and atomic number of the material. As mentioned previ-

ously, the basis of X-ray tomography is X-ray radiography. X-rays pass through a

material sample according to the Beer-Lambert law [118]. The ratio of the number

of transmitted to incident photons is related to the integral of the absorption coef-

ficient, µ, along the path that the photons follow through the sample [118] and is

also dependent upon the energy of the incident photons. This can be represented in

Eq. 2.2 [117] with the number of incident photons, N0, of energy E, the number of

transmitted photons, N1, of energy E, and the corresponding attenuation coefficient,

µ, of the sample along the X-ray path, s :

N1

N0= e[−

∫sεray

µ(s)δs] (2.2)

2.4.1.3 Tomography Fundamentals

Transmitted photons are recorded by a detector, typically a CCD, with counts recorded

at each pixel. It is necessary to use a scintillating material between the sample and

detector to change the wavelength of the transmitted photons from the X-ray spec-

trum to the visible light spectrum. Optical objectives are often placed between the

scintillator and the detector as well for magnification purposes. The counts collected

by the CCD are transposed into grey level intensities of an image of the sample. This

image represents a two-dimensional projection of the three-dimensional object. In

order to obtain 3D information about the sample, a large number of 2D projections

of the sample are radiographically recorded between periodic rotations of the sample

between 0◦ and 180◦ about a single axis. With enough projections of high signal to

noise ratio throughout the 180◦ scan, a 3-D reconstruction of the sample comprised


of stacked 2D slices can be produced using a filtered back-projection algorithm. An

explanation of the calculations made during filtered back-projection are beyond the

scope of this dissertation. A simplified representation of a tomographic setup is pro-

vided in Fig. 2.13.

Figure 2.13: Simplified schematic of an X-ray tomographicsetup [120]. The source shown is that of a lab-scale X-ray tubeproducing a conical beam. The sample is typically mountedon a stage capable of rotation and Cartesian translation. Itshould be noted that unlike what is depicted in the schematic,specimens are typically of lesser width than field of view madeavailable at the CCD by the optics of the system.

There are three typical modes in which to perform tomography: absorption mode,

phase contrast mode, and holotomography mode. Absorption mode is the most typ-

ical and develops contrast between constituents in a material based upon their re-

spective absorption coefficients. The greater the difference in the density and the

atomic number of constituents, the greater the contrast that is developed between

them. The detector needs to be placed close to the sample to avoid phase effects [118].

The degree of transmission through the sample is also of importance; too great, and


sufficient contrast is not developed between constituents; too low, and the signal to

noise ratio of projections is inadequate [118]. For synchrotron XµCT, a reasonable

compromise between both effects is a transmission of around 10% [118].

2.4.1.4 Artifacts

In the context of XµCT, an artifact refers to any systematic discrepancy between

greyscale values in a reconstructed volume and the true attenuation coefficients of

the material within that volume [121]. These artifacts may hinder qualitative and

quantitative interpretation of reconstructions. The most common artifacts to affect

reconstructions of tomographic datasets captured using lab-scale XµCT are outlined

below.

Beam Hardening

Beam hardening is a phenomenon that affects tomographic reconstructions produced

using a polychromatic X-ray beam. The spectra of energy levels which the photons of

the beam possess is the root cause of this type of artifact. As the polychromatic X-ray

beam passes through an object, its mean energy level increases as lower-energy pho-

tons are attenuated more easily than higher-energy photons; hence the term “harden-

ing”. Obviously, attenuation of lower-energy photons occurs to a greater degree with

increasing path length through an attenuating material. Thus, X-ray projections

of an object of uniform attenuation coefficient, but variable thickness, i.e. variable

photon path length, will exhibit a characteristically darker intensity in the regions

of greater thickness where the beam has been hardened. In reconstructions, beam

hardening artifacts are exhibited as a distinct cupping effect in greyscale intensity


through specimen thickness, such as in Fig. 2.14.

Beam hardening can be minimized by using physical filters to attenuate some of

the lower-energy photons from the X-ray beam prior to interaction with the specimen

being imaged. As well, post-processing may be applied to provide a correction to

reconstructions suffering from beam hardening artifacts.

Figure 2.14: Intensity profiles plotted across a reconstructedslice of a uniform water phantom: a) suffering from a beamhardening artifact; and b) corrected for beam hardening viapost-processing [121].

Ring Artifacts

Inhomogeneities, i.e. defects, in the scintillators used to convert radiation from the X-

ray spectrum to the visible light spectrum produce repeatable artifacts in tomographic

projections. These artifacts occur at the same locations relative to the field of view

(FOV) and result in ring artifacts in reconstructed slices, such as in Fig. 2.15.


Figure 2.15: Severe ring artifacts in a reconstructed slice of afailed DP steel uniaxial tension specimen. It should be notedthat the signal to noise ratio in this reconstruction is very pooras well.


Streak Artifacts

Higher energy X-rays, i.e. 100 to 150 kV, are likely to sometimes pass right through the

thinner scintillating screens on the 10x and 20x objectives of Xradia’s Micro-XCT 400.

When this occurs, the X-ray photons may carry on and impact the CCD, resulting

in a saturated pixel which will appear as a bright “speckle” in single projections and

line or streak artifacts in reconstructed slices as shown in Fig. 2.16.

Figure 2.16: A streak artifact (line) in a reconstructed sliceof a failed DP steel IPPS tension specimen, resultant from aspeckle in projection data.


2.4.2 Previous XµCT Experimentation

Previous studies have taken advantage of XµCT’s capability to provide a wealth of

information regarding void damage morphology in steels for uniaxial tensile loading

[22,24,122], but these have been performed on a synchrotron beamline where current

generation synchrotron X-ray sources can deliver fluxes greater than 1000 times those

generated by X-ray tubes [118]. This high flux allows for better quality images in

terms of signal-to-noise ratio. The highly collimated nature of synchrotron X-ray

photons also allows for submicron resolutions in some setups [123].

Due to the high linear absorption coefficient (LAC) of steel, the only study in the

literature to date that is known to have used a lab-scale X-ray tube source to perform

micro-computed tomography of a steel specimen is that of Gupta et al. [23]. Such

a high LAC leads to reduced contrast development between voids and surrounding

material. For a CrMoV steel uniaxial tensile specimen loaded to a nominal strain of

17%, Gupta et al. reported 11261 voids within the reconstructed region of the neck

(1.4 mm3), with the largest voids generally elongated in the tensile direction. This

represented a void volume fraction of 0.03%. Voids were predominantly in the range

of 5-19 µm in size.

An important conclusion drawn from the synchrotron XµCT in-situ tensile testing

of cold forging steel by Bouchard et al. [122] was the influence of inclusion orienta-

tion on damage anisotropy. Voids were observed to nucleate and grow at inclusions

primarily in the direction of inclusion orientation. Thus, tensile specimens in which

inclusions were oriented perpendicular to the principal loading direction were observed

to nucleate and grow voids primarily through the thickness of the tensile specimen, as

evident in the radial ‘R’ specimens of Fig. 2.17. This led to void coalescence, strain


localization, and final fracture occurring more rapidly in specimens with transversely

oriented inclusions compared to specimens with longitudinally oriented inclusions.

(a)

(b)

Figure 2.17: Void evolution observed by XµCT for a longitudi-nal and radial cold forging steel tensile specimen on: a) a radialcutting plane; and b) a longitudinal cutting plane. [122]


For synchrotron XµCT in-situ uniaxial tensile testing of dual-phase steel, Maire

et al. [22] have quantitatively computed void fraction to increase with increasing

proximity to the center of a neck. This trend becomes stronger with increasing strain,

especially after diffuse necking begins (Fig. 2.18(a)). As well, void fraction has been

shown to decrease with increasing proximity to the specimen surface (Fig. 2.18(b)).

This is explained by increased stress triaxiality at the center of a tension specimen.

A novel finding was a quasi-stagnation of the average equivalent diameter of voids

during tension testing of the DP steel studied due to nucleation of new small voids

balancing the growth of larger voids.

2.5 Digital Image Processing

2.5.1 Image Denoising

It is imperative that a filtering operation used on reconstructed tomography slices for

the purposes of denoising not cause any significant loss of fidelity of void morphology.

A typically used Gaussian filter essentially produces a convolution of an image by a

linear symmetric kernel [124]. This form of filtering is optimal for harmonic functions

but does not perform as well in image regions with texture or edges [124]. In these

regions, a blurring effect is produced by a Gaussian filter and results in a loss of fine

detail. A loss of fine detail in the slices produced by tomographic study of deformed

steel specimens would result in a removal of distinctly contrasted edges between voids

and surrounding steel, translating to a degradation in the accuracy of subsequent

thresholding operations’ capture of true void morphology.

A review of image denoising methods performed by Buades et al. [124] revealed a


(a)

(b)

Figure 2.18: Profiles of the fraction of voids produced fromin-situ XµCT data for a DP600 steel tension specimen in slicesperpendicular to: a) the tensile axis for various deformationsteps prior to failure; and b) the tensile axis and the two or-thogonal directions in the last deformation stage recorded priorto fracture. [22]


Non Local Means (NL-Means) algorithm to be optimal in removing noise from natu-

ral images while preserving fine structures. The method takes advantage of the high

degree of redundancy present in natural images by comparing small windows within

an image for similarity. The estimated true greyscale intensity value for every pixel in

an image is computed as a weighted average of all the pixels in the image, with similar

pixel neighbourhoods given a larger weighting than dissimilar neighbourhoods [125].

This concept is given visual context in Fig. 2.19. An example of the superior perfor-

mance of the NL-means algorithm in preserving fine detail while smoothing greyscale

gradients relative to conventional filtering techniques is demonstrated in Fig. 2.20 and

Fig. 2.21 for a natural image and in Fig. 2.22 for a periodic image. Fig. 2.21 provides

the method noise produced by various algorithms, which is equivalent to the point

operation of subtracting the denoised image from the original image. Ideally, the

method noise resembles white noise as much as possible, is as small as possible, and

does not show any detail from the original image.


Figure 2.19: Scheme of NL-means strategy. Similar pixel neigh-borhoods give a large weight, w(p,q1) and w(p,q2), while muchdifferent neighborhoods give a small weight w(p,q3). [125]


(a) Original image.

(b) From left to right and from top to bottom: noisy image (standard deviation 20), Gaussian

filtering, anisotropic filtering, Total variation, Neighborhood filtering and NLmeans algorithm. The

removed details must be compared with the method noise (see Fig. 2.21).

Figure 2.20: Denoising of a typical natural image, “Lena”, usingvarious algorithms [125].


(a) Original image.

(b) Image method noise. From left to right and from top to bottom: Gaussian

convolution, Mean curvature motion, Total Variation, Iterated Total Varia-

tion, Neighborhood filter, Hard TIWT, Soft TIWT, DCT empirical Wiener

filter and NL-means.

Figure 2.21: Denoising of a typical natural image, “Lena”, usingvarious algorithms. [124]


Figure 2.22: Denoising experience on a periodic image. Fromleft to right and from top to bottom: noisy image (standard de-viation 35), Gaussian filtering, Total variation, Neighborhoodfilter, Wiener filter (ideal filter), Hard TIWT, DCT empiricalWiener filtering, NL-means algorithm. [124]

2.5.2 Image Segmentation

An exhaustive review performed by Sezgin et al. [126] of image thresholding tech-

niques and their performance distinguished six general categories of thresholding tech-

niques: histogram shape-based methods, clustering-based methods, entropy-based

methods, object attribute-based methods, spatial methods, and local methods.

Forty algorithms encompassing the six thresholding technique categories were used

to threshold each of forty different non-destructive testing (NDT) images. Perfor-

mance of the algorithms was based upon five criteria: misclassification error, edge

mismatch, relative foreground area error, modified Hausdorff distance, and region

nonuniformity. The clustering-based method of Kittler and Illingworth [127] and the


entropy-based methods of Kapur, Sahoo, and Wong [128], and Sahoo, Wilkins, and

Yeager [129], were determined, in that order, to be the best performing thresholding

algorithms in the case of NDT images.

Chapter 3

Experimental Methods and

Materials

This chapter contains a description of the sheet steels provided by U.S. Steel Corpora-

tion for this study. The metallographic techniques employed to characterize the steel

microstructures are described. The heat treatment paths and methodologies used to

produce variants of ferrite-martensite microstructures are documented. Mechanical

testing methods are outlined along with XµCT techniques for subsequent analysis of

void damage within failed specimens.

3.1 Received Material Characteristics

Four steels were used for this study: two classified as DP780 and two as DP980. The

DP780 and DP980 sheets were received in both a cold-rolled (CR) and a galvannealed

(GA) condition. This material was provided by U.S. Steel Corporation. The chem-

ical compositions for these four sheets are given in Table 3.1. It is clear that the

58

CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 59

compositions of the two DP780 and DP980 sheets respectively are comparable and

that the carbon content of each alloy is relatively low. The thickness of each sheet is

listed in Table 3.2. It is evident that the gauges of the two DP780 and DP980 sheets,

respectively, are comparable as well.

Table 3.1: Elemental compositions of the sheet steels providedby U.S. Steel Corporation (wt.%); balance is iron. ‘GA’ signi-fies commercial galvannealed sheet and ‘CR’ signifies sheet inthe cold-rolled condition.

DP780 DP780 DP980 DP980GA CR GA CR

C 0.09 0.09 0.1 0.11Mn 2.05 2.1 2.34 2.42P 0.007 0.012 0.01 0.014S 0.006 0.006 0.004 0.006Si 0.016 0.02 0.02 0.02Cu 0.01 0.03 0.02 0.02Ni 0.01 0.01 0.01 0.01Cr 0.25 0.26 0.24 0.25Mo 0.285 0.29 0.33 0.362Sn 0.001 0.003 0.011 0.002Al 0.044 0.039 0.036 0.046N 0.006 0.004 0.004 0.004V 0.001 0.001 0.001 0.001B 0.0001 0 0.0001 0.0001Ti 0.001 0.001 0.001 0.001Cb 0.001 0.002 0.001 0.002

Table 3.2: Thicknesses of the sheet steels provided by U.S. SteelCorporation. ‘GA’ signifies commercial galvannealed sheet and‘CR’ signifies sheet in the cold-rolled condition.

DP780 DP780 DP980 DP980GA CR GA CR

Thickness (mm) 1.02 0.98 1.18 1.19

3.2 DP Steel Microstructural Variant Design

The primary goal of this study was to examine the effects of NFP (particularly marten-

site) volume percent, spatial distribution, and morphology on the failure behaviour


and accumulation of damage for strained DP steels. As such, microstructural variants

of DP steels with differing martensite particle populations had to be produced. To

accomplish this task, heat treatment procedures were tailored to make use of the cold-

rolled sheet available. A particular goal was to develop two microstructural variants

per cold-rolled alloy with similar NFP volume percent to that of the galvannealed DP

steel alloy of corresponding chemical composition; both variants were to be comprised

entirely of ferrite and martensite, but with differing martensite populations.

To produce these variants, two forms of thermal treatment path were applied

to cold-rolled specimens and various IC annealing temperatures were employed to

control the NFP volume percent.

3.2.1 Thermal Path One

Thermal Path One (TP1) consisted of a simple IC annealing of the cold-rolled steels.

TP1 is represented graphically in Fig. 3.1(a) and described in detail in Sec. 3.2.4.4.

Cold-rolled steel blanks were rapidly heated to a temperature within the alloy’s IC

range (715◦C or 733◦C or 743◦C) and held for 2 minutes before rapidly quenching in

an ice-water bath. This treatment produced a microstructure of banded NFP in a

ferrite matrix due to the highly deformed microstructure of the cold-rolled steel which

also contained banded NFP.

A short IC hold time of 2 minutes was selected to mimic industrial annealing times

and reduced experimental heat treatment time. As well, the short IC hold minimized

the slow growth of austenite into ferrite grains during annealing, leading to desirable

finer-scaled NFP after quenching, while still likely providing sufficient time for full

carbide dissolution.


3.2.2 Thermal Path Two

Thermal Path Two (TP2) consisted of an austempering pretreatment of the cold-

rolled steels prior to IC annealing. TP2 is represented graphically in Fig. 3.1(b) and

described in detail in Sec. 3.2.4.2. Austempering produces a bainitic microstructure,

causing a redistribution of carbon relative to the microstructures of the cold-rolled

steels. The bainite laths spatially segregate carbides in a relatively uniform fashion.

Upon subsequent IC annealing, this results in a uniform spatial distribution of NFP

with a bi-modal distribution of particle sizes: coarse grains with a high aspect ratio

and fine grains with a low aspect ratio.

Cold-rolled steel blanks were heated to 917◦C for 30 minutes to transform the

microstructure to 100% austenite. The blanks were then rapidly transferred to a

custom salt bath, quickly cooling to the bath temperature of 500◦C, and then held

in the bath for 20 minutes before being quenched in water. At this point, the blanks

were IC annealed as per TP1 at a temperature of 725◦C or 737◦C. The same IC

annealing time of 2 minutes was used for reasons explained in Sec. 3.2.1.

3.2.3 Heat Treatment Procedures and Apparatus

Three apparatus were used for the heat treatments employed in this study. Austem-

pering was performed using a Lindberg type 54232 tube furnace coupled to a Lindberg

type 59344 temperature controller for austenitizing (Fig. 3.2) and using a custom-built

salt bath furnace for the bainite hold (Fig. 3.3). IC annealing was performed in a salt

pot fit within a Lindberg type 56622 vertical crucible furnace coupled to a Lindberg

type 59344 temperature controller (Fig. 3.4).


(a)

(b)

Figure 3.1: Representative heat treatment paths for a) ThermalPath One (TP1); and b) Thermal Path Two (TP2). Not toscale.


Figure 3.2: Lindberg type 54232 tube furnace coupled to aLindberg type 59344 temperature controller. Used for austen-itization during austempering heat treatments.

Figure 3.3: Custom-built salt bath used for the bainite holdportion of austempering heat treatments.


Figure 3.4: Lindberg type 56622 vertical crucible furnace andsalt pot coupled to a Lindberg type 59344 temperature con-troller. Used for IC annealing heat treatments.


3.2.4 IPPS Specimen Heat Treatment Schedule

IC annealing heat treatment temperatures for IPPS specimens were selected based on

the NFP content calibration curves presented in Appendix A. First, an IC annealing

temperature for each cold-rolled alloy was selected which would produce a microstruc-

ture with comparable NFP content to its corresponding galvannealed alloy: 733◦C

for cold-rolled DP780 and 743◦C for cold-rolled DP980. These IC annealing temper-

atures were used to generate DP variants for both alloys in an effort to minimize

necessary salt bath temperature changes. To produce a clearer trend between NFP

volume percent and void damage accumulation, a third IC annealing temperature

(715◦C) was selected to produce a DP steel variant with lower NFP volume percent.

This approach was expected to produce three DP steel microstructural variants with

similar NFP morphology, but varying NFP content.

To determine the effect of a differing population of NFP on damage accumulation,

an IC annealing temperature for TP2 was selected for each cold-rolled DP steel alloy

with the intent of producing the same volume percent of NFP as in the corresponding

galvannealed alloys. Due to the bainitic microstructure produced during austemper-

ing, a larger proportion of carbides existed in TP2 specimens prior to IC annealing

than in the TP1 specimens. It was expected that this increased carbide content would

result in a higher volume percent of NFP for any given IC-annealing temperature on

the calibration curve of Fig. A.4. This is because the first step in the formation of

austenite during IC annealing is almost instantaneous nucleation at cementite parti-

cles, followed by rapid growth until the carbide phase is fully dissolved [6]. Speich

show that this takes less than 1 minute to complete for low-carbon 1.5-Mn steels [6].

With the second step of austenite formation being slow growth into ferrite grains,


which takes hours to fully complete [6], it was assumed that the higher bainite content

of the austempered blanks relative to the cold-rolled blanks would result in a higher

NFP content for equivalent IC annealing treatments of the two input microstructures.

Based on the experience of Seyedrezai [130] with austempering and IC annealing of

the DP780 cold-rolled alloy, it was predicted that shifting the IC annealing calibra-

tion curve of Fig. A.4 by approximately 7◦C to the left would result in a reasonable

prediction of NFP content. As such, IC annealing temperatures of 725◦C and 737◦C

were selected for TP2 for the DP780 and DP980 cold-rolled alloys, respectively.

Given the highly banded nature of NFP along the rolling direction in the mi-

crostructure of TP1-treated blanks, it was postulated that both mechanical proper-

ties and void damage accumulation would vary between IPPS specimens in which the

tensile direction was aligned with either the sheet rolling direction or the transverse

direction. To determine if this was the case, IPPS specimens for all heat treatments

were produced with both sheet orientations.

The location at which failure occurs within the gauge region of IPPS mechani-

cal testing specimens was known to be highly unpredictable for the inhomogeneous

microstructures of the DP steel variants used in this study. As such, production of

a large number of IPPS specimens per variant batch was necessary to result in a

sufficient number of failed specimens suitable for accurate analysis of strain at failure

(via tracking of the deformation pattern of a grid of dots painted onto the specimen

surface). Seven specimens per heat-treated variant batch were produced. The full

schedule for the IPPS specimens is presented in Table 3.3.

A naming convention was applied to specimens as follows, where # represents a

numerical digit and n represents an alphabetic character: #(TP#)-(##)-n#. The


first digit, #, is either a 7 or 9, identifying respectively whether the specimen was pro-

duced from DP780 or DP980 sheet. The next three alphanumeric characters, (TP#),

represent the thermal path undertaken by the specimen; TP1 or TP2. The brackets

signify that these characters will not appear for galvannealed material; rather, a ‘GA’

will take their place. The next two numerical digits, (##) are representative of the

IC annealing temperature used during heat treatment. All IC annealing temperatures

were within the range of 715◦C to 743◦C, thus the 7 is dropped and only the remain-

ing 2 digits are used in the naming convention. Again, these two numerical digits will

not appear for galvannealed material. The alphabetic character, n, represents the

principal sheet direction of the specimen aligned with the tensile axis: ‘R’ indicates

the rolling direction is aligned with the tensile axis and ‘T’ indicates the transverse

direction is aligned with the tensile axis. The final numerical digit, #, indicates the

specimen number within the given condition/treatment batch.


Table 3.3: Full schedule for the production of IPPS rectangularblank specimens, detailing their condition/treatment prior tomechanical testing.

(a) DP780 blanks.

Condition / TreatmentIC Annealing

Temperature (◦C)

Alignment of

Tensile

Direction

Number of

Specimens

Galvannealed N/A RD 7

Galvannealed N/A TD 7

TP1 715 RD 7

TP1 715 TD 7

TP1 733 RD 7

TP1 733 TD 7

TP1 743 RD 7

TP1 743 TD 7

TP2 725 RD 7

TP2 725 TD 7

(b) DP980 blanks.

Condition / TreatmentIC Annealing

Temperature (◦C)

Alignment of

Tensile

Direction

Number of

Specimens

Galvannealed N/A RD 7

Galvannealed N/A TD 7

TP1 715 RD 7

TP1 715 TD 7

TP1 733 RD 7

TP1 733 TD 7

TP1 743 RD 7

TP1 743 TD 7

TP2 737 RD 7

TP2 737 TD 7


3.2.4.1 Austempering Apparatus

Austempering was performed in a tube furnace with a custom-made glass tube, shown

in Fig. 3.2, and with the custom-built salt bath shown in Fig. 3.3. The tube furnace

was used for austenitizing, while the salt bath was used for a bainite hold at 500◦C.

Treatment of steel at high temperature results in accelerated oxidation. The tube

furnace allowed for the treatment of steel blanks at high temperature without oxida-

tion by using a steady flow of argon to provide an inert atmosphere. The salt used

for the bainite hold was draw salt #275.

Tube Furnace Preparation

With an exit nozzle clamped to the glass tube, the temperature controller for the

tube furnace was set to a target temperature of 900◦C and the system was allowed

to heat up. Upon temperature stabilization, the volume of air within the glass tube

was purged with argon gas at a flow rate of 2000 cc/minute. The argon was al-

lowed to continue to flow at this rate for the duration of heat treatments. A 915 mm,

Chromega R©-Alomega R© Omega R© brand K-type thermocouple with Inconel sheath was

inserted into the glass tube through its exit nozzle such that the tip of the thermocou-

ple was located at the center of the tube furnace and suspended at the center of the

circular tube cross-section. The target temperature on the controller was adjusted

until the thermocouple reading stabilized at 917◦C.

For a stabilized hold temperature while argon was flowing, a temperature gradient

existed within the glass tube. For a temperature of 917◦C at the center of the tube

furnace within the glass tube, the temperature 43 mm away from this location along

the length of the tube was 7◦C lower, which means the temperature at the edge of an


IPPS steel blank may have been nominally lower than the center of the blank during

austenitization for TP2.

Custom Salt Bath Preparation

The temperature controller for the salt bath was set to a target temperature of 500◦C.

Upon reaching the target, a 610 mm long Chromega R©-Alomega R© Omega R© brand K-

type thermocouple with 304 stainless steel sheath was suspended in the molten salt

with its tip at a depth of 135 mm. This depth is where the center of the sample

gauge region would be located during heat treatment. The target temperature of

the salt bath temperature controller was adjusted until the temperature of the salt

measured using the suspended thermocouple reached 500◦C. A piece of steel rebar

was laid across the top of the salt bath to hang blanks from during heat treatments.

Due to the very large volume of salt within the custom-designed bath, no vertical

temperature gradient was detected within the molten salt after stabilization to target

temperature.

3.2.4.2 Austempering Procedure

A steel blank was wrapped in thermocouple wire around its 50 mm side length. A

small loop was made in the free end of the thermocouple wire 245 mm away from the

top of the blank. This loop would facilitate the hanging of the blank from the rebar

positioned above the salt bath such that the center of the blank gauge region was at

the same depth as the tip of the suspended thermocouple. After confirming the tube

furnace and custom salt bath had stabilized at the desired temperature, the blank

and thermocouple wire were pushed into the tube furnace and located such that the


center of the blank was at the center of the furnace.

The blank remained within the tube furnace for 30 minutes before being quickly

extracted and dipped into the custom salt bath. The transfer from the tube furnace

to the salt bath was made rapidly to ensure the cooling rate between austenitization

temperature and bainite hold temperature was high enough to prevent any austenite

within the blank from transforming to pearlite. After being held in the salt bath

for 20 minutes, producing a bainitic microstructure, the blank was extracted and

quenched in water.

At this time, the blank was taken through the procedure for TP1, producing

a ferrite-martensite microstructure. The IC annealing temperatures used for the

AT blanks are provided in Sec. 3.2.4, as well as the reasons underlying the selected

temperatures.

3.2.4.3 IC Annealing Apparatus

IC annealing was performed in a bath of molten salt to provide a nearly uniform tem-

perature environment around specimens during treatment; the temperature gradient

in the salt from the top to the bottom of specimens was approximately 3◦C. The salt

selected for IC annealing was NuSal based on its recommended operating tempera-

ture range, low reactivity with the surface of steel, and its melting temperature [131].

NuSal is produced by APCO Industries Co. Ltd. and is a mixture of potassium and

sodium chlorides.


Salt Bath Preparation

Prior to IC annealing of specimens, the temperature controller for the salt bath

furnace was set to 840◦C which allowed the solid salt within the pot to melt after a

period of time. After the salt was completely molten, more salt was gradually added

to the pot until the top surface of the molten salt was 25 mm from the top of the

pot. This allowed for complete immersion of specimens in the molten salt, well away

from the surface where a significant temperature gradient existed.

At this time, a 610 mm, Chromega R©-Alomega R© Omega R© brand K-type thermo-

couple with 304 stainless steel sheath was suspended into the salt bath and clamped

into position 10 mm from the edge of the salt pot. The tip of the thermocouple was

located at the same depth as the center of the gauge region of IPPS specimen blanks

being IC annealed, 82 mm below the surface of the salt. Bricks were located on either

side of the thermocouple on top of the salt pot to minimize convection between the

salt and the atmosphere. A gap of approximately 40 mm was maintained between

the bricks.

For simplicity and time-saving reasons, the thermocouple was not welded or

peened onto the sample. It is shown in Appendix B that the heating response of

the rectangular steel blanks being treated is quite predictable for a specified target

temperature.

3.2.4.4 IC Annealing Procedure

The set-point of the furnace controller was adjusted until the temperature reported

using the submerged thermocouple stabilized to the desired value within ±1◦C for 10

minutes. A rectangular blank sheet specimen, 85 mm x 50 mm, was then secured to a


custom specimen holder, detailed in Fig. 3.5, by wrapping thermocouple wire around

the specimen and forks. The blank was oriented with its 85 mm edges horizontal to

prevent any variation in microstructure along the width of the gauge region of the

blank due to the small vertical temperature gradient within the salt bath. Due to

the lack of an intimate interface between the specimen holder and steel blanks, and

the short annealing times (<3 minutes), diffusion of elements between the specimen

holder and blanks was highly improbable and therefore considered negligible.

The blank was submerged quickly in the center of the salt pot and the three legs

of the specimen holder rested on the bricks located on top of the salt pot. The blank

remained in the salt pot for as long as was required to heat up to the target temper-

ature, calculated in Appendix B, plus 2 minutes. At this time, the specimen holder

and attached blank were rapidly withdrawn from the molten salt and submerged in

an ice-water bath for quenching. The rapid nature of this sample extraction was

employed to minimize the production of any non-martensitic NFP.

The blank and specimen holder were blown dry shortly thereafter to prevent cor-

rosion of the blank and to prevent any water from entering the salt pot and causing

potentially harmful bubbling during a subsequent treatment. Before another blank

was IC annealed in the salt pot, the salt pot temperature was allowed to stabilize

within its target range again. This required time is calculated in Appendix B. To con-

firm that the target temperature was reached after this time period, the temperature

reported by the suspended thermocouple in the salt bath was also examined. After

every 7 blanks were IC annealed, the depth of the molten salt surface below the top of

the pot was measured and more salt added accordingly. If salt was added, no further

treatments were performed until the salt had stabilized at the target temperature,


±1◦C, for 15 minutes.

Figure 3.5: Custom-built IC annealing IPPS rectangular blankspecimen holder. Center rod collinear with axis of dipping intosalt pot.

3.3 Metallography

This section describes in detail the metallographic procedures applied to character-

ize the microstructures of the steels used in this study. Metallographic specimen

extraction is described, followed by preparatory procedures for microscopy, includ-

ing etchant descriptions, and techniques for quantitative analysis of microstructural

constituents. Procedures described within this section were developed as per the

recommendations of ASM Handbook Volume 9 [132], and ASTM Standards E3 and

E407 [133, 134].


3.3.1 Specimen Preparation

Sectioning of metallographic specimens from ‘D’-shaped cutouts at the location of

the IPPS specimen gauge region (Fig. 3.6) was performed using a Struers Accutom

precision cut-off machine equipped with an aluminum oxide cut-off wheel and contin-

uously flowing coolant. The scrap ‘D’-shaped cutouts were considered representative

of undeformed gauge regions for IPPS specimens. Referring to the IPPS specimen

heat treatment schedule (Table 3.3), one ND-RD and one ND-TD metallographic

section were extracted per IPPS specimen condition.

Figure 3.6: IPPS specimen with waterjet-cut ‘D’-shaped scrapsused for the production of ND-RD and ND-TD metallographicspecimens at the center of the gauge region.

3.3.1.1 Grinding and Polishing

Prior to grinding and polishing, metallographic sections were mounted in short-glass

reinforced diallyl phthalate using a Simplimet 1000 automatic mounting press. The

heat developed in the mounting process was not expected to affect the microstructures


of the steels examined.

Grinding

Rough grinding using 80 grit silicon carbide rotary discs was performed initially for

one minute to remove any heat affected zone that may have resulted from the unlikely

possibility of insufficient cooling during sectioning with the cut-off saw. Grinding and

polishing media with progressively finer particle sizes were used in sequence to remove

all artifacts and deformation produced by the previous step of grinding/polishing until

the specimen surface became free of any artifacts. The full sequence of grinding media

used is presented in Table 3.4. Grinding papers were continuously flushed with water

to keep specimens cool and to remove debris.

Table 3.4: Stages of grinding employed for metallographic spec-imen preparation.

Grinding Stage Details

Rough

• 80 grit silicon carbide• rotary wheel manual grind• moderate-heavy pressure• one minute• water flush

1

• 220 grit silicon carbide• stationary paper manual grind• moderate-heavy pressure• water flush

2


3


4

• 600 grit silicon carbide• stationary paper manual grind• moderate-heavy pressure• cotton and water clean, ethanol flush, compressed air jet dry


Polishing

The polishing stages employed for all specimens are outlined in Table 3.5. Etching

was performed immediately after the final polishing stage to prevent passivation of

the specimen surface.

3.3.1.2 Etching

Several attack etchants and tint etchants were used in this study to develop contrast

between microstructural constituents for the purposes of optical and scanning electron

microscopy. Most of these etchants were mixed and applied following the procedures

outlined in ASTM Standard E407-07 [134]. A summary of the etchants used, their

purpose in microstructural characterization, and associated procedures is provided in

Table 3.6.


Table 3.5: Stages of polishing employed for metallographic spec-imen preparation.

Polishing Stage Details

1

• 6 µm diamond solution with 50% glycerin lube

• rotary wheel manual polish

• cotton cloth

• heavy pressure

• 2 minutes

• cotton and water clean, ethanol flush, compressed air jet dry

2

• 1 µm diamond solution with 50% glycerin lube


• cotton cloth

• heavy pressure

• 1 minute

• cotton and water clean, ethanol flush, compressed air jet dry

3

• 0.05 µm colloidal suspension of silicon dioxide


• Alphalap synthetic cloth (Micro Metallurgical Ltd.)

• light pressure

• 1 minute

• ethanol flush, compressed air jet dry


Table 3.6: Etchants used for microstructural characterizationand their associated procedures. The ‘Stage’ column denotesthe step number in a multi-stage etching procedure.

Microstructural CharacterizationMicroscopy

MethodDetails

• 10% Sodium metabisulfite (SMB)

NFP Volume Percent in Specimens of

Preliminary Heat TreatmentsOptical • 20 s immersion with light agitation

• ethanol flush, warm air dry

NFP Volume Percent in Cold-rolled Steels • 2% Nital

NFP Volume Percent in IPPS SpecimensScanning

Electron• 13 s immersion

NFP Particle Size in IPPS Specimens • ethanol flush, compressed air jet dry

• 2% Nital

Void Nucleation Sites in XµCT Match-head

Specimens

Scanning

Electron• 40 s immersion

• ethanol flush, compressed air jet dry

3.3.2 Microstructure Characterization Methods

This section outlines the procedures undertaken for quantitative analysis of the mi-

crostructural characteristics of metallographic specimens prepared from the DP steel

variants of this study.

3.3.2.1 Volume Percent Measurement

The volume percentages of microstructural constituents within metallographic spec-

imens were statistically estimated according to the guidelines for systematic point

counting of ASTM standard E562-08 [135]. This technique actually measures area

fraction; however, it has been shown that stereological area fraction measurements

are directly related to volume percent [136]. A JEOL JSM-840 SEM instrument was


used in secondary electron mode to capture greyscale micrographs measuring 1024

x 768 pixels. Mounted, nital-etched specimens were gold-coated and grounded with

copper tape attached to the specimen holder prior to being placed in the SEM cham-

ber. A working distance of 15 mm and an accelerating voltage of 20 kV were used.

For each DP steel microstructural variant examined from Table 3.3, 15 micrographs

were captured from each of the ND-RD and ND-TD sections at a magnification of

5000x. These micrographs were captured along the through-thickness centerline of

the steel sheet where NFP banding was most prevalent. A manual stage control knob

was rotated a random magnitude while looking away from the SEM display to move

the specimen along the sheet centerline to the location of the next field to avoid any

operator field selection bias.

A regular grid of test points was overlayed onto these micrographs using ImageJ

software and the number of test points falling within the constituent of interest were

counted, using manual tally software, and then divided by the total number of test

points. The average of the mean point fraction for ten ND-RD fields and the mean

point fraction for ten ND-TD fields provided an estimate of the volume percent of said

constituent within the DP steel variants. The 95% confidence interval and percent

relative accuracy were calculated for each volume percent estimate.

Due to the periodicity of the distribution of NFP in many of the microstructures

examined, a custom grid of 131 test points in the shape of five equidistant circles was

developed and used as a Java plug-in within ImageJ for point-counting, as opposed to

a typical rectangular array of grid-points. The use of circles eliminated any bias that

would be associated with NFP regularly falling on the horizontal grid-lines of a rect-

angular array. The test points of the grid were made to be as small as possible while


remaining visually detectable, thereby reducing bias caused by operator perception

when points appear to fall upon multiple constituents.

3.3.2.2 Particle Size Measurement

The sizes of NFP particles within metallographic specimens were measured according

to the guidelines for determining average grain size in ASTM standard E112-96 [137].

A modified Abrams Three-Circle Intercept Procedure was used to produce an unbi-

ased particle size measurement because of the non-equiaxed NFP particles within

many of the DP steel microstructures examined. Circular test arrays automatically

compensate for non-equiaxed grain shapes, without overweighting any local region of

the field [137].

Secondary electron micrographs captured for NFP volume percent measurements

as in Sec. 3.3.2.1 were used for the NFP particle size measurement procedure. Three

concentric, equidistant circles with a total circumference of 121.1 µm were overlaid

onto the micrographs using ImageJ freeware. Intercept counting was performed with

manual tally software for 10 micrographs in each of the ND-RD and ND-TD sections.

A minimum of 500 total counts were recorded, a number found to produce acceptable

precision [137]. The mean lineal intercept length, 95% confidence interval, and percent

relative accuracy were calculated for each DP steel variant.

3.4 In-Plane Plane-Strain Mechanical Testing

It was expected that mechanically testing the DP steels along a near plane-strain

forming path and performing XµCT examinations of failed specimens would shed


insight into the significance of void damage accumulation in the failure of these ma-

terials.

3.4.1 Sample Geometry and Preparation

The IPPS specimens used in this study were prepared from 85 x 50 mm rectangular

blanks of the DP steel sheets received from U.S. Steel. The blanks were first rough

cut with a hydraulic shear press. After heat treating the cold-rolled blanks, according

to the schedule of Table 3.3, the blanks were waterjet cut into the IPPS geometry

detailed in Fig. 3.7. This geometry allowed for testing to failure for all of the DP

steel microstructural variants using an 8521 Instron tensile testing machine equipped

with custom wide grips and a 100 kN load cell.

Figure 3.7: IPPS tension test specimen dimensions, adaptedfrom the work of Kilfoil [61].

The IPPS testing required the application of a grid of dots to each specimen

surface to facilitate measurement of the strains developed during testing based upon


tracking the deformation produced between dot centroids using a digital camera and

intervalometer. These dots were applied in an 8 x 8 array with the center of the array

located at the center of the gauge region of the IPPS specimen, where deformation

conditions are nearest to plane-strain. The dots were applied using a custom marker-

press attached to a micro-controlled microscope stage (Fig. 3.8). A script written

in Image-Pro PlusR© was used to move the stage in 3.175 mm intervals, producing

a uniform, square array of dots using a SharpieR© Paint marker. As mentioned by

Kilfoil [61], this grid application method was found to be superior to silk-screening

prior to machining as it helped prevent rubbing off or smudging of the dots. As

well, the custom tray used to hold IPPS specimens during the dot application process

allowed for consistent location of the array at the center of the gauge region [61].

The dots applied were approximately 1 mm in diameter. The small diameter dots

assisted in producing failure surfaces between rows of dots rather than through the

dots themselves [61]. The spacing of the dot array is detailed in Fig. 3.9.

3.4.1.1 Specimen Cleaning

Preliminary testing was performed to determine if cleaning of the IPPS specimens

to remove any oxide developed during heat treatments was necessary to produce

sufficient contrast between the dots and background steel for accurate image analysis.

Both a red and a green paint were applied to oxide-covered IPPS specimens which

were taken through the full testing procedure described in Sec. 3.4.2 and Sec. 3.4.3.

Subsequent thresholding of captured digital photographs of the dot arrays during

testing proved difficult to threshold with accurate representation of dot geometry due

to the dark oxide. The cleaning procedures of Kitney [131], detailed in Appendix C,


Figure 3.8: Custom paint plotting press used for application ofa grid of dots to IPPS specimens.

Figure 3.9: Inter-dot spacing for the grid applied to IPPS spec-imens.


were thus applied to IPPS specimens prior to subsequent application of a grid of

dots. Only IPPS specimens which had been heat treated were given an inhibited acid

cleaning; the galvannealed sheets had a matte finish which provided sufficient contrast

between dots and the steel in digital images. It was determined from preliminary

testing that red paint provided for more accurate segmentation than green paint

using the thresholding methods outlined in Sec. 3.4.3.

3.4.2 IPPS Testing Methodology

Custom 101.6 mm wide grips with a load rating of 133 kN [61] were attached to the

8521 Instron machine to apply the tensile force to IPPS specimens. Grip modifications

were previously made by Kilfoil [61] and Kitney [131] to the wedge-style grips to

facilitate more consistent alignment of specimens and reduce setup time. A constant

actuator speed of 2.5 mm/min was employed for all tests until specimens failed,

providing a nominal initial strain rate of approximately 0.01 s-1 averaged over the

entire gauge region. Clearly the local strain rate in the central region of specimens

differed from that near sample edges due to the differing strain states caused by

varying degrees of physical constraint in the minor direction.

Throughout the IPPS testing, an intervalometer equipped with an infrared (IR)

emitter was used to trigger digital camera exposures of the grid of dots. A Nikon D70

6.0 MP DSLR camera with CCD dimensions of 3008 x 2000 pixels was used. The

camera was mounted on a tripod and equipped with a 2x teleconverter lens followed

by 105 mm macro lens. The teleconverter acts to increase the camera’s focal length,

which was helpful considering the macro lens is suited to close-range applications.

The macro lens alone would not allow for fitting of a grid of dots in the field of view


(FOV). However, the teleconverter lens reduced light intake [61]; thus, additional

lighting was necessary to maintain contrast between the dots and the surrounding

steel. A distance of 890 mm between the IPPS specimen surface and the front face of

the macro lens was used to maintain both the grid of dots and a digital timer within

the FOV during testing. A single undeformed grid, i.e. four nearest-neighbour dots

forming a square, had dimensions of 93 x 93 pixels measured centroid to centroid in

captured images.

3.4.2.1 IPPS Testing Procedure

IPPS specimens were vertically aligned in the bottom grip using a squared block of

steel seated on the grip housing as a visual reference, as shown in Fig. 3.10. The

IPPS specimen was re-aligned within the grips until the top edge of the steel block

was parallel with top edge of the IPPS specimen before tightening the bottom grip.

The top grip’s center of mass was not coincident with the central axis of the shaft

used for attachment to the tensile testing machine. Since the top grip attached to a

universal joint to maintain uniaxial loading during testing, it did not hang plumb. To

ensure proper initial alignment of the top grip with respect to the IPPS specimen, a

level was placed on the upper housing surface of the top grip. The wedges of the top

grip were allowed to tighten on the IPPS specimen once it had been rotated about

the universal joint to be plumb, as depicted in Fig. 3.11. The experimental apparatus

setup for IPPS testing is displayed in Fig. 3.12.

At the beginning of each test, an image of the grid of dots in the un-deformed

condition was captured as a reference for subsequent calculation of strains developed

throughout the test. An intervalometer, The Time MachineTM, manufactured by


Mumford Micro Systems, was used to remotely trigger exposures of the deforming

grid every 30 seconds during each test. Shortly before failure of a specimen, the

IR trigger rate was increased to 20 Hz, activating the maximal exposure rate of the

camera (approximately 1.5 fps). Only specimens which failed between rows of dots

were used for strain analysis and tomographic analysis of damage accumulation.

Figure 3.10: Squared steel block used to visually align IPPSspecimens in bottom grip. The block was seated on the griphousing and the top edge of the IPPS specimen was alignedwith the top edge of the block.


Figure 3.11: Alignment of top grip using a level to ensureuniaxial loading of IPPS specimens.


Figure 3.12: Experimental setup of the apparatus for IPPStesting.


3.4.3 Image Processing and Strain Analysis

The segmentation technique used to binarize the digital images of dot grids captured

during IPPS testing was based upon the methods of Kitney [131]. This technique

allowed for semi-automation of the segmentation procedure and a more accurate

capture of dot geometry than a simple greyscale histogram shape-based thresholding

method. This procedure led to more accurate calculation of strains.

Images of IPPS specimens in the undeformed condition and throughout testing

were first cropped to contain only the grid of dots on the specimen (see Fig. 3.13(a)).

The RGB colour model used to record .jpeg images of grids was converted to a Lu-

minance, In-Phase, and Quadrature (YIQ) model using Image-Pro PlusR© software

(see Fig. 3.13(b) and Fig. 3.13(c)). The In-phase and Quadrature channels were then

automatically thresholded using a simple automatic convex hull thresholding. The

resulting black masks on white backgrounds were then combined using an OR logic

operation as shown in Fig. 3.14. The OR operation produced a new image where bits

are turned on (white) if the corresponding bit is on in either one of the input images.

Using Image-Pro PlusR©, the centroids of each dot were calculated and written to a

.txt file. These .txt files were imported into MicrosoftR© Excel and used with a macro

to calculate major and minor engineering strains for each group of four dots within

the gridded region of IPPS specimens. The strain calculation for each grid is one

used for 4-noded quadrilateral elements in FEM software, based upon the changing

distance between dot (node) centroids. Major and minor engineering strains were

calculated within the entire gridded region of the specimens for the last 5 images

captured prior to specimen failure. A check was made to ensure that strain within

the specimen was increasing reasonably with respect to time for these five exposures.


(a)

(b) (c)

Figure 3.13: IPPS grid image segmentation process (part 1 of2) showing: a) cropped RGB colour image of dots on an IPPSspecimen; b) In-Phase channel of a YIQ colour model for theimage of dots; c) Quadrature channel of a YIQ colour modelfor the image of dots.


(a) (b)

(c)

Figure 3.14: IPPS grid image segmentation process (part 2 of 2)showing: a) automatic convex hull thresholding of Fig. 3.13(b);b) automatic convex hull thresholding of Fig. 3.13(c); c) finalthresholded image used for strain calculations, created from anOR logic operation of the masks in a) and b).


It was assumed that the principal engineering strains were aligned with the principal

sheet directions (rolling and transverse).

The major and minor engineering strains just prior to failure within the grid row

where final specimen failure occurred were averaged for comparative purposes with

respect to specimens of other microstructural variants. As well, the major and minor

engineering strains were calculated at the position of the coupons removed for XµCT

analysis.

An example strain path for the central region of a TP2-treated DP780 IPPS

specimen is provided in Fig. 3.15, illustrating that the applied strain path is very

close to plane-strain.

3.4.4 Experimental Error Analysis

An error analysis was performed to determine the systematic error and variance in-

herent in the procedures previously outlined for image capture, post-processing, and

strain analysis. Using a typical IPPS test setup (including camera placement), an

undeformed, dotted specimen placed within the grips was imaged 40 times in succes-

sion at approximately 1.5 fps using the intervalometer and DSLR camera. The strain

analysis techniques outlined in Sec. 3.4.3 were applied to these 40 images with the

expectation that the strains calculated with respect to image capture time would be

normally distributed around a mean of zero. A 95% confidence interval for engineering

strain measurements was calculated to be ± 0.00003.


-0.08 -0.04 0.00 0.04 0.08

0.05

0.10

0.15

Minor Engineering Strain

Maj

or E

ngin

eeri

ng S

trai

n

Figure 3.15: An example strain path for a TP2-treated DP780IPPS specimen (7AU25-R4). Strain data points shown are theaverage of the strains calculated for the 7 grid points withinthe failure row.


3.5 X-ray Micro-computed Tomography Damage

Analysis

X-ray micro-computed tomography was the technique of choice for probing the in-

ternal structure of failed IPPS specimens in order to determine the degree of void

damage present. It allowed for the extraction of quantitative data concerning void

morphology in 3-D, using a non-destructive approach. Time and complexity for spec-

imen preparation and testing were greatly reduced by using XµCT compared to serial

2-D metallography methods.

The instrument used to perform XµCT projection capture was a Micro-XCT 400

produced by Xradia Inc. (Fig. 3.16). The approximately 5 µm spot size of the X-ray

source for this system allows for high resolution tomographic imaging. Specifications

of the instrument pertinent to this study are presented in Table 3.7.

Table 3.7: Micro-XCT 400 Specifications. 1Modulation transferfunction (MTF) measured using Xradia’s standard 2-D resolu-tion target.

Source

Max Voltage (kV) 150Min Voltage (kV) 40Max Power (W) 10

Objective Best Resolution at 10% MTF1 (µm)

Macro-70 204x 510x 2.520x 1.5

CCD

Pixel Array 2048 x 2048


Figure 3.16: Micro-XCT 400 instrument produced by XradiaInc.


3.5.1 Sample Preparation and Geometry

To achieve the best resolution possible with the Micro-XCT 400 system and thus

garner the most accurate information regarding void morphology in the failed IPPS

specimens, the 20x objective was used for this study. So-called “match-head” speci-

mens were produced from the failed IPPS specimens for tomographic analysis because

specimens that fit completely within the field of view (FOV) of an X-ray tomogra-

phy imaging system avoid truncated projection artifacts during image reconstruc-

tion [138]. The most common artifact produced is bright shading near the edge of

truncation [138, 139].

The “match-head” specimens for tomographic analysis were extracted from se-

lected IPPS specimens using a wafering saw so as to minimize artifacts near the plane

of sectioning, while minimizing the cost of the process. Twenty “match-head” speci-

mens were produced in total: one per IPPS specimen condition outlined in Table 3.3.

The selection criteria applied to determine which satisfactorily failed IPPS specimen

per condition would be sectioned to produce a tomography sample were: failure oc-

curred between two rows of dots, failure initiated from the center of the specimen (if

this was visually perceptible during mechanical testing), and, if possible, the major

engineering failure strain was representative of all satisfactorily failed specimens of

that particular DP steel microstructure.

The size of the match-head specimens was determined by the size of the FOV

available using the 20x lens of the Micro-XCT 400. For the conditions of placing

the X-ray source and 20x lens as close as physically possible (which is optimal for

producing a high flux of X-ray photons) the FOV was approximately 1.3 mm x 1.3 mm.

Match-head specimens were thus sectioned with a geometry of 1 mm x sheet thickness


x arbitrary height from the center of the width of IPPS specimens, where height

refers to the direction of tensile loading during mechanical testing. This location fell

directly between the 4th and 5th columns of dots on IPPS specimens, as detailed in

the schematic of Fig. 3.17.

In order to bring the X-ray source and detector as close to the match-head speci-

mens as possible during tomographic scanning (Fig. 3.18 and Fig. 3.19), an extension

mount was required to provide vertical clearance of the sample mount from the X-ray

source and detector. Match-head specimens were mounted to 60 mm long sections of

steel welding rod using LePageR© Epoxy SteelR©, as depicted in Fig. 3.19.

Figure 3.17: Schematic detailing the location within IPPSspecimens from which match-head specimens (green) were ex-tracted. Not to scale.


Figure 3.18: Micro-XCT 400 interior components set up intypical positions for a tomography capture of this study.


Figure 3.19: Close-up photograph detailing the small sourceto specimen and specimen to detector distances. These weremade possible by use of an extension rod mount for match-headspecimens.


3.5.2 Tomography Acquisition

The acquisition parameters for tomographic captures in this study are summarized

in Table 3.8. The acquisition procedure is outlined in the following sections.

Table 3.8: XµCT acquisition parameters used for IPPS match-head specimens.

Projections 3400

Exposure Time (s) 45

Source Voltage (kV) 100

Source Power (W) 10

Objective 20x

Source to Sample Distance (mm) 27.5

Sample to Detector Distance (mm) 4.0

Sample Rotation (◦) 184

Filter Xradia’s LE#5

Binning 2

Multiple Reference Imaging Average of 5 exposures every 850 projections

Dithering (Dynamic Ring Removal) On

Camera Readout Time Fast

3.5.2.1 Tomography Acquisition Procedure

A pin-vice sample holder equipped with kinematic stops was used to hold and kine-

matically locate a match-head specimen for tomographic capture. The source and

detector were carefully moved towards the specimen with incremental movements,

being sure to avoid any collisions. These were not brought as close as possible to the

specimen at this time, due to the specimen not yet being aligned with the stage axis of

rotation. Thus, stage rotation would result in a circular path of the sample, possibly

colliding with the stage or detector. The stage and sample holder were then taken

through a procedure of iterative rotation and translation in the X and Z axes to align

the central longitudinal axis of the match-head specimen with the rotational axis of


the stage. This alignment procedure is important for keeping the specimen within the

FOV throughout tomography capture while the stage rotates through 184◦. At this

time, the source and detector were then moved to the positions specified in Table 3.8.

The match-head specimen was then translated vertically along the Y axis to place

the top of its fracture surface just inside the top of the FOV. At this time, a physical

filter was selected to minimize global beam hardening using Xradia’s application notes

for filter selection. The filter attenuates X-ray photons from the lower end of the radi-

ation spectrum produced by the X-ray source, which are more likely to be attenuated

by following a path through thick specimen regions, but are likely to pass through

the specimen and reach the detector along shorter paths such as specimen corners.

Filtering these low energy photons helps minimize a “cupping effect” in greyscale in-

tensity variation traversing the cross-section of reconstructed specimen slices. Using

a source power of 10 W, the source voltage necessary to produce a transmission ratio

of 0.25-0.35 in the region of interest (ROI) below the fracture surface was experi-

mentally determined. This transmission ratio is recommended as optimal by Xradia

applications engineers. Finally, the exposure time necessary to produce a minimum of

2000 counts within the ROI at the specimen orientation which produced the longest

photon paths through the specimen was determined experimentally. It was observed

that photon counts received by the CCD generally have a linear relationship with

exposure time. The minimum value of 2000 counts was recommended by Xradia Inc.

to produce an adequate signal-to-noise ratio (SNR) for quality reconstructions.

After completing the above steps, the determined parameters were entered into a

recipe interface of Xradia’s XM Controller software and the tomography acquisition

was started. Projections were saved in a proprietary .xrm file.


3.5.2.2 Projections

The number of projections selected for each tomographic scan in this study was

determined based upon capturing a minimum number of views, Nmin, to satisfy the

Nyquist criterion for angular sampling: theoretically, the length of a 180◦ arc divided

by the linear sampling distance, defined by:

Nmin ≥ πd

2∆r(3.1)

where Nmin represents the minimum number of projections required to satisfy the

Nyquist criterion, D represents the diameter of the FOV, and ∆r represents the

linear sampling distance.

Equation 3.1 is valid for a parallel beam geometry and acts only as an approxima-

tion of the Nyquist criterion for the cone beam geometry produced in the Micro-XCT

400. As well, other factors beyond satisfying the Nyquist criterion must be considered

when determining the minimum number of projections that produce the best image

quality using tomography: the noise floor of data acquisition electronics, availabil-

ity of X-ray photon flux, etc [140]. As such, “oversampling” beyond the criterion of

Eq. 3.1 was performed in this study.

For the 2048 x 2048 CCD used in this study, the resulting minimum number

of projections dictated by Eq. 3.1 is 3217. However, a binning of 2 was used during

projection capture to increase SNR. Thus, 1609 projections are the minimum required

to approximately satisfy the Nyquist criterion for a parallel beam geometry. This

value was significantly “oversampled”, as 3400 projections were captured for each

tomography scan. This “oversampling” should not be viewed as detrimental due to

the extra projection capture time involved; rather, the “oversampling” increases the


SNR of the final reconstruction due to the additional data it provides for filtered back

projection reconstruction.

3.5.2.3 Exposure Time

A tradeoff exists between achieving higher resolution reconstructions and the photon

fluxes possible with higher magnification objectives during projection capture. Due

to the scale of microvoid damage within the IPPS specimens, a high resolution was

necessary. This was the reasoning underlying the selection of the 20x objective for all

tomographic captures performed in this study. However, the photon flux through the

20x objective is significantly lower than that possible for any of the lower magnifica-

tion objectives. To maintain a satisfactory SNR at this relatively lower flux, longer

projection exposures were necessary to produce a minimum of 2000 counts in the

ROI. At the same time, it was necessary to avoid saturation of projections in regions

of specimens which were very thin, i.e. at the top of fracture surfaces. A balance was

struck with a 45 second exposure time for the tomographic setup previously outlined

for the match-head specimens.

3.5.2.4 Source Power

The maximum power of the X-ray source, 10 W, was used to generate as great a

photon flux as possible, thereby decreasing tomography acquisition time.

3.5.2.5 Rotation

Using 180◦ of rotation for XµCT capture with a cone-beam source may produce cone

angle defects in reconstructions due to insufficient sampling. Extending this range of


rotation to 184◦ assisted in avoiding these defects.

3.5.2.6 Binning

Binning is the process of combining charges from adjacent pixels in a CCD during

readout. The parameter quoted for binning represents the side length of the square

matrix of pixels that have their charges averaged into one new superpixel after CCD

readout. It was determined from preliminary experiments that the SNR produced

using the 20x lens in conjunction with a binning of 1 was far too low to justify the

increased resolution offered with this setup. Exposures on the order of 7 minutes were

required to produce a minimum of 2000 counts in the ROI of projections; translating

to tomographic captures that would have required 18 days to complete per specimen.

Thus, a binning of 2 was used which required only 45 second exposures to produce

adequate counts.

3.5.2.7 Dynamic Ring Removal

Dithering, also known as dynamic ring removal, was used for all tomographic captures

to minimize ring artifacts caused by the defects in the scintillating material located

on the objective lens. Between projections, the stage is randomly translated a few

micrometers in the three principal axes. These stage movements are recorded by the

software and accounted for during reconstruction, with the end result being a “smear-

ing” of the ring artifacts produced by scintillator defects across several reconstructed

slices rather than resulting in a distinct, high contrast ring artifact.


3.5.2.8 Multiple Reference Imaging

Also known as flat-fielding, reference imaging divides projections by an image with

the sample out of the FOV (at the same magnification and with the same source

settings) to remove background noise. This includes dust particles in the imaging

apparatus and the “fish bowl” effect of most photons from the conical beam being

centralized in the FOV of the CCD, leaving the fringes of projections darker. The

intensity across projections is thus “flattened” after application of a reference image.

In general, it is best to have multiple referencing enabled, which acquires several

reference images throughout the course of the tomography and averages these into

one reference image which is applied to all of the projections captured throughout

the tomography scan. In this manner, variations in the environment within the

instrument over the duration of the tomography scan are better accounted for than

if a single reference image is used. A good rule of thumb according to Xradia Inc. is

to set the number of frames between references to one quarter of the total number

of projections to be taken in the tomography scan and to use an average of 5 images

at each interval. This translated to a reference image being captured after every 850

projections in the current study.

3.5.3 3-D Reconstruction

3.5.3.1 Projection Post-processing

Prior to reconstruction of the 2-D data captured in the form of X-ray projections of

match-head specimens, two forms of post-processing were applied to the projections.

The first was a plug-in included in Xradia’s software package which “de-speckled”

projections. The de-speckling filter was applied only to those projection sets which


suffered from speckling. It should be mentioned that when using the term ‘slice’,

reference is being made to reconstruction of the internal structure at a 1 voxel thick

plane through the cross-section of match-head specimens; i.e. this plane has a normal

vector parallel to the longitudinal axis of the match-head.

The other post-processing applied to projection sets was a correction to account for

any source/specimen drift during the course of tomographic acquisition. The plasma,

or spot, of the X-ray source has a tendency to drift location slightly, especially shortly

after the source has been aged. This drift would slightly change the typical path

followed by X-ray photons compared to paths taken during earlier projections, thereby

causing a shift of the specimen within the FOV that would not be accounted for during

filtered backprojection reconstruction. As well, any motion of the specimen itself

during the course of tomographic capture would produce the same effect; however,

for the non-biological specimens examined in this study, the likelihood of specimen

motion was very low. To account for both of these possible motions, a drift file is

automatically acquired during tomography acquisition to correct for both specimen

and source drift. A projection of the specimen at 0◦ of stage rotation is automatically

captured after every 60 non-reference image exposures and these drift projections are

automatically correlated to determine how much drift occurred. A plug-in was used

for each projection in this study to apply the source/specimen drift file recorded for

each specimen and make corrections to projections by corresponding translations.


3.5.3.2 Reconstruction Procedure

Center Shift Correction

After importing projections into Xradia’s proprietary reconstruction software, the first

step to producing a 3-D stack of 2-D reconstructed slices representing the match-head

volume being examined was to determine a center shift correction factor to prevent a

center shift artifact. This type of artifact arises from the vertical axis of the specimen

not being perfectly centered upon the CCD, even if it is centered upon the stage

rotation axis. Symptoms of this type of artifact are reconstructed slices which appear

blurry and out of focus. A center shift correction factor equal to the distance in

pixels that the rotation axis is offset from the center of the CCD must be determined

experimentally. This correction is accomplished via reconstruction of a single slice

using a range of center shift values and manually selecting the value which appears

to render an artifact free slice reconstruction.

The correct center shift value was relatively easy to determine by reconstructing,

with a range of center shift correction values, a slice in a region of a match-head

specimen that contained voids. For center shift values progressively further from the

true value, voids became progressively more ‘C’-shaped in the corresponding slices.

As such, the correct center shift correction factor effectively eliminated the ‘C’-shaped

void artifact. To be certain the correct value was selected for final reconstruction of

the entire stack of slices, several other specimen slice reconstruction locations were

tested with this procedure.


Beam Hardening Correction

A correction factor was also determined to minimize beam hardening in reconstructed

slices. Due to the non-uniform shape of the failed match-head IPPS specimens, a sin-

gle correction factor (which is all that is available using Xradia’s proprietary XM

Reconstructor software) does not perfectly minimize beam hardening for all slices

within the reconstructed stack. In fact, selecting a correction factor which adequately

minimized beam hardening for reconstructed slices in the thickest region of the spec-

imen would cause a very slight over-correction in reconstructed slices in thin regions

of the specimen, i.e. near the fracture surface. As the population of voids tended

to be concentrated near the fracture surface in many specimens, this over-correction

effect could possibly be detrimental to later thresholding of slices due to the resulting

reduction in greyscale contrast between voids near the specimen surface and sur-

rounding steel. As such, the “test” slice selected for determination of the optimal

beam hardening correction constant was chosen from a moderately thin region of the

specimen; a region which would yield a correction factor that would adequately min-

imize beam hardening in upper slices of the reconstructed stack without producing a

reverse-cupping radial greyscale intensity distribution artifact (over-correction).

After selecting this “test” slice location, the slice was reconstructed with a range

of beam hardening correction factors. A lineal greyscale intensity plot was produced

for each reconstructed slice; beam hardening was evident as a “cupping” artifact

in the intensity distribution through the thickness of the specimen. The correction

factor which eliminated this cupping effect and produced a flat greyscale intensity

distribution through the thickness of the specimen was selected. This factor was 0.25

for all match-head specimens.


Other Reconstruction Parameters

To produce the best contrast possible within reconstructed slices via better use of the

effective intensity range, manual byte scaling was used during reconstruction. A mini-

mum and maximum greyscale intensity value for slices within the reconstructed stack

were selected which would map the greyscale intensity histogram of reconstructed

slices as broadly across available bins as possible without saturation. If manual byte

scaling had not been employed, the proprietary reconstruction software would have

automatically set the min and max greyscale intensity histogram bins by first recon-

structing and sampling 6 slices from unknown specimen regions. Thus, clipping and

saturation could occur for some of the slices in the fully reconstructed stack.

Reconstructions were performed using 16-bits in order to have a large number

of greyscale bins and thus increase dynamic range. Final reconstruction of the full

stack of slices for each projection set was performed using the filtered backprojection

algorithms of Xradia’s XM Reconstructor software, producing a .txm file.

3.5.4 Slice Post-processing

Once a stack of slices had been fully reconstructed as a .txm file, they were converted

to a stack of uncompressed .tiff images to avoid data loss. These images were then

cropped about the largest match-head specimen cross-section, removing background

corresponding to the air surrounding the specimen, which would only lengthen post-

processing calculations. The goal with these slices was to perform segmentation of

voids from within slices to allow for automated quantitative analysis of void mor-

phology, size, and spatial distribution. However, unlike a synchrotron X-ray source


equipped with a monochromator, the beam produced in the Micro-XCT 400 is poly-

chromatic. Thus, greyscale intensity in reconstructed slices is not directly linked to

absorption coefficient. This translates to greyscale intensity mapping variation for a

material with an essentially homogeneous absorption coefficient throughout its vol-

ume. Noise inherent to reconstruction from projections of finite exposure time also

contributes to this greyscale intensity mapping variation (shown in Fig. 3.20 for a

cropped 16-bit slice of IPPS match-head specimen 9TP1-33-R10).

This greyscale intensity mapping variation led to poor results for preliminary

testing of thresholding methods, where pixels with low-level greyscale intensities that

were incorrectly captured as voids. Examples of these poor thresholding results are

provided in Fig. 3.21. As such, it was determined that a filtering operation prior to

thresholding was required to smooth out the noise. As described in Chap. 2, the filter

of choice for preserving void morphology in slices is the NL-means algorithm. The

algorithm was expected to perform well in preserving fine void detail while flattening

noise, given the high degree of redundancy produced by the pixels corresponding to

steel in the slices.

In order to make effective use of the NL-Means Denoising algorithm, a parametric

study was required to determine the optimal values for the window and patch size

used by this algorithm, detailed in Appendix D. These optimal parameters were used

for the NL-means denoising of all of the match-head specimen .tiff slice stacks. This

denoising step was performed using a scripted MATLAB implementation of the NL-

means algorithm written by Jose Vicente Manjon-Herrera, available on the MATLAB

Central File Exchange. The script was modified to process a folder containing a stack

of reconstructed slices using parallel computing; one image was denoised per CPU


core at a time, which vastly improved processing times.

3.5.4.1 Segmentation

NL-means denoising vastly improved thresholding results for cropped slices by accu-

rately capturing voids in the resulting masks without capturing low-intensity pixels

related to noise. This improvement is evident in Fig. 3.22. However, the thresholding

algorithms used up to this point performed very poorly with uncropped slices. As

shown in Fig. 3.23, even after NL-means denoising, the following algorithms from

five of the six categories outlined in Chap. 2 failed to elicit proper thresholding

masks of uncropped slices: histogram shape-based methods, clustering-based meth-

ods, entropy-based methods, object attribute-based methods, and spatial methods.

The clustering-based method of Kittler and Illingworth [127] and the entropy-based

methods of Kapur, Sahoo, and Wong [128], and Sahoo, Wilkins, and Yeager [129],

determined by Sezgin et al. [126] to be optimal for the thresholding of NDT images,

were included in this set. It appears that the relatively dark background surround-

ing the specimen in uncropped slices, which had lower greyscale intensity than void

pixels, was the most detrimental factor contributing to the poor thresholding results.

It was necessary to use uncropped slices because one single crop size for an entire

stack of slices would either leave background in upper slices near the specimen frac-

ture surface for a large crop window, or would eliminate some portion of the specimen

volume from analysis for a smaller crop window. It was desirable to extract as much

void damage data as possible in IPPS specimens. Therefore, the idea of cropping slice

stacks was discarded. It should be noted that each slice could have been individually


(a)

(b) (c)

Figure 3.20: a) A cropped 16-bit slice reconstructed from spec-imen 9TP1-33-R10 showing a large variation in greyscale in-tensity throughout. The yellow line represents the location ofsampling for the line intensity plot shown in b). The greyscaleintensity histogram for the cropped image is provided in c).


(a)

(b) (c)

Figure 3.21: a) A raw, cropped slice containing dark voids froma DP steel failed mechanical testing specimen of preliminarytesting. Poor thresholding results due to noise with: b) algo-rithm 2 of Pal and Pal [141]. c) algorithm of Sahoo, Wilkins,and Yeager [129].


(a) (b) (c)

(d) (e) (f)

Figure 3.22: a) A raw, cropped slice from a DP steel failed me-chanical testing specimen of preliminary testing. Poor thresh-olding results of a) due to noise using: b) algorithm 2 of Paland Pal [141]; c) algorithm of Sahoo, Wilkins, and Yeager [129].d) The slice of a) after being denoised with the NL-means algo-rithm. Accurate thresholding of voids from d) without captureof noise pixels using: e) algorithm 2 of Pal and Pal [141]; f)algorithm of Sahoo, Wilkins, and Yeager [129].


(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n)

Figure 3.23: a) A denoised, uncropped slice reconstructed froman XµCT scan of a match-head IPPS specimen. Poor thresh-olding results for this slice are displayed for the algorithms of:b) Abutaleb [142]; c)3-class fuzzy c-means clustering; d) Ka-pur, Sahoo, and Wong [128]; e) Kittler and Illingworth [127];f) Li and Lee [143]; g) Otsu [144]; h) Pal and Pal (algorithm1) [141]; i) Pal and Pal (algorithm 2) [141]; j) Ridler and Cal-vard [145]; k) Sahoo, Wilkins, and Yeager [129]; l) Tsai [146];m) Wong and Sahoo [147]; n) Yen, Chang, and Chang [148].


cropped to eliminate most background from the slice, but alignment of these vari-

ously sized slices into a 3D stack for void accumulation analysis would have proved

challenging.

A locally adaptive thresholding method was found to be the most viable option

for accurately segmenting voids in uncropped slices. The algorithm of choice, con-

tributed to the MATLAB Central File Exchange by Guanglei Xiong, makes use of

local contrast data to threshold an image. Pixels within a specified neighbourhood

window size in an image have their intensity compared to the average intensity of

the entire neighbourhood. If the intensity of any given pixel is significantly darker

than the average (beyond a set threshold controlled by a filtering parameter within

the algorithm), it is classified as foreground; otherwise it is classified as background.

The algorithm was used within MATLAB to threshold all of the NL-means denoised

slices from the match-head specimen tomography stacks.

The local contrast thresholding method performed very well in accurately cap-

turing void morphology in masks of uncropped slices for the IPPS match-heads, as

shown in Fig. 3.24. However, due to the high contrast with background at specimen

surfaces, these regions were captured as “voids” in masks. Typically, due to the con-

tinuous nature of these specimen edge artifacts in thresholded slices when stacked in

3-D, it was possible to eliminate them by applying a maximum volume criterion in

later void image analysis. However, some isolated pixels were produced in masks at

the specimen edge regions of slices which needed to be manually removed. Streak

artifacts were also often captured in masks.

All thresholded slices from each match-head specimen stack were visually cor-

related to their corresponding raw slices to ensure accurate thresholding had taken


place and to manually remove any artifacts present. If an accurate thresholding had

not taken place, i.e. some voids had not been captured in the resulting masks or were

of improper shape, then the local thresholding algorithm parameters (window size

and filtering degree) were modified and thresholding was re-performed until all slices

had accurately produced masks. To improve the ease with which manual correlation

could be made between masks and their corresponding raw slices, custom software

(Fig. 3.25) was developed which overlaid a red mask in a semi-transparent fashion

onto its corresponding raw slice.

3.5.4.2 Quantitative and Qualitative Volume Analysis

The thresholded stacks corresponding to each IPPS match-head specimen reconstruc-

tion were imported into Avizo R© Fire software for quantitative analysis of void dam-

age present. The pixel sizes calculated by Xradia’s proprietary software for the slices

within these stacks were used as calibrations for the voxel size of reconstructed vol-

umes. The accuracies of these calibrations were confirmed to within ±1% by com-

paring match-head specimen widths measured with the calibrated software with mea-

surements using Vernier calipers. Voids were identified within the segmented volume

by the software and their geometric parameters automatically calculated.

A size criterion was used to remove voids that approached the resolving power of

the Micro-XCT 400 instrument. To be confident that foreground pixels captured in

binary masks truly represented voids within specimens and not just noise, a minimum

volume criterion was applied to the 3D threshold image. Voids were required to be

a minimum size of 27 voxels, i.e. (3 x pixel size)3 in volume, in order to be included

in the analysis. Data that was calculated for each void identified included: volume,


(a)

(b)

Figure 3.24: a) The denoised slice from Fig. 3.23(a). b) Athreshold mask accurately capturing the morphology of thevoids from a); produced using a locally adaptive thresholdingalgorithm.


Figure 3.25: Custom software capable of overlaying a red maskproduced from thresholding in a semi-transparent fashion ontoits corresponding raw slice.


surface area, centroid location within the 3D volume bounding box, maximal length,

and spherical coordinates of the orientation of the maximal length vector.

The denoised match-head slices were also thresholded using an automated greyscale

histogram shape-based method to produce a mask of the steel volume. These stacks

of slices were analyzed in Avizo R© Fire in the same manner outlined above for the

void mask slice stacks to determine the total volume of each match-head specimen

that was reconstructed. Using these calculated match-head specimen volumes, the

volume percent of void damage within each specimen was computed.

Finally, 3-D renderings of the voids were produced using the Avizo R© Fire soft-

ware. A closed 3-D surface was generated for the binarized voids. A semi-transparent

rendering of the IPPS match-head specimen volume was produced using raw recon-

structed slices around this void surface rendering to lend context to the locations of

voids within the specimen.

3.6 Fractography

The match-head specimen fracture surfaces were examined using a JEOL JSM-840

SEM instrument in secondary electron mode to capture greyscale micrographs mea-

suring 1024 x 768 pixels. Fractographs were captured at 85x magnification to image

the entire fracture surface. Fractographs were also captured at 500x magnification

at locations that were one-quarter and one-half through the sheet thickness at the

location of failure. These locations detailed any transition in fracture mode from

ductile to shear.

Despite being stored in a dessicator, the match-head specimens oxidized to a minor

degree. Hence, prior to fractographic examination a cleaning procedure was applied


to remove the oxidation while introducing minimal artifacts to the fracture surface. A

15 second dip in the inhibited sulphuric acid described in Appendix C was employed

based upon the recommendations of Tartaglia [149]. This was followed immediately

by an ultrasonic cleaning in ethanol to remove any dust and debris which may have

collected in the fracture surface.

3.7 Metallographic Damage Analysis

Post SEM-examination, the match-head specimens were mounted in epoxy for metal-

lographic examination of through-thickness tensile axis plane. These mounted spec-

imens were ground and polished as per the procedures outlined in Table 3.4 and

Table 3.5, but with a significantly longer rough grind to be certain artifacts were not

introduced into the polished surface from the wafer-saw sectioning. A 10% Sodium

metabisulfite etchant was used to stain and provide colour contrast between ferrite

grains and NFP particles. A Zeiss Axioskop 2 MAT light microscope equipped with

an Olympus EvolutionTMMP Colour CCD camera was used to capture colour micro-

graphs measuring 2560 x 1920 pixels for each match-head specimen. A 100x Zeiss

Epiplan-NEOFLUAR oil immersion lens was used during micrograph acquisition.

Micrographs were captured in regions where void damage was evident to allow for

interpretation of void nucleation mechanisms active in each specimen.

Chapter 4

Results

This chapter presents the results of the experiments outlined in Chap. 3. The mi-

crostructures of the ten DP steel variants used for the IPPS mechanical testing pro-

tocol are quantitatively and qualitatively characterized. The failure strains of valid

IPPS specimens are reported. Void damage accumulation within “match-head” spec-

imens, extracted from the failure surface of IPPS specimens, as determined by XµCT

is quantified and qualified.

4.1 Microstructure Characterization

The quantitative measures of microstructural parameters which are presented in the

succeeding sub-sections were calculated in the manner dictated in Sec. 3.3. The mi-

crostructures of the cold-rolled DP steels are presented. Microstructures of DP steel

variants used for the IPPS mechanical testing protocol are presented and described

in the following order: commercial galvannealed DP steels, TP1-treated DP steels,

and TP2-treated DP steels. The fine-grained nature of the steels necessitated high

123

CHAPTER 4. RESULTS 124

magnifications not achievable via light microscopy for accurate microstructural char-

acterization. Thus, colour contrast was not available for the differentiation of phases

and constituents. This led to a simplified characterization of NFP as a whole in

the microstructures, due to a lack of readily physically-distinguishable features be-

tween martensite, pearlite, bainite, and austenite at 5000x magnification in scanning

electron micrographs.

4.1.1 Cold-rolled DP Steels

The sheets received in the cold-rolled condition contained ferrite and NFP in a heavily

deformed microstructure, as shown in Fig. 4.1. Both ferrite grains and NFP particles

were elongated in the rolling direction. The volume percents of constituents for both

cold-rolled steels are provided in Table 4.1.

Table 4.1: As-received cold-rolled sheet steel constituent volumepercents with 95% confidence interval.

NFP Ferritevolume % volume %

DP780 CR 9.8 ± 1.1% balanceDP980 CR 11.8 ± 1.0% balance

4.1.2 Galvannealed DP Steels

The microstructures of the multiphase galvannealed DP780 and DP980 steels received

from U.S. Steel are presented in the representative optical micrographs of Fig. 4.2.

Both the DP780GA and DP980GA steels were observed to consist of a matrix of

ferrite grains which were elongated in the rolling direction. The NFP particles in

these microstructures were observed to be located at ferrite grain boundaries.


(a) DP780CR (b) DP780CR

(c) DP980CR (d) DP980CR

Figure 4.1: Representative optical micrographs of a) and b)cold-rolled DP780 steel at the sheet centerline; c) and d)cold-rolled DP980 steel at the sheet centerline. 10% Sodiummetabisulfite etch. Martensite and bainite/pearlite tinted dark,ferrite tinted light.


Both the volume percent and size of NFP particles are clearly larger in the

DP980GA steel than in the DP780GA steel. The results of quantitative measure-

ments are summarized in Table 4.2. For both steels, NFP was observed to be dis-

tributed heterogeneously. Heavy and continuous banding of NFP was present along

the rolling direction and to a lesser extent along the transverse direction for both

steels. This banding was most prevalent at the sheet centerline, with NFP bands

becoming slightly more discontinuous and finer in scale with increasing proximity to

the sheet surface.

Table 4.2: Volume percent and mean lineal intercept of NFPparticles in the galvannealed DP steel sheets provided by U.S.Steel. A 95% confidence interval and percent relative accuracy(R.A.) are provided for both measures.

DP Steel Variant NFP Vol. % % R.A. NFP mean lineal intercept (µm) % R.A.

DP780GA 22.5 ± 2.9 12.9 1.07 ± 0.07 6.5

DP980GA 36.3 ± 3.5 9.6 1.43 ± 0.10 7.0

4.1.3 TP1-treated DP Steels

The microstructures of the DP steel variants produced via TP1-treatment of the

DP780 and DP980 cold-rolled steel received from U.S. Steel are presented respectively

in the representative micrographs of Fig. 4.3 and Fig. 4.4. TP1-treated microstruc-

tures were somewhat similar to those of the commercial galvannealed sheets; both

consisted of a matrix of ferrite grains which were elongated in the rolling direction

and NFP particles in both microstructures were located at ferrite grain boundaries.

For TP1-treated DP780CR steels, NFP bands were present along both the RD and

TD. The bands aligned along the RD were thicker and more continuous. Banding of

NFP along the RD and TD near the sheet centerline was observed to be more severe


(a) DP780GA (b) DP780GA

(c) DP980GA (d) DP980GA

Figure 4.2: Representative optical micrographs of a) and b)galvannealed DP780 steel at the sheet centerline; c) and d)galvannealed DP980 steel at the sheet centerline. 10% Sodiummetabisulfite etch. Martensite and bainite/pearlite tinted dark,ferrite tinted light.


and continuous in TP1-treated DP780CR steels than in the galvannealed DP780 steel.

As well, this banding was heavily concentrated and most continuous at the sheet

centerline with little banding observed elsewhere through the sheet thickness. The

7TP1-33-T10 IPPS specimen in particular was noted to contain a singular continuous

NFP band at the sheet centerline in the RD.

For TP1-treated DP980CR steels, NFP was observed to be dispersed in clusters

and slightly more discontinuous bands due to irregularly shaped ferrite grains. The

volume percent and mean lineal intercept of NFP particles in TP1-treated IPPS spec-

imens are provided in Table 4.3. It is clear that increasing IC annealing temperature

resulted in increased NFP content.

Table 4.3: Volume percent and mean lineal intercept of NFPparticles in TP1-treated DP steel variants. A 95% confidenceinterval and percent relative accuracy (R.A.) are provided forboth measures.

DP Steel VariantIC AnnealingTemperature

(◦C)NFP Vol. % % R.A.

NFP meanlineal intercept

(µm)% R.A.

7TP1-15 715 11.7 ± 0.8 6.8 0.59 ± 0.04 6.8

7TP1-33 733 29.4 ± 3.3 11.2 1.22 ± 0.09 7.4

7TP1-43 743 37.8 ± 2.4 6.3 1.2 ± 0.07 5.8

9TP1-15 715 17.3 ± 1.6 9.2 0.79 ± 0.09 11.4

9TP1-33 733 38.3 ± 2.3 6.0 1.29 ± 0.07 5.4

9TP1-43 743 40.4 ± 2.1 5.2 1.39 ± 0.08 5.8


The microstructures produced by TP2-treatment of the cold-rolled steels of this study

are presented in the representative micrographs of Fig. 4.5. The relatively discontinu-

ous, uniform distribution of NFP is evident, but so is some residual banding of NFP at

the sheet centerline. This banding was more continuous for the TP2-treated variants


(a) 7TP1-15 (IC annealed @ 715◦C) (b) 7TP1-15 (IC annealed @ 715◦C)

(c) 7TP1-33 (IC annealed @ 733◦C) (d) 7TP1-33 (IC annealed @ 733◦C)

(e) 7TP1-43 (IC annealed @ 743◦C) (f) 7TP1-43 (IC annealed @ 743◦C)

Figure 4.3: Representative optical micrographs captured at thesheet centerline for DP780CR steel after TP1-treatment. Con-tinuous banding of NFP is present in both ND-RD and ND-TDsections. 10% Sodium metabisulfite etch. Martensite tinteddark, ferrite tinted light.


(a) 9TP1-15 (IC annealed @ 715◦C) (b) 9TP1-15 (IC annealed @ 715◦C)

(c) 9TP1-33 (IC annealed @ 733◦C) (d) 9TP1-33 (IC annealed @ 733◦C)

(e) 9TP1-43 (IC annealed @ 743◦C) (f) 9TP1-43 (IC annealed @ 743◦C)

Figure 4.4: Representative optical micrographs captured at thesheet centerline for DP980CR steel after TP1-treatment. Con-tinuous banding of NFP is present in both ND-RD and ND-TDsections. 10% Sodium metabisulfite etch. Martensite tinteddark, ferrite tinted light.


produced from DP980CR than from DP780CR. For TP2-treated variants produced

from DP980CR, the banding in the longitudinal direction was also not confined solely

to the sheet centerline. Like DP980GA, banding was most prevalent at the material

centerline, with NFP bands becoming slightly more discontinuous and finer in scale

with increasing proximity to the sheet surface.

The NFP particles in TP2-treated microstructures had a bimodal size distribution,

with many thin, elongated particles, but this was not taken into account during

measurement of NFP particle size. The mean sizes of NFP particles in the TP2-

treated specimens were relatively similar to those of the galvannealed steels. The

volume percent and mean lineal intercept of NFP particles in TP2-treated IPPS

specimens are provided in Table 4.4.

Table 4.4: Volume percent and mean lineal intercept of NFPparticles in TP2-treated DP steel variants. A 95% confidenceinterval and percent relative accuracy (R.A.) are provided forboth measures.


7TP2-25 30.5 ± 1.8 5.9 0.84 ± 0.03 3.6

9TP2-37 34.2 ± 2.2 6.4 1.23 ± 0.09 7.3

4.1.5 Summary of Microstructures

The volume percent and mean lineal intercept of NFP particles in all of the DP steel

variants used for IPPS testing are summarized in Table 4.5. The goal of performing

heat treatments on cold-rolled sheet to produce two DP steel variants with similar

NFP volume percent to the galvannealed DP steels was accomplished for the DP980

series of steels with 9TP1-33 and 9TP2-37. However, for the DP780 series of steels,

two variants were produced with similar NFP volume percent through 7TP1-33 and


(a) 7TP2-25 (b) 7TP2-25

(c) 9TP2-37 (d) 9TP2-37

Figure 4.5: Representative optical micrographs captured at thesheet centerline for DP780CR and DP980CR steel after TP2-treatment. Residual banding of NFP is present in both ND-RDand ND-TD sections. 10% Sodium metabisulfite etch. Marten-site tinted dark, ferrite tinted light.


7TP2-25 treatments, but this volume percent was not similar to that of the corre-

sponding DP780GA steel.

The galvannealed DP steel microstructures consisted of NFP, heavily and contin-

uously banded at the sheet centerline in the rolling direction, embedded in a ferrite

matrix. The NFP banding was finer and more discontinuous with increasing prox-

imity to the sheet surface. The TP1-treated DP780 steel microstructures consisted

of NFP, heavily and continuously banded at the sheet centerline in the rolling direc-

tion, embedded in a ferrite matrix. The NFP banding was heavily concentrated at

the sheet centerline with little banding observed away from this region. In the TP1-

treated DP980CR steels, NFP was observed to be dispersed in clusters and slightly

more discontinuous bands. The TP2-treated DP steel microstructures consisted of

relatively uniformly spatially distributed NFP, with light banding at the sheet cen-

terline in the rolling direction, embedded in a ferrite matrix. The NFP particles

in TP2-treated microstructures were bimodal in size with many elongated particles

present. Mean NFP particle size varied throughout the microstructures, essentially

increasing in a relatively linear fashion with NFP volume percent.

4.2 IPPS Mechanical Testing

The results of the IPPS tensile testing are provided in this section. For all specimens

which failed in a satisfactory manner according to the criteria outlined in Sec. 3.5.1,

strains in the grid row where final failure occurred were calculated just prior to frac-

ture. The strains calculated for the 7 grid-points in this failure row were averaged

to a single value. The failure strains for the entire population of valid specimens are

presented in Appendix E.


Table 4.5: Volume percent and mean lineal intercept of the NFPparticles in all of the DP steel variants used for IPPS testing.A 95% confidence interval and percent relative accuracy (R.A.)are provided for both measures.


DP780GA 22.5 ± 2.9 12.9 1.07 ± 0.07 6.5

DP980GA 36.3 ± 3.5 9.6 1.43 ± 0.10 7.0

7TP1-15 11.7 ± 0.8 6.8 0.59 ± 0.04 6.8

7TP1-33 29.4 ± 3.3 11.2 1.22 ± 0.09 7.4

7TP1-43 37.8 ± 2.4 6.3 1.2 ± 0.07 5.8

9TP1-15 17.3 ± 1.6 9.2 0.79 ± 0.09 11.4

9TP1-33 38.3 ± 2.3 6.0 1.29 ± 0.07 5.4

9TP1-43 40.4 ± 2.1 5.2 1.39 ± 0.08 5.8

7TP2-25 30.5 ± 1.8 5.9 0.84 ± 0.03 3.6

9TP2-37 34.2 ± 2.2 6.4 1.23 ± 0.09 7.3

To elucidate the general behaviour of each of the DP steel variants tested, the

mean failure row strains for specimens of a given condition/treatment were averaged

and are provided in Table 4.6(a). As only one or two specimens failed satisfactorily for

many of the DP steel variants tested, a measure of standard deviation is not provided

for the failure strain results. For the IPPS specimens selected for XµCT analysis, the

strain measured at the gridpoint which was in the middle column of the failure row

where the match-head specimens were extracted is reported in Table 4.6(b). For both

of the aforementioned tables, results are not ordered numerically by failure strain,

but rather by the heat treatment/condition and orientation of DP steel variants.

Due to problems with surface pitting caused by improper acid cleaning procedures,

some IPPS specimen batches required reproduction; hence the identification numbers

greater than 7 for some of the XµCT specimens.

In many cases, IPPS specimens oriented with the rolling direction along the tensile

axis (RD specimens) had a higher major failure strain than those with the transverse


sheet direction aligned with the tensile axis. The DP steel variants which were the ex-

ception to this observation were the 7TP1-15 and the 7TP2-25 variants. The variant

with the highest major failure strains was 7TP1-15 and the lowest 9TP2-43. These

variants respectively had the lowest and highest volume percents of NFP in their

microstructures. Major engineering failure strain and NFP volume percent are corre-

lated in Fig. 4.6 and Fig. 4.7 for all valid IPPS specimens produced from DP780 and

DP980, respectively. A general trend of major engineering strain at failure decreasing

with increasing NFP content was clearly evident.


Table 4.6: Strain just prior to failure in IPPS DP steel variantspecimens.

(a) Mean major and minor engineer-

ing strains computed in the failure

row, just prior to failure, averaged

for the IPPS specimens of a given

condition/treatment. The numerals

in brackets appended to the variant

name indicate the number of valid

tests used to compute the mean strain

values.

VariantEngineering Strain

Major Minor

7GA-R(2) 0.106 -0.005

7GA-T(2) 0.093 -0.005

9GA-R(3) 0.070 0.000

9GA-T(2) 0.049 -0.001

7TP1-15-R(1) 0.202 -0.015

7TP1-15-T(1) 0.242 -0.016

7TP1-33-R(1) 0.131 -0.008

7TP1-33-T(3) 0.125 -0.007

7TP1-43-R(5) 0.063 -0.003

7TP1-43-T(3) 0.053 -0.003

9TP1-15-R(2) 0.157 -0.010

9TP1-15-T(5) 0.138 -0.010

9TP1-33-R(3) 0.087 -0.005

9TP1-33-T(2) 0.076 -0.006

9TP1-43-R(2) 0.051 -0.003

9TP1-43-T(4) 0.020 -0.001

7TP2-25-R(1) 0.129 -0.006

7TP2-25-T(2) 0.135 -0.007

9TP2-37-R(2) 0.093 -0.004

9TP2-37-T(3) 0.064 -0.003

(b) Major and minor engineering

strain computed in the central grid-

point of the failure row, just prior to

failure, for IPPS specimens subjected

to XµCT analysis.

SpecimenEngineering Strain

Major Minor

7GA-R4 0.109 -0.004

7GA-T2 0.079 -0.004

9GA-R3 0.059 0.002

9GA-T4 0.040 0.001

7TP1-15-R4 0.197 -0.010

7TP1-15-T11 0.229 -0.014

7TP1-33-R11 0.130 -0.003

7TP1-33-T10 0.136 -0.006

7TP1-43-R3 0.065 -0.002

7TP1-43-T5 0.051 -0.002

9TP1-15-R7 0.179 -0.012

9TP1-15-T1 0.125 -0.009

9TP1-33-R10 0.094 -0.005

9TP1-33-T10 0.072 -0.008

9TP1-43-R11 0.052 0.000

9TP1-43-T7 0.020 -0.001

7TP2-25-R4 0.118 -0.006

7TP2-25-T2 0.092 -0.005

9TP2-37-R4 0.090 -0.003

9TP2-37-T1 0.071 -0.002


Figure 4.6: Relationship between NFP volume percent in IPPSspecimens produced from DP780 and mean major engineeringstrain in the failure row just prior to specimen failure. Hori-zontal error bars are derived from the 95% confidence intervalof NFP volume percent measurements. Vertical error bars,derived from the systematic error associated with IPPS gridstrain measurements, are too small to be visible.


Figure 4.7: Relationship between NFP volume percent in IPPSspecimens produced from DP980 and mean major engineeringstrain in the failure row just prior to specimen failure. Hori-zontal error bars are derived from the 95% confidence intervalof NFP volume percent measurements. Vertical error bars,derived from the systematic error associated with IPPS gridstrain measurements, are too small to be visible.


4.3 Void Damage Accumulation and Failure

The results of the XµCT scans of the 20 match-head IPPS specimens are presented in

this section. For each of the reconstructions produced, voxel size was 1.1815 x 1.1815

x 1.1815 µm. The size distribution, spatial distribution, and number of microvoids

varied throughout the reconstructed specimens. Microvoid damage was generally

concentrated most densely near the fracture surface, but significant damage was ob-

served hundreds of microns away from the fracture surface for many specimens. As

well, there was a significant localization of void populations to a region near the sheet

centerline for many specimens.

Fracture surfaces and micrographs of polished through-thickness tensile axis planes

for the match-head specimens are also presented in this section. It was clear from the

metallographic micrographs that the smallest voids in match-head specimens were

not captured using XµCT and the minimum void volume criterion of Sec. 3.5.4.2.

However, the distribution of larger voids observed in metallographic micrographs

and XµCT reconstructions had a high degree of correlation. A general trend of

reduced through-thickness specimen thinning with decreasing nominal failure strain

was observed.

The data computed for the reconstructed voids of each specimen is summarized

in Table 4.7 and Table 4.8. For all specimens examined, void volume percent within

the reconstructed volumes totalled less than 0.3%. To more clearly illustrate the re-

lationships between microstructure, void damage accumulation, and strain at failure

each specimen will be discussed in a subsection devoted to DP steel variants of its

particular treatment/condition. The order of presentation begins with the commer-

cial galvannealed DP steel, followed by TP1-treated DP variants, and TP2-treated


DP variants. A summarial examination of the role played by NFP volume percent,

morphology, and spatial distribution in damage accumulation for the IPPS DP steel

variants follows in Chap. 5.

Table 4.7: Number of voids, void volume percent, and total voidvolume in the XµCT reconstructed portions of IPPS match-head specimens. Standard deviation is represented by σ.

Specimen # of Voids Volume Percent (%)Volume (µm3)

Mean (x 103) σ (x 103) Max (x 103)

7GA-R4 116 0.006 0.361 0.42 2.1

7GA-T2 318 0.024 0.448 1.07 12.6

9GA-R3 51 0.005 0.559 1.15 7.5

9GA-T4 84 0.014 0.977 2.02 12.5

7TP1-15-R4 65 0.020 1.956 7.31 57.6

7TP1-15-T11 158 0.032 1.129 2.88 26.5

7TP1-33-R11 167 0.025 0.855 2.47 21.2

7TP1-33-T10 260 0.273 5.719 32.12 453.9

7TP1-43-R3 165 0.071 2.561 15.07 189.8

7TP1-43-T5 83 0.011 0.736 3.16 28.2

9TP1-15-R7 304 0.031 0.692 1.57 13.9

9TP1-15-T1 551 0.037 0.446 0.95 12.9

9TP1-33-R10 60 0.006 0.527 1.16 7.7

9TP1-33-T10 593 0.044 0.521 1.32 13.0

9TP1-43-R11 42 0.001 0.181 0.18 0.7

9TP1-43-T7 123 0.009 0.392 0.49 3.9

7TP2-25-R4 63 0.008 0.705 1.95 14.9

7TP2-25-T2 282 0.036 0.722 1.67 19.6

9TP2-37-R4 155 0.036 1.216 2.93 20.4

9TP2-37-T1 282 0.016 0.324 0.46 3.2


Table 4.8: Equivalent spherical diameter, maximum length ofFeret distribution (Length3D), and modified spherical coordi-nate orientations of voids in the XµCT reconstructed portionsof IPPS match-head specimens. Phi, φ, was defined as the an-gle between the principal inertia axis of a void and the globalZ-axis in degrees between [0,+90]. The major strain axis ofIPPS specimens was assumed to be aligned with global Z-axisof XµCT reconstructions. Theta, θ, was defined as the an-gle between the principal inertia axis projection of a void inthe global XY-plane and the global X-axis in degrees between[0,+90]. The minor strain axis of IPPS specimens was assumedto be aligned with the global X-axis of XµCT reconstructions.Standard deviation is represented by σ.

SpecimenEq. Diameter (µm) Length3D (µm) φ (◦) θ (◦)

Mean σ Mean σ Mean σ Mean σ

7GA-R4 6.47 8.8 11.8 15.5 85 25 32 24

7GA-T2 5.67 5.3 13.0 8.7 78 74 12 15

9GA-R3 12.85 17.6 24.8 24.5 3 37 35 27

9GA-T4 5.21 6.5 9.2 11.6 66 86 18 23

7TP1-15-R4 5.01 9.7 13.8 18.9 59 89 27 27

7TP1-15-T11 7.97 10.5 12.1 20.2 71 84 11 15

7TP1-33-R11 5.21 6.7 7.1 9.8 16 28 21 24

7TP1-33-T10 8.90 5.2 34.3 10.6 90 83 5 9

7TP1-43-R3 5.86 4.7 14.2 7.5 83 64 17 22

7TP1-43-T5 5.64 4.6 10.6 7.5 80 7 7 8

9TP1-15-R7 9.74 4.4 18.2 7.9 23 10 33 29

9TP1-15-T1 4.60 6.2 10.9 9.8 72 57 8 11

9TP1-33-R10 5.83 8.4 8.5 13.0 77 11 33 26

9TP1-33-T10 4.93 4.5 8.7 7.9 65 16 9 13

9TP1-43-R11 4.70 8.4 7.8 13.0 78 86 30 24

9TP1-43-T7 4.55 4.9 8.7 8.5 43 75 11 15

7TP2-25-R4 6.52 6.0 10.6 10.5 17 27 33 26

7TP2-25-T2 12.80 4.7 27.2 6.8 78 45 14 17

9TP2-37-R4 5.83 5.8 10.6 11.8 30 87 22 26

9TP2-37-T1 8.43 6.4 13.2 9.2 13 11 10 14


4.3.1 Galvannealed DP Steels

4.3.1.1 Degree of Damage

The degree of damage in each of the galvannealed XµCT specimens is qualitatively

provided in 3-D renderings of the outer surfaces of voids within a semi-transparent

rendering of the match-head specimen volumes in Fig. 4.8 through Fig. 4.21. These

images highlight in 3-D the size of voids (shown in red), their shape, and their spatial

arrangement within the reconstructed match-head volumes. For instance, Fig. 4.8 and

Fig. 4.9 illustrate a general concentration of sphere-shaped voids accumulated near the

fracture surface of the 7GA-R4, that the voids were generally distributed throughout

the sheet thickness, but with some concentration towards the sheet centerline, and

that many small voids are visible hundreds of microns away from the fracture surface.

Fig. 4.10(a) displays a polished RD-ND plane of the 7GA-R4 specimen, providing

evidence to back-up the void damage accumulation observed via XµCT. Fig. 4.10(b)

exhibits detail of void nucleation sites in the 7GA-R4 specimen using a 2% nital

etch to colour NFP a tan/blue hue, leaving ferrite light and voids black. Fig. 4.11

provides fractographs of the 7GA-R4 specimen fracture surface at two magnifications

to provide insight to the failure mechanisms which were at work.

The size distribution of accumulated void damage for each specimen is provided

in Fig. 4.24. The frequency distribution of void damage through the thickness is

presented in Fig. 4.25 and the distribution of void volumes through the thickness by

geometric centroid is presented in Fig. 4.26. All of the aforementioned figures have

been prepared for each of the specimens of galvannealed, and TP1- and TP2-treated

condition in the following subsections; for the sake of brevity, these figures will not be

introduced in the text. Summarial tables are provided for each of the the three types


of DP steel variants highlighting the important damage accumulation observations

for each specimen. Table 4.9 provides this summary for the galvannealed specimens.

4.3.1.2 Damage Distribution

Void damage was generally more concentrated within the region just below the frac-

ture surface of the galvannealed match-head specimens, where strains were larger. No

significant trends were elicited in the spatial distribution of void damage through the

thickness of specimens in terms of the number of voids present (Fig. 4.25) or their vol-

umes (Fig. 4.26). At the most, it can be stated that the distribution of voids through

the sheet thickness resembles a normal distribution and that voids were somewhat

clustered towards the mid-thickness of the sheet. This spatial distribution of void

damage through the thickness of the sheet closely mimics the spatial distribution of

NFP bands through the thickness of the galvannealed sheets.

4.3.1.3 Void Orientations

For the most part, void orientation in the galvannealed match-head specimens was

relatively random (see Table 4.8). However, the 7GA-T2 specimen had a large pro-

portion of voids which were very much aligned with its minor strain axis as evidenced

qualitatively in Fig. 4.12 and quantitatively by its low mean θ value in Table 4.8 with

relatively low standard deviation.

4.3.1.4 Failure Mechanism

The galvannealed specimens tended to fail via a shear-dominated mechanism. Signif-

icant surface roughening is evident for 7GA-R4 and 7GA-T2 respectively in Fig. 4.9


and Fig. 4.13.

Table 4.9: Damage accumulation observations, inferences, andcomputations for galvannealed DP steel specimens.

Specimen # of Voids

Void Volume (µm3)

ObservationsMean σ Max(x 103) (x 103) (x 103)

7GA-R4 116 0.361 0.42 2.1

• Moderately ductile cup-cone type failure• NFP particle cracking dominated voidnucleation• Uniform size distribution of fracture sur-face dimples (2-4 µm)• Mild clustering of void damage to sheetcenterline

7GA-T2 318 0.448 1.07 12.6

• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Many fracture surface dimples elongatedin RD, surrounded by uniform size dimples(2-5 µm)• Random spatial distribution of voiddamage through sheet thickness

9GA-R3 51 0.559 1.15 7.5

• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Uniform size distribution of fracture sur-face dimples (1-3 µm)• Mild clustering of void damage to sheetcenterline

9GA-T4 84 0.977 2.02 12.5

• Shear mechanism dominated failure• NFP particle cracking and some ferrite-NFP decohesion void nucleation• Many fracture surface dimples very elon-gated in RD• Mild clustering of void damage to sheetcenterline region


Figure 4.8: 3-D semi-transparent volume rendering of the 7GA-R4 IPPS match-head specimen displaying an isosurface render-ing of the void damage within (three-point perspective). Theperspective view makes the insertion of a scale bar inappropri-ate. The dimensions of the bounding box of the reconstructionare 1066 x 963 x 1152 µm.


Figure 4.9: 3-D semi-transparent volume rendering of the 7GA-R4 IPPS match-head specimen displaying an isosurface render-ing of the spatial distribution of void damage in the ND-RDplane (one-point perspective). The perspective view makes theinsertion of a scale bar inappropriate. The dimensions of thefrontal plane of the bounding box of the reconstruction are 963x 1152 µm.


(a) Polished

(b) 2% Nital etch

Figure 4.10: Typical optical micrographs of the failed 7GA-R4match-head specimen showing void damage.


(a) Entire fracture surface detailing locations of

higher magnification fractographs.

(b)

(c) Center of sheet thickness.

Figure 4.11: SEM fractographs of the failed 7GA-R4 match-head specimen.


Figure 4.12: 3-D semi-transparent volume rendering of the7GA-T2 IPPS match-head specimen displaying an isosurfacerendering of the void damage within (three-point perspective).The perspective view makes the insertion of a scale bar inap-propriate. The dimensions of the bounding box of the recon-struction are 987 x 932 x 1150 µm.


Figure 4.13: 3-D semi-transparent volume rendering of the7GA-T2 IPPS match-head specimen displaying an isosurfacerendering of the spatial distribution of void damage in the ND-RD plane (one-point perspective). The perspective view makesthe insertion of a scale bar inappropriate. The dimensions ofthe frontal plane of the bounding box of the reconstruction are932 x 1150 µm.


(a) Polished

(b) 2% Nital etch

Figure 4.14: Typical optical micrographs of the failed 7GA-T2match-head specimen showing void damage.




(b)


Figure 4.15: SEM fractographs of the failed 7GA-T2 match-head specimen.


Figure 4.16: 3-D semi-transparent volume rendering of the9GA-R3 IPPS match-head specimen displaying an isosurfacerendering of the void damage within (three-point perspective).The perspective view makes the insertion of a scale bar inap-propriate. The dimensions of the bounding box of the recon-struction are 1081 x 1087 x 1148 µm.


Figure 4.17: 3-D semi-transparent volume rendering of the9GA-R3 IPPS match-head specimen displaying an isosurfacerendering of the spatial distribution of void damage in the ND-RD plane (one-point perspective). The perspective view makesthe insertion of a scale bar inappropriate. The dimensions ofthe frontal plane of the bounding box of the reconstruction are1087 x 1148 µm.


(a) Polished

(b) 2% Nital etch

Figure 4.18: Typical optical micrographs of the failed 9GA-R3match-head specimen showing void damage.




(b)


Figure 4.19: SEM fractographs of the failed 9GA-R3 match-head specimen.


Figure 4.20: 3-D semi-transparent volume rendering of the9GA-T4 IPPS match-head specimen displaying an isosurfacerendering of the void damage within (three-point perspective).The perspective view makes the insertion of a scale bar inap-propriate. The dimensions of the bounding box of the recon-struction are 958 x 1081 x 1147 µm.


Figure 4.21: 3-D semi-transparent volume rendering of the9GA-T4 IPPS match-head specimen displaying an isosurfacerendering of the spatial distribution of void damage in the ND-RD plane (one-point perspective). The perspective view makesthe insertion of a scale bar inappropriate. The dimensions ofthe frontal plane of the bounding box of the reconstruction are1081 x 1147 µm.


(a) Polished

(b) 2% Nital etch

Figure 4.22: Typical optical micrographs of the failed 9GA-T4match-head specimen showing void damage.




(b)


Figure 4.23: SEM fractographs of the failed 9GA-T4 match-head specimen.


0 10 20 300

10

20

30

40

50

60

Freq

uenc

y

Equivalent Diameter (µm)

(a) 7GA-R4

0 10 20 300

10

20

30

40

50

60

Freq

uenc

y


(b) 7GA-T2

0 10 20 300

10

20

30

40

50

60

Freq

uenc

y


(c) 9GA-R3

0 10 20 300

10

20

30

40

50

60Freq

uenc

y


(d) 9GA-T4

Figure 4.24: Histograms of equivalent spherical void diame-ter in reconstructed galvannealed DP steel variant match-headspecimens.


-400 -300 -200 -100 0 100 200 300 4000

5

10

15

20

25

30

35

40

Freq

uenc

y

Distance to Center (µm)

(a) 7GA-R4

-400 -200 0 200 4000

5

10

15

20

25

30

35

40

Freq

uenc

y

Distance to center (µm)

(b) 7GA-T2

-400 -200 0 200 4000

5

10

15

20

25

30

35

40

Freq

uenc

y


(c) 9GA-R3

-400 -200 0 200 4000

5

10

15

20

25

30

35

40Freq

uenc

y


(d) 9GA-T4

Figure 4.25: Histograms of the spatial distribution of voidsthrough the sheet thickness in reconstructed galvannealed DPsteel variant match-head specimens.


-400 -300 -200 -100 0 100 200 300 400

100

1000

10000

Vol

ume

(µm

3 )


(a) 7GA-R4

-400 -300 -200 -100 0 100 200 300 400

100

1000

10000

Vol

ume

(µm

3 )


(b) 7GA-T2

-500 -400 -300 -200 -100 0 100 200 300 400 500

100

1000

10000

Vol

ume

(µm

3 )


(c) 9GA-R3

-400 -200 0 200 400

100

1000

10000V

olum

e (µ

m3 )


(d) 9GA-T4

Figure 4.26: Profiles of the volumes of voids through thesheet thickness in reconstructed galvannealed DP steel variantmatch-head specimens.



Table 4.10 and Table 4.11 highlight the important damage accumulation observations

for each of the 7TP1-treated and 9TP1-treated specimens, respectively. The effect of

NFP content on damage accumulation is examined in terms of void volume percent

in Fig. 4.27 and Fig. 4.28 for 7TP1 and 9TP1 variants, respectively; and in terms of

number of voids in Fig. 4.29 and Fig. 4.30 for 7TP1 and 9TP1 variants, respectively.

No clear trends are evident.


The degree of damage in each of the TP1-treated XµCT specimens is qualitatively


rendering of the match-head specimen volumes in Fig. 4.31 through Fig. 4.76. Several

of the TP1-treated specimens contained the largest void volume percent of all the

variants.


For all TP1-treated specimens, damage was concentrated most populously just below

the fracture surface. As well, voids were often concentrated heavily in the sheet center-

line plane, especially those of the largest volume, reflective of the spatial distribution

of microstructural NFP banding in these variants. A spatial and volumetric distri-

bution of void damage which was heavily centerline clustered in many of the more

ductile microstructures (i.e. lower NFP volume percent) can be seen in Fig. 4.81,

Fig. 4.82, Fig. 4.83, and Fig. 4.84.



Significant alignment of voids in directions within the plane produced by the major

and minor strain axes was present for the TP1-treated specimens in which the sheet

rolling direction aligned with the minor strain axis. This is evident in Table 4.8 for

7TP1-15-T11, 7TP1-33-T10, 7TP1-43-T5, 9TP1-15-T1, 9TP1-33-T10, and 9TP1-43-

T7, and is qualitatively observed in Fig. 4.35, Fig. 4.43, Fig. 4.51, Fig. 4.59, Fig. 4.67,

and Fig. 4.75 respectively.


The failure mechanism of TP1-treated specimens progressed from a mixed ductile-

shear mechanism to a progressively more shear-dominated mechanism with increasing

NFP content.


Table 4.10: Damage accumulation observations, inferences, andcomputations for 7TP1-treated DP steel specimens.

Specimen # of Voids

Void Volume (µm3)


7TP1-15-R4 65 1.956 7.31 57.6

• Mixed ductile-shear type fracture• NFP particle cracking dominated voidnucleation• Large size distribution of deep fracturesurface dimples (1-11 µm), largest dimpleslocated near sheet centerline• Mild clustering of void damage to sheetcenterline

7TP1-15-T11 158 1.129 2.88 26.5

• Mixed ductile-shear type fracture• NFP particle cracking and some ferrite-NFP decohesion void nucleation• Many fracture surface dimples very elon-gated in RD• Mild clustering of void damage to sheetcenter region

7TP1-33-R11 167 0.855 2.47 21.2

• Mixed ductile-shear type fracture• NFP particle cracking at sheet center-line and some ferrite-NFP decohesion voidnucleation elsewhere• Large size distribution of fracture surfacedimples (1-9 µm)• Major clustering of void damage to sheetcenter region

7TP1-33-T10 260 5.719 32.12 453.9

• Shear mechanism dominated failure• NFP particle cracking at sheet center-line and some ferrite-NFP decohesion voidnucleation elsewhere• Many fracture surface dimples very elon-gated in RD at sheet centerline, moreequiaxed elsewhere• Major clustering of void damage to sheetcenter region

7TP1-43-R3 165 2.561 15.07 189.8

• Shear mechanism dominated failure• NFP particle cracking at sheet centerline• Relatively uniform size distribution offracture surface dimples (1-5 µm)• Major clustering of void damage to sheetcenter region

7TP1-43-T5 83 0.736 3.16 28.2

• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Many fracture surface dimples very elon-gated in RD• Uniform spatial distribution of voiddamage through sheet thickness


Table 4.11: Damage accumulation observations, inferences, andcomputations for 9TP1-treated DP steel specimens.

Specimen # of Voids

Void Volume (µm3)


9TP1-15-R7 304 0.692 1.57 13.9

• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Large size distribution of deep fracturesurface dimples (1-13 µm), largest dimplesgenerally located near sheet centerline• Major clustering of void damage to sheetcenter region

9TP1-15-T1 551 0.446 0.95 12.9

• Shear mechanism dominated failure• Particle cracking dominated void nucle-ation at NFP bands• Many fracture surface dimples very elon-gated in RD• Relatively uniform spatial distribution ofvoid damage through sheet thickness

9TP1-33-R10 60 0.527 1.16 7.7

• Shear mechanism dominated failure• Particle cracking dominated void nucle-ation at NFP bands• Large size distribution of fracture surfacedimples (2-9 µm)• Uniform spatial distribution of voiddamage through sheet thickness

9TP1-33-T10 593 0.521 1.32 13.0

• Shear mechanism dominated failure• NFP particle cracking at sheet center-line and some ferrite-NFP decohesion voidnucleation elsewhere• Many fracture surface dimples increas-ingly elongated in RD with increasingproximity to sheet centerline• Relatively uniform spatial distribution ofvoid damage through sheet thickness

9TP1-43-R11 42 0.181 0.18 0.7

• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Relatively uniform size distribution offracture surface dimples (1-3 µm)• Uniform spatial distribution of voiddamage through sheet thickness

9TP1-43-T7 123 0.392 0.49 3.9

• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Many fracture surface dimples increas-ingly elongated in RD with increasingproximity to sheet centerline• Relatively uniform spatial distribution ofvoid damage through sheet thickness


Figure 4.27: Relationship between NFP volume percent in IPPSspecimens and the volume percent of void damage accumulatedin the 7TP1 match-head region examined using XµCT. Hori-zontal error bars are derived from the 95% confidence intervalof NFP volume percent measurements. Vertical error bars arenot provided as systematic error in computing the number ofvoids present in match-head specimens was not performed inthis study.


Figure 4.28: Relationship between NFP volume percent in IPPSspecimens and the volume percent of void damage accumulatedin the 9TP1 match-head region examined using XµCT. Hori-zontal error bars are derived from the 95% confidence intervalof NFP volume percent measurements. Vertical error bars arenot provided as systematic error in computing the number ofvoids present in match-head specimens was not performed inthis study.


Figure 4.29: Relationship between NFP volume percent inIPPS specimens and the number of voids accumulated in the7TP1 match-head region examined using XµCT. Horizontal er-ror bars are derived from the 95% confidence interval of NFPvolume percent measurements. Vertical error bars are not pro-vided as systematic error in computing the number of voidspresent in match-head specimens was not performed in thisstudy.


Figure 4.30: Relationship between NFP volume percent inIPPS specimens and the number of voids accumulated in the9TP1 match-head region examined using XµCT. Horizontal er-ror bars are derived from the 95% confidence interval of NFPvolume percent measurements. Vertical error bars are not pro-vided as systematic error in computing the number of voidspresent in match-head specimens was not performed in thisstudy.


Figure 4.31: 3-D semi-transparent volume rendering of the7TP1-15-R4 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 1063 x 838 x 1145 µm.


Figure 4.32: 3-D semi-transparent volume rendering of the7TP1-15-R4 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 838 x 1145 µm.


(a) Polished

(b) 2% Nital etch

Figure 4.33: Typical optical micrographs of the failed 7TP1-15-R4 match-head specimen showing void damage.




(b)


Figure 4.34: SEM fractographs of the failed 7TP1-15-R4 match-head specimen.


Figure 4.35: 3-D semi-transparent volume rendering of the7TP1-15-T11 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 938 x 793 x 1145 µm.


Figure 4.36: 3-D semi-transparent volume rendering of the7TP1-15-T11 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 793 x 1145 µm.


(a) Polished

(b) 2% Nital etch

Figure 4.37: Typical optical micrographs of the failed 7TP1-15-T11 match-head specimen showing void damage.




(b)


Figure 4.38: SEM fractographs of the failed 7TP1-15-T11match-head specimen.






(a) Polished

(b) 2% Nital etch





(b)


Figure 4.42: SEM fractographs of the failed 7TP1-33-R11match-head specimen.






(a) Polished

(b) 2% Nital etch





(b)








(a) Polished

(b) 2% Nital etch





(b)








(a) Polished

(b) 2% Nital etch





(b)


Figure 4.54: SEM fractographs of the failed 7TP1-43-T5 match-head specimen.






(a) Polished

(b) 2% Nital etch





(b)








(a) Polished

(b) 2% Nital etch





(b)








(a) Polished

(b) 2% Nital etch





(b)








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(b)








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(f) 7TP1-43-T5

Figure 4.79: Histograms of equivalent spherical void diame-ter in reconstructed TP1-treated DP steel variant match-headspecimens.


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(f) 7TP1-43-T5

Figure 4.81: Histograms of the spatial distribution of voidsthrough the sheet thickness in reconstructed TP1-treated DPsteel variant match-head specimens.


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(f) 9TP1-43-T7



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Figure 4.83: Profiles of the volumes of voids through the sheetthickness in reconstructed TP1-treated DP steel variant match-head specimens.


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The degree of damage for each of the TP2-treated XµCT specimens is qualitatively


rendering of the match-head specimen volumes in Fig. 4.85 through Fig. 4.97.


For the most part, damage was concentrated near the fracture surface where strains

were larger. Again the void damage spatial distribution closely mimicked the distri-

bution of NFP in the TP2-treated microstructures.


Void orientation in the TP2-treated variants was fairly randomized. As observed for

the previously discussed variants subject to NFP banding along the RD, alignment

of voids in the plane produced by the major and minor strain axes was present for

the TP2-treated specimens in which the sheet rolling direction was aligned with the

minor strain axis. Evidence of this observation is provided by the low θ values in

Table 4.8 for specimens 7TP2-25-T2 and 9TP2-37-T1 and the corresponding rela-

tively low standard deviations.


A shear dominated failure mechanism was apparent for all TP2-treated specimens.


Table 4.12: Damage accumulation observations, inferences, andcomputations for TP2-treated DP steel specimens.

Specimen # of Voids

Void Volume (µm3)


7TP2-25-R4 63 0.705 1.95 14.9

• Shear mechanism dominated failure• NFP particle cracking and some ferrite-NFP decohesion void nucleation• No fractographs due to severe corrosionartifacts• Moderate clustering of void damage tosheet center region

7TP2-25-T2 282 0.722 1.67 19.6

• Shear mechanism dominated failure• Mix of NFP particle cracking and ferrite-NFP decohesion void nucleation• Some fracture surface dimples elongatedin RD, sparse population of small dimples(1-4 µm), evidence of cleavage• Moderate clustering of void damage tosheet centerline

9TP2-37-R4 155 1.216 2.93 20.4

• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Large size distribution of shallow frac-ture surface dimples (1-9 µm)• Severe clustering of void damage to sheetcenterline

9TP2-37-T1 282 0.324 0.46 3.2

• Shear mechanism dominated failure• NFP particle cracking and some ferrite-NFP decohesion void nucleation• Many fracture surface dimples elongatedin RD, large size distribution (1-8 µm)• Very mild clustering of void damage tosheet centerline region






(a) Polished

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Chapter 5

Discussion

5.1 Microstructural Variants

The production of microstructural variants of DP steels in this study was accom-

plished though intercritical heat treatment; that is, intercritical temperature and

input microstructure were varied to produce DP microstructures of different NFP

volume percentages and different NFP particle morphology. Explanation is provided

within this section for the microstructural variation observed between TP1- and TP2-

treated DP steel variants.

5.1.1 TP1

Thermal Path One (TP1) consisted of a rapid IC annealing of cold-rolled steel spec-

imens. During the two minute hold within the IC temperature range, austenite was

expected to have nucleated at cementite grains within pearlite colonies, consumed the

pearlite colonies entirely, and then continued to slowly grow into ferrite grains. It is

246

CHAPTER 5. DISCUSSION 247

believed that due to the highly banded nature of the distribution of pearlite colonies

within the cold-rolled DP microstructure, the austenite phase formed in grains that

were highly banded as well. Upon rapid quenching from the IC annealing temperature

to 5◦C, the FCC austenite within the now ferrite-austenite microstructure underwent

a diffusionless transformation to BCT martensite. Martensite grains were observed at

ferrite grain boundaries and triple points due to parent austenite having nucleated in

pearlite colonies at these locations. There is a possibility that some very small frac-

tion of stabilized austenite was retained within the microstructure after quenching.

The effects of any metastable austenite content within TP1-treated mechanical test

specimens were considered to be negligible. Due to the high rate of cooling produced

by ice-water quenching, it is expected that no austenite transformed to pearlite or

bainite.

5.1.2 TP2

Thermal Path Two (TP2) consisted of an austempering pre-treatment of cold-rolled

DP steel specimens followed by rapid IC annealing. The austempering pre-treatment

was employed to produce a more uniform spatial distribution of carbon relative to the

cold-rolled material via the production of a bainitic microstructure. A microstructure

composed mostly of bainite resulted in the segregation of carbon into the partitioned

cementite laths of bainite, spread uniformly throughout the microstructure. This

more uniform spatial distribution of cementite relative to the cold-rolled sheet resulted

in a more uniform spatial distribution of nucleation sites for austenite grains during

IC annealing, which subsequently resulted in a more uniform spatial distribution of

NFP upon quenching. Microstructures after austempering were not directly observed


metallographically, thus the actual bainite volume percent at this stage of treatment

is unknown.

5.1.2.1 Explanation of Residual Banding for TP2

Residual banding of NFP in the TP2 microstructure likely persists due to presumed

manganese segregation to the sheet centerline region. Manganese is an austenite sta-

bilizer, so it is quite plausible that a higher concentration of manganese present within

the sheet centerline region (for reasons explained in Sec. 2.1.2.4) lead to an increased

hardenability of the austenite formed within this region. Thus, during the bainite hold

portion of the austempering treatment, it is believed that austenite which had been

sufficiently stabilized by an increased manganese content, remained stable at 500◦C

and did not transform to bainite prior to quenching to room temperature. Therefore,

the austenite would have presumably transformed to martensite upon quenching, pro-

viding a preferable nucleation site for austenite under subsequent IC annealing and

thus resulting in a banded final microstructure.

5.2 IPPS Variant Ductility and Failure

5.2.1 Effect of NFP Content on Ductility

The macroscopic major engineering failure strain, computed as the average of the

seven grid measurements within the failure row, serves as a first approximation of the

ductility of each IPPS specimen. As observed in Fig. 4.6 and Fig. 4.7, the general

trend quoted within the literature of ductility decreasing with increasing martensite

content [47,49] has been confirmed. Whether or not this trend is linear or non-linear


for the IPPS specimens of this study cannot be ascertained from the limited data-set.

5.2.2 DP Steel Variant Failure Behaviour

Failure of all DP steel IPPS variant specimens appears to have been ductile in nature

from the dimples evident in captured fractographs, an observation in agreement with

the literature [49,53,58,63–78]. Mean dimple size generally increased with increasing

fracture strain of specimens. Logically, this makes sense as increasing strain to failure

would allow for increased void growth and coalescence prior to fracture. Transition

from a more ductile, cup-cone type fracture to a shear fracture generally occurred with

increasing NFP content. This is interpreted to be a result of increased NFP content

providing a greater number of microstructural inhomogeneities, leading to earlier

onset of strain localization and increased ease of shear band formation, explained

further in Sec. 5.4.3. Most DP variant IPPS specimens failed via shear fracture.

Given the near plane-strain nature of the deformation, this behaviour was expected

as shear fracture of DP steels has been reported in regions of plane-strain bending

during premature forming failure [10].

Nearly all of the shear-mechanism dominated fracture surfaces were oriented ap-

proximately 45◦ with respect to the tensile axis. This agrees with the characteristic

surfaces upon which failure was predicted to occur under plane-strain conditions in

Sec. 2.3.4. Fracture surfaces were reflective of the spatial distribution of NFP in

the plane formed by the through-thickness and minor strain directions. Long, deep

cracks/dimples were observed for specimens with the sheet RD aligned along the mi-

nor strain direction. This was interpreted to be reflective of the NFP bands aligned

in the rolling direction causing void nucleation via particle cracking, subsequent void


growth, and possibly coalescence.

It should be noted that significant surface roughening is evident for 7GA-R4 and

7GA-T2, respectively, in Fig. 4.9 and Fig. 4.13. Surface roughening may be partially a

result of the galvannealed sheet surface containing zinc. This surface roughening could

have resulted in a field of reduced thickness inhomogeneities [59] which contributed

to the initiation of a final shear mechanism of failure. The DP980GA material did

not exhibit notable surface roughening, but also incurred reduced strain to failure.

5.3 XµCT for Characterization of Damage

XµCT proved to be a very valuable tool for assessing void size, morphology, and dis-

tribution in 3-D. Tomographic reconstructions of the internal structure of the failed

IPPS DP steel variant specimens of this study confirmed three-dimensionally the

general trend within the literature of void damage density increasing towards the

fracture surface of DP steel tension specimens [14, 22, 72]. As well, a trend of signif-

icantly sized void damage generally being concentrated at the sheet centerline was

observed for many of the DP steel variants. The smallest voids were not detected

using the XµCT protocol of this study as any void computed to be less than 44.53

µm3 in volume was removed from the analysis, but it is the larger voids which are

more likely to have an important effect on the failure process [22]. Systematic er-

ror in computing the quantitative characteristics of voids via the XµCT protocol of

this study was not examined. Hence, no confidence interval is provided for void size

measurements.


5.4 DP Steel Damage Accumulation in Plane-

Strain Fracture

5.4.1 Void Nucleation

Voids were generally inferred via post-failure metallography to have nucleated via

NFP particle cracking for the galvannealed and TP1-treated DP steel variants, espe-

cially at NFP bands and large particles. Coarse NFP bands were inferred to produce

the most number and the largest voids. This agrees with the results of Winkler et

al. [18] who observed void nucleation to occur preferentially at the thicker or denser

martensitic bands for both DP steels of their study. Some void nucleation via ferrite-

NFP decohesion was inferred in this study to have occurred away from NFP bands

for the galvannealed and TP1-treated DP steel variants. In general, the amount of

damage nucleated via ferrite-NFP decohesion decreased with increasing NFP content

for these variants. According to a mass balance, carbon content of the martensite

would have decreased with increasing NFP content. As such, these results agree with

the bulk of the literature with lower-carbon martensite producing a tendency for void

nucleation via martensite particle cracking and higher-carbon martensite producing a

tendency for void nucleation via ferrite-martensite decohesion [14,49,75,100]. A mix

of ferrite-NFP decohesion and NFP particle cracking was inferred to have produced

the void damage in TP2-treated DP steel variants.


5.4.2 Failure Behaviour Variation with Degree of NFP Band-

ing

The two DP780-series variants with similar NFP volume percent (within uncertainty),

but differing particle populations, were 7TP1-33 and 7TP2-25. Both variants had

quite similar mean major engineering strains at failure for RD and TD specimens,

respectively (see Table 4.6(a)). However, it is evident from Fig. 4.6 that the 7TP2-

25 series had a much larger variance in failure strains for TD specimens than did

the 7TP1-33 series. The lack of an increased ductility for the 7TP2-25 specimens

composed of more uniformly spatially distributed NFP particles relative to the 7TP1-

33 series may be in part caused by the residual NFP banding present in the 7TP2-25

specimens. Increased nucleation and growth of void damage at these residual bands

may have led to an earlier onset of localization and formation of a critical flaw leading

to failure.

Interestingly, both of the aforementioned variants had mean failure strains for RD

and TD oriented specimens more than 22% higher than those of the DP780 galvan-

nealed steel, despite both having a larger volume percent of NFP by approximately

7%. Although, these results are subject to a small sample size and an associated

high uncertainty, the disparity cannot be explained simply by the DP780GA steel

containing a small portion of bainite comprising its NFP content. It seems likely that

the larger prevalence of NFP banding throughout the thickness of the DP780GA ma-

terial led to earlier strain localization within the gauge region of the DP780GA IPPS

specimens. This explanation is plausible when considering the cooperative interaction

between voids and shear bands in precipitating strain localization [150].

For the DP980-series of variants, the 9TP1-33 and 9TP2-37 variants both had


similar NFP volume percent (within uncertainty) to the DP980 galvannealed steel.

The RD-oriented and TD-oriented specimens of the TP1- and TP2-treated variants

had higher mean major engineering strains at failure than the correspondingly ori-

ented DP980GA specimens. While the small number of samples casts some doubt

upon this observation, the greater frequency of NFP banding across the thickness

of the galvannealed steel leading to earlier strain localization represents a plausible

explanation for these results.

5.4.3 Explanation for Reduced Ductility with Increased NFP

Banding

A schematic depicting how increased void nucleation in a microstructure with in-

creased NFP banding frequency through the sheet thickness is thought to lead to

earlier strain localization and failure is shown in Fig. 5.1. The steps leading to failure

shown in Fig. 5.1 are outlined more clearly for the two degrees of banding in the

cropped schematics of Fig. 5.2 and Fig. 5.3. The term NFP banding describes a mi-

crostructural state of highly aligned, highly proximal NFP particles, so proximal in

fact that under a light microscope at 1000x magnification, these bands often appear

to be a continuous particle.

The reasoning for a greater strain to failure in a less banded microstructure is

thought to be its effect of delaying strain localization and the formation of shear

bands. Voids were observed to have formed preferentially at NFP bands throughout

the microstructural variants of this study. The low critical local void nucleation strain

of 0.029 for martensite cracking and 0.09 for ferrite-martensite decohesion reported

by Avramovic-Cingara et al. [14] for a DP steel assists in explaining this behaviour.


As discussed in Sec. 2.3.1.1, coarser NFP particles are predicted to crack first and

the coarsest NFP particles were generally located within bands. This leads to the

idea that the first voids to nucleate during deformation of the IPPS specimens do so

primarily at NFP bands, as shown in Fig. 5.1. It is predicted that these voids grow

by continued cracking while further voids are nucleated at the bands and eventually

away from the bands via ferrite-NFP decohesion, as reported by Avramovic-Cingara

et al. [14]. This behaviour continues until the void inhomogeneities result in a loss of

load carrying capacity and strain localization [14].

It follows that, an increasing number of NFP bands through the thickness of a

sheet represents a greater number of void nucleation sites for producing a critical

string of void inhomogeneities, leading to strain localization at a lower level of global

strain. Thus, as shown in Fig. 5.1, the formation of a shear band across the neck

of a specimen due to the presence of a critical population of microstructural inho-

mogeneities (voids, NFP particles, inclusions) occurs at a lower global strain for a

DP steel microstructure with increased NFP banding. It is worth noting that the

intense strain within the shear band likely causes a rapid nucleation of secondary

voids, called void sheeting, assisting in the final failure process of inter-void ligament

shearing. Void sheeting during shear fracture of DP steel has also been considered by

Avramovic-Cingara et al. [14].

Despite specimen 7TP1-33-T10 accumulating the largest total volume of void dam-

age of all specimens, it still maintained a higher failure strain than that of 7GA-T2,

which had significantly lower damage accumulation and NFP content. To demon-

strate that this is not just a singular event, consider the 7TP1-33 and 7TP2-25 series

of variants in comparison to the 7GA specimens; the lab-treated variants had mean


Figure 5.1: Schematic depicting how the proposed increasedvoid nucleation in a microstructure with increased NFP band-ing frequency through the sheet thickness is thought to leadto earlier strain localization in IPPS specimens. The uppersequence roughly depicts typical galvannealed DP steel mi-crostructural NFP banding; bands are situated throughout thesheet thickness. The lower sequence depicts typical TP1- andTP2- treated DP steel variant microstructural NFP banding;the bands are concentrated at the sheet centerline. Step 1: voidnucleation via particle cracking at NFP bands and growth; step2a: void nucleation via ferrite-martensite decohesion through-out the sheet thickness; step 2b: formation of a shear bandalong a plane weakened by inhomogeneities; step 3: void sheet-ing and coalescence across shear band; step 4: fracture.


(a) Step 1 - void nucleation via particlecracking at NFP bands and growth

(b) Step 2b - formation of a shear bandalong a plane weakened by inhomogeneities

(c) Step 3 - void sheeting and coalescenceacross the shear band

Figure 5.2: Detailed schematic depicting what is thought tobe the simplified typical stages leading to failure of the gal-vannealed DP steels of this study exhibiting a large number ofNFP bands throughout the sheet thickness.


(a) Step 1 - void nucleation via particlecracking at NFP bands and growth

(b) Step 2a - void nucleation via ferrite-martensite decohesion throughout thesheet thickness

(c) Step 2b - formation of a shear bandalong a plane weakened by inhomogeneities

(d) Step 3 - void sheeting and coalescenceacross the shear band

Figure 5.3: Detailed schematic depicting what is thought to bethe simplified typical stages leading to failure of the TP1- andTP2-treated DP steels of this study exhibiting a small numberof NFP bands concentrated at the sheet centerline.


failure strains more than 22% higher than those of the DP780 galvannealed steel,

despite both having a 7% higher volume percent of NFP. The major microstructural

difference between the lab-treated variants and the galvannealed sheet is the greater

number and more continuous nature of NFP bands throughout the thickness of the

galvannealed sheet. This provides further evidence that, from the perspective of de-

signing DP steels which have improved formability under plane-strain conditions, it

is desirable to design microstructures where strain localization is not induced at early

global strains due to void damage developing rapidly at many “easy” nucleation sites

throughout the sheet thickness. It seems that a reduction of NFP banding through

the thickness of DP sheet would assist in delaying the onset of strain localization by

providing fewer sites for void nucleation.

To elaborate using one final example, the one coarse NFP band and finer surround-

ing NFP bands were localized distinctly to the sheet centerline within the 7TP1-33-

T10 microstructure. While these bands caused a very high volume of void damage to

be produced at the sheet centerline, they did not result in a critical flaw leading to

failure until a much higher strain than for 7GA-T2. This difference was due to the

increased prevalence of banding in multiple RD-TD planes throughout the thickness

of the 7GA-T2 sheet. In turn, voids readily nucleated at many points through the

thickness of the sheet, leading to an inhomogeneity sufficient for strain localization

and the formation of a shear band along a characteristic surface (45◦ with respect to

the tensile axis), and rapid failure assisted by void sheeting.


5.5 Effects of Microstructure on Damage Accumu-

lation

5.5.1 Effect of NFP Volume Percent

For a higher NFP volume percent, it is expected that the resulting increase in the

number of void nucleation sites would result in an increased amount of void damage

measured using XµCT. However, the confounding factors of strain to failure, and the

rapidity of onset of strain localization must also be considered when analyzing the

void damage data of the TP1-treated specimens. A reduced strain to failure and

earlier strain localization would afford reduced opportunity for void nucleation and

growth to occur globally, thereby concentrating void damage to the specimen region

which would in turn become the fracture surface, reducing void damage accumulation

in a failed specimen.

The TP1-treated IPPS specimens may be compared in terms of void damage ac-

cumulation due to their similar NFP morphology. Fig. 4.27 and Fig. 4.28 provide

such a comparison in terms of void volume percent measured within the portion of

match-head specimens reconstructed using XµCT. A bias is introduced into the re-

sults because of the variance in the distance of specimens below the fracture surface

that was fit into the FOV during XµCT capture. It should be mentioned that the data

point for the 7TP1-33-T10 specimen is interpreted as an outlier due to the uncharac-

teristically coarse NFP band contained at its sheet centerline shown in Fig. 4.45(b).

Fig. 4.27 and Fig. 4.28 provide no evidence of a strong relationship between NFP con-

tent and void damage accumulation. As well, no clear trend is evident in Fig. 4.29 or

Fig. 4.30 for the number of voids present in the reconstructions of TP1-treated IPPS


match-head specimens with respect to NFP volume percent. No consideration was

given to the effect of NFP particle size as this was moderately similar throughout the

TP1-treated DP steel variants. IPPS testing of additional TP1-treated DP variants

with a further variety of NFP volume percents, plus performing XµCT analysis of

multiple match-head specimens per DP steel variant may have elicited a more clear

trend.

It is postulated that there exists an NFP volume percent for a singular DP steel

microstructural morphology which would produce a peak level of void damage accu-

mulation away from the failure surface. This NFP volume percent would provide the

optimal damage accumulation blend of having a large number of void nucleation sites

at NFP particles, but not so large as to cause rapid onset of strain localization, thus

allowing void growth and further void nucleation to occur for a longer period prior

to failure. The relationship between DP steel NFP content and void damage accu-

mulation for a singular NFP morphology is expected to hold a Chi-Square-type fit.

Such a trend may be very weakly fit to the data of this study in Fig. 4.27, Fig. 4.28,

Fig. 4.29, and Fig. 4.30.

5.5.2 Effect of NFP Morphology

No evidence of a strong correlation between NFP morphology and void damage accu-

mulation was observed when comparing TP1-treated, TP2-treated, and galvannealed

DP steel variants. However, it is thought that the more uniformly spatially distributed

NFP of TP2-treated DP steel variants relative to the TP1-treated and galvannealed

DP steels caused the greater occurrence of ferrite-NFP decohesion; a notion that

agrees with the work of He et al. [19]. In order to better determine morphological


effects, if any exist, residual banding in the TP2-treated DP steel variants must be

eliminated.

5.5.3 Effect of NFP Spatial Distribution

Many major trends were observable in void damage spatial distribution with respect

to NFP morphology. The first is that the largest volume of void damage was generally

observed to be concentrated at the sheet centerline in both TP1- and TP2-treated

DP steel variants. This observation is presumably due to NFP banding being concen-

trated to this region for the aforementioned variants. Polished and etched match-head

specimens revealed that void nucleation was most prevalent at NFP bands and that

the bands were the most coarse and continuous near the sheet centerline. The lack

of a concentration of void damage at the sheet centerline for the galvannealed DP

sheets is reflective of the greater frequency of NFP banding throughout the thickness

of these steels.

Generally, more voids and a greater void volume percent were computed in match-

head variants with the sheet RD aligned with the minor strain direction of IPPS spec-

imens. As well, these ‘TD’ specimens exhibited slightly lower failure strains in general

than their ‘RD’ counterparts. These trends are attributed to the increased prevalence

of NFP banding aligned in the sheet rolling direction relative to the transverse di-

rection. It has been shown by Thomson et al. [151] through finite element modeling

that the orientation of particle clusters/stringers with respect to major loading di-

rection in a ductile material plays an important role in the evolution of damage. In

agreement with the present work, transverse particle clusters/stringers were shown

to produce higher damage rates and lower failure strains than those aligned with the


major loading direction. This behaviour also agrees with the work of Bouchard et

al. [122] described in Sec. 2.4.2. Further evidence supporting the idea that transverse

orientation of the NFP banding relative to the major loading direction is respon-

sible for higher damage rates is observed in the 3-D reconstruction images of such

‘TD’ specimens, the histograms of the spatial distribution of voids through the sheet

thickness, the profiles of the volumes of voids through the sheet thickness, and in the

fractographs of Chap. 4.

The 7TP1-33-T10 specimen stands out as a prime example due to the relatively

large volume of sheet centerline damage evident in Fig. 4.43 and Fig. 4.44. This

damage was due to the presence of an exceptionally coarse and exceptionally con-

tinuous NFP band aligned in the rolling direction at the sheet centerline of this

variant, shown in Fig. 4.45(b). High levels of void damage nucleated and coalesced

at this band, resulting in the sheet centerline concentrated distribution of damage

highlighted in Fig. 4.81(d) and Fig. 4.83(d). Fractographs reveal long, deep dimples

at the sheet centerline (Fig. 4.46(c)) where NFP banding was most prevalent and gen-

erally smaller, less elongated dimples approaching the sheet surfaces (Fig. 4.46(b));

reflective of the microstructure described in Sec. 4.1.3. The corresponding 7TP1-33-

R11 specimen also exhibited void concentration at the sheet centerline where NFP

banding was most prevalent (Fig. 4.40), but its fracture surface lacks any elongated

dimples, providing further evidence that NFP bands aligned transverse to the major

loading direction are responsible for increased damage rates.

Localization of voids at the sheet centerline was generally greater for ‘RD’ speci-

mens than ‘TD’ specimens. This trend is to be expected as once localization begins

to occur void formation would be confined to a smaller region of the specimen where


strains are large enough for nucleation. It is readily recognizable that more NFP

bands aligned in the major strain direction would fall into this neck region than those

aligned in the minor strain direction. Thus, as void nucleation has been shown to

occur preferentially at NFP bands, it would occur in greater frequency at the sheet

centerline for ‘RD’ specimens than ‘TD’ specimens.

5.5.4 Importance of NFP Banding to Damage

Understanding the anisotropy of damage behaviour in DP steels due to NFP banding

in the rolling direction, as presented in this study, is important to both steel producers

and auto parts manufacturers. For parts manufacturers, this knowledge could possibly

lead to simple solutions for avoiding premature part-forming failures. An act as

straightforward as being sure DP steel sheet used in a part forming operation is always

oriented such that the rolling direction is aligned parallel to the largest imposed strains

could potentially prevent many premature failures, if this practice is not already in

place. The same idea applies to orienting sheet during a part forming operation

in order to minimize damage and thus maximize ductility and energy absorption

during a crash-scenario. For steel producers, the present study highlights the need

for developing a cost-effective method to reduce or eliminate NFP banding in DP

steels in order to obtain improved levels of formability.

Chapter 6

Conclusions and Recommendations

6.1 Conclusions

An in-plane plane-strain (IPPS) tensile testing methodology, originally devel-

oped by Valletta [60] and modified by Kilfoil and Kitney [61,131], was used to

deform DP steel microstructural variants in a near plane-strain forming path

under constant crosshead displacement at a nominal initial strain rate of ap-

proximately 0.01 s-1 averaged over the entire specimen gauge region. Testing

was performed to the point of fracture while tracking major and minor strain

developed. Failure strains, a first approximation of ductility, were observed

to decrease with increasing non-ferritic phase/constituent (NFP) content.

264

CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS 265

Fractured specimens were examined for damage accumulation in the bulk us-

ing 3-D X-ray micro-computed tomography (XµCT) with a spatial resolution

of approximately 2 µm and 2-D metallographic procedures, and at the sur-

face via scanning electron fractography. The DP steel microstructural variants

failed in a ductile manner with a shear mechanism becoming more dominant

with increasing NFP content.

It was observed that DP microstructures with an increased severity of NFP

banding (generally aligned in the sheet rolling direction) incurred reduced

strain to failure. In many cases, particularly for the DP980 microstructural

variants, IPPS specimens with the sheet rolling direction transverse to the ma-

jor loading direction incurred a reduce strain to failure than the same variants

with the sheet rolling direction aligned with the major loading direction.

This study has clearly demonstrated the capability of extracting quantitative

and qualitative measures of void damage in 3-D for deformed DP steel sheet

using lab-scale XµCT.

Void damage in all DP steel microstructural variants was observed to be

concentrated most populously near the fracture surface.

No quantitative relationship could be established between NFP content and

void damage accumulation.

Void damage was inferred metallographically to nucleate preferentially at mi-

crostructural bands of NFP via particle cracking, especially at the coarsest of

bands.


Void damage spatial distribution was generally reflective of the spatial distri-

bution of the most coarse NFP bands through the sheet thickness, i.e. voids

were concentrated to regions in which NFP banding was observed to be most

severe.

In general, microstructural variants with the sheet rolling direction transverse

to the major loading direction were observed to accumulate a greater number

of voids and a larger void volume percent than the same variants with the

sheet rolling direction aligned with the major loading direction. This damage

anisotropy reflected the general alignment of NFP bands in the sheet rolling

direction.

In microstructural variants with NFP bands aligned transverse to the major

loading direction, accumulated void damage was often observed to be highly

elongated in the direction of NFP banding.

6.2 Recommendations

Future studies elaborating upon the work of this dissertation may consider the fol-

lowing:

An increased number of valid IPPS specimens per microstructural variant

may afford a more robust analysis of the effect of NFP content and spatial

distribution on ductility and damage accumulation under plane-strain defor-

mation.


Further TP1-treated specimens could be produced using additional IC an-

nealing temperatures and tested to better elucidate the relationship between

NFP content and damage accumulation.

Producing multiple match-head specimens per microstructural variant, ex-

tracted from different valid IPPS specimens, for XµCT scanning would have

provided insight into how representative the damage accumulation behaviour

observed for each variant was.

Eliminating residual NFP banding in a DP steel microstructural variant would

provide an opportunity to better determine the importance of NFP spatial

distribution to damage accumulation.

Examination of the void populations in microstructural variants prior to test-

ing may reveal pre-existing voids.

Performing plane-strain testing at a rate closer to that of typical automotive

forming operations and observing the accumulated damage would be useful

in eliciting strain rate effects for this deformation path.

Ideally, interrupted IPPS tests could be performed to garner some data con-

cerning the development of void damage within the DP steel variants for this

deformation path.

In-situ sub-size tensile testing of DP steel variants within the Micro-XCT 400

may be performed to determine the differences in void evolution behaviour

during straining in relation to known NFP content and spatial distribution.


Digital image correlation (DIC) software (freeware available for MATLAB

made by Christoph Eberl) may be paired with smaller media applied to the

IPPS specimen surface to possibly track strains in IPPS specimens with an in-

creased spatial resolution and thus better capture the strain gradient existing

within regions of intense localization.

The effect of ferrite grain size should be investigated. The rate of surface

roughening increases with grain size, which may result in a field of reduced

thickness inhomogeneities and through-thickness shearing under severe con-

ditions [59]

The effects of what were thought to be manganese sulfide stringers present in

the microstructures of the DP steel variants of this study on void nucleation

could be assessed.

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Appendix A

Preliminary IC Annealing

Experiments

This appendix details the experiment conducted to produce a calibration curve for

NFP content in the cold-rolled steels of this study after IC annealing treatments at

various temperatures. This curve was used to select three IC annealing temperatures

used for the production of DP microstructural variants for IPPS tensile testing.

A.1 Preliminary Heat Treatment Experiment

Lacking software, such as Thermo-CalcR©, to calculate the phase diagram for the cold-

rolled dual-phase steel alloys used in this study for heat treatments, an experiment

was designed to create a calibration curve correlating the volume percent of NFP in

TP1-treated microstructures to IC annealing temperature.

281

APPENDIX A. PRELIMINARY IC ANNEALING EXPERIMENTS 282

A.1.1 Alloy Intercritical Temperature Ranges

Firstly, the eutectoid (Ac1) and minimum austenitizing (Ac3) temperatures needed to

be determined to distinguish the intercritical treatment temperature range for each

of the cold-rolled DP steel alloys. Andrews’ formulae [152], provided in Eq. A.1 and

Eq. A.2, were used to provide an estimate of these temperatures where elemental

composition is input in weight percent. These equations are valid for low alloy steels

with less than 0.6%C. The martensite start (Ms) and finish (Mf) temperatures of

these alloys were also calculated using Andrews’ formulae [152], provided in Eq. A.3

and Eq. A.4 respectively. These equations are valid for low alloy steels with less than

0.6%C, 4.9%Mn, 5.0%Cr, 5.0%Ni, and 5.4%Mo. The results of the calculations of

the aforementioned temperatures are provided for both cold-rolled DP steel alloys in

Table A.1.

Ac1 (◦C) = 723− 10.7Mn− 16.9Ni+ 29.1Si+ 16.9Cr + 290As+ 6.38W (A.1)

Ac3 (◦C) = 910− 203

√C − 15.2Ni+ 44.7Si+ 104V + 31.5Mo+ 13.1W (A.2)

Ms (◦C) = 512− 453C − 16.9Ni+ 15Cr − 9.5Mo

+ 217(C)2 − 71.5(C)(Mn)− 67.6(C)(Cr)

(A.3)


Mf (◦C) = Ms − 215 (A.4)

Table A.1: Approximated solid state transformation tempera-tures for the cold-rolled DP steel alloys.

Ac1 Ac3 Ms Mf

(◦C) (◦C) (◦C) (◦C)

DP780 CR 705 859 459 244DP980 CR 702 855 444 239

A.1.2 IC-Annealing Calibration Curves for NFP Content

With knowledge of the approximate range of temperatures falling within the inter-

critical region for each alloy, five IC annealing temperatures were selected from within

this range to produce microstructural variants of DP steel with varying NFP volume

percent. The five semi-arbitrarily selected temperatures were: 707◦C, 716◦C, 729◦C,

739◦C, and 751◦C. These temperatures were selected from the lower portions of the

approximated cold-rolled alloy IC annealing ranges in an attempt to produce typi-

cal dual-phase steel microstructures in which the ferrite content is greater than NFP

content. IC annealing treatments of IPPS blanks at these temperatures for both of

the cold-rolled DP steel alloys were undertaken following the procedures for TP1 in

Sec. 3.2.4.4.

After treatment, a microstructural characterization of NFP volume percent was

performed for each specimen. Metallographic through-thickness (ND) sections were

extracted from the blanks along the rolling direction (RD) and transverse direction

(TD) from the locations detailed in Fig. A.3 using a Struers Accutom precision cut-

off machine equipped with an aluminum oxide cut-off wheel and continuously flowing

coolant. Samples were also sectioned from the DP780 and DP980 galvannealed steel


and subjected to the same microstructural characterization to determine the volume

percent of NFP present. The etchant used was 10% sodium metabisulfite (SMB)

which left ferrite untinted and tinted both martensite and bainite dark.

A.1.2.1 Optical Microscopy Procedure

This section describes point counting procedures specific to NFP volume percent es-

timates for preliminary heat treatment DP steel specimens. A Zeiss Axioskop 2 MAT

light microscope equipped with an Olympus EvolutionTMMP Colour CCD camera

was used to capture colour micrographs measuring 2560 x 1920 pixels. A 100x Zeiss

Epiplan-NEOFLUAR oil immersion lens was used during micrograph acquisition.

Each captured micrograph was the average of 10 accumulated exposures to account

for any vibrations of the system during acquisition.

For each DP steel microstructural variant, 10 micrographs were captured each from

ND-RD and ND-TD sections. These micrographs were captured along the through-

thickness centerline of the steel sheet where banding of NFP was most prevalent. A

software-driven microcontroller was used to automatically shift the microscope stage

0.5 mm along the through-thickness sheet centerline between micrograph captures,

thereby eliminating operator bias in field selection. The capture of fields along sheet

centerlines introduces a bias into the constituent volume percent estimates; however

this region is thought to control plane strain formability for the IPPS testing method

[131].

ImageJ, image analysis freeware written in Java, was used to overlay a grid of

test points over acquired micrographs. A custom grid consisting of 110 test points

distributed about five equidistant circles was developed as a Java plug-in within


ImageJ for the optical micrographs and used for point-counting.

Representative micrographs of the resulting microstructures for each IC annealed

variant and of the galvannealed steel are provided in Fig. A.1 for DP780 and in

Fig. A.2 for DP980. The NFP contents measured for the galvannealed and heat-

treated blanks are summarized in Table A.2 and presented graphically in Fig. A.4.

Table A.2: Volume percent of NFP measured in the as-receivedgalvannealed DP steels and in the gauge region of the TP1-treated IPPS blanks of preliminary heat treatments.

ConditionNFP

ConditionNFP

Volume % Volume %

DP780 Galvannealed 34.9 ± 1.2 % DP980 Galvannealed 47.2 ± 1.3DP780CR + TP1 @ 707◦C 20.6 ± 1.2 % DP980CR + TP1 @ 707◦C 23.0 ± 1.1 %DP780CR + TP1 @ 716◦C 27.5 ± 1.4 % DP980CR + TP1 @ 716◦C 27.3 ± 1.4 %DP780CR + TP1 @ 729◦C 31.2 ± 1.4 % DP980CR + TP1 @ 729◦C 35.7 ± 1.7 %DP780CR + TP1 @ 739◦C 40.0 ± 1.3 % DP980CR + TP1 @ 739◦C 41.5 ± 1.9 %DP780CR + TP1 @ 751◦C 50.5 ± 1.5 % DP980CR + TP1 @ 751◦C 60.2 ± 1.8 %

A.2 Optical vs. SE Quantitative Metallography

The attentive reader will note that the NFP contents predicted in Fig. A.4 for the

TP1 IC annealing temperatures used do not correlate within uncertainty with the

NFP contents measured for the TP1-treated DP steel variants in Chap. 4. The ex-

planation for this non-correlation hinges primarily on the ineffectiveness of 1000x

optical micrographs in magnifying the fine-grained microstructures of the sheet steels

used in this research to a size which allowed for accurate delineation of whether or

not grid-points fell upon a constituent. A micrograph demonstrating the difficulty in

performing manual volume percent counting using 1000x optical micrographs due to

the low ratio of grid-point size to NFP particle size is provided in Fig. A.5. Despite

having provided a high degree of precision in measuring NFP volume percent, the


(a) (b)

(c) (d)

(e) (f)

Figure A.1: Representative microstructures at the sheet centre-line of: a) as-received DP780 galvannealed steel; b) DP780CRTP1 @ 707◦C; c) DP780CR TP1 @ 716◦C; d) DP780CR TP1@ 729◦C; e) DP780CR TP1 @ 739◦C; and f) DP780CR TP1@ 751◦C. (10% SMB etch)


(a) (b)

(c) (d)

(e) (f)

Figure A.2: Representative microstructures at the sheet centre-line of: a) as-received DP980 galvannealed steel; b) DP980CRTP1 @ 707◦C; c) DP980CR TP1 @ 716◦C; d) DP980CR TP1@ 729◦C; e) DP980CR TP1 @ 739◦C; and f) DP980CR TP1@ 751◦C. (10% SMB etch)


Figure A.3: IPPS blank detailing the locations of ND-RD (red)and ND-TD (green) metallographic specimen extraction at thecenter of the gauge region for preliminary heat treatments.


700 710 720 730 740 750

20

30

40

50

60

70

DP780 DP980

NFP

Vol

ume

Per

cent

IC Annealing Temperature (°C)

Figure A.4: NFP content calibration curve constructed for TP1heat treatment of the DP780 and DP980 cold-rolled alloys.Lines of best fit are polynomial functions.


accuracy of point counting using optical micrographs was clearly questionable. As

such, all point counting of NFP for non-preliminary experiments was performed using

5000x SE micrographs. The superior resolving power of the SEM and the increased

magnification allowed for what was expected to be quantitative metallographic mea-

surements of greater accuracy. A convergence study was not performed to assess

the accuracy of 5000x SE micrographs in mean lineal intercept and volume percent

measurements.

Figure A.5: Optical micrograph taken at 1000x of TP1-treatedDP780 (729◦C IC annealing temperature) demonstrating thedifficulty inherent in classifying whether grid points (small reddots) fall on a NFP particle. The etchant used was 10% SMB.

Appendix B

IPPS Blanks - Time to Heat to IC

Temperature

The heating times required within the vertical crucible furnace salt bath to reach

desired IC temperature for 85 mm x 50 mm x sheet thickness rectangular blanks of

cold-rolled DP780 and DP980 were measured using a thermocouple and data acqui-

sition software. Small slots were cut into the 50 mm side at the center of the gauge

region of a blank from each steel grade. A K-type thermocouple’s two wires were

peened tightly into place using a hammer and punch to plastically deform the mouth

of each slot. Prior to IC annealing heat treatment, the other end of the thermocouple

was connected to a data acquisition (DAQ) card on a PC with Instrunet data acqui-

sition software. The blank was then dipped in the salt bath following the procedures

outlined in Sec. 3.2.1, being sure to prevent the bare thermocouple wires from touch-

ing conductive objects. The temperature of the salt bath in the location of the gauge

region of the submerged blanks as recorded by the shielded thermocouple submerged

in the salt bath was approximately 700◦C. This is shown in Appendix A to be above

291

APPENDIX B. IPPS BLANKS - TIME TO HEAT TO IC TEMPERATURE 292

the Ac1 temperature for both steels. The transient temperature responses of the cold-

rolled DP780 and DP980 blanks for repeated TP1 trials are provided in Fig. B.1(a)

and Fig. B.1(b) respectively. It was determined that the time for the IPPS blanks

to heat to target IC annealing temperature was approximately 37 seconds and 50

seconds for the DP780 and DP980 cold-rolled alloys respectively. The longer time for

the DP980 material is due to its increased thickness.

The response of the salt bath to the addition of the steel blanks was also recorded

using the data acquisition software. The shielded K-type thermocouple suspended

in the salt bath 10 mm away from the pot edge was connected to the DAQ card.

The transient response of the bath was recorded to determine what length of time

was necessary between IC annealing treatments for the salt bath to re-stabilize at

the target temperature. The transient temperature responses of the salt bath for

repeated trials with the DP780CR and DP980CR blanks are provided in Fig. B.2(a)

and Fig. B.2(b) respectively. It was determined that the time for the salt bath to re-

stabilize to target IC annealing temperature was approximately 18 minutes between

TP1 treatments of both the DP780 and DP980 cold-rolled alloys.


(a)

(b)

Figure B.1: Heating curves for the TP1 heat treatment of: a)cold-rolled DP780 IPPS rectangular blanks; and b) cold-rolledDP980 IPPS rectangular blanks. Also shown are ±1% K-typethermocouple accuracy bounds on the target temperature of700◦C. The short plateau prior to reaching the target temper-ature of 700◦C is explained by energy rapidly being consumedin the transformation of carbides to austenite.


(a)

(b)

Figure B.2: Salt bath transient temperature response for theTP1 heat treatment of: a) cold-rolled DP780 IPPS rectangu-lar blanks; and b) cold-rolled DP980 IPPS rectangular blanks.Also shown are ±1% K-type thermocouple accuracy bounds onthe target temperature of 700◦C.

Appendix C

IPPS Specimen Cleaning

Procedure

The inhibited acid cleaning solution was prepared in a fume hood. Seven-hundred

milliliters of water was added into a 1000 milliliter volumetric flask. One-hundred

milliliters of concentrated (98%) sulphuric acid was added to the flask. Seventeen

drops of Activol inhibitor, produced by Harry Miller Corporation, were added to the

solution. This inhibitor assists in facilitating attack of the oxide layer only and not

the base steel [131]. Finally, the solution was diluted to one liter with water, mixed

well, and allowed to cool to room temperature.

Prior to inhibited acid treatment, all heat-treated IPPS specimens were wiped

with acetone to remove any grease. Two-hundred milliliters of inhibited acid solution

were poured into a glass dish of 100 mm inner diameter. This 200 mL of solution was

used to treat seven IPPS specimens in succession before being disposed of following

standard waste acid disposal procedures. A treatment consisted of immersing an IPPS

specimen in the inhibited solution for 2 minutes with the sheet surface flat on the

295

APPENDIX C. IPPS SPECIMEN CLEANING PROCEDURE 296

bottom of the glass dish. During this time, the specimen was given a light scrub with

a soft-bristled toothbrush, scrubbing in the direction of the major strain axis only to

prevent development of any small surface striations perpendicular to the applied load

direction of mechanical testing. The specimen was then flipped and re-immersed in

solution for 2 minutes with light-scrubbing taking place throughout. After this, the

specimen was dunked in a flask filled with water, flushed under running water, rinsed

with ethanol, and dried using compressed air. Example photographs of the condition

of a heat-treated IPPS specimen prior to and after an inhibited acid cleaning are

provided in Fig. C.1.

APPENDIX C. IPPS SPECIMEN CLEANING PROCEDURE 297

(a) Heavy oxidation of an IPPS specimen resulting from both theIC annealing process and water remaining on the surface of thespecimen after waterjet-cutting.

(b) IPPS specimen after inhibited acid bath treatment and dot plot-ting.

Figure C.1: a) ‘Before’ and b) ‘after’ photographs of a heat-treated IPPS specimen subjected to inhibited sulfuric acidcleaning.

Appendix D

NL-Means Denoising Parametric

Study

In order to make effective use of the NL-Means Denoising algorithm, a parametric

study was required to determine the optimal values for a window and patch size used

by the algorithm. The window size, t, determines the side length of a square region

(window) of pixels within an image that will be compared with other windows within

the image. A patch size parameter, f, determines the square pixel array sample size

within these windows that will be sampled and compared to the same patch locations

within other windows for contribution to the weighted average computation resulting

in image denoising.

For experimental purposes, it was ideal to use a test image with the parametric

study for which the method noise was known, i.e. the true pixel intensities that should

result from denoising were known. To accomplish this, a manually produced image

simulating a reconstructed slice of a failed DP steel mechanical testing specimen

was produced. This image, shown in Fig. D.1(a), would act as the standard for

298

APPENDIX D. NL-MEANS DENOISING PARAMETRIC STUDY 299

a noise free reconstruction. Thresholding of the slice was performed manually to

produce a standard for what a 100% accurate thresholding operation would result

in (Fig. D.1(b)). Gaussian noise of a standard deviation equivalent to that seen in

reconstructions of the match-head specimens was added to Fig. D.1(a) to simulate

true noisy reconstruction conditions (Fig. D.1(c)).

NL-means denoising was performed on the test image with added Gaussian noise

using 100 combinations of window and patch parameters, varying both with integers

from one to ten. Subsequently, these denoised images were thresholded using the

algorithm of Sahoo, Wilkins, and Yeager [129]. The mean squared error (MSE)

between the thresholds of the denoised image and the standard for 100% accurate

thresholding were compared. The results are presented graphically in Fig. D.2. Just

as Buades stated, the results indicate that a 7 x 7 similarity window is large enough

to be robust to noise, but small enough to preserve fine structure and detail [125].

Combined with a patch size of 1 x 1, the most optimal thresholding results in terms

of MSE were obtained. Visual comparison of the threshold masks of the denoised

images and the standard for 100% accurate thresholding confirmed that a window

size of 7 combined with a patch size of 1 produced the most accurate correlation and

retention of fine detail.

The last parameter that needed to be determined to use the NL-means algorithm

optimally was a filtering factor, h. A reconstructed and cropped slice of a failed DP

steel specimen was tested with the NL-means denoising algorithm with the newly

selected window size of 7 and patch size of 1. The filtering factor was varied through

a range of values to determine the optimal degree of filtering. It was determined, that

the standard deviation of the pixel greyscale intensities in regions correlating to steel


(a)

(b) (c)

Figure D.1: a) Standard NL-means denoising parametric studytest image for a noise free reconstruction. b) Standard for a100% accurate thresholding of the “voids” in a). c) Gaussiannoise added to a) to simulate noisy reconstructions producedby X-ray tomography of match-head specimens.


Figure D.2: Mean square error between the threshold masks(produced using the algorithm of Sahoo, Wilkins, and Yea-ger [129]) of images resulting from NL-means denoising ofFig. D.1(c) and the standard for 100% accurate thresholdingfrom Fig. D.1(b).


in reconstructed slices provided the best value for h in terms of flattening intensity

distribution while preserving detail (Fig. D.3). Based upon the recommendations of

Buades, this made sense; the optimal filtering parameter is dependent mainly upon

the standard deviation of noise in the image [124].


(a)

(b) (c) (d)

(e) (f) (g)

Figure D.3: a) Reconstructed and cropped slice of a failed DPsteel mechanical testing specimen. This image was denoisedwith the NL-means algorithm with a window size of 7, patchsize of 1, and filtering parameter, h, of the following factorsof the standard deviation, σ, of the greyscale intensities of theoriginal cropped slice: b) 0.42σ; c) 0.83σ; d) 1.0σ; e) 1.25σ; f)1.67σ; g) 2.08σ.

Appendix E

Complete IPPS Testing Results

Table E.1 below provides a complete list of the mean strains just prior to fracture in

the failure row for all the IPPS specimens which failed satisfactorily according to the

criteria outlined in Sec. 3.5.1.

304

APPENDIX E. COMPLETE IPPS TESTING RESULTS 305

Table E.1: Mean major and minor engineering strain just prior tofailure within the row of the grid of IPPS dots in which fractureoccurred. All IPPS specimens which failed satisfactorily areprovided, ordered according to treatment/condition.


Major Minor

7GA-R4 0.1141 -0.0051

7GA-R1 0.0974 -0.0047

7GA-T2 0.0843 -0.0051

7GA-T1 0.1022 -0.0041

9GA-R3 0.0658 -0.0002

9GA-R4 0.0795 -0.0012

9GA-R5 0.0641 -0.0007

9GA-T4 0.0451 -0.0005

9GA-T1 0.0524 -0.0007




Major Minor

7TP1-15-R4 0.2019 -0.0149

7TP1-15-T11 0.2423 -0.0162

7TP1-33-R11 0.1308 -0.0083

7TP1-33-T10 0.1369 -0.0067

7TP1-33-T9 0.1138 -0.0069

7TP1-33-T12 0.1244 -0.0076

7TP1-43-R3 0.0699 -0.0034

7TP1-43-R2 0.0577 -0.0039

7TP1-43-R5 0.0488 -0.0020

7TP1-43-R7 0.0685 -0.0028

7TP1-43-R1 0.0679 -0.0033

7TP1-43-T1 0.0609 -0.0029

7TP1-43-T5 0.0507 -0.0032

7TP1-43-T4 0.0467 -0.0032




Major Minor

9TP1-15-R7 0.1816 -0.0122

9TP1-15-R6 0.1323 -0.0078

9TP1-15-T1 0.1301 -0.0089

9TP1-15-T3 0.1423 -0.0094

9TP1-15-T2 0.1286 -0.0109

9TP1-15-T4 0.1671 -0.0134

9TP1-15-T5 0.1235 -0.0088

9TP1-33-R10 0.0965 -0.0046

9TP1-33-R12 0.0929 -0.0052

9TP1-33-R13 0.0723 -0.0042

9TP1-33-T10 0.0714 -0.0069

9TP1-33-T8 0.0814 -0.0044

9TP1-43-R11 0.0563 -0.0016

9TP1-43-R12 0.0452 -0.0035

9TP1-43-T7 0.0206 -0.0008

9TP1-43-T1 0.0179 -0.0007

9TP1-43-T4 0.0211 -0.0005

9TP1-43-T5 0.0207 -0.0007




Major Minor

7TP2-25-R4 0.1290 -0.0061

7TP2-25-T2 0.0963 -0.0066

7TP2-25-T4 0.1730 -0.0076

9TP2-37-R4 0.0962 -0.0030

9TP2-37-R3 0.0898 -0.0044

9TP2-37-T1 0.0783 -0.0028

9TP2-37-T5 0.0645 -0.0033

9TP2-37-T4 0.0481 -0.0017

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