NORTHWESTERN UNIVERSITY

Systems Design of Transformation Toughened Blast-Resistant Naval Hull Steels

A DISSERTATION

SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

for the degree

DOCTOR OF PHILOSOPHY

Field of Materials Science and Engineering

By

Arup Saha

EVANSTON, ILLINOIS

June 2004

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© Copyright by Arup Saha 2004 All Rights Reserved

iii

ABSTRACT

Systems Design of Transformation Toughened Blast-Resistant Naval Hull Steels

Arup Saha

A systems approach to computational materials design has

demonstrated a new class of ultratough, weldable secondary hardened plate steels

combining new levels of strength and toughness while meeting processability

requirements. A first prototype alloy has achieved property goals motivated by

projected naval hull applications requiring extreme fracture toughness (Cv > 85 ft-lbs

(115 J) corresponding to KId > 200 ksi.in1/2 (220 MPa.m1/2)) at strength levels of 150-

180 ksi (1034 – 1241 MPa) yield strength in weldable, formable plate steels.

A theoretical design concept was explored integrating the mechanism of

precipitated nickel-stabilized dispersed austenite for transformation toughening in an

alloy strengthened by combined precipitation of M2C carbides and BCC copper both at

an optimal ~3nm particle size for efficient strengthening. This concept was adapted to

plate steel design by employing a mixed bainitic/martensitic matrix microstructure

produced by air-cooling after solution-treatment and constraining the composition to

low carbon content for weldability. With optimized levels of copper and M2C carbide

formers based on a quantitative strength model, a required alloy nickel content of

6.5 wt% was predicted for optimal austenite stability for transformation toughening at

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the desired strength level of 160 ksi (1100 MPa) yield strength. A relatively high Cu

level of 3.65 wt% was employed to allow a carbon limit of 0.05 wt% for good

weldability.

Hardness and tensile tests conducted on the designed prototype

confirmed predicted precipitation strengthening behavior in quench and tempered

material. Multi-step tempering conditions were employed to achieve the optimal

austenite stability resulting in significant increase of impact toughness to 130 ft-lb

(176 J) at a strength level of 160 ksi (1100 MPa). Comparison with the baseline

toughness-strength combination determined by isochronal tempering studies indicates

a transformation toughening increment of 60% in Charpy energy. Predicted Cu particle

number densities and the heterogeneous nucleation of optimal stability high Ni 5 nm

austenite on nanometer-scale copper precipitates in the multi-step tempered samples

was confirmed using three-dimensional atom probe microscopy. Charpy impact tests

and fractography demonstrate ductile fracture with Cv > 90 ft-lbs (122 J) down to

− 400C, with a substantial toughness peak at 250C consistent with designed

transformation toughening behavior. The properties demonstrated in this first prototype

represent a substantial advance over existing naval hull steels.

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ACKNOWLEDGEMENTS

No word or phrase can completely express the gratitude I feel for all the

people who have made this journey such an amazing and wonderful experience. Nor

can I adequately thank all those people who have been directly or indirectly involved,

without writing another document as lengthy as this thesis. I can’t imagine surviving

through all the hardship of “graduate” life without the committed and unfailing help of

many. I would specially like to thank a few of them and apologize to those whom I fail

to mention.

Professor Greg Olson, you are simply the best. I still remember the excitement

on your face when you saw the 3D reconstruction of the austenite particle on the

copper precipitates and uttered spontaneously, “This is as good as it gets…” It is your

constant push towards the very limits in every aspect of research that has been my

inspiration over the years. Thank you for introducing me to the exciting and

challenging world of the systems design approach. I am forever indebted to you for

your guidance, encouragement and friendliness; they have meant a lot to me. Your vast

breadth of knowledge about apparently everything, analytical capability and extremely

sharp memory have always amazed me. I am truly honored to have the opportunity to

work with you, and the interactions with you have been very enriching for me.

My Mom and Dad, your constant enthusiasm in all my efforts and your belief

in me have helped me overcome a lot of pain and hardship. Nothing can appropriately

express my respect and gratitude towards you.

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Professors Morris Fine and Mark Asta for agreeing to serve on my committee

and providing helpful insights about this research. I deeply regret the sudden illness of

one of my committee members, Professor Brian Moran. I wish him a speedy recovery

and good luck for his health. I am thankful to Professor Horacio Espinosa for

accepting to be on my committee in such a short notice.

Dr. Gautam Ghosh for your patience and answering every little question I had.

I am thankful to you for helping me out with ThermoCalc and DICTRA during my

initial years.

Rick Kraemer, thank you for the help with the furnaces, seal-off and

dilatometry. Without your help none of the experiments would have been possible. I

would also like to thank Dr. Kathleen Stair for helping me with the salt-pot and

answering much-needed metallography questions, Mark Seniw for the help with tensile

testing and Jerry Carsello for the x-ray diffraction work. I am especially thankful to

Jesse Becker for taking good care of “thor”. Thang Bui in the machine shop for

providing the samples whenever I demanded them.

Dr. Herng-Jeng Jou, for providing useful expert advice about computational

modeling, Dr. Frode Stavehaug and Dr. Charlie Kuehmann for providing useful

experimental tips.

Jim Herman, your help makes all the complicated paperwork look so easy.

Thank you for giving your priority to every small detail and of course, I can’t thank

you enough for all the cups of coffee I had from your office. Thanks, Sharon for all the

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help with course registrations and paychecks. Joanna and the MSE staff for all the

administrative help.

Dr. Dieter Isheim, Stephan and Chantal in Seidman Research Group for being

so helpful while I was using the atom-probe. Your expert opinions helped to avoid a lot

of problems.

The Olson Group members, past and present. Jim and Rachel, you have been

excellent office-mates. Jin-won, thanks for all the long hours with the atom-probe and

the TEM. Abhijeet, for the company during lunch and being a good friend. Ben and

Dave you are an enthusiastic bunch and great company. I’ll miss office-basketball and

“would you rather” questions! Michelle, Matt and Yana, good luck with your research.

All my friends in NU, especially, JP, Naveen and Smita. Thanks for the fun

during the “dinner & movie” nights and the “board-game” parties.

My girlfriend, Mayurakshi for always being there for me. Life would have been

much difficult without the motivation and encouragement you provided during the

difficult times. I hope I can bring in the same enthusiasm and excitement in your life.

This research was supported by the Office of Naval Research under grant

number N00014–01–1–0953.

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TABLE OF CONTENTS

ABSTRACT iii ACKNOWLEDGEMENTS v LIST OF FIGURES xi LIST OF TABLES xx CHAPTER 1 INTRODUCTION 1

1.1 Goals and Context 4 1.2 Document Outline 8

CHAPTER 2 BACKGROUND 9

2.1 Design Approach 9 2.2 Bainitic Transformation 15 2.2.1 Carbon Redistribution under Paraequilibrium 18 2.2.2 Kinetics of Bainite Transformation 20 2.2.2.1 Bainitic Ferrite Nucleation and Growth 21 2.3 Strengthening Dispersions 29 2.3.1 Carbide Strengthening Dispersion 31 2.3.2 Copper Strengthening Dispersion 36 2.4 Transformation Toughening 45 2.3.1 Retained Austenite 51 2.3.2 Precipitated Austenite 55

CHAPTER 3 ALLOY DESIGN 61

3.1 Modeling Tools 62 3.1.1 ThermoCalc™ 62 3.1.2 CMD™ (Computational Materials Dynamics) 64

3.2 Design Approach 65 3.2.1 Strength Design 68

3.2.1.1 Quantitative Strengthening Contributions 68 3.2.1.2 M2C Carbide Strengthening 74 3.2.1.3 Copper Precipitation Strengthening 81

3.2.2 Transformation Toughening Design 83 3.2.3 Design Integration 90 3.2.4 Processing Considerations 94

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3.2.4.1 Solution Treatment Temperature and 94 Allotropic Transformations

3.2.4.2 Scheil Simulation for Microsegregation Behavior 95 3.2.4.3 Optimal Tempering Temperature 99

CHAPTER 4 MATERIALS AND 101

EXPERIMENTAL PROCEDURES

4.1 Materials 101 4.2 Experimental Procedures 102

4.2.1 Heat Treating 102 4.2.2 Metallographic Sample Preparation 103 4.2.3 Dilatometry 104 4.2.4 Microhardness Testing 105 4.2.5 Impact Toughness Testing 106 4.2.6 Tensile Testing 107 4.2.7 X-ray Diffraction (XRD) 109 4.2.8 Magnetometry 110 4.2.9 Electron Microscopy 113 4.2.10 Atom Probe/Field Ion Microscopy (AP-FIM) 114

CHAPTER 5 PROTOTYPE EVALUATION 119 5.1 Microsegregation and Hot-working behavior 119 5.2 Evaluation of Allotropic Kinetics 125 5.3 Isochronal Tempering Response 134 5.4 Toughness Optimization by Multi-step Tempering 143 5.5 Evaluation of Tensile Properties 150 5.6 Toughness – Temperature Dependence 153 5.7 Microstructural Characterization 159

5.7.1 X-ray Diffraction 160 5.7.2 Magnetometry 162 5.7.3 Transmission Electron Microscopy (TEM) 163 5.7.4 Three-Dimensional Atom Probe (3DAP) Microscopy 166

CHAPTER 6 CONCLUSIONS 187 6.1 Alloy Design 187 6.1 Prototype Evaluation 190

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CHAPTER 7 SUGGESTIONS FOR FUTURE WORK 194 7.1 Further Prototype Evaluation 194 7.2 Next Design Iteration 195 REFERENCE LIST 197 APPENDICES APPENDIX A 214

Design and Evaluation of Concept A Alloy APPENDIX B 226

Assessment of Interfacial Dissipation Effects at Reconstructive Ferrite-Austenite Interfaces

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LIST OF FIGURES

Figure 1.1 KIC toughness vs. RC hardness cross-plot for ultra-high strength

martensitic steels 2

Figure 1.2 KIC toughness vs. σy yield strength cross-plot for different classes of materials [10] 5

Figure 2.1 Systems design chart for blast resistant naval hull steels 10

Figure 2.2 Correlation between KIc and CV test results [134] for high Ni steels 12

Figure 2.3 Schematic representation of TTT diagrams illustrating the flat-tops of

bainite C-curves [15] 15

Figure 2.4(a) TEM micrograph of upper bainite with austenite (A) between the lath sub-units in Fe-0.6%C-2.0%Si steel transformed at 4000C (magnification, 40000X) [16] 16

Figure 2.4(b) TEM micrograph of lower bainite with midribs in a 1.10% C steel

transformed at 1900C for 5hours [16] 17

Figure 2.5 Schematic illustration of bainite microstructural features relevant to the kinetic description [15,26] 21

Figure 2.6 Schematic illustration of thermodynamics to determine the driving force

for bainitic transformation [21,26] 22

Figure 2.7 Schematic illustration of nucleation/growth velocity as a function of

bainite sub-unit length [26] 24

Figure 2.8 Schematic representation of potency size distribution for pre-existing

and autocatalytic defects respectively [26,30] 25

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Figure 2.9 Schematic representation of transition from shearing to looping mechanism as a function of particle size at constant volume fraction [12] 30

Figure 2.10 M2C carbide precipitation behavior in AF1410 steel as a function of

tempering temperature at 5100C following 1 hour solution treatment at 8300C [42] 33

Figure 2.11 Plot of maximum increase in yield strength vs. (volume fraction of precipitates)1/2. The points represent experimental data and the line is predicted by the theory for dislocation core radius equal to 2b(burgers vector). The arrow indicates the limit of solid solubility [59] 40

Figure 2.12 Lower yield stress of Fe-1.4 at% Cu alloy as a function of aging time at

5000C [60] 40

Figure 2.13 Mean particle diameter of copper precipitates as a function of the

square-root of tempering time in Fe-1.4 at% Cu alloy at 5000C [60]

41

Figure 2.14 Number density of copper precipitates as a function of tempering time

in Fe-1.4 at% Cu alloy at 5000C [60] 42

Figure 2.15 Volume fraction of copper precipitates determined from measured

number density and mean diameter as a function of tempering time in Fe-1.4 at% Cu alloy at 5000C. The relative amounts are coherent and non-coherent precipitates are shown schematically by dashed lines [60]

42

Figure 2.16 Mean composition of copper precipitates as a function of tempering time in Fe-1.4 at% Cu alloy at 5000C [61] 42

Figure 2.17 Schematic representation of stress-assisted and strain-induced regimes

for mechanically-induced transformation [95] 46

Figure 2.18 J-integral toughness enhancement at Ms

σ for precipitation-hardened metastable austenitic steels [9] 51

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Figure 2.19 Temperature dependence of the 0.2% tensile and compressive flow stresses [100] 54

Figure 2.20 Optimal Ni content vs. normalized austenite particle volume in Fe-

14Co-Ni system [100] 56

Figure 2.21 Conventional TEM dark field image of an interlath austenite film (A)

and dispersed intralath (B) austenite after 5070C/30minute + 4550C/7hour temper in AerMet100 [6] 57

Figure 2.22 Correlation of Cr and Ni from embedded austenite precipitates prior to

partitioning of STEM EDS signal into matrix and precipitate portions [6]. The data points are from multi-step tempered AerMet100 samples aged at 4050C for longer times after a short time 5070C nucleation treatment. 59

Figure 3.1 Schematic of the design optimization procedure 67

Figure 3.2 Power-law relationship relating hardness of related steels to yield stress

from experimental data from Foley [77] (circles), Kuehmann [2] (triangles) and Spaulding [138] (diamonds) shown in comparison to straight-line relationship for ideal plastic material 69

Figure 3.3 Graville diagram for determining susceptibility to HAZ cracking in

plate steels [137] 71

Figure 3.4 Change in hardness as a function of alloy carbon content for M2C

carbide strengthening contribution [12]. The arrows represent hardness increment of 175 VHN is achieved at C level of 0.05 wt% set for the alloy. Experimental results of other secondary hardening steels are shown 73

Figure 3.5 Graphical representation for contributions of the individual mechanisms

to achieve the strength goal equivalent to 389 VHN 73

Figure 3.6 Cr-Mo Phase Diagram at 9000C with alloy composition in atomic %:

Fe-0.234C-1.32Cu-6.21Ni-0.055V. This diagram shows the phase fields of the FCC austenite and FCC+M6C revealing that the M2C stoichiometry (red) line is well within the solubility limit 76

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Figure 3.7 Driving Forces (in kJ/mole) for M2C carbide nucleation contour plot

varying at% (Mo) and at% (Cr) with superimposed M2C stoichiometric (red) line at 500°C at alloy compositions at% Fe-0.234C-1.32Cu-6.21Ni-0.055V 77

Figure 3.8 Driving Force (in kJ/mole) for M2C carbide nucleation contour plot

varying at% (Mo) and at% (V) with superimposed M2C stoichiometric line at 500°C at alloy compositions at% Fe-0.234C-1.32Cu-6.2Ni

79

Figure 3.9 Mo-V Phase Diagram at 9000C with alloy composition in atomic %: Fe-0.234C-1.32Cu-6.2Ni. This diagram shows the phase fields of the FCC austenite and FCC+V3C2 revealing that the M2C stoichiometric (red) line is well within the solubility limit 80

Figure 3.10 Change in hardness as a function of alloy copper content for BCC

copper strengthening contribution [59]. Experimental results of other copper strengthened steels are shown. The dotted line represents the best-fit line for one-half power law given by equation (3.4) 82

Figure 3.11 Room temperature (300K) austenite stability plotted as a function of

Vickers Hardness Number (VHN). The shaded region shows our range of interest for austenite stability Concept B alloy corresponding to yield strength requirement of 150-180 ksi after extrapolation of data from previous alloys, AF1410 and AerMet100 87

Figure 3.12 Fraction of Ni in austenite and phase fraction of austenite in alloy vs.

mole fraction of Ni at 5000C with alloy composition in weight fraction: Fe-0.05C-3.65Cu-1.85Cr-0.6Mo-0.1V 89

Figure 3.13 Equilibrium composition of austenite as a function of alloy Cr content

(wt. fraction) at 5100C 90 Figure 3.14 Quasi-ternary section of the designed multicomponent alloy system at

5100C. Other alloying elements are fixed at Fe – 0.24C – 3.25Cu – 6.26Ni – 0.35Mo – 0.11V. The tie-triangles shown by thin solid lines indicate three-phase equilibrium between BCC Cu, austenite and ferrite. The dashed arrow traces out the trajectory of the austenite phase composition (solid dots) as a function of increasing alloy Cr content

92

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Figure 3.15 Equilibrium phase fractions at 5100C as a function of alloy Cr content (wt fraction) 93

Figure 3.16 Plot showing the variation of equilibrium mole fraction of different

phases in the alloy as a function of temperature, showing that the alloy is solution treatable at 9000C 94

Figure 3.17 Scheil simulation for evolution of the fraction solid with cooling for

designed alloy Fe-0.05C-6.5Ni-3.65Cu-1.84Cr-0.6Mo-0.1V (wt%) in comparison with equilibrium solidification 97

Figure 3.18 Scheil simulation for composition profile of each alloying element after

solidification for designed alloy Fe-0.05C-6.5Ni-3.65Cu-1.84Cr-0.6Mo-0.1V (wt%). Solid fraction corresponds to position relative to dendrite arm center 98

Figure 3.19 Room Temperature (300K) stability of austenite as a function of

tempering temperature. The required stability is predicted for 4900C. 99 Figure 4.1 Charpy V-notch impact specimen dimensions (Standard ASTM E23)

with longitudinal axis corresponding to the L-T orientation 107 Figure 4.2 Tensile test specimen dimensions (Standard ASTM E23) 108 Figure 4.3 An example of magnetometry data processing to determine saturation

magnetization 112 Figure 5.1 Optical micrograph of the as-received plate viewed transverse to the

rolling direction at the oxide-metal interface after etching with 2% nital 120 Figure 5.2 Optical micrograph of the hot-rolled plate viewed transverse to the

rolling direction at the centerline after etching with 2% nital 121 Figure 5.3 Higher magnification optical micrograph of the hot-rolled plate at the

centerline 122 Figure 5.4 Line profile compositions for as-received material from oxide-metal

interface 123 Figure 5.5 Optical micrograph showing the oxide scale in the as-received plate 125

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Figure 5.6 Relative sample length change and temperature trace during heating and cooling (quench) cycle from dilatometry experiment 126

Figure 5.7 Relative sample length change and temperature trace during heating,

cooling and isothermal hold at 3770C from dilatometry experiment 128 Figure 5.8 Volume fraction evolution of bainite as a function of time for isothermal

temperature of 3770C 129 Figure 5.9 Time-temperature-transformation (TTT) curve for bainite

transformation reaction 130 Figure 5.10 Experimental data fit to saturation volume fraction of bainite predicted

by model [26] using ASTM grain size number 15 132 Figure 5.11 Microstructure showing 60% bainite and 40% martensite mix after 2-

hour isothermal hold at 3600C during dilatometry 132 Figure 5.12 TTT diagram representing 1% bainite transformation calculated from

model [26] after calibration to fit experimental data 134 Figure 5.13 Isochronal (1 hour) tempering response of prototype alloy. The arrow

superimposed on the plot shows that the design objective is achieved by tempering at 5000C in agreement with design prediction. 136

Figure 5.14 Isochronal tempering response represented by Charpy toughness –

Vickers hardness trajectory. The label corresponding to each data point indicates the tempering temperature. 138

Figure 5.15 Hollomon-Jaffe Parameter correlating the hardness data obtained for

different tempering conditions in the overaged region 140 Figure 5.16 SEM micrograph of quasi-cleavage fracture surface for prototype

tempered at 4500C for 1 hour 141 Figure 5.17 SEM micrograph of ductile fracture surface for prototype tempered at

5250C for 5 hours 142 Figure 5.18 SEM micrograph of ductile fracture surface representing toughness

enhancement due to transformation toughening for prototype tempered at 5500C for 5 hours 142

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Figure 5.19 SEM micrograph of ductile fracture surface representing toughness enhancement due to transformation toughening for prototype tempered at 5750C for 5 hours 143

Figure 5.20 Multi-step tempering treatments designed to maximize transformation

toughening response represented by Charpy toughness – Vickers hardness trajectory. The label corresponding to each data point indicates the tempering time during the first tempering step. The condition for the second step is listed on the legend. 145

Figure 5.21 SEM micrograph of ductile fracture surface representing toughness

enhancement due to transformation toughening for the 5500C 30min + 4500C 5hrs multi-step tempering treatment 148

Figure 5.22 SEM micrograph of a primary void in the fracture surface of prototype

for 5500C 30min + 4500C 5hrs multi-step tempering treatment 149 Figure 5.23 True stress – true plastic strain response. The stress (σ) - plastic strain

(εp) behavior is shown by solid lines until uniform elongation and by dotted line after necking. 151

Figure 5.24 Hardness – Yield Strength Correlation developed from previous data.

The heavy black points represent data from current investigation. 153 Figure 5.25 Charpy impact energy absorbed as a function of testing temperature for

prototype tempered at 5500C 30min + 4500C 5hr. Toughness increment of 30ft-lb due to dispersed phase transformation toughening is shown. The toughness band defined by 5 hour and 10 hour single step tempering is superimposed. 155

Figure 5.26 SEM micrograph of quasicleavage fracture surface showing flat facets

with dimples and tear ridges for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 840C 157

Figure 5.27 SEM micrograph of mixed ductile/brittle mode fracture surface showing

microvoids with some tear ridges for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 400C 157

Figure 5.28 SEM micrograph of purely ductile mode fracture surface showing

primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 200C 158

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Figure 5.29 SEM micrograph of purely ductile mode fracture surface showing primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at 00C 158

Figure 5.30 SEM micrograph of purely ductile mode fracture surface showing

primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at 1000C 159

Figure 5.31 XRD Pattern of prototype tempered at 5500C for 5 hours (lower plot)

scanned from 630 to 670 from 71.50 to 77.50 2θ angles shown in comparison with standard (upper plot) containing 4 vol% austenite

161 Figure 5.32 Bright-field TEM micrograph showing martensite laths in multi-step

tempered prototype at 5500C for 30min + 4500C for 5hrs 164 Figure 5.33 Higher magnification bright-field TEM micrograph showing martensite

laths in multi-step tempered prototype at 5500C for 30min + 4500C for 5hrs 164

Figure 5.34 Bright-field TEM micrograph showing dense dislocation structure

within a martensite lath in multi-step tempered prototype at 5500C for 30min + 4500C for 5hrs 165

Figure 5.35 3DAP reconstruction for prototype tempered at 4500C for 1 hour. The

elements in the reconstruction are indicated by their color code. Iron is not shown to provide more clarity in viewing the particles. z is the direction of analysis. 169

Figure 5.36 3DAP reconstruction for prototype tempered at 5000C 30min + 4500C

5hrs. The elements in the reconstruction are indicated by their color code. Iron is not shown to provide more clarity in viewing the particles. z is the direction of analysis. 170

Figure 5.37 3DAP reconstruction for prototype tempered at 4500C for 1 hour

showing copper precipitates defined at 10 at % isoconcentration surface overlaid on atomic positions of copper atoms. All other atoms in the reconstruction are not shown. z is the direction of analysis. 171

Figure 5.38 3DAP reconstruction for prototype tempered at 5000C 30min + 4500C

5hrs showing copper precipitates defined by 10 at % isoconcentration surface overlaid on atomic positions of copper atoms. z is the direction of analysis. 172

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Figure 5.39 Example of a cross-section of analyzed volume for prototype tempered at 4500C for 1 hour showing copper precipitates in red. All other atoms in the reconstruction are hidden. 174

Figure 5.40 Example of a cross-section of analyzed volume for prototype tempered

at 5000C 30min + 4500C 5hrs showing copper precipitates in red. All other atoms in the reconstruction are hidden. 174

Figure 5.41 Proxigram of all the solute species detected in the 4500C 1hr temper

specimen with respect to 10 at% copper isoconcentration surface in the analysis volume 180

Figure 5.42 Proxigram of all the solute species detected in the 5000C 30min + 4500C

5hrs temper specimen with respect to 10 at% copper isoconcentration surface in the analysis volume 181

Figure 5.43 3DAP reconstruction for prototype tempered at 5000C 30min + 4500C

5hrs showing austenite defined by 10 at % Ni level isoconcentration surface overlaid on atomic positions of nickel and copper atoms. z is the direction of analysis. 183

Figure 5.44 One-dimensional composition profile along the atom-probe analysis

direction in the 5000C 30min + 4500C 5hrs temper specimen with respect to 10 at% copper isoconcentration surface in the analysis volume. z is the direction of analysis. 184

Figure 6.1 Toughness-yield strength comparison plot of Blastalloy160 with other

commercial and experimental steels 191

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LIST OF TABLES

Table 3.1: Target Chemical Driving Force (∆Gch) + Frictional Work (Wf) Value 86

Table 3.2: Amplitude of microsegregation with respect to each alloying element predicted by Scheil simulation at 95% solidification 98

Table 4.1A: Designed and Measured Composition (in wt. %) of Concept A alloy 102 Table 4.1B: Designed and Measured Composition (in wt. %) of Concept B alloy 102 Table 5.1: Saturation volume fraction of bainite as a function of isothermal

temperature 129

Table 5.2: Room temperature tensile properties of prototype 151 Table 5.3: Fitting parameters for Hollomon power law equation (5.1) from tensile

data of prototype (Fig. 5.23) 153 Table 5.4: Austenite Volume fraction measured by magnetometry for different

heat treatment conditions 163 Table 5.5: Comparison between the actual composition of prototype and the

compositions determined by 3DAP analysis 168 Table 5.6: Average copper precipitate compositions determined by 3DAP analysis

for selected heat treatment compositions. ND means not detected 176 Table 5.7: Average matrix compositions determined by 3DAP analysis for selected

heat treatment compositions compared with equilibrium prediction from ThermoCalc. ND means not detected 177

Table 5.8: Average austenite composition determined by 3DAP analysis for

selected heat treatment compositions compared with equilibrium prediction from ThermoCalc. ND means not detected 185

1

1. INTRODUCTION

Over the years, the multi-institutional university/government/industry

interdisciplinary Steel Research Group (SRG) program has directed its research at

scientific principles for the design of new classes of steels driven by specific property

objectives of importance to the government and industry. With scientific advances in

the past century, the property-driven view of structure and processing for the creation

of value has motivated the development of a systems approach in the design of

materials [1]. The systems approach to computational design of materials combines

materials science, quantum physics and continuum mechanics in the integration of

process/structure/property/performance relations for predictive design of high

performance steels as multilevel dynamic structures.

Throughout the history of materials development, there has been an

ever-increasing need for stronger, tougher, more fracture resistant and easily weldable

plate steels for structural applications at minimal cost. Unfortunately, however, any

increase in strength is rarely achieved without concomitant decreases in toughness and

ductility, which limits the utility of most ultrahigh-strength steels. The best

combinations of strength and toughness have usually been obtained from martensitic

microstructures as shown in Fig.1.1. High strength bainitic steels have not been as

successful in practice because of the coarse cementite particles in bainite that are

detrimental to toughness. If a mixed microstructure consisting of bainitic ferrite

separated by carbon-enriched regions of austenite is developed, it could be an ideal

2

combination for achieving our quantitative property objectives. The primary benefit

motivating the research of air-hardened steels containing bainite/martensite mixtures is

the ease of processing, which finally leads to a product with good performance at a

relatively lower cost. There is then the possibility of improving the strength and

toughness simultaneously using fine-grained bainitic ferrite plates and enhancing the

toughness by transformation toughening effects. Further improvements of strength can

be achieved with co-precipitation of alloy carbides and bcc copper for easily weldable

low-carbon steels [3].

Figure 1.1 KIC toughness vs. RC hardness cross-plot for ultra-high strength martensitic steels

3

It is now well established that the interaction of deformation-induced

martensitic transformation of dispersed austenite with fracture-controlling processes

such as microvoid induced shear localization results in substantial improvements in

fracture toughness called Dispersed Phase Transformation Toughening (DPTT). This is

the toughening mechanism modeled and investigated in this work. Transformation

toughening is partly attributed to modification of the constitutive behavior of the

matrix and partly to a modification of the stress state because of transformation volume

change [100]. Both the transformation behavior and the toughening effects are

controlled by the stability of the austenite dispersion. For transformation toughening,

the required stability of the austenite dispersion is quite high and can be achieved only

by size refinement and compositional enrichment of the austenite particles. The size

influences the characteristic potency of nucleation sites in the particles while the

composition influences the chemical driving force and interfacial friction for the

martensitic transformation. The size refinement and the compositional enrichment of

the austenite can be controlled with heat treatments such as multi-step tempering.

Combining new levels of strength, toughness and hydrogen resistance

while meeting processability requirements, the design addressed here will focus on a

new class of ultratough, weldable secondary-hardened bainitic plate steels for blast

resistant hull materials for the navy to adapt to a new “age of terror”.

4

1.1 Goals and Context

Looking ahead to the projected naval hull material requirements in the

year 2020, the primary design objectives motivating this research will be the

achievement of extreme impact fracture toughness (Cv > 85 ft-lbs corresponding to

fracture toughness, KId > 200 ksi.in1/2 and KIc > 250 ksi.in1/2) at high strength levels of

150-180 ksi yield strength in weldable, formable plate steels with high resistance to

hydrogen stress corrosion cracking (KISCC/KIC > 0.5). Because of difficulties in

measurement of KId and KIc fracture toughness at such extreme levels, toughness of

prototypes has been assessed by Charpy impact energy (CV) absorption measurements;

details of the KIc – CV and KId - CV toughness correlation will be discussed in Chapter

2. The primary design goals are marked by the star in the cross-plot of KIc fracture

toughness and yield strength illustrated in Fig. 1.2. This design aims to substantially

expand the envelope marked as “steels” to the top right corner of the plot.

5

Figure 1.2 KIC toughness vs. σ yield strength cross-plot for different classes of materials [10]

The initial research will focus on secondary hardening mixed

bainitic/martensitic steels produced as air-cooled plates, which appears to be the most

promising candidate class of steels.

Earlier SRG research [5,6] has emphasized achieving acceptable

toughness and hydrogen resistance in much higher strength steels needed for

lightweight aviation applications, integrating quantum mechanical modeling for the

enhancement of hydrogen resistance. With a new priority on toughness, the

“Cybersteel 2020” program of the ONR (Office of Naval Research) Grand Challenge

6

in “Naval Materials by Design”, of which this research is a part, expands quantum

mechanical modeling beyond intergranular hydrogen fracture resistance to address

alloying effects in transgranular cleavage resistance and the role of metal/ceramic

adhesion in voiding/microvoiding phenomena, integrating the latter into multiscale

mechanics of ductile fracture simulation. The resulting toughness models will be

combined with existing computational thermodynamics based models for phase

selection and microstructural dynamics in the integrated systems design of new alloys.

The design approach will build on the primary microstructural strategy ultimately

adding new optimization to both the dispersion geometry and metal/ceramic interfacial

characteristics associated with the combined effect of primary inclusions and

secondary grain-refining dispersions.

Looking at the overall program in a broad perspective, it involves a multi-

disciplinary team working together closely to insure purposeful modeling activities

supporting the materials design strategy of the SRG. Studies on grain-refining particle

dispersions are being performed for different systems starting with TiC by Professor

Freeman’s physics group at Northwestern University for selection of metal/ceramic

interfaces of importance to particle dispersions in steels. Thereafter, CSL-based slab

supercells are being constructed for FLAPW (Full-potential Linearized Augmented

Plane Wave) and FLMTO (Full-potential Linear Muffin-Tin Orbital) total energy

quantum mechanical calculations. Professors Liu and Moran in mechanical

engineering at Northwestern University are focusing on representation of particle

7

dispersion geometries based on current steel microstructures and subsequently assess

the roles of dispersion geometry and interfacial properties in multiscale mechanics

simulation of ductile fracture toughness. In parallel with these efforts, the materials

design synthesis of this thesis research integrates materials science design models such

as precipitation strengthening and dispersed phase transformation toughening. To

achieve the required strength level in weldable low-carbon air-hardened bainitic

structures, this will involve a combination of overaged alloy carbides and precipitated

Cu. Conceptual designs also integrate previous models of transformation toughening.

The ultimate design integration of the ONR project will thus combine new quantum

physics and multiscale mechanics models with our existing suite of computational

materials science design models to address new phase selection and quantitative

microstructural design for a new generation of “cybersteels” to meet the navy’s new

requirements.

8

1.2 Document Outline

This work applies the systems based approach to design ultratough high-

strength weldable plate steels by utilizing existing models where applicable and

developing new models where needed in order extend the properties of the existing

steels to higher performance levels. Chapter 2 gives a detailed description of the

systems based design approach and describes each of the subsystems involved in the

design with the current level of quantitative modeling available. Chapter 3 describes

the alloy design process detailing the concepts used. The material and experimental

procedures used in this study are outlined in Chapter 4. Chapter 5 presents the

properties obtained from the evaluation of the prototype and validates the design based

on microstructural characterization. Chapters 6 and 7 discuss the conclusions of this

investigation and suggestions for future research respectively.

9

2. BACKGROUND

2.1 Design Approach

Based on Cyril Smith’s [7] modern view of materials structure as

“universal multilevel structure with strong interactions among different levels…” this

materials design approach breaks down the complex nature of the structural hierarchy

to better understand the structure and property relations underlying the technological

and economic value of materials. Once the final goal has been set, the structure is

broken down into subsystems with graphical representation of the interactions through

a system flow block diagram. The flow block diagram represents the key

microstructural subsystems, links them to the properties they control and then to the

stages of processing that govern their dynamic evolution. Because of the complex

nature of materials, it should be realized that the interaction between the subsystems is

as important as the subsystems themselves. The systems analysis is then applied to

identify and prioritize the key structure-property and processing-structure relations.

Optimization of such a complicated system can thus be effectively achieved by the

method of systems design. Fig. 2.1 describes the systems approach that will be used in

the thesis to design steel with the specified strength, toughness levels as well as

optimum weldability and hydrogen resistance.

10

PROCESS STRUCTURE PROPERTIES

PERFORMANCE

MatrixBainitic Ferrite / Martensite

Morphology (lower bainite/lath martensite)Composition

Kinetics

MatrixBainitic Ferrite / Martensite

Morphology (lower bainite/lath martensite)Composition

Kinetics

Grain Boundary ChemistryCohesion Enhancement: B,W

Impurity Gettering: La,Zr

Grain Boundary ChemistryCohesion Enhancement: B,W

Impurity Gettering: La,Zr

InclusionsMultiphaseInterface

Distribution

InclusionsMultiphaseInterface

Distribution

Austenite DispersionStability (Size, Composition)

AmountDilatation

Austenite DispersionStability (Size, Composition)

AmountDilatation

Grain Refining Dispersion

d/fMicrovoid Nucleation Resistance TiCx

Grain Refining Dispersion

d/fMicrovoid Nucleation Resistance TiCx

Grain Refining Dispersion

d/fMicrovoid Nucleation Resistance TiCx

Strengthening Dispersion(Mo,Cr,V,Fe)2C

BCC Cu precipitationDissolve para-eq Fe3C, M6C, M23C6

Strengthening Dispersion(Mo,Cr,V,Fe)2C

BCC Cu precipitationDissolve para-eq Fe3C, M6C, M23C6

Strengthening Dispersion(Mo,Cr,V,Fe)2C

BCC Cu precipitationDissolve para-eq Fe3C, M6C, M23C6

Tempering

Cooling Rate

Solidification

Deoxidation

Refining

Solution Treatment

Hot Rolling

Toughness

Strength

Weldability

HydrogenResistance

Figure 2.1 Systems design chart for blast resistant naval hull steels

With toughness being a major priority for this design, the matrix was

chosen as a secondary hardened bainite/martensite mixture, in which cementite

particles should be eliminated, as they are detrimental to the toughness of the steel.

Bainite may have a large variety of morphologies and have intermediate properties

between pearlite and martensite. These intermediate properties of bainite offer more

degrees of freedom by designing the kinetics of formation to achieve the desired matrix

toughness. In addition, an optimum-stability austenite dispersion in the

11

bainitic/martensitic matrix can also help in increasing the toughness of the steel.

Several investigators [8,9] have reported exceptionally large fracture toughness values

in high-strength precipitation-hardened metastable austenitic steels. This remarkable

increase in the fracture toughness is attributable to the process of transformation

toughening which will be discussed in greater detail later. Recent SRG studies [128]

have also shown that fine Ti(C,N) inclusions have contributed to increasing the

fracture resistance by delaying the coalescence of microvoids among the primary

voids. The Ti(C,N) particles also have a grain refining effect helpful for strength and

toughness. Studies by Garrison [140] have suggested that the resistance to primary

void formation and coalescence is proportional to inclusion spacing. It is thus desirable

to reduce the volume fraction of inclusions or coarsen inclusions for a given volume

fraction. This can be achieved by clean melt practices and tight composition control.

However, engineering design fracture toughness parameters like KIc and KId are

difficult and expensive to measure. Thus for preliminary design analyses, small-scale

inexpensive fracture measurements like Charpy V-notch impact energy (CV) values can

be used to estimate KIc and KId. Studies of fracture toughness dependence on loading

rate measured over a temperature range [134] have shown that KIc fracture toughness

values under static and intermediate loading are about 20% higher than the KId

measured under impact loading. On the basis of various previous investigations,

Barsom and Rolfe [134] established a correlation between KIc and CV test results:

(2.1) VIC ACK =2

12

where A is a constant of proportionality. Fitting equation (2.1) to results from high Ni

steels shown in Fig. 2.2, an empirical correlation can be established for the class of

steels explored in this study.

Figure 2.2 Correlation between KIc and CV test results [134] for high Ni steels

According to this relationship, the CV impact toughness objective of 85 ft-lbs

corresponds to a KIc fracture toughness under static loading of 250 ksi.in1/2 and a

dynamic KId of 200 ksi.in1/2.

13

A fine carbide dispersion must be obtained in order to achieve the

desired strength level. Coherent M2C carbides have been used in secondary hardened

steels that are currently in use [11]. Previous work [12] to optimize the carbide particle

size for maximizing the strength has shown that 3nm carbide precipitates provide

minimum distance between particles within the Orowan looping regime for a

maximum barrier to dislocation movement. Thermodynamics and kinetics of carbide

precipitation has to be controlled to obtain fine-enough M2C carbide dispersion. The

driving force for M2C nucleation should be maximized by proper control of the amount

and ratio of carbide formers in the alloy to refine the M2C particle size. Cementite

dissolution must accompany M2C carbide precipitation to attain the desired toughness

levels because coarse cementite particles are extremely deleterious as microvoid

nucleation sites. Tempering times should also be minimized to prevent impurity

segregation at grain boundaries.

Even if we maintain low alloy carbon levels, steels containing higher

alloying content might help in achieving the desired combination of mechanical

properties, but they reduce the weldability of the material by increasing hardenability.

For any structural material, the heat-affected zones (HAZ) adjacent to the welded joints

are considered to be the weakest links. Weldability of steels is controlled by both the

matrix and the strengthening dispersion structures. As a rule of thumb, for adequate

weldability of the steel C content of the alloy should be kept below 0.15 wt %. This in

turn limits the C available for M2C strengthening. For the bainitic matrix, if we modify

14

the hardenability of the steel, we can obtain bainite with a much lower cooling rate.

This becomes a trade off since weldability can deteriorate as the hardenability

increases.

Ultra-high strength steels are prone to a decrease of fracture toughness

in aqueous environments due to hydrogen assisted cracking. This reduction of

toughness is caused by intergranular brittle fracture associated with impurity

segregation to grain boundaries, which may reduce toughness of the steel by as much

as 80% in a corrosive environment. The common impurities in steel are P and S, both

of which are embrittlers since they have lower free energy on a surface than at a grain

boundary. So the most effective way of reducing them is by cleaner processing

techniques or impurity gettering. Impurity gettering can tie up P and S as stable

compounds formed during solidification. La and Zr have been found to be effective

impurity gettering elements. Another approach to minimize impurity effects is by

design of grain boundary chemistry. By placing elements like W and Re [13,14]

preferentially on the grain boundaries that enhance grain boundary cohesion is

beneficial to the stress corrosion cracking resistance. Small amounts of B also help in

grain boundary cohesion.

15

2.2 Bainitic Transformation

Bainite grows from austenite as a non-lamellar aggregate of ferrite laths

or platelets and carbides forming in a coupled manner. These aggregates of bainitic

ferrite laths/platelets are called sheaves and the individual sub-structures are called

sub-units. Within a sheaf, the sub-units tend to be in a common crystallographic

orientation. Bainite forms either during the isothermal transformation condition or

athermal treatments at cooling rates too fast to generate pearlite but not rapid enough to

produce martensite. Fig 2.3 [15] gives a schematic representation of a TTT (Time-

Temperature Transformation) diagram showing flat tops on the bainite curve

representing bainite start (BS) temperature.

Figure 2.3 Schematic representation of TTT diagrams illustrating the flat-tops of

bainite C-curves [15]

16

Depending on the cooling rate or the isothermal hold temperature, there

are two major morphologies of bainite, upper bainite and lower bainite. Upper bainite

forms at temperatures just below that of pearlite formation, while lower bainite forms

at temperatures closer to martensite start (MS) temperature. Fig. 2.4 [16] displays

representative TEM micrographs of upper bainite (a) and lower bainite (b).

Figure 2.4(a) TEM micrograph of upper bainite with austenite (A) between the lath sub-units in Fe-0.6%C-2.0%Si steel transformed at 4000C (magnification, 40000X) [16]

17

Figure 2.4(b) TEM micrograph of lower bainite with midribs in a 1.10% C steel transformed at 1900C for 5hours [16]

The mechanism of bainitic transformation has been the subject of

numerous investigations and studies [17-19]. Bainitic transformation occurs in two

separate stages that consist of the growth of ferrite followed by precipitation of

carbides, unlike pearlite where ferrite and cementite grow cooperatively. This means

that growth rates are coupled in a manner that excess solute displaced during ferrite

growth is incorporated in cementite. The relatively high dislocation density of bainitic

ferrite indicates that it forms by a shear displacive mechanism. But unlike martensitic

transformations, in which concentrations of both interstitial and substitutional atoms

18

are identical to those of parent austenite, bainitic ferrite seems to have different carbon

contents compared to austenite although the substitutional alloy content is the same.

This results from the significant difference in the mobility of carbon atoms and

substitutional atoms in the bainitic transformation range and is known as the

paraequilibrium condition. Thus, bainite is considered to form by a coupled

diffusional/displacive transformation mechanism [20-21]. After nucleation of the

bainitic laths, growth is limited by the partitioning of carbon into the remaining

austenite. As the austenite becomes enriched in carbon, bainitic growth rate slows

down as the austenite carbon content approaches the paraequilibrium limit at which

point bainitic ferrite ceases to grow until carbides precipitate.

2.2.1 Carbon Redistribution under Paraequilibrium

The formation of bainite enriches the carbon content of the residual

austenite. Substitutional alloying elements are unable to partition during transformation

in the time scale of experiments. Since carbon is a fast diffusing interstitial element it

redistributes between phases and reaches equilibrium under “paraequilibrium”

constraint. Bainite formation begins with nucleation of ferrite of paraequilibrium

carbon concentration, so the residual austenite is enriched with respect to carbon [15].

When substitutional alloying elements redistribute during transformation it occurs

under orthoequilibrium. Paraequilibrium is defined as a kinetically constrained

19

equilibrium in which the diffusivity of the substitutional species is negligible compared

to that of the interstitial species.

The paraequilibrium constraint is useful in modeling the

thermodynamics and kinetics at different stages prior to the bainite transformation

[22]. Since substitutional alloying elements are not allowed to partition, the

thermodynamic behavior of these elements is expressed by one hypothetical element

N. Thus, the paraequilibrium model is defined by a uniform carbon potential and

uniform site fraction of substitutional elements across the transforming interface. For

ferrite(α)/austenite(γ) transformation, the thermodynamic conditions for

paraequilibrium are given by

γα µµ CC = (2.2)

γαjj yy = (2.3)

)()( ∑ ∑⇒=⇒j j

jjNjjN yy γγαα µµµµ (2.4)

where µip represents the chemical potential of elements i in phase p and yj represents

the site fraction of the substitutional elements j (= Fe, Al, Co, Cr, Cu, Mn, Mo, Nb, Ni,

Si, Ti, V, W) in the corresponding phase.

20

For a system containing both substitutional(j) and interstitial(C and N)

species, the site fractions are related to the mole fractions(x) by:

C

jj x

xy

−=

1 (2.5)

C

CC x

xqpy

−=

1 (2.6)

where, p=1 and q=3 for ferrite and p=q=1 for austenite, according to the two sublattice

model [23].

2.2.2 Kinetics of Bainite Transformation

Unlike martensitic transformation, the progress of bainite

transformation can be represented by a C curve on a TTT diagram with a well-defined

incubation period before isothermal transformation [24]. Since bainite forms at a more

elevated temperature than martensite, less driving force is available for transformation

of austenite. Ko and Cottrell [25] suggested that coherent growth of bainite can occur if

the strain due to density change is relieved by diffusion of carbon from bainite that

would lead to reduction of free energy. Bhadeshia [15] summarized the bainite reaction

as a coupled mechanism of diffusion and interface migration so that the carbide

precipitation within ferrite (for lower bainite) or carbon rejection to austenite (for upper

bainite) takes place at the moving interface. Fig 2.5 gives a schematic view relevant to

the kinetic description of the bainite reaction.

21

Figure 2.5 Schematic illustration of bainite microstructural features relevant to the kinetic description [15,26]

2.2.2.1 Bainitic Ferrite Nucleation and Growth

As bainite transformation occurs by coupled diffusional/displacive

transformation, the driving force to form bainite consists of two terms: one is to

overcome the critical energy associated with the shape change of lattice from austenite

to bainitic ferrite and the other is the carbon partitioning from supersaturated bainitic

ferrite to retained austenite. This is illustrated schematically in Fig 2.6 and is

represented by equations (2.7) and (2.8) where x0 is the nominal carbon composition,

xα and xI are the carbon concentrations of α and γ at the interface respectively,

is the chemical driving force to form bainite with carbon concentration ),( TxGchem ααγ →∆

22

xα at temperature T, is the energy dissipation associated with carbon diffusion

from bainite to retained austenite,

dG∆

critG∆ is the critical driving force for displacive

transformation.

Figure 2.6 Schematic illustration of thermodynamics to determine the driving force for bainitic transformation [21,26]

)(2),( αµααγ σ xW

ndGGGGTxG el

dcritdchem +++∆=∆+∆=∆ → (2.7)

where is the elastic strain energy per unit volume associated with distortions in the

nucleus interface plane, σ is the nucleus specific interfacial energy, n is the potency of

a nucleation site expressed as thickness in numbers of crystal planes, d is the crystal

interplanar spacing and W

elG

µ is the frictional work of interfacial motion.

23

)()()()()1( 00 ICCIMMd xxxxxxG γγα

γγα µµµµ −+−−=∆ (2.8)

where and are the chemical potentials of alloying elements in γ with

carbon concentrations x

)( 0xMγµ )( IM xγµ

0 and xI respectively.

Bainite transformation starts at heterogeneous nucleation sites of

existing defect embryos in austenite, which grow as individual sub-units coupled with

carbon diffusion at the interface. This transformation accompanied by shear causes

plastic deformation leading to large dislocation density both in the parent and product

phases. The forest dislocation friction stops the motion of the glissile sub-unit, which

grows only to a limited size, much smaller than the austenite grain size. Grujicic et al

[27] established the theory of the detailed mechanism of halt by plastic strain. Thus,

the sheaf as a whole grows by repeated nucleation of new sub-units from the tip of

those already formed. Fig. 2.7 illustrates the nucleation and growth of a sub-unit

showing the dependence of nucleation velocity on the length of sub-unit.

24

Figure 2.7 Schematic illustration of nucleation/growth velocity as a function of

bainite sub-unit length [26]

Heterogeneous nucleation due to the displacive mechanism becomes

more frequent as defects are introduced into austenite by deformation although their

growth is soon terminated as the moving interface encounters accumulated

dislocations. Accelerated transformation rate in the initial stage of transformation can

be explained by the shifted distribution of defect potency in both pre-existing and

autocatalytically formed sites, while the average volume of sub-units is almost constant

and independent of volume fraction [28]. Based on previous studies on potency

distribution of pre-existing nucleation [29] that increases monotonically with

decreasing defect potency following an exponential function, Lin et al [30] found that

25

the autocatalytic defect potency distribution follows a Gaussian function. The defect

potency size distribution of both pre-existing and autocatalytic defects is given in Fig.

2.8 where nm* and nb* are the respective critical defect potency sizes for martensitic

and bainitic phase transformations. Both of these parameters can be determined from

the critical condition of nucleation. The accumulated distributions for the preexisting

and autocatalytic defect potencies can be calculated by equations (2.9) and (2.10)

respectively.

Figure 2.8 Schematic representation of potency size distribution for pre-existing

and autocatalytic defects [26,30]

26

The cumulative density of preexisting nucleation defects is represented

by the exponential function [31]:

).exp()().exp()()( 121

0 nDkknNndnNnN mv

nii αα −+=−=′= −

∞

∫ (2.9)

where Nv0 is the total number density of preexisting defects with all potencies, α is a

factor that represents the distribution shape and k1, k2 and m1 are parameters that

describe the grain-size (D in meters) dependence of Nv0.

The autocatalytic defect size distribution can be described as a Gaussian distribution

[30]:

⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛ −−== ∫

∞

σ21

21)()( max

nnerfPndnPnPn

ii (2.10)

where, Pmax, ⎯n and s are the amplitude, mean and standard deviation of the

distribution respectively, each of which depend on the grain size.

Olson et al [21] proposed a kinetic model for bainitic transformation by

considering transformation of the substitutional lattice by a displacive mechanism

while carbon atoms undergo paraequilibrium partitioning between the parent and

product phases. They assumed that the rate at which the ferrite(α)-austenite(γ) interface

moves depends both on the intrinsic mobility and the ease with which the partitioned

solute (i.e., carbon) can diffuse ahead of the moving interface. Since both the processes

are coupled, the interfacial velocity calculated from interfacial mobility must equal that

computed from the diffusion ahead of the interface. As there are three unknowns to

27

)

solve for (supersaturation, austenite composition at the interface and growth rate) but

only two velocity laws available, they attempted a more complete analysis by utilizing

an additional interface response function derived by Aziz [32-34] for the case of solute

trapping during rapid solidification processes. Thus, based on these interface response

functions two kinetic relationships were set up as given by

(2.11) kdn VVnV ==)(

Vn(n) is the nucleation velocity for potency n as discussed earlier;

Vd is the steady-state growth velocity of ferrite of constant composition xα in a steel of

composition⎯x (transformed at temperature T) expressed in terms of carbon

concentration in austenite at the interface xI ; and

Vk is the velocity response function determined from solute trapping law relating

interfacial velocity to the partitioning coefficient kp(=xα/xI).

The set of three non-linear equations, two kinetic equations given by equation (2.11)

and the thermodynamic driving force equation (2.7) are used to solve for the three

unknowns Vn (n), xa and xI.

Considering the sequential growth characteristics of bainite sub-units as

in Fig 2.7, the nucleation velocity of the defect embryo is the rate controlling term in

determining the bainite start kinetics. The number of nucleating defects available to

operate at any given time and temperature per unit volume of alloy has been described

as [35]:

1)(( bvbiit fNfPNN −−+= (2.12)

28

which leads us to the evolution equation for the number of sub-units (Nv) of potency n

)()1)](()()()[()()(

bbvbiinv fVfnNfnPnNnVnCdt

ndN−−′+′= (2.13)

with Nv(n) = 0 for all n > nb* at t = 0.

fb : Volume fraction of bainite, ∑= ))(()( nNfVf vbb

V (fb) : Mean volume of bainite sub-unit

C (n) : Time scaling factor with geometry effects due to defect size (calibrated against

experimental data)

and Ni and Pi are defined in equations (2.9) and (2.10) respectively.

For a small volume fraction of bainite (fb) at the beginning of bainite

transformation, the number density (Nv(n)) of defects already transformed to bainite is

considered negligible. Thus equation (2.13) can be simplified to:

)1)(( bbb fBfA

dtdf

−+= (2.14)

where A and B are coefficients derived by approximating equation (2.13), and the

bainite start time is computed when the volume fraction of bainite (fb) is 0.01.

Based on the evolution equation (2.12), an executable program (“Runbmk”) to predict

bainite transformation kinetics under isothermal condition was developed by Jou et al

[26].

29

2.3 Strengthening Dispersions

The most effective mechanism of strengthening in high strength alloys

is achieved through fine dispersion of precipitates. The extent of strengthening depends

on particle size and volume fraction (mean particle separation distance is defined by

these two factors), particle shape, chemical and mechanical properties and coherency

with the matrix [36]. These factors determine the degree and the means of particle-

dislocation interaction. For cases in which the dislocation shears a particle, the

strengthening mechanisms by precipitate dispersions include coherency strain,

modulus effect, chemical, stacking fault and order hardening. Non-deforming hard

particles that cannot be cut force the dislocations to bow around them by the Orowan

mechanism.

The contribution to strength of the precipitate dispersion depends on

whether dislocation “cutting” or “bowing” is the predominant slip mechanism.

Coherent boundaries of small size or of low elastic modulus precipitates generally

result in dislocations passing through or cutting the particle. As the particles grow or

the particle-matrix interface becomes disordered, shearing becomes more difficult. The

increase in size usually leads to loss of coherency and does not permit the dislocation

to pass through the particle. Thus, there occurs a transition between the shearing

mechanism to Orowan bypass. Dislocations now have to bow around the particles.

While the dislocation is pinned by the particle, the free segments continue to glide

under applied stress. After the particle is circumvented the dislocation ends combine

30

and leave behind a loop. The Orowan mechanism of particle bypass becomes easier as

the particles coarsen at a constant volume fraction and consequently the strength

decreases. This offsets the increase in strength as shearing becomes more difficult with

increasing particle size and we reach a condition of maximum stress to move the

dislocations. Fig. 2.9 [12] illustrates this effect.

Figure 2.9 Schematic representation of transition from shearing to looping mechanism as a function of particle size at constant volume fraction [12]

31

2.3.1 Carbide Strengthening Dispersion

Strengthening in secondary hardened ultrahigh strength steels is

achieved through fine scale precipitation of a carbide (M2C) phase. Many researchers

have extensively studied carbide strengthening of steels due to its importance in the

modern industrial world. An earlier paper by Jack and Jack [37] has comprehensively

summarized previous research of carbides in steels. Gil Speich [38] demonstrated

carbide strengthening in his original research on ultrahigh strength Co-Ni steels.

Alloy carbides precipitate to give substantial strengthening during the

secondary hardening (4500C to 7000C) tempering stage. To achieve a higher

strength/toughness combination, the alloy carbide precipitation reaction must be

carried to completion so that the relatively coarse cementite carbides, which act as

microvoid nucleation sites limiting ductile fracture resistance, are eliminated. The

strength of these overaged precipitation hardened structures is controlled by the

Orowan bypass mechanism. For a given volume fraction of carbides (determined by

carbon content), a fine dispersion provides higher strength since the strength is

determined by the mean free path between the dislocations. However as

aforementioned, dislocations will shear the particles instead of looping them if the

particles are too fine. So an optimal particle size is desired at the transition between

particle shearing and Orowan bypass to maximize strengthening. During the secondary

hardening stage, a variety of alloy carbides form, namely MC, M2C, M7C3, M23C6

(M = Cr, Mo, V, W) depending on the alloy composition thermodynamics and kinetics.

32

Of these carbides, M2C is the preferred strengthening precipitate due to its coherent

nature of precipitation in the martensitic matrix that ensures finer size and helps in

microvoid nucleation resistance. Although, M2C is not the most stable carbide phase at

intermediate tempering temperatures (~5000C), it is the phase with the highest driving

force for precipitation from martensite [39]. It also dissolves the relatively coarse

embrittling cementite phase as carbon partitions to the alloy carbides. Previous

researchers [12,40,41] have determined the optimal size distribution of the carbides for

maximum strengthening at a given carbon content. The critical M2C diameter for peak

strengthening has been found to be 3nm, corresponding to the transition of the

deformation mechanisms.

It is necessary to control the thermodynamics and kinetics of carbide

precipitation in order to obtain a fine M2C carbide dispersion. It is desirable to

maximize the driving force for M2C nucleation to obtain a fine initial dispersion. M2C

nucleation driving force can be increased by controlling the amount and ratio

(stoichiometric balance) of carbide formers in the alloy. Mo2C is more stable than

Cr2C, so Mo has a positive effect on M2C nucleation when substituted for Cr [42].

However, segregation during solidification limits the Mo content in steels. Small

additions of V greatly increase the M2C driving force, but it is limited by V’s low

solubility.

33

Figure 2.10 M2C carbide precipitation behavior in AF1410 steel as a function of tempering temperature at 5100C following 1 hour solution treatment at 8300C [42]

34

Montgomery [40] and Olson [42] have done a comprehensive

investigation with integration of previous research [43-53] on thermodynamics and

kinetics of M2C carbide precipitation in AF1410 alloy. The results are summarized in

Fig 2.10 which shows the M2C carbide particle size, shape, number density, volume

fraction, lattice parameters, composition and overall hardness as a function of

tempering time at a standard secondary tempering temperature of 5100C, following

solution treatment of 1 hour at austenizing temperature of 8300C. The information

obtained from this summary plot (Fig 2.10) helps in improving alloy compositions for

more efficient strengthening from precipitation kinetic theory through control of

appropriate scaling factors.

The average particle size of rod-shaped M2C carbides has been

expressed as equivalent diameter of a sphere of diameter ds. The analysis of the SANS

(Small Angle Neutron Scattering) data and TEM (Transmission Electron Microscopy)

of extracted particles helped in determining the evolution of the carbide aspect ratio, β

smoothly varying from near unity (at initial nucleation) to 4 (near equilibrium). The

time dependence of the average particle size with smooth transition in aspect ratio

evolution indicates transition from nucleation to coarsening with suppressed growth

characteristic of precipitates at high supersaturations as theorized by Langer and

Schwartz [49]. They studied that the average particle size is always close to critical

particle size for growth or dissolution at high supersaturation (work of formation of

critical nucleus, kTW 10* ≤δ ). At high supersaturations, the nucleation rate is high,

35

which in turn reduces the supersaturation rapidly. Now, the critical particle size

increases as supersaturation decreases during the nucleation process. Thus, particles

that were above critical nucleus size now become subcritical and dissolve as

supersaturation decreases. This competition between the nucleating particles and

critical particle size inhibits the growth of the particle distribution. The average particle

size is initially governed by the nucleation process and smoothly transitions to a regime

governed by coarsening, as shown by the top two plots of Fig 2.10. This shows that the

critical particle size and coarsening rate determine the effect of coherency (or particle

size) on precipitation and hence the strength. This fact is supported by plot 3 of Fig

2.10 where a second stage of nucleation, between 1 and 2 hours, reduces the average

particle size through increased number of finer particles, passing the number density

Nv, through a maximum. This observation that the average particle size never differs

greatly from critical size because of suppression of the growth region at high

supersaturation constitutes a useful phenomenon for maintaining the finest possible

particle size at high supersaturation. The volume fraction curve (plot 3) shows that the

precipitation is complete after 10hr tempering with complete dissolution of transient

cementite. The lattice parameter plot (plot 4) gives conclusive information about the

interfacial coherency of the carbide particles. In the coherent state, the precipitate tends

to reduce the elastic energy by shifting composition to reduce the overall lattice

deformation relating the coherent HCP carbide to the BCC matrix. The observed lattice

parameter shift indicates that the precipitates are coherent below 10hr tempering and

36

become fully incoherent beyond 100hr. Based on the M2C composition dependence on

the lattice parameter (plots 4 and 5), the depletion of C and enrichment of Fe are

consistent with observed lattice parameter shifts. The lattice parameter shifts and the

volume fraction measurements also suggest that the carbides are close to coherent

equilibrium after an 8hr tempering treatment. The hardness curve (plot 5) further

verifies the completion of M2C precipitation at 8-10hrs of tempering corresponding to

the overaged state, which controls the strength by Orowan bypass mechanism.

Similar experiments by Yoo and others [54-56] have demonstrated the

tempering evolution of M2C carbides in AerMet100, an alloy having superior

properties than AF1410. The reason for higher strength is attributed to finer particle

size distribution and higher carbide volume fraction in AerMet100 compared to

AF1410. Thus, through the investigative study of evolution characteristics of M2C

carbide precipitation, it can concluded that by the control of the appropriate scaling

factors, improved alloy compositions can be designed which will lead to more efficient

strengthening and hence improved properties.

2.3.2 Copper Strengthening Dispersion

The precipitation of copper as a strengthening dispersion in iron and

steels has been extensively studied in the past [57-70] and has been basis for the

development of high strength, low alloy steels (HSLA) for applications particularly in

shipbuilding, pressure vessels and gas pipelines [71-76]. Copper precipitation is used

37

as an alternative strengthening mechanism in these steels with comparatively low

hardenability, where the limited strengthening by alloy carbides because of low carbon

requirements is partially recovered [77]. The unusual feature of this system is that the

high-work hardening rates associated with overaging is not observed, i.e., the

precipitates stay shearable even in the overaged conditions. Thus, the standard models

associated with peak hardening to the shearing/bypass transition as described in

Section 2.3 cannot be applied in this case.

The precipitation sequence in copper bearing steels has been well

established from several studies [60,63,71,78,79]. Initially, copper precipitates from

the supersaturated solid solution as metastable body centered cubic (BCC) phase,

which is fully coherent with the ferritic/martensitic matrix. These coherent precipitates

with an average diameter of 1-5 nm are not pure copper, containing a significant

amount of iron [61,71]. As these BCC-copper precipitates reach a critical size of 2.3 to

3 nm [71,80], a martensitic transformation to the intermediate 9R structure occurs

[63,69,79,81,82]. The 9R structure can be regarded as a face centered cubic (FCC)

lattice with intrinsic stacking faults on every third close-packed plane [82]. These

intermediate 9R precipitates were observed [65] to grow subsequently as spherical,

multiply-twinned particles up to ~ 17 nm. At sizes larger than 17 nm, a second

transformation to more stable 3R structure occurs. The 3R corresponds to an

untwinned distorted FCC structure. The 3R evolves into the equilibrium FCC ε-phase,

suggesting that lattice relaxation occurs during the diffusional growth of the 3R

38

precipitates. These incoherent equilibrium ε-phase copper precipitates formed at high

aging temperatures and longer aging periods have ellipsoidal [65] or rod-shaped with

hemispherically capped [58] morphology.

The contribution of the precipitates in the strengthening mechanism is

complicated by the precipitation sequence [70]. It is well established that the

strengthening precipitates in the peak aging condition have a BCC structure. However,

studies [60,70] show that maximum strength is reached well before precipitation is

complete. This is attributed to dynamic strain-induced martensitic nucleation and

subsequent growth of the precipitates from the BCC to the 9R structure continuously

throughout the broad age hardening peak. Precipitation hardening in the Fe-Cu system

has been described by the Russell-Brown model [59] in which the strengthening is

related to the difference in the shear modulus between the copper precipitate and the

ferrite matrix. Since BCC copper precipitates are assumed elastically softer than the

matrix, no increase in work hardening results from overaging and the strength is solely

achieved by particle cutting. The strength contribution from chemical hardening caused

by increase in total particle-matrix interfacial energy when a dislocation cuts through a

particle is thought to be much smaller than the contribution from modulus

strengthening. The Russell-Brown model proposed a theory based on interaction

between matrix slip dislocations and copper particles of lower elastic modulus and

accounted for the observed yield strength and work hardening behavior. They

considered a random distribution of spherical precipitates having lower modulus than

39

the matrix and calculated the yield stress dependence both in the underaged and the

overaged state. The peak aging stage is the upper limit of the underaged state when the

radius of the precipitate reaches twice the core radius of the dislocation. So applying

modulus strengthening [83,84] to the stress solution at which a dislocation can move

through an array of softer copper precipitates in the underaged state, they derived that

the maximum strength which can be achieved is proportional to the square root of the

volume fraction of the precipitate phase. Fig. 2.11 is a plot of the experimentally

available data for maximum hardening increment against volume fraction, f1/2. Thus,

according to this model, a copper precipitation strengthened system can be designed by

evaluating the phase fraction of the metastable BCC precipitate at the tempering

temperature. Osamura et al [64] proposed an alternative hardening mechanism by

analyzing structural parameters during the interaction of dislocations with precipitates,

assuming that hardening during initial stages of precipitation is controlled by

coherency strains. Charleux et al [66] also proposed a hardening model combining the

viscous motion of screw dislocations and the dislocation-precipitate interaction.

However, recently Deschamps et al [70] investigated the various models and

confirmed that the Russell-Brown model is in very good agreement with their

experiments.

40

Figure 2.11 Plot of maximum increase in yield strength vs. (volume fraction of atoms)1/2. The points represent experimental data and the line is predicted by the theory for a dislocation core radius equal to 2b(burgers vector). The arrow indicates the limit of solid solubility [59]

Figure 2.12 Lower yield stress of Fe-1.4 at% Cu alloy as a function of aging time at 5000C [60]

41

Goodman et al [60,61] studied the size, number density and

composition evolution of the copper precipitates during the early stages of precipitation

in a Fe-1.4 at. % Cu at 5000C using Field-Ion Microscopy (FIM). Particles as small as

8Å were detected, most of which were spherical with a few rod-shaped exceptions. The

yield stress dependence on the aging time at 5000C is given in Fig 2.12. Fig 2.13 shows

the evolution of the mean size of the particles. It was confirmed that the mean diameter

of the particles at maximum strength is about 2.4nm. The linear dependence of the plot

between mean particle diameter and time (t1/2) shows that the growth of the copper

particles is purely diffusion controlled (slope = 2αD1/2; [84] where α is the growth

coefficient and D is the diffusivity). Fig. 2.14 and Fig. 2.15 give the particle number

density and volume fraction as a function of aging time respectively.

Figure 2.13 Mean particle diameter of copper precipitates as a function of the square-root of tempering time in Fe-1.4 at% Cu alloy at 5000C [60]

42

Figure 2.14 Number density of copper precipitates as a function of tempering time in Fe-1.4 at% Cu alloy at 5000C [60]

Figure 2.15 Volume fraction of copper precipitates determined from measured number density and mean diameter as a function of tempering time in Fe-1.4 at% Cu alloy at 5000C. The relative amounts of coherent and non-coherent precipitates are shown schematically by dashed lines [60]

Figure 2.16 Mean composition of copper precipitates as a function of tempering time in Fe-1.4 at% Cu alloy at 5000C [61]

43

The number density remained nearly constant at 1018 precipitates/cm3

until the peak strength was reached and then decreased to 1016 precipitates/cm3 as the

alloy overaged and softened. The volume fraction of the precipitates was calculated

from the number density and the mean size of the particles. It shows that the volume

fraction increases gradually until the mean particle size reaches 10nm. The mean

composition evolution of the copper precipitates as a function of aging time is given in

Fig 2.16. It shows that during the initial stages of precipitation, the particle

compositions remain constant at nearly 50% Cu until the peak aged condition. This

contradicts values reported by Kampmann and Wagner [62] who suggested by

thermodynamic analysis that precipitates with radius greater than 0.5nm are expected

to be almost pure copper. However, for longer tempering times, the average

composition reached close to 100% Cu although some precipitates were observed to

contain appreciable amounts of iron.

In addition to strengthening by a fine dispersion of coherent

precipitates, copper precipitates act as heterogeneous nucleation sites for other phases

such as, Ni-rich Ni3(Ti,Al) in maraging steels [86] and α-Fe in iron-based amorphous

glass [87,88]. Earlier work by Hornbogen [57] suggested that copper precipitates

nucleate by homogeneous clustering in a matrix of α-iron. However, recent studies by

Dunne et al [75], Maruyama et al [81] and Deschamps et al [70] have shown that

nucleation of copper precipitates is promoted by the presence of dislocations through

TEM and SAXS (Small Angle X-ray Scattering) observations where most of the

44

copper clusters precipitated on martensite laths and dislocations during isothermal

aging.

The influence of copper precipitation on impact toughness in low

carbon steels has been studied by Aroztegui et al [89]. They observed no evidence of

copper precipitates aiding in nucleating cleavage cracks and their influence on fracture

stress was negligible. Copper additions of up to 4% in austenitic steels help improve

corrosion resistance [73]. However, it is also known that copper addition to steels

cause hot shortness during rolling, which can be prevented by the addition of nickel

[90,91]. There has thus been considerable interest in characterizing the effect of nickel

on copper precipitates. Worrall et al [71] and Buswell et al [92] found that for smaller

particle sizes in the underaged condition nickel segregates at the interface of the

coherent BCC copper particles while they found that nickel is not contained in the

overaged FCC precipitates. This was confirmed by Atom Probe studies by Osamura et

al [93]. Recent 3DAP (Three-dimensional Atom Probe) studies of segregation at

coherent precipitate/matrix heterophase interfaces by Isheim [94] also show Ni

segregation with an excess of 1.47 ± 0.43 nm-2 at the interface.

45

2.4 Transformation Toughening

The interaction of deformation-induced martensitic transformation of

dispersed austenite with fracture-controlling processes, such as microvoid induced

shear localization, results in dispersed-phase transformation toughening [95]. In

metastable fully austenitic steels, transformation plasticity is also responsible for

significant enhancement in elongation and fracture strain. The transformation behavior

and toughening effects are controlled by the stability of the austenitic dispersion

determined by size and chemical composition of the austenite particles. The size

affects the probability of finding the nucleation site in the particle and the composition

determines the chemical driving force for martensitic transformation. The stability also

depends on the stress state through interaction of the transformation volume change

with stress triaxiality. The Msσ temperature for the stress-state of interest provides a

single-parameter characterization for the stability of dispersed austenite. It is the

temperature at which there is a transition in the deformation mechanism. Above the

Msσ temperature the initial yield is by slip, while below Ms

σ initial yield is by

transformation. Toughness is increased when austenite particles undergo martensitic

transformation under the crack-tip stress state. This transformation creates a strain

hardening effect, which offsets softening due to microvoid formation and thus delays

the onset of shear localization. The toughening effect is maximum at the crack tip MSσ

temperature [8,9,135]. Thus one would like to have the Msσ temperature around the

46

room temperature for maximum transformation toughening. This can be explained in

greater detail using the schematic diagram in Fig 2.17.

Figure 2.17 Schematic representation of stress-assisted and strain-induced regimes for mechanically-induced transformation [95]

Spontaneous transformation is triggered by pre-existing nucleation sites,

i.e., through stress assisted nucleation above the Ms temperature represented by point A

in Fig 2.17. At the Msσ temperature the stress reaches the yield stress σy level for slip

in the parent phase represented by point C in the diagram. Above Msσ up to Md

(maximum temperature above which martensitic transformation cannot be induced by

deformation), plastic strain introduces new potent nucleation sites, which trigger strain-

47

induced nucleation. As mentioned, Msσ thus creates a boundary between the

temperature regimes where two different modes of transformation operate. Thus below

Msσ, yield stress follows the stress for stress-assisted transformation during

transformation plasticity. The change in the deformation mechanism around Msσ can be

characterized by the difference in the transformation product morphologies: stress-

assisted transformation forms relatively coarse plates while strain-induced

transformation forms fine laths at intersections of shear micro-bands.

• Stress-assisted mode of transformation

In this case, the applied elastic stress modifies the effective potency

distribution of pre-existing nucleation sites, which helps in the transformation kinetics.

Based on the Olson-Cohen [96] dislocation dissociation model of classical

heterogeneous martensitic nucleation by elastic interactions with internal stress

concentrations, the potency distribution of nucleation sites under an applied elastic

stress σ can be expressed by equation (2.15):

str

fch

SVV EWGG

dNN++∆+∆

=)(

/2exp)(max

0

σαγσ σ (2.15)

where γs is the interfacial energy, d is the interplanar spacing and α is a constant. The

force term in the denominator is a sum of the mechanical driving force ∆Gσ(σ),

chemical driving force ∆Gch, elastic strain energy per unit volume Estr and frictional

work of interfacial motion Wf. At a given stress level, the value of the mechanical

driving force changes with the orientation of the nucleus relative to the stress state. The

48

mechanical driving force is related to the applied stress through the Patel-Cohen

criterion [97]:

)(σ

σσ

∂∆∂

=∆GG (2.16)

For considering the stress effects on the potency distribution, the two

extreme cases would be; the operative nucleation sites are of optimum orientation for

maximum interaction with applied stress, i.e., ∆Gσ=∆Gσmax and the other extreme is a

fully random distribution [31]. The actual behavior should be between these two

extremes. Equation 2.15 thus gives the potency distribution under an applied elastic

stress in the case when stress-assisted transformation of a well-spaced dispersion of

metastable particles in a stable matrix is controlled by pre-existing nucleation sites. For

an average particle volume Vp, the fraction of particles to transform due to sufficient

potency of the sites is equal to the probability of finding at least one nucleation site in

the particle, which is given by

(2.17) ).exp(1 pV VNf −−=

assuming that a single initial nucleation event transforms the particle to martensite. NV

is the cumulative number density.

• Strain-assisted mode of transformation

During strain-induced transformation new nucleation sites are created

by plastic strain. In this case, the nucleation sites would be activated by the applied

49

stress and created by the plastic strain simultaneously. The potency distribution can be

found as:

str

fch

SVV EWGG

dNN++∆+∆

=)(

/2exp)()(max

0

σαγεε σ (2.18)

with all variables having their usual meaning. A fully biased distribution was used for

the strain-induced part and Kuroda [98] expressed the strain dependence of NVO for

strain-induced nucleation by non-linear curve fitting:

(2.19) )]exp(1[)(0 nV KNN εε −−=

where K and N are constants.

Since stress-assisted transformation (T<MSσ) takes place in the absence

of any slip, it represents a softening phenomenon relative to the flow behavior of the

parent phase. But for T>MSσ where strain-induced nucleation dominates the

deformation behavior, transformation and slip act in parallel. While a dynamic

softening operates with transformation as a deformation mechanism, a static hardening

effect also arises from the transformation product acting as a slip obstacle. For

transformation plasticity, dynamic softening is dominant at low strains while static

hardening is dominant at high strains as the rate of transformation decreases. This

distorts the usual σ−ε curve into an upward curving shape.

Prior work on austenitic transformation toughened steels investigated

the condition for optimum toughening enhancement, which has led to the development

of TRIP (TRansformation Induced Plasticity) steels [8,9]. Their experiments

50

demonstrated that the flow-stabilizing influence of transformation plasticity could

maximize the toughness at the MSσ temperature for the crack-tip stress state. Fig 2.18

shows the plot of the relative increment of J-integral toughness enhancement as a

function of relative transformation stability represented by a normalized temperature

parameter, θ (=T − MS

σ

Md − MSσ ). The transformation toughening reaches a maximum near

the MSσ temperature, which is consistent with the effect of transformation plasticity on

flow stability.

The dispersed metastable austenite discussed here may either be in the

form of retained austenite or precipitated austenite. The former is the austenite that

remains untransformed after cooling down from the solution temperature, while the

latter forms upon high-temperature tempering or intercritical annealing. Retained

austenite is typically associated with low temperature tempering, whereas precipitated

austenite is found in secondary hardening alloy steels.

51

Figure 2.18 J-integral toughness enhancement at Msσ for precipitation-hardened

metastable austenitic steels [9]

2.4.1 Retained Austenite

Conventionally, this is the austenite that is the leftover from a

martensitic transformation when steels are quenched from the solution temperature.

This austenite can be designed appropriately for the necessary high stability to achieve

the transformation plasticity phenomena under deformation. Previous work [4,99]

shows that the ductility of this class of steels can be increased by the TRIP effect that

led to the design of triple phase steels: ferrite, austenite and bainite being the three

phases. Coarse cementite particles formed during bainitic transformation are

detrimental to the toughness of these steels, but the precipitation of cementite can be

52

suppressed by alloying with about 1.5 wt % Si, which has very low solubility in

cementite. The carbon that is rejected by the bainitic ferrite enriches the residual

austenite thereby stabilizing it. Thus, on slow cooling followed by quenching we

obtain fine plates of bainitic ferrite separated by carbon enriched retained austenite.

This mixed microstructure has high resistance to cleavage fracture and void formation

because of the absence of cementite carbides. The strength and toughness can be

further enhanced by an ultrafine grain size of the bainitic ferrite plates as well as the

TRIP effect.

All the promising properties of this microstructure might not reach full

potential if the large blocky regions of austenite trapped between sheaves of bainite are

unstable. These unstable blocks then tend to transform into coarse high carbon

untempered martensite, leading to an embrittling effect. On the other hand, austenite

trapped between subunits of bainitic ferrite is more stable, not only because they have

higher carbon concentration but also due to a finer particle size. Thus, the aim of the

design should be to maximize the degree of transformation of bainitic ferrite and in the

process reduce the fraction of blocky austenite and increase its stability with respect to

martensitic transformation. Chemical stabilization due to the enrichment of carbon in

retained austenite is the most important operational mechanism for austenite retention.

Both bainitic transformation and the retention of stable austenite after transformation

from ferrite have been explored in considerable detail, which will be described later

(Appendix B). Since the stabilization of austenite largely depends on the kinetics of

53

carbon diffusion and does not involve the larger substitutional atom diffusion, it can be

simulated using paraequilibrium (PE) growth models [22], as described in Section

2.2.1.

Haidemenopoulos [100] has characterized the stability of retained

austenite in terms of the Msσ temperature. The Ms

σ temperature was measured in

uniaxial tension Msσ(u.t.) and uniaxial compression Ms

σ(u.c.). The temperature

dependence of 0.2% flow stress in tension and compression for a material containing

4% retained austenite showed an increase with decreasing temperature. The tensile

flow stress region has a plateau region around the Msσ (u.t.) temperature (Fig 2.19),

which is attributed to the mechanical relaxation due to transformation of retained

austenite. In the stress-assisted nucleation regime (T< Msσ), initial yielding is

controlled by transformation of retained austenite. The stress-strain behavior can be

described by nucleation-site potency distribution models described in the previous

section.

54

Figure 2.19 Temperature dependence of the 0.2% tensile and compressive flow stresses [100]

Strain-induced transformation of retained austenite delays shear

instability during pure shear deformation. Since fracture is often controlled by shear

localization, it is expected that delocalizing effects arising from transformation

plasticity of retained austenite should enhance the fracture toughness. It was found that

retained austenite is sufficiently stable for a pure-shear stress state but too unstable for

a crack-tip stress state when tests are performed at room temperature. A toughening

effect associated with strain-induced transformation would be only observed at or

above the Msσ temperature. Thus, transformation toughening can result only by

lowering the crack-tip Msσ below room temperature by stabilizing the austenite.

55

2.4.2 Precipitated Austenite

Precipitated austenite is the form of dispersed austenite that precipitates

during intercritical annealing or during tempering at high-temperature above ~470OC.

This difference in the mode of formation from retained austenite makes precipitated

austenite very attractive for application of transformation toughening since there are

more easily controllable degrees of freedom. Since it is formed as a result of

precipitation reaction, its amount and distribution can be controlled. Its size and

composition can be varied through heat treatment and its stability can be tuned for

transformation toughening effects.

The most important factors affecting the dispersed-phase transformation

toughening in steels are the stability of the dispersed austenite and the transformation

volume change, both of which depend on the composition of the steel. Studies on

precipitated austenite have been mostly performed on high Ni-Co secondary hardened

martensitic steels [6,100]. Similar to retained austenite, transformation behavior and

toughening effects are controlled by the stability of the austenitic dispersion with the

microstructural parameters again being size and chemical composition of the austenite

particles. Other than that, stability of austenite also depends on the stress state due to

the interaction of the transformational volume change and strength of the matrix.

Haidemenopoulos showed that in order to get a very high stability of dispersed

austenite, so that the Msσ temperature for the crack–tip stress state can be below room

temperature, the austenite has to be very fine and enriched in Ni. By equating the

56

transformation stress (σt) derived from equation (2.15) and the yield stress (σy), he

obtained the Msσ temperature as:

MSσ = σ y[0.121+ 0.0542(σ h /σ )]+

1465.3−4.6 − lnNV

OVP

+ [1418.92 −33.92(wt%Ni) − 0.5(wt%Ni)2/ 3](2.20)

At room temperature (300K) for the crack-tip stress state, the required Ni content of

the austenite particles can be plotted vs. particle size as given in Fig 2.20 for a fixed

yield strength of 1400 MPa.

Figure 2.20 Optimal Ni content vs. normalized austenite particle volume in Fe-14Co-Ni system [100]

57

Precipitated austenite occurs in two competing morphologies: as thin

interlath films and as intralath dispersion of fine precipitates. Fig 2.21 shows the

presence of both interlath films and dispersed intralath austenite in AerMet100 after

two-stage tempering.

Figure 2.21 Conventional TEM dark field image of an interlath austenite film (A) and dispersed intralath (B) austenite after 5070C/30minute + 4550C/7hour temper in AerMet100 [6]

The thin interlath austenite films are located on martensite lath

boundaries. The dispersed austenite precipitates are located at heterogeneous sites

within the martensitic laths. However, both interlath films and dispersed precipitates of

austenite nucleate during tempering above 500OC. The austenite films are enriched by

58

FCC stabilizing elements like Ni. The small width of the film is also responsible for

the resistance to martensitic transformation upon cooling to room temperature. The

competition between the two types of austenitic morphologies is crucial to the

transformation toughening properties of the alloy. The lath boundary films do not

generally possess the requisite stability for effective transformation toughening. The

intralath precipitates are sufficiently enriched with Ni and refined in size to increase

the alloy toughness, provided an adequate volume fraction is present. Lippard [6]

studied the commercial alloy AerMet100 that displays transformation toughening

enhanced properties when given a specific two-stage tempering. The first stage of

treatment precipitates both interlath films and a fine dispersion of intralath precipitates.

But the intralath austenite precipitates have small (~8nm) size with highly enriched Ni

content at the second stage of tempering that provided sufficient stability to produce

transformation toughening properties. Overaging treatments coarsened both the

austenite dispersion and carbide strengthening dispersion. But the dispersed intralath

austenite maintained its composition while the interlath films became enriched with

carbon. Thus, interaction of the carbide dispersion and matrix dislocation network was

found to be important for austenite precipitation.

Lippard consistently found evidence of a high Cr signal much greater

than either the equilibrium matrix or precipitate contents associated with STEM EDS

data gathered from dispersed intralath austenite precipitates as shown in Fig. 2.22.

Based on this indirect evidence, he proposed a mechanism of austenite precipitate

59

nucleation on an M2C carbide or in its immediate coherency strain field. He concluded

that dispersed intralath austenite requires an M2C carbide to provide an energetically

favorable nucleation site. He suggested that direct evidence of the precipitation

sequence and the spatial relationship of the M2C carbides and austenite precipitates

could best be obtained by three-dimensional reconstruction from position sensitive

atom probe microanalysis.

Figure 2.22 Correlation of Cr and Ni from embedded austenite precipitates prior to partitioning of STEM EDS signal into matrix and precipitate portions [6]. The data points are from multi-step tempered AerMet100 samples aged at 4050C for longer times after a short time 5070C nucleation treatment.

60

Grujicic [101] studied stabilization of precipitated austenite in C-Mn

steels via heterogeneous precipitation to produce compositional control of austenite.

He considered two modes of austenite formation under para-equilibrium conditions:

heterogeneous nucleation at a ferrite-cementite interface with subsequent growth into

either ferrite or cementite and heterogeneous precipitation on ferrite grain boundaries.

A reduction of Mn content of cementite below its equilibrium value was found to favor

austenite nucleation at ferrite-cementite interfaces and subsequent conversion of

cementite to austenite. Through thermodynamic calculations, the nucleation of

austenite at ferrite-cementite interfaces and the subsequent conversion of cementite

into austenite are most likely to take place during intercritical or supercritical

treatment. The precipitated austenite is very stable due to higher Mn content. Only at

high temperatures can complete cementite → austenite conversion be achieved. Yet at

such high temperatures the likelihood of formation of less-stable austenite via massive

transformation of ferrite increases. This can be suppressed by adding elements that

lower the activity of C in ferrite such as Mn, Cr, Mo or W.

61

3. ALLOY DESIGN

The design of high toughness plate steels at high strength levels has

been pursued employing transformation toughening phenomena while constraining the

alloy carbon content of the steel for weldability. Two toughening concepts have been

explored, both based on mechanisms of dispersed austenite stabilization for

transformation toughening adapted to weldable bainitic plate steels. Concept A is

based on low alloy, low cost C-stabilized austenite in high Si steels with Cu

precipitation strengthening. This design focuses on precipitation-strengthened bainitic

steels with carbon-stabilized austenite for transformation toughening. Silicon, in this

concept, acts to suppress the precipitation of cementite to keep C available for

austenite stabilization. The second, Concept B, higher strength, lower risk and higher

cost concept is primarily nickel-stabilized austenite, in an alloy strengthened by

precipitation of M2C carbides in combination with copper. These two design concepts

are based on a trade-off between the risk of the design and the cost of the product. The

Concept A prototype proved to be too stable to allow full assessment of the

compatibility of simultaneous bainitic transformation and copper precipitation

strengthening and the design principles and prototype evaluation are described in

Appendix A, while the Concept B prototype proved successful in meeting its

objectives and became the focus of the research effort.

62

3.1 Modeling Tools

Two primary software systems were used for analyzing and integrating

the design parameters: ThermoCalc™ and CMD™ (Computational Materials

Dynamics).

3.1.1 ThermoCalc™

ThermoCalc™ is a generalized thermodynamic database and calculation

package developed by the Royal Institute of Technology in Stockholm, Sweden (KTH)

[102]. The database is comprised of thermodynamic assessments, mostly compiled

from experimental results, of binary, ternary and quaternary systems used to

extrapolate to higher order systems. The program uses the compiled information in the

database to calculate equilibrium (or constrained equilibrium) thermodynamic values

such as phase fractions, phase compositions and driving forces as functions of

chemical composition, temperature, pressure, chemical potential and other user defined

functions by solving for the state of lowest Gibbs free energy. The separation of the

calculation package from the database makes this tool extremely versatile and

powerful, since it allows use of different thermochemical models to describe the

thermodynamics of the system. ThermoCalc™ uses sublattice models to describe the

different lattice sites within a crystalline phase like the general sublattice model [108]

(includes the regular solution model as a special case) and the two sublattice ionic

63

model [109]. For example, a two-sublattice model is used for the description of BCC

iron in the form ApBq where A is the first sublattice (substitutional) consisting of p

sites and B is the second sublattice (interstitial: allowing non-occupied sites or

vacancies) consisting of q sites.

The thermodynamic databases used were created by the Scientific

Group Thermodata Europe (SGTE), a consortium of European research centers

developing databases for inorganic chemistry and metallurgy. For alloy design in this

thesis, the SGTE solution database or SSOL has been primarily used. It includes data

for over 150 binary, 70 ternary and 20 higher systems. In addition to the SSOL

database, two other custom databases developed in SRG research were examined

during the design process. The MART 4 database was developed by Ghosh and Olson

[105] to calculate martensite start temperature. The database includes modified low

temperature thermodynamic parameters for FCC and BCC phases for iron based

systems. This database modification was necessary for a more accurate description of

the lower temperature thermodynamics since the parameters in the SSOL database is

based only on high temperature data. The COHERENT3 database was also used for

modeling the coherent precipitation behavior of M2C carbides from a BCC iron matrix.

This database was modified to include a thermodynamic description of the elastic

strain energy associated with lattice misfit. Since we were aiming at a high martensite

start temperature (>3000C), the SSOL database proved adequate for MS prediction.

Introduction of a miscibility gap in the BCC phase to define the coherent BCC copper

64

phase led to erroneous phase descriptions when the COHERENT 3 database was used.

Thus, the SSOL database was used for all the thermodynamic calculations of the

design.

3.1.2 CMD™ (Computational Materials Dynamics)

CMD™ is a user-friendly computational materials design software

system developed by Questek Innovations LLC, Evanston [103]. It is composed of a

collection of mechanistic models describing both processing-structure and structure-

property relations integrated with their software implementation. The models link up

with ThermoCalc™ and DICTRA™ (DIffusion Controlled TRAnsformation) to gather

all the thermodynamic and mobility information for multicomponent computation. The

user has to establish the material design criteria for using the CMD™ model programs.

The software relies on user’s input and manual optimization guided by parametric

contour plots to meet the design criteria. The process of materials design using CMD™

involves a large number of calculations using different models to study the trade-offs

and perform optimization of the design strategies. For alloy design in this thesis,

CMD™ has been used to optimize the driving force of the M2C carbides for dispersion

refinement with respect to the various carbide formers, Cr, Mo and V within the

stoichiometric balance limit. The model for calculating carbide driving forces from a

supersaturated solid solution of BCC has been primarily used for this purpose.

65

3.2 Design Approach

The objective of this design is to maximize the toughness-strength

combination in weldable and affordable plate steels. The desired microstructure is a

matrix containing a bainite-martensite mix, BCC copper and M2C carbide for

strengthening with a fine dispersion of optimum stability austenite for transformation

toughening. The bainite-martensite mix will be formed by air-cooling from solution

treatment temperature and subsequent aging at secondary hardening temperatures will

precipitate the toughening and strengthening dispersions. The strengthening approach

is based on design concepts of the current Navy HSLA100 steel (Fe-0.06C-0.9Mn-

0.4Si-3.5Ni-1.6Cu-0.6Mo-0.03Nb; in wt%) with a quench and temper processing

treatment. This is integrated with modeling of nickel-stabilized austenite produced by

precipitation as demonstrated in transformation toughened AerMet100 and AF1410

steels with multi-step tempering treatments [2,6,100]. The proposed methods of

toughening and precipitation strengthening have been modeled in this design to assess

theoretical feasibility in order to minimize necessary experimentation.

The structural hierarchy in this alloy system with strong interactions

among levels has been organized by the systems design chart, presented in Fig. 2.1,

through relationships between the processing/structure/property/performance

interactions with adequate description of the substructure present within each

microstructural element. During the design process, the systems approach emphasized

the interaction of the various subsystems and addressed the role of each individual

66

component within the larger system. As outlined by Jenkins [136], a breakdown of the

steps involved in the systems design process can be represented as:

Systems Analysis → Systems Design/Synthesis → Implementation → Operation.

The first step, systems analysis, involves identifying the application and the material

property/performance objectives expressed by the systems design chart. The models

necessary to characterize the subsystems and their interactions are subsequently

decided based on the priorities of the interactions necessary to achieve the properties.

Once the appropriate models are developed, the models are integrated to design a new

material for the specific application. It is important not to optimize a particular

subsystem at the expense of the total system. Moreover, the designed composition

should be robust; all the design parameters are ensured to be insensitive over a range so

that small deviations in the composition will not result in dramatic differences in

properties. Fig. 3.1 presents a schematic process flow of the design optimization

procedure to determine an optimal composition. Once the optimal composition is

determined, a prototype alloy is made and evaluation of the prototype is done.

Prototype evaluation not only characterizes the alloy, but also verifies the effectiveness

of models and their integration in the design. If needed, another design iteration is run

before the material is used for its intended application.

67

igure 3.1 Schematic of the design optimization procedure

CSet Carbon Level

Weldability

CSet Carbon Level

Weldability

Castability Cu, Ni, CrCastability Cu, Ni, Cr

Refine M2C Strengthening Dispersion Mo, V, Cr, C

Maximize M2CDriving Force

SolutionTemperature

Predicted StrengthIncrement

Refine M2C Strengthening Dispersion Mo, V, Cr, C

Maximize M2CDriving Force

SolutionTemperature

Predicted StrengthIncrement

Optimize Transformation Toughening Dispersion

Austenite NickelContent

Austenite PhaseFraction

Meet StabilityRequirement

NiOptimize Transformation Toughening Dispersion

Austenite NickelContent

Austenite PhaseFraction

Meet StabilityRequirement

Ni

Set Matrix Composition Fe, Ni, Cr, Cu

Martensite StartTemperature

BainiticTransformation

CleavageResistance

Set Matrix Composition Fe, Ni, Cr, Cu

Martensite StartTemperature

BainiticTransformation

CleavageResistance

Set Copper for Strengthening Dispersion

Additional StrengthIncrement

Volume fraction ofCopper Precipitates

Cu, Cr

Partitioning of Copper by Chromium

Set Copper for Strengthening Dispersion

Additional StrengthIncrement

Volume fraction ofCopper Precipitates

Cu, Cr

Partitioning of Copper by Chromium

Optim

al Com

position

F

68

.2.1 Strength Design

An efficient approach to strengthen the steel while limiting carbon

content for weldability is co-precipitating M2C carbides and BCC copper. By

optimizing the particle size and the phase fraction of the precipitates, the goal of high-

strength can be achieved.

3.2.1.1 Quantitative Strengthening Contributions

As highlighted by the system design chart (Fig. 2.1), the strength of the

alloy will be designed by using quantitative strengthening models to predict its

dependence on the structure of the steel. To achieve a goal of 160ksi yield strength,

quantitative models will be employed to relate the contribution from dispersions of

M2C carbide precipitates [12] and BCC copper precipitates [59] in secondary-hardened

steels. The levels of M2C carbide formers and copper will be optimized based on the

strength contribution from each of these substructures. In this work, assessment of the

yield strength of the material has been made directly from the hardness data because of

the ease and convenience in measurement of the latter. Hardness of a material is a

direct manifestation of its resistance to plastic flow, monotonically relating to yield

stress. An empirical relationship has been developed between hardness and yield stress

based on experimental data from previous research on related steels: HSLA100 data

from Foley [77], AerMet100 data from Kuehmann [2] and SRG C2 carburizable gear

steel data from Spaulding [138]. The best-fit curve in a log-log plot of hardness vs.

3

69

yield stress has been used to determine the relationship based on strain hardening

associated with the alloy. Fig. 3.2 presents the experimentally measured hardness –

yield stress data from previous research superimposed with the best-fit power-law

relationship and the theoretical straight-line relation describing the same for an ideal

plastic material [107]. The higher hardness of the empirical power-law relationship

relative to the ideally-plastic case represents the effect of strain hardening, which

appears to be more pronounced at lower strength levels. The point at which the two

curves meet represents the prediction limit of the relationship.

Figure 3.2 Power-law relationship relating hardness of related steels to yield stress from experimental data from Foley [77] (circles), Kuehmann [2] (triangles) and Spaulding [138] (diamonds) shown in comparison to straight-line relationship for ideal plastic material

70

Thus, the hardness estimate for the target yield strength of 160 ksi from the power-law

relationship is 389 VHN. The relation obtained is:

(3.1) 8184.0116.6 YSVHN =

where, VHN (Vickers Hardness Number) is in kg/mm2 and YS (Yield Strength) is in

ksi.

The first step in the design involved setting the carbon content of the

alloy to ensure good weldability. Fig. 3.3 presents the Graville diagram of overall

carbon content in the alloy as a function of carbon equivalent. This shows that at 0.05

wt% C, the steel is not susceptible to hydrogen – induced cold cracking in heat affected

zone (HAZ) of weldments. Consistent with the carbon level in current Navy HSLA100

steel, the lower limit C content of 0.05 wt % C was set for the alloy.

71

Figure 3.3 Graville diagram for determining susceptibility to HAZ cracking in plate steels [137]

Based on the effect of M2C carbide precipitates in the Orowon bypass

regime, Wise [12] developed a quantitative strength model to predict the strengthening

achieved for a given carbon level. The predictions assume that a given carbon content

of the alloy specifies the carbide volume fraction and considers carbides of fixed

particle diameter. Based on the change in hardness-carbon content (wt%) plot shown in

Fig. 3.4, at a C level of 0.05 wt% the hardness increment due to M2C carbide

precipitation is estimated to be 175 VHN provided a sufficient driving force is

maintained to achieve the particle size range in Fig. 3.4. The base strength of the lath

72

martensitic substructure was estimated as 63 VHN by Wise [12]. The additional

strength increment of 151 VHN to achieve the strength goal of 389 VHN will be

attained through BCC copper precipitation strengthening, described in Section 3.2.1.2.

The effect of solid solution strengthening is assumed to be negligible for steels having

low carbon and low hardenability. Thus, the total strength of the alloy has been

modeled by breaking it down into its individual mechanisms. The strength is described

by the effects of M2C carbide precipitates, τM2C; BCC copper precipitates, τCu and

matrix martensitic structure, τα’.

VHNCuCM 389'2 ≡∆+∆+∆= αττττ (3.2)

The contributions of the individual mechanisms to achieve the strength goal equivalent

to 389 VHN are graphically presented in Fig. 3.5.

73

Figure 3.4 Change in hardness as a function of alloy carbon content for M2C

carbide strengthening contribution [12]. The arrows represent hardness increment of 175 VHN is achieved at C level of 0.05 wt% set for the alloy. Experimental results of other secondary hardening steels are shown.

Figure 3.5 Graphical representation for contributions of the individual mechanisms to achieve the strength goal equivalent to 389 VHN

74

3.2.1.2 M2C Carbide Strengthening

For the high-strength design, we want to ensure that all of the carbon is

taken up by the M2C carbide formers (Cr, Mo and V) in order to dissolve the cementite

in the matrix. Cementite negatively affects strength and toughness. Therefore, we

want the sum of the atomic concentrations of Cr, Mo, and V to double the

concentration of C for the M2C stoichiometry.

A series of calculations were performed in order to design a steel that

meets the strength requirements. Preliminary compositions were set using the guideline

(consistent with the HSLA100 alloy) that carbon content should be limited to 0.05

weight % for weldability (Fig. 3.3); Cu should be at least 1.5 weight % for significant

strengthening [76,77], minimum Ni content should be at least half that of Cu to avoid

hot shortness, and the relative amounts of carbide formers Cr, Mo and V was initially

set equal in atomic percent. A feasibility study was then performed to ensure that this

strengthening concept, in conjunction with Concept B for toughening (described in

Section 3.2.2) is thermodynamically possible, i.e. all of the phases needed for

precipitation strengthening and nickel-stabilized austenite could coexist at least in

metastable equilibrium at processing temperatures. A BCC Cu-rich precipitate is

necessary for Cu precipitation strengthening, an M2C carbide phase is necessary for

carbide strengthening, and FCC austenite is critical for transformation toughening.

Considering these constraints, thermodynamic feasibility of the preliminary alloy

75

composition was verified by ThermoCalc™ calculations at kinetically reasonable

tempering temperatures of 400-5000C.

After the feasibility study demonstrated that these concepts were

thermodynamically compatible, detailed driving force calculations were performed.

The M2C precipitation driving force determines the degree of particle size refinement

for efficient strengthening. Using the CMD™ interface, the driving force for M2C

carbides with respect to the content of each of the carbide formers was determined,

assuming initial paraequilibrium with cementite (prior precipitation of cementite with

only interstitial carbon partitioning) and neglecting coherency. The tempering

temperature used is 500°C to allow sufficient substitutional diffusion. By increasing

the driving force, a finer dispersion of precipitates is formed in the matrix. Ideally,

therefore, the driving force should be maximized while maintaining an M/C ratio in the

M2C stoichiometry.

Before the driving forces were calculated, a Mo-Cr phase diagram

section at a solution temperature of 900°C was calculated in order to determine the

relative solubility of the carbide formers in the austenite phase at a reasonable solution

temperature. The solubility limit should not be exceeded in order to achieve full

conversion to M2C for maximum carbide strengthening. Recalling that the M2C

stoichiometry must be maintained, the stoichiometric constraint, as well as the

solubility limit, can be superimposed onto a contour plot of driving force vs. Mo and

Cr concentration to optimize the M2C driving force. The Mo-Cr phase diagram section

76

is shown in Fig. 3.6. It is apparent from the phase diagram that solubility is not a

limiting factor in the region of interest, due to the relatively limited C content.

StoichiometricLine

FCC (γ) + M6C

FCC (γ)

Figure 3.6 Cr-Mo Phase Diagram at 9000C with alloy composition in atomic %:

Fe-0.234C-1.32Cu-6.21Ni-0.055V. This diagram shows the phase fields of the FCC austenite and FCC+M6C revealing that the M2C stoichiometry (red) line is well within the solubility limit.

The stoichiometric constraints of the M2C carbide dictated that the total

amount of carbide formers (Cr, Mo, V) needed to balance the carbon content would be

0.468 at%. Using this constraint, initial plots were constructed of the driving force for

M2C nucleation vs. at%(Mo) and at%(Cr), setting V at different levels. Fig.3.7 is a

77

representative plot of driving force contours with varying at%(Mo) and at%(Cr) at an

alloy composition of 0.05at% V and at 5000C. The stoichiometric constraint line has

been drawn on the plot indicating the line of allowed compositions for M2C. This

study indicated that Cr has the least effect on driving force, especially at the higher

contents of interest.

Figure 3.7 Driving Forces (in kJ/mole) for M2C carbide nucleation contour plot

varying at% (Mo) and at% (Cr) with superimposed M2C stoichiometric (red) line at 500°C at alloy compositions at% Fe-0.234C-1.32Cu-6.21Ni-0.055V.

78

Based on this finding, another set of driving force plots were created

varying at%(Mo) and at%(V) while setting the Cr level at fixed values. Due to the

very small Cr dependence, all the plots were very similar and so only a representative

graph (Fig. 3.8) was included at 0 at%(Cr). A similar M2C stoichiometric line was

drawn as before, constraining a maximum driving force at about 14.4 (kJ/mole). This

plot revealed an almost equal effect on driving force for Mo and V, indicating that any

allowed ratio of the two should give a maximum driving force value, so a series of

calculations were done along the stoichiometric line (maximum driving force). We

found a feasible alloy composition where all the desired phases as mentioned before

co-existed, which is indicated by the dot and arrow in Fig. 3.8. An initial feasible alloy

composition in wt % was thus determined without any Cr: Fe-0.05C-1.5Cu-6.5Ni-

0.6Mo-0.1V.

79

Figure 3.8 Driving Force (in kJ/mole) for M2C carbide nucleation contour plot

varying at% (Mo) and at% (V) with superimposed M2C stoichiometric line at 500°C at alloy compositions at% Fe-0.234C-1.32Cu-6.2Ni.

The V-Mo phase diagram section at a solution temperature of 900°C

with the feasible alloy composition was then calculated. Again, the solubility of these

carbide formers is not a limiting factor in the region of interest. This plot is shown in

Fig. 3.9.

80

Stoichiometric Line

FCC (γ) + V3C2

FCC (γ)

Figure 3.9 Mo-V Phase Diagram at 9000C with alloy composition in atomic %:

Fe-0.234C-1.32Cu-6.2Ni. This diagram shows the phase fields of the FCC austenite and FCC+V3C2 revealing that the M2C stoichiometric (red) line is well within the solubility limit

81

3.2.1.2 Copper Precipitation Strengthening

In addition to M2C carbide strengthening, BCC copper precipitation

strengthening will be modeled to control the phase fraction of the precipitates through

the alloy copper content to provide the additional increment of strength (≡ 151 VHN).

As described in Section 2.3.2, the copper precipitates that contribute to strengthening

in steels have a metastable BCC structure, which are fully coherent with the matrix

having an average diameter of 1-5 nm. The strengthening mechanism has been

described by the Russell-Brown model [59] based on the interaction between the

matrix slip dislocation and the second phase copper-rich particle of lower shear

modulus than the matrix. They derived an expression to calculate the minimum

included angle, φ, reached by the arms of a dislocation while cutting the precipitate as a

function of the energy of the dislocation on either side of the precipitate/matrix

interface. This angle is used to calculate the yield stress as a function of interparticle

spacing. Since these coherent copper particles effective for strengthening are small in

size, they calculated the flow stress by considering energy of the dislocation per unit

length in an infinite medium of the matrix. The shear stress has a maximum value, τmax,

given by Equation 3.3.

0

2/1

max041.0

rGbf

=τ (3.3)

where G is the matrix shear modulus, b is the burgers vector, f is the volume fraction of

atoms and r0 is the core radius of the dislocation. Thus the maximum strength that can

82

be achieved is proportional to the square root of the volume fraction of the precipitate.

Based on this volume fraction dependence of the precipitate on yield stress, the

hardening increment from available data of copper precipitation strengthened steels

[59] was plotted as shown in Fig. 3.10. The best-fit line described by a one-half power

law defined the hardening increment dependence on the alloy content (at%) of copper.

(3.4) 2/1807.83)( CuXVHN =∆τ

Based on this relationship, the hardness increment of 151 VHN can be achieved by

addition of 3.25 at% Cu to the alloy composition.

Figure 3.10 Change in hardness as a function of alloy copper content for BCC copper strengthening contribution [59]. Experimental results of other copper strengthened steels are shown. The dotted line represents the best-fit line for one-half power law given by equation (3.4).

83

3.2.2 Transformation Toughening Design

For design of tough steels for such high strength levels (160 ksi YS) we

need to develop a fully secondary hardened microstructure with higher stability

austenite produced by precipitation. At high strength levels we need the higher stability

of precipitated austenite since the mechanical driving force for transformation is very

high. This design seeks to improve the toughness of higher strength steels by utilizing

the beneficial properties of Ni-stabilized precipitated austenite. This form of austenite

can precipitate during annealing or tempering at elevated temperatures above about

470°C. The fact that this dispersed austenite forms by precipitation is significant

because it allows greater overall control of the amount and stability of the austenite.

Further processing and treatments can be used in the form of multi-step tempering to

first nucleate particles in a fine form at a higher tempering temperature and then

complete Ni enrichment during completion of precipitation strengthening (cementite

conversion to 3nm M2C) at a lower final tempering temperature.

Shear localization by microvoid nucleation is known to be the most

dominant fracture mode in high strength steels. As discussed in Section 2.4, studies

[104] have shown that fine particle dispersions with adherent interfaces are optimal for

controlling microvoid nucleation. The most promising microstructure modification is

achieved by nucleating an optimal stability austenite dispersion, which increases

toughness by suppressing microvoid nucleation to higher strain levels. Thus, emphasis

84

will be put on the design of intralath dispersions, as the greater stability associated with

their finer size makes them the primary toughening form of austenite precipitates.

The austenite dispersion must have sufficient stability and proper

formation kinetics to ensure maximum toughening enhancement. Other factors

controlling the stability of austenite are particle size and stress state sensitivity, the

latter being related to the transformational volume change. The Olson-Cohen classical

heterogeneous martensitic model can be applied to describe dispersed austenite

stability for transformation toughening [100]. Stability of an austenite precipitate is

defined by chemical and mechanical driving force terms. According to the model, at

the Msσ temperature for the crack-tip stress state, the total driving force equals the

critical driving force for martensite nucleation, as represented by Equation 3.5.

Combining Equations 2.15, 2.16 and 2.17 in Chapter 2,

⎥⎦⎤

⎢⎣⎡ ++−=

∆+∆ f

cracktipy

ch WGndd

GdG 02γ

σσ

σ

(3.5)

Rearranging the terms and substituting the dependence of defect potency on particle

volume Vp, we can define a convenient stability parameter:

⎥⎥⎦

⎤

⎢⎢⎣

⎡+

∆−=++∆ 0)ln(

GdGd

VKWG

cracktipy

pf

ch

σσ

σ

(3.6)

85

∆Gch is the transformation chemical free energy change and Wf is the athermal

frictional work term described in Section 2.4. ∆Gch is temperature and composition

dependent while Wf is only composition dependent. Wf will vary with tempering

temperature due to the change in austenite composition. σy is the yield stress of the

material, ∆Gσ is set by the stress state and G0 is a nucleus elastic strain energy term. K

is a proportionality constant, γ is the nucleus-specific interfacial energy and d is the

crystal interplanar spacing.

The austenite stability for a given set of conditions or service

temperature for a given dispersion can be assessed by the parameter given by the left-

hand side of Equation 3.6. If we assume an austenite particle size equivalent to that

achieved in previous studies of AF1410 and AerMet100 steels, our austenite stability

parameter becomes the sum of the chemical driving force for transformation of FCC

austenite to BCC martensite at room temperature (300K) and the frictional work term

for martensitic interfacial motion: ∆Gch + Wf. ThermoCalc™ can be used to predict the

temperature and compositional dependence of the chemical energy term. Ghosh and

Olson [105,106] have modeled the composition dependence of the frictional work term

as a power law with an exponent of 0.5 and a fit to experimental data was achieved.

Appropriate superposition laws considering relative strengths of the solutes were

applied for complex systems. The model is represented in Equation 3.7.

2/12/12/12/1 )()()( CoCo

kk

k

jj

j

ii

if XKXKXKXKW +++= ∑∑∑ (3.7)

86

where the K’s represent the coefficients used to fit the solid solution strengthening data

and i = C, N; j = Cr, Mn, Mo, Nb, Si, Ti, V; and k = Al, Cu, Ni, W.

Equation 3.7 further indicates that the stability parameter is a linear function of the

yield strength of the material.

The strength dependence of the optimal stability level was determined

from previous transformation toughening experiments on the AF1410 and AerMet100

steels [6]. Fig. 3.11 gives the plot of the austenite stability parameter, ∆Gch + Wf, at

room temperature against Vickers hardness of the alloy. The room temperature

stability of the austenite dispersion projected from the hardness (or strength)

requirement of the design is marked by the shaded region in the figure and

quantitatively expressed in Table 3.1. To achieve a goal of 160ksi yield strength

equivalent to Vickers hardness of 389 (Rc40 equivalent), the estimated optimum ∆Gch

+ Wf value of 2837 J/mole was found for the required stability.

Table 3.1: Target Chemical Driving Force (∆Gch) + Frictional Work (Wf) Value

Alloy Rockwell C Hardness

Vickers Hardness ∆Gch + Wf

Rc VHN (kg/mm2) J/mol

AerMet 100 54 577 4350

AF1410 48 484 3600

Concept B Steel 40 389 2837

87

RT (300K) Stability of Austenite

0

1000

2000

3000

4000

5000

280 330 380 430 480 530 580 630

Hardness (Vickers)

Gch

+Wf (

J/m

ol)

AerMet 100AF1410

Concept B Design Alloy

Figure 3.11 Room temperature (300K) austenite stability plotted as a function of

Vickers Hardness Number (VHN). The shaded region shows our range of interest for austenite stability Concept B alloy corresponding to yield strength requirement of 150-180 ksi after extrapolation of data from previous alloys, AF1410 and AerMet100.

The design of transformation-toughened austenite has been calibrated

against this stability parameter to determine the optimal level of austenite-stabilizing

nickel in the alloy. Plots of both the phase fraction of austenite and nickel content in

the austenite phase vs. alloy atomic fraction Ni were computed. Fig. 3.12 was

calculated at an estimated final tempering temperature of 500ºC for substitutional

88

diffusion and revealed that a minimum of 3.5at% Ni is required to get austenite and a

maximum fraction of nickel in the austenite of about 0.30 could be obtained. It also

showed that at the 6.25 at% Ni composition from feasibility studies, about a 0.10 phase

fraction of austenite would be formed as shown by the red arrows. This compares well

to the phase fraction of austenite employed in previous transformation toughened

steels. We thus set the alloy Ni level to 6.25at%, which also saturates the austenite Ni

content to 30 at%.

After conducting the feasibility study mentioned previously in Section

3.2.1.1 and verifying that the corresponding austenite stability was within the design

limits given in Fig. 3.11, a thermodynamically viable alloy composition was found

using 6.25 at% Ni. This Ni level was deemed acceptable as it fell well within the

nickel content guidelines, while being low enough to limit the material cost.

89

T= 5000C

Figure 3.12 Fraction of Ni in austenite and phase fraction of austenite in alloy vs.

mole fraction of Ni at 5000C with alloy composition in weight %: Fe-0.05C-3.65Cu-1.85Cr-0.6Mo-0.1V

90

3.2.3 Design Integration

The overall composition was optimized so that all of the phases

necessary for strengthening and toughening are simultaneously present. Since the

maximum M2C driving force is obtained with no chromium, equilibrium phase

calculations were done for the initial feasible composition. For this composition, it was

found that the copper added for precipitation strengthening went instead into the

austenite phase. A study of the equilibrium austenite composition with varying alloy Cr

content was then undertaken as given in Fig.3.13. It was found that Cr partitions Cu

out of austenite and into the BCC precipitate phase effectively at 2wt% and above.

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

0 0.02 0.04 0.06 0.08 0.1 0.12

Alloy Weight Fraction of Cr

Mol

e fr

actio

n of

ele

men

ts

x(Cu)x(Ni)x(Cr)x(Mo)x(V)x(C)

Ni

Cu

Cr

Figure 3.13 Equilibrium composition of austenite as a function of alloy Cr content

(wt. fraction) at 5100C

91

Further, to understand the effect of Cr on partitioning of Cu out of the

austenite phase, a detailed investigation was done based on a quasi-ternary section of

the multicomponent system at 5100C as presented in Fig. 3.14. The equilibrium Cr and

Cu phase compositions of BCC Cu, austenite and the ferrite phases connected with tie-

triangles are presented for different Cr contents of the alloy. An interesting feature to

note in the figure is that the austenite equilibrium point abruptly shifts to a much lower

Cu level with an increase of alloy Cr level from 1 at% to 1.2 at%. This study confirms

that Cu partitions to the BCC precipitate phase above 1.2 at% Cr. From a robust alloy

design consideration as discussed earlier in the section, 2 at%Cr (equivalent to 1.84

wt% Cr) was set for the alloy to make the copper in the alloy available for precipitation

strengthening.

92

Figure 3.14 Quasi-ternary section of the designed multicomponent alloy system at 5100C. Other alloying elements are fixed at Fe – 0.24C – 3.25Cu – 6.26Ni – 0.35Mo – 0.11V (at%). The tie-triangles shown by thin solid lines indicate three-phase equilibrium between BCC Cu, austenite and ferrite. The dashed arrow traces out the trajectory of the austenite phase composition (solid dots) as a function of increasing alloy Cr content

93

The relative fractions of the different phases in the microstructure were

then calculated as a function of the alloy Cr content to confirm the effect of chromium

as shown in Fig. 3.15 This confirms that at 2wt% Cr, there is sufficient precipitation of

austenite (> 0.1 mole fraction) for transformation toughening and bcc Cu (~0.03 mole

fraction) for strengthening.

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

0 0.02 0.04 0.06 0.08 0.1 0.12

Alloy wt. fraction of Cr

Phas

e fr

actio

ns

FCC austenite

BCC copper

M2C

MC

Figure 3.15 Equilibrium phase fractions at 5100C as a function of alloy Cr content

(wt fraction)

94

3.2.4 Processing Considerations

3.2.4.1 Solution Treatment Temperature and Allotropic Transformations

A solution treatment temperature of 9000C was chosen based on

optimization studies [2, 117] of grain size dependence on hardness and toughness on 1

hour solution treated samples in secondary hardened steels. With the increased levels

of Cu and Cr it was confirmed that the alloy was solution treatable at 9000C as shown

by the ThermoCalc™ plot in Fig. 3.16.

Figure 3.16 Plot showing the variation of equilibrium mole fraction of different phases in the alloy as a function of temperature, showing that the alloy is solution treatable at 9000C

95

For this alloy composition, the martensite and bainite kinetic models

predict an MS temperature of 2980C and a bainite start (BS) temperature of 3360C.

These should be sufficiently high to ensure formation of bainite/martensite mixtures

with air-cooling.

3.2.4.2 Scheil Simulation for Microsegregation behavior

Solidification of alloys generally occurs with segregation, which can

have a strong effect on the alloy’s final properties. Thus, it is important to model

segregation to assess the processability of the designed alloy. This investigation uses

thermodynamic modeling to predict microsegregation of the as-cast material.

Macrosegregation effects can also be addressed by modeling liquid buoyancy

associated with the microsegregation amplitude but are not addressed in this

assessment.

Scheil simulation is a fast method of estimating microsegregation [118].

The main approximations are infinite diffusion in the liquid but no diffusion in the

solid phase. This has been coupled to the multicomponent SGTE thermodynamic

database using ThermoCalc™ from which the solid/liquid equilibrium was calculated

repeatedly during the simulation. Fig. 3.17 presents the solidification simulation result

as temperature vs. fraction solid using the non-equilibrium Scheil simulation and

compares it with the full equilibrium case. Fig. 3.18 presents the composition profiles

calculated by the Scheil simulation showing the degree of microsegregation in the solid

96

after solidification. Here, the fraction of solid is equivalent to position relative to a

dendrite arm center. Previous comparison with more rigorous calculations

incorporating solid back diffusion indicate that the Scheil result at 95% solid is a

reasonable estimate of the maximum microsegregation amplitude under typical ingot

solidification conditions. The results presented in Table 3.2 predict that Mo has the

greatest potential for segregation. However, since the level of Mo in the alloy is low,

no serious microsegregation problems are predicted for the designed composition.

97

Figure 3.17 Scheil simulation for evolution of the fraction solid with cooling for designed alloy Fe-0.05C-6.5Ni-3.65Cu-1.84Cr-0.6Mo-0.1V (wt%) in comparison with equilibrium solidification

98

Figure 3.18 Scheil simulation for composition profile of each alloying element after

solidification for designed alloy Fe-0.05C-6.5Ni-3.65Cu-1.84Cr-0.6Mo-0.1V (wt%). Solid fraction corresponds to position relative to dendrite arm center

Table 3.2: Amplitude of microsegregation with respect to each alloying element

predicted by Scheil simulation at 95% solidification

Alloying Elements Ni Cu Cr Mo V Nominal Alloy Composition

Calloy (at %)

6.38 3.31 2.04 0.36 0.11

Microsegregation Amplitude

C0.95 – C0 (at %)

1.29

1.67

0.72

0.34

0.05

99

3.2.4.3 Optimal Tempering Temperature

The austenite stability for this transformation toughened alloy is

dependent on the optimal tempering temperature condition. With the alloy composition

fixed, the austenite stability was then calculated as a function of tempering temperature

as shown in Fig. 3.19. It illustrates that the ∆Gch + Wf value of 2836 J/mole desired for

this alloy is achieved for a tempering temperature of 4900C, very close to the originally

assumed temperature of 5000C.

Figure 3.19 Room Temperature (300K) stability of austenite as a function of tempering temperature. The required stability is predicted for 4900C

100

Based on the design calculations, we derive a composition for the

ultratough, high strength weldable plate steel (in wt%) to be tempered at 4900C:

Fe – 0.05C – 3.65Cu – 6.5Ni – 1.84Cr – 0.6Mo – 0.1V.

The composition should be solution treatable at 9000C, with predicted MS and BS

transformation temperatures of 2980C and 3360C respectively. Based on previous

transformation toughened steels, it is expected that initial tempering at a slightly

elevated temperature will help nucleate the austenite before tempering at 4900C to

enrich the Ni content to the designed level.

101

4. MATERIALS AND EXPERIMENTAL PROCEDURES

4.1 Materials

The compositions of the alloys studied in this research have been

designed using a systems-based approach as presented in Appendix A (Concept A

alloy) and in Chapter 3 (Concept B alloy). The alloys were designed to provide an

effective transformation toughening austenite dispersion and an efficient combination

of carbide and copper strengthening dispersions. Special Metals Corporation in New

Hartford, New York produced the alloys as 34-pound experimental heats by Vacuum

Induction Melting (VIM) from 100% virgin raw materials and cast into 9.5” X 8” X

1.75” (24.1cm X 20.3cm X 4.5cm) slab ingots as a simulation of a continuous casting

process. The as-cast ingots were subsequently homogenized at 22000F (12040C) for 8

hours and then hot rolled to 0.45” (1.1cm) thickness followed by air-cooling to room

temperature by Huntington Alloys in Huntington, West Virginia. The final dimension

of the plate measured roughly 33” X 10” X 0.45” (83.8cm X 25.4cm X 1.1cm). The

hot-rolled plate was annealed at 9000F (4820C) for 10 hours to improve machinability

of the material. The designed and the actual compositions (in wt %) of the Concept A

and Concept B alloys are given in Tables 4.1A and 4.1B respectively. The impurity

levels in the Concept A alloy were measured as 0.002 wt % S, 13 ppm O and 2 ppm N,

and are expected to be similar in the Concept B alloy based on its identical melt

practice. The measured compositions are very close to the designed compositions and

the variations are within the tolerance limits of the design.

102

Table 4.1A: Designed and Measured Composition (in wt. %) of Concept A* alloy

Alloy Fe C Cu Ni Mn Si

Design Bal. 0.10

± 0.01

1.37

± 0.05

0.82

± 0.05

7.6

± 0.2

1.5

± 0.05

Measured Bal. 0.10 1.39 0.84 7.42 1.45

*Prototype Evaluation of Concept A alloy is described in Appendix A

Table 4.1B: Designed and Measured Composition (in wt. %) of Concept B alloy

Alloy Fe C Cu Ni Cr Mo V

Design Bal. 0.05

± 0.01

3.65

± 0.05

6.5

± 0.2

1.84

± 0.05

0.6

± 0.05

0.1

± 0.01

Measured Bal. 0.040 3.64 6.61 1.78 0.58 0.11

4.2 Experimental Procedures

4.2.1 Heat Treating

All samples were solution treated at 9000C for 1 hour and quenched in

water followed by a liquid nitrogen cool for 30 minutes prior to every tempering

treatment to ensure a fully martensitic starting microstructure and eliminate any

retained austenite. Solution treatments were done in an argon atmosphere to prevent

103

oxidation of samples. To ensure rapid heating of the entire sample, the short-time

nucleation stage heat treatments were conducted using a molten salt bath followed by

water-quenching to room temperature. The salt used for the molten bath was Thermo-

Quench Salt (300 – 11000F) produced by Heat Bath Corporation. The residue layer

from the salt pot treatment was ground off before the second step aging treatment. The

standard aging treatments for longer times (1 – 10 hours) were performed in a box

furnace under vacuum (to prevent oxidation and decarburization) and then air-cooled

to room temperature. Vacuum was achieved by encapsulating the samples in 0.75”

diameter pyrex tubes connected to a vacuum system. The pyrex tubes were evacuated

by a mechanical roughing pump followed by a diffusion pump. During evacuation, the

tubes were backfilled with argon three times before reaching a final vacuum of < 5

mtorr. Each tube was then sealed with an oxygen/propane torch.

4.2.2 Metallographic Sample Preparation

All samples were ground and polished directly to 1 µm finish using a

Buehler Ecomet-4 variable speed automatic grinder/polisher. The samples prepared for

measuring hardness were mounted in room temperature curing acrylic, while those

prepared for microsegregation studies were hot mounted with conductive phenolic

resin using a Stuers LaboPress-1 after nickel-plating for edge retention of the oxide

layer during grinding and polishing. Microsegregation samples were etched by

submersion in a 2% nital (2% nitric acid in ethanol) solution for 10 – 30 seconds to

104

reveal the compositional banding close to the metal-oxide interface associated with

scale formation during hot working. Following etching, the samples were viewed with

an optical microscope to study the banded structure in the as-cast material.

4.2.3 Dilatometry

Dilatometry is used to study phase transformations by recording length

changes versus temperature. For these studies a computer controlled MMC Quenching

Dilatometer was used. Specimens were prepared by EDM (Electro-Discharge

Machining) wire cutting into cylindrical rods 10 mm long and 3 mm in diameter. The

samples are heated by an induction furnace and cooled by jets of helium gas. They are

mounted between two low expansion quartz platens, which are lightly spring-loaded

and are connected to an LVDT transducer that records the length. The temperature is

monitored by a Pt-Pt 10%Rh thermocouple spot welded directly to the sample surface.

The sample stage is enclosed in a vacuum chamber connected to a turbo-mechanical

pump and mechanical backing pump capable of achieving a vacuum of 10-4 torr.

Dilatometry was used for determining the martensite start temperature

(MS) and for evaluating the bainite transformation kinetics. For estimating the

experimental MS temperature, samples were heated at a rate of 2-30C/sec to 10500C,

held for 5 minutes for homogenization and then rapidly quenched (> 1000C/sec) to

room temperature. The MS temperature was determined as the transition at which the

sample started expanding on cooling. For studying the bainite kinetics, samples were

105

held isothermally for 2 hours at bainite transformation temperatures between 360 –

4200C after quenching (Cooling rate from 8000C to 5000C, T8/5 = 500C/sec) from the

austenizing temperature. The length change at the isothermal hold temperature is a

measure of the amount of bainitic transformation. All samples were austenized at

10500C for 5 minutes and then rapidly quenched prior to the actual runs of martensite

and bainite transformation in order to ensure uniform starting microstructure.

4.2.4 Microhardness Testing

Vickers hardness was measured for every aging condition as a measure

of strength. The relationship between hardness and yield strength (Fig. 3.2) helped to

assess the mechanical properties directly from the hardness data. Hardness

measurements of materials in this study were performed using the Buehler Micromet II

Micro Hardness Tester based on the method prescribed in ASTM standard E384. A

diamond Vickers pyramidal indenter with face angles of 1360 is used to make the

indentations. After applying a load of 200g for 5 seconds, the diagonals of the indent

were measured at 400X magnification to obtain the Vickers Hardness (VHN)

according to Equation 4.1.

2

854.1d

PVHN = (4.1)

where P is the load in kg. and d is the average length of the diagonal in millimeters of

the indent. Prior to testing, all the heat-treated samples were mounted in acrylic mold

106

and polished to 1 µm. The samples were at least 8mm thick and ground to reveal

opposite surfaces to avoid any errors due to anvil effects. At least ten hardness

measurements were recorded uniformly across the cross-section for every sample

tested and the average was documented as the hardness value.

4.2.5 Impact Toughness Testing

The impact toughness properties for the different heat treatment

conditions of the alloy were measured using a Tinius Olsen 260 ft-lb (352J) impact-

testing machine. Prior to testing, the samples were machined according to the ASTM

standard Charpy V-notch dimensions (1996 ASTM E23) 10mm X 10mm X 55mm

(0.39” X 0.39” X 2.17”) with a 450 notch of depth 2mm and root radius of 0.25mm

placed at the center of the long side. The longitudinal axis of the specimen

corresponded to the L-T orientation. A schematic view of the sample geometry is given

in Fig. 4.1. The impact fracture energy was measured directly on analog scale and the

given impact energy data was mostly based on a two-sample average. Most impact

properties were evaluated at room temperature. For the low temperature impact

fracture properties, the aged samples were held for 20 minutes at the test temperature

in an Instron low temperature furnace connected to a liquid nitrogen supply. Within 5

seconds of removal from the furnace, the samples were placed inside the machine and

struck with the 100-lbf hammer.

107

Rolling Direction

Figure 4.1 Charpy V-notch impact specimen dimensions (Standard ASTM E23) with longitudinal axis corresponding to the L-T orientation

4.2.6 Tensile Testing

Tensile test specimens were machined from blanks measuring

approximately 10mm X 10mm X 70mm (0.39” X 0.39” X 2.76”) from the original

plate parallel to the longitudinal rolling direction. Prior to machining, the samples were

solution-treated and aged as discussed in Section 4.2.1. From each blank, sub-sized

tensile specimens, scaled in accordance to ASTM standards (1996 ASTM E8M) were

machined as shown schematically in Fig. 4.2. The final specimen had a gage diameter

of 6 mm (0.24”) and a gage length of 30 mm (1.18”).

108

Rolling Direction

G (gage length) 30 ± 0.1 mm (1.18” ± 0.004”) D (gage diameter) 6 ± 0.1 mm (0.24” ± 0.004”) R (radius of fillet) 6 mm (0.24”) A (length of reduced section) 36 mm (1.42”) Figure 4.2 Tensile test specimen dimensions (Standard ASTM E23)

All tensile tests were performed at room temperature using a computer

controlled Sintech 20/G screw driven mechanical testing machine with a 20,000 lb

(8896 N) load cell at a constant cross-head speed of 0.005 in/sec (0.127 mm/sec). The

load cell was calibrated prior to every data set using the computer controlled

calibration test. A calibrated extensometer of gage length 1” (25.4 mm) was attached to

the sample during testing to measure the displacement. The load-time response was

recorded using the TestWorks computer software package interfaced with the Sintech

tensile testing machine. The actual cross-sectional areas and gage lengths of the

specimens were measured prior to testing and listed in the testing program. Area

reduction and extension were measured manually upon completion of the test.

Engineering stress-strain curves were obtained directly thorough the TestWorks

109

program. Based on a two-sample average for select processing conditions, the ultimate

tensile strengths, 0.2% offset yield strengths and total elongations were obtained.

4.2.7 X-Ray Diffraction (XRD)

The measurement of the volume fraction of austenite was attempted by

X-ray Diffraction. Metallographically polished samples were centered in a Scintag

diffractometer equipped with CuKα radiation source and a solid-state detector. For

austenite volume fraction measurements the ratio of the integrated intensities of (200)

reflection of martensite and (220) reflection of austenite were compared with that of a

standard specimen of known volume fractions of ferrite and austenite. The 2θ ranges

scanned were from 630 to 670 for the (200) reflection of martensite and from 71.50 to

77.50 for the (220) reflection of austenite. The data collection times were 50s and 100s

for the austenite and the martensite reflection, respectively, at each step with a step size

of 0.0250. The volume fraction of austenite was measured after water quenching from

solution treatment for 1 hour at 9000C followed by liquid nitrogen cooling and

tempering treatment.

In a two phase alloy consisting of martensite (α) and austenite (γ), the

ratio of the diffracted intensities is given by [139]

α

γ

γαα

γ

V

V

ff

RII

220200200

220 = (4.1)

110

where Iγ220 and Iα200 are the integrated intensities and fVγ and fV

α are the volume

fractions of austenite and martensite respectively. The Rij-factor includes the structure

factor, the multiplicity factor, the Lorentz-Polarization factor and the temperature

factor. For a given experimental setup and a selected pair of austenite-ferrite reflection,

the R-factor is a constant relating intensity to volume fraction by Equation 4.1. In this

work, the Rα200γ220 factor for the above experimental condition was evaluated using a

Standard Reference Material (SRM # 485) from the National Bureau of Standards

(NBS) containing 4 ± 0.2 vol% austenite in ferrite. The volume fraction of austenite in

the tempered prototype can then be determined by following the relation:

γγαα

γγαγ

IRIIR

fV += (4.2)

The (220) reflection of austenite was not discernable above the background, attributed

to a very fine particle size established by atom-probe observations.

4.2.8 Magnetometry

Magnetometry measurements were performed to determine the austenite

volume fraction in the heat treated alloys. The difference in the magnetic moments of

the martensite and austenite phases are used to determine the phase fractions based on

the total measured magnetic moment and the rule of mixtures. Magnetometry was

selected in addition to standard X-ray diffraction method because of the matrix strain,

111

texture in the alloys tested, nanometer-sized austenite precipitates and low precipitate

volume fraction which reduces the signal to noise ratio to unacceptable levels.

A Quantum Design Magnetic Property Measurement System with a

superconducting quantum interference device (SQUID) detector was used in these

experiments. The apparatus is equipped with a superconducting magnet capable of

supplying a maximum of 50,000 gauss to the sample. The resulting magnetization was

measured using a SQUID detector. The magnetic signal was measured at 298K by

passing the specimen through the detector with applied magnetic field strengths

ranging from 5000 – 50000 gauss and measuring the response of the detector as a

function of distance within the detector. Each data point was measured three times to

ensure accuracy and provide error estimations. The specimen weight was limited to

less than 5mg to avoid saturating the detector with induced moments of greater than

1.25 emu. To produce samples of this size, thin discs were sectioned from the heat-

treated samples, ground using 600 grit SiC and then finally electro-polished using a

perchloric and acetic acid solution to remove any surface cold work introduced during

sample preparation. The completed specimen is contained in a gelatin capsule and is

suspended with a nonmagnetic plastic rod in the measurement chamber kept under

vacuum. The specific magnetization is calculated from the recorded data and plotted

against the reciprocal of the applied field as shown in Fig. 4.3. The intercept with the

y-axis is taken as the saturation magnetization.

112

σ = mH-1 + σS

σS = 204.21m = -783999R2 = 0.9892

0

50

100

150

200

250

0 0.00005 0.0001 0.00015 0.0002 0.00025

H-1 (gauss-1)

Spec

ific

Mag

netiz

atio

n (e

mu/

g)

Figure 4.3 An example of magnetometry data processing to determine saturation magnetization

The saturation magnetization can be related to the experimentally

measured room temperature magnetic moments by the Miodownik [110]

approximation to the Brillouin-Langevin function represented by Equations 4.2 and

4.3.

⎥⎦

⎤⎢⎣

⎡−= 60 )(1

CSS T

Tσσ T < 0.9 TC (4.2)

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎠⎞

⎜⎝⎛=

8100

21 CT

T

SS σσ T > 0.9 TC (4.3)

where σS0 is the magnetic moment at absolute zero, TC is the Curie temperature and σS

is the magnetic moment at temperature T. The Bohr magneton moment at absolute zero

113

and the Curie temperature for FCC and BCC phases can be calculated using the

ThermoCalc™ SGTE-SSOL database. The saturation magnetization value at absolute

zero is calculated from the predicted magnetic moment per atom (from ThermoCalc™)

by multiplying the moment per atom by Avagadro’s number and dividing by the

atomic weight of the phase. The contribution from carbides and copper precipitates is

neglected because their magnetic moments are much less that either that of austenite

(γ) or martensite (α). The rule of simple mixtures is then solved to determine the molar

fractions of each phase.

(4.4) γγαα σσσ SmSmalloyS ff +=

where, σSalloy is the measured saturation magnetic moment, fm is the molar fraction of

the denoted phases. The molar fraction is then converted to volume fraction using the

relation:

)( 11

1

−−

−

+=

αα

γγ

γγ

γ

ρρρ

ww

wv ff

ff (4.5)

where ρ is the density of the indicated phase.

4.2.9 Electron Microscopy

A Hitachi S-3500 scanning electron microscope (SEM) with a tungsten

hairpin filament was used to investigate the composition banding in the as-rolled

samples and the fracture surfaces of the Charpy impact specimens. The microscope

uses Quartz PCI Image Management Software for capturing images and for conducting

114

quantitative analysis. For analysis, the samples were mounted on graphite tape and

examined in the SEM with a 20 kV electron beam at a vacuum level of 10-4 torr inside

the specimen chamber. The secondary electron (SE) detector was used for imaging

both the etched and fracture surfaces. The compositionally banded structure of the

etched sample was characterized quantitatively from the metal-oxide interface using

the PGT Energy Dispersive X-ray analyzer with digital pulse processing. Fractography

analysis was done to characterize the fracture surface and micrographs containing

interesting features were taken.

Conventional transmission electron microscopy (TEM) was performed

in a Hitachi H-8100 200kV thermionic-emission (W hairpin filament) TEM. The

samples were obtained by sectioning thin slices approximately 150 µm thick directly

from the hardness specimens. The samples were then ground to a thickness of

approximately 50 µm and then punched into small discs. The discs were then jet-

polished until a small hole was present using a Twin Jet electropolishing system with a

20 vol.% perchloric acid in methanol electrolyte at a temperature of –400C and an

operating voltage in the range of 35-40 V.

4.2.10 Atom Probe/ Field Ion Microscopy (AP-FIM)

A three-dimensional atom probe microscope (MRC Atom-Probe

Facility, Northwestern University) described in [111], was used for characterizing the

size, number-density and composition of nanoscale strengthening (Cu precipitates) and

115

toughening (Ni-stabilized austenite) dispersions in the heat-treated samples. The atom

probe, operated and maintained under an ultra-high vacuum system (10-10- 10-11 torr)

combined with a field ion microscope, operated with imaging gas at a pressure level of

10-5 torr, makes it an extremely high-resolution microscopy technique.

The specimens (atom probe tips) were prepared by a two-step

electropolishing sequence of small rods (100mm long with 200µm X 200µm square

cross-section) cut from heat-treated hardness samples. Initial polishing was done using

a solution of 10% perchloric acid in butoxyethanol at room temperature applying a DC

voltage of 23V until the square rods were shaped into long needles with a small taper

angle. A solution of 2% perchloric acid in butoxyethanol at room temperature was used

for necking and final polishing to produce a sharply pointed tip, with a radius of

curvature less than 50nm. The voltage was gradually decreased from 12V DC to 5V

DC during the final stages of electropolishing.

Each atom probe specimen of tip radius 10 to 50 nm is raised to a high

positive potential of 5-15 kV, resulting in an exceptionally strong electric field on the

order of 50 V/nm. FIM analysis was performed at temperatures between 50K – 80K

with a chamber pressure of 10-5 torr consisting of neon gas. The voltage on the tip was

raised until an FIM image was observed on the monitor. Neon atoms, which are used

as an imaging gas for steel, are ionized in the high electric field causing the positively

charged ions to accelerate to a microchannel plate array. The ionization process occurs

at prominent atomic sites at the edge of a crystallographic plane corresponding to a

116

particular atom. A continuous stream of ions form an image on a phosphorus screen

that represents the nanometer-scale structure of the specimen tip. FIM images were

captured during analysis using the Scion Image imaging software. For atom probe

analysis, the specimen is then rotated towards the reflectron for aligning the primary

detector on the region of interest in the FIM image (usually near a pole or on a

precipitate in the FIM image). Atom probe analysis is then conducted at temperatures

50K and 70K under ultra-high vacuum conditions (10-10- 10-11 torr) for pulsed field-

evaporation with a pulse fraction (pulse voltage/ steady state DC voltage) of 20% at a

pulse frequency of 1500Hz.

Atom probe microanalysis is the study of the specimen composition by

pulsed evaporation. Field evaporation of the specimen occurs at higher electric fields

than ionization of imaging gas ions. The positively charged ions evaporated from the

specimen are accelerated towards a detector. By measuring the time of flight, it is

possible to determine the mass to charge ratio of the ions according to the following

equation [112]:

( )2

0 ⎟⎠

⎞⎜⎝

⎛ ++=

dtt

VVknm

pulsedc βα (4.6)

where m is the atomic mass, n is the charge, k is a constant related to the elementary

charge of an electron, V is the DC or pulse voltage, t is the time, t0 is a time offset from

electronic delays, and α and β are system specific calibration parameters.

117

The standard error, σ, for compositions measured using an atom probe is

calculated using binomial statistics to account for the statistical uncertainty associated

with small sampling sizes according to the equation [113]:

σ =ci 1 − ci( )

N (4.7)

where ci is the measured composition of element i and N is the total number of ions

sampled. This standard error does not account for any overlapping mass to charge

ratios between different elements. Systematic errors that may interfere with the

collection of specific elements such as carbon may be an additional source of error.

Three-dimensional atom probe (3DAP) records the two-dimensional

location of atoms and determines the third dimension (z) by the sequence of arrival of

atoms to the detector, thus providing a three-dimensional reconstruction of the

specimen tip. The evaporated ion collides with a primary detector that records the time

of flight, and the phosphorus screen emits light. The light is split by a partially

silvered mirror at 45° to both a camera and an 8 by 10 array of anodes which determine

the position of the ion.

The data from 3DAP was analyzed and visualized by the software

ADAM developed by Hellman et al [114]. Different elemental isotopes were

distinguished by their mass/charge ratio. The overlap of isotope masses between

elements contributed to the experimental error in addition to the statistical counting

error. A range of tools is available in ADAM to analyze the data from the 3DAP [115].

118

One feature of ADAM is the ability to define planar or cylindrical regions of interest

and to perform analyses such as concentration profiles, ladder diagrams and

composition maps with respect to that region of interest. For the data containing copper

precipitates, varying in composition from the matrix, it was possible to define

isoconcentration surfaces of constant composition. The three-dimensional

representation of these isoconcentration surfaces allows for a qualitative view of the

approximate size and shape of the precipitates being studied. ADAM has been designed

to employ this method by creating a discrete lattice of nodes for which the local

composition is calculated. The isoconcentration surfaces then have discrete positions.

The creation of isoconcentration surfaces allows for another method of 3DAP data

analysis referred to as the proximity histogram, or proxigram [116]. The minimum

distance to an isoconcentration surface is calculated for each ion in the data set and the

ions are then assigned to bins according to distance. The concentration of each bin is

calculated and plotted as a function of distance to the isoconcentration surface. The

standard error of each bin is calculated and displayed on the proxigram.

119

5. PROTOTYPE EVALUATION

Characterization of the Concept B prototype alloy demonstrated the

effectiveness of the systems approach to computational materials design as described

in Chapter 3. The primary goal of prototype evaluation in this study is to

experimentally verify the processing-structure and structure-property relationships

quantified during the alloy design process. This will reveal the strength and

weaknesses of the design models and their integration. The analysis began with

evaluation of the processability characteristics of the designed alloy at an

experimental-heat scale. Optimization of the tempering response of the alloy designed

for multi-step treatment helped to attain a toughness/strength combination exceeding

the design objectives. Characterization of the strengthening and toughening dispersions

related the structure to the properties and verified the prototype design.

5.1 Microsegregation and Hot-working behavior

The achievement of the property objectives begins with meeting the

initial processability requirements, i.e., castability of the steel. Microsegregation is a

common problem observed in high-alloyed castings and hot-worked products, which

limits the mechanical properties. For example, the mechanical properties of the

stainless prototype alloy from a previous project, NASA2, suffered from Cr

segregation resulting in high amounts of retained austenite [117]. This occurs because

of interdendritic segregation of alloying elements during solidification, which leads to

120

a concentration banding in the cast structure. The regions enriched in these elements

are elongated during rolling. When etched, the inherited segregation produces a banded

appearance on both the transverse and the longitudinal sections. Differential etching

effects reveal this banded structure arising from a non-uniform concentration profile

across the sample.

To study the microsegregation behavior in our cast prototype, the as-

received material (homogenized for 8 hours at 12040C, hot-rolled for 75% reduction to

0.45” or 4.5cm thick plate and then annealed at 4820C for 10 hours) in the form of a

10mm X 10mm X 20mm sample, was etched with 2% nital following standard

metallographic polishing to 1µm. Low magnification transverse optical micrographs

revealed both the banded structure oriented along the longitudinal rolling direction and

the oxide-metal interface as shown in Fig. 5.1.

Rolling Direction

Figure 5.1 Optical micrograph of the as-received plate viewed transverse to the rolling direction at the oxide-metal interface after etching with 2% nital

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The centerline of the hot-rolled plate did not reveal as much of a banded

structure as the surface region, as shown in Fig. 5.2. Higher magnification optical

micrograph at the centerline of the plate presented in Fig. 5.3 shows an equiaxed

microstructure, which is predominantly lath martensite in the form of packets within

the prior austenite grain boundaries of an average size of ~50µm.

Rolling Direction

Figure 5.2 Optical micrograph of the hot-rolled plate viewed transverse to the

rolling direction at the centerline after etching with 2% nital

122

Figure 5.3 Higher magnification optical micrograph of the hot-rolled plate at the

centerline

The composition bands revealed on etching in Fig. 5.1 were estimated

to be of 40-50 µm thickness. The extent of microsegregation within these bands was

determined by measuring the composition profile across the thickness of the plate near

the oxide-metal interface. Composition data was collected every 4µm starting from the

metal-oxide interface and proceeding towards the center of the plate. The composition

variation across the bands with respect to the major alloying elements Ni, Cu, Cr and

Mo is presented in Fig. 5.4. It was found that compositional banding in the plate was

limited to an amplitude of approximately 6 - 7.5 wt% Ni, 3.5 - 5 wt% Cu, 1.6 – 2 wt%

Cr, and 0.2 – 0.5wt% Mo and agree well with the microsegregation predictions

obtained from Scheil simulation in Chapter 3. From the strength model, a variation in

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the level of Cu across the bands within 3.5 to 5 wt% corresponds to a predicted

hardness variation of 30 VHN equivalent to 6.8 ksi (~47 MPa) in yield strength. This

will promote a smooth yielding behavior as confirmed by the tensile property behavior

in Section 5.5.

Figure 5.4 Line profile compositions for as-received material from oxide-metal

interface

Another important factor determining the processability of an alloy is

the material response during high temperature deformation or formability. Hot

shortness is a common problem associated with high copper steel production. During

the rolling stage of the fabrication process, the effect of hot shortness is observed by

124

the appearance of surface cracks or fissures leading to unacceptable products.

Investigations in the past [119, 120, 121] have shown that copper is a particularly

detrimental element associated with this phenomenon. At hot rolling temperatures

above 10500C in an oxidizing atmosphere, iron is selectively oxidized leaving an

enrichment of copper near the oxide-metal interface. If the composition of the copper

enriched region exceeds the liquid-austenite equilibrium limit, the copper enriched

liquid phase enters the grain boundary of the austenite causing intergranular fracture

during hot rolling. But the advantages of copper addition to steels for strengthening as

well as improving atmospheric-corrosion resistance has led to extensive research [122-

126] to prevent hot-shortness in copper-bearing steels. These studies have explored the

mechanism by which addition of nickel in an amount equal to 0.5 – 1 times that of

copper shows negligible surface cracking. The prevention of hot shortness by Ni in Cu-

steels has been rationalized by several demonstrated theories. Salter [122]

demonstrated that Ni increases the solubility of Cu in austenite while another theory

[126] proposes that Ni raises the melting point of the Cu-rich phase above the

oxidation temperature. However, Fisher [123] later proposed that Ni causes occlusion

into the oxide scale of the enriched Cu-rich layer formed at the oxide-metal interface.

Based on the findings of previous research, a high Ni/Cu ratio of 1.8 was maintained in

our design to prevent any hot-shortness problems during processing. Successful hot

rolling of the designed alloy was demonstrated during processing. As further

verification, the oxide layer of the as-received material was examined carefully for any

125

evidence of Cu-rich regions. Fig. 5.5 shows an optical micrograph of the oxide layer in

the as-received plate. The oxide-metal interface does not show any evidence of hot

shortness. Composition analysis of various regions in the oxide layer did not reveal any

Cu rich phase but did show some Ni-enriched phases varying from 20 to 80% within

the Fe-rich oxide. This study thus supports the ability of Ni to cause occlusion of the

Cu-enriched liquid during oxidation as proposed by Fisher thus preventing hot

shortness in this steel containing 3.64 wt% Cu.

Figure 5.5 Optical micrograph showing the oxide scale in the as-received plate

5.2 Evaluation of Allotropic Kinetics

A dilatometry study was next conducted to determine the allotropic

kinetics of the prototype. The first step involved the measurement of the martensite

start temperature (MS) of the designed alloy. Fig. 5.6 presents a plot of the relative

126

length change vs. temperature, used to determine the transformation points during the

heating and cooling (quench) cycle of a dilatometry experiment. Straight lines are fit to

the single phase portions of heating and cooling curves, the full width between them

defining full transformation. The series of dashed lines superimposed on the length and

temperature trace represent varying degrees of partial martensitic transformation

during rapid quench from an austenizing temperature of 10500C. The threshold for

transformation is taken as 1% [2]. Thus, MS was determined from the 1% martensitic

transformation point as shown in Fig. 5.6.

Figure 5.6 Relative sample length change and temperature trace during heating and

cooling (quench) cycle from dilatometry experiment

127

The MS temperature, averaged over 15 dilatometry runs, is 360 ± 8.4 0C.

The predicted MS temperature from the Ghosh-Olson model [105] using the SSOL

database was 2980C.

Since the alloy was designed to produce a bainite/martensite

microstructure during air-cooling of plates, the bainite kinetics was determined by

studying the isothermal time-temperature-transformation characteristics of the steel

through dilatometry. This information is useful in determining the processing

necessary in order to achieve bainitic transformation of 50%, for example. With the

help of senior project student Jamie Heisserer, the amount of bainitic transformation

was determined by isothermal hold experiments (after an initial quench step)

performed at incremental temperatures above the martensite start temperature. This

data was then compiled and analyzed in order to plot a time-temperature-

transformation (TTT) curve.

The relative length change vs. temperature dilatometry trace for a two-

hour isothermal hold at 377°C is presented in Fig. 5.7. The percent of bainitic

transformation is determined by measuring the length increase upon arrival at the

isothermal hold temperature and dividing it by the total FCC(γ) - BCC(α) length

difference (defined from the martensitic transformation in Fig. 5.6) at the isothermal

hold temperature. In this case, the total bainitic transformation that took place after 2

hours is 44.1%. The evolution of bainitic transformation with respect to time can be

determined from the measurement presented in Fig. 5.7. This behavior at 377 °C is

128

shown in Fig. 5.8. From this plot it is apparent that the volume fraction of bainite is

saturated after a two-hour isothermal hold. Similar analyses were carried out for each

two-hour test performed at isothermal temperatures ranging from 3620C to 4070C.

Table 5.1 summarizes the maximum transformation levels at all the temperatures. The

TTT curve was then determined by analyzing the data at each isothermal hold

temperature. For example, a 1% transformation curve is plotted by finding the time at

which the sample exhibits 1% transformation at different isothermal temperatures. The

TTT curve based on the data from all of the isothermal runs is presented in Fig. 5.9. It

shows that we can achieve a 50% bainite/martensite mix in approximately 4 minutes at

3600C. The experimental BS temperature was determined to be 4100C, 500C higher

than the corresponding MS temperature (3600C).

Figure 5.7 Relative sample length change and temperature trace during heating,

cooling and isothermal hold at 3770C from dilatometry experiment

129

Table 5.1: Saturation volume fraction of bainite as a function of isothermal temperature

Temperature (C) Saturation Volume Fraction of Bainite 362 0.609629 367 0.526697 372 0.5003 377 0.440938 382 0.242981 387 0.265119 392 0.098382 402 0.015628 407 0.007966

Figure 5.8 Volume fraction evolution of bainite as a function of time for isothermal

temperature of 3770C

130

Figure 5.9 Time-temperature-transformation (TTT) curve for bainite

transformation reaction

Based on this experimental data, the thermodynamic model of bainite

kinetics as described in Chapter 2, Section 2.2.2.1 was calibrated to accurately reflect

the actual kinetics of the alloy in preparation for further design iterations. The model

implemented by the bainite kinetics software (“RunBmk”) yields an output of a TTT

curve, volume fraction vs. temperature and other additional plots, when the alloy

composition and other thermodynamic terms are input. The model was calibrated to the

experimental data by employing two factors namely, nucleant potency and strain

energy.

131

One of the terms in the model is the ASTM Grain Size number, as

described in ASTM method E 112. Through the number density of nucleation sites,

grain size is a controlling factor of volume fraction, as well as the concavity of the TTT

model, and thus was used to fit the model volume fraction vs. temperature curve to the

experiment. The ASTM grain size number of 15 allowed for the best fit of the model

to the data. The saturation volume fraction of bainite was fit to the experimental data as

a function of temperature to determine the best fitting nucleation density (grain size)

parameter (Fig. 5.10). Metallographic etching did not reveal the prior austenite grain

boundaries as shown in Fig. 5.11, and thus the grain size used for the fit was not

validated. Based on the nital etching response, the larger blocks that are lighter in

color are potentially martensite with the darker, finer microstructure being that of

bainite. The microstructure contains roughly 60% bainite and 40% martensite mix, as

determined from dilatometry.

132

Figure 5.10 Experimental data fit to saturation volume fraction of bainite predicted by model [26] using ASTM grain size number 15

Figure 5.11 Microstructure showing 60% bainite and 40% martensite mix after 2-hour isothermal hold at 3600C during dilatometry

133

The model initially predicted much slower bainite transformation

kinetics than observed experimentally (Fig. 5.9) because the MS temperature was

underestimated by ~600C. However, the interval between the model BS and the MS

temperatures was in reasonable agreement with the experimental result of 500C. The

model MS temperature was fit to the experimental MS of 3600C by adjusting the strain

energy correction factor G (J/mole) in CMD™ to –384 J/mole. This is equivalent to a

shift of the free energy curve by a constant. The resulting bainite start temperature of

4030C is very close to the experimental BS temperature of 4100C. Fig. 5.12 presents the

TTT curve output from the model after correction of the transformation temperature.

After calibration, the bainite kinetics model curve is in reasonable agreement at lower

temperatures (where the highest bainite saturation levels are achieved) with the start

kinetics of the bainite transformation reaction determined experimentally (Fig. 5.9).

134

Figure 5.12 TTT diagram representing 1% bainite transformation calculated from

model [26] after calibration to fit experimental data

5.3 Isochronal Tempering Response

An isochronal tempering study was conducted to evaluate the tempering

characteristics of the prototype and provide a baseline for later studies of multi-step

tempering treatments. For simplicity, the tempering response investigation was done in

a uniform martensite matrix to minimize retained austenite effects. Deleterious

transformation products from retained austenite decomposition during tempering could

negatively affect the toughness. After a solution treatment at 9000C for 1 hour followed

by a water quench and liquid nitrogen cool, tempering was performed for 1, 5 and 10

hours under vacuum. Samples were finish machined, notched and then tested at room

135

temperature for Charpy impact toughness. Hardness measurements were taken directly

from the polished surface of the Charpy specimens.

The tempering response for 1 hour isochronal tempering was

investigated over a temperature range of 2000C - 6000C in the solution-treated

prototype alloy and is shown in Fig. 5.13. The 1-hour isochronal tempering study

demonstrates that a peak hardness level is reached at 4200C followed by gradual

overaging. This is consistent with the peak aging temperature for 30 minute tempering

reported by Maruyama et al [81] in martensitic steels strengthened by copper

precipitation. The retention of high hardness even after the peak aging condition to

5000C can be attributed to precipitation of M2C carbides and a fine austenite dispersion

observed at secondary hardening temperature of 4820C in carbide strengthened ultra-

high strength steels like AerMet100 and AF1410 [2]. The hardness at 5000C

(represented by an arrow in Fig. 5.13) is in very good agreement with that predicted for

the calculated final tempering temperature (4900C) in Chapter 3 to achieve the design

objectives.

136

Figure 5.13 Isochronal (1 hour) tempering response of prototype alloy. The arrow

superimposed on the plot shows that the design objective is achieved by tempering at 5000C in agreement with design prediction.

After confirming the basic secondary hardening characteristics of the

prototype alloy, a series of isochronal tempering treatments of Charpy specimens were

done for 1, 5 and 10 hours within a temperature range of 400 – 6000C. Fig. 5.14

illustrates the room temperature Charpy toughness (CV) – Vickers hardness (VHN)

trajectory for the indicated tempering temperatures. This establishes the baseline of the

toughness-hardness (strength) combination in tempered martensitic microstructures.

137

The shape of the trajectory is consistent with earlier studies of HSLA100 [77], AF1410

and AerMet100 [2] where the best combination of strength and toughness are obtained

in slightly overaged condition corresponding to complete cementite dissolution.

At the shortest tempering time of 1 hour we see from Fig. 5.14 that

cementite formation limits toughness, and as Cu precipitates in its presence, strength

increases from 4000C to 4500C tempering treatment while there is a sharp decline in

toughness. With further tempering, cementite begins to dissolve as a result of M2C

carbide formation in combination with BCC copper precipitation at the peak aging

condition. This results in an increase of both strength and toughness. The toughness-

hardness trajectory takes a sharp turn thereafter, as the strengthening precipitates begin

to coarsen exceeding their optimum sizes and the strength continues to decrease with

overaging. Fig. 5.14 suggests that peak hardness occurs at 4500C 5 hour tempering and

the corresponding toughness resides on an upper band indicating complete dissolution

of paraequilibrium cementite by precipitation of an optimal size M2C strengthening

dispersion.

138

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139

The highly overaged region is also likely associated with precipitation

of a fine dispersion of austenite, which increases in stability due to Ni enrichment at

higher tempering times. An interesting feature observed in the toughness-hardness

trajectory for 5 hour tempering in Fig. 5.14 between tempering temperatures of 5250C

and 5750C is a toughness enhancement from the baseline toughness of 144 ft-lbs to 170

ft-lbs respectively, a toughness increment by 18% at a strength level corresponding to

355 VHN. This is characteristic of the transformation toughening phenomenon caused

by the austenite reaching an optimal stability for the lower strength condition.

The tempering response of the hardness (strength) can be correlated to

an empirical Larson-Miller type parameter, known as the Hollomon-Jaffe tempering

parameter [127]. The parameter is defined as T(18 + ln(t)) where T is tempering

temperature in K and t is the tempering time in minutes, and is used for correlation of

hardness data at higher tempering temperatures between 4000C and 6000C. Fig. 5.15

presents the measured values of hardness for different tempering conditions as a

function of the Hollomon-Jaffe tempering parameter. Fairly good agreement with the

parameter is obtained for hardnesses under overaged tempering conditions. The

parameter can provide a simple interpolation scheme to adjust tempering for a desired

strength level.

140

Figure 5.15 Hollomon-Jaffe Parameter correlating the hardness data obtained for different tempering conditions in the overaged region

The fracture surfaces of the broken Charpy impact testing

samples were observed under SEM to characterize the mode of fracture. The fracture

surface for the 4500C 1 hour tempering condition is presented in Fig. 5.16. The SEM

micrograph reveals that the sample failed by quasi-cleavage fracture with signs of

intergranular embrittlement. Quasi-cleavage is characterized by an array of cleavage

failures connected by ductile tear ridges but is a much more desired fracture mode

compared to intergranular fracture. The fracture mode represents relatively brittle

behavior attributed to the presence of undissolved cementite at short tempering times.

141

Figure 5.16 SEM micrograph of quasi-cleavage fracture surface for prototype

tempered at 4500C for 1 hour

For higher tempering times and temperatures, ductile fracture occurred

by microvoid nucleation and coalescence. Representative SEM micrographs showing

ductile mode of fracture for 5 hour tempering marked by toughness enhancement due

to transformation toughening in Fig. 5.14 are presented in order of increasing

tempering temperature in Figs. 5.17 through 5.19. Fig. 5.17 clearly shows that a

completely ductile mode of fracture is achieved with 5 hour 5250C tempering and

micrographs presented in Figs. 5.18 and 5.19 represent fracture surfaces with increased

toughness due to transformation toughening, indicated by the relatively higher degree

of primary void growth.

142

Figure 5.17 SEM micrograph of ductile fracture surface for prototype tempered at

5250C for 5 hours

Figure 5.18 SEM micrograph of ductile fracture surface representing toughness enhancement due to transformation toughening for prototype tempered at 5500C for 5 hours

143

Figure 5.19 SEM micrograph of ductile fracture surface representing toughness

enhancement due to transformation toughening for prototype tempered at 5750C for 5 hours

5.4 Toughness Optimization by Multi-step Tempering

Heat treatment for stabilization of austenite for dispersed phase

transformation toughening phenomenon is directed towards combined size refinement

and compositional enrichment of the austenite particles. A two-step tempering process

consisting of an initial high temperature, short time treatment followed by a standard

isothermal tempering treatment is employed to achieve this goal. The first step is

designed to nucleate a fine, uniform dispersion of intralath austenite and strengthening

particles of sub-optimal size formed directly by increasing the driving force for

precipitation. This is achieved by a short time, high-temperature tempering step

144

designed to give an underaged state based on the isochronal tempering study. At this

stage, it is important to understand the implications of the kinetic competition between

the precipitation of austenite and strengthening dispersions namely, BCC copper and

M2C carbides. In the prototype alloy, the austenite precipitation kinetics is slower than

the BCC copper precipitation kinetics, which in turn is considerably slower than the

carbide precipitation process at intermediate tempering temperatures. It is, therefore,

critical to optimize the time for the high-temperature austenite nucleation step, since

the carbides might become overaged at higher times and full hardness cannot be

achieved. Yet this uncertainty in loss of strength by overaging of carbides is overcome

in the prototype because of additional strengthening of nearly 40% provided by BCC

copper precipitation (Chapter 3), which has slower coarsening kinetics than the

carbides. The second tempering step is optimized to enhance Ni-enrichment of the

austenite particles coupled with completion of precipitation strengthening for peak

aging condition involving enrichment of the 3nm Cu precipitates and cementite

conversion to 3nm M2C carbides. This is achieved by a longer-time final tempering at

a lower temperature characterized by the peak strengthening condition. Thus, from the

toughness-hardness trajectory for isochronal tempering presented in Fig. 5.14, the

optimal final stage tempering condition was determined to be 5 hours at 4500C, which

produced a peak hardness of 436 VHN. The first step was optimized by varying the

tempering time from 5 to 90 minutes over a temperature range of 5000C to 5750C in

intervals of 250C.

145

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146

Fig. 5.20 shows the variety of two-step heat treatments investigated to

maximize the toughness-strength combination in comparison with the HSLA100 alloy

and is superimposed on the isochronal tempering plot. The labels in the plot represent

the tempering time in minutes corresponding to the first step and the bold black arrow

points to the condition for maximum strengthening, which is the final step in the

tempering sequence. The short time, high temperature nucleation treatments were

conducted in a molten salt-bath to reduce heating time followed by water quench to

reduce cooling time. The initial solution treatment was conducted in argon atmosphere

and isothermal aging was conducted under vacuum as described in Chapter 4.

The optimal combination of toughness and strength is determined from

Fig. 5.20 to be a 5500C 30 minutes + 4500C 5 hours heat treatment. The apparent

achievement of optimal austenite stability by multi-step tempering results in significant

increase of impact toughness to 130 ft-lbs at a hardness level of 415 VHN. Comparing

with the baseline toughness-strength combination from isochronal tempering data, a

transformation toughening increment of 50% from 87 ft-lbs for the 10 hour isothermal

treatment and 70% from 77 ft-lbs for the 5 hour isothermal treatment is observed at the

same strength level. So an average of 60% toughness increment due to dispersed phase

transformation toughening can be attributed to multi-step tempering when compared to

standard isothermal tempering at the same strength level. This toughness level exceeds

the design goal of 85 ft-lbs by almost 55%.

147

The competition of several substructures begins with the first higher

temperature nucleation treatment. Within the carbide subsystem, cementite has an

initial advantage of precipitation because it involves only rapid interstitial carbon

diffusion. As aging time increases, the more stable but kinetically slower M2C carbides

attract carbon from cementite as they coherently precipitate at heterogeneous sites

provided by the high dislocation density of the martensitic matrix. In parallel, the

copper atoms also partition out of solution and nucleate on the dislocation substructure.

This should promote not only dissolution of cementite but also heterogeneous

nucleation of austenite particles on the carbide and copper strengthening precipitates.

Lippard [6] has demonstrated through microanalytical analysis that high Cr signals

corresponding to M2C are observed near dispersed intralath precipitates suggesting

carbide precipitates act as nucleation sites for the fine austenite. The precipitation

phenomenon is halted after the first step nucleation treatment by water quenching. At

this point, the microstructure consists of embryonic BCC copper and M2C precipitates

acting as nucleation sites for intralath austenite with some undissolved cementite. The

second heat treatment step continues the precipitation of M2C at the expense of

cementite and enriches the fine austenite in Ni while continuing the precipitation of

Cu. The lower temperature of this second tempering step is likely to produce additional

nucleation of the strengthening precipitates as more dislocation sites are activated by

the higher driving force. The embrittling cementite dispersion is eventually consumed

by the very fine dispersion of M2C.

148

SEM analysis of the fracture surfaces for the multi-step treatment

specimens indicate transition from quasi-cleavage to ductile mode of failure as the time

of initial tempering is increased, attributed to transformation toughening increment as

described in the previous section. Fig. 5.21 presents a representative micrograph of the

fracture surface for the optimal toughness-strength combination for tempering

treatment of 5500C 30min + 4500C 5hrs. Fig. 5.22 shows a higher magnification

micrograph of a primary void in the same sample. The relatively higher degree of

primary void growth is consistent with delayed microvoid instability, as expected for

transformation toughening.

Figure 5.21 SEM micrograph of ductile fracture surface representing toughness enhancement due to transformation toughening for the 5500C 30min + 4500C 5hrs multi-step tempering treatment

149

Figure 5.22 SEM micrograph of a primary void in the fracture surface of prototype for 5500C 30min + 4500C 5hrs multi-step tempering treatment

150

5.5 Evaluation of Tensile Properties

An evaluation of the tensile properties was conducted to determine the

actual yield strength of the prototype under the optimized tempering conditions and to

provide a basis for comparison of the hardness – strength correlation for this class of

steels. Room temperature tensile properties were assessed for the chosen heat treatment

conditions based on the results of the toughness – hardness data from both isochronal

and multi-step tempering response. The tempering conditions were chosen to cover the

full width of the toughness – strength combination plot (Fig.5.20). The same

processing route of solution treatment at 9000C for 1 hour followed by water and liquid

nitrogen quench and isothermal aging (short time aging was done using molten salt

bath) was followed for the tensile samples, prior to final machining into dimensions

described in Section 4.2.6. Duplicate samples for each heat treatment condition were

tested to determine the scatter in the data. Table 5.2 summarizes the results of the

tensile testing for the solution treated and aged samples for each heat treatment

condition and provides hardness values for comparison. Fig. 5.23 presents the true

stress vs. true plastic strain curves for all the samples tested. The curves are

represented as solid lines until the point of tensile instability (necking) or uniform

elongation and by dotted lines thereafter. The tensile data presented in Fig. 5.23 and

Table 5.2 confirms the design of a 160 ksi yield strength steel. The multi-step

tempering treatments helped to achieve the 160 ksi yield strength goal. Thus, the

prototype has been named “BlastAlloy160”.

151

Table 5.2: Room temperature tensile properties of prototype

Figure 5.23 True stress – true plastic strain response. The stress (σ) - plastic strain

(εp) behavior is shown by solid lines until uniform elongation and by dotted line after necking.

152

From data on the reduction in area at fracture and uniform elongation in

Table 5.2, all the heat treatment conditions show reasonably high values of ductility.

The ratio of YS/UTS (strength ratio) is a general measure of work hardening behavior.

The low values of strength ratio for the “transformation toughening optimized” multi-

step treatments compared to that for the single-step treatment condition suggests that

the work hardening of the steel is appreciably improved by the optimal tempering

treatments. The load-displacement curves for all the conditions showed smooth

yielding without any distinguishable upper and lower yield points. Analysis revealed

that the plastic stress strain behavior could be described by the Hollomon power law

equation (Equation 5.1) [129]. The fitting parameters are summarized in Table 5.3.

nplpl Kεσ = (5.1)

n is the strain-hardening exponent and K is the strength coefficient in ksi.

The yield strength and hardness data from Table 5.2 is superimposed on

the hardness – yield strength correlation plot developed earlier in Fig. 5.24. The black

heavy points represent the data from the current tensile properties study of

BlastAlloy160. The data lies within the experimental scatter of the relationship,

supporting the assumptions in specifying the hardness and strength goals.

153

Table 5.3: Fitting parameters for Hollomon power law equation (5.1) from tensile data of prototype (Fig. 5.23)

Figure 5.24 Hardness – Yield Strength Correlation developed from previous data.

The heavy black points represent data from current investigation.

154

5.6 Toughness – Temperature Dependence

To characterize the effect of service temperature on toughness, Charpy

V-notch impact tests were performed over temperatures ranging from – 840C to 1000C

for the tempering condition that optimized the austenite for room-temperature

dispersed phase transformation toughening. Thus, from Fig. 5.20 the tempering

condition displaying the best toughness-strength combination, 5500C 30min + 4500C

5hrs was chosen. The prototypes were solution treated at 9000C for 1 hour, water

quenched, liquid nitrogen cooled and then multi-step tempered. The samples were

thermally equilibrated at the test temperature for 20 minutes prior to testing.

Fig. 5.25 shows the Charpy impact energy of the prototype as a function

of test temperature. The corresponding impact energy values for 5 hour and 10 hour

tempering treatments at room temperature are superimposed on the plot. Consistent

with the concept that our composition and process design optimized the dispersed

phase transformation toughening phenomenon at room temperature (Chapter 3), the

plot shows that there is a 30 ft-lbs toughness increment at 250C compared to the

baseline ductile fracture toughness at lower and higher test temperatures. This supports

our concept that additional toughening occurs in the prototype because of the delay of

microvoid shear localization during ductile fracture by the optimum stability austenite

dispersion. At higher and lower test temperatures austenite becomes less stable than

required for transformation toughening to occur although the fracture still occurs in a

purely ductile mode, as confirmed by fractography.

155

Figure 5.25 Charpy impact energy absorbed as a function of testing temperature for

prototype tempered at 5500C 30min + 4500C 5hr. Toughness increment of 30ft-lb due to dispersed phase transformation toughening is shown. The toughness band defined by 5 hour and 10 hour single step tempering is superimposed.

SEM micrographs of the fracture surfaces presented in Figs. 5.26 to

5.30 at each of the test temperatures establish the mode of fracture. Fig. 5.26 shows

that the fracture surface for the prototype tested at – 840C is representative of

quasicleavage fracture characterized by the array of flat facets with dimples and tear

ridges around the periphery of the facets. This indicates a brittle mode of failure.

However, as the test temperature is increased to – 400C, the fracture surface primarily

156

consists of microvoids. Although most of the fracture surface is characteristic of

ductile mode of fracture, closer investigation of Fig. 5.27 shows that there are a few

tear ridges with facets, indicating a slightly mixed fracture mode. Figs. 5.28, 5.29 and

5.30 are representative micrographs from fracture surfaces of prototypes tested at –

200C, 00C and 1000C respectively showing purely ductile mode of fracture

characterized by primary voids and microvoids without any evidence of flat facets. The

micrographs for the fracture surface of the prototype tested at room temperature are

presented in Figs. 5.21 and 5.22, which contain mostly primary voids with very few

microvoids. The delay of microvoid shear localization caused by the dispersed phase,

transformation toughened, optimal stability austenite at the crack-tip stress state leads

to more extensive growth of the primary voids before they coalesce by microvoiding.

This finding further supports the design for transformation toughening by multi-step

tempering to precipitate an optimal stability dispersion of austenite. Transformation

toughening studies by Leal [9] in fully austenitic steels indicate a toughness

enhancement of 20 – 50 % relative to the toughness of stable austenite depending on

the transformational volume change as shown in Fig. 2.17. Toughness enhancement is

increased by a larger volume change. Fig. 5.25 indicates that the toughness

enhancement in the prototype is 30%. Toughness measurements within closer

temperature intervals need to be done to find the true maximum for toughness

enhancement.

157

Figure 5.26 SEM micrograph of quasicleavage fracture surface showing flat facets with dimples and tear ridges for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 840C

Figure 5.27 SEM micrograph of mixed ductile/brittle mode fracture surface showing microvoids with some tear ridges for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 400C

158

Figure 5.28 SEM micrograph of purely ductile mode fracture surface showing primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at – 200C

Figure 5.29 SEM micrograph of purely ductile mode fracture surface showing primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at 00C

159

Figure 5.30 SEM micrograph of purely ductile mode fracture surface showing primary voids and microvoids for the 5500C 30min + 4500C 5hrs multi-step tempering treatment tested at 1000C

5.7 Microstructural Characterization

Optimization of the processing conditions of the prototype for dispersed

phase transformation toughening in combination with a fine dispersion of

strengthening precipitates has been supported by property evaluation in the previous

sections. Microanalytical characterization of the austenite dispersion and the

strengthening precipitates and their interaction with the other substructures in the

prototype was performed next to fully validate the systems design and the results are

presented in this section.

160

5.7.1 X-ray Diffraction (XRD)

X-ray diffraction studies were undertaken to find the volume fraction of

austenite in the prototype as a function of tempering temperature. Since low X-ray

peak intensity is associated with low austenite volume fraction, tempering conditions

that will maximize the austenite content in the prototype were chosen. Corresponding

to the toughness enhancement due to optimal stability austenite as observed during the

5 hour isochronal tempering study (Fig. 5.14), tempering conditions for projected

maximum austenite content were selected; temperatures ranging from 500 – 6000C

aged for 5 hours. All samples were solution treated at 9000C for 1 hour, water and

liquid nitrogen quenched and then tempered prior to XRD measurements.

The Rij-factor described in Section 4.2.6 was estimated by calibration

with the standard (NBS SRM 485) and was used in Equation 4.2 as

⎥⎦

⎤⎢⎣

⎡=

200

220254.0α

γα

γ

II

ff

V

V to find the volume fraction of austenite as a function of tempering

temperature. However, no austenite peak was discernable above background for the

tempered samples and thus the austenite volume fraction could not be estimated. As an

example, Fig. 5.31 presents the raw XRD data (counts/sec vs. 2θ angle) for the

prototype tempered at 5500C for 5 hours (lower plot) in comparison to the data

obtained for the standard (upper plot) containing 4 ± 0.2 volume % austenite. The 2θ

angle ranges scanned were from 630 to 670 for the (200) reflection of martensite and

from 71.50 to 77.50 for the (220) reflection of austenite. It is clear from the figure that

161

the background intensity level is twice of that for the standard specimen. It is well

known that appreciable peak broadening takes place for small crystals resulting in

smearing of the diffraction peak with the background. Since we are expecting a fine

(10nm scale) dispersion of austenite, the absence of the (220) austenite peak in the

diffraction pattern might be attributed to peak broadening effect. Moreover, for a hot-

worked quenched and tempered sample like the prototype, matrix strain and texture

effects may be responsible for reducing the signal to noise ratio to unacceptable levels.

0

20

40

60

80

100

120

62 64 66 68 70 72 74 76 78

2θ (degrees)

Cou

nts

per S

econ

d

(200)α

0

50

100

150

200

250

300

Cou

nts

per S

econ

d

(200)α

(220)γ

Figure 5.31 XRD Pattern of prototype tempered at 5500C for 5 hours (lower plot)

scanned from 630 to 670 from 71.50 to 77.50 2θ angles shown in comparison with standard (upper plot) containing 4 vol% austenite

162

5.7.2 Magnetometry

Because of the limitations of X-ray diffraction technique to characterize

the volume fraction of fine dispersion of austenite, magnetometry specimens were

prepared from the XRD samples to determine the austenite content in the heat treated

alloys. The austenite calculations are based on estimates of BCC and FCC magnetic

moment and Curie point from ThermoCalc™ equilibrium calculations. The results of

the austenite volume fraction measurements are given in Table 5.3. The error bars

indicate ± σ confidence levels. Without calibrations from standard samples or

observations of the actual state of the microstructure, the predicted austenite cannot be

considered accurate, however comparisons among the different tempering conditions

are possible. Absolute values of austenite fraction ranging from 2.3 –3.1 % for the

different tempering conditions are much lower than the equilibrium value of ~10%.

Calibration with respect to fully martensitic standard needs to be done to obtain

accurate estimates of the volume fraction of austenite. However, the variation in the

level of austenite volume fractions observed among different tempering conditions

corresponds very well with the variation of toughness as presented in Fig. 5.14. The

toughness increment due to transformation toughening for the 5500C 5 hours tempering

condition relates very well to the peak austenite volume fraction measured for the same

condition compared to higher (5000C) and lower (6000C) tempering temperatures. A

higher increment in toughness is recorded for varying the tempering temperature from

5000C to 5500C than the decrease in toughness related to changing the tempering

163

temperature from 5000C to 5500C. This correlates with the relative austenite volume

fraction measured.

Table 5.4: Austenite Volume fraction measured by magnetometry for different

heat treatment conditions

Tempering Condition Austenite Volume fraction 5000C 5 hours 0.0233 ± 0.005

5500C 5 hours 0.0308 ± 0.007

6000C 5 hours 0.0295 ± 0.008

5.7.3 Transmission Electron Microscopy (TEM)

Conventional TEM was used to search for austenite at lath boundaries

of the martensitic matrix. Investigations were conducted on the best toughness-strength

condition, corresponding to 5500C 30min + 4500C 5hr tempering treatment, based on

the bulk mechanical property measurement of the prototype. Thin foils with large

electron transparent regions were prepared by mechanical and electro-polishing

(described in Section 2.4.9) from the hardness specimens. Figs. 5.32 and 5.33 show

bright field images of martensite laths at two different magnifications.

164

Figure 5.32 Bright-field TEM micrograph showing martensite laths in multi-step

tempered prototype at 5500C for 30min + 4500C for 5hrs

Figure 5.33 Higher magnification bright-field TEM micrograph showing martensite laths in multi-step tempered prototype at 5500C for 30min + 4500C for 5hrs

165

Examination of the substructure inside the martensite laths revealed a highly dislocated

structure as presented in Fig. 5.34. This dense dislocation network within the laths is

known to provide nucleation sites for the strengthening dispersions of BCC copper

precipitates and M2C carbides. Intralath austenite could not be resolved at the

magnification at which the investigation was performed. Conventional dark field

imaging was also done, but the diffraction from austenite could not be clearly

identified because of interactions with signals from other phases and dislocation strain

fields in the microstructure.

Figure 5.34 Bright-field TEM micrograph showing dense dislocation structure within a martensite lath in multi-step tempered prototype at 5500C for 30min + 4500C for 5hrs

166

5.7.4 Three-Dimensional Atom Probe (3DAP) Microscopy

The modern 3DAP microscope is a unique ultrahigh resolution

microstructural characterization technique that is capable of identifying and

characterizing individual atoms and then generating three-dimensional reconstructions

of the internal structures. Since XRD, magnetometry and TEM studies were

unsuccessful in identifying the nanometer scale intra-lath austenite and the optimal

3nm particle size strengthening precipitates in the transformation toughened

BlastAlloy160, 3DAP microscopy was chosen to the be the preferred method of

characterization. This characterization tool was used as a means of evaluating the

matrix composition as well as precipitate compositions, sizes, morphologies and their

average number density.

The choice of samples for analysis was based on the condition of

tempering treatment for the highest obtainable number density of the precipitates,

determined from the assessed mechanical properties (Fig. 5.20). Thus, the tempering

condition corresponding to the highest observed strength (Table 5.2) namely, 5000C

30min + 4500C 5hrs was chosen. The 4500C 1 hour tempering condition was also

chosen as a reference for comparison with 3DAP data on similar Cu-strengthened

steels [76] as well as with the other tempering condition. For simplification, the 4500C

1 hour tempering treatment specimen will be referred to as the “single-step temper”

and the 5000C 30min + 4500C 5hrs tempering treatment specimen will be referred to as

167

the “multi-step temper” in this section. The data for both the tempering conditions will

be presented simultaneously for easier comparison.

The analyzed tips were isothermally aged according to their respective

schedules, following solution treatment at 9000C for 1 hour, water quench and liquid

nitrogen quench. The overall composition of the reconstructed volume from atom

probe analysis was obtained and compared with the actual composition of the

prototype as shown in Table 5.5. It is seen that the actual compositions compare well

with that for the elements detected. The error for the concentrations is given by 2σc,

where Nccc /)1( −=σ , with c being the measured composition and N being the total

number of atoms detected. Thus, the statistical error associated with composition

analysis decreases as the total number of atoms detected increases.

168

Table 5.5: Comparison between the actual overall composition of prototype and the overall compositions determined by 3DAP analysis

Overall Composition from 3DAP

Actual Overall

Composition 4500C 1 hr 5000C 30 min + 4500C 5 hrs

Element wt % at % at % at %

Fe 87.2 90 89.90 ± 0.08 88.58 ± 0.18

C 0.04 0.192 0.11 ± 0.24 0.12 ± 0.53

Cu 3.64 3.30 2.37 ± 0.23 1.13 ± 0.53

Ni 6.61 6.49 5.34 ± 0.23 7.01 ± 0.52

Cr 1.78 1.97 1.86 ± 0.23 2.1 ± 0.53

Mo 0.58 0.35 0.31 ± 0.24 0.89 ± 0.53

V 0.11 0.124 0.11 ± 0.24 0.16 ± 0.53

Atom probe analysis of the single-step temper was conducted at 50K

while that for the multi-step temper at 70K with a pulse fraction of 20% at a pulse

frequency of 1.5 kHz from 7kV to 10kV steady state DC voltage. The complete

analysis for the single-step temper contained a total of 751,608 atoms in a

reconstruction volume of dimensions 13nm X 13nm X 84nm. The multi-step temper

169

analysis collected 254,917 atoms in a reconstruction volume dimension of 17nm X

16nm X 28nm. Figs. 5.35 and 5.36 show partial 3D reconstruction of all the atoms

detected after being field evaporated from the specimen with their positions and

elemental identities for single-step and multi-step tempering conditions respectively.

Iron is not shown in any reconstruction in this section for purpose of clarity, enabling

larger microstructural features like precipitates to be seen distinctly.

z

13nm

13nm

84nm

Cu Ni Cr Mo V C

Figure 5.35 3DAP reconstruction for prototype tempered at 4500C for 1 hour. The

elements in the reconstruction are indicated by their color code. Iron is not shown to provide more clarity in viewing the particles. z is the direction of analysis.

170

mz

m

m Figure 5.36 3DAP reconstruction for prototype

5hrs. The elements in the reconstruccode. Iron is not shown to provide mz is the direction of analysis.

The regions of high copper concent

Figs. 5.35 and 5.36 confirming the presence of a n

distribution in the microstructure. These copper – r

by an isoconcentration surface at 10 at % copper le

positions of copper atoms as shown in Figs. 5.37 a

28n

16n

17n

Cu Ni Cr Mo V C

tempered at 5000C 30min + 4500C tion are indicated by their color ore clarity in viewing the particles.

ration are clearly noticeable in both

anometer sized copper particle

ich precipitates can be represented

vel overlaid with the atomic

nd 5.38. The isoconcentration

171

surfaces clearly outline the Cu-rich precipitates. The size of the copper precipitates for

the single-step temper is relatively smaller than that for the multi-step temper, while

the number density of precipitates for the former is much higher.

Cu11nm

11nm

31nmz

Figure 5.37 3DAP reconstruction for prototype tempered at 4500C for 1 hour

showing copper precipitates defined at 10 at % isoconcentration surface overlaid on atomic positions of copper atoms. All other atoms in the reconstruction are not shown. z is the direction of analysis.

172

Cu Ni Cr Mo V C

z

14nm

14nm

28nm

Figure 5.38 3DAP reconstruction for prototype tempered at 5000C 30min + 4500C

5hrs showing copper precipitates defined by 10 at % isoconcentration surface overlaid on atomic positions of copper atoms. z is the direction of analysis.

The shape of the copper precipitates appears to be elliptical and

stretched in the direction of analysis for both the tempering conditions. The distortion

is an instrument artifact due to a magnification effect caused by the difference in field

evaporation of copper precipitates compared to the matrix. The precipitates are

believed to be spherical in shape as evidenced by other researchers [59, 76,141].

173

Having defined the copper precipitates by the isoconcentration surface,

the size, number densities and compositions of these copper precipitates can be

determined with the help of the 3DAP analysis software, ADAM [114]. Cross-sectional

views from an analyzed volume of the reconstruction were used to measure the size of

the precipitates, examples of which for each tempering condition are shown in Figs.

5.39 and 5.40. For the single-step temper, the average diameter of the copper

precipitates contained completely within the analysis volume was found to be 2.67 ±

0.57 nm while that for the multi-step temper is 3.79 ± 0.13 nm. From the hardness data

it is apparent that the multi-step temper corresponds to the peak aging condition.

However, considering the statistical error of the measurement and a distribution of

particle sizes in the material, the optimal particle size of BCC Cu-precipitates for

maximum particle size lies within 2.5 – 4 nm. This measurement is consistent with the

optimal particle size value of 2.9 nm obtained from atom-probe measurements by

Isheim and Gagliano [76,141] for copper strengthened steel aged for 100 minutes at

4900C and also with the peak aging size of 1 – 5 nm for BCC copper precipitates

determined from previous literature (Section 2.3.2).

174

Cu 5nm

Figure 5.39 Example of a cross-section of analyzed volume for prototype tempered

at 4500C for 1 hour showing copper precipitates in red. All other atoms in the reconstruction are hidden.

Cu 5nm

Figure 5.40 Example of a cross-section of analyzed volume for prototype tempered

at 5000C 30min + 4500C 5hrs showing copper precipitates in red. All other atoms in the reconstruction are hidden.

175

It is apparent from Figs. 5.39 and 5.40 that the number density of

strengthening Cu precipitates is higher for the single-step temper than the multi-step

temper. The number density of the copper precipitates in the analyzed volume was

estimated by equation (5.3) [112]:

Ω

=n

NN p

V

ζ (5.3)

Np and n are the number of particles and the total number of atoms detected in the

volume, Ω is the average atomic volume and ζ is the detection efficiency of a single

ion detector, equal to 0.6 in this case. The number density of copper precipitates for the

single-step temper was calculated to be 5.42 X 1018 precipitates/cm3 while that for

multi-step temper was calculated to be 1.2 X 1018 precipitates/cm3. The high number

density measured for the single-step temper (4.5 times that for multi-step temper) is

consistent with the high Cu content of the alloy. Evidence for cementite dissolution in

the toughness-hardness plots of Fig. 5.20 support the presence of M2C carbides

contributing to the strength of the multi-step tempered material.

The average matrix and precipitate compositions can be determined

from the analyzed volume by calculating the fraction of atoms of each element within

the phase. To analyze the composition of the inner core of the precipitates, a higher

threshold level of 15 at % was set to isolate them. Tables 5.6 and 5.7 give the

composition of the Cu-precipitates and the matrix respectively with 2σ error bar limits

for both the single-step and multi-step conditions. Table 5.7 also compares alloy matrix

176

composition with the homogeneous phase composition of the BCC matrix predicted

using ThermoCalc at the optimal tempering temperature for required austenite stability

(Chapter 3).

Table 5.6: Average copper precipitate compositions determined by 3DAP analysis for selected heat treatment compositions. ND means not detected

BCC Cu Precipitate Composition

from 3DAP analysis

4500C 1 hr 5000C 30 min + 4500C 5 hrs

Element at % at %

Fe 30.25 ± 3.53 43.79 ± 6.52

Cu 63.50 ± 2.55 46.69 ± 6.35

Ni 5.40 ± 4.11 8.76 ± 8.31

C ND ND

Cr 0.40 ± 4.21 0.57 ± 8.67

Mo 0.13 ± 4.22 ND

V ND 0.19 ± 8.69

177

Table 5.7: Average matrix compositions determined by 3DAP analysis for selected heat treatment compositions compared with equilibrium prediction from ThermoCalc. ND means not detected

BCC Matrix Composition

from 3DAP analysis

Equilibrium

Prediction

4500C 1 hr 5000C 30 min + 4500C 5 hrs 4900C

Element at % at % at %

Fe 91.22 ± 0.49 92.01 ± 0.22 94.1

Cu 0.73 ± 0.66 0.22 ± 0.77 0.12

Ni 5.32 ± 1.62 6.33 ± 0.74 3.78

C 0.014 ± 1.67 0.041 ± 0.77 0.000044

Cr 2.18 ± 1.65 0.88 ± 0.76 1.88

Mo 0.44 ± 1.66 0.39 ± 0.77 0.10

V 0.09 ± 1.67 0.12 ± 0.77 0.02

The results of the 3DAP analysis indicate that the matrix composition

for both heat treatment conditions compare reasonably well with the predicted

equilibrium calculations. The matrix Cu composition is near the predicted equilibrium

composition at the earliest evolution stage, indicating a high degree of Cu precipitation

178

and it remains at the equilibrium condition for the multi-step temper composition

analyzed. The relatively higher Ni level observed for both conditions may be

associated with the microsegregation compositional banding described earlier in

Section 5.1. The difference between the homogeneous equilibrium matrix Ni

prediction and the 3DAP microanalysis results is consistent with the level of banding

microsegregation observed with respect to Ni.

From Table 5.6, the Cu composition of the precipitates from 3DAP

analysis is consistent with previous atom-probe results by Goodman [61] (Fig. 2.15)

and Isheim – Gagliano [76, 141] during the early stages of evolution. They reported

values ranging from 50 to 70 % Cu in the precipitates during the initial stages of

precipitation until the peak aged condition is reached. However, these values are much

lower than the equilibrium prediction of 94% Cu in the precipitates. As mentioned by

Gagliano [76] this may be the lower limit of the true concentration value caused by

aberrations of ion trajectories and local magnification effects in 3DAP, which limits

the spatial resolution of this nanoanalytical technique to a few tenths of a nanometer

[131]. It is well established now [132,133] that spatial overlap effects due to the

difference in the field evaporation between the matrix and the precipitate in the Fe-Cu

system leads to matrix atoms being projected into the precipitate, especially for

particles smaller than 5nm in size. The high uncertainty for the concentration values in

the multi-step temper sample is because of the limited data available for analysis.

179

The average matrix and precipitate compositions and the concentration

of the various solute atoms near the matrix/precipitate interface can be investigated by

a proximity histogram, or “proxigram”, available in ADAM, developed and

implemented by Hellman et al [116]. The concentration values were determined by

averaging the concentration in 0.2 nm peripheral shells around all the precipitates with

respect to the 10 at% copper isoconcentration surface, within and outside the

precipitates. The negative values in abscissa represent the matrix composition while

the positive values are indicative of the precipitate compositions. However, the zero

point is not necessarily a correct estimate of the precipitate/matrix interface and serves

as an approximate reference point [116]. The proxigrams obtained from analysis of

copper precipitates in single-step temper and multi-step temper samples are presented

in Figs. 5.41 and 5.42 respectively. The proxigrams indicate that for both cases of

tempering condition, Ni shows considerable partitioning to the precipitate/matrix

interface while that for other solute atoms is within the error limit of estimation. The

level of Ni enrichment at the interface is about 50% higher than the matrix Ni content

for the single-step temper observed in Fig. 5.41, which is consistent with the proxigram

analysis results of Isheim and Gagliano [76,141]. Other researchers have also reported

Ni segregation at the interface of the coherent BCC Cu precipitates as described in

Section 2.3.2.

180

Figure 5.41 Proxigram of all the solute species detected in the 4500C 1hr temper

specimen with respect to 10 at% copper isoconcentration surface in the analysis volume

181

Figure 5.42 Proxigram of all the solute species detected in the 5000C 30min + 4500C

5hrs temper specimen with respect to 10 at% copper isoconcentration surface in the analysis volume

182

Furthermore, it is interesting to see from Fig. 5.42 that the level of Ni

located near the interface was more than 50% with respect to the matrix Ni content for

the multi-step temper condition. This led to further investigation of the

precipitate/matrix interface region by varying Ni concentration threshold levels in the

3D reconstruction for the multi-step temper. Setting a 10 at % level for Ni, the

isoconcentration surface of a Ni-rich precipitate at the interface of the Cu-rich

precipitates could be identified. Fig. 5.43 shows the isoconcentration surface outlining

the Ni-rich precipitate defined at 10 at % Ni, overlaid with atomic positions of Cu and

Ni from three different orientations. Composition analysis for the Ni-rich precipitate

and its comparison with equilibrium prediction of austenite composition is shown in

Table 5.8. Ni concentration of 19.5 at% in the precipitate strongly supports that the

precipitate is the desired austenite of optimum stability for transformation toughening.

Lower than equilibrium concentration of the Ni in the austenite estimated as 30 at%

may be attributed to the local magnification effects previously mentioned. This

argument is further supported by the higher (twice) Cu level in austenite than

equilibrium prediction due to the possibility of having copper atoms from the adjacent

copper precipitates projected into the austenite precipitate because of the solute overlap

effect. Since only a single austenite particle was observed, the statistical error

associated with the composition estimation is significant. To confirm the Ni content of

austenite, further investigation was done by a one-dimensional composition profile

183

plotted along the atom-probe analysis direction in Fig. 5.44. This confirmed that the Ni

content of austenite is 30 at% and is consistent with equilibrium values.

Figu

re 5

.43

3DA

P re

cons

truct

ion

for p

roto

type

tem

pere

d at

500

0 C 3

0min

+ 4

500 C

5hr

s sho

win

g au

sten

ite d

efin

ed b

y 10

at %

Ni l

evel

isoc

once

ntra

tion

surf

ace

over

laid

on

atom

ic

posi

tions

of n

icke

l and

cop

per a

tom

s. z

is th

e di

rect

ion

of a

naly

sis.

184

Figure 5.44 One-dimensional composition profile along the atom-probe analysis direction in the 5000C 30min + 4500C 5hrs temper specimen with respect to 10 at% copper isoconcentration surface in the analysis volume. z is the direction of analysis.

185

Table 5.8: Average austenite composition determined by 3DAP analysis for selected heat treatment compositions compared with equilibrium prediction from ThermoCalc. ND means not detected

Austenite Composition

from 3DAP analysis

Equilibrium

Prediction

5000C 30 min + 4500C 5 hrs 4900C

Element at % at %

Fe 65.9 ± 5.6 61.5

Cu 13.9 ± 8.9 6.97

Ni 19.3 ± 8.6 29.8

C ND 0.00068

Cr 0.93 ± 9.6 1.47

Mo ND 0.03

V ND 0.00084

The size and location of the austenite precipitate, measured as 5nm from

Fig. 5.44, confirms that it is intralath austenite nucleated on two adjacent Cu

precipitates. The size of the precipitate is consistent with that from dark-field TEM

observation of intralath austenite of 5-10 nm by Lippard in multi-step tempered

AerMet100 alloy (Fig. 2.20). Lippard also proposed a mechanism of austenite

186

nucleation on an M2C carbide or in its intermediate coherency strain field from

evidence of high Cr signals associated with STEM EDS data gathered from dispersed

austenite intralath precipitates. This result thus provides direct visual evidence of the

heterogeneous nucleation of intralath austenite on a fine dispersion of strengthening

precipitates; Cu precipitates in this case. This finding also strengthens the

transformation toughening design of achieving an optimal stability austenite dispersion

by employing a multi-step tempering treatment to nucleate the austenite in the first

tempering step followed by a Ni-enrichment final tempering step.

Even with the optimized conditions for C ion detection efficiency

suggested by Carinci [50], no M2C carbide precipitate was identified in the atom-probe

reconstructions. Because of the low equilibrium phase fraction of M2C calculated for

the optimal tempering treatment, the precipitates might have been excluded from the

analysis volume of the atom probe. Also, detection of carbide particles is difficult

because of differences in the field evaporation rates between the carbide and the

surrounding matrix that cause the carbide to stick out in relief leading to tip-fracture.

Such a situation was encountered during the multi-step temper atom-probe run, when a

high level of carbon and molybdenum was observed in the in-situ composition profile

during data collection and the tip fractured soon thereafter. No data could thus be

obtained for 3D reconstruction and characterization of M2C carbide in the prototype.

187

6. CONCLUSIONS

A systems approach to computational materials design has been

successfully applied to the creation of an ultratough high-strength weldable plate steel

for naval hull applications, conducted under the ONR (Office of Naval Research)

grand challenge initiative in “Naval Materials by Design”. The systems approach

integrated processing/structure/property/performance relations with mechanistic

models to achieve the desired quantitative property objectives. The alloy design began

with a study of the structure-property relationships, with special emphasis on

understanding each of the structural subsystems to optimize the corresponding

properties. Quantitative models were then used to design the toughening and

strengthening dispersions, which were the two major property requirements to be met

under stringent processability constraints. Prototype evaluation validated the designs

and characterization of the mechanical properties of Blastalloy160 indicates significant

improvement in strength-toughness combination compared to other commercial steels

currently used by the Navy. The success of the prototype alloy reinforces the strengths

of the design models and their integration.

6.1 Alloy Design

The overall strategy behind the thermodynamic modeling has been to

map the mechanical properties objectives to thermodynamic parameters to set goals for

the design of the microstructural subsystems. The Olson-Cohen model for

188

heterogeneous nucleation aided the determination of a thermodynamic stability

parameter for the austenite. The stability of the transformation-toughened austenite was

calibrated against the parameter (∆Gch + Wf) combining thermodynamic driving force

and interfacial friction to obtain the required toughness, which was the top priority of

this design. Then, based on the strength requirement projected to hardness values, the

design space was identified. The alloy composition and the processing conditions were

subsequently determined by conforming to these parametric design requirements.

The explored design concept is based on the mechanism of dispersed

austenite stabilization for transformation toughening adapted to weldable high strength

steels. The concept employs mixed bainitic/martensitic microstructures produced by

air-cooling of solution-treated plate, combined with copper and alloy carbide

precipitation strengthening during lower temperature isothermal treatment, constrained

by a low carbon content for weldability. A fine particle dispersion of optimal ~ 3nm

size for effective strengthening was designed by precipitation of M2C carbides and

BCC copper from a highly supersaturated BCC solution. The carbon content of the

alloy was set at 0.05 wt% to meet weldability constraints. Based on the carbon level

set, a quantitative carbide-strengthening model was used to determine the strength

contribution from M2C carbides, with the driving force for M2C precipitation

maximized at ~14 kJ/mole (while maintaining a stoichiometric balance between carbon

and the carbide formers Mo, Cr, V) to obtain a fine 3-4nm precipitate particle size. The

additional strengthening required to meet the yield strength goal of 160ksi was

189

achieved by setting an optimal level of copper at 3.65 wt% based on a quantitative

copper-strengthening model. This relatively high Cu level was necessary to allow the

low carbon limit. A high Ni/Cu ratio (1.8) was also maintained in the multicomponent

alloy design to prevent hot shortness problems during processing.

Transformation toughening arises from dispersed austenite precipitates,

which undergo a martensitic transformation at the crack-tip stress state. This leads to

impediment of crack growth by delay of microvoid shear localization during ductile

fracture. Thus to achieve high toughening by this mechanism, optimum stability of the

austenite was designed by optimizing Ni as an FCC stabilizer. Thermodynamic

calculations predicted an alloy Ni content of 6.5 wt% to enable the equilibrium nickel

content of 30% in the austenite to meet the requirement for transformation toughening.

The design also revealed that although Cr did not have a strong effect

on the driving force for carbide precipitation, it helped in partitioning Cu out of the

austenite phase for effective copper precipitation strengthening above 1.1 wt%. For a

robust composition design, the alloy Cr level was set at 1.8 wt%. The processability

conditions were then evaluated under stringent restrictions for the designed alloy (Fe-

0.05C-3.65Cu-6.5Ni-1.84Cr-0.6Mo-0.1V) based on solution treatment condition,

microsegregation behavior and optimal tempering condition. A design solution

treatment condition of 9000C for 1 hour was found sufficient to dissolve M2C carbides

without excessive austenite grain growth. No serious microsegregation problems were

predicted for the designed composition based on results from Scheil simulation. An

190

optimal final tempering temperature of 4900C (after a higher temperature austenite

nucleation step) was predicted to achieve sufficient austenite stability for

transformation toughening. Thus, thermodynamic calculations demonstrated feasibility

of combining copper and M2C carbide precipitation for strengthening in combination

with nickel-stabilized austenite for transformation toughening in a relatively low cost

weldable plate steel.

6.2 Prototype Evaluation

The characterization of the first Blastalloy160 prototype yielded very

encouraging results. The principal design objective of toughness-strength combination

was met. Impact toughness of 130ft-lb was achieved at 160ksi yield strength for a

multi-step tempering condition of the prototype, which is a significant improvement of

properties over other conventional alloys. Fig 6.1 graphically represents the toughness-

strength combination of the Blastalloy160 prototype for three different tempering

conditions in comparison to other commercial and experimental alloys.

191

Figure 6.1 Toughness-yield strength comparison plot of Blastalloy160 with other

commercial and experimental steels

To simulate a continuous casting process, a 34lb (15.4kg) Vacuum

Induction Melt (VIM) heat of the Concept B prototype was slab cast as 1.75” (4.45cm)

plate, homogenized for 8 hours at 22000F (12040C), hot-rolled to 0.45” (1.14cm) and

then annealed at 9000F (4820C) for 10 hours. Consistent with microsegregation /

homogenization simulations, compositional banding in the plate was limited to an

amplitude of 6 - 7.5 wt% Ni, 3.5 - 5 wt% Cu, 1.6 – 2 wt% Cr, and 0.2 – 0.5wt% Mo.

Examination of the oxide scale showed no evidence of hot shortness in the alloy during

hot working. The evaluation of the prototype alloy for different tempering conditions

192

was conducted under an initial martensitic condition obtained by austenizing solution

treatment at 9000C for 1hour followed by a water-quench and a liquid nitrogen cool.

Since this was a design for low-cost air-hardenable plate steel, isothermal

transformation kinetics measurements were also conducted, demonstrating

achievement of 50% bainite in 4 minutes at 3600C. Reasonable agreement was

obtained between the experimental and calculated transformation behavior with the

transformation temperatures (MS / BS) higher by ~600C. The experimental data was fit

to saturation volume fraction of bainite predictions to calibrate the kinetic model for

future prediction of bainite start kinetics in this alloy system. Hardness and tensile tests

confirmed predicted precipitation strengthening behavior in quench and tempered

material. Isochronal tempering studies at 1 hour confirmed peak strengthening at

4200C with gradual overaging, consistent with literature findings for copper bearing

systems. Multi-step tempering was employed to optimize the austenite and a

significant enhancement in toughness was observed with minimal loss in strength for a

5500C 30min + 4500C 5hrs tempering condition. An optimal austenite stability was

indicated by a significant increase of impact toughness to 130 ft-lb at a strength level

of 160 ksi. Comparison with the baseline toughness-strength combination determined

by isochronal tempering studies indicates a significant transformation toughening

increment of 60% in Charpy energy, exceeding the actual toughness goal of 85 ft-lbs

by almost 55%. Tensile tests were conducted on the optimum tempering conditions to

confirm the predicted strength levels. Charpy impact tests and fractography

193

demonstrate ductile fracture with Cv > 80 ft-lbs down to –400C, with a substantial

toughness peak at 250C consistent with designed transformation toughening behavior.

Predicted Cu particle number densities and the heterogeneous nucleation of optimal

stability high Ni 5nm austenite on nanometer-scale copper precipitates in the multi-step

tempered samples were confirmed using three-dimensional atom probe microscopy.

The copper precipitate size was verified for peak strengthening at 2-3 nm and

precipitate composition of 50-60% copper for short tempering times agreed with

results from previous studies. The fine austenite showed a Ni content near the

theoretical prediction of 30%.

The properties demonstrated in this first prototype represent a

substantial advance over existing naval hull steels. Achieving these improvements in a

single design iteration is a significant progress in computational materials design

capability.

194

7. SUGGESTIONS FOR FUTURE WORK

Initial evaluation and characterization of the prototype has demonstrated

the success of the systems approach in achieving the design objectives. However, it has

also opened new research horizons to be explored for further enhancement of

properties. In addition, the achievement of major improvements in properties over

current commercial steels in a single design iteration displays the strengths and

robustness of the design models and opens up opportunities to widen their application.

7.1 Further Prototype Evaluation

The amount of optimal stability austenite for the dispersed phase

transformation toughening phenomenon in the initial prototype could not be

characterized appropriately with the techniques used in the present work. Although the

relative variation of austenite volume fraction from magnetometry measurements are

consistent with the toughness results, calibrations with respect to standard samples in

fully martensitic state needs to be done to make accurate measurements. Another

possibility will be to use X-ray diffraction with high-energy synchrotron radiation to

obtain a higher signal to noise ratio over the background for precise estimation of

integrated intensities from austenite diffraction peaks.

A more detailed evaluation of the toughness dependence on temperature

also should be done to accurately define the toughness increment due to transformation

toughening over baseline ductile fracture toughness. The transformation toughening

195

peak then can be redesigned based on the operating temperature of the alloy to achieve

the best property combination under service conditions through a design iteration of

composition and processing.

Further atom-probe investigations should be conducted to detect and

characterize the designed 3-4nm sized M2C carbide particles to validate the strength

model used in the design.

Following the success of the initial prototype, processing of the

designed alloy should be scaled up to larger heats with small elemental additions for

grain refinement and impurity gettering. Addition of B will help improve the grain

boundary cohesion and is beneficial to stress corrosion cracking resistance. A Ti

addition during melt de-oxidation can provide an effective grain refining dispersion

during solution treatment with good interfacial adhesion for toughness. The properties

should also be characterized with bainite/martensite mixtures formed by air-cooling.

7.2 Next Design Iteration

Further exploration with respect to optimal combinations of austenite

stabilizers in the next design iteration can predict leaner alloy compositions leading to

improved weldability and lower cost of the material. Further calibration of the bainite

kinetics model with more experiments is necessary for the design of robust air-cooled

plate steels. Building on this research to study transformation toughening mechanisms,

196

a more radical design concept of a non-magnetic, fully austenitic precipitation-

hardening alloy can be investigated for maximum toughening.

197

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214

APPENDICES

APPENDIX A

Design and Evaluation of Concept A Alloy

The design of the higher risk Concept A alloy was based on a lower cost

low alloy carbon-stabilized austenite in a high silicon steel strengthened by BCC Cu

precipitation. The design focused on precipitation-strengthened, 150 ksi yield strength

bainitic steels with carbon-stabilized austenite for transformation toughening. By

judicious use of Si as an alloying element to suppress the precipitation of cementite

and thus avoiding large regions of unstable austenite, Bhadeshia [4] has achieved

impressive combinations of strength (YS=160ksi) and toughness levels

(KIC=140ksi.in1/2). Design Concept A employs the phenomenon of bainitic

stabilization of austenite during low temperature isothermal treatment on a low

hardenability plate steel air-cooled from solution treatment temperature. The strength

levels will be increased by precipitation of bcc Cu since not enough carbon would be

available for carbide strengthening. Thus the aim of research using this concept was to

combine carbon stabilization of austenite with simultaneous Cu precipitation.

A preliminary composition of the Concept A alloy was set based on

strict design and cost constraints. Since this concept employs carbon stabilization of

austenite for achieving optimal stability for transformation toughening, an upper limit

carbon level of 0.1 wt% was set within the zone to avoid susceptibility to HAZ

215

cracking of weldments, specified by the Graville diagram (Fig. 3.3). As a result,

carbide strengthening is ruled out so that all of the carbon is available for partitioning

into austenite. Thus, the design requires BCC copper precipitation strengthening to

provide the additional strength increment over the solid solution strengthening and the

bainitic substructure strengthening in the alloy. However, initial calculations showed

that C partitions to austenite at low alloy Cu content, so a lower concentration of 1.37

wt%, sufficient for strengthening was selected [76]. Consistent with the Ni level in

similar steels to avoid hot-shortness, the alloy Ni content was set to 0.82 wt%. This

corresponds to the addition of Ni in an amount equal to 0.5 – 1 times that of copper to

prevent surface cracking during hot rolling as discussed in Section 5.1. During the

bainitic stabilization of austenite by isothermal transformation as depicted by the

schematic of the thermal processing route employed in this design (Fig. A1), it is

important to suppress cementite formation in order to allow more carbon to partition

into austenite. Moreover, since cementite negatively affects the toughness of the alloy,

suppression of cementite formation to higher temperature by addition of Si up to 1.5

wt% is well established [4]. Addition of higher Si results in the formation of a thick

oxide layer on the surface of the steel during hot rolling. Mn is usually present in small

amounts in most steels to getter sulfur as sulfides. But Mn addition in this alloy is

crucial since it has a substantial effect on the amount of C in the retained austenite.

The MS temperature is also strongly affected by the alloy Mn content, which in turn

216

sets the lowest temperature at which bainitic transformation can be achieved

isothermally.

Figure A1 A schematic of the thermal processing of Concept A alloy

The calculations performed for Concept A mainly concerned the

optimization of the alloy Mn content. The calculations were performed under para-

equilibrium constraint, where only carbon diffuses during isothermal transformation.

The fixed values of the other alloying elements are shown in Table A1.

Table A1 Initial composition of Concept A steel

Element Fe C Cu Ni Si Mn

wt % Balance 0.1 1.37 0.82 1.5 Optimized

217

Figure A2 shows the effect of alloy Mn content on the MS temperature.

The MS temperature decreases with increase in the alloy Mn content. Since isothermal

treatment just above MS is necessary for bainitic transformation, it is important to

estimate the C content of the austenite at such temperatures. The isothermal bainitic

hold temperature (or processing temperature) was set to be 100C above the MS

temperature. Paraequilibrium calculations were performed to find the C content of

retained austenite for varying isothermal hold temperature corresponding to the

variation in alloy Mn content. The results are shown in Figure A3. This plot shows

that a lower processing temperature or MS is beneficial because more C is partitioned

to the austenite. The amount of C in austenite is a primary measure of the stability of

the austenite phase—more carbon provides more stable austenite. It is shown that Mn

decreases the C content of austenite calculated at the fixed processing (Ms+100C)

temperatures. So Figures A2 and A3 show the importance of Mn in decreasing the Ms

temperature, which increases the C content of austenite and hence the stability for

transformation toughening.

218

Figure A2 Variation of Martensite Start (Ms) temperature with alloy Mn content

(wt%)

Figure A3 Carbon content of retained austenite (wt%) as a function of alloy Mn content (wt%) calculated at processing temperature (Ms+100C) corresponding to Mn content in Figure A2

219

The room temperature stability of dispersed retained austenite for

transformation toughening was calculated by the sum of the chemical and mechanical

driving force terms (∆Gch + Wf) as described in Section 3.2.2. Similar to the

transformation toughening design for Concept B alloy, a linear relation was fit between

the austenite stability parameter and the alloy hardness (Fig. A4), and an estimate of

the required optimum stability was thus obtained. Fig. A4 show that for a yield

strength of 150 ksi, the optimal value of ∆Gch + Wf would be 2.2 kJ/mol, for the

required austenite stability.

RT (300K) Stability of Austenite

0500

100015002000250030003500400045005000

280 330 380 430 480 530 580 630

Vickers Hardness (VHN)

∆G

ch+W

f, J

/mol

AerMet 100AF1410

Concept A Design Alloy

Figure A4 Room Temperature (300K) austenite stability plotted as a function of Vickers Hardness Number (VHN). The shaded region shows our range of interest for austenite stability Concept A alloy corresponding to yield strength requirement of 140-160ksi.

220

Based on the requirement of austenite stability, calculations were performed to

estimate the value of ∆G + Wf with varying alloy Mn content as shown in Fig A5. The

stability calculations were performed maintaining para-equilibrium, so the

compositions of all elements except for C are the same in austenite as they are in the

alloy. Only carbon atoms are diffusing, so the austenite carbon content is determined

from Fig A3. From Fig A5 it was found that the required level of stability (2200

J/mol) was reached at 7.5 wt% Mn. Figure A6 shows the ∆Gch + Wf stability

parameter plotted against processing temperature according to the corresponding Mn

levels and we reach the required austenite stability at 3150C (MS = 3050C).

Figure A5 Room Temperature (300K) stability of austenite as a function of alloy

Mn (wt%). The required stability was achieved at 7.5wt% Mn.

221

Figure A6 Room Temperature (300K) stability of austenite as a function of

processing temperature (Ms+100C). The required stability was achieved at 3150C.

Based on these computed results, the composition of the Concept A steel (in wt%) was

determined as Fe-0.1C-1.37Cu-0.82 Ni-1.5Si-7.5Mn with an isothermal transformation

temperature of 315oC. Steel of this composition and processing should give optimal

performance at a reasonable cost.

Initial evaluation of the prototype to determine the allotropic kinetics

revealed that the austenite is too stable to allow any bainitic transformation.

Dilatometry studies were done to measure the MS temperature of the designed alloy

determined from the 1% martensitic transformation point shown in Fig. A7. The actual

MS averaged over 10 dilatometry runs is 227 ± 8.80C. This is 780C lower than the MS

222

predicted by the Ghosh-Olson model employing the SSOL database. Because of

overestimation of the lower transformation temperature, the kinetics of bainite

transformation were too slow and no discernable length change was observed after 2

hours of isothermal hold at temperatures just above the MS. Thus the bainite kinetics

could not be evaluated.

Figure A7 Relative sample length change and temperature trace during heating and cooling cycle from dilatometry experiment. MS was determined from 1% martensitic transformation point.

223

Since evaluation of the transformation toughening behavior of the

retained austenite in the prototype could not be done by bainitic stabilization, some

preliminary characterization of the retained austenite was performed in the martensitic

state in quenched and tempered samples. To vary the amount of retained austenite in

the sample, one batch of the prototype was cooled in liquid nitrogen following water

quench after solution treatment. Consistent with the peak aging temperature of 4200C

for Cu precipitation strengthening (Fig. A8), 1 hour isochronal tempering response of

the prototype for both the cases exceeded the strength goal of the design. X-ray

diffraction measurement of volume fraction of austenite, confirmed that the liquid

nitrogen cool led to further transformation of retained austenite to martensite. The

decrease in the amount of retained austenite associated with the peak aging condition

indicates that maximum strengthening at 4200C is also contributed by the precipitation

of cementite through decomposition of austenite. This was confirmed by the sharp drop

in Charpy impact toughness as shown by the toughness – hardness trajectory in Fig.A9.

224

Figure A8 Isochronal (1 hour) tempering response of Concept A prototype

Figure A9 Isochronal (1 hour) tempering response of Concept A prototype represented by Charpy toughness – Vickers hardness trajectory.

225

The prototype evaluation demonstrates the shortcoming of the design in

terms of improper estimation of transformation temperatures. Since the actual MS

temperature was much lower than that predicted by the design, the retained austenite

was too stable to transform to bainite for isothermal hold just above MS while it

decomposed to form cementite near peak aging temperature for copper precipitation

strengthening, thus lowering the toughness. Hence, the compatibility of simultaneous

bainitic transformation and copper precipitation strengthening could not be assessed in

the Concept A prototype.

226

APPENDIX B

Assessment of Interfacial Dissipation Effects at Reconstructive

Ferrite-Austenite Interfaces

Accurate prediction of carbon content in austenite is important to

control the stability of austenite for design of “Triple-Phase” steels. The design

Concept A described in Appendix A was adapted from this study employing carbon

stabilization of austenite during isothermal bainitic transformation. This included

investigation of carbon enrichment of austenite during “epitaxial” growth of

reconstructive ferrite. Paraequilibrium growth simulation in a multicomponent system

was run using the DICTRA (DIffusion Controlled Transformation) software to study

the carbon concentration profile at the ferrite-austenite interface during rapid cooling

from an intercritical annealing temperature to a bainitic transformation temperature. A

mobility model was developed from previous literature data to estimate a temperature

dependent interfacial dissipation energy function. Addition of the interfacial

dissipation energy to the ferrite free energy lowers the interface carbon content in

austenite to levels consistent with experimental measurements of retained austenite.

There are two main factors that determine the stability of retained

austenite. The enrichment of austenite with carbon is a widely acknowledged technique

to stabilize retained austenite. Secondly, retained austenite pool size is predicted to

provide a significant stabilizing effect by the Olson-Cohen statistical kinetic model

227

[B1]. In order to control the stability of the retained austenite, it is important to

quantify the evolution of the size and carbon content of austenite pools. This will

define the phase fraction and carbon content distribution in austenite pools at the

isothermal hold temperature, that is, the initial conditions for bainite transformation.

This can be modeled by a spherical simulation of “epitaxial” ferrite growth with carbon

partitioning into the austenite pools using the DICTRA software. The implementation

of the paraequilibrium constraint in the thermodynamic and kinetic calculations is

schematically represented in Fig. B1.

Figure B1 Schematic representation of the Implementation of Paraequilibrium Growth in DICTRA.

The metal sublattice is approximated by a hypothetical element NU

whose thermodynamic and mobility parameters are expressed by the weighted average

of the thermodynamic parameters and mobilities of the substitutional alloying

elements. This allows calculation of the paraequilibrium phase diagrams and the

228

paraequilibrium growth simulations directly in the ThermoCalc and DICTRA software

respectively. In DICTRA the paraequilibrium constraint modifies the different mobility

parameters and diffusion of C in the sublattice, which becomes the rate-controlling

process.

Paraequilibrium Ferrite Growth for an Infinitely Mobile Interface

The evolution of retained austenite stability in triple-phase sheet steels

during rapid cooling to the bainitic transformation temperature after intercritical

annealing has been studied by Brandt [99] in a Fe-0.26C-1.22Mn-1.52Si-0.05Al alloy.

The alloy was intercritically annealed at 1043K followed by rapid cooling to 673K

where isothermal treatment forms bainite. We simulated ferrite growth for the same

alloy under paraequilibrium constraint at the experimental cooling rate of 450C/sec

using the DICTRA diffusion software. The Gibbs energy and the mobility data files

for the austenite and the ferrite phases were rewritten so that the paraequilibrium phase

diagram calculation and the growth simulation can be performed for any composition

of the Fe-C-Mn-Si-Al system. The paraequilibrium phase diagram for ferrite and

austenite in the Fe-xC-1.22Mn-1.52Si-0.05Al system is given in Fig B2.

229

Figure B2 Paraequilibrium phase diagram of Fe-xC-1.22Mn-1.52Si-0.05Al.

At 0.26wt% C and a temperature of 1043K, the phase fractions of

paraequilibrium ferrite and austenite are 0.42 and 0.58 respectively. We considered a

spherical geometry for the austenite grain with an outer shell of ferrite growing

inwards to simulate a uniform microstructure. This is considered a reasonable

approximation for the overall ferrite formation starting from equiaxed austenite pools

[B10, B11]. Our starting cell is set with austenite in the middle covered uniformly by a

layer of ferrite. Based on the ratio of the phase fractions, we set the initial radius of the

austenite cell at 10µm and the ferrite cell as a 2µm thickness shell enclosing the

austenite cell. This is schematically represented in Fig B3.

230

Ferrite (α)

rα+γ = 12µm

rγ = 10µmAustenite (γ)

Figure B3 Schematic representation of the initial ferrite growth cell.

The initial carbon composition for the austenite and ferrite cells were set at those given

by the paraequilibrium phase diagram at 1043K in Fig B2. The simulation result of the

paraequilibrium ferrite growth model at a cooling rate of 450C/sec from 1043K to

673K is shown in Fig B4.

Figure B4 Carbon content profile of an infinitely mobile paraequilibrium austenite-ferrite interface during rapid cooling from 1043K to 673K at 450C/sec.

231

It should be noted that at 673K for an infinitely mobile interface, the local carbon

composition of austenite reaches 3.65 wt% C, close to the paraequilibrium value of

3.76 wt% C as predicted by the phase diagram (Fig. B2) at 673K. A steep carbon

concentration profile develops in austenite near the transforming interface because of

much lower diffusivity of C in austenite compared to ferrite while the far-field C level

remains the same as the initial profile. Also, about 40% of the original austenite pool

has been converted to ferrite while cooling from 1043K to 673K. This is in fair

agreement with the results of Brandt [99] who reported 30% conversion and also

consistent with results obtained by Ghosh [B2].

Interfacial Dissipation Energy

Measurement of carbon levels in retained austenite [99] shows that

initially there is a rapid increase in carbon level, which saturates at about 1.4 wt%. We

interpret the retained austenite as representing the highest carbon regions, with the

lower carbon austenite transforming to martensite or bainite on subsequent cooling.

Our predicted level of interface carbon by ferrite growth with infinite interfacial

mobility predicts a much higher value corresponding to the paraequilibrium value.

Additional X-ray diffraction measurements were employed to determine the retained

austenite lattice parameter, using the Ridely, Stuart and Zwell relationship [B3]:

CwtAa %044.0555.3)(0

+= (B1)

232

The austenite carbon content was estimated to be 1.37wt%C. This value is in excellent

agreement with experimentally determined average C content in retained austenite of

1.36 wt% as reported by Brandt [99] for intercritially annealed (at 1043K) and

quenched alloy of same composition. Thus, the DICTRA paraequilibrium ferrite

growth model predicted a much higher value of interface carbon composition. This

higher value may be due to a dissipation energy at the interface neglected in the growth

model simulation.

The velocity of the interface should depend both on its intrinsic mobility

which is related to the process of structural change from austenite to ferrite and on the

diffusion of interstitial carbon ahead of the moving interface. The two processes are

coupled so that interfacial velocity associated with interfacial mobility matches that for

diffusion. The net free energy available for interfacial motion is a sum of the amount of

energy dissipated in the interface process (Gid) and the quantity dissipated in the

diffusion process (Gdd) [B4]. The two dissipation energies Gid and Gdd are then related

by equation (B2):

ddid GGG +=∆ (B2)

When ∆G ≈ Gdd, growth is diffusion-controlled while, interface-controlled growth

occurs when ∆G ≈ Gid. Interfacial motion is generally under mixed control where each

process causes some dissipation of free energy.

233

Figure B5 Constant temperature free energy curves showing ∆G, Gdd and Gid for a ferrite(α)-austenite(γ) interface [B6].

For bainitic transformation, Brandt [99] also considered the addition of an energy term,

which reduces the carbon in austenite by effectively raising the ferrite free energy

curve with respect to the austenite free energy curve (Fig B6). Based on a value

comparable to martensitic transformation critical driving forces, he found a stored

energy term of 1500J/mole modified the level of carbon in austenite to his

experimentally determined value after bainitic transformation.

234

Figure B6 Schematic illustration of the effect of stored energy term added to free energy curve of ferrite upon the carbon content of the austenite as determined by the common tangent construction method [99].

For simulating the reconstructive ferrite growth at higher temperatures, we need to

establish an interfacial dissipation energy function. At high undercooling continuous

reconstructive growth kinetics are expected to follow a linear-viscous behavior [B5]:

idMGV = (B3)

where, V is the interface velocity and M is the interface mobility.

For thermally activated motion, the interfacial dissipation energy is a function of

interface velocity and temperature, where

)*exp(kTHAM ∆

−= (B4)

Thus,

),()*exp(

TVf

kTHA

VMVGid =

∆−

== (B5)

235

where, ∆H* is the enthalpy of activation, T is the temperature in Kelvin and k is the

Universal Boltzmann constant. Thus, the calculation of ferrite growth under conditions

of finite interface mobility requires measures of M. Only two mobility models are

available in the literature as reported by Hillert [B10] and Kierlaart and Van der Zwagg

[B11].

Researchers [B12, B13] have used the two descriptions to estimate the

velocity of the austenite/ferrite interface through its mobility. But unfortunately their

estimates differ by several orders of magnitude. Recently, Inden and Hutchinson [B14]

have shown that the two mobility values at 7000C vary by four orders of magnitude.

Because of this uncertainty in available mobility measures and difficulty to obtain

them experimentally, researchers have often neglected the effect of interfacial

dissipation energy during ferrite growth.

To estimate the mobility of a reconstructive interface we interpret the

kinetics of massive transformation as reconstructive motion in the partitionless limit.

Speich [B6] and Perepezko [B7] performed experimental studies on the kinetics of

massive transformations in the Fe-C and Fe-Ni systems respectively. They fit their

experimental observations to equation (B4) with the mobility for the corresponding

systems by equations (B6) and (B7) assuming an activation of about ½ that for self-

diffusion.

236

For the Fe-C system [B6] this gives,

)10585.1exp(4.21205

RTGVM

id

×−== (B6)

and for the Fe-Ni system [B5, B7] we get,

)10733.1exp(63.1455

RTGVM

id

×−== (B7)

where, R is the universal gas constant.

From these proposed mobility relations, we obtained an upper bound interfacial

dissipation energy function (equation (B5)) employing the same velocities obtained

from the previous diffusional growth simulations and re-ran the simulation with a

temperature-dependent dissipation energy. The carbon profiles for the simulation of the

ferrite growth using the interfacial mobilities proposed by Speich [B6] and Perepezko

[B5, B7] are given in Fig. B7(a) and Fig. B7(b) respectively.

237

(a)

(b)

Figure B7 Carbon content profile of a paraequilibrium austenite-ferrite interface during rapid cooling from 1043K to 673K at 450C/sec using interfacial mobilities proposed by (a) Speich et al [B6] (b) Perepezko et al [B5, B7].

238

We find that neither mobility models suppresses the interfacial carbon level close to

that measured experimentally. We then adopted a single mobility law for iron based

alloys by fitting one curve through the two experimentally determined mobility points

(represented by heavy dots) points of Perepezko (at 840K) and Speich (at 1223K) as

shown in Fig. B8.

M = 2120.4e-(158448.2/RT)

M = 145.63e-(173288.7/RT)

M = 7.900E+07e-(265475.5/RT)

1E-121E-111E-101E-091E-081E-071E-061E-05

0.00010.001

0.010.1

10 0.0005 0.001 0.0015

(1/T) in K

Mob

ility

in m

ole.

(N.s

ec)-1

Fe-C(Speich & Szirmae)

Fe-Ni(Perepezko et al)

Mobility Model

Figure B8 Plot of Interface mobility as a function of Inverse Temperature representing the different models [B5-B7].

239

While it is commonly assumed that the enthalpy of activation for the massive mobility

law [B5-B7, B10-B11] is about 50% of that of volume self diffusion, that for our new

empirical model is about 75% corresponding to the high end of reasonable values for a

boundary diffusion controlled process. The new mobility relation is then expressed as:

)106548.2exp(109.75

7

RTGVM

id

×−×== (B8)

A comparison with the various experimental data available on mobility measurements

and those suggested by earlier researchers [B10, B11] with our mobility model adapted

from massive transformation kinetics has been made as shown in Fig. B9. It clearly

suggests that historically all researchers have assumed nearly constant enthalpy of

activation (50% of that of volume self diffusion of α-Fe) while their relationships

varied in terms of pre-factor estimation. Our relation described by equation (B8)

assumes a higher enthalpy of activation and is consistent with most of the experimental

mobility measurements especially with that of Hu [B15] for α-Fe grain growth. These

literature experimental data support our model using activation energy as 75% of that

for self-diffusion of α-Fe.

240

Figure B9 Comparison of current mobility model with experimentally measured mobility [B15-B17] and suggested mobility relationships [B5, B6, B10, B11].

Using the velocity values obtained from the simulation for an infinitely

mobile interface, a fourth order polynomial was fit (R2=0.9975) to describe a

temperature dependent interfacial dissipation energy. This function was then added to

the chemical free energy of ferrite and employed in a paraequilibrium spherical ferrite

growth simulation. To test convergence of the proposed model, the ferrite growth

simulation was run for two more iterations using velocity values from previous

simulations. The temperature dependent interfacial dissipation energy function was

similarly fitted (R2=0.9988 and R2=0.9992 respectively) from the velocity values. The

241

percent ferrite corresponding to the two iterations of simulation was plotted (Fig. B10)

as a function of temperature and compared with experimental values obtained directly

from dilatometry runs by Brandt [99] under identical conditions of 450C/sec cooling

rate. Fig. B10 clearly shows that the iterations converged and gave good agreement

with the measured experimental result.

Figure B10 Comparison of amount of ferrite (%) as a function of temperature (K)

between DICTRA simulation iterations and Dilatometry data from Brandt [99] for cooling rate of 450C/sec.

242

The evolution of the carbon content at the interface during ferrite growth after addition

of interfacial dissipation energy according to the mobility model described by equation

(B8) is given in Fig. B11.

Figure B11 Carbon content profile of a paraequilibrium austenite-ferrite interface during rapid cooling from 1043K to 673K at 450C/sec using interfacial dissipation energy function generated by the mobility law given in equation (B8).

243

From Fig. B10 we see that our new dissipation energy function decreases the

interfacial carbon content to about 1.8wt%. Once again due to a much lower diffusivity

of C in austenite, we observe a steep profile in front of the interface. Ghosh and Olson

[B2] have evaluated different methods to estimate the average C content in the

austenite in a steep concentration profile at the interface based on cutoff values of C

levels in regions that will transform to martensite upon quenching to room temperature.

They proposed that the best criterion is to consider the C content that will give 90%

transformation on cooling to room temperature and estimated it to be at 0.8 wt% C. So,

the average (Fig. B11) carbon content at the austenite-ferrite interface applying a

dissipation energy as given by equation (B8) was found to be 1.32 wt% when averaged

from 1.8wt% C at the interface over to 0.8wt% C. This is in excellent agreement with

experimental X-ray diffraction values obtained for the average C content of the

austenite retained on cooling determined to be 1.37wt% in this study and 1.36wt% by

Brandt [99]. For an infinitely mobile interface (Fig. B4), the average carbon content for

90% transformation was determined to be 2.23wt% C at the interface. Thus, comparing

these values the addition of interfacial dissipation energy interpreted from massive

transformation kinetics in the partitionless limit lowers the average carbon content at

the interface by 0.9 wt% to a reasonable level.

244

Conclusions

We have demonstrated that reconstructive mobility can significantly affect the carbon

partitioning level at the ferrite-austenite interface. By adding a temperature dependent

interfacial dissipation energy term we predict a carbon level at the interface close to

values obtained experimentally for the retained austenite. The developed mobility

model will help predict austenite stabilization behavior both by carbon partitioning as

well as the size of the austenite pools. This can be of significant help for designing

optimum austenite stability in triple-phase steels that exploit dispersed-phase

transformation plasticity more effectively.

References:

[B1] G. B. Olson, M.Cohen, “A General Mechanism of Martensitic Nucleation” Metall Trans A 7A (1976) 1897

[B2] G. Ghosh, G. B. Olson, “Simulation of Paraequilibrium Growth in

Multicomponent Systems Using DICTRA”, Metall Mater Trans A 32A (2001) 455

[B3] N. Ridley, H. Stuart, L. Zwell, Trans AIME 245 (1969) 1834

[B4] G. B. Olson, H. K. D. H. Bhadeshia, M. Cohen, “Coupled

Diffusional/Displacive Transformations”, Acta Metall 37 (1989) 381 [B5] J. H. Perepezko, “Growth Kinetics and Mechanism of the Massive

Transformation”, Metall. Trans. A 15A (1984) 437 [B6] G.R.Speich, A. Szirmae, “Formation of Austenite from Ferrite and Ferrite-

Carbide Aggregates”, Trans AIME 245 (1969) 1063

245

[B7] T. B. Massalski, J. H. Perepezko, J. Jaklovsky, “A Microstructural Study of Massive Transformations in the Fe-Ni System”, Mater. Sci. Engg. 18 (1975) 193

[B8] R. A. Vandermeer, “Modeling Diffusional Growth During Austenite

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[B9] R. G. Kamat, E. B. Hawbolt, L. C. Brown, J. K. Brimacombe, “The Principle of

Additivity and the Proeutectoid Ferrite Transformation”, Metall. Trans. A 23A (1992) 2469

[B10] M. Hillert, “Diffusion and Interface Control of Reactions in Alloys”, Metall.

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[B12] M. Militzer, “Challenges in Modeling the Overall Austenite Decomposition

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[B13] T. Iung, M. Kandel, S. Lacroix, A. Perlade, D. Quidort, “Prediction of Phase

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[B14] G. Inden, C. R. Hutchinson, “Interfacial Conditions at the Moving Interface

during Growth of Ferrite from Austenite in Fe-C-(X) Alloys”, Austenite Formation and Decomposition Symposium in Mat. Sci. & Tech. 2003 Proc., p.65, Chicago, IL (2003)

[B15] H. Hu, “Grain growth in zone-refined iron”, Can. Met. Quart. 13 (1975) 275

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Purity α-Iron”, Sov. Phy. Dok., 6 (1961) 425 [B17] G. P. Krielaart, S. van der Zwaag, “Kinetics of γ −> α phase transformation in

Fe-Mn alloys containing low manganese”, Mater. Sci. Tech., 14 (1998) 10