Problems of Fracture Mechanics and Fatigue

Problems of Fracture Mechanics and Fatigue A Solution Guide

Edited by

E.E. GDOUTOS Democritus University ofThrace, Xanthi, Greece

C.A. RODOPOULOS Materials Research Institute, Sheffield Hallam University, Sheffield, United Kingdom

J.R. YATES University of Sheffield, Sheffield, United Kingdom

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-90-481-6491-2 ISBN 978-94-017-2774-7 (eBook) DOI 10.1007/978-94-017-2774-7

Printed on acid-free paper

Ali Rights Reserved

© 2003 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2003 Softcover reprint of the hardcover 1 st edition 2003 No part of this work rnay be reproduced, stored in a retrieval system, or transrnitted in any form or by any means, electronic, rnechanical, photocopying, rnicrofilrning, recording or otherwise, without written perrnission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

A book dedicated to those who can think, observe and imagine

Table of Contents

Editor's Preface on Fracture Mechanics

Editors Preface on Fatigue

List of Contributors

PART A: FRACTURE MECHANICS

1. Linear Elastic Stress Field

Problem 1: Airy Stress Function Method

E.E. Gdoutos

Problem 2: Westergaard Method for a Crack Under Concentrated Forces

E.E. Gdoutos

Problem 3: Westergaard Method for a Periodic Array of Cracks Under

Concentrated Forces

E.E. Gdoutos

Problem 4: Westergaard Method for a Periodic Array of Cracks Under

xix

xxiii

XXV

3

11

17

Uniform Stress 21

E.E. Gdoutos

Problem 5: Calculation of Stress Intensity Factors by the Westergaard Method 25

E.E. Gdoutos

Problem 6: Westergaard Method for a Crack Under Distributed Forces

E.E. Gdoutos

Problem 7: Westergaard Method for a Crack Under Concentrated Forces

E.E. Gdoutos

Problem 8: Westergaard Method for a Crack Problem

E.E. Gdoutos

Problem 9: Westergaard Method for a Crack Subjected to Shear Forces

E.E. Gdoutos

31

33

39

41

Vlll Table of Contents

Problem 10: Calculation of Stress Intensity Factors by Superposition

M.S. Konsta-Gdoutos

Problem 11: Calculation of Stress Intensity Factors by Integration

E.E. Gdoutos

Problem 12: Stress Intensity Factors for a Linear Stress Distribution

E.E. Gdoutos

Problem 13: Mixed-Mode Stress Intensity Factors in Cylindrical Shells

E.E. Gdoutos

Problem 14: Photoelastic Determination of Stress Intensity Factor K1

E.E. Gdoutos

Problem 15: Photoelastic Determination of Mixed-Mode Stress Intensity

Factors K1 and Kn

M.S. Konsta-Gdoutos

Problem 16: Application of the Method of Weight Function for the

Determination of Stress Intensity Factors

L. Banks-Sills

2. Elastic-Plastic Stress Field

Problem 17: Approximate Determination of the Crack Tip Plastic Zone

for Mode-l and Mode-ll Loading

E.E. Gdoutos

Problem 18: Approximate Determination of the Crack Tip Plastic Zone

for Mixed-Mode Loading

E.E. Gdoutos

Problem 19: Approximate Determination of the Crack Tip Plastic Zone

According to the Tresca Yield Criterion

M.S. Konsta-Gdoutos

Problem 20: Approximate Determination of the Crack Tip Plastic Zone

According to a Pressure Modified Mises Yield Criterion

E.E. Gdoutos

Problem 21: Crack Tip Plastic Zone According to Irwin's Model

E.E. Gdoutos

Problem 22: Effective Stress Intensity factor According to Irwin's Model

E.E. Gdoutos

45

49

53

57

63

65

69

75

81

83

91

95

99

Table of Contents

Problem 23: Plastic Zone at the Tip of a Semi-Infinite Crack According

to the Dugdale Model

E.E. Gdoutos

ix

103

Problem 24: Mode-III Crack Tip Plastic Zone According to the Dugdale Model 107

E.E. Gdoutos

Problem 25: Plastic Zone at the Tip of a Penny-Shaped Crack According

to the Dugdale Model

E.E. Gdoutos

3. Strain Energy Release Rate

Problem 26: Calculation of Strain Energy Release Rate from Load - Displacement -

113

Crack Area Equation 117

M.S. Konsta-Gdoutos

Problem 27: Calculation of Strain Energy Release Rate for Deformation Modes I, II and III

E.E. Gdoutos

Problem 28: Compliance of a Plate with a Central Crack

E.E. Gdoutos

121

127

Problem 29: Strain Energy Release Rate for a Semi-Infinite Plate with a Crack 131

E.E. Gdoutos

Problem 30: Strain Energy Release Rate for the Short Rod Specimen

E.E. Gdoutos

Problem 31: Strain Energy Release Rate for the Blister Test

E.E. Gdoutos

Problem 32: Calculation of Stress Intensity Factors Based on Strain Energy

Release Rate

E.E. Gdoutos

Problem 33: Critical Strain Energy Release Rate

E.E. Gdoutos

4. Critical Stress Intensity Factor Fracture Criterion

135

139

143

147

Problem 34: Experimental Determination of Critical Stress Intensity Factor K1c 155

E.E. Gdoutos

X Table of Contents

Problem 35: Experimental Determination of K1c

E.E. Gdoutos

Problem 36: Crack Stability

E.E. Gdoutos

161

163

Problem 37: Stable Crack Growth Based on the Resistance Curve Method 169

M.S. Konsta-Gdoutos

Problem 38: Three-Point Bending Test in Brittle Materials

A. Carpinteri, B. Chiaia and P. Cometti

Problem 39: Three-Point Bending Test in Quasi Brittle Materials

A. Carpinteri, B. Chiaia and P. Cometti

Problem 40: Double-Cantilever Beam Test in Brittle Materials

A. Carpinteri, B. Chiaia and P. Cometti

Problem 41: Design of a Pressure Vessel

E.E. Gdoutos

Problem 42: Thermal Loads in a Pipe

E.E. Gdoutos

5. J-integral and Crack Opening Displacement Fracture Criteria

173

177

183

189

193

Problem 43: J-integral for an Elastic Beam Partly Bonded to a Half-Plane 197

E.E. Gdoutos

Problem 44: J-integral for a Strip with a Semi-Infinite Crack 201

E.E. Gdoutos

Problem 45: J-integral for Two Partly Bonded Layers

E.E. Gdoutos

Problem 46: J-integral for Mode-l

E.E. Gdoutos

Problem 47: J-integral for Mode III

L. Banks-Sills

Problem 48: Path Independent Integrals

E.E. Gdoutos

207

211

219

223

Problem 49: Stresses Around Notches 229

E.E. Gdoutos

Problem 50: Experimental Determination of J1c from J - Crack Growth Curves 233

Table of Contents Xl

E.E. Gdoutos

Problem 51: Experimental Determination of J from Potential Energy - Crack

Length Curves 239 E.E. Gdoutos

Problem 52: Experimental Determination of J from Load-Displacement Records 243 E.E. Gdoutos

Problem 53: Experimental Determination of J from a Compact Tension Specimen 247 E.E. Gdoutos

Problem 54: Validity of J1c and K1c Tests E.E. Gdoutos

Problem 55: Critical Crack Opening Displacement E.E. Gdoutos

Problem 56: Crack Opening Displacement Design Methodology E.E. Gdoutos

6. Strain Energy Density Fracture Criterion and Mixed-Mode Crack Growth

Problem 57: Critical Fracture Stress of a Plate with an Inclined Crack M.S. Konsta-Gdoutos

Problem 58: Critical Crack Length of a Plate with an Inclined Crack

E.E. Gdoutos

Problem 59: Failure of a Plate with an Inclined Crack E.E. Gdoutos

251

253

257

263

269

273

Problem 60: Growth of a Plate with an Inclined Crack Under Biaxial Stresses 277

E.E. Gdoutos

Problem 61: Crack Growth Under Mode-ll Loading 283 E.E. Gdoutos

Problem 62: Growth of a Circular Crack Loaded Perpendicularly to its Cord by Tensile Stress

E.E. Gdoutos

Problem 63: Growth of a Circular Crack Loaded Perpendicular to its Cord by Compressive Stress

E.E. Gdoutos

287

291

xu Table of Contents

Problem 64: Growth of a Circular Crack Loaded Parallel to its Cord E.E. Gdoutos

Problem 65: Growth of Radial Cracks Emanating from a Hole E.E. Gdoutos

293

297

Problem 66: Strain Energy Density in Cuspidal Points of Rigid Inclusions 301 E.E. Gdoutos

Problem 67: Failure from Cuspidal Points of Rigid Inclusions 305 E.E. Gdoutos

Problem 68: Failure of a Plate with a Hypocycloidal Inclusion 309 E.E. Gdoutos

Problem 69: Crack Growth From Rigid Rectilinear Inclusions 315 E.E. Gdoutos

Problem 70: Crack Growth Under Pure Shear 319 E.E. Gdoutos

Problem 71: Critical Stress in Mixed Mode Fracture L Banks-Sills

Problem 72: Critical Stress for an Interface Crack L Banks-Sills

Problem 73: Failure of a Pressure Vessel with an Inclined Crack E.E. Gdoutos

Problem 74: Failure of a Cylindrical bar with a Circular Crack E.E. Gdoutos

327

333

339

343

Problem 75: Failure of a Pressure Vessel Containing a Crack with Inclined Edges 347 E.E. Gdoutos

Problem 76: Failure of a Cylindrical Bar with a Ring-Shaped Edge Crack 351 G.C. Sih

Problem 77: Stable and Unstable Crack Growth 355 E.E. Gdoutos

7. Dynamic Fracture

Problem 78: Dynamic Stress Intensity Factor E.E. Gdoutos

Problem 79: Crack Speed During Dynamic Crack Propagation

359

365

Table of Contents

E.E. Gdoutos

Problem 80: Rayleigh Wave Speed

E.E. Gdoutos

Problem 81: Dilatational, Shear and Rayleigh Wave Speeds E.E. Gdoutos

Problem 82: Speed and Acceleration of Crack Propagation

E.E. Gdoutos

8. Environment-Assisted Fracture

xiii

369

373

377

Problem 83: Stress Enhanced Concentration of Hydrogen around Crack Tips 385 D.J. Unger

Problem 84: Subcritical Crack Growth due to the Presence of a Deleterious Species 397 D.J. Unger

PARTB: FATIGUE

1. Life Estimates

Problem 1: Estimating the Lifetime of Aircraft Wing Stringers

J.R. Yates

Problem 2: Estimating Long Life Fatigue of Components J.R. Yates

Problem 3: Strain Life Fatigue Estimation of Automotive Component

J.R. Yates

Problem 4: Lifetime Estimates Using LEFM J.R. Yates

Problem 5: Lifetime of a Gas Pipe A. Afagh and Y.-W. Mai

Problem 6: Pipe Failure and Lifetime Using LEFM M.N.James

405

409

413

419

423

427

Problem 7: Strain Life Fatigue Analysis of Automotive Suspension Component 431

J. R. Yates

XIV Table of Contents

2. Fatigue Crack Growth

Problem 8: Fatigue Crack Growth in a Center-Cracked Thin Aluminium Plate 439 Sp. Pantelakis and P. Papanikos

Problem 9: Effect of Crack Size on Fatigue Life 441 A. Afaghi and Y.-W. Mai

Problem 10: Effect of Fatigue Crack Length on Failure Mode of a Center-Cracked Thin Aluminium Plate 445

Sp. Pantelakis and P. Papanikos

Problem 11: Crack Propagation Under Combined Tension and Bending 449 J. R. Yates

Problem 12: Influence of Mean Stress on Fatigue Crack Growth for Thin and Thick Plates 453

Sp. Pantelakis and P. Papanikos

Problem 13: Critical Fatigue Crack Growth in a Rotor Disk Sp. Pantelakis and P. Papanikos

Problem 14: Applicability ofLEFM to Fatigue Crack Growth C.A. Rodopoulos

455

457

Problem 15: Fatigue Crack Growth in the Presence of Residual Stress Field 461 Sp. Pantelakis and P. Papanikos

3. Effect of Notches on Fatigue

Problem 16: Fatigue Crack Growth in a Plate Containing an Open Hole Sp. Pantelakis and P. Papanikos

Problem 17: Infinite Life for a Plate with a Semi-Circular Notch C.A. Rodopoulos

Problem 18: Infinite Life for a Plate with a Central Hole C.A. Rodopoulos

Problem 19: Crack Initiation in a Sheet Containing a Central Hole C.A. Rodopoulos

467

469

473

477

Table of Contents

4. Fatigue and Safety Factors

Problem 20: Inspection Scheduling C.A. Rodopoulos

Problem 21: Safety Factor of aU-Notched Plate C.A. Rodopoulos

Problem 22: Safety Factor and Fatigue Life Estimates C.A. Rodopoulos

Problem 23: Design of a Circular Bar for Safe Life Sp. Pantelakis and P. Papanikos

Problem 24: Threshold and LEFM C.A. Rodopoulos

XV

483

487

491

495

497

Problem 25: Safety Factor and Residual Strength 501 C.A. Rodopoulos

Problem 26: Design of a Rotating Circular Shaft for Safe Life 505 Sp. Pantelakis and P. Papanikos

Problem 27: Safety Factor of a Notched Member Containing a Central Crack 509 C.A. Rodopoulos

Problem 28: Safety Factor of a Disk Sander C.A. Rodopoulos

S. Short Cracks

Problem 29: Short Cracks and LEFM Error C.A. Rodopoulos

Problem 30: Stress Ratio effect on the Kitagawa-Takahashi diagram C.A. Rodopoulos

Problem 31: Susceptibility of Materials to Short Cracks C.A. Rodopoulos

Problem 32: The effect of the Stress Ratio on the Propagation of Short Fatigue Cracks in 2024-T3

C.A. Rodopoulos

519

529

533

539

543

xvi Table of Contents

6. Variable Amplitude Loading

Problem 33: Crack Growth Rate During Irregular Loading Sp. Pantelakis and P. Papanikos

Problem 34: Fatigue Life Under two-stage Block Loading Sp. Pantelakis and P. Papanikos

Problem 35: The Application of Wheeler's Model C.A. Rodopoulos

Problem 36: Fatigue Life Under Multiple-Stage Block Loading Sp. Pantelakis and P. Papanikos

Problem 37: Fatigue Life Under two-stage Block Loading Using Non-Linear Damage Accumulation

Sp. Pantelakis and P. Papanikos

Problem 38: Fatigue Crack Retardation Following a Single Overload Sp. Pantelakis and P. Papanikos

Problem 39: Fatigue Life of a Pipe Under Variable Internal Pressure Sp. Pantelakis and P. Papanikos

Problem 40: Fatigue Crack Growth Following a Single Overload Based on Crack Closure

Sp. Pantelakis and P. Papanikos

Problem 41: Fatigue Crack Growth Following a Single Overload Based on

551

553

555

559

563

565

569

573

Crack-Tip Plasticity 575 Sp. Pantelakis and P. Papanikos

Problem 42: Fatigue Crack Growth and Residual Strength of a Double Edge Cracked Panel Under Irregular Fatigue Loading 579

Sp. Pantelakis and P. Papanikos

Problem 43: Fatigue Crack Growth Rate Under Irregular Fatigue Loading 583 Sp. Pantelakis and P. Papanikos

Problem 44: Fatigue Life of a Pressure Vessel Under Variable Internal Pressure 585 Sp. Pantelakis and P. Papanikos

Table of Contents

7. Complex Cases

Problem 45: Equibiaxial Low Cycle Fatigue J.R. Yates

XVll

589

Problem 46: Mixed Mode Fatigue Crack Growth in a Center-Cracked Panel 593 Sp. Pantelakis and P. Papanikos

Problem 47: Collapse Stress and the Dugdale's Model 597 C.A. Rodopoulos

Problem 48: Torsional Low Cycle Fatigue 601 J.R. Yates and M. W Brown

Problem 49: Fatigue Life Assessment of a Plate Containing Multiple Cracks 607 Sp. Pantelakis and P. Papanikos

Problem 50: Fatigue Crack Growth and Residual Strength in a Simple MSD Problem 611

Sp. Pantelakis and P. Papanikos

INDEX 615

Editor's Preface On Fracture Mechanics

A major objective of engineering design is the determination of the geometry and

dimensions of machine or structural elements and the selection of material in such a

way that the elements perform their operating function in an efficient, safe and

economic manner. For this reason the results of stress analysis are coupled with an

appropriate failure criterion. Traditional failure criteria based on maximum stress, strain

or energy density cannot adequately explain many structural failures that occurred at

stress levels considerably lower than the ultimate strength of the material. On the other

hand, experiments performed by Griffith in 1921 on glass fibers led to the conclusion

that the strength of real materials is much smaller, typically by two orders of magnitude,

than the theoretical strength.

The discipline of fracture mechanics has been created in an effort to explain these

phenomena. It is based on the realistic assumption that all materials contain crack-like

defects from which failure initiates. Defects can exist in a material due to its

composition, as second-phase particles, debonds in composites, etc., they can be

introduced into a structure during fabrication, as welds, or can be created during the

service life of a component like fatigue, environment-assisted or creep cracks. Fracture

mechanics studies the loading-bearing capacity of structures in the presence of initial

defects. A dominant crack is usually assumed to exist. The safe design of structures

proceeds along two lines: either the safe operating load is determined when a crack of a

prescribed size exists in the structure, or given the operating load, the size of the crack

that is created in the structure is determined.

Design by fracture mechanics necessitates knowledge of a parameter that characterizes

the propensity of a crack to extend. Such a parameter should be able to relate laboratory

test results to structural performance, so that the response of a structure with cracks can

be predicted from laboratory test data. This is determined as function of material

behavior, crack size, structural geometry and loading conditions. On the other l}.and, the

critical value of this parameter, known as fracture toughness, is a property of the

material and is determined from laboratory tests. Fracture toughness is the ability of the

material to resist fracture in the presence of cracks. By equating this parameter to its

critical value we obtain a relation between applied load, crack size and structure

geometry, which gives the necessary information for structural design. Fracture

mechanics is used to rank the ability of a material to resist fracture within the

framework of fracture mechanics, in the same way that yield or ultimate strength is used

to rank the resistance of the material to yield or fracture in the conventional design

criteria. In selecting materials for structural applications we must choose between

materials with high yield strength, but comparatively low fracture toughness, or those

with a lower yield strength but higher fracture toughness.

XX Editor's Preface

The theory of fracture mechanics has been presented in many excellent books, like those written by the editor of the first part of the book devoted to fracture mechanics entitled: "Problems of Mixed Mode Crack Propagation," "Fracture Mechanics Criteria and Applications," and "Fracture Mechanics-An Introduction." However, students,

scholars and practicing engineers are still reluctant to implement and exploit the potential of fracture mechanics in their work. This is because fracture is characterized by complexity, empiricism and conflicting viewpoints. It is the objective of this book to

build and increase engineering confidence through worked exercises. The first part of the book referred to fracture mechanics contains 84 solved problems. They cover the

following areas: • The Westergaard method for crack problems

• Stress intensity factors

• Mixed-mode crack problems

• Elastic-plastic crack problems

• Determination of strain energy release rate

• Determination of the compliance of crack problems

• The critical strain energy release rate criterion

• The critical stress intensity factor criterion

• Experimental determination of critical stress intensity factor. The !-integral and

its experimental determination

• The crack opening displacement criterion

• Strain energy density criterion

• Dynamic fracture problems

• Environment assisted crack growth problems

• Photoelastic determination of stress intensity factors

• Crack growth from rigid inclusions

• Design of plates, bars and pressure vessels

The problems are divided into three groups: novice (for undergraduate students),

intermediate (for graduate students and practicing engineers) and advanced (for

researchers and professional engineers). They are marked by one, two and three

asterisks, respectively. At the beginning of each problem there is a part of "useful

information," in which the basic theory for the solution of the problem is briefly

outlined. For more information on the theory the reader is referred to the books of the

editor: "Fracture Mechanics Criteria and Applications," "Fracture Mechanics-An

Introduction," "Problems of Mixed-Mode Crack Propagation." The solution of each

problem is divided into several easy to follow steps. At the end of each problem the

relevant bibliography is given.

Editor's Preface XXl

I wish to express my sincere gratitude and thanks to the leading experts in fracture mechanics and good friends and colleagues who accepted my proposal and contributed to this part of the book referred to fracture mechanics: Professor L. Banks-Sills of the Tel Aviv University, Professor A. Carpinteri, Professor B. Chiaia and Professor P.

Cometti of the Politecnico di Torino, Dr. M. S. Konsta-Gdoutos of the Democritus University of Thrace, Professor G. C. Sib of Lehigh University and Professor D. J.

Unger of the University of Evansville. My deep appreciation and thanks go to Mrs Litsa Adamidou for her help in typing the

manuscript. Finally, a special word of thanks goes to Ms Nathalie Jacobs of Kluwer

Academic Publishers for her kind collaboration and support during the preparation of the book.

April, 2003 Xanthi, Greece

Emmanuel E. Gdoutos Editor

Editor's Preface On Fatigue

The second part of this book is devoted to fatigue. The word refers to the damage caused by the cyclic duty imposed on an engineering component. In most cases, fatigue will result into the development of a crack which will propagate until either the component is retired or the component experiences catastrophic failure. Even though fatigue research dates back to the nineteenth century (A. Wohler1860, H. Gerber 1874 and J. Goodman 1899), it is within the last five decades that has emerged as a major area of research. This was because of major developments in materials science and fracture mechanics which help researchers to better understand the complicated mechanisms of crack growth. Fatigue in its current form wouldn't have happened if it wasn't for a handful of inspired people. The gold medal should be undoubtedly given to G. Irwin for his 1957 paper Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate. The silver medal should go to Paris, Gomez and Anderson for their 1961 paper A Rational Analytic Theory of Fatigue. There are a few candidates for the bronze which makes the selection a bit more difficult. In our opinion the medal should be shared by D.S. Dugdale for his 1960 paper Yielding of Steel Sheets Containing Slits, W. Biber for the 1960 paper Fatigue Crack Closure under Cyclic Tension and K. Kitagawa and S. Takahashi for their 1976 paper Applicability of Fracture Mechanics to Very Small Cracks or the Cracks in the Early Stage. Unquestionably, if there was a fourth place, we would have to put a list of hundreds of names and exceptionally good works. To write and editor a book about solved problems in fatigue it is more difficult than it seems. Due to ongoing research and scientific disputes we are compelled to present solutions which are well established and generally accepted. This is especially the case for those problems designated for novice and intermediate level. In the advanced level, there are some solutions based on the author's own research. In this second part, there are 50 solved problems. They cover the following areas:

• Life estimates • Fatigue crack growth • Effect of Notches on Fatigue • Fatigue and Safety factors • Short cracks • Variable amplitude loading • Complex cases

As before, the problems are divided into three groups: novice (for undergraduate students), intermediate (for graduate students and practicing engineers) and advanced (for researchers and professional engineers). Both the editors have been privileged to scientifically mature in an department with a long tradition in fatigue research. Our minds have been shaped by people including Bruce Bilby, Keith Miller, Mike Brown, Rod Smith and Eduardo de los Rios. We thank them. We wish to express our appreciation to the leading experts in the field of fatigue who contributed to this second part of the book: Professor M. W. Brown from the University of Sheffield, Professor M. N. James from the University of Plymouth, Professor Y-M.

xxiv Editor's Preface

Mai from the University of Sydney, Dr. P. Papanikos from the Institute of Structures and Advanced Materials, Dr. A. Afaghi-Khatibi from the University of Melbourne and Professor Sp. Pantelakis from the University of Patras. Finally, we are indebted to Ms. Nathalie Jacobs for immense patience that she showed during the preparation of this manuscript.

April, 2003 Sheffield, United Kingdom

Chris A. Rodopoulos John R. Yates

Editors

List of Contributors

Afaghi-Khatibi, A., Department of Mechanical and Manufacturing Engineering. The University of Melbourne, Victoria 3010, Australia.

Banks-Sills, L., Department of Solid Mechanics, Materials and Systems, Faculty of Engineering, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel.

Brown, M. W., Department of Mechanical Engineering, The University of Sheffield, Sheffield, S1 3JD, UK.

Carpinteri, A., Department of Structural Engineering and Geotechnics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Chiaia, B., Department of Structural Engineering and Geotechnics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Cometti, P., Department of Structural Engineering and Geotechnics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Gdoutos, E. E., School of Engineering, Democritus University ofThrace, GR-671 00 Xanthi, Greece.

James, M. N., Department of Mechanical and Marine Engineering, University of Plymouth, Drake Circus, Plymouth, Devon PL4 8AA, UK.

Konsta-Gdoutos, M., School of Engineering, Democritus University of Thrace, GR-671 00 Xanthi, Greece.

Mai, Yiu-Wing, Centre for Advanced Materials Technology, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia.

Pantelakis, Sp., Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26500, Patras, Greece.

Papanikos, P., ISTRAM, Institute of Structures & Advanced Materials, Patron-Athinon 57, Patras, 26441, Greece.

Rodopoulos, C. A., Structural Integrity Research Institute of the University of Sheffield, Department of Mechanical Engineering, The University of Sheffield, Sheffield, S1 3JD, UK.

Unger, D. J., Department of Mechanical and Civil Engineering, University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722, USA.

Yates, J. R, Department of Mechanical Engineering, The University of Sheffield, Sheffield, S1 3JD, UK.