Viscoplastic Flow in Solids Produced by Shear Banding

Ryszard B. Pęcherski, PhD, DSc, is researching in the Department of Theory of Continuous Media and Nanostructures at the Institute of Fundamental Technological Research, Polish Academy of Sciences in Warsaw. He received his MEng from the Gdańsk Polytechnic Department of Shipbuilding in Gdańsk, Poland, in 1973, his PhD in 1979 and his DSc in 1998 from the Institute of Fundamental Technological Research, Warsaw, Poland. He has been a member of the research staff since 1977. He was a Fellow of the Japan Society for Promotion of Sciences, Tohoku University, Sendai (Takeo Yokobori), Japan, from 1979–1980 and a Fellow of the Aleksander von Humboldt Foundation, University of Hanover, Hanover, Germany, from 1983–1987 (Erwin Stein). He was a member of the faculty of Civil Engineering at Cracow University of Technology, Kraków, Poland, from 2000–2007, and he received the title of Professor in October 2007. Finally, from July 2007–February 2022, as a member of the Mechanical Engineering and Robotics faculty at AGH University of Science and Technology in Kraków, he taught English courses on mechanics of materials. He also invited lecture courses delivered in the International Centre for Mechanical Sciences, CISM, Udine, 2012, and the Summer School of Mechanics in Agadir, Maroc, 2013, related to modelling inelastic behaviour of solids accounting for micro-shear banding. His lectures on the mechanics of modern materials in École Nationale d’Ingeniéurs de Metz, 2014 (Alexis Rusinek – host professor) contained the earlier threads and ideas woven into the concept of the work.

Preface xi

1 Introduction 1

1.1 The Objective of the Work 1

1.2 For Whom Is This Work Intended? 2

1.3 State of the Art 3

1.3.1 Motivation Resulting from Industrial Applications 3

1.3.2 KOBO Processes Resulting in Viscous Effects 7

1.4 Summary of the Work Content 8

Acknowledgements 9

References 9

2 Physical Basis 11

2.1 Introductory Remarks 11

2.2 Deformation Mechanisms in Single Crystals 12

2.2.1 Plastic Glide and Twinning 12

2.2.2 Hierarchy of Plastic Slip Processes 14

2.2.3 Localised Forms of Plastic Deformation 17

2.2.4 Physical Nature of Shear Bands 19

2.3 Plastic Deformation in Polycrystals 23

2.3.1 Mechanisms of Plastic Deformation and the Evolution of Internal Micro- Stresses 23

2.3.2 Micro- shear Bands Hierarchy and Their Macroscopic Effects 25

2.3.3 Physical Nature of Micro- shear Bands in Polycrystals 28

2.3.4 Comments on ‘adiabatic’ Micro- shear Bands 29

References 29

3 Incorporation of Shear Banding Activity into the Model of Inelastic Deformations 37

3.1 Plastic Deformation of Metallic Solids vis- à- vis the Continuum Mechanics 37

3.2 Hypothesis on the Extension of the RVE Concept 39

3.3 Model of Shear Strain Rate Generated by Micro- shear Bands 41

References 46

4 Basics of Rational Mechanics of Materials 49

4.1 A Recollection of Rational Continuum Mechanics 49

4.2 The Rational Theory of Materials – Epilogue 52

4.2.1 The Concept of the Deformable Body 54

4.2.2 The Motion of the Body 55

4.2.3 The Deformation of a Body 56

4.2.4 The Deformation Gradient 56

References 59

5 Continuum Mechanics Description of Shear Banding 63

5.1 System of Active Micro- shear Bands Idealised as the Surface of Strong Discontinuity 63

5.1.1 On Finite Inelastic Deformations with High Lattice Misorientation 67

5.2 Macroscopic Averaging 67

References 73

6 Deformation of a Body Due to Shear Banding – Theoretical Foundations 75

6.1 Basic Concepts and Relations of Finite Inelastic Deformation of Crystalline Solids 75

6.2 Continuum Model of Finite Inelastic Deformations with Permanent Lattice Misorientation 77

6.3 Basic Concepts and Relations of Constitutive Description – Elastic Range 82

6.4 The Yield Limit Versus Shear Banding – The ‘extremal surface’ 83

References 85

7 The Failure Criteria Concerning the Onset of Shear Banding 87

7.1 The Yield Condition for Modern Materials – the State of the Art 87

7.2 The Yield Condition for the Isotropic Materials Revealing the Strength Differential Effect 90

7.3 Examples and Visualisations of the Particular Burzyński Failure Criteria 94

7.3.1 Ellipsoidal Failure Surface 94

7.3.2 Paraboloid Failure Surfaces 95

7.4 Remarks on the Extension Including Anisotropic Materials 98

References 101

8 Constitutive Description of Viscoplasticity Accounting for Shear Banding 107

8.1 The Model of Plastic Flow with Nonlinear Development of Kinematic Hardening 107

8.2 The Perzyna Viscoplasticity Model Accounting for Shear Banding 112

8.3 Identification of the Viscoplasticity Model 114

8.4 The Crystal Plasticity Modelling of Deformation Processes in Metals Accounting for Shear Banding 118

8.5 Viscoplastic Deformation of Nanocrystalline Metals 122

References 126

9 Conclusions 131

9.1 Concluding Remarks 131

9.1.1 Shear Banding- Mediated Flow vis- à- vis Ductile Failure Analysis 131

9.1.2 Application of Peridynamic Numerical Simulations of Shear Banding Processes 132

References 135

Subject Index 139

Name Index 141