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 xi1 Introduction 11.1 The Objective of the Work 11.2 For Whom Is This Work Intended? 21.3 State of the Art 31.3.1 Motivation Resulting from Industrial Applications 31.3.2 KOBO Processes Resulting in Viscous Effects 71.4 Summary of the Work Content 8Acknowledgements 9References 92 Physical Basis 112.1 Introductory Remarks 112.2 Deformation Mechanisms in Single Crystals 122.2.1 Plastic Glide and Twinning 122.2.2 Hierarchy of Plastic Slip Processes 142.2.3 Localised Forms of Plastic Deformation 172.2.4 Physical Nature of Shear Bands 192.3 Plastic Deformation in Polycrystals 232.3.1 Mechanisms of Plastic Deformation and the Evolution of Internal Micro- Stresses 232.3.2 Micro- shear Bands Hierarchy and Their Macroscopic Effects 252.3.3 Physical Nature of Micro- shear Bands in Polycrystals 282.3.4 Comments on ‘adiabatic’ Micro- shear Bands 29References 293 Incorporation of Shear Banding Activity into the Model of Inelastic Deformations 373.1 Plastic Deformation of Metallic Solids vis- à- vis the Continuum Mechanics 373.2 Hypothesis on the Extension of the RVE Concept 393.3 Model of Shear Strain Rate Generated by Micro- shear Bands 41References 464 Basics of Rational Mechanics of Materials 494.1 A Recollection of Rational Continuum Mechanics 494.2 The Rational Theory of Materials – Epilogue 524.2.1 The Concept of the Deformable Body 544.2.2 The Motion of the Body 554.2.3 The Deformation of a Body 564.2.4 The Deformation Gradient 56References 595 Continuum Mechanics Description of Shear Banding 635.1 System of Active Micro- shear Bands Idealised as the Surface of Strong Discontinuity 635.1.1 On Finite Inelastic Deformations with High Lattice Misorientation 675.2 Macroscopic Averaging 67References 736 Deformation of a Body Due to Shear Banding – Theoretical Foundations 756.1 Basic Concepts and Relations of Finite Inelastic Deformation of Crystalline Solids 756.2 Continuum Model of Finite Inelastic Deformations with Permanent Lattice Misorientation 776.3 Basic Concepts and Relations of Constitutive Description – Elastic Range 826.4 The Yield Limit Versus Shear Banding – The ‘extremal surface’ 83References 857 The Failure Criteria Concerning the Onset of Shear Banding 877.1 The Yield Condition for Modern Materials – the State of the Art 877.2 The Yield Condition for the Isotropic Materials Revealing the Strength Differential Effect 907.3 Examples and Visualisations of the Particular Burzyński Failure Criteria 947.3.1 Ellipsoidal Failure Surface 947.3.2 Paraboloid Failure Surfaces 957.4 Remarks on the Extension Including Anisotropic Materials 98References 1018 Constitutive Description of Viscoplasticity Accounting for Shear Banding 1078.1 The Model of Plastic Flow with Nonlinear Development of Kinematic Hardening 1078.2 The Perzyna Viscoplasticity Model Accounting for Shear Banding 1128.3 Identification of the Viscoplasticity Model 1148.4 The Crystal Plasticity Modelling of Deformation Processes in Metals Accounting for Shear Banding 1188.5 Viscoplastic Deformation of Nanocrystalline Metals 122References 1269 Conclusions 1319.1 Concluding Remarks 1319.1.1 Shear Banding- Mediated Flow vis- à- vis Ductile Failure Analysis 1319.1.2 Application of Peridynamic Numerical Simulations of Shear Banding Processes 132References 135Subject Index 139Name Index 141