Ryszard B. Pecherski - Viscoplastic Flow in Solids Produced by Shear Banding

1 Cover

2 Title Page

3 Copyright Page

4 Dedication Page

5 Preface Acknowledgements References

6 1 Introduction1.1 The Objective of the Work 1.2 For Whom Is This Work Intended? 1.3 State of the Art 1.4 Summary of the Work Content Acknowledgements References

7 2 Physical Basis2.1 Introductory Remarks 2.2 Deformation Mechanisms in Single Crystals 2.3 Plastic Deformation in Polycrystals References

8 3 Incorporation of Shear Banding Activity into the Model of Inelastic Deformations 3.1 Plastic Deformation of Metallic Solids vis‐à‐vis the Continuum Mechanics 3.2 Hypothesis on the Extension of the RVE Concept 3.3 Model of Shear Strain Rate Generated by Micro‐shear Bands References

9 4 Basics of Rational Mechanics of Materials 4.1 A Recollection of Rational Continuum Mechanics 4.2 The Rational Theory of Materials – Epilogue References

10 5 Continuum Mechanics Description of Shear Banding 5.1 System of Active Micro‐shear Bands Idealised as the Surface of Strong Discontinuity 5.2 Macroscopic Averaging References

11 6 Deformation of a Body Due to Shear Banding – Theoretical Foundations6.1 Basic Concepts and Relations of Finite Inelastic Deformation of Crystalline Solids 6.2 Continuum Model of Finite Inelastic Deformations with Permanent Lattice Misorientation 6.3 Basic Concepts and Relations of Constitutive Description – Elastic Range 6.4 The Yield Limit Versus Shear Banding – The ‘extremal surface’ References

12 7 The Failure Criteria Concerning the Onset of Shear Banding7.1 The Yield Condition for Modern Materials – the State of the Art 7.2 The Yield Condition for the Isotropic Materials Revealing the Strength Differential Effect 7.3 Examples and Visualisations of the Particular Burzyński Failure Criteria 7.4 Remarks on the Extension Including Anisotropic Materials References

13 8 Constitutive Description of Viscoplasticity Accounting for Shear Banding 8.1 The Model of Plastic Flow with Nonlinear Development of Kinematic Hardening 8.2 The Perzyna Viscoplasticity Model Accounting for Shear Banding 8.3 Identification of the Viscoplasticity Model 8.4 The Crystal Plasticity Modelling of Deformation Processes in Metals Accounting for Shear Banding 8.5 Viscoplastic Deformation of Nanocrystalline Metals References

14 9 Conclusions9.1 Concluding Remarks References

15 Subject Index

16 Name Index

17 End User License Agreement

1 Chapter 1 Figure 1.1 The historical AGH UST emblem. Figure 1.2 Scheme of metal extrusion throughout the oscillating die (KOBO me... Figure 1.3 The pattern of the aluminium rest and extruded wire. The extrusio... Figure 1.4 Examples of the KOBO extrusion and forging products received in s... Figure 1.5 Fine tube of magnesium alloy AZ91 extruded at room temperature us... Figure 1.6 Schematic presentation of the forging process by the KOBO method:...

2 Chapter 2 Figure 2.1 An overview diagram of the multiscale hierarchy of plastic slip p... Figure 2.2 Schematic view of channel‐die test idea.

3 Chapter 3Figure 3.1 Schematic illustration of the multilevel hierarchy of micro‐shear...

4 Chapter 4Figure 4.1 The own display of local configuration of a deformable continuous...

5 Chapter 5Figure 5.1 The dual representation of a strong discontinuity surface of tang...Figure 5.2 The effect of shear strain increments, taken in the logarithmic s...

6 Chapter 6Figure 6.1 Configurations of a single crystal during the finite elastic and ...Figure 6.2 Deformation of the material point Xneighbourhood with the positi...

7 Chapter 7Figure 7.1 UBER function for copper reconstructed by symmetry‐based Voter po...Figure 7.2 Illustration of different cases of Burzyński quadrics depicted in...Figure 7.3 The hypothetical yield curve in the plane σ 2= 0 for the cas...Figure 7.4 (a, b) Failure limit condition for the magnesium alloy AZ31: (a) ...Figure 7.5 (a, b) Visualisation of the paraboloid failure surface according ...Figure 7.6 (a, b) Visualisation of the paraboloid yield surface according to...Figure 7.7 (a, b) Visualisation of the Burzyński paraboloidal failure surfac...Figure 7.8 The limit curves describe the experimental data for E335 steel, t...

8 Chapter 8Figure 8.1 Swift effect for unconstrained shear as predicted numerically by ...Figure 8.2 The plot of the absolute value of compression stress | σ 3| as...Figure 8.3 Comparison of the results of simple identification with the postu...Figure 8.4 The variation of the instantaneous shear‐banding contribution fun...Figure 8.5 The variation of the invariant ξ for the prescribed constant...Figure 8.6 Axial stress versus logarithmic axial strain in simple compressio...Figure 8.7 Axial stress versus logarithmic axial strain for plane strain com...Figure 8.8 Shear stress versus amount of shear in simple shear compared with...Figure 8.9 True stress‐true strain curves for quasi‐static compression tests...Figure 8.10 True stress–true strain curves for dynamic compression tests for...

1 Cover Page

2 Title Page

3 Copyright Page

4 Dedication Page

5 Preface

6 Table of Contents

7 Begin Reading

8 Subject Index

9 Name Index

10 Wiley End User License Agreement

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Ryszard B. Pęcherski

Institute of Fundamental Technological Research

Polish Academy of Sciences, Warsaw, Poland

This edition first published 2022