Introduction to Engineering Plasticity

Chapter 1 Plasticity of Metallic Materials

1.1 Introduction

1.2 Plastic properties of metallic materials

1.2.1 Simple tensile tests

1.2.2 Hydrostatic pressure test

1.3 Physical basis of plastic deformation

1.4 Plastic instability during axial tension

1.5 Idealization of plastic behavior of materials

1.5.1 Basic assumptions about plastic behavior of materials

1.5.2 Idealized model for stress-strain relationship

1.5.3 Strain-hardening model
Exercises
References

Chapter 2 Basic Characteristics of Structural Plasticity

2.1 Three-bar truss structure made of elastic, perfectly plastic material

2.2 Three-bar truss structure made of linear hardening elastic-plastic material

2.3 Influence of large deformation on the load-carrying capacity of truss
structure

2.4 Effect of loading path on stress and strain of the truss

2.5 Yield curve and limit curve on load plane

2.5.1 Load plane

2.5.2 Yield curve

2.5.3 Limit curve

2.5.4 Subsequent yield curve
Exercises
References

Chapter 3 Stress and Strain

3.1 Stress analysis

3.1.1 Stress tensor and its decomposition

3.1.2 Principal stresses and stress invariants

3.1.3 Stress on an octahedral plane

3.1.4 Effective stress

3.1.5 Three-dimensional Mohr’s circle and lode parameters

3.1.6 Stress space and principal stress space

3.2 Strain analysis

3.2.1 Displacement and strain

3.2.2 Decomposition of strain tensor and invariants of strain tensor

3.2.3 Equivalent strain and lode strain parameter

3.2.4 Strain rate tensor and strain increment tensor
Exercises
References

Chapter 4 Yield Criteria

4.1 Initial yield criteria

4.2 Two widely used yield criteria

4.2.1 Tresca yield criterion

4.2.2 von Mises yield criterion

4.2.3 Comparison between the two yield criteria

4.2.4 Other yield criteria

4.3 Experimental verification of yield criteria

4.4 Subsequent yield criteria
Exercises
References

Chapter 5 Plastic Constitutive Equations

5.1 Elastic constitutive equations

5.2 Drucker’s Postulate

5.3 Loading and unloading criteria

5.3.1 Loading and unloading criteria for perfectly plastic materials

5.3.2 Loading and unloading criteria for hardening materials

5.4 Incremental Theory (Flow Theory)

5.4.1 Overview

5.4.2 Flow rules of perfectly plastic materials associated with von Mises criterion

5.4.3 Flow rules of perfectly plastic materials associated with Tresca criterion

5.4.4 Incremental constitutive relationship of hardening materials

5.5 Deformation Theory (Total Theory of Plasticity)

5.5.1 Илъюшин theory

5.5.2 Simple loading and unique curve assumption

5.5.3 Theorem on simple loading

5.5.4 Summary and comparison of plastic constitutive relationships

5.6 Coulomb yield criterion and flow rule in rock mechanics
Exercises
References

Chapter 6 Simple Elastic-plastic Problems

6.1 Formulation of elastic-plastic boundary value problems

6.1.1 Boundary value problems based on the elastic-plastic deformation theory

6.1.2 Boundary value problems based on the incremental theory of plasticity

6.2 Deformation of thin-walled cylinder under combination of tension and torsion

6.3 Elastic-plastic bending of beams (Engineering Theory)

6.3.1 Pure bending of elastic-plastic beams

6.3.2 Elastic-plastic bending of beams under transverse loads

6.3.3 Combined loading of bending moment and axial force

6.4 Plastic bending of plate under plane strain condition (accurate theory)

6.4.1 Stress distribution

6.4.2 Deformation during bending

6.4.3 Movement of layers inside the plate

6.5 Free torsion of elastic-plastic cylinder

6.5.1 Scope and basic equations

6.5.2 Elastic torsion and membrane analogy

6.5.3 Fully plastic torsion and sand heap analogy

6.5.4 Elastic-plastic torsion and membrane-glass cover analogy

6.5.5 Unloading, springback and residual stress

6.5.6 Torsion of cylinder made of elastic-plastic strain-hardening material

6.6 Thick-walled cylinder under internal pressure

6.6.1 Basic equations

6.6.2 Elastic solution

6.6.3 Elastic-plastic solution for perfectly plastic material

6.6.4 Unloading and residual stress

6.6.5 Influence of geometric change on load-carrying capacity

6.6.6 Analysis for long thick-walled cylinder made of strain-hardening material

6.7 Rotating disc

6.7.1 Elastic solution

6.7.2 Elastic-plastic Solution
Exercises
References

Chapter 7 Plane Strain Problems for Rigid Perfectly Plastic Materials

7.1 Basic concepts

7.2 Basic equations of plane strain problems

7.3 Slip line and its geometric properties

7.3.1 Stress equation and slip line

7.3.2 Velocity equations

7.3.3 Hencky’s First Theorem

7.3.4 Hencky's Second Theorem

7.3.5 Stress discontinuity theorem

7.3.6 Summary

7.4 Boundary condition

7.4.1 Stress boundary

7.4.2 Rigid-plastic boundary

7.4.3 Boundary between two plastic regions

7.5 Applications of slip line field theory

7.5.1 Wedge under unilateral compression

7.5.2 A half plane pressed by a rigid stamper

7.5.3 Limit load of uniform pressure acting along a circular hole

7.5.4 Notched specimens in tension

7.6 Steady plastic flow problems

7.6.1 Slip line field of strip drawing

7.6.2 Stress distribution and drawing force

7.6.3 Velocity distribution

7.6.4 Check of rigid region
Exercises
References

Chapter 8 Principles of Limit Analysis

8.1 Limit state and limit analysis

8.2 Principle of virtual work-rate

8.3 Principle of limit analysis

8.3.1 Kinematically admissible velocity field and static field

8.3.2 Limit analysis theorems

8.3.3 Inferences of bound theorems

8.3.4 Summary

8.4 Applications of bound theorems
Exercises
References

Chapter 9 Limit Analysis of Beams and Frames

9.1 Collapse mechanism including plastic hinges

9.2 Bound theorems in limit analysis of beams and frames

9.3 Kinematical method and statical method

9.3.1 Kinematical method

9.3.2 Statical method

9.3.3 Limit curve and its applications

9.4 Limit curve and its application
Exercises
References
Chapter 10 Limit Analysis of Plates

10.1 Fundamental equations of plate

10.1.1 Basic assumptions on bending of thin plates

10.1.2 Generalized stress and strain

10.1.3 Generalized yield criteria

10.2 Limit analysis of axisymmetric bending of circular plates

10.2.1 Principal directions and general stresses

10.2.2 Limit load of simply supported circular plates

10.2.3 Limit load of clamped circular plate

10.3 Kinematic solutions of non-circular plates

10.4 Load-carrying capacity of plates under large deformation

10.4.1 Overview

10.4.2 Calladine method

10.4.3 Membrance Factor Method (MFM)

10.5 Stamping of circular plates
Exercises
References

Chapter 11 Utilzing Plastic Deformation for Energy Absorption

11.1 Introduction

11.2 Ring and circular tube under transverse compression

11.2.1 Rings compressed by two flat plates

11.2.2 Rings under a pair of compressive forces

11.2.3 Laterally constrained rings

11.2.4 Ring and tube systems

11.3 Circular and square tubes under axial compression

11.3.1 Axial crushing modes and typical force vs. displacement curves

11.3.2 Theoretical models of circular tube under axial crushing

11.3.3 Square tube under axial crushing

11.4 Comparison of various energy absorption elements

11.5 Energy absorption of cellular materials
Exercises
References

Chapter 12 Introduction to Dynamic Plasticity

12.1 Introduction

12.2 Propagation of elastic-plastic stress waves

12.2.1 One-dimensional wave equation

12.2.2 Propagation of elastic stress wave

12.2.3 Reflection and transmission of elastic waves

12.2.4 Elastic-plastic wave and formation of shock wave

12.3 Dynamic characteristics of materials under high strain rate

12.3.1 Strain rate

12.3.2 Strain rate sensitivity

12.3.3 Hopkinson bar technology

12.4 Dynamic response of rigid perfectly plastic beam

12.4.1 Basic assumptions

12.4.2 Cantilever beam subjected to a pulse load at free end

12.5 Effects of loading speed on energy absorption

12.5.1 Effects of loading speed on the deformation mode

12.5.2 Sensitivity of structural deformation to impact velocity

12.5.3 Static and dynamic behavior of Type II structure