
Introduction to Engineering Plasticity
Fundamentals with Applications in Metal Forming, Limit Analysis and Energy Absorption
- 1st Edition - June 20, 2022
- Imprint: Elsevier
- Authors: Tongxi Yu, Pu Xue
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 9 8 9 8 1 - 7
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 9 8 9 8 2 - 4
The theory of plasticity is a branch of solid mechanics that investigates the relationship between permanent deformation and load, and the distribution of stress and strains of… Read more
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- Brings together plasticity theory with engineering applications and problem solving
- Elaborates problem solving methods and demonstrates plasticity in various engineering fields
- Covers the recent decades of research on metal forming and limit analysis
- Includes energy absorption of new structures and materials where plasticity dominates analysis and design
- Gives a systematic account of the theory of plasticity alongside its engineering applications
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
- Edition: 1
- Published: June 20, 2022
- Imprint: Elsevier
- Language: English
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Tongxi Yu
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