Engineering Plasticity

Z. R. Wang, Harbin Institute of Technology, China.W. L. HU, Troy Design and Manufacturing Co., USA.S. J. Yuan, Harbin Institute of Technology, China.X. S. Wang, Harbin Institute of Technology, China.

• Preface xiii1 Fundamentals of Classical Plasticity 11.1 Stress 11.1.1 The Concept of Stress Components 11.1.2 Description of the Stress State 21.1.2.1 Stresses on an Arbitrary Inclined Plane 21.1.2.2 Stress Components on an Oblique Plane 41.1.2.3 Special Stresses 61.1.2.4 Common Stress States 71.1.3 Stress Tensors and Deviatoric Stress Tensors 71.1.4 Mohr Stress Circles 91.1.4.1 Mohr Circles for a Two-Dimensional Stress System 91.1.4.2 Mohr Circles for a Three-Dimensional Stress System 121.1.5 Equations of Force Equilibrium 131.2 Strain 151.2.1 Nominal Strain and True Strain 151.2.2 Strain Components as Functions of Infinitesimal Displacements 171.2.3 The Maximum Shear Strains and the Octahedral Strains 201.2.4 Strain Rates and Strain Rate Tensors 211.2.5 Incompressibility and Chief Deformation Types 231.3 Yield Criteria 251.3.1 The Concept of Yield Criterion 251.3.2 Tresca Yield Criterion 261.3.3 Mises Yield Criterion 261.3.4 Twin Shear Stress Yield Criterion 271.3.5 Yield Locus and Physical Concepts of Tresca, Mises, and Twin Shear Stress Yield Criteria 271.3.5.1 Interpretation of Tresca Yield Criterion 291.3.5.2 Interpretation of Twin Shear Stress Yield Criterion 301.3.5.3 Interpretation of Mises Yield Criterion 311.4 A General Yield Criterion 331.4.1 Representation of General Yield Criterion 331.4.2 Yield Surface and Physical Interpretation 341.4.3 Simplified Yield Criterion 341.5 Classical Theory about Plastic Stress–Strain Relation 351.5.1 Early Perception of Plastic Stress Strain Relations 361.5.2 Concept of the Gradient-Based Plasticity and Its Relation with Mises Yield Criterion 371.5.2.1 Concept of the Plastic Potential 371.5.2.2 Physical Interpretation of the Plastic Potential 381.5.2.3 Physical Interpretation of Mises Yield Function (Plastic Potential) 391.6 Effective Stress, Effective Strain, and Stress Type 421.6.1 Effective Stress 421.6.2 Effective Strain 421.6.3 Stress Type 44References 442 Experimental Research on Material Mechanical Properties under Uniaxial Tension 472.1 Stress–Strain Relationship of Strain-Strengthened Materials under Uniaxial Tensile Stress State 472.2 The Stress–Strain Relationship of the Strain-Rate-Hardened Materials in Uniaxial Tensile Tests 482.3 Stress–Strain Relationship in Uniaxial Tension during Coexistence of Strain Strengthening and Strain Rate Hardening 502.4 Bauschinger Effect 562.5 Tensile Tests for Automotive Deep-Drawing Steels and High-Strength Steels 572.5.1 Test Material and Experiment Scheme 572.5.2 True Stress–Strain Curves in Uniaxial Tension 582.5.3 Mechanical Property Parameters of Sheets 582.5.3.1 Strain-Hardening Exponent n 592.5.3.2 Lankford Parameter R 622.5.3.3 Plane Anisotropic Exponent ΔR 622.5.3.4 Yield-to-Tensile Ratio σ s ∕σ b 622.5.3.5 Uniform Elongation δ m 622.6 Tensile Tests on Mg-Alloys 632.7 Tension Tests on Ti-Alloys 632.7.1 Mechanical Properties of Ti-3Al-2.5V Ti-Alloy Tubes at High Temperatures 652.7.2 Strain Hardening of Ti-3Al-2.5V Ti-Alloy in Deformation at High Temperatures 69References 713 Experimental Research on Mechanical Properties of Materials under Non-Uniaxial Loading Condition 733.1 P-p Experimental Results of Thin-Walled Tubes 733.1.1 Lode Experiment 733.1.2 P-p Experiments on Thin-Walled Tubes Made of Superplastic Materials 783.1.2.1 Experiment Materials and Specimens 783.1.2.2 Loading Methods 803.1.2.3 Experimental Results and Analysis 803.1.3 Experiments on Tubes Subjected to Internal Pressure and Axial Compressive Forces 863.1.3.1 Experimental Device 863.1.3.2 Material Properties 883.1.3.3 Experimental Results 893.2 Results from P-M Experiments on Thin-Walled Tubes 913.2.1 Taylor-Quinney Experiments 913.2.2 P-M Experiments on Superplastic Material 943.3 Biaxial Tension Experiments on Sheets 953.3.1 Equipment for Biaxial Tension of Cruciform Specimens 963.3.2 Design of Cruciform Tensile Specimens 963.3.3 Application of Cruciform Biaxial Tensile Test 973.3.3.1 Forming Limit 973.3.3.2 Prediction of Yielding Locus 973.3.3.3 Analysis of Composite Materials 993.4 Influences of Hydrostatic Stress on Mechanical Properties of Materials 1003.4.1 Testing Technique in High-Pressure Experiments 1013.4.2 Influences of Hydrostatic Stresses on Flow Behavior of Materials 1033.4.3 Influences of Hydrostatic Pressure on Fracture Behavior of Materials 1063.5 Experimental Researches Other Than Non-Uniaxial Tension 1143.5.1 Plane Compression Experiments 1143.5.2 Loading Experiments along Normal and Tangential Directions 1183.5.3 Other Combined Loading Methods 119References 1194 Yield Criteria of Different Materials 1234.1 Predicting Capability of a Yield Criterion Affected by Multiple Factors 1234.2 Construction of a Proper Yield Criterion in Consideration of Multifactor-Caused Effects 1294.2.1 A Proper Frame of Yield Criterion 1304.2.2 Practical Yield Criterion with Multifactor-Caused Effects 1334.2.3 Material Yielding Behavior Affected by Different Factors 1364.2.3.1 Convexity of Yield Locus at Plane Stress State 1374.2.3.2 Stress-Type-Caused Effects 1434.2.3.3 Hydrostatic-Stress-Caused Effects 1454.2.4 Simplified Forms of the Yield Criterion 1484.2.5 Verification of the Yield Criterion Through Experiments 1514.3 Anisotropic Materials 1564.3.1 Experimental Description of Anisotropic Behavior of Rolled Sheet Metals 1564.3.1.1 Uniaxial Tension 1574.3.1.2 Biaxial Tension 1594.3.2 Brief Review of the Anisotropic Yield and Plastic Potential Functions 1604.3.3 Nonassociated-Flow-Rule-Based Yield Function and Plastic Potential 1654.3.3.1 Anisotropic Yield Criterion 1654.3.3.2 Anisotropic Plastic Potential 1724.3.4 Associated-Flow-Rule-Based Anisotropic Yield Criterion 1744.3.5 Experimental Verification of Two Kinds of Anisotropic Yield Criteria 178References 1845 Plastic Constitutive Relations of Materials 1875.1 Basic Concepts about Plastic Deformation of Materials and Relevant Plastic Constitutive Relations 1875.1.1 Effects of Material Strength Property Transformation on Material Plastic Deformation 1875.1.2 General Description of Subsequent Hardening Increments and Convexity of Yield Function 1895.1.3 Effects of Flow Rules on Judgment of Condition of Stable Plastic Deformation of Materials 1965.2 Equivalent Hardening Condition in Material Plastic Deformation 1975.2.1 Universal Forms of Plastic Potential and Yield Criterion in Constructing Plastic Constitutive Relations 1985.2.2 Relationship between Yield Function and Plastic Potential in Describing Equivalent Hardening Increments 1995.2.3 Equivalent Hardening Condition Corresponding to Associated Flow Rule 2015.2.4 Equivalent Hardening Condition Related to Nonassociated Flow Rule 2065.3 “Softening” and Strength Property Changes in Plastic Deformation of Materials 2095.3.1 Mechanical Models Mimicking Plastic Deformation of Sensitive-to-Pressure Materials 2105.3.2 Dynamic Models to Imitate the Stress–Strain Relation of Anisotropic Material 2155.3.3 Softening and Material Strength Property Changes in a Stable Plastic Deformation 2195.4 Influences of Loading Path on Computational Accuracy of Incremental Theory 2275.4.1 Discontinuous Stress Path 2275.4.2 Unrealistic Strain Path 229References 2316 Description of Material Hardenability with Different Models 2336.1 Plastic Constitutive Relations of Sensitive-to-Pressure Materials 2336.1.1 Experimental Characterizations of Yield Function and Corresponding Plastic Potential 2346.1.2 Theoretical Predictions in Comparison with Experimental Results 2376.1.2.1 Influences of Hardening Models upon Description of Plastic Deformation of Materials 2386.1.2.2 Yieldability and Plastic Flowability of Sensitive-to-Pressure Materials 2396.1.2.3 Prediction of the Volumetric Plastic Strain 2406.1.2.4 Predictions of Stress–Strain Relations in Uniaxial Tension and Compression 2436.1.2.5 Stress–Strain Relations in Compression Affected by Superimposed Pressures 2476.2 Anisotropic Hardening Model of Rolled Sheet Metals Characterized by Multiple Experimental Stress–Strain Relations and Changeable Anisotropic Parameters 2486.2.1 A Constitutive Model to Describe Anisotropic Hardening and Anisotropic Plastic Flow of Rolled Sheet Metals 2496.2.2 Transformation from Special 3D Stress State into 2D Stress States 2526.2.3 Predictions of Anisotropic Hardening and Plastic Flow Behavior 2546.2.3.1 Subsequent Yield Locus of Anisotropic Materials 2546.2.3.2 Predictions of All Experimental Stress–Strain Relations in Yield Function 2606.2.4 Experimental Verification 2626.2.4.1 Predictions of Stress–Strain Relations in Uniaxial Tensions in Different Directions 2626.2.4.2 Predictions of Changeable Anisotropic Parameters 2676.3 Plastic Constitutive Relation with the Bauschinger Effects 2716.3.1 Basic Concepts of the Bauschinger Effects 2716.3.2 Consideration of the Bauschinger Effect in Constructing a Constitutive Relation 2746.3.3 Exotic Anisotropic Behavior of Material Element Induced by Kinematic Hardening Model Based on Associated Flow Rule 2766.3.3.1 Anisotropic Flowability Borne of Kinematic Yield Model 2766.3.3.2 Calculations of the Exotic Anisotropy by Means of Yoshida’s Modified Kinematic Model 2816.3.4 A Method to Generate a Kinematic Plastic Potential Function 286References 2937 Sequential Correspondence Law between Stress and Strain Components and Its Application in Plastic Deformation Process 2957.1 Sequential Correspondence Law between Stress and Strain Components and Its Experimental Verification 2957.1.1 Sequential Correspondence Law between Stress and Strain Components 2957.1.2 Experimental Verification of the Sequential Correspondence Law between Stress and Strain Components 2987.1.3 Application of the Sequential Correspondence Law between Stress and Strain Components 3007.2 Zoning of Mises Yield Ellipse and Typical Plane Stress Forming Processes on It 3027.3 Stress and Strain Analysis of Plane-Stress Metal-Forming Processes 3067.3.1 Tube Drawing 3067.3.2 Deep Drawing 3077.3.3 Tube Hydroforming 3087.4 Spreading of Mises Yield Cylinder and Characterization of Three-Dimensional Stresses Therein 3097.5 Zoning in Three-Dimensional Stress Yield Locus and Positioning Typical Forming Processes Thereon 311References 3168 Stress and Strain Analysis and Experimental Research on Typical Axisymmetric Plane Stress-Forming Process 3178.1 Incremental-Theory-Based Solution to Stress and Strain Distribution of Steady Axisymmetric Plane Stress-Forming Processes 3178.1.1 Two Expressions of Stress and Strain Distribution 3178.1.2 Division of Steady Thin-Walled Tube-Forming Processes 3198.1.3 Basic Formulas and Assumption 3208.1.4 Stress and Strain Distribution in Steady Frictionless Forming Process 3218.1.4.1 General Equilibrium Equation 3218.1.4.2 Stress Distribution σ(r) 3228.1.4.3 Strain Rate dε/dφ 3248.1.4.4 Strain Distribution ε(φ) 3258.1.5 Stress and Strain Distribution in Steady Forming Processes in the Presence of Friction 3288.1.5.1 General Equilibrium Equation 3298.1.5.2 Stress and Strain Distribution 3318.2 Experimental Study on Thickness Distribution in Tube Necking and Tube Drawing 3318.2.1 Thickness Distribution in Tube-Necking Processes 3318.2.2 Experimental Research on Thickness Distribution during Tube Drawing [6] 3338.3 Experiments on Thin-Walled Tube under Action of Biaxial Compressive Stresses 3368.3.1 Introduction of Experimental Setup 3378.3.2 Results and Discussion 339References 3419 Shell and Tube Hydroforming 3439.1 Mechanics of Dieless Closed Shell Hydro-Bulging 3439.1.1 Equilibrium Equation for an Internally Pressurized Closed Shell 3439.1.2 Yield Equation of an Internally Pressurized Closed Shell 3459.1.3 Principle of Spheroidization of Plastic Deformation in Shell Hydro-Bulging 3459.2 Dieless Hydro-Bulging of Spherical Shells 3479.2.1 Stress Analysis of Dieless Hydro-Bulging of Spherical Shells 3479.2.2 Manufacture of Spherical Shells 3479.2.3 Shell Structure before Hydro-Bulging 3489.2.4 Dieless Hydro-Bulging of Single-Curvature Polyhedral Shells 3499.3 Dieless Hydro-Bulging of Ellipsoidal Shells 3509.3.1 Stress Analysis of Internally Pressurized Ellipsoidal Shells 3519.3.2 Wrinkling of Internally Pressurized Ellipsoidal Shell and Anti-Wrinkling Measures 3529.4 Dieless Hydro-Bulging of Elbow Shell 3559.5 Tube Hydroforming 3569.5.1 Principle of Tube Hydroforming and Its Stress States 3569.5.2 Yield Criterion for Tube Hydroforming 3579.5.3 Position of Tube Hydroforming on Yield Ellipse 3589.5.4 Typical Stress States and Their Distribution on Yield Ellipse 3589.5.5 Effect of Stress State on the Tube Deformation Characteristics 3599.5.6 Formation Mechanism of Wrinkles in Thin-Walled Tube Hydroforming 360References 36210 Bulk Forming 36510.1 Load Calculation in Tool Movement Direction 36510.2 Upsetting of Cylinders and Rings 36810.2.1 Load Calculation for Cylinder Upsetting 36910.2.2 Inhomogeneous Deformation in Cylinder Upsetting 37310.2.3 Metal Flow and Pressure Distribution during Ring Compression 37610.3 Characteristics of Die Forgings and Calculation of Required Loads 37810.4 Isothermal Forging 38110.4.1 Stress Analysis in Isothermal Forging 38110.4.2 Stress Analysis of a Single Rib Piece in Isothermal Forging 38210.4.3 Isothermal Forming of Cross-Rib-Born Pieces 38410.4.3.1 Analysis of Forming Processes 38410.4.3.2 Stress Analysis 38410.4.4 Control and Analysis of Flow Defects during Isothermal Forging 38610.4.4.1 Folds 38610.4.4.2 Formation and Control of Flow Lines 38810.5 Calculation of Required Load in Rolling 38910.5.1 Derivation of Formula for Calculating Unit Pressure Distribution on Rollers’ Contact Arc Surface 39110.5.2 Total Rolling Force and Average Pressure 39510.5.3 Rolling Torque 39610.5.4 Energy Consumption in Rolling 39710.6 Extrusion and Drawing 39710.6.1 Extrusion 39710.6.2 Drawing 40010.7 Rotary Forging 40310.7.1 Introduction 40310.7.2 Stress and Strain Analysis in Rotary Forging of Cylinders 40310.7.3 Stress–Strain Analysis in Rotary Forging of Discs 40910.8 Strain Distribution Measurement in Bulk Forming 41110.8.1 Introduction 41110.8.2 Screw Method 41210.8.3 Applications of Screw Method in Determining Strain Distribution 414References 41911 Sheet Forming 42111.1 Deep Drawing 42111.1.1 Basic Principles 42111.1.2 Strain Analysis in Flange Area 42111.1.3 Stress Analysis of the Flange Area 42411.1.3.1 Equilibrium Equation 42411.1.3.2 Yield Criteria 42511.2 Sheet Hydroforming Process 42611.2.1 Basic Principles 42611.2.2 Characteristics and Application Scope 42711.2.3 Assessment of Experimental Parameters 42811.2.3.1 Critical Liquid Pressure p cr 42811.2.3.2 Drawing Force 42911.2.3.3 Blank Holder Force (BHF) 42911.2.4 Influences of Normal Stress on SHP [10] 43011.2.5 Influences of Pre-Bulging on the Deformation Uniformity in SHP 43011.3 Hole-Flanging 43411.3.1 Basic Principles 43411.3.2 Analysis of Stress and Strain 43411.3.3 Limiting Flanging Coefficient 43611.4 Viscous Pressure Forming 43811.4.1 Mechanism and Features 43811.4.1.1 Forming Sequence 43811.4.1.2 Properties of Pressure Medium 43911.4.1.3 Reverse Pressure 43911.4.1.4 Surface Quality 43911.4.2 Constitutive Equations of Viscous Medium 43911.4.3 Influences of BHP on Forming Process 44111.5 Multipoint Sandwich Forming 44511.5.1 Introduction 44511.5.2 Working Principles of MPSF 44611.5.3 Advantages of MPSF and Applications 44711.5.4 FE Model of MPSF 44811.5.5 Forming of Ellipsoidal Workpiece 45111.5.6 Saddle-Type Pieces Forming 45511.6 Formability of Sheet Metals 46211.6.1 Introduction 46211.6.2 Forming Limit Diagram 46211.6.3 Experimental Determination of FLC 46411.6.3.1 Uniaxial Tensile Test 46511.6.3.2 Hydro-Bulging Test 46511.6.3.3 Nakazima Test 46511.6.4 Advanced Experimental Methods 46611.6.5 Theoretical Prediction of FLC 46911.6.6 New Developments in FLCs 47511.7 Improvements of Panel Stamping Process 47811.7.1 Designs of Draw-Bars Corresponding to the Wrinkling Types 47911.7.2 Replacement of Stretching Wall with Local Nondeformable Design 482References 484Index 489