Mechanics of Sheet Metal Forming

Contents
Preface to the second edition ix
Preface to the first edition xi
Disclaimer xii
Introduction xi


1 Material properties 1
1.1 Tensile test 1
1.2 Effect of properties on forming 10
1.3 Other mechanical tests 12
1.4 Exercises 13


2 Sheet deformation processes 14
2.1 Introduction 14
2.2 Uniaxial tension 14
2.3 General sheet processes (plane stress) 16
2.4 Yielding in plane stress 17
2.5 The flow rule 22
2.6 Work of plastic deformation 24
2.7 Work hardening hypothesis 25
2.8 Effective stress and strain functions 26
2.9 Summary 27
2.10 Exercises 27


3 Deformation of sheet in plane stress 30
3.1 Uniform sheet deformation processes 30
3.2 Strain distributions 31
3.3 Strain diagram 31
3.4 Modes of deformation 33
3.5 Effective stress–strain laws 36
3.6 The stress diagram 39
3.7 Principal tensions or tractions 41
3.8 Summary 43
3.9 Exercises 43

4 Simplified stamping analysis 45
4.1 Introduction 45
4.2 Two-dimensional model of stamping 46
4.3 Stretch and draw ratios in a stamping 57
4.4 Three-dimensional stamping model 57
4.5 Exercises 59


5 Load instability and tearing 61
5.1 Introduction 61
5.2 Uniaxial tension of a perfect strip 62
5.3 Tension of an imperfect strip 64
5.4 Tensile instability in stretching continuous sheet 67
5.5 Factors affecting the forming limit curve 75
5.6 The forming window 79
5.7 Exercises 80


6 Bending of sheet 82
6.1 Introduction 82
6.2 Variables in bending a continuous sheet 82
6.3 Equilibrium conditions 84
6.4 Choice of material model 85
6.5 Bending without tension 86
6.6 Elastic unloading and springback 92
6.7 Small radius bends 96
6.8 The bending line 100
6.9 Bending a sheet in a vee-die 104
6.10 Exercises 106


7 Simplified analysis of circular shells 108
7.1 Introduction 108
7.2 The shell element 108
7.3 Equilibrium equations 110
7.4 Approximate models of forming axisymmetric shells 111
7.5 Applications of the simple theory 112
7.6 Summary 115
7.7 Exercises 116


8 Cylindrical deep drawing 117
8.1 Introduction 117
8.2 Drawing the flange 117
8.3 Cup height 123
8.4 Redrawing cylindrical cups 123
8.5 Wall ironing of deep-drawn cups 125
8.6 Exercises 127


9 Stretching circular shells 129
9.1 Bulging with fluid pressure 129
9.2 Stretching over a hemispherical punch 132
9.3 Effect of punch shape and friction 134
9.4 Exercises 135


10 Combined bending and tension of sheet 136
10.1 Introduction 136
10.2 Stretching and bending an elastic, perfectly plastic sheet 136
10.3 Bending and stretching a strain-hardening sheet 142
10.4 Bending a rigid, perfectly plastic sheet under tension 144
10.5 Bending and unbending under tension 145
10.6 Draw-beads 150
10.7 Exercises 151


11 Hydroforming 152
11.1 Introduction 152
11.2 Free expansion of a cylinder by internal pressure 153
11.3 Forming a cylinder to a square section 155
11.4 Constant thickness forming 159
11.5 Low-pressure or sequential hydroforming 161
11.6 Summary 163
11.7 Exercises 163

Appendix A1 Yielding in three-dimensional stress state 165
Appendix A2 Large strains: an alternative definition 168
Solutions to exercises 176
Index 205

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