Material Forming Processes Simulation, Drawing, Hydroforming and Additive Manufacturing

Manufacturing industries strive to improve the quality and reliability of their products, while simultaneously reducing production costs. To do this, modernized work tools must be produced; this will enable a reduction in the duration of the product development cycle, optimization of product development procedures, and ultimately improvement in the productivity of design and manufacturing phases.

Numerical simulations of forming processes are used to this end, and in this book various methods and models for forming processes (including stamping, hydroforming and additive manufacturing) are presented.  The theoretical and numerical advances of these processes involving large deformation mechanics on the basis of large transformations are explored, in addition to the various techniques for optimization and calculation of reliability.

The advances and techniques within this book will be of interest to professional engineers in the automotive, aerospace, defence and other industries, as well as graduates and undergraduates in these fields.

Preface xi

Chapter 1. Forming Processes 1

1.1. Introduction& 1

1.2. Different processes 1

1.2.1. Smelting 2

1.2.2. Machining 3

1.2.3. Powder metallurgy 5

1.3. Hot and cold forming 6

1.3.1. Influence of the static parameters 9

1.3.2. Hydroforming 12

1.3.3. The limitations of the process 13

1.3.4. Deep drawing 14

1.4. Experimental characterization 14

1.5. Forming criteria 16

1.5.1. Influence of the structure of sheet metal 18

1.5.2. Physical strain mechanisms 20

1.5.3. Different criteria 21

Chapter 2. Contact and Large Deformation Mechanics 23

2.1. Introduction 23

2.2. Large transformation kinematics 23

2.2.1. Kinematics of the problem in spatial coordinates 24

2.3. Transformation gradient 25

2.4. Strain measurements 26

2.4.1. Polar decomposition of F 26

2.4.2. Strain rate tensor 27

2.4.3. Canonical decomposition of F 28

2.4.4. Kinematics of the problem in convective coordinates 28

2.4.5. Transformation tensor 29

2.4.6. Strain rate measures 32

2.4.7. Strain tensor 35

2.5. Constitutive relations 36

2.5.1. Large elastoplastic transformations 38

2.5.2. Kinematic decomposition of the transformation 41

2.6. Incremental behavioral problem 42

2.6.1. Stress incrementation 42

2.6.2. Strain incrementation 44

2.6.3. Solution of the behavior problem 46

2.7. Definition of the P.V.W. in major transformations 49

2.7.1. Equilibrium equations 49

2.7.2. Definition of the P.V.W 50

2.7.3. Incremental formulation 51

2.8. Contact kinematics 52

2.8.1. Definition of the problem and notations 52

2.8.2. Contact formulation 53

2.8.3. Formulation of the friction problem 53

2.8.4. Friction laws 54

2.8.5. Coulomb's law 54

2.8.6. Tresca's law 55

Chapter 3. Stamping 57

3.1. Introduction 57

3.2. Forming limit curve 59

3.3. Stamping modeling: incremental problem 60

3.3.1. Modeling of sheet metal 61

3.3.2. Spatial discretization: finite elements method 62

3.3.3. Choice of sheet metal and finite element approximation 63

3.4. Modeling tools 64

3.4.1. Tool surface meshing into simple geometry elements 64

3.4.2. Analytical representation of tools 65

3.4.3. Bezier patches 65

3.5. Stamping numerical processing 72

3.5.1. Problem statement 73

3.5.2. The augmented Lagrangian method 75

3.6. Numerical simulations 79

3.6.1. Sollac test 81

Chapter 4. Hydroforming 83

4.1. Introduction  83

4.2. Hydroforming 85

4.2.1. Tube hydroforming 85

4.2.2. Sheet metal hydroforming 86

4.3. Plastic instabilities in hydroforming 87

4.3.1. Tube buckling 88

4.3.2. Wrinkling 90

4.3.3. Necking 91

4.3.4. Springback 92

4.4. Forming limit curve 92

4.5. Material characterization for hydroforming 94

4.5.1. Tensile testing 95

4.5.2. Bulge testing 95

4.6. Analytical modeling of a inflation test 97

4.6.1. Hill48 criterion in planar stresses 97

4.7. Numerical simulation 100

4.8. Mechanical characteristic of tube behavior 101

Chapter 5. Additive Manufacturing 105

5.1. Introduction 105

5.2. RP and stratoconception 107

5.3. Additive manufacturing definitions 109

5.4. Principle 113

5.4.1. Principle of powder bed laser sintering/melting 114

5.4.2. Principle of laser sintering/melting by projecting powder 116

5.5. Additive manufacturing in the IT-based development process 117

5.5.1. Concept "from the object to the object" 117

5.5.2. Key element of the IT development process 118

Chapter 6. Optimization and Reliability in Forming 121

6.1. Introduction 121

6.2. Different approaches to optimization processes 122

6.2.1. Limitations of the deterministic approaches 124

6.3. Characterization of forming processes by objective functions 125

6.4. Deterministic and probabilistic optimization of a T-shaped tube 126

6.4.1. Problem description 126

6.4.2. Choice of the objective function and definition of the stresses 127

6.4.3. Choice of the uncertain parameters 128

6.4.4. Choice of the objective function and the stresses 130

6.4.5. Deterministic formulation of the optimization problem 132

6.4.6. Probabilistic formulation of the optimization problem 133

6.4.7. Optima sensitivity to uncertainties 140

6.5. Deterministic and optimization-based reliability of a tube with two expansion regions 142

6.5.1. Problem description 142

6.5.2. Deterministic and reliabilist formulation of the optimization problem 147

6.6. Optimization-based reliability of circular sheet metal hydroforming 150

6.6.1. Problem description 150

6.6.2. Construction of the objective function and of the stresses 151

6.6.3. Effects diagram 151

6.6.4. Deterministic solution of the optimization problem 155

6.6.5. Reliabilist solution of the optimization problem 157

6.6.6. Effect of uncertainties on the optimal variables 159

6.7. Deterministic and robust optimization of a square plate 160

6.7.1. Robust resolution of the optimization problem 166

6.8. Optimization of thin sheet metal 168

Chapter 7. Application of Metamodels to Hydroforming 171

7.1. Introduction 171

7.2. Sources of uncertainty in forming 172

7.3. Failure criteria 173

7.3.1. Failure criteria for necking 174

7.3.2. Failure criteria for wrinkling 174

7.4. Evaluation strategy of the probability of failure 175

7.4.1. Finite element model and choice of uncertainty parameters 176

7.4.2. Identification of failure modes and definition of boundary states 180

7.4.3. Identification of elements and critical areas 181

7.5. Critical strains probabilistic characterization 185

7.5.1. Choice of numerical experimental design 186

7.5.2. Construction of metamodels 186

7.5.3. Validation and statistical analysis of metamodels 187

7.5.4. Fitting of distributions 187

7.6. Necking and wrinkling probabilistic study 193

7.7. Effects of the correlations on the probability of failure 196

7.7.1. Spatial estimation of the probability of failures 197

Chapter 8. Parameters Identification in Metal Forming 199

8.1. Introduction 199

8.2. Identification methods 199

8.2.1. Validation test 200

8.3. Welded tube hydroforming 203

8.3.1. Thin sheet metal hydroforming 205

Appendices  213

Appendix 1. Optimization in Mechanics 215

Appendix 2. Reliability in Mechanics 223

Appendix 3. Metamodels 233

Bibliography 243

Index 253

Abdelkhalak El Hami is Full Professor at INSA Rouen, University of Normandy, France. His research interests include optimization, reliability and structural dynamics.