Sheet Metal Forming Processes: Constitutive Modelling and Numerical Simulation

by Dorel Banabic

Overview

The concept of virtual manufacturing has been developed in order to increase the industrial performances, being one of the most ef cient ways of reducing the m- ufacturing times and improving the quality of the products. Numerical simulation of metal forming processes, as a component of the virtual manufacturing process, has a very important contribution to the reduction of the lead time. The nite element method is currently the most widely used numerical procedure for s- ulating sheet metal forming processes. The accuracy of the simulation programs used in industry is in uenced by the constitutive models and the forming limit curves models incorporated in their structure. From the above discussion, we can distinguish a very strong connection between virtual manufacturing as a general concept,finite element method as a numerical analysis instrument and constitutive laws,aswellas forming limit curves as a speci city of the sheet metal forming processes. Consequently, the material modeling is strategic when models of reality have to be built. The book gives a synthetic presentation of the research performed in the eld of sheet metal forming simulation during more than 20 years by the members of three international teams: the Research Centre on Sheet Metal Forming—CERTETA (Technical University of Cluj-Napoca, Romania); AutoForm Company from Zürich, Switzerland and VOLVO automotive company from Sweden. The rst chapter presents an overview of different Finite Element (FE) formu- tions used for sheet metal forming simulation, now and in the past.

Product Details

ISBN-13:	9783540881124
Publisher:	Springer Berlin Heidelberg
Publication date:	06/30/2010
Edition description:	2010
Pages:	301
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1 FE-Models of the Sheet Metal Forming Processes 1

1.1 Introduction 2

1.2 Fundamentals of Continuum Mechanics 3

1.2.1 Introduction 3

1.2.2 Strain Measures 4

1.2.3 Stress Measures 8

1.3 Material Models 9

1.4 FE-Equations for Small Deformations 11

1.5 FE-Equations for Finite Deformations 13

1.6 The 'Flow Approach' -Eulerian FE-Formulations for Rigid-Plastic Sheet Metal Analysis 16

1.7 The Dynamic, Explicit Method 18

1.8 A Historical Review of Sheet Forming Simulation 21

References 24

2 Plastic Behaviour of Sheet Metal 27

2.1 Anisotropy of Sheet Metals 30

2.1.1 Uniaxial Anisotropy Coefficients 30

2.1.2 Biaxial Anisotropy Coefficient 36

2.2 Yield Criteria for Isotropic Materials 39

2.2.1 Tresca Yield Criterion 41

2.2.2 Huber-Mises-Hencky Yield Criterion 42

2.2.3 Drucker Yield Criterion 43

2.2.4 Hershey Yield Criterion 44

2.3 Classical Yield Criteria for Anisotropic Materials 45

2.3.1 Hill's Family Yield Criteria 45

2.3.2 Yield Function Based on Crystal Plasticity (Hershey's Family) 61

2.3.3 Yield Criteria Expressed in Polar Coordinates 74

2.3.4 Other Yield Criteria 75

2.4 Advanced Anisotropic Yield Criteria 76

2.4.1 Barlat Yield Criteria 77

2.4.2 Banabic-Balan-Comsa (BBC) Yield Criteria 81

2.4.3 Cazacu-Barlat Yield Criteria 84

2.4.4 Vegter Yield Criterion 87

2.4.5 Polynomial Yield Criteria 88

2.5 BBC 2005 Yield Criterion 91

2.5.1 Equation of the Yield Surface 91

2.5.2 Flow Rule Associated to the Yield Surface 92

2.5.3 BBC 2005 Equivalent Stress 92

2.5.4 Identification Procedure 94

2.5.5 Particular Formulations of the BBC 2005 Yield Criterion 105

2.6 BBC 2008 Yield Criterion 106

2.6.1 Equation of the Yield Surface 107

2.6.2 BBC 2008 Equivalent Stress 108

2.6.3 Identification Procedure 109

2.7 Recommendations on the Choice of the Yield Criterion 113

2.7.1 Comparison of the Yield Criteria 113

2.7.2 Evaluating the Performances of the Yield Criteria 116

2.7.3 Mechanical Parameters Used by the Identification Procedure of the Yield Criteria 118

2.7.4 Implementation of the Yield Criteria in Numerical Simulation Programmes 118

2.7.5 Overview of the Anisotropic Yield Criteria Developing 120

2.7.6 Perspectives 120

2.8 Modeling of the Bauschinger Effect 121

2.8.1 Reversal Loading in Sheet Metal Forming Processes 121

2.8.2 Experimental Observations 122

2.8.3 Physical Nature of the Bauschinger Effect 124

2.8.4 Phenomenological Modelling 125

References 135

3 Formability of Sheet Metals 141

3.1 Introduction 142

3.2 Evaluation of the Sheet Metal Formability 147

3.2.1 Methods Based on Simulating Tests 147

3.2.2 Limit Dome Height Method 151

3.3 Forming Limit Diagram 152

3.3.1 Definition: History 152

3.3.2 Experimental Determination of the FLD 156

3.3.3 Methods of Determining the Limit Strains 162

3.3.4 Factors Influencing the FLC 165

3.3.5 Use of Forming Limit Diagrams in Industrial Practice 175

3.4 Theoretical Predictions of the Forming Limit Curves 179

3.4.1 Swift's Model 180

3.4.2 Hill's Model 182

3.4.3 Marciniak-Kuckzynski (M-K) and Hutchinson-Neale (H-N) Models 182

3.4.4 Implicit Formulation of the M-K and H-N Models 185

3.4.5 Linear Perturbation Theory 194

3.4.6 Modified Maximum Force Criterion (MMFC) 195

3.5 Commercial Programs for FLC Prediction 197

3.5.1 FORM-CERT Program 198

3.6 Semi-empirical Models 203

References 204

3 Numerical Simulation of the Sheet Metal Forming Processes 213

4.1 AutoForm Solutions 213

4.1.1 The Role of Simulation in Process Planning 213

4.1.2 Material Data in Digital Process Planning 215

4.1.3 Feasibility (Part Feasibility) 218

4.1.4 Manufacturability (Process Validation) 225

4.1.5 Capability (Robustness) 230

4.1.6 Simulation Result 'Quality' 236

4.1.7 Comprehensive Digital Process Planning 236

4.2 Simulation of the Elementary Forming Processes 238

4.2.1 Simulation of the Bulge Forming Process 238

4.2.2 Simulation of Stretch Forming of Spherical Cup 241

4.2.3 Simulation of Cross Die 244

4.3 Simulation of the Industrial Parts Forming Processes 250

4.3.1 Simulation of an Outer Trunklid 251

4.3.2 Simulation of a Sill Reinforcement for Volvo C30 254

4.4 Robust Design of Sheet Metal Forming Processes 255

4.4.1 Variability of the Material Parameters 256

4.4.2 AutoForm-Sigma 257

4.4.3 Robust Design: Case Studies 258

4.4.4 Conclusion 267

4.5 The Springback Analysis 267

4.5.1 Introduction 267

4.5.2 Example Description 268

4.5.3 The Influences on the Accuracy of Springback Simulation 269

4.5.4 The Optimized Numerical Parameters of Springback Simulation: Final Validation Settings 277

4.5.5 The Simulation of Numisheet 2005 Benchmark #1: Decklid Inner Panel 277

4.5.6 Conclusion 281

4.6 Computer Aided Springback Compensation 282

4.6.1 Introduction 282

4.6.2 The Basic Methodologies of Computer-Aided Springback Compensation 283

4.6.3 The Influences of the Quality of Computer Aided Springback Compensation 284

4.6.4 The Recommended Work Flow of Computer-Aided Springback Compensation 285

4.6.5 The Springback Compensation of Numisheet 2005 Benchmark #1 287

4.6.6 Conclusion 293

References 294

Index 297