Sheet Metal Forming Processes: Constitutive Modelling and Numerical Simulation

✍ Scribed by Dorel Banabic

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 312
• Category: Library

✦ Synopsis

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, ?nite 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.

✦ Table of Contents

Preface
Contents
List of the Authors
Contributions of the Authors
Chapter
1 FE-Models of the Sheet Metal Forming Processes
1.1 Introduction
1.2 Fundamentals of Continuum Mechanics
1.2.1 Introduction
1.2.2 Strain Measures
1.2.3 Stress Measures
1.3 Material Models
1.4 FE-Equations for Small Deformations
1.5 FE-Equations for Finite Deformations
1.6 The Flow ApproachEulerian FE-Formulations for Rigid-Plastic Sheet Metal Analysis
1.7 The Dynamic, Explicit Method
1.8 A Historical Review of Sheet Forming Simulation
References
Chapter
2 Plastic Behaviour of Sheet Metal
2.1 Anisotropy of Sheet Metals
2.1.1 Uniaxial Anisotropy Coefficients
2.1.2 Biaxial Anisotropy Coefficient
2.2 Yield Criteria for Isotropic Materials
2.2.1 Tresca Yield Criterion
2.2.2 Huber--Mises--Hencky Yield Criterion
2.2.3 Drucker Yield Criterion
2.2.4 Hershey Yield Criterion
2.3 Classical Yield Criteria for Anisotropic Materials
2.3.1 Hill's Familly Yield Criteria
2.3.1.1 Hill 1948 Yield Criterion
2.3.1.2 Comments on the Hill'48 Yield Criterion
2.3.1.3 Hill 1979 Yield Criterion
2.3.1.4 Hill 1990 Yield Criterion
2.3.1.5 Hill 1993 Yield Criterion
2.3.2 Yield Function Based on Crystal Plasticity (Hershey's Familly)
2.3.2.1 Hosford Yield Criterion
2.3.2.2 Barlat 1989 Yield Criterion
2.3.2.3 Barlat 1991 Yield Criterion
2.3.2.4 Yield Criteria by Barlat 1994 and 1996
2.3.2.5 Karafillis--Boyce Yield Criterion
2.3.3 Yield Criteria Expressed in Polar Coordinates
2.3.3.1 Budiansky Yield Criterion
2.3.4 Other Yield Criteria
2.3.4.1 Gotoh Yield Criterion
2.4 Advanced Anisotropic Yield Criteria
2.4.1 Barlat Yield Criteria
2.4.2 Banabic--Balan--Comsa (BBC) Yield Criteria
2.4.3 Cazacu--Barlat Yield Criteria
2.4.4 Vegter Yield Criterion
2.4.5 Polynomial Yield Criteria
2.4.5.1 Hu Yield Criteria
2.4.5.2 Wang Yield Criterion
2.4.5.3 Comsa Yield Criterion
2.4.5.4 Soare Yield Criteria
2.5 BBC 2005 Yield Criterion
2.5.1 Equation of the Yield Surface
2.5.2 Flow Rule Associated to the Yield Surface
2.5.3 BBC 2005 Equivalent Stress
2.5.4 Identification Procedure
2.5.4.1 Theoretical Yield Stress in Pure Tension
2.5.4.2 Theoretical Coefficient of Uniaxial Plastic Anisotropy
2.5.4.3 Theoretical Yield Stress in Biaxial Tension Along RD and TD
2.5.4.4 Theoretical Coefficient of Biaxial Plastic Anisotropy
2.5.5 Particular Formulations of the BBC 2005 Yield Criterion
2.6 BBC 2008 Yield Criterion
2.6.1 Equation of the Yield Surface
2.6.2 BBC 2008 Equivalent Stress
2.6.3 Identification Procedure
2.7 Recommendations on the Choice of the Yield Criterion
2.7.1 Comparison of the Yield Criteria
2.7.2 Evaluating the Performances of the Yield Criteria
2.7.3 Mechanical Parameters Used by the Identification Procedure of the Yield Criteria
2.7.4 Implementation of the Yield Criteria in Numerical Simulation Programmes
2.7.5 Overview of the Anisotropic Yield Criteria Developing
2.7.6 Perspectives
2.8 Modeling of the Bauschinger Effect
2.8.1 Reversal Loading in Sheet Metal Forming Processes
2.8.2 Experimental Observations
2.8.3 Physical Nature of the Bauschinger Effect
2.8.4 Phenomenological Modelling
2.8.4.1 Prager's Model
2.8.4.2 Model of Armstrong and Frederick
2.8.4.3 Chaboche's Model
2.8.4.4 Yoshida--Uemori Model
2.8.4.5 AutoForm-Model
References
Chapter
3 Formability of Sheet Metals
3.1 Introduction
3.2 Evaluation of the Sheet Metal Formability
3.2.1 Methods Based on Simulating Tests
3.2.1.1 Typical Punch-Stretching Methods
3.2.1.2 Typical Deep-Drawing Methods
3.2.1.3 Combined Deep-Drawing Methods
3.2.2 Limit Dome Height Method
3.3 Forming Limit Diagram
3.3.1 Definition: History
3.3.2 Experimental Determination of the FLD
3.3.2.1 Experimental Tests
3.3.2.2 Uniaxial Tensile Test
3.3.2.3 Hydraulic Bulge Test
3.3.2.4 Punch Stretching Test
3.3.2.5 Keeler Test
3.3.2.6 Hecker Test
3.3.2.7 Marciniak Test
3.3.2.8 Nakazima Test
3.3.2.9 Hasek Test
3.3.2.10 Comparison of Different Tests
3.3.3 Methods of Determining the Limit Strains
3.3.4 Factors Influencing the FLC
3.3.4.1 Sheet Thickness
3.3.4.2 Grid Size
3.3.4.3 Strain Path
3.3.4.4 Mechanical Properties
3.3.4.5 Influence of the Punch Curvature
3.3.4.6 Influence of the Temperature
3.3.4.7 Influence of the Strain Rate
3.3.4.8 Influence of the Normal Pressure
3.3.4.9 Other Parameters
3.3.5 Use of Forming Limit Diagrams in Industrial Practice
3.4 Theoretical Predictions of the Forming Limit Curves
3.4.1 Swift's Model
3.4.2 Hill's Model
3.4.3 Marciniak--Kuckzynski (M--K) and Hutchinson--Neale (H--N) Models
3.4.4 Implicit Formulation of the M--K and H--N Models
3.4.5 Linear Perturbation Theory
3.4.6 Modified Maximum Force Criterion (MMFC)
3.5 Commercial Programs for FLC Prediction
3.5.1 FORM-CERT Program
3.5.1.1 Identification Module Associated to the Yield Criterion
3.5.1.2 Calculation and Displaying the Planar Distribution of the Uniaxial Yield Stress and r -Coefficient
3.5.1.3 Calculation and Displaying the Strain Hardening Law
3.5.1.4 Calculation and Displaying the FLC
3.5.1.5 'Experimental Data' Module
3.6 Semi-empirical Models
References
Chapter
4 Numerical Simulation of the Sheet Metal Forming Processes
4.1 AutoForm Solutions
4.1.1 The Role of Simulation in Process Planning
4.1.2 Material Data in Digital Process Planning
4.1.3 Feasibility (Part Feasibility)
4.1.3.1 Applied Technology
4.1.3.2 Input Data
4.1.3.3 Output Data
4.1.4 Manufacturability (Process Validation)
4.1.4.1 Applied Technology
4.1.4.2 Input Data
4.1.4.3 Output Data
4.1.5 Capability (Robustness)
4.1.5.1 Applied Technology
4.1.5.2 Input Data
4.1.5.3 Output Data
4.1.6 Simulation Result 'Quality'
4.1.7 Comprehensive Digital Process Planning
4.2 Simulation of the Elementary Forming Processes
4.2.1 Simulation of the Bulge Forming Process
4.2.1.1 Hardening Description
4.2.1.2 Yield Surface Description
4.2.1.3 Bulge Tests
4.2.1.4 Bulge Simulations
4.2.1.5 Discussion
4.2.2 Simulation of Stretch Forming of Spherical Cup
4.2.3 Simulation of Cross Die
4.2.3.1 Hardening Description
4.2.3.2 Yield Surface Description
4.2.3.3 Cross Die Experiments
4.2.3.4 Cross Die Simulations
4.2.3.5 Discussion
4.3 Simulation of the Industrial Parts Forming Processes
4.3.1 Simulation of an Outer Trunklid
4.3.2 Simulation of a Sill Reinforcement for Volvo C30
4.4 Robust Design of Sheet Metal Forming Processes
4.4.1 Variability of the Material Parameters
4.4.2 AutoForm-Sigma
4.4.3 Robust Design: Case Studies
4.4.3.1 Case 1: Front Side Member Inner
4.4.3.2 Case 2: Hood Inner
4.4.4 Conclusion
4.5 The Springback Analysis
4.5.1 Introduction
4.5.2 Example Description
4.5.3 The Influences on the Accuracy of Springback Simulation
4.5.3.1 The Influence of the Element Formulation
4.5.3.2 The Influence of the Element Size
4.5.3.3 The Influence of the Integration Scheme and Integration Points
4.5.3.4 The Influence of the Time Step
4.5.3.5 The Influence of the Material Model
4.5.3.6 The Influence of the Drawbead Model
4.5.4 The Optimized Numerical Parameters of Springback Simulation: Final Validation Settings
4.5.5 The Simulation of Numisheet 2005 Benchmark #1: Decklid Inner Panel
4.5.5.1 Description of the Benchmark
4.5.5.2 The Result of Numerical Simulation
4.5.6 Conclusion
4.6 Computer Aided Springback Compensation
4.6.1 Introduction
4.6.2 The Basic Methodologies of Computer-Aided Springback Compensation
4.6.3 The Influences of the Quality of Computer Aided Springback Compensation
4.6.3.1 The Robustness and Accuracy of Springback Calculation
4.6.3.2 The Robustness of Springback Responding to Variation of Material and Process Parameters
4.6.4 The Recommended Work Flow of Computer-Aided Springback Compensation
4.6.4.1 The Optimization of Process Layout
4.6.4.2 Compensability Analysis and Optimization of Tooling Concept
4.6.4.3 Robustness Analysis and Optimization Before Compensation
4.6.4.4 Computer Aided Springback Compensation
4.6.4.5 Robustness Analysis and Optimization After Compensation
4.6.5 The Springback Compensation of Numisheet 2005 Benchmark #1
4.6.5.1 The Feasibility Analysis of the Forming Processes and Springback
4.6.5.2 The Robustness Analysis of Springback Before Compensation
4.6.5.3 Computer-Aided Springback Compensation
4.6.5.4 Robustness Analysis of Springback After Compensation
4.6.6 Conclusion
References
Index