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Mechanics Modeling of Sheet Metal Forming

2007 Edition, April 10, 2007

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Product Details:

  • Revision: 2007 Edition, April 10, 2007
  • Published Date: April 10, 2007
  • Status: Active, Most Current
  • Document Language: English
  • Published By: SAE International (SAE)
  • Page Count: 324
  • ANSI Approved: No
  • DoD Adopted: No

Description / Abstract:

Preface

Beverage cans and many parts in aircraft, appliances, and automobiles are made of thin sheet metals formed by stamping operations at room temperature. Thus, sheet metal forming processes play an important role in mass production. Conventionally, the forming process and tool designs are based on the trial-and-error method or the pure geometric method of surface fitting that requires an actual hardware tryout that is called a die tryout. This design process often is expensive and time consuming because forming tools must be built for each trial. Significant savings are possible if a designer can use simulation tools based on the principles of mechanics to predict formability before building forming tools for tryout. Due to the geometric complexity of sheet metal parts, especially automotive body panels, development of an analytical method based on the mechanics principles to predict formability is difficult, if not impossible. Because of modern computer technology, the numerical finite element method at the present time is feasible for such a highly nonlinear analysis using a digital computer, especially one equipped with vector and parallel processors.

Although simulation of sheet metal forming processes using a modern digital computer is an important technology, a comprehensive book on this subject seems to be lacking in the literature. Fundamental principles are discussed in some books for forming sheet metal parts with simple geometry such as plane strain or axisymmetry. In contrast, detailed theoretically sound formulations based on the principles of continuum mechanics for finite or large deformation are presented in this book for implementation into simulation codes. The contents of this book represent proof of the usefulness of advanced continuum mechanics, plasticity theories, and shell theories to practicing engineers. The governing equations are presented with specified boundary and initial conditions, and these equations are solved using a modern digital computer (engineering workstation) via finite element methods. Therefore, the forming of any complex part such as an automotive inner panel can be simulated. We hope that simulation engineers who read this book will then be able to use simulation software wisely and better understand the output of the simulation software. Therefore, this book is not only a textbook but also a reference book for practicing engineers. Because advanced topics are discussed in the book, readers should have some basic knowledge of mechanics, constitutive laws, finite element methods, and matrix and tensor analyses.

Chapter 1 gives a brief introduction to typical automotive sheet metal forming processes. Basic mechanics, vectors and tensors, and constitutive laws for elastic and plastic materials are reviewed in Chapters 2 and 3, based on course material taught at the University of Michigan by Dr. Jwo Pan. The remaining chapters are drawn from the experience of Dr. Sing C. Tang, who had been working on simulations of real automotive sheet metal parts at Ford Motor Company for more than 15 years. Chapter 2 presents the fundamental concepts of tensors, stress, and strain. The definitions of the stresses and strains in tensile tests then are discussed. Readers should pay special attention to the kinematics of finite deformation and the definitions of different stress tensors due to finite deformation because extremely large deformation occurs in sheet metal forming processes.

Chapter 3 reviews the linear elastic constitutive laws for small or infinitesimal deformation. Hooke's law for isotropic linear elastic materials, which is widely used in many mechanics analyses, is discussed first. Anisotropic linear elastic behavior also is discussed in detail. Then, deviatoric stresses and deviatoric strains are introduced. These concepts are used as the basis for development of pressure-independent incompressible anisotropic plasticity theory. Chapter 3 also discusses fundamentals of mathematical plasticity theories. In sheet metal forming processes, most of the deformation is plastic. Therefore, knowledge of plasticity is essential in using simulation software and in understanding simulation results. Different mathematical models for uniaxial tensile stress-strain relations are introduced first. Then the yield conditions for isotropic incompressible materials under multiaxial stress states are presented. Because sheet metals generally are plastically anisotropic, the anisotropic yield conditions are discussed in detail. The basic concepts of the formation of constitutive laws with consideration of plastic hardening behavior of materials also are presented. Finally, the principles of plastic localization and modeling of failure processes based on void mechanics are summarized.

Chapter 4 introduces formulations for analyses of sheet metal forming processes, including binder closing, stretching/ drawing, trimming, flanging, and hemming. More attention is paid to the most basic analysis of the stretching/drawing process, which then can be extended to analyses of all other processes. The formulations include equations of motion, constitutive equations, tool surface modeling, surface contact forces, and draw-bead modeling.

Chapter 5 discusses thin shell theories. Tensors with reference to the curvilinear coordinate system are used. Most sheet metal parts are made of thin sheets and can be modeled by thin shells for numerical efficiency and accuracy. Engineers may be tempted to use three-dimensional (3-D) solid elements, which are more general, to model a metal sheet under plastic deformation. However, the solid element model contains too many degrees of freedom to be solved using the current generation of digital computers. Even for the explicit time integration method, we cannot handle a finite element model with too many degrees of freedom for reasonable computation accuracy and time. The reason is that the dimension in the thickness direction of the sheet is very small compared to other dimensions. To satisfy the stability requirement for a numerical solution using the explicit time integration method, an extremely small time increment for a three-dimensional mesh must be used. However, it still is not practical at the present time, and the shell model is emphasized in this book.
AIA/NAS Aerospace Standards