附录A 外文文献Effects of geometry and fillet radius on die stresses in stamping processesAbstract: This paper describes the use of the finite element method to analyze the failure of dies in stamping processes. For the die analyzed in the present problem, the cracks at different locations can be attributed to a couple of mechanisms. One of them is due to large principal stresses and the other one is due to large shear stresses. A three-dimensional model is used to simulate these problems first. The model is then simplified to an axisymmetric problem for analyzing the effects of geometry and fillet radius on die stresses. 2000 Elsevier Science S.A. All rights reserved.Keywords: Stamping; Metal forming; Finite element method; Die failure1. IntroductionIn metal forming processes, die failure analysis is one of the most important problems. Before the beginning of this decade, most research focused on the development of the- oretical and numerical methods. Upper bound techniques 1,2, contact-impact procedures 3 and the finite element method (FEM) 4,5 are the main techniques for analyzing stamping problems. With the development of computer technology, the FEM becomes the dominant technique 6-12.Altan and co-workers 13,14 discussed the causes of failure in forging tooling and presented a fatigue analysis concept that can be applied during process and tool design to analyze the stresses in tools. In these two papers, they used the punching load as the boundary force to analyze the stress states that exist in the inserts during the forming process and determined the causes of the failures. Based on these concepts, they also gave some suggestions to improve die design.In this paper, linear stress analysis of a three-dimensional (3D) die model is presented. The stress patterns are then analyzed to explain the causes of the crack initiation. Some suggestions about optimization of the die to reduce the stress concentration are presented. In order to optimize the design of the die, the effects of geometry and fillet radius are discussed based on a simplified axisymmetric model.2. Problem definitionThis study focuses on the linear elastic stress analysis of the die in a typical metal forming situation (Fig. 1). The die (Fig. 2) with a half-moon shaped ingot on the top surface is punched down towards the workpiece which is held inside the collar, and the pattern is made onto the workpiece. Cracks were found in the die after repeated operation: (i) when the die punched the workpiece, there is crack initiation between the tip of the moon shaped pattern and one of the edges (Crack I); and (ii) after repeated punching, there is also a crack at the fillet of the die (Crack II).The present work was carried out with the following objectives: (i) to establish the causes of the crack initiation; and (ii) to study the effects of geometry and fillet radius.3. Simulation and analysis3.1. 3D simulationThe simulation is performed with the FEM code Abaqus 15. Twomeshes are created for the die shown in Fig. 3a and b. The 3D solid elements for the workpiece are C3D8 (8- node linear brick) elements. There are about 4000 nodes and 3343 elements in the coarse mesh model, and 7586 nodes and 6487 elements in the fine mesh model. The boundary condition involves fixing the bottomof the die, i.e., U2=0 for all the nodes on the die bottom. A pressure of 200 MPa is applied on the top surface of the half-moon pattern. Youngs modulus is 200 GPa and Poissons ratio is 0.3.In order to analyze the principal stress concentration area in the region of Crack I, different cases are studied. Let the models shown in Fig. 3a and b be Case 1. A new 3D model (Case 2) is used as shown in Fig. 3c. The die is separated into three parts. The Abaqus command *CONTACT PAIR, TIED is used to tie separate surfaces together for joining dissimilar meshes. The advantage of this model is its convenience in changing the mesh of the half-moon pattern and its position. First, the half-moon pattern is moved 6 mm towards the center (Case 3) as shown in Fig. 3d. Second, the fillet radius of the half-moon pattern is changed from 0 to 0.5 mm (Case4) as shown in Fig. 3e.3.2. Results and discussionFor the two meshes used in Case 1. The maximum principal shear stress (S12) distribution at the region of fillet are shown in Fig. 4a and b. The results show that the stress distribution patterns are the same for the two different meshes, and therefore, the convergence of the solutions is established.Altan and co-workers 14 have presented the stress analysis of an axisymmetric upper die. In their work, when the material of the workpiece flows to fill the volume between the dies and collar, the contact surface of the die is stretched. At the area of the transition radius, the principal stresses change direction and reach high tensile values.According to their analysis, the fatigue failure is due to two factors: (i) when the stress exceeds