【正文】 oworkers [13,14] discussed the causes of failure in fing 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 threedimensional (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 halfmoon 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 analysis. 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, ., U2=0 for all the nodes on the die bottom. A pressure of 200 MPa is applied on the top surface of the halfmoon pattern. Young39。s modulus is 200 GPa and Poisson39。s ratio is .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 mand *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 halfmoon pattern and its position. First, the halfmoon pattern is moved 6 mm towards the center (Case 3) as shown in Fig. 3d. Second, the fillet radius of the halfmoon pattern is changed from 0 to mm (Case4) as shown in Fig. 3e.. 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 coworkers [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 the yield strength of the die material, a localized plastic zone generally forms during the first load cycle and undergoes plastic cycling during subsequent unloading and reloading, thus microscopic cracks initiate。 and (ii) tensile principal stresses cause the microscopic cracks to grow and lead to the subsequent propagation of the cracks.The Von Mises stress distribution is shown in Fig. 5a. Very high stress occur in the halfmoon and fillet regions. If the contact pressure keeps increasing, plastic zones will form first in these two regions.Fig. 5b shows the maximum principal stress (SP3) distribution pattern. In order to show the area of Crack I initiation, Fig. 5c provides a zoomed view of the area. It is clear that a tensile principal stress (SP3) concentration of MPa exists between the halfmoon pattern and the free edge and is the cause of crack initiation.Since Crack I propagates nearly normal to the 12 plane, the direction of the stresses which cause the crack initiation must be parallel to that plane. Fig. 5d shows the direction of the maximum principal tensile stress at node 145 and confirms Crack I is normal to the 12 plane.After repeated punching, Crack II initiates in the fillet region, and gives rise to fatigue failure. The geometry in the local area is very similar to the case which Altan and coworkers [14] have analyzed. However, there are no contacts tresses in that area for the present case, and Fig. 5b shows that the maximum principal stresses are all pressive at the fillet. Fig. 5e shows that there is high shear stress (S12) concentration at the fillet which is about 30 MPa. The shear stresses seem to be the stresses which lead to the initiation and propagation of cracks.The results of the four cases (Cases 14) for the largest maximum principal stresses are listed in Table 1.When the number of elements for the halfmoon pattern is increased from 10 to 70, the largest principal stress at the position of Crack I initiation is increased by ()/ =16%(Case 2). The principal stresses are very sensitive to the halfmoon pattern.Cases 24 show the effect of location of the ha