Compression of a block between cylindrical dies and its application to the workability diagram

摘要

In engineering practice two methods are commonly used for modeling technological processes of metal forming, the slab method and the upper bound method (see, for example, (1,2)). Despite the recent development of the upper bound method, its applications are restricted to the special friction laws and material models for which the necessary variation principle is proven. On the other hand, the slab method often gives reasonably good predictions for average stresses. However, this method does not permit the description of the kinematic variables, which are of great importance for initiation and growth of microdefects during technological processes. Therefore, in the present paper Hill's method (5) is used to determine the stress-strain components in the deforming region during upsetting performed with two identical cylindrical dies. The material is assumed to be rigid-plastic, hardening. The friction law proposed by Carter (6) is applied on the die surface. This problem was investigated by Vilotic and Shabaik (7) using the slab method. Brovman (8) found a slip line solution for a rigid perfectly plastic material.