Abstract:

Avitzur has pointed out that the use of the upper bound theorem to handle defects during metal forming is a relatively new-development in recent years.Up to now, analyzing the macro-defects in metal forming with the help of upper bound approach has become a common practice. However, most of the related works dealt with the macro-defect separately. In fact, several macro-defects may occur simultaneously in manufacturing processes.In this paper, the critical condition under which a number of macro-defects co-exist has been put forward with upper bound theorem.On the basis of analytical expression, the influence of reduction in area and the relative thickness of bottom on the region of two coexisting defects has been studied in cup-cup axisymmetric combined extrusion. It has been showed that when the differences between the forward and backward reduction in area are large enough, only one kind of macro-defect may occur, when the differences are small enough, several kinds of macro-defects may appear simultaneously, the kinds of macro-defect increase from one to two as the relative thickness of bottom of billet reduces. The experimental results have proved that the analytical model is better than the model which deals with each macro-defect separately.

Key words: cup-cup combined extrusion, defect, analysis