A study of cup-cup axisymmetric combined extrusion by the upper-bound approach II. Prediction of defects

In this paper, the critical conditions for defect formation in the final stage of cup-cup axisymmetric combined extrusion are derived, using the upper-bound approach. The analytical results show that cracks may occur on the outer circumferential surface of the bottom of the billet and on the inner surface of the billet near to the corner of the lower ram. The critical relative thickness of the bottom of the billet during crack formation is affected mainly by the combination of the reduction in area of the forward-extrusion part and that of the backward-extrusion part. The relative dimensions of the defects vary with the reduction in area and with the relative thickness of the bottom of the billet. The results computed agree very well with experimental data.