Prediction of central bursting in extrusion

Abstract

Abstract Central burst defects which are also called chevron cracks, in extruded products are analyzed. The criterion based on plastic instability was used in order to predict central bursting. It satisfies sufficient condition s ˙ i ɛ ˙ i = 0 for the multiplicity of the solution, which is derived from the necessary condition, Δ s ˙ i Δ ɛ ˙ i = 0 where s ˙ i denotes the nominal stress rate, and Δ the difference of any two multiple solutions. The criterion gives the limit strain identical to that derived from Swift's criterion (diffuse necking) under plane stress condition, but conceptually it is entirely different from Swift's. Stress and strain on the specimen were evaluated using the finite element method (FEM). We proposed a measure y M which represents the risk probability of cracking and calculated it using the stress and strain on the central axis of the product. When y M ≤0, bursting occurs. The value of y M is shown in the range of combinations of the die half angle and the reduction area. Boundary curve that separates the defect zone from the non-defect zone in the relationship with respect to the above combinations takes a nose-like shape, which is quite different from that based on Avitzur's prediction.