An improved upper bound analysis for study of the void closure behavior in the plane strain extrusion

In this paper, a new mathematical model has been developed to predict the void closure behavior in metal billets during the plane strain extrusion process. For this purpose, an improved upper bound analysis has been conducted by applying the power balance between the internal work rate, energy release rate along the void, and the external power. Considering the limiting condition of the derived equations on the verge of the void closure, a mechanical criterion has been obtained for finding the minimum extrusion ratio required for the closure of the elliptical voids. The formulation has been developed for both frictionless and frictional conditions on the die-billet interface. The process has also been modeled by the finite element method (FEM) and good agreement has been observed between the results of the derived analytical criterion and the FEM modeling for the minimum required extrusion ratio. It has been found that the minimum extrusion ratio required for the void closure is only a function of the extrusion die angle, the void aspect ratio, and the frictional condition on the die-billet interface. Furthermore, extruding the material under the frictional condition, and in a die with a smaller cone angle is beneficial for closing the voids.