Plane Strain Slip Line Fields for Polymer Deformation Processes

Abstract

Basic equations of plane strain slip line fields in plastics are proposed. The pressure dependence and orthotropy of the material are incorporated in the yield criterion employed. Hencky's and Prandtl's theorems are found to be valid in the same form as in Mises' material. The first, second, and third boundary value problems, well established in the slip line theory of Mises' material, are amenable to the similar method of solution. The proposed solution can include the work-hardening characteristics of the material. The examples solved by applying the method include the limit pressure of thick-walled cylinders and rings subjected to internal or external pressure, plane strain tension and compression tests, the indentation of a semi-infinite body by a lubricated punch, and extrusion through a lubricated die. The extrusion pressure predicted is in agreement with experimental results on hydrostatic extrusion of high-density polyethylene.