Mathematical relations related to the lode parameter for studies of ductility

Abstract

During plastic flow, hydrostatic pressure and plastic strain control the size of the yield surface while the Lode angle is responsible for its shape. The von Mises yield condition shows no dependency of the Lode angle while the Tresca condition shows. It has been concluded that the deviation from the von Mises criterion is real and could not be explained on the basis of lack of experimental accuracy and isotropy. What is notable is that from an engineering viewpoint the accuracy of the von Mises yielding is amply sufficient. However, it has been forecast that Lode dependency must be included to describe ductility. It has been shown that internal necking down of ligaments between voids that have become significantly enlarged in size dominates at high triaxiality, while internal shear localization of plastic strain between voids of limited growth dominates at low stress triaxiality. The Lode angle has been used to account for these effects. In this paper, various mathematical relations are examined that may be useful for further studies of the Lode angle and its relation to fracture and ductility.