The modified generalized Tresca yield condition with application to mode I perfectly plastic crack problems

Abstract

Basic properties of a newly defined yield criterion are explored and then applied to plane stress, mode I, perfectly plastic crack problems. This yield condition began as a perturbation of the traditional Tresca yield condition. In a previous study, a relationship was found for a yield criterion that spanned the Tresca to the von Mises yield criteria in the principal stress plane. In this study, a distinct but related yield criterion is used for those cases where the yield criterion lies on or outside the von Mises yield condition in the principal stress plane. For these cases, the associated mathematics becomes more complicated than those cases where the yield condition lies within or on the von Mises yield condition in the principal stress plane. The perfectly plastic mode I crack problem is solved for this modified version of the generalized Tresca yield condition. It is found that the maximum normal stress for this yield condition is higher than that for the equivalent mode I crack problem under the von Mises yield condition. Material parameters associated with the generalized Tresca yield condition are found for both the BCC and FCC crystal structures based on models proposed previously in the literature.