Roles of in-plane and out-of-plane T-stresses in crack tip plastic zones and fracture toughness under mixed mode I/II loading

Abstract

Crack tip plasticity and fracture toughness are usually connected with T-stresses under mixed mode I/II loading conditions. By means of von Mises yield criterion, a new analytical solution of plastic zone size is proposed for mixed mode I/II cracks, and the theoretical relation is determined between plastic zone size and in-plane and out-of-plane T-stresses. Then three constraint parameters, i.e. rpmin1/2, rpmax1/2 and Apz1/4, are theoretically derived from plastic zone sizes and area. Subsequently, the influences of T-stresses and mode mixity on plastic zones are investigated. Based on the experimental data, the combined effects of in-plane and out-of-plane T-stresses on fracture toughness are analyzed in Al 7075-T651 and Al 7075-T6 alloys by using constraint parameters. The results show that, the size and shape of plastic zone are significantly affected by both in-plane and out-of-plane T-stresses, and also strongly influenced by mode mixity. For small scale yielding, the new analytical solution of plastic zone size is reasonable, and the constraint parameters rpmin1/2, rpmax1/2 and Apz1/4 are applicable for characterizing the in-plane and out-of-plane constraint effects comprehensively in mixed mode I/II cracks, then there are linear correlations between constraint parameters and fracture toughness.