Calculation of mixed-mode stress field at a sharp notch tip using M _1ε-integral

Direct computation of the mixed-mode stress field at a sharp notch tip appears to be difficult in that the mode I and mode II asymptotic stresses are in general governed by different orders of singularity. In this paper, we first present a path-independent integral termed M_1ε. The relation between M_1ε and the generalized stress intensity factors is then derived and expressed as function of the notch angle. Once the M _1ε-integrals are accurately computed, the generalized SIF's and, consequently, the asymptotic mixed-mode stress field can thus be properly determined. No extra complementary solutions are required in the formulation. Further, no particular singular elements are required when the integration is performed by using finite elements.