Studies of elastic and elastic-plastic J integral for mixed mode cracked plate under biaxial loading

Analyses of I-II mixed mode central cracked plate by finite element method are performed in this paper, and some different phenomena are found. First for I-II mixed mode crack, the distribution of J integral along crack tip thickness depends on biaxiality factors because of the existence of vertex (corner) singularity, which is unlike that for mode I or mode II crack. Then J integrals at middle layer keep constant for any cracked plates with different inclined angles β when the biaxiality ratio is equal to 1 or -1, which implies that the inclined angle or the extent of I-II mixed mode has no effect on the J integral for positive or negative equal axial loading conditions. And the decreasing trend of J integral with the inclined angle β for biaxiality ratio λ being between-1 and 1 is just opposite with that for biaxiality ratio λ being larger than 1 and smaller than -1. Finally, proposed h₁ (a/W, n, λ, β) of cracked plate with different inclined angles under different biaxial loading are calculated.