In order to study the crack initiation characteristics of polymer bonded explosive(PBX) structures under complex stress conditions, the implicit governing equation of PBX Ⅰ-Ⅱ mixed mode crack failure zone was obtained. The equation considered tension-compression ratio, Poission′s ratio, hydrostatic pressure, stress state, crack surface closure friction and T-stress theoretically. The whole model was based on a infinite plate model with a centeral slanting crack and the crack tip stress field considering T-stress and Drucker-Prager strength criterion. By applying the minimum radius fracture criterion of crarck tip failure zone, the effects of T-stress on crack tip failure zone and fracture of PBX was studied. Theoretical study indicates that, for far field tension state, T-stress leads to an increase (0°<β<45°) or decrease (45°<β<90°) in the crack tip failure zone and decrease of the fracture angle; for far field compression state, the crack is only in the II mode state. Due to crack closure, friction effect leads to a significant reduction of the crack tip failure zone, but does not influence the fracture angle. T-stress leads to the increase of the fracture angle and the decrease of the crack tip failure zone for compression-shear crack. Meanwhile, T-stress leads to the obvious increase of the most dangerous crack angle β₀. Therefore, it is necessary to consider the effects of T-stress on studying the crack initiation behavior of PBX.