An anti-plane crack perpendicular to the weak/micro-discontinuous interface in a bi-FGM structure with exponential and linear non-homogeneities

Treated was an anti-plane crack perpendicular to the interface of an exponential-type FGM strip bonded to another linear-type FGM substrate with infinite thickness. Through Fourier integral transform, the problem was reduced as a Cauchy singular integral equation, which was further solved numerically by the Lobatto–Chebyshev collocation method. Based on the numerical solution, the effects of the geometrical and physical parameters on the stress intensity factor (SIF) were analyzed and the following conclusions were obtained: (a) A notable discrepancy between the interface-perpendicular crack and the interfacial one is that, to reduce the weak-discontinuity of interface or to make the interface micro-discontinuous will not necessarily decrease the SIF of the former, but will surely decrease that of the latter. (b) When a crack tip is situated very near to the interface (or free surface), its SIF will be high and totally dominated by the interface (or free surface). (c) To increase the stiffness of the FGM on one side of the interface is beneficial to preventing the crack on the other side from growing toward the interface. Besides, some practical suggestions were further given for material design in the field of composites.