Anti-plane transient fracture analysis of the functionally gradient elastic bi-material weak/infinitesimal-discontinuous interface

Abstract

The mechanical model was established for the Dirac-type anti-plane transient fracture problem of the weak-discontinuous interface between two FGMs half-planes. Integral transform was adopted to derive Cauchy singular integral equation and Erdogan’s allocation method was used to calculate transient stress intensity factors numerically. The numerical solutions of the weak-discontinuous case were contrasted with those of the infinitesimal-discontinuous one. Two possible effective methods to diminish the peak values of transient stress intensity factors are discussed. One is to reduce the weak-discontinuity of the interface, i.e., to make the ratio of the two non-homogeneity parameters be close to 1.0 and to avoid the case that the signs of the two non-homogeneity parameters are different. Another is to make a compromise between the weak-discontinuity and the all-continuity, i.e., to make FGMs interface infinitesimal-discontinuous. Simple method was suggested for the realization of the infinitesimal-discontinuity of FGMs interface. From the strong-discontinuous interface to the weak- discontinuous one, and then to the infinitesimal-discontinuous one, this is a law and trend of the development of composite interfaces. To design and manufacture infinitesimal-discontinuous interfaces may be a brand-new effective approach to enhance the reliability of composite structures, and the first rank infinitesimal-discontinuity is enough to improve the mechanical performances of composites notably.