Boundary element analysis of interface cracks subjected to non-uniform thermal loading

Abstract

This work applies the method of multi-region boundary element to analyze the thermal stress intensity factor (TSIF) of the bi-material interface cracks subjected to linear and quadratic temperature distribution. An attempt is also made to resolve the problem containing body force which is caused by the inhomogeneous thermal loading by, initially, separating the solution of the inhomogeneous problem of each material into homogeneous and particular solutions, as proposed by Sung. The particular solution can be obtained by expanding the body force into Fourier series and, then, solving each term of the Fourier series. Next, inserting the obtained particular solutions into the boundary conditions of the original problem allows us to reduce the inhomogeneous problem to a homogeneous one. Moreover, the program of thermal multi-region BEM (TMBEM), which neither requires a domain integral nor changes the kernel functions, is established by imposing the continuity conditions on the interfaces. Finally, the applications of TMBEM are illustrated by evaluating the TSIFs of the interface cracks of bi-material subjected to linear and quadratic temperature distributions.