In many fracture studies of metal matrix composite materials, it is generally conjectured that the crack of solid initiates at and propagates from a dominant flaw. This may be a manufacturing flaw or may result from the difference of thermal expansion. In studies relating to structural integrity and reliability, one needs to solve the mechanics problem for the composite materials consisting of an inclusion and surrounding matrix which contains the flaw.
In this study, an elastic interaction between a circular inclusion and an arbitrarily oriented finite crack located in the infinite matrix under mechanical loading and thermal loading (uniform heat flow) at infinity is studied. The present problem can be considered as a superposition of two problems. The first is a simple problem of a circular elastic inclusion inserted into a matrix without a crack. In the second problem, the stress disturbance due to the existence of the crack in the matrix is considered. Using the complex variable theory and existing singularity solutions, the thermo-elastic problem of a crack in the vicinity of the circular interface is solved. The plane interaction solutions are successfully given in terms of complex potentials so that the whole fields of displacement and stress can be easily constructed.
The integral equations for the straight crack are obtained as a system of singular integral equations with logarithmic singular kernels. The integral equations are converted into the linear algebraic equations using Gauss-Chebyshev quadrature. By solving the algebraic equations, dislocation distribution functions can be determined and the stress intensity factors are obtained in terms of the dislocation distribution functions.
The numerical analysis is verified via finite element analysis and known exact solutions. Several numerical examples are given to demonstrate the effect of geometrical parameters and material properties on the stress intensity factors. Some errors in the previous works by Chao and Lee, and Perlman and Sih are corrected.
