Analysis of an arbitrarily shaped interface crack in a three-dimensional isotropic thermal elastic bi-material. Part 2: Numerical method

The displacement discontinuity method is developed to analyze an arbitrarily shaped planar interfacial crack in a three-dimensional isotropic thermal elastic bi-material under combined thermo-mechanical loadings. The fundamental solutions for uniformly distributed displacement and temperature discontinuities applied over a triangular element are obtained via the displacement and temperature discontinuity- boundary integral-differential equation method. In order to eliminate the oscillatory singularity near the crack front, the Delta function in the fundamental solutions is approximated by the Gaussian distribution function, and accordingly, the unit Heaviside step function is replaced by the Error function. The stress and heat flux intensity factors without the oscillatory singularity as well as the Energy release rate are presented. An elliptical interface crack is analyzed as an example to validate the fundamental solutions and the proposed numerical method. The influences of thermal loading and material-mismatch on the thermo-mechanical response are studied, the difference between the homogeneous material and bi-material is also analyzed.