Evaluation of thermal stress intensity factors of an interface crack in FGMs with varying thermal expansion coefficient by multi-region BEM

Functionally Graded Materials (FGMs) with constant Young's modulus and Poisson's ratio but varying thermal expansion coefficients termed $\alpha \text{FGM}$ are the focus of this study. The objective is to evaluate the thermal stress intensity factors (TSIF) of interface cracks in $\alpha \text{FGMs}$ under thermal loading using the Boundary Element Method (BEM). The thermal loading on $\alpha \text{FGM}$, equated to body forces, is addressed by deriving a particular solution to Navier's equation through Fourier series expansion. This enables the application of BEM without necessitating kernel function modifications. Then with this particular solution integrated, the boundary conditions of the homogeneous problem are defined. Subsequently, the homogeneous solution is computed using the multi-region BEM. Finally, the complete solutions are obtained by combining both the homogeneous and particular solutions. This study evaluates the TSIFs of an edge crack in a single-layer $\alpha \text{FGM}$ and an interface crack in a two-layer. $\alpha \text{FGM}$. under temperature loadings. The correlations between TSIF, bi-material characteristics, thermal expansion coefficient mismatch, and varying crack lengths are under investigation.