Mathematical study of an arbitrary-oriented crack crossing the interface of bonded functionally graded strips under thermo-mechanical loading

Abstract

This article intends to explore the behavior of an arbitrary oriented crack that crosses the interface of bonded finitely thick functionally graded strips under thermo-mechanical loading. The angled crack is partially insulated. Application of the superposition technique and Fourier transformation on the governing equations of heat conduction and plane elasticity help to reduce the boundary-continuity conditions to Fredholm type singular integral equations. For solving these integral equations, the jump of the temperature and displacement across the crack surface are expressed as a series of Jacobi polynomials. Employing the residue theory and Schmidt method, the expressions of stress intensity factors (SIFs) are obtained which along with the local material parametric function determine strain energy release rates (SERRs). The novelty of the article is the investigation of the impact of thermo-mechanical loading on mode I and II crack tip SIFs and SERRs to study the behavior of arbitrary oriented partially insulated crack when it crosses the interface. The results of the present study are also validated. The key feature of the article is the graphical presentations of crack tip SIFs andSERRs for different values of crack insulation parameter, crack orientation angle, strips’ thickness, and non-homogeneity parameters.