Employing Hypersingular Integral Equations to Obtain Stress Intensity Factor for Two Slanted Cracks in Thermoelectric Bonded Materials

Abstract

This research focuses on solving hypersingular integral equations (HSIEs) numerically for thermoelectric bonded materials (TEBM) subjected to shear stress and weakened by two slanted cracks. The modified complex variable function (MCVF) method is applied, integrating continuity conditions (CC) for both the electric field effect (EFE) and the displacement electric function (DEF), which are used to formulate the governing HSIEs. Utilizing a curved length coordinate approach, the unknown functions associated with crack opening displacement (COD), as well as constants for current vector field and surface energy load, are expressed in terms of the fracture singularity basis function. These HSIEs are solved numerically using suitable quadrature techniques, with the crack traction as the right-hand term. The solutions for COD, current vector field, and surface energy load are then employed to calculate the dimensionless stress intensity factors (DSIFs), which offer insights into the stability of TEBM with two slanted cracks. Numerical simulations demonstrate that the computed DSIFs at the crack tips are consistent with previous research. Additionally, the results show that DSIFs are significantly affected by factors such as the ratio of elastic constants (ECR), crack geometry, and current vector field coefficients.