Numerical Solution for a Slanted Crack Issues in Thermoelectric Bonded Materials under Diverse Mechanical Loading Conditions

Abstract

A new mathematical model is devised for the analytical examination of slanted crack issues in thermoelectric bonded materials (TEBMs) under diverse mechanical loading conditions, including shear, normal, tearing, and mixed stresses. To tackle these problems, we utilize the modified complex variable function (MCVF) method and introduce continuity conditions for both the resultant electric force and displacement electric function. This enables us to formulate hypersingular integral equations (HSIEs). The crack opening displacement (COD) function, electric current density, and energy flux load are transformed into a square root singularity function using the curved length coordinate method. Subsequently, we employ appropriate quadrature formulas to solve these equations numerically, with the traction along the crack serving as the right-hand term. The COD function obtained from our analysis is then used to compute dimensionless stress intensity factors (DSIFs). These DSIFs play a pivotal role in determining the stability behavior of TEBMs containing a slanted crack. Our numerical results for DSIFs at all crack tips are presented, and they are found to be in excellent agreement with previous research. It is important to note that the DSIFs at the crack tips are influenced by mechanical loading conditions, the ratio of elastic constants, crack geometries, and electric conductivity.