An Extended Dielectric Crack Model for Fracture Analysis of a Thermopiezoelectric Strip

Abstract

An extended dielectric crack model is proposed to capture the effects of the physical properties of crack interior on crack-tip thermoelectroelastic fields. The typical crack-face boundary conditions can be retrieved by considering the limiting cases of electrical permeability and thermal conductivity inside a crack. Making use of the Fourier transform technique, the problem of a thermopiezoelectric strip weakened by a Griffith crack is investigated and transformed to solve the system of the second kind Fredholm integral equations with Cauchy kernel. The Lobatto–Chebyshev collocation method is used to form a nonlinear system of algebraic equations, which is solved by elaborating on an algorithm. The crack-tip thermoelectroelastic fields are determined by using the approximate solutions. Numerical simulations are carried out to show the variations of the fracture parameters of concern under applied thermoelectromechanical loads, the physical properties of the dielectric medium inside the crack and the geometry of the cracked thermopiezoelectric strip. Some comparisons with the experimental results are reported to reveal the effectiveness of the extended dielectric crack model.