Fractional Modeling of Thermoelastic Fracture Behavior in a Cracked PZT-4 Strip under Transient Thermal Loading

TL;DR

This study models the thermoelastic fracture behavior of a cracked PZT-4 strip under transient thermal shock using fractional heat conduction, revealing wave-like thermal effects and memory-dependent responses.

Contribution

It introduces a fractional heat conduction framework combined with fracture mechanics to analyze piezoelectric ceramics under thermal shocks, incorporating memory effects and advanced numerical methods.

Findings

Significant deviations from classical Fourier predictions in temperature and stress fields.

Wave-like thermal behavior observed due to fractional heat conduction.

Influence of fractional order and relaxation time on fracture parameters analyzed.

Abstract

This paper investigates the thermoelastic fracture response of a transversely isotropic piezoelectric strip containing a vertical insulated crack under transient thermal shock loading and pre-existing stress fields. The analysis is conducted within the framework of generalized fractional heat conduction using the Ezzat model, which incorporates thermal relaxation and memory-dependent effects. The problem is formulated as a mixed boundary value problem governed by fractional thermoelastic equations. The Laplace transform technique is employed to obtain temperature and coupled fields in the transform domain. The resulting system of singular integral equations is solved using the Lobatto-Chebyshev collocation method to determine the displacement discontinuity and the associated thermal stress intensity factors at the crack tips. The transient response in the time domain is recovered through numerical inversion of the Laplace transform using the Stehfest algorithm. Numerical results for PZT-4 are presented to examine the influence of fractional order, thermal relaxation time, pre-existing stresses, and geometric parameters on temperature distribution, thermoelastic stress fields, and stress intensity factors. The results demonstrate significant deviations from classical Fourier predictions, revealing wave-like thermal behavior and inherent memory effects associated with fractional heat conduction. The present formulation establishes a unified framework for the analysis of thermoelastic fracture in piezoelectric ceramics and provides insights into the design and reliability of smart structures operating under severe thermal conditions.