An analytical model for thermoelastic crack problems in a strip incorporating convective heat transfer between lateral surfaces and ambient environment

Most existing thermoelastic crack models commonly overlook the convective heat exchange occurring on the lateral surfaces of the structures being studied. Consequently, there is often a concern regarding the accurate estimation of temperature fields and the resulting thermal stresses. To address this concern, this paper presents a two-dimensional (2D) thermoelastic model for a cracked strip that incorporates convective heat transfer between the lateral surfaces and the ambient environment. The crack problem is reduced to a set of singular integral equations with Cauchy kernels which are solved numerically. Analytical solutions for temperature distribution, stress intensity factors (SIFs) and energy release rate at crack tips are obtained. The influence of the ratios of convective heat transfer coefficient to thermal conductivity and thickness to height of the strip on the key fracture parameters is investigated through the numerical results. It has been discovered that classical thermoelastic crack models often exhibit a significant underestimation of the SIFs and energy release rates for cracks located near the hot boundary of the strip. The analytical model proposed in this paper has significant potential to advance our understanding of thermoelastic fracture mechanics.