Analytical solution of the temperature-dependent thermoelastic problem induced by Joule heating and the presence of an elliptic cavity

AbstractJoule heat induced by electric current may well lead to thermal stress and contribute to structural failure and crack evolution in a range of modern materials. In this paper, we use complex variable methods to obtain the thermoelastic fields around an elliptic cavity in a plate subjected to remote electric and thermal loads. Of particular interest is the fact that we consider the temperature dependency of the corresponding thermoelastic coefficients. We introduce an analytical method which is verified by the fact that it leads to results which reduce to the classical analytical results in the literature when the thermoelastic coefficients are taken to be temperature-independent. We find that when the elliptic cavity is reduced to the representation of a linear crack, the corresponding stress intensity factor increases to a greater extent under the temperature-dependent assumption versus the corresponding classical results. Our findings are significant in forming the basis for the analysis of the evolution of crack growth under severe temperature gradients such as those occurring as a result of Joule heat loading.Keywords: Crack arrestelectric currentJoule heatstress intensity factorstemperature-dependentthermoelastic fields Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe authors would like to thank support from the National Natural Science Foundation of China (NSFC) (11872203) and China Scholarship Council (CSC). This work is also supported by the Joint Fund of Advanced Aerospace Manufacturing Technology Research (U1937601) and the National Natural Science Foundation of China for Creative Research Groups (No. 51921003). Schiavone thanks the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN – 2017 - 03716115112).