Thermomechanical interactions due to mode-I crack under modified temperature-rate dependent two-temperature thermoelasticity theory

Abstract

Temperature-rate dependent two-temperature (TRDTT) thermoelasticity is reformulated by Shivay and Mukhopadhyay [On the temperature-rate dependent two-temperature thermoelasticity theory. J Heat Transfer. 2020;142(2):022102.] and it is suggested that the effect of the temperature-rate term should not be neglected in the two-temperature relation. As a result, an improved two-temperature theory has been proposed that generalize the TRDTT theory suggested by Youssef [Theory of two-temperature-generalized thermoelasticity. IMA J Appl Math 2006;71(3):383–390.]. The present work aims to investigate thermo-mechanical interactions due to the presence of crack under this modified TRDTT theory. We consider a homogeneous and isotropic 2D infinite medium weakened by mode-I crack of finite length. The boundary of the crack is subjected to time-dependent thermal and stress distributions. Laplace and Fourier transformations are used to solve the present problem in the transformed domain. Two different sets of dual integral equations are derived, which are solved by reducing them to the Fredholm integral equation of the first kind. The regularization method, along with a numerical integration technique, is used to solve this integral equation. Present results are validated with the results derived under GL (temperature-rate dependent) theory. Some interesting points highlighting the effects of a crack in the present context are concluded.