Transient response of hygrothermoelastic field in an elastic plate with an edge crack

Abstract

AbstractIn order to describe the complex interaction in the heat and moisture transfer process, a coupled time‐fractional hygrothermal theory is developed to describe the anomalous phenomenon of coupled heat and moisture diffusion. The hygrothermoelastic behaviors in a plate with an edge crack are investigated. The surfaces of the plate are both subjected to hygrothermal shocks. The Laplace transform and the finite Fourier transform are applied to seek an analytical solution of temperature change, moisture distribution, and stress response that are expressed in terms of the Mittag‐Leffler function. With this solution, the stress intensity factors at the crack tip are numerically calculated through the weight function method. The coupling effects of the heat and moisture on the stress intensity factors are illustrated graphically for sub‐diffusion, normal diffusion, and super‐diffusion respectively. The results show that the coupling hygrothermal effects are significant and different when compared with the uncoupled model.