Thermoelastic problem in an infinite space with a Griffith crack under a uniform heat flow

Abstract In this work, we analyze thermomechanical deformation of an infinite elastic material with a heat‐permeable Griffith crack. A uniform heat flux is applied remotely to the material in the direction perpendicular to the crack surface. Using Fourier transform and the second‐order partial differential equations of displacement components, the temperature and deformation fields are found to be functions of the heat flux, crack size, and thermal conductance of the crack. An auxiliary function in the form of orthogonal sine series is used to represent the temperature distribution on the crack surfaces. Closed‐form solutions of the temperature on the crack surfaces, the stress in front of the crack tips, and the Mode‐II stress intensity factor are obtained. The stress intensity factor decreases with the increase of the product of the crack size and the thermal conductance of the crack. The numerical results reveal that the temperature on the crack surfaces exhibits oscillatory behavior around the crack tip for large values of the product of the crack size and the thermal conductance of the crack, which likely implies the presence of “contact/healing” of the crack near the crack tips.