Thermoelastic deformation of a medium weakened by an annular crack

Abstract

This research investigates the thermo-mechanical behavior of cracked media by analyzing heat conduction, elastic and thermoelastic deformations within a medium containing a circular or annular crack. Formulated as mixed boundary value problems, the problems are solved using the Hankel integral transform technique, reducing them to dual or triple integral equations. Solutions are then derived through infinite sets of algebraic equations utilizing some integral relations and Gegenbauer’s addition formulas. Consequently, closed-form expressions for various key parameters are obtained, including thermal and mechanical fields, heat flux intensity factors and mixed mode I-II stress intensity factors. Excellent agreement with numerical simulations and existing results for limiting cases validates the obtained solutions. Selected graphical representations provide valuable insights into the behavior and dependence of these physical quantities on various parameters, such as the size and depth of the crack. This research contributes significantly to the understanding of thermo-mechanical behavior in cracked media. This research significantly contributes to the understanding of heat conduction, elastic and thermoelastic deformations in cracked media.