On the non-Fourier thermal fracture of an edge-cracked cylindrical bar

Abstract

The fracture behavior of a cylindrical bar containing a circumferential edge crack under transient thermal loading is analyzed in this paper using the dual phase lag heat conduction model. The lateral surface of the bar is subjected to an asymmetric, convective thermal boundary condition. The Laplace transform method is adopted to solve the one-dimensional, hyperbolic heat conduction equation in the un-cracked bar, and the corresponding thermal stress is obtained in the Laplace domain under plane strain condition. Then, based on the superposition method, the axial stress with minus sign is applied on the crack surface to form a mode I crack problem in the cylindrical coordinate. Love’s potential function is introduced to solve the crack problem and a singular integral equation is obtained by using the Fourier and Hankel transform methods. Furthermore, a numerical Laplace inversion technique is employed to transform all the results to the time domain. Finally, the effect of heat conduction model, phase-lag parameters, Biot number, and the crack depth on the transient temperature, thermal axial stress, stress intensity factor, and crack opening displacement is analyzed.