13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Thermo-elastic analysis of a cracked substrate bonded to a coating using the hyperbolic heat conduction theory Zengtao Chen 1,* , Keqiang Hu 1 1 Department of Mechanical Engineering, University of New Brunswick, Fredericton NB E3B 5A3, Canada * Corresponding author: ztchen@unb.ca Abstract In this paper, the dynamic thermal stresses around a crack in a substrate bonded to a coating are obtained using the hyperbolic heat conduction theory. Fourier and Laplace transforms are applied and the hyperbolic heat conduction and thermo-elastic crack problems are reduced to solving singular integral equations. The crack kinking phenomenon under thermal loading is investigated by applying the criterion of maximum hoop stress. Numerical results show that the hyperbolic heat conduction parameters, the material properties and the geometric size of the composite have significant influence on the dynamic stress field. It seems that high temperature loading on the surface may lead to crack kinking away from the surface and low temperature loading may cause crack kinking toward the coating. Moreover, the hyperbolic heat conduction theory may give more conservative results than that the Fourier’s heat conduction theory. Keywords Cracked Substrate, Coating, Hyperbolic heat conduction, Singular integral equations, Crack kinking 1. Introduction High-rate heat transfer has become a major concern in modern industries especially in material processing, such as the pulsed laser heat and ultrasonic waves, and accurate heat conduction analysis is of great importance for the material and structural integrity. Investigation of the temperature and stress fields is essential to the safety design of the composite structures under severe temperature loading. The Fourier heat conduction model, although give sufficient accuracy for many engineering applications, implies infinite thermal wave propagation speed, and renders ineffective at the very small length and time scales associated with small-scale systems [1]. Consideration of the hyperbolic heat conduction model becomes important if irreversible physical processes, such as crack or void initiation in a solid, are involved in the process of heat transport. In these cases, the hyperbolic heat conduction model should be used [2]. Inherent defects in materials such as dislocations and cracks may disturb the temperature distribution when thermal loading is applied, and singularities may be developed in the neighborhood of discontinuities. The singular behavior of temperature gradient around crack tip has been studied based on the classical Fourier heat conduction model [3]. Some investigations on crack problems in thermo-elastic materials have been made using the hyperbolic heat conduction model. The problem of a finite crack in a material layer under transient non-Fourier heat conduction was investigated by Wang and Han [4] and the problem of an interface crack in layered composite media under applied thermal flux was studied using the hyperbolic heat conduction theory [5]. A thermo-elastic analysis of a cracked substrate under a thermal shock was given in Chen and Hu [6] based on the hyperbolic heat conduction theory; and based on the same theory the transient temperature and thermal stresses around a partially insulated crack in a thermoelastic strip under a temperature impact were obtained [7]. The transient temperature field around a thermally insulated crack in a substrate bonded to a coating has been obtained by using the hyperbolic heat conduction model [8].