Research Cite this article: Wang BL, Li JE. 2013 Thermal shock resistance of solids associated with hyperbolic heat conduction theory. Proc R Soc A 469: 20120754. http://dx. The thermal shock resistance of solids is analysed for a plate subjected to a sudden temperature change under the framework of hyperbolic, non-Fourier heat conduction. The closed form solution for the temperature field and the associated thermal stress are obtained for the plate without cracking. The transient thermal

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... intensity factors are obtained through a weight function method. The maximum thermal shock temperature that the plate can sustain without catastrophic failure is obtained according to the two distinct criteria: (i) maximum local tensile stress criterion and (ii) maximum stress intensity factor criterion. The difference between the non-Fourier solutions and the classical Fourier solution is discussed. The traditional Fourier heat conduction considerably overestimates the thermal shock resistance of the solid. This confirms the fact that introduction of the non-Fourier heat conduction model is essential in the evaluation of thermal shock resistance of solids. is the well-known stress-based criterion. In a series of investigations, Hasselman [2-5] introduced thermal shock resistance parameters by means of comparing the thermal shock behaviour of ceramic materials in terms of their physical and mechanical properties. After the initiation of the fracture mechanics concept, the thermal shock resistance of materials has been determined by the fracture mechanics-based criterion as well as the stress-based criterion. The motivation is that cracks or defects are commonly observed during thermal shock [6, 7] . Li et al. [8] modelled the thermal shock of ultra-high temperature ceramics under active cooling. Rangaraj & Kokini [9] investigated the fracture behaviour of single-layer zirconia-bond coat alloy composite coatings under thermal shock. Zhou & Kokini [10] analysed the effect of surface pre-crack on the fracture of thermal barrier coatings under thermal shock. Zhou et al. [11] studied the thermal shock resistance of ceramics through biomimetically inspired nanofins. It is well accepted that the thermal shock resistance of solids ceramic is strongly affected by factors such as the heat conductivity, the geometric shape and the size of the sample, which govern the temperature gradient, the crack density and the duration of thermal stresses [6, 12, 13] . The influence of surface cracking, crack depth and shape on the structural integrity of the reactor pressure vessel during pressurized thermal shock was studied [14] . In addition, the material non-homogeneity, temperature dependence of the material properties and multiple cracking also have considerable influence on the thermal shock resistance behaviour of solids [15] [16] [17] . Traditionally, analysis and prediction of thermal shock resistance of solids have been based on classical Fourier heat conduction, which has very different physical bases from those in non-Fourier approaches. According to the classical Fourier heat conduction law, it is assumed that the speed of heat propagation in a body is infinite. The body will be affected by the boundary condition or initial condition at the instant. However, in reality, the speed of heat propagation in a body is always finite, making a thermal response behave like a wave [18] . Laser heating and nanotechnology have created the problems of heat conduction within very small time and length scales. For example, a carefully controlled incident beam can be used to heat up a very small area at a rate of up to 180 K s −1 for a few nanoseconds [19] . In such situations, researchers have reported that the predictions by Fourier heat conduction do not agree well with experimental observations. Maurer & Thompson [20] observed that the surface temperature of a slab taken immediately after a sudden thermal shock is 300 K higher than that predicted by Fourier law. The disagreement between Fourier prediction and the experimental observation is rooted in the unrealistic propagation speed of the thermal signal adopted by Fourier law. To better describe the wave-like behaviour of heat conduction, instead of using Fourier law, the hyperbolic equation, which takes finite heat travelling speed into account, was presented as a constitutive equation that was coupled with the local energy balance [21, 22] . Since then, considerable effort has been devoted to the solutions for the non-Fourier heat conduction equation for the cases of one-dimensional heat media [23] [24] [25] [26] [27] [28] , semi-infinite media [29] and layered composite media [30, 31] . Further, temperature dependence of the thermal conductivity, specific heat and thermal diffusivity was also studied [32] . It is well established that hyperbolic, non-Fourier theories of heat conduction are required for certain problems of practical interest in contemporary engineering. Wang et al. [33] studied the non-Fourier heat conductions in nanomaterials based on the thermomass theory and suggested that the inertial effect of high-rate heat and the interactions between heat and surface in confined nanostructures dominate the non-Fourier heat conduction in nanomaterials. In fact, Fourier's law has met great challenges in heat conductions in many situations, such as ultra-small scales (both temporal and spatial scales) [34], heat conduction in bio-materials [35], large heat flux and quick heating or cooling [36, 37] . In particular, under high heating rate, the non-Fourier effect is expected to have a pronounced influence on the stress state around the crack border [38] [39] [40] . In this situation, without considering the non-Fourier effect, error and misinterpretation of the predicted temperature and thermal stress may result. A better understanding of thermal shock resistance behaviour of materials associated with non-Fourier heat conduction is critical. However, there are still open questions that need to be addressed regarding the thermal shock of solids associated with non-Fourier heat conduction.