13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- residual strength is one of the most important properties that evaluate the ceramic materials for further use after thermal shock. However, few researchers do it in theoretical way [17] , and they didn’t consider the effects of temperature on the thermo-physical properties. But in its actual operating condition the temperature range of the UHTCs is very large and the material properties are always function of temperature, the effects of temperature on the UHTCs material properties must been taken into consideration [7]. In this paper, thermal shock residual strength of UHTCs is studied. As basic research, firstly we only consider the strength degradation due to propagation of a single crack, which has proven reasonable in evaluating thermal shock residual strength of monolithic ceramics [18,19]. Effects of multiple crack propagation and particle-reinforced on strength degradation will be considered in the future study. And the material properties are function of temperature to take the effects of temperature on the UHTCs material properties into account. The critical thermal shock temperature that causes the material strength drop and thermal shock residual strength is determined by calculation and the results demonstrate the differences from the one without temperature-dependent material properties. 2. Temperature and thermal stress fields 2.1. Temperature fields of UHTC strip under cold shock Consider a long UHTC strip with an edge crack as shown Fig. 1, where 2a is the thickness of the strip and c0 is the crack length. The strip is initially at a constant temperature T0, and its surfaces x = 0 are suddenly cooled by cooling media of temperatures T∞ with the heat transfer coefficients h. Figure 1. A UHTC strip with an edge cracks subjected to thermal shock Assume that the crack whose plane is normal to the surface of the strip does not perturb the transient temperature distribution. Therefore, this is a one-dimensional heat conduction problem as the Fig. 1 shows. Taking the temperature-dependent material properties into account, the governing equation can be written in the form ( ) ( ) ( ) ( ) ( ) p , , , 0 2 , 0 T x t T x t k T T C T x a t x x t ρ ∂ ∂ ⎛ ⎞ ∂ = < < > ⎜ ⎟ ∂ ∂ ∂ ⎝ ⎠ (1) The corresponding boundary and initial conditions are as follows ( ) ( ) ( ) ( ) , , , 0, 0 T x t k T h T x t T x t x ∞ ∂ = − = > ∂ (2) a a T0 T∞, h x y c0
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