13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Figure 6. (a) Influence on the threshold stress of cohesive zone n 0 and prediction of the V-KI curve for Polycrystal of Zirconia with G = 0.8 m, (b) Cracks paths for stopped cracks corresponding to the threshold load K0 for n 0 = 900 MPa and 1150 MPa. 3.2. Influence of thermal initial stresses on the prediction of SCG During the sintering process, the material is cooled down from a temperature at approximately 1500 °C to the room temperature. This process will induce thermal stresses that originate from both the anisotropic coefficients of thermal expansion and anisotropic elastic constants of the grains. We consider the case with 8 8 grains, a grain size G of 0.8 m for a uniform temperature cooling T = -1500 K. The corresponding boundary conditions are presented in Fig. 7a, and the distributions of the stress component yy reported in Fig. 7b, region under traction and compression are observed. From this initial state, we apply an external load KI and we allow intergranular failure. For n 0 = 400 MPa, 900 MPa and 1150 MPa, we report the corresponding V-KI curves represented in Fig. 8a, 8b and 8c. For the three cases investigated, we observe that the presence of initial thermal stresses lead to a reduction of the crack kinetics. The curves V-KI are shifted towards higher KI values, preserving the slope of the curves corresponding to the polycrystals that are initially stress free. For the case with n 0 = 400 MPa (see Fig. 8a) we observe that a threshold load K0 now appears when we consider the initial thermal stresses. For n 0 = 900 MPa and 1150 MPa, the magnitude of the threshold load of SCG increases when initial stresses are accounted for. We report in Fig. 9a, 9b and 9c the cracks paths for arrested cracks corresponding to the threshold load K0 below which the crack is stopped for n 0 = 400 MPa, 900 MPa and 1150 MPa respectively. The crack arrest is observed when the crack reaches a region where the compression is initially high enough with a locally stress level lower than threshold stress n 0 of cohesive zone. The account of thermal initial stress contributes to a reduction of SCG kinetics. The magnitude of K0 is also increased with initial thermal stress are accounted for. In the next section, we examine the influence of the water concentration on the predicted regime I and load threshold of SCG K0.
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