13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Figure 4 shows some different steps of the cracking process. The crack growth scheme can be summarized by observing these images. At the beginning, the thermal shock cracks initiate and propagate uniformly with approximately a nearly equal spacing (Fig. 4-a). At this step, the thermal shock cracks propagate simultaneously and very rapidly, then the propagation speed decreases gradually with release of the thermal stresses until the strain energy cannot support simultaneous propagation of all the cracks. Consequently, only a reduced number of cracks continue to propagate, whereas the other cracks stop. The crack spacing increases until 2 or 3 times larger than the previous one (Fig. 4-b). In the following steps, the crack growth may deviate and attempt to form equal crack spacing (Fig. 4-c). This procedure may repeat several times until the strain energy induced by thermal stresses cannot support propagation of any crack. The final simulation crack patterns (Fig. 4-d) are very similar to those observed in experimental results. This remark supports the cracking process above described. The colouring map represents the levels of first principal stresses (unity in MPa). From Figure 4, the locations of stress concentrations can clearly be observed. The competition amongst the stress concentrations at different locations leads to the formation of multi-crack failure patterns. The proposed damage model provides a natural manner in reproducing them. Comparing to the traditional treatment of fracture mechanics in which the crack growth conditions should be examined at each crack tip, the present method is much more simple and robust to deal with multi-cracking problems. Figure 4: Crack patterns at different times, T0=500°C 5. Conclusions and future works In this work, a non-local failure model was described to predict crack initiation and crack growth in brittle materials and then implemented into a finite element code. This non-local fracture model was
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