13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Although the morphologies are very similar between the experimental crack patterns and the numerical ones, the quantitative comparison on crack lengths p is not evident due to the data scattering of the experimental results. By assuming that each crack level obeys a Gaussian distribution, Jiang et al. [14] described the crack length distribution by a combined Gaussian function. This analysis allowed the classification of the cracks according to their length in a statistical manner. In Table 2, we list the average lengths of the longest cracks of the experimental and numerical crack patterns. The comparison shows a good agreement, even though the numerical simulations provide smaller crack lengths comparing to the experiments. The principal reason of this difference may be the blunt form of the crack tips in numerical models, in which the cracks were represented by damaged bands with a finite thickness. Table 3: Dimensionless crack length p=p/L2 300°C 350°C 400°C 500°C 600°C T0 test simulation Test simulation test simulation Test simulation test simulation p 0.72 0.64 0.74 0.65 0.72 0.68 0.78 0.73 0.8 0.75 4.3: Cracking process during the thermal shock Figure 3 shows the first crack initiations at the specimen surface. The distribution of the first principal stresses is also shown by means of a colouring map. From this image, we can observe that, at a critical time where the temperature gradient reaches a sufficiently high level, the first crack will appear at the location where the non-local first principal stress is maximal and fulfils the failure criterion (3). After that, the stresses are relaxed at this location, and the stress redistribution furnishes another location where the first principal stress is maximal. If the fracture criterion (3) is always fulfilled, a new crack onset takes place. Since the stress distribution is nearly uniform along the specimen surface, the first crack initiations are somewhat randomly located, depending only on the scattering of the numerical results. The following cracks will appear between the most distant cracks previously formed. This procedure will repeat until the temperature gradient is no longer capable to produce sufficient stress concentration to onset new cracks. Figure 3: First crack initiations
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