13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 3.1 Experiments Jiang et al. [14] carried out quenching experiments on ceramics plates from different temperatures. This experimental study will be used in the validation of the proposed model. In Jiang et al. [14], 99% Al2O3 powder was thermoformed into 50mm×10mm×1mm thin specimens. They were bound up with inconel wires and heated to a temperature T0 ranged from 300 °C to 600°C. After that, the heated specimens were dropped into a water bath of T∞=20 °C by free fall. Figure 1 shows the thermal shock crack patterns. From Figure 1, we can remark the following points: - The number of cracks increases as the initial temperature increases; - The lengths of the cracks increase as the initial temperature increases; - The crack spacing decreases as the initial temperature increases; - A tendency towards equal spacing between cracks can be observed; - The crack patterns exhibit a hierarchical structure. One can distinguish 2 classes’ cracks for quenching tests with T0=300°C, and 3 classes’ cracks for quenching tests with T0=350°C ~ 600°C. However, the frontiers of the different classes are not always clear. T0=300°C T0=350°C T0=400°C T0=500°C T0=600°C Figure 1: Crack patterns after quenching experiments 3.2 Model By considering the symmetry of the specimen, a quart of it was meshed by using three-node plane stress elements. The side size of the elements is about d= 0.05mm, e.g. about a half of the non-local action radius R. When the failure criterion is fulfilled in an element, it will be eliminated from the model, together with its immediate neighbouring elements. The successive damaged spots form a damaged band with a width of about 0.12mm. 3.3 Temperature and thermal stress fields The experimental conditions allow us to regard the temperature field as two-dimensional. Establish a Cartesian coordinate system Oxy with the origin at the centre of the specimen and x and y
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