13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- successfully applied to simulating the crack evolution in ceramic materials subjected to thermal shock. From the results of the numerical simulations, the following conclusions can be formulated: 1. The numerical simulations reproduced faithfully the crack patterns in ceramic specimens after quenching tests. The periodical and hierarchical characteristics of the crack patterns were accurately predicted; 2. The parameters describing the crack patterns such as the average crack spacing and the crack lengths were correctly estimated from the numerical results; 3. The numerical simulations allow a direct observation on crack initiation and growth in the specimens, which is quite a difficult task in experimental studies. 4. The finite element implementation of the proposed non-local criterion allows accurate cracking simulations for real structures under thermal shock. The theoretical concept is clear and simple. The numerical model is robust, easy to apply to different engineering structures subjected to thermal shock. Acknowledgements This work was supported by the funding from the French ANR program T-Shock ANR-10-INTB-0915 and the National Natural Science Foundations of China (Grants Nos. 11061130550 and 11172023). References [1] W. D. Kingery, Metal-ceramic interaction: IV, absolute measurement of metal-ceramic interfacial energy and interfacial adsorption of silicon from iron-silicon alloys, J. Am. Ceram. Soc., 1954, 37: 42~25. [2] W.D. Kingery, Factors affecting thermal stress resistance of ceramic materials, J. Am. Ceram. Soc., 1955, 38: 3~15. [3] D.P.H. Hasselman, Approximate theory of thermal stress resistance of brittle ceramics involving creep, J. Am. Ceram. Soc., 1969, 50: 454~457. [4]. Mai, Y. W., Thermal stress resistance and fracture toughness of two tools ceramics. J. Mat. Sc., 1976, 11, 1430–1438. [5]. Hasselman, D. P. H., Strength behaviour of polycristalline alumina subjected to thermal shock. J. Am. Ceram. Soc., 1970, 53(9), 490–495. [6]. Ziegler, G. and Heinrich, J., Effect of porosity on the thermal shock behaviour of reaction sintered silicon nitride. Ceramurgia Inter., 1980, 6(1), 25–30. [7] T.K. Gupta, Strength degradation and crack propagation in thermally shocked alumina, J. Am. C eram. Soc., 1972, 55(5): 249~253. [8] J.A. Coppola, D.P.H. Hasslman, Strength loss of brittle ceramics subjected to severe thermal sho ck, J. Am. Ceram. Soc., 1972, 55(9): 481~489. [9] T. J. LU and N. A. FLECK, THE THERMAL SHOCK RESISTANCE OF SOLIDS , Acta mater. Vol. 46, No. 13, pp. 4755-4768, 1998 [10] Bažant ZP, Ohtsubo H, Aoh K. Stability and post-critical growth of a system of cooling or shrinkage cracks. Int J Fract 1979; 15(5): 443-456. [11] Nemat-Nasser S, et al. Unstable growth of thermally induced interacting cracks in brittle solids.
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