Abstract：Growth and evolution of micro-cracks are the mechanism of damage and failure for quasi-brittle materials. The principle for growth and evolution of micro-cracks in quasic-brittle material subjected to loading is studied. The analytical solution is given for the growth of elliptical micro-cracks in elastic deformation stage by the method of complex potential functions. The critical stress condition for the starting damage is derived based on micro-crack growth criterion. The constitutive relation is developed based on the conservation of energy during the wing-crack propagating.
 任会兰, 宁建国, 王颖. 陶瓷材料破坏的声发射特性[J]. 材料工程, 2009, (2): 54-57. 任会兰, 方敏杰, 贺建华. 压缩载荷下陶瓷材料声发射特性的实验研究[J]. 材料工程, 2012, (2): 30-34. BRACE W F, BOMBOLAKIS E G. A note on brittle crack growth in compression[J]. Journal of Geophysical Research, 1963, 68(12): 3709-3713. KACHANOV M. A microcrack model of rock inelasticity[J]. Mechanics of Materials, 1982, 1(1): 19-41. HORII H, NEMAT-NASSER S. Overall moduli of solids with microcracks: load-induced anisotropy[J]. Journal of the Mechanics and Physics of Solids, 1983, 31(2):155-171. HORII H, NEMAT-NASSER S. Brittle failure in compression: splitting, faulting and brittle-ductile transition[J]. Philosophical Transactions for the Royal Society of London,A, 1986, 319(1549): 337-374. CHUDNOVSKY A, DOLGOPOLSKY A, KACHANOV M. Elastic interaction of a crack with a microcrack array Part Ⅰand Ⅱ[J]. International Journal of Solids and Structures, 1987, 23(1): 1-21. CHUDNOVSKY A, WU S. Evaluation of energy release rate in the crack-microcrack interaction problems[J]. International Journal of Solids and Structures, 1992, 29(14-15): 1699-1709. FENG Xi-qiao, GROSS D. Micromechanical analysis of microcrack-induced residual strains in quasi-brittle solids[J]. Computational Materials Science,1999, 16(1-4): 362-371. YU Shou-wen, FENG Xi-qiao. A micromechanics-based damage model for microcrack-weakened brittle solids[J]. Mechanics of Materials,1995, 20(1): 59-76. TIMOSHENKO S P, GOODIER J N. Theory of Elasticity[M].Third Edition.Beijing:Tsinghua University Press, 2004. RAVICHANDRAN, G. SUBHASH, G. A micromechanical model for high strain rate behavior of ceramics[J]. International Journal of Solids and Structures, 1995, 32(17-18): 2627-2646. 叶裕恭, 刘道川. 含微裂纹的95%Al2O3陶瓷的力学性能[J]. 固体力学学报, 1990, 11(2):117-127.