基于尺寸效应的分形Griffith裂纹扩展准则
首发时间:2009-04-10
摘要:本文应用分形Griffith裂纹长度的分数阶变化率讨论了基于尺寸效应的分形Griffith裂纹临界扩展准则。在此基础上,提出了基于尺寸效应的分形Griffith裂纹失稳扩展准则。本文研究结果表明:在分形Griffith裂纹扩展中,在分形裂纹的临界扩展状态时,裂纹扩展力与裂纹的扩展阻力仍然保持比例关系,其比例系数与分形裂纹长度、特征尺寸和裂纹分形维数有关。在经典的裂纹扩展过程中,分形维数、裂纹长度和比例尺寸对比例系数的影响隐蔽了。经典的裂纹扩展准则是基于尺寸效应的分形Griffith裂纹扩展准则的极限。而且,基于尺寸效应的分形Griffith裂纹扩展准则的建立加深了对经典裂纹扩展准则的理解。
关键词: 尺寸效应 分形Griffith裂纹 裂纹扩展力 准则 裂纹扩展阻力
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The criterion of fractal Griffith’s crack propagation dependent on size effects
Abstract:Crack propagation paths are often irregular, producing rough fracture surface which have a fractal nature. A crack tip motion along a fractal crack propagation trace dependent on size effects is analyzed in this paper. A fractal model of the size-effect crack propagation path is established to be described the size effects and fractal crack propagation and the criterion of fractal Griffith’s crack propagation dependent size effects is obtained using the crack length of the fractional rate of change. It is shown that for fractal crack propagation the ratio of the crack propagation force to resistance is all the same kept, whose ratio coefficient has a relation to fractal crack length, characteristic size and fractal dimension of the crack propagation trace. The fact is hided for classical crack propagation and the classical criterion of the crack propagation is the limit of that of fractal crack propagation. And it enhances a increasing knowledge for the classical theory.
Keywords: size effects fractal Griffith\
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