Effects of the orientational distribution of cracks in isotropic solids
Effects of the orientational distribution of cracks in isotropic solids
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DOI：
10.1016/j.engfracmech.2006.10.006
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发表时间：
2007-09
影响因子：
5.4
通讯作者：
S. Giordano;L. Colombo
中科院分区：
文献类型：
--
作者：
S. Giordano;L. Colombo
本文论述了微裂纹固体的弹性特性：我们分析了任意非随机取向分布的裂纹的分散体。角分布的特殊情况是由所有定向在给定方向上的裂纹或在空间中均匀随机定向的裂纹给出的。一个统一的理论涵盖了随机和平行之间的所有取向分布。复合材料内部的微观力学平均是通过明确的结果进行的，这使我们能够获得整体材料的宏观或等效弹性模量的封闭形式的表达式。分析已在二维（2D）弹性（平面应力和平面应变）与狭缝状裂纹和平面圆形裂纹的三维（3D）弹性。微裂纹固体的弹性行为取决于裂纹的密度和它们的取向分布。特别是，这项研究使我们能够说明，在二维的这种微裂纹材料的弹性行为是完全由一个顺序参数，这取决于给定的角分布，而在三维的弹性表征取决于两个顺序参数定义。各向同性取向的裂纹（无论是在2D和3D）的特殊情况下，已被推广到更高的值的裂纹密度的迭代均匀化的方法，这导致一些微分方程。结果表明，等效弹性模量与裂纹密度呈指数关系。
The paper deals with the elastic characterisation of microcracked solids: we analyse dispersions of cracks with arbitrary non-random orientational distributions. Particular cases of angular distributions are given by cracks all oriented in a given direction or cracks uniformly random oriented in the space. A unified theory covers all the orientational distributions between the random and the parallel ones. The micromechanical averaging inside the composite material is carried out by means of explicit results which allows us to obtain closed-form expressions for the macroscopic or equivalent elastic moduli of the overall material. The analysis has been performed in two-dimensional (2D) elasticity (plane stress and plane strain) with slit like cracks and in three-dimensional (3D) elasticity with planar circular cracks. The elastic behaviour of the microcracked solid depends upon the density of cracks and upon their orientational distribution. In particular, this study allows us to state that in two-dimensions the elastic behaviour of such a microcracked material is completely defined by one order parameter, which depends on the given angular distribution while the elastic characterisation in three-dimensions depends on two order parameters. The particular cases of isotropic orientations of cracks (both in 2D and in 3D) have been generalised to higher values of the cracks density by means of the method of the iterated homogenisation, which leads to some differential equations. Their solutions show that the equivalent elastic moduli depend exponentially on the cracks density.