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Dominance of asymptotic crack tip fields in elastic functionally graded materials

机译:弹性功能梯度材料中渐近裂纹尖端场的优势

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摘要

The stress field surrounding an edge crack in an elastic functionally graded plate is calculated using two dimensional finite element analysis. The property gradient direction is parallel to the crack line and loading is constrained to be symmetric such that a pure mode I situation is achieved. The extent of dominance of asymptotic fields is evaluated by comparing the stress field calculated from the finite element analysis to that calculated by asymptotic equations. Two separate forms of the asymptotic stress fields, one for homogeneous materials and another for continuously nonhomogeneous materials are used. The shape and extent of the dominance regions of each asymptotic field and their dependence on crack length and material nonhomogeneity is also presented. Under the pure mode I conditions considered here, it is seen that both asymptotic fields exist around the crack tip with the one for homogeneous materials in general being embedded in the one for continuously nonhomogeneous materials. The ligament length is seen to primarily control the extent of development of the asymptotic stress field for nonhomogeneous materials. The steepness of the material gradient affects the relationship between the two asymptotic stress fields and therefore the extent of their dominance.
机译:使用二维有限元分析计算弹性功能梯度板中边缘裂纹周围的应力场。特性梯度方向平行于裂纹线,并且载荷被限制为对称,从而实现了纯模式I的情况。通过将有限元分析计算出的应力场与渐近方程计算出的应力场进行比较,可以评估渐近场的优势程度。使用两种独立形式的渐进应力场,一种用于均质材料,另一种用于连续非均质材料。还介绍了每个渐近场的优势区域的形状和范围,以及它们对裂纹长度和材料非均质性的依赖性。在这里考虑的纯模式I条件下,可以看到裂纹尖端周围存在两个渐近场,其中一个用于均质材料的区域通常嵌入在一个用于连续非均质材料的区域中。可以看到,韧带长度主要控制非均质材料渐近应力场的发展程度。材料梯度的陡度会影响两个渐近应力场之间的关系,从而影响其主导程度。

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