约束裂纹扩展中的普适类
Universality Classes in Constrained Crack Growth
摘要：
基于扩展的纤维束模型，我们数值研究了裂纹前缘通过一个分离一个软块和一个无限刚性块的弱平面的运动。我们发现有两种制度。在大尺度上的运动是一致的钉扎弹性线模型，我们发现一个粗糙度指数等于0.39 +/- 0.04表征它在较小的尺度上，孔的合并占主导地位的运动，而不是钉扎的裂纹前缘。我们发现一个粗糙度指数与2/3一致，这是梯度渗流值。在这些小尺度上，裂纹前缘的长度是分形的。我们确定它的分形维数为1.77 +/- 0.02，符合壳的渗滤集群，7/4。这表明，裂纹前缘是由两个普适类：在大尺度上，钉扎弹性线和小尺度上，渗透普适类。
英文摘要：
Based on an extension of the fiber bundle model we investigate numerically the motion of the crack front through a weak plane separating a soft and an infinitely stiff block. We find that there are two regimes. At large scales the motion is consistent with the pinned elastic line model and we find a roughness exponent equal to 0.39 +/- 0.04 characterizing it. At smaller scales, coalescence of holes dominates the motion rather than pinning of the crack front. We find a roughness exponent consistent with 2/3, which is the gradient percolation value. The length of the crack front is fractal on these smaller scales. We determine its fractal dimension to be 1.77 +/- 0.02, consistent with the hull of percolation clusters, 7/4. This suggests that the crack front is described by two universality classes: on large scales, the pinned elastic line one and on small scales, the percolation universality class.
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