断裂强度：应力集中、极值统计和威布尔分布的命运
Fracture strength: Stress concentration, extreme value statistics and the fate of the Weibull distribution
摘要：
材料的断裂强度分布通常用威布尔定律来描述，如果忽略弹性相互作用，威布尔定律可以通过极值统计来推导。在这里，我们考虑明确的弹性和无序之间的相互作用，并通过数值模拟的二维随机引信模型的威布尔分布的渐近有效性进行测试。即使当局部断裂强度遵循威布尔分布时，全局失效分布也由裂纹尖端的应力增强决定，并且有时偏离威布尔定律。只有在裂纹宽度为幂律分布的情况下，我们才发现破坏强度服从威布尔分布。与传统的假设相反，即使在这种情况下，威布尔指数也不能简单地从初始裂纹宽度分布的指数推断。因此，我们的研究结果提出了一些关注的Weibull分布在大多数实际情况下的适用性。
英文摘要：
The fracture strength distribution of materials is often described in terms of the Weibull law which can be derived by using extreme value statistics if elastic interactions are ignored. Here, we consider explicitly the interplay between elasticity and disorder and test the asymptotic validity of the Weibull distribution through numerical simulations of the two-dimensional random fuse model. Even when the local fracture strength follows the Weibull distribution, the global failure distribution is dictated by stress enhancement at the tip of the cracks and sometimes deviates from the Weibull law. Only in the case of a pre-existing power law distribution of crack widths do we find that the failure strength is Weibull distributed. Contrary to conventional assumptions, even in this case, the Weibull exponent can not be simply inferred from the exponent of the initial crack width distribution. Our results thus raise some concerns on the applicability of the Weibull distribution in most practical cases.
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