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首页> 外文期刊>Proceedings of the National Academy of Sciences of the United States of America >Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics
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Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

机译：基于原子断裂力学的准脆性结构强度和寿命概率分布的标度

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The failure probability of engineering structures such as aircraft, bridges, dams, nuclear structures, and ships, as well as microelectronic components and medical implants, must be kept extremely low, typically <10~(-6). The safety factors needed to ensure it have so far been assessed empirically. For perfectly ductile and perfectly brittle structures, the empirical approach is sufficient because the cumulative distribution function (cdf) of random material strength is known and fixed. However, such an approach is insufficient for structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared with the structure size. The reason is that the strength cdf of quasibrittle structure varies from Gaussian to Weibullian as the structure size increases. In this article, a recently proposed theory for the strength cdf of quasibrittle structure is refined by deriving it from fracture mechanics of nanocracks propagating by small, activation-energy-controlled, random jumps through the atomic lattice. This refinement also provides a plausible physical justification of the power law for subcritical creep crack growth, hitherto considered empirical. The theory is further extended to predict the cdf of structural lifetime at constant load, which is shown to be size- and geometry-dependent. The size effects on structure strength and lifetime are shown to be related and the latter to be much stronger. The theory fits previously unexplained deviations of experimental strength and lifetime histograms from the Weibull distribution. Finally, a boundary layer method for numerical calculation of the cdf of structural strength and lifetime is outlined.
机译：工程结构（例如飞机，桥梁，水坝，核结构和轮船，以及微电子部件和医疗植入物）的失效概率必须保持极低，通常<10〜（-6）。到目前为止，已通过经验评估了确保它所需的安全系数。对于完全延展性和完全脆性的结构，经验方法就足够了，因为随机材料强度的累积分布函数（cdf）是已知的并且是固定的。然而，这种方法对于由准脆性材料组成的结构是不够的，准脆性材料是具有不均匀性的脆性材料，与结构尺寸相比，不均匀性是不可忽略的。原因是，随着结构尺寸的增加，准脆性结构的强度cdf从高斯到魏布尔连。在本文中，拟议的准脆性结构的强度cdf的理论是通过从纳米裂纹的断裂力学中衍生而来的，该理论是通过由活化能控制的，随机的小跃迁通过原子晶格传播而来的。这种改进还为亚临界蠕变裂纹扩展（迄今为止被认为是经验性的）的幂律提供了合理的物理证明。进一步扩展了该理论，以预测在恒定载荷下结构寿命的cdf，这表明尺寸和几何形状相关。尺寸对结构强度和寿命的影响是相关的，后者要强得多。该理论适合先前无法解释的实验强度和寿命直方图与Weibull分布的偏差。最后，概述了一种边界层方法，用于数值计算结构强度和寿命的cdf。

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