Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling
Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling
复制标题
DOI：
10.1016/j.jmps.2011.03.002
复制
发表时间：
2011-07-01
影响因子：
5.3
通讯作者：
Bazant, Martin Z.
中科院分区：
文献类型：
--
作者：
Le, Jia-Liang;Bazant, Zdenek P.;Bazant, Martin Z.
工程结构的设计必须考虑极低的失效概率，如10（-6），这超出了直方图测试的直接验证手段。这对于脆性或韧性材料不是问题，因为结构强度的概率分布类型是固定和已知的，使得可以从均值和方差预测尾部概率。这是一个问题，虽然，准脆性材料的强度分布类型的过渡从高斯到韦伯的结构尺寸的增加。这些是具有脆性成分的异质材料，其特征在于与结构尺寸相比不可忽略的材料不均匀性。例子包括混凝土，纤维复合材料，粗颗粒或增韧陶瓷，岩石，海冰，硬质泡沫和骨，以及许多材料中使用的纳米和微米级的设备，这项研究提出了一个统一的理论，强度和寿命为此类材料，基于激活能控制的随机跳跃的纳米裂纹前端，和纳米宏观多尺度过渡的尾部概率。本研究的第一部分涉及单调和持续（或蠕变）加载的情况下，第二部分与疲劳（或循环）加载。在材料代表体积元的尺度上，强度概率分布具有高斯核，在失效概率为10（-3）量级时，将远程威布尔尾嫁接到该高斯核上。随着结构尺寸的增加，威布尔尾进入高斯核。静态（蠕变）寿命的概率分布与静态裂纹扩展速率的强度分布有关，并给出了物理解释。目前的理论产生一个简单的关系，这个法律的指数和威布尔模量的强度和寿命。这样做的好处是，寿命分布可以预测从短期试验的平均尺寸效应的强度和测试的幂律的裂纹扩展速率。该理论与陶瓷和混凝土的强度和静态寿命的大量试验数据非常吻合，并解释了为什么它们的直方图系统地偏离威布尔标度的直线。虽然目前的统一理论是建立在以前的几个进展之上的，但这里提出了新的贡献：（i）无序纳米结构中的裂纹（如水合波特兰水泥），（ii）纤维束的尾部概率（iii）该模型收敛于高斯分布，（iv）恒定载荷下的应力-寿命曲线，以及（v）原子晶格中裂纹前沿跳跃的详细随机游走分析。在本理论中，通过最弱链路模型中链路数量的有限性捕获了非局部行为，这解释了为什么平均尺寸效应与先前制定的非局部Weibull理论相一致。脆性结构对应于本理论的大尺寸极限。一个重要的实际结论是，大型准脆性结构（例如，混凝土结构和复合机身或船体，以及各种微型装置）应当作为结构尺寸和几何形状的函数来计算。(C)2011爱思唯尔有限公司版权所有。
Engineering structures must be designed for an extremely low failure probability such as 10(-6), which is beyond the means of direct verification by histogram testing. This is not a problem for brittle or ductile materials because the type of probability distribution of structural strength is fixed and known, making it possible to predict the tail probabilities from the mean and variance. It is a problem, though, for quasibrittle materials for which the type of strength distribution transitions from Gaussian to Weibullian as the structure size increases. These are heterogeneous materials with brittle constituents, characterized by material inhomogeneities that are not negligible compared to the structure size. Examples include concrete, fiber composites, coarse-grained or toughened ceramics, rocks, sea ice, rigid foams and bone, as well as many materials used in nano- and microscale devices.This study presents a unified theory of strength and lifetime for such materials, based on activation energy controlled random jumps of the nano-crack front, and on the nano-macro multiscale transition of tail probabilities. Part I of this study deals with the case of monotonic and sustained (or creep) loading, and Part II with fatigue (or cyclic) loading. On the scale of the representative volume element of material, the probability distribution of strength has a Gaussian core onto which a remote Weibull tail is grafted at failure probability of the order of 10(-3). With increasing structure size, the Weibull tail penetrates into the Gaussian core. The probability distribution of static (creep) lifetime is related to the strength distribution by the power law for the static crack growth rate, for which a physical justification is given. The present theory yields a simple relation between the exponent of this law and the Weibull moduli for strength and lifetime. The benefit is that the lifetime distribution can be predicted from short-time tests of the mean size effect on strength and tests of the power law for the crack growth rate. The theory is shown to match closely numerous test data on strength and static lifetime of ceramics and concrete, and explains why their histograms deviate systematically from the straight line in Weibull scale.Although the present unified theory is built on several previous advances, new contributions are here made to address: (i) a crack in a disordered nano-structure (such as that of hydrated Portland cement), (ii) tail probability of a fiber bundle (or parallel coupling) model with softening elements, (iii) convergence of this model to the Gaussian distribution, (iv) the stress-life curve under constant load, and (v) a detailed random walk analysis of crack front jumps in an atomic lattice. The nonlocal behavior is captured in the present theory through the finiteness of the number of links in the weakest-link model, which explains why the mean size effect coincides with that of the previously formulated nonlocal Weibull theory. Brittle structures correspond to the large-size limit of the present theory. An important practical conclusion is that the safety factors for strength and tolerable minimum lifetime for large quasibrittle structures (e.g., concrete structures and composite airframes or ship hulls, as well as various micro-devices) should be calculated as a function of structure size and geometry. (C) 2011 Elsevier Ltd All rights reserved.