非晶材料的屈服、剪切带和脆性破坏
Yielding, shear banding and brittle failure of amorphous materials
摘要：
在自然界和技术中广泛存在的过程是由动力学转变控制的，由此最初处于固体状状态的材料然后塑性屈服。主要未解决的问题涉及任何材料是否会顺利和逐渐屈服（韧性行为）或突然和灾难性地失败（脆性行为）;样品退火，无序和剪切带形成在屈服和失败的开始中的作用;最重要的是，从实践的角度来看，任何即将发生的灾难性失败是否可以在它发生之前预测。我们解决这些问题，通过研究缓慢剪切非热非晶材料的屈服，在一个最小的介观晶格弹塑性模型。我们的贡献是四方面的。首先，我们阐明是否屈服将是韧性或脆性，对于任何给定的样品退火水平。第二，我们表明，屈服包括两个不同的阶段：一个预失效阶段，在此阶段中，小水平的应变异质性慢慢积累，其次是一个灾难性的脆性破坏事件，在此过程中，裂纹迅速传播通过合作线的塑性事件的样品。第三，我们提供了一个表达式的缓慢增长水平的应变不均匀性在破坏前的阶段，表示在宏观应力-应变曲线和样本大小，并与我们的模拟结果非常一致。第四，我们阐明的基本机制，通过该裂纹然后成核，并提供一个近似表达式的概率分布的剪切应变发生故障时，确定由一个单一的退火参数，和系统的大小方面表示的样品中固有的无序。
英文摘要：
Widespread processes in nature and technology are governed by the dynamical transition whereby a material in an initially solid-like state then yields plastically. Major unresolved questions concern whether any material will yield smoothly and gradually (ductile behaviour) or fail abruptly and catastrophically (brittle behaviour); the roles of sample annealing, disorder and shear band formation in the onset of yielding and failure; and, most importantly from a practical viewpoint, whether any impending catastrophic failure can be anticipated before it happens. We address these questions by studying the yielding of slowly sheared athermal amorphous materials, within a minimal mesoscopic lattice elastoplastic model. Our contributions are fourfold. First, we elucidate whether yielding will be ductile or brittle, for any given level of sample annealing. Second, we show that yielding comprises two distinct stages: a pre-failure stage, in which small levels of strain heterogeneity slowly accumulate, followed by a catastrophic brittle failure event, in which a crack quickly propagates across the sample via a cooperating line of plastic events. Third, we provide an expression for the slowly growing level of strain heterogeneity in the pre-failure stage, expressed in terms of the macroscopic stress-strain curve and the sample size, and in excellent agreement with our simulation results. Fourth, we elucidate the basic mechanism via which a crack then nucleates and provide an approximate expression for the probability distribution of shear strains at which failure occurs, as determined by the disorder inherent in the sample, expressed in terms of a single annealing parameter, and the system size.
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