[论文解读] Yielding, shear banding and brittle failure of amorphous materials

Suzanne M. Fielding, Fielding, Suzanne M|arXiv (Cornell University)|Mar 11, 2021

Metallic Glasses and Amorphous Alloys被引用 4

一句话总结

本研究提出了一套理论框架，用于预测在缓慢剪切下无热非晶材料的延性或脆性屈服行为，采用介观格点弹塑性模型。研究识别出一个两阶段失效过程：首先是应变不均匀性缓慢累积的预失效阶段，随后是通过协同塑性事件传播的灾难性剪切带，其应变不均匀性和失效应变分布具有精确的解析表达式，依赖于退火处理和样品尺寸。

ABSTRACT

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.

研究动机与目标

• 确定非晶材料以延性或脆性方式屈服的条件，特别是其作为样品退火和尺寸的函数。
• 理解导致灾难性失效的动力学序列，重点关注应变不均匀性和剪切带形核的作用。
• 推导预失效阶段应变不均匀性增长的解析精确表达式。
• 根据样品尺寸和本征无序性（退火水平）预测失效应变的概率分布。

提出的方法

• 使用最小化的介观格点弹塑性模型模拟缓慢剪切的无热非晶材料。
• 施加周期性边界条件以隔离剪切带的均匀形核，排除表面缺陷的影响。
• 采用Eshelby传播器来模拟屈服单元之间的弹性应力传递。
• 利用宏观应力-应变曲线和系统尺寸，推导出应变不均匀性增长的精确解析表达式。
• 通过大量模拟验证不同退火水平和系统尺寸下的解析预测。
• 分析塑性事件的协同动力学，以解释剪切带的形核与传播。

实验结果

研究问题

• RQ1 在何种条件下，给定的非晶材料表现出延性或脆性屈服？
• RQ2 样品尺寸如何影响其从延性到脆性行为的转变，特别是在退火不良的材料中？
• RQ3 预失效阶段的本质是什么？应变不均匀性在灾难性失效前如何演化？
• RQ4 剪切带通过何种机制在样品中形核并传播？
• RQ5 能否从可测量的宏观特性与材料无序性预测失效应变的分布？

主要发现

• 高度退火的样品在所有系统尺寸下均表现出脆性屈服，而退火不良的样品则随样品尺寸增大，表现出从延性到脆性屈服的尺寸依赖性转变。
• 屈服过程分为两个阶段：预失效阶段为应变不均匀性缓慢增长，随后通过传播的剪切带发生快速灾难性失效。
• 推导出应变不均匀性增长的精确解析表达式，仅依赖于宏观应力-应变曲线和样品尺寸，与模拟数据高度一致。
• 剪切带形核源于局部塑性事件之间协同性的出现，通过弹性应力传递在一条线上形成连通链。
• 基于样品尺寸和退火水平（无序性）预测了失效应变的概率分布，为早期失效预测提供了潜在途径。
• 该模型预测更强烈退火的样品应在更小的系统尺寸下表现出脆性屈服，这一可检验假设已由近期分子模拟结果证实。