Department of Materials Science & Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA.
Paulson School of Engineering & Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
Phys Rev E. 2017 May;95(5-1):053001. doi: 10.1103/PhysRevE.95.053001. Epub 2017 May 5.
The primary mode of failure in disordered solids results from the formation and persistence of highly localized regions of large plastic strains known as shear bands. Continuum-level field theories capable of predicting this mechanical response rely upon an accurate representation of the initial and evolving states of the amorphous structure. We perform molecular dynamics simulations of a metallic glass and propose a methodology for coarse graining discrete, atomistic quantities, such as the potential energies of the elemental constituents. A strain criterion is established and used to distinguish the coarse-grained degrees-of-freedom inside the emerging shear band from those of the surrounding material. A signal-to-noise ratio provides a means of evaluating the strength of the signal of the shear band as a function of the coarse graining. Finally, we investigate the effect of different coarse graining length scales by comparing a two-dimensional, numerical implementation of the effective-temperature description in the shear transformation zone (STZ) theory with direct molecular dynamics simulations. These comparisons indicate the coarse graining length scale has a lower bound, above which there is a high level of agreement between the atomistics and the STZ theory, and below which the concept of effective temperature breaks down.
无序固体的主要失效模式是由于形成和持续存在高度局部化的大塑性应变区域，称为剪切带。能够预测这种力学响应的连续场理论依赖于对非晶态结构的初始和演化状态的准确表示。我们对金属玻璃进行了分子动力学模拟，并提出了一种将离散的原子量（如元素成分的势能）进行粗粒化的方法。建立了应变判据，并用于区分新形成的剪切带内的粗粒化自由度与周围材料的自由度。信噪比为评估剪切带信号强度提供了一种方法，作为粗粒化的函数。最后，我们通过将剪切转变区（STZ）理论的有效温度描述的二维数值实现与直接分子动力学模拟进行比较，研究了不同粗粒化长度尺度的影响。这些比较表明，粗粒化长度尺度有一个下限，在该下限以上，原子论和 STZ 理论之间有很高的一致性，在该下限以下，有效温度的概念就失效了。
