Spatiotemporal Analysis of Nonaffine Displacements in Disordered Solids Sheared Across the Yielding Point

Abstract

The time evolution and spatial correlations of nonaffine displacements in deformed amorphous solids are investigated using molecular dynamics simulations. The three-dimensional model glass is represented via the binary mixture, which is slowly annealed well below the glass transition temperature and then sheared at a constant strain rate. It is shown that with increasing strain, the typical size of clusters of atoms with large nonaffine displacements increases, and these clusters remain spatially homogeneously distributed, until the yielding point when mobile atoms become localized within a system-spanning shear band. Furthermore, the yielding transition is associated with an abrupt change in the spatial correlation of nonaffine displacements, which varies from exponential to power-law decay. We also find that the height of the first peak in the pair correlation function of small atoms exhibits a distinct increase at the yielding strain. These results are discussed in relation to the yielding transition in amorphous materials under cyclic loading.

Shear Band Formation in Amorphous Materials under Oscillatory Shear Deformation

“…Therefore, these results demonstrate that the location of the shear band can be predicted at least several periods before the yielding transition. This is in sharp contrast to the shear band formation during the startup deformation, where the strain localization in well-annealed glasses becomes apparent only at the critical strain [14].…”

“…This definition was first introduced by Falk and Langer and used to identify accurately the location of shear transformations in strained disordered solids [40]. More recently, the spatiotemporal analysis of nonaffine displacements was applied to investigate shear band formation in steadily [12][13][14]42] and periodically [21,23,25,29,30,34] driven amorphous solids, as well as the structural relaxation in thermally cycled [43,44] and elastostatically loaded [45] glasses. Interestingly, the accumulation of atoms with large nonaffine displacements along the xy plane, shown in Fig.…”

“…It has long been recognized that localized plastic events in deformed amorphous materials involve collective rearrangements of small clusters of atoms, or shear transformations [5,6]. In recent years, the processes of shear band initiation and propagation have been extensively studied at the atomic level during startup uniaxial [7][8][9][10][11] and shear [12][13][14] deformation with a constant strain rate. While the initiation of a shear band typically occurs at a free surface during tension or compression, the transition to plastic flow in a sheared periodic domain involves the formation of a percolating cluster of mobile regions at the critical strain [12].…”

Accelerated rejuvenation in metallic glasses subjected to elastostatic compression along alternating directions

“…More recently, the appearance of clusters of atoms with relatively large nonaffine displacements was connected to rejuvenation of elastostatically loaded binary glasses [18]. In recent years, the collective rearrangements of atoms in disordered solids were also reported during steady [53][54][55][56][57] and periodic [28][29][30][31][32][33][34][35][39][40][41]43,45] deformation and thermal cycling [58][59][60].…”

Alternating Shear Orientation During Cyclic Loading Facilitates Yielding in Amorphous Materials

“…While during startup continuous shear deformation of well annealed glasses, the position of strain localization cannot be determined until the yielding strain [34], the location of a 2 shear band during time periodic deformation can be identified at least several cycles before the yielding transition [30]. Furthermore, it was previously demonstrated that mechanical annealing during small-amplitude cyclic shear can be accelerated by periodically alternating shear orientation in two or three spatial dimensions [27].…”