Yielding of glass under shear: A directed percolation transition precedes shear-band formation

Abstract

Under external mechanical loading, glassy materials, ranging from soft matter systems to metallic alloys, often respond via formation of inhomogeneous flow patterns, during yielding. These inhomogeneities can be precursors to catastrophic failure, implying that a better understanding of their underlying mechanisms could lead to the design of smarter materials. Here, extensive molecular dynamics simulations are used to reveal the emergence of heterogeneous dynamics in a binary Lennard-Jones glass, subjected to a constant strain rate. At a critical strain, this system exhibits for all considered strain rates a transition towards the formation of a percolating cluster of mobile regions. We give evidence that this transition belongs to the universality class of directed percolation. Only at low shear rates, the percolating cluster subsequently evolves into a transient (but long-lived) shear band with a diffusive growth of its width. Finally, the steady state with a homogeneous flow pattern is reached. In the steady state, percolation transitions also do occur constantly, albeit over smaller strain intervals, to maintain the stationary plastic flow in the system.

Collective nonaffine displacements in amorphous materials during large-amplitude oscillatory shear

“…We observed that the orientation of a shear band is parallel to either yz or xy planes in different samples. This is consistent with the formation of shear bands parallel or perpendicular to the shear flow direction in binary LJ glasses subjected to a constant strain rate [8]. It also should be mentioned that a discontinuous transition from a reversible dynamics to a diffusive behavior upon increasing strain amplitude resembles a first order phase transition; however, the appearance of a percolating cluster of mobile atoms in a form of a shear band is a signature of a continuous transition.…”

“…The non-equilibrium MD simulations were performed in the constant NVT ensemble, where the temperature was controlled by the dissipative particle dynamics (DPD) thermostat [39]. The DPD thermostat is based on the relative atom velocities and thus the particle dynamics is not coupled to a flow profile, and, as a result, the formation of shear bands or other flow inhomogeneities are not suppressed during deformation of the material [8,39].…”

Shear Band Formation in Amorphous Materials under Oscillatory Shear Deformation

“…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].…”

Correlations of non-affine displacements in metallic glasses through the yield transition

“…Our five calculations at 0, 50, 100, 200 and 300 K show that the system softened as temperature increased; from a yield stress of around 1.7 GPa in the athermal limit to 0.8 GPa at 300 K. )). After yield, these localized events coalesce to shear-bands, first vertical (figure 3(c), see also [27,[43][44][45]) but later horizontal ( figure 3(d)), developing a clear anisotropic structure. Note that such vertical shear-bands occurred only in some of our calculations.…”