Strain Localization Above the Yielding Point in Cyclically Deformed Glasses

Abstract

We study the yielding behaviour of a model glass under cyclic athermal quastistatic deformation computationally, and show that yielding is characterised by the discontinuous appearance of shear bands, whose width is about ten particle diameters at their initiation, in which the strain gets localised. Strain localisation is accompanied by a corresponding change in the energies, and a decrease in the density in the shear band. We show that the glass remains well annealed outside the shear band whereas the energies correspond to the highest possible energy minima at the given density within the shear band. Diffusive motion of particles characterising the yielded state are confined to the shear bands, whose mean positions display movement over repeated cycles. Outside the shear band, particle motions are sub-diffusive but remain finite. Despite the discontinuous nature of their appearance, shear bands are reversible in the sense that a reduction in the amplitude of cyclic deformation to values below yielding leads to the healing and disappearance of the shear bands.The mechanical response of amorphous solids to applied stresses is of obvious importance in characterising their behaviour. Beyond the elastic regime at small applied stresses, such response is characterised by plastic deformations, and beyond yielding, by flow. Considerations associated with yielding are of relevance to a wide range of phenomena, from irreversible deformation and failure in atomic and molecular glasses, such as metallic glasses, to the complex rheology of soft materials such as foams, emulsions, colloidal suspensions, and granular matter [1][2][3][4][5]. Although yielding and flow may apparently be continuous and homogeneous for some yield stress fluids, it is a sharp, discontinuous event at the other end of the spectrum, as in brittle failure, characterised by localisation of strain and the formation of shear bands. Systems and questions of interest range from the mechanical properties of nanostructures to large scale phenomena such as mud-slides and earthquakes [6][7][8][9]. Viewed as a nonequilibrium transition in a driven system, the phenomena associated with yielding have in recent years been investigated in a large number of studies experimentally, through computer simulations, and the analysis of elastoplastic and other models . Many studies have focussed on the anisotropic interactions arising between localised plastic events or STZs [17,[33][34][35][36][37][38], and, in particular, how they may influence strain localisation. Yielding has been analysed through the application of STZ theory [3,14], described as a critical transition in analogy with depinning of manifolds in random media [13,19], a discontinuous transition associated with a spionodal [28,29], etc., and the relationship between these descriptions is a subject of ongoing investigations (e. g., [31,32]). The role of the degree of annealing in determining the nature of the yielding transition, and in the formation and character of shear bands, has increasingly been appr...

Embedding orthogonal memories in a colloidal gel through oscillatory shear

“…Further studies have argued that this oscillatory shear memory effect should apply to disordered systems in generalshearing causes rearrangement which continues until a reversible state is found [6][7][8]. Indeed, similar memory effects have been found in experiments and simulations of model amorphous systems [2,9,10], granular systems [11], and glasses [12][13][14][15]. The interactions between particles can vary and even the nature of the reversibility can vary for different systems [9,[16][17][18][19][20].…”

Aging and rejuvenation during elastostatic loading of amorphous alloys: A molecular dynamics simulation study

“…It should be emphasized that there is a crucial difference between rejuvenated states obtained via elastostatic loading and cyclic shear with the strain amplitude above the yield-7 ing point. In the latter case, the increase in the potential energy is directly related to the formation of a fluidized shear band [20,21,23,25], while in the former case, the plastic deformation under static stress is distributed more homogeneously in the regions with relatively low local yield stress. The next comment is regarding the structural characteristics at different energy states.…”

Shear Band Formation in Amorphous Materials under Oscillatory Shear Deformation

“…A number of recent molecular dynamics simulations studies have shown that disordered solids under cyclic loading either continue exploring deeper energy states at sufficiently small strain amplitudes or eventually undergo a transition to plastic flow within a shear band if the strain amplitude is above a certain value [18,19,24,25,28,29,33,34]. The precise determination of the critical strain amplitude, however, is a challenging problem because the number of cycles required to reach a dynamic steady state appears to diverge upon approaching the critical value [18,19].…”

“…The precise determination of the critical strain amplitude, however, is a challenging problem because the number of cycles required to reach a dynamic steady state appears to diverge upon approaching the critical value [18,19]. In addition, the estimate of the critical amplitude for binary glasses was shown to be system size [18] and temperature [17,29,33] dependent.…”