Rate-dependent shear bands in a shear-transformation-zone model of amorphous solids

Abstract

We use shear transformation zone (STZ) theory to develop a deformation map for amorphous solids as a function of the imposed shear rate and initial material preparation. The STZ formulation incorporates recent simulation results [T. K. Haxton and A. J. Liu, Phys. Rev. Lett. 99, 195701 (2007)] showing that the steady state effective temperature is rate dependent. The resulting model predicts a wide range of deformation behavior as a function of the initial conditions, including homogeneous deformation, broad shear bands, extremely thin shear bands, and the onset of material failure. In particular, the STZ model predicts homogeneous deformation for shorter quench times and lower strain rates, and inhomogeneous deformation for longer quench times and higher strain rates. The location of the transition between homogeneous and inhomogeneous flow on the deformation map is determined in part by the steady state effective temperature, which is likely material dependent. This model also suggests that material failure occurs due to a runaway feedback between shear heating and the local disorder, and provides an explanation for the thickness of shear bands near the onset of material failure. We find that this model, which resolves dynamics within a sheared material interface, predicts that the stress weakens with strain much more rapidly than a similar model which uses a single state variable to specify internal dynamics on the interface.

Fragmentation and shear band formation by slow compression of brittle porous media

“…The spontaneous emergence of the shear band and its position, orientation, and structure are all important characteristics of the compressive failure of heterogeneous, disordered, or amorphous materials [1][2][3][4][5]25]. Since localization is preceded by random microcracking, the algorithmic determination of the position of the shear band is rather complex in DEM simulations.…”

“…They can also occur by locally brittle failure in disordered granular media such as concrete, ice, rock, and some ceramics, where the microscopic failure mechanism involves tensile or shear fracture [4,5]. In particular, natural faults and localized shear bands in brittle porous media often contain a loose aggregate of fragments known as a "fault gouge."…”

Structure in sheared supercooled liquids: Dynamical rearrangements of an effective system of icosahedra

“…Some suggested mechanisms for the formation of shear bands are via the percolation of STZs [39,50] or from high stress localization in inherent defects or voids in the system [51]. Shearing has also been shown to increase the energy of soft glassy materials, called rejuvenation [52,53], and varying the shear rate can yield systems with different effective temperatures [54][55][56]. That is, increasing (decreasing) the shear rate is akin to increasing (decreasing) the temperature of the system.…”

Simulations of a stretching bar using a plasticity model from the shear transformation zone theory

“…Manning et al [9,10] have simulated a variety of models to investigate shear-localization in a one-dimensional model, compared with analytic results. Pechenik [11] has derived a multi-dimensional elastoplastic model, and a two-dimensional model has been developed to study the necking instability in a stretched bar [12].…”