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

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 [Haxton and Liu, PRL 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.Comment: 10 pages, 13 figures, corrected typos, added section on rate strengthening vs. rate weakening material

The yielding dynamics of a colloidal gel

Attractive colloidal gels display a solid-to-fluid transition as shear stresses above the yield stress are applied. This shear-induced transition is involved in virtually any application of colloidal gels. It is also crucial for controlling material properties. Still, in spite of its ubiquity, the yielding transition is far from understood, mainly because rheological measurements are spatially averaged over the whole sample. Here, the instrumentation of creep and oscillatory shear experiments with high-frequency ultrasound opens new routes to observing the local dynamics of opaque attractive colloidal gels. The transition proceeds from the cell walls and heterogeneously fluidizes the whole sample with a characteristic time whose variations with applied stress suggest the existence of an energy barrier linked to the gelation process. The present results provide new test grounds for computer simulations and theoretical calculations in the attempt to better understand the yielding transition. The versatility of the technique should also allow extensive mesoscopic studies of rupture mechanisms in soft solids ranging from crystals to glassy materials.Comment: 8 pages, 5 figure

Steady-state, effective-temperature dynamics in a glassy material

We present an STZ-based analysis of numerical simulations by Haxton and Liu (HL). The extensive HL data sharply test the basic assumptions of the STZ theory, especially the central role played by the effective disorder temperature as a dynamical state variable. We find that the theory survives these tests, and that the HL data provide important and interesting constraints on some of its specific ingredients. Our most surprising conclusion is that, when driven at various constant shear rates in the low-temperature glassy state, the HL system exhibits a classic glass transition, including super-Arrhenius behavior, as a function of the effective temperature.Comment: 9 pages, 6 figure

Thermal weakening friction during seismic slip experiments and models with heat sources and sinks

Experiments that systematically explore rock friction under crustal earthquake conditions reveal that faults undergo abrupt dynamic weakening. Processes related to heating and weakening of fault surfaces have been invoked to explain pronounced velocity weakening. Both contact asperity temperature Ta and background temperature T of the slip zone evolve significantly during high-velocity slip due to heat sources (frictional work), heat sinks (e.g., latent heat of decomposition processes), and diffusion. Using carefully calibrated High-Velocity Rotary Friction experiments, we test the compatibility of thermal weakening models: (1) a model of friction based only on T in an extremely simplified, Arrhenius-like thermal dependence; (2) a flash heating model which accounts for the evolution of both V and T; (3) same but including heat sinks in the thermal balance; and (4) same but including the thermal dependence of diffusivity and heat capacity. All models reflect the experimental results but model (1) results in unrealistically low temperatures and model (2) reproduces the restrengthening phase only by modifying the parameters for each experimental condition. The presence of dissipative heat sinks in stage (3) significantly affects T and reflects on the friction, allowing a better joint fit of the initial weakening and final strength recovery across a range of experiments. Temperature is significantly altered by thermal dependence of (4). However, similar results can be obtained by (3) and (4) by adjusting the energy sinks. To compute temperature in this type of problem, we compare the efficiency of three different numerical approximations (finite difference, wavenumber summation, and discrete integral)