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

Strain localization in a shear transformation zone model for amorphous solids

We model a sheared disordered solid using the theory of Shear Transformation Zones (STZs). In this mean-field continuum model the density of zones is governed by an effective temperature that approaches a steady state value as energy is dissipated. We compare the STZ model to simulations by Shi, et al.(Phys. Rev. Lett. 98 185505 2007), finding that the model generates solutions that fit the data,exhibit strain localization, and capture important features of the localization process. We show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization. By estimating the effects of these interactions, we derive a criterion that determines which materials exhibit shear bands based on the initial conditions alone. We also show that the shear band width is not set by an inherent diffusion length scale but instead by a dynamical scale that depends on the imposed strain rate.Comment: 8 figures, references added, typos correcte

Spontaneous thermal runaway as an ultimate failure mechanism of materials

The first theoretical estimate of the shear strength of a perfect crystal was given by Frenkel [Z. Phys. 37, 572 (1926)]. He assumed that as slip occurred, two rigid atomic rows in the crystal would move over each other along a slip plane. Based on this simple model, Frenkel derived the ultimate shear strength to be about one tenth of the shear modulus. Here we present a theoretical study showing that catastrophic material failure may occur below Frenkel's ultimate limit as a result of thermal runaway. We demonstrate that the condition for thermal runaway to occur is controlled by only two dimensionless variables and, based on the thermal runaway failure mechanism, we calculate the maximum shear strength $\sigma_c$ of viscoelastic materials. Moreover, during the thermal runaway process, the magnitude of strain and temperature progressively localize in space producing a narrow region of highly deformed material, i.e. a shear band. We then demonstrate the relevance of this new concept for material failure known to occur at scales ranging from nanometers to kilometers.Comment: 4 pages, 3 figures. Eq. (6) and Fig. 2a corrected; added references; improved quality of figure

Hay Quality Sensory Evaluation Form - Timothy; Export & Horse

Hay Quality Sensory Evaluation Form – Timothy; Export & Hors

Hay Quality Sensory Evaluation Form - Cereal

Hay Quality Sensory Evaluation Form – Cerea

Hay Quality Sensory Evaluation Form - Mixed Cereal/Pea or Vetch

Hay Quality Sensory Evaluation Form – Mixed Cereal/Pea or Vetc

Further biembeddings of twofold triple systems

We construct face two-colourable triangulations of the graph 2Kn in an orientable surface; equivalently biembeddings of two twofold triple systems of order n, for all n ξ 16 or 28 (mod 48). The biembeddings come from index 1 current graphs lifted under a group ℤn/4 × 4

Distributive and anti-distributive Mendelsohn triple systems

We prove that the existence spectrum of Mendelsohn triple systems whose associated quasigroups satisfy distributivity corresponds to the Loeschian numbers, and provide some enumeration results. We do this by considering a description of the quasigroups in terms of commutative Moufang loops. In addition we provide constructions of Mendelsohn quasigroups that fail distributivity for as many combinations of elements as possible. These systems are analogues of Hall triple systems and anti-mitre Steiner triple systems respectively