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Shear banding characterization of Zr_64.13Cu_15.75Ni_10.12Al₁₀ and Zr₆₅Cu₁₅Ni₁₀Al₁₀ bulk metallic glasses (BMGs) with significant difference in inherent plasticity and quite similar chemical composition was studied by depth sensitive macroindentaion tests with conical indenter. Well-developed shear band pattern can be found for both BMGs after indentation. Distinct difference in the shear band spacing, scale of plastic deformation region and the shear band branching in the two BMGs account for the different plasticity.

Continuum models for granular flow generally give rise to systems of nonlinear partial differential equations that are linearly ill-posed. In this paper we introduce discreteness into an elastoplasticity model for granular flow by approximating spatial derivatives with finite differences. The resulting ordinary differential equations have bounded solutions for all time, a consequence of both discreteness and nonlinearity.

We study how the large-time behavior of solutions in this model depends on an elastic shear modulus ℰ. For large and moderate values of ℰ, the model has stable steady-state solutions with uniform shearing except for one shear band; almost all solutions tend to one of these as t→∞. However, when ℰ becomes sufficiently small, the single-shear-band solutions lose stability through a Hopf bifurcation. The value of ℰ at the bifurcation point is proportional to the ratio of the mesh size to the macroscopic length scale. These conclusions are established analytically through a careful estimation of the eigenvalues. In numerical simulations we find that: (i) after stability is lost, time-periodic solutions appear, containing both elastic and plastic waves, and (ii) the bifurcation diagram representing these solutions exhibits bi-stability.

The initiation and steady-state dynamics of granular shear flow are investigated experimentally in a Couette geometry with independently moveable outer and inner cylinders. The motion of particles on the top surface is analyzed using fast imaging. During steady state rotation of both cylinders at different rates, a shear band develops close to the inner cylinder for all combinations of speeds of each cylinder we investigated. Experiments on flow initiation were carried out with one of the cylinders fixed. When the inner cylinder is stopped and restarted after a lag time of seconds to minutes in the same direction, a shear band develops immediately. When the inner cylinder is restarted in the opposite direction, shear initially spans the whole material, i.e. particles far from the shear surface are moving significantly more than in steady state.

An overview of modeling arbitrary discontinuities within the numerical manifold method (NMM) framework is presented. The NMM employs a dual cover system, namely mathematical covers (MCs) and physical covers (PCs), to describe a physical problem. MCs are constructed totally independent of geometries of the problem domain, over which a partition of unity is defined. PCs are the intersections of MCs and the problem domain, over which local approximations with unknowns to be determined are defined. With such a dual cover system, arbitrary discontinuities involving jumps, kinks, singularities, and other nonsmooth features can be modeled in a convenient manner by constructing special PCs and designing tailored local approximations. Several typical discontinuities in solid mechanics are discussed. Among them are the simulations of material boundaries, voids, brittle cracks, cohesive cracks, material interfaces, interface cracks, dislocations, shear bands, high gradient zones, etc.

We study the failure mode transition in double-notched and single-notched steel plates under impact loading. For low impact velocities, brittle crack growths is observed while shear bands occur when the speed of the impactor is increased. We employ the meshless reproducing Kernel particle method (RKPM) that is well suited for problems involving large deformation and localization. The key feature of the proposed methodology is that it (1) treats brittle and ductile failure in the same manner and (2) employs the same constitutive model and failure criterion for both brittle and ductile failure. Therefore, cracks and shear bands are both treated as strong discontinuity in the context of the RKPM. Material stability analysis performed at every sampling point determines automatically the failure mode. We demonstrate the validity of the method by comparison to experimental data.

In this paper, a mechanism-based strain gradient dependent constitutive equation for two-phase particle reinforced metal matrix composites is presented. By using this strain gradient dependent constitutive equation and the linear perturbation analysis, the effect of strain gradient on adiabatic shear banding in particle reinforced metal matrix composites is investigated. The results have demonstrated that the onset of adiabatic shear banding in the composite with small particles is more prone to occur than in the composite with large particles. This result also means that high strain gradient is a strong driving force for adiabatic shear banding in metal matrix composites.

Characteristics of localized behavior of saturated soil with pore water is examined via Element-Free Galerkin (EFG) method while comparing with the FEM solutions under elasto-plastic constitutive equation. A set of weak forms of the nominal stress rate for soil skeleton and the continuity of pore water is derived for the field of finite deformation. An example problem concerning the triaxial test is dealt with where numerical difficulties are appeared in the computation. The mesh-free method provides the wellposed solution for this type of problem while overcoming the mesh dependency of the localization of the test specimen.

The initiation and steady-state dynamics of granular shear flow are investigated experimentally in a Couette geometry with independently moveable outer and inner cylinders. The motion of particles on the top surface is analyzed using fast imaging. During steady state rotation of both cylinders at different rates, a shear band develops close to the inner cylinder for all combinations of speeds of each cylinder we investigated. Experiments on flow initiation were carried out with one of the cylinders fixed. When the inner cylinder is stopped and restarted after a lag time of seconds to minutes in the same direction, a shear band develops immediately. When the inner cylinder is restarted in the opposite direction, shear initially spans the whole material, i.e. particles far from the shear surface are moving significantly more than in steady state.

The microstructure evolution of the localized shear band in a cold-rolled commercial titanium was systematically investigated by Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM). A shear band with a width of approximately 25 μm was formed in the cold-rolled titanium and the microstructure inside the shear band was mainly nanograins with average size of 70 nm after 83% cold rolling reduction. TEM observations revealed that the grain refinement inside shear band was completely via a shear deformation-induced splitting and breaking-down of twin lamellae process.

In sheet fine-blanking process, severe plastic deformation localized in a narrow shear band near blanking clearance, and ductile fracture present at the final stage. Since the combinations of large nonlinear strain localization, displacement discontinuity and ductile fracture, a new ductile fracture initiation criterion model and elasto-plastic FEM are used to simulate localized severe plastic deformation. The distributions and developing trends of effective strain and damage are investgated, and an experiment also performed to research the forming mechanism and process parameters.