Emergence Of Shear Bands Research Articles

Grain size-dependent mechanical response of metal nitride coating under nanoindentation and its sand erosion performance

In this paper, TiN coatings with grain sizes of 54.8 nm, 68.8 nm, 91.5 nm and 136.9 nm was prepared on the aluminum alloy by extending the coating deposition duration. The mechanical performance under nanoindentation and sand erosion were evaluated. The results show that there is a positive correlation between the hardness of the TiN coating and the grain size. Under the shear stress, the primary mechanism governing the mechanical behavior of the TiN coating is grain boundary sliding when the grain size is less than 70 nm. However, when the grain size surpasses 90 nm, the mechanical response shifts towards the emergence of shear bands and lateral cracks. During nanoindentation loading, TiN coatings with different grain size shows amorphous transformation. Sand erosion experiments demonstrate that refining the grain structure enhances the coordination capability of the TiN coating during plastic deformation, leading to a substantial increase in the amount of sand needed to initiate coating cracks. Simultaneously, the augmentation in the quantity of grain boundaries enhances the TiN coating's capacity for coordinating during plastic deformation, ultimately bolstering its resistance to crack propagation and erosion.

Pattern transitions of localized deformation in high-porosity sandstones: Insights from multiscale analysis

We employ a hierarchical multiscale modeling approach to investigate the transitions of localized deformation patterns in high-porosity sandstone subjected to sustained shear to understand their underlying physics. The multiscale approach is based on hierarchical coupling between finite element method (FEM) with discrete element method (DEM) to offer cross-scale predictions for granular rocks without assuming phenomenological constitutive relations. Our simulations show that when a high-porosity sandstone specimen is subjected to continuous deviatoric loading, compaction bands may occur and evolve, featuring a steady movement of the compaction front (i.e. the boundary between the compaction band and the rest uncompacted zone). The specimen reaches a homogeneous state of reduced porosity when the compaction fronts traverse the entire specimen. A re-hardening response is initiated in the specimen under further shear, which is followed by a shearing dominating stage with the emergence of shear bands. The material responses inside the ultimate shear bands approach a “steady state” of constant porosity and stress ratio. Cross-scale analyses reveal that debonding and pore collapse are dominant mechanisms for the compaction stage of the specimen, and debonding and particle rotation dictate the physics for the shear banding stage. The transitions from compaction to shear banding occurs due to the degradation of the cohesive contact network and significant reduction in porosity. There are limited number of interparticle bonds remaining at the “steady state” under sustained shear, with a preferential direction perpendicular to the loading direction, leading to a higher steady void ratio than the critical state void ratio of non-cohesive sand.

Emergence of Shear Bands in Confined Granular Systems: Singularity of the q-Statistics.

The statistics of grain displacements probability distribution function (pdf) during the shear of a granular medium displays an unusual dependence with the shear increment upscaling as recently evinced (see “experimental validation of a nonextensive scaling law in confined granular media”). Basically, the pdf of grain displacements has clear nonextensive (q-Gaussian) features at small scales, but approaches to Gaussian characteristics at large shear window scales—the granulence effect. Here, we extend this analysis studying a larger system (more grains considered in the experimental setup), which exhibits a severe shear band fault during the macroscopic straining. We calculate the pdf of grain displacements and the dependency of the q-statistics with the shear increment. This analysis has shown a singular behavior of q at large scales, displaying a non-monotonic dependence with the shear increment. By means of an independent image analysis, we demonstrate that this singular non-monotonicity could be associated with the emergence of a shear band within the confined system. We show that the exact point where the q-value inverts its tendency coincides with the emergence of a giant percolation cluster along the system, caused by the shear band. We believe that this original approach using Statistical Mechanics tools to identify shear bands can be a very useful piece to solve the complex puzzle of the rheology of dense granular systems.

Some Aspects of Shear Yielding and Emergence of Shear Bands in Solid Polymers

Some Aspects of Shear Yielding and Emergence of Shear Bands in Solid Polymers

Arrest stress of uniformly sheared wet granular matter.

We conduct extensive independent numerical experiments considering frictionless disks without internal degrees of freedom (rotation, etc.) in two dimensions. We report here that for a large range of the packing fractions below random-close packing, all components of the stress tensor of wet granular materials remain finite in the limit of zero shear rate. This is direct evidence for a fluid-to-solid arrest transition. The offset value of the shear stress characterizes plastic deformation of the arrested state which corresponds to dynamic yield stress of the system. Based on an analytical line of argument, we propose that the mean number of capillary bridges per particle, ν, follows a nontrivial dependence on the packing fraction, ϕ, and the capillary energy, ɛ. Most noticeably, we show that ν is a generic and universal quantity which does not depend on the driving protocol. Using this universal quantity, we calculate the arrest stress, σ(a), analytically based on a balance of the energy injection rate due to the external force driving the flow and the dissipation rate accounting for the rupture of capillary bridges. The resulting prediction of σ(a) is a nonlinear function of the packing fraction, ϕ, and the capillary energy, ɛ. This formula provides an excellent, parameter-free prediction of the numerical data. Corrections to the theory for small and large packing fractions are connected to the emergence of shear bands and of contributions to the stress from repulsive particle interactions, respectively.

The formation and properties of shear bands in viscoplastic materials

Shear bands, localized regions of high strain, form in ductile materials as a result of severe plastic flow. The formation of shear bands occurs in a variety of materials; for example, polycrystalline structural metals, rocks, ductile single crystals, polymers and other solids. These shear bands may be triggered by inhomogeneities in the material or can occur in notched bars or at a crack tip in homogeneous mediums. The emergence of shear bands, often precursors to failure, can signify the possibility of further deformation. Shear bands may denote weak areas or areas of plastic flow and are accompanied by strain rates which are orders of magnitude higher than strain rates found in undeformed portions of the material. We employ an adaptive Chebyshev pseudo-spectral method for the numerical computation of shear bands in one dimension. The method allows very high resolution of the spatial structure of the band and can accurately simulate both the dynamics of band formation and the spatial structure. We consider in detail the role of imperfections on band formation and morphology and the effect of cyclic loading. Both isothermal and adiabatic shear bands are considered.

The emergence of shear bands in plane strain

In this paper, we examine the effect of a slight material imperfection on the deformation field in an otherwise homogeneous body subjected to a plane bi-axial stretch at infinity. Both hyper-elastic and hypo-elastic materials are considered, with the constitutive equations assumed to be such that the governing equilibrium equations lose ellipticity at some strain level. A straightforward regular perturbation analysis is performed and attention is focussed on the features of the first order terms. It is found that the effect of the imperfection is negligible at small values of the applied load. As the load increases, the imperfection more or less abruptly gets “activated” and causes a rapid concentration of strain within certain narrow bands—shear bands—passing through the imperfection. In order to estimate the accuracy of the linearized analysis, a finite element solution of the nonlinear problem is also carried out and results are compared.