Pure shear

About: Pure shear is a research topic. Over the lifetime, 3285 publications have been published within this topic receiving 93198 citations.

XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals

Abstract: Relations between the elastic and plastic properties of pure polycrystalline metals are discussed and a systematic relation between shear modulus, Burgers vector and plastic shear strength of metals possessing the same lattice structure is proposed. In addition reasons are given for believing that in a limited temperature range malleability is related to Poisson's ratio.

Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber

Abstract: It is shown in this part how the theory of large elastic deformations of incompressible isotropic materials, developed in previous parts, can be used to interpret the load-deformation curves obtained for certain simple types of deformation of vulcanized rubber test-pieces in terms of a single stored-energy function. The types of experiment described are: (i) the pure homogeneous deformation of a thin sheet of rubber in which the deformation is varied in such a manner that one of the invariants of the strain, I 1 or I 2 , is maintained constant; (ii) pure shear of a thin sheet of rubber (i.e. pure homogeneous deformation in which one of the extension ratios in the plane of the sheet is maintained at unity, while the other is varied); (iii) simultaneous simple extension and pure shear of a thin sheet (i.e. pure homogeneous deformation in which one of the extension ratios in the plane of the sheet is maintained constant at a value less than unity, while the other is varied); (iv) simple extension of a strip of rubber; (v) simple compression (i.e. simple extension in which the extension ratio is less than unity); (vi) simple torsion of a right-circular cylinder; (vii) superposed axial extension and torsion of a right-circular cylindrical rod. It is shown that the load-deformation curves in all these cases can be interpreted on the basis of the theory in terms of a stored-energy function W which is such that δ W /δ I 1 is independent of I 1 and I 2 and the ratio (δ W /δ I 2 ) (δ W /δ I 1 ) is independent of I 1 and falls, as I 2 increases, from about 0*25 at I 2 = 3.

Contact force measurements and stress-induced anisotropy in granular materials.

Abstract: Interparticle forces in granular media form an inhomogeneous distribution of filamentary force chains. Understanding such forces and their spatial correlations, specifically in response to forces at the system boundaries, represents a fundamental goal of granular mechanics. The problem is of relevance to civil engineering, geophysics and physics, being important for the understanding of jamming, shear-induced yielding and mechanical response. Here we report measurements of the normal and tangential grain-scale forces inside a two-dimensional system of photoelastic disks that are subject to pure shear and isotropic compression. Various statistical measures show the underlying differences between these two stress states. These differences appear in the distributions of normal forces (which are more rounded for compression than shear), although not in the distributions of tangential forces (which are exponential in both cases). Sheared systems show anisotropy in the distributions of both the contact network and the contact forces. Anisotropy also occurs in the spatial correlations of forces, which provide a quantitative replacement for the idea of force chains. Sheared systems have long-range correlations in the direction of force chains, whereas isotropically compressed systems have short-range correlations regardless of the direction.

Theory of Shear Banding in Metallic Glasses and Molecular Dynamics Calculations

Abstract: The aged-rejuvenation-glue-liquid (ARGL) shear band model has been proposed for metallic glasses (Acta Mater. 54 (2006) 4293), based on small-scale molecular dynamics simulations up to 20,000 atoms and thermomechanical analysis. The model predicts the existence of a critical lengthscale � 10 nm, above which melting could occur in shear-alienated glass. Large-scale molecular dynamics simulations with up to 5 million atoms have directly verified this prediction. When the applied stress exceeds the glue traction (computed separately before in a shear cohesive zone, or an amorphous-amorphous ‘‘generalized stacking fault energy’’ calculation), we indeed observe maturation of the shear band embryo into bona fide shear crack, accompanied by melting. In contrast, when the applied stress is below the glue traction, the shear band embryo does not propagate, becomes diffuse, and eventually dies. Thus this all-important quantity, the glue traction which is a property of shearalienated glass, controls the macroscopic yield point of well-aged glass. We further suggest that the disruption of chemical short-range order (‘‘chemical softening’’) governs the glue traction microscopically. Catastrophic thermal softening occurs only after chemical alienation and softening in our simulation, after the shear band embryo has already run a critical length. [doi:10.2320/matertrans.MJ200769]

Cavity formation from inclusions in ductile fracture

Abstract: The previously proposed conditions for cavity formation from equiaxed inclusions in ductile fracture have been examined. Critical local elastic energy conditions are found to be necessary but not sufficient for cavity formation. The interfacial strength must also be reached on part of the boundary. For inclusions larger than about 100A the energy condition is always satisfied when the interfacial strength is reached and cavities form by a critical interfacial stress condition. For smaller cavities the stored elastic energy is insufficient to open up interfacial cavities spontaneously. Approximate continuum analyses for extreme idealizations of matrix behavior furnish relatively close limits for the interfacial stress concentration for strain hardening matrices flowing around rigid non-yielding equiaxed inclusions. Such analyses give that in pure shear loading the maximum interfacial stress is very nearly equal to the equivalent flow stress in tension for the given state of plastic strain. Previously proposed models based on a local dissipation of deformation incompatibilities by the punching of dislocation loops lead to rather similar results for interfacial stress concentration when local plastic relaxation is allowed inside the loops. At very small volume fractions of second phase the inclusions do not interact for very substantial amounts of plastic strain. In this regime the interfacial stress is independent of inclusion size. At larger volume fractions of second phase, inclusions begin to interact after moderate amounts of plastic strain, and the interfacial stress concentration becomes dependent on second phase volume fraction. Some of the many reported instances of inclusion size effect in cavity formation can thus be satisfactorily explained by variations of volume fraction of second phase from point to point.