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On shear bands in ductile materials. (English) Zbl 0625.73041
(Authors’ summary.) Spatially non-uniform solutions are found here for the field relations that govern the behaviour in shear of a class of rigid-plastic materials that have rate-independent responses and, after a certain amount of plastic flow, exhibit strain softening, i.e., a decline of yield stress with further flow. As strain softening can destabilize homogeneous configurations and result in the concentration of strain in narrow bands, the constitutive relations have been chosen to account for a possibly important influence upon the stress of the spatial variation of the accumulated strain. It is shown that for simple non-steady shearing flows, the shear strain, as a function of time and position, can be expressed in terms of easily evaluated elliptic functions. The theory yields strain fields showing shear bands that are remarkably similar to those observed in ballistic tests of metals under conditions in which inertial forces are negligile but the combined effects of adiabatic heating and thermal softening result in apparent strain softening. Although quantitative comparison with observation is not yet possible, it is expected that the theory will be applicable to slow deformations of geological materials that are ductile at elevated pressures and temperatures and are often softer after flowing as the result of an accumulation of internal damage with deformation.
Reviewer: M.N.L.Narasimhan

MSC:
74C99 Plastic materials, materials of stress-rate and internal-variable type
74R99 Fracture and damage
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