Shear band
In solid mechanics, a shear band (or, more generally, a strain localization) is a narrow zone of intense strain due to shearing, usually of plastic nature, developing during severe deformation of ductile materials.
Initially the sample was cylindrical in shape and, since symmetry was tried to be preserved during the test, the cylindrical shape was maintained for a while during the test and the deformation was homogeneous, but at extreme loading two X-shaped shear bands had formed and the subsequent deformation was strongly localized (see also the sketch on the right of Fig.
As a consequence, localization of deformation has been the focus of an intense research activity since the middle of the 20th century.
Shear band formation is an example of a material instability, corresponding to an abrupt loss of homogeneity of deformation occurring in a solid sample subject to a loading path compatible with continued uniform deformation.
In this sense, it may be interpreted as a deformation mechanism ‘alternative’ to a trivial one and therefore a bifurcation or loss of uniqueness of a ‘perfect’ equilibrium path.
Consider an infinite body made up of a nonlinear material, quasi-statically deformed in a way that stress and strain may remain homogeneous.
Conditions are sought for the emergence of a surface of discontinuity (of unit normal vector
This condition represents the so-called 'loss of ellipticity' of the differential equations governing the rate equilibrium.
[14] Moreover, great progresses have been made on numerical simulations,[15][16][17][18] so that shear band nucleation and propagation in relatively complex situations can be traced numerically with finite element models, although still at the cost of a great computational effort.
Of further interest are simulations that reveal the crystallographic orientation dependence of shear banding in single crystal and polycrystals.
The stacking fault energy plays an important role for the prevailing mechanisms of plastic deformation and the resultant textures.
In contrast, in Cu–30 wt.% Zn (alpha-brass) and related metals and alloys with low SFE, mechanical twinning and shear banding occur together with dislocation glide as main deformation carriers, particularly at large plastic deformations.
In either case non-crystallographic shear banding plays an essential role for the specific type of deformation texture evolved.
In particular, an infinite, incompressible, nonlinear elastic material, homogeneously deformed under the plane strain condition can be perturbed through superposition of concentrated forces or by the presence of cracks or rigid line inclusions.
It has been shown that, when the unperturbed state is taken close to the localization condition (4), the perturbed fields self-arrange in the form of localized fields, taking extreme values in the neighbourhood of the introduced perturbation and focussed along the shear bands directions.
[24] Within the perturbative approach, an incremental model for a shear band of finite length has been introduced[25] prescribing the following conditions along its surface: Employing this model, the following main features of shear banding have been demonstrated:
