Localized shear bands

Shear bands can be either localized or diffuse. In the case of localized shear bands, they develop at about 45° to the tensile direction, which corresponds to the maximum shear stress direction (see Fig. 1.48 in Part II). Thicker shear bands are usually constituted of a set of microshear bands. The interface between the bulk and the shear bands is diffuse and up to some 100 nm wide. The molecular micromechanism is stretching and gliding. The patterns of crossed shear bands as well as the broad shear bands are visible macroscopically in the tensile bars as short necking zones or longer cold-drawing zones. 

So, for given strain rate s and v (a function of the applied shear stress in the shock front), the rate of mixing that occurs is enhanced by the factor djhy due to strain localization and thermal trapping. This effect is in addition to the greater local temperatures achieved in the shear band (Fig. 7.14). Thus we see in a qualitative way how micromechanical defects can enhance solid-state reactivity. 

In the unstrained material far from the center of an indentation, dislocations can move freely at much lower stresses than in the material near the center where the stress (and the deformation) is much larger. Thus, local plastic shear bands can form at the edges of the indenter, and do (Chaudhri, 2004). The lengths of these shear bands are often several times the size of an indentation. The leading dislocations in these bands move in virgin (undeformed) material, so they can move at lower stresses than the dislocations in the strain-hardened material near the center of an indentation.. The patterns they form are called rosettes. ... 

These theoretical calculations predict that the generation of a porous morphology leads to a decrease in modulus and yield strength, and are in good agreement with experimental data. Furthermore, the calculation of stress distribution, which takes into account the interaction of randomly dispersed voids, predicts the buildup of local stress concentrations which in turn can initiate shear banding. 

Shear yielding in the form of a quasi-homogeneous,bulk process can contribute substantially to the crack resistance of a polymeric solid. On the other hand, however, localized shear yielding in the form of shear micro-bands is befleved to be a precursor of brittle fracture in many semicrystalline and glassy thermoplas-... 

The explanation of the effect of secondary inclusions on the delocalization of shear banding is based on the concept of modification of the local stress fields and achieving favorable distribution of stress concentrations in the matrix due to presence of inclusions. This leads to a reduction in the external load needed to initiate plastic deformation over a large volume of the polymer. As a result, plastically deformed matter is formed at the crack tip effectively reducing the crack driving force. Above approximately 20 vol% of the elastomer inclusions. 

A flaw may be considered active if its stress concentration factor gives rise to local conditions suitable for craze, shear band, or failure initiation. Similarly the activity of the flaw spectrum may be considered as the collective fraction of all flaws that are active for a given set of conditions. The activity (or active fraction of flaws) depends on the external state of stress or strain and on sample orientation or anisotropy... 

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