Bands, shear

Given that a shear band has formed in isotropic material under uniaxial conditions, a simple analysis is available to predict the angle at which it occurs with respect to the 

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Fig. 11. Scanning electron micrograph showing the intersection of primary shear bands with the glassy ribbon surface produced by simple bending.

A ubiquitous feature accompanying large deformations in inelastic materials is the appearance of various instabilities. For example, plastic deformation may lead to shear banding, and the development of damage frequently leads to the formation of fault zones. As remarked in Section 5.2.7, normality conditions derived from the work assumption may imply stability which is too strong for such cases. Physical instabilities are likely to be associated with loss of normality and violation of the work assumption. 

Two examples of path-dependent micromechanical effects are models of Swegle and Grady [13] for thermal trapping in shear bands and Follansbee and Kocks [14] for path-dependent evolution of the mechanical threshold stress in copper. 

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. 

This is the approximation used in (7.53). Assume that the volumetric strain e is a function of t only i.e., that its spatial variation is negligible over the dimensions of the shear band. 

The thermal diffusivity for aluminum is = 5.2 x 10 m s [50]. Use this value to determine the time necessary for substantial temperature change over the length scale of 10 following creation of shear bands in the shock front. Should the temperature evolution of the shear band be included in a constitutive description on time scales of compression and release ... 

J.W. Swegle and D.E. Grady, Calculation of Thermal Trapping in Shear Bands, in Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena (edited by L.E. Murr, K.P. Staudhammer, and M.A. Meyers), Marcel Dekker, New York, 1986, pp. 705-722. 

When crazing limits the ductility in tension, large plastic strains may still be possible in compression shear banding (Fig. 23.12). Within each band a finite shear has taken place. As the number of bands increases, the total overall strain accumulates. 

Fig. 23.12. Shear banding, an alternative form of polymer plasticity which appears in compression.

Friedrich, K. Crazes and Shear Bands in Semi-Crystalline Thermoplastics. Vol. 52/53, pp. 225-274. 

Michelin s new innovation tweel is a single unit consisting of four pieces hub, PU spokes, a shear band surrounding the spokes, and tread band. TweeTs hub functions as it would in a normal wheel. 

Shear-banded Flow in Wormlike Micelle Solutions... 

Banding effects have also been seen in these wormlike micelle materials via optical birefringence [31, 32], although it is not clear that birefringence banding necessarily corresponds to shear banding [33], Of course, the anisotropy of bi-... 

Fig. 2.8.11 Schematic constitutive relationship (shear stress versus shear rate) for a wormlike micelle system exhibiting constitutive instability. When the average shear rate exceeds yc the fluid subdivides into two coexisting shear bands residing on stable branches of the constitutive relationship.

One characteristic of shear banded flow is the presence of fluctuations in the flow field. Such fluctuations also occur in some glassy colloidal materials at colloid volume fractions close to the glass transition. One such system is the soft gel formed by crowded monodisperse multiarm (122) star 1,4-polybutadienes in decane. Using NMR velocimetry Holmes et al. [23] found evidence for fluctuations in the flow behavior across the gap of a wide gap concentric cylindrical Couette device, in association with a degree of apparent slip at the inner wall. The timescale of these fluctuations appeared to be rapid (with respect to the measurement time per shear rate in the flow curve), in the order of tens to hundreds of milliseconds. As a result, the velocity distributions, measured at different points across the cell, exhibited bimodal behavior, as apparent in Figure 2.8.13. These workers interpreted their data... 

Shear-banded Flow in a Semi-dilute Polymer Solution - T2 Effects... 

M. M. Britton, R. W. Mair, R. K. Lambert, P.T. Callaghan 1999, (Transition to shear banding in pipe and Couette flow of wormlike micellar solutions), /. Rheol. 43, 897. 

Plastic deformation is mediated at the atomic level by the motion of dislocations. These are not particles. They are lines. As they move, they lengthen (i.e., they are not conserved). Therefore their total length increases exponentially. This leads to heterogeneous shear bands and shear instability. 

Figure 2.2 Schematic shear bands (rosette) and diagonal cracks at an indentation in MgO (after Armstrong and Wu, 1978).

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. ... 

Figure 6.8 Schematic shear band in a grain surrounded by other grains. Strong concentrations of shear stress reside at each end of the glide band which has a length D (the grain diameter). The radii of curvature at the ends of the band are taken to be atomic diameters.

A. Yu. Vinogradov and V. A. Khonik, Kinetics of Shear Banding in Bulk Metallic Glasses Monitored by Acoustic Emission Measurments, Phil. Mag., 84, 2147 (2004). 

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