Shear planar

In most flat-plate impact experiments, the direction of motion of the impacting plate is normal to its surface, such that only a planar compressive shock is introduced into the specimen. Within the last fifteen years, however, techniques have been developed for dynamic pressure-shear loading of specimens (Abou-Sayed et al., 1976 Chhabildas and Swegle, 1980). These involve an oblique impact, as illustrated in Fig. 3.6, in which the impact surface on the... 

Samples are most frequently shock deformed under laboratory conditions utilizing either explosive or gun-launched flyer (driver) plates. Given sufficient lateral extent and assembly thickness, a sample may be shocked in a onedimensional strain manner such that the sample experiences concurrently uniaxial-strain loading and unloading. Based on the reproducibility of projectile launch velocity and impact planarity, convenience of use, and ability to perform controlled oblique impact (such as for pressure-shear studies) guns have become the method of choice for many material equation-of-state and shock-recovery studies [21], [22]. 

We first consider strain localization as discussed in Section 6.1. The material deformation action is assumed to be confined to planes that are thin in comparison to their spacing d. Let the thickness of the deformation region be given by h then the amount of local plastic shear strain in the deformation is approximately Ji djh)y, where y is the macroscale plastic shear strain in the shock process. In a planar shock wave in materials of low strength y e, where e = 1 — Po/P is the volumetric strain. On the micromechanical scale y, is accommodated by the motion of dislocations, or y, bN v(z). The average separation of mobile dislocations is simply L = Every time a disloca-... 

Assume the edge dislocation density to be divided into positive and negative populations, N+ and N, moving only on slip planes at 45° (maximum shear stress) to the planar shock front. For a dislocation multiplication (annihilation) rate M, show that conservation of dislocations requires that... 

Obviously, properties like the shear modulus might well be different for close-packed planes and cube planes, because the number of bonds attaching them per unit area is different. This is one of the reasons that it is important to have a method of describing various planar packing arrangements. 

Two alternate core structures of the ordinary 1/2[110] dislocation, shown schematically in 1 gs. 2a amd b, respectively, were obtained using different starting configurations. The core shown in Fig. 2a is planar, spread into the (111) plame, while the core shown in Fig. 2b is non-plamar, spread concomitcmtly into the (111) amd (111) plames amd thus sessile. The sessile core is energetically favored since when a shear stress parallel to the [110] direction was applied in the (111) plane the planar core transformed into the non-plamar one. However, in a similar study emplo3dng EAM type potentials (Rao, et al. 1991) it was found that the plamar core configuration is favored (Simmons, et al. 1993 Rao, et al. 1995). 

Schematic illustration of shear-plane formation. Structure (a) with aligned oxygen vacancies shears to eliminate these vacancies in favour of an extended planar defect in the cation lattice as in (b). % cations oxygen ions are at the mesh intersections...

For planar flow in a viscous fluid, frictional forces between the flow planes give rise to shear stress across the planes of the flow. For flow along x, the shear stress across an area A is... 

Flow is generally classified as shear flow and extensional flow [2]. Simple shear flow is further divided into two categories Steady and unsteady shear flow. Extensional flow also could be steady and unsteady however, it is very difficult to measure steady extensional flow. Unsteady flow conditions are quite often measured. Extensional flow differs from both steady and unsteady simple shear flows in that it is a shear free flow. In extensional flow, the volume of a fluid element must remain constant. Extensional flow can be visualized as occurring when a material is longitudinally stretched as, for example, in fibre spinning. When extension occurs in a single direction, the related flow is termed uniaxial extensional flow. Extension of polymers or fibers can occur in two directions simultaneously, and hence the flow is referred as biaxial extensional or planar extensional flow. 

Simple shear (also known as planar Couette flow) is achieved when fluid is contained between two plane parallel plates in relative in-plane motion. If the velocity direction is taken to be x, one has x = y, all other xa 3 zero and... 

This flow field is somewhat idealized, and cannot be exactly reproduced in practice. For example, near the planar surfaces, shear flow is inevitable, and, of course, the range of % and y is consequently finite, leading to boundary effects in which the extensional flow field is perturbed. Such uniaxial flow is inevitably transient because the surfaces either meet or separate to laboratory scale distances. 

The degree of deformation and whether or not a drop breaks is completely determined by Ca, p, the flow type, and the initial drop shape and orientation. If Ca is less than a critical value, Cacri the initially spherical drop is deformed into a stable ellipsoid. If Ca is greater than Cacrit, a stable drop shape does not exist, so the drop will be continually stretched until it breaks. For linear, steady flows, the critical capillary number, Cacrit, is a function of the flow type and p. Figure 14 shows the dependence of CaCTi, on p for flows between elongational flow and simple shear flow. Bentley and Leal (1986) have shown that for flows with vorticity between simple shear flow and planar elongational flow, Caen, lies between the two curves in Fig. 14. The important points to be noted from Fig. 14 are these ... 

These are shear waves. Planar waves result from stress sources of infinite dimension. In practise planar waves are considered as the sum of spherical waves. 

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