Amorphous shear plane

Above the transition, the quiescent system forms an (idealized) glass [2, 38], whose density correlators arrest at the glass form factors fq from Fig. 10, and which exhibits a flnite elastic constant G , that describes the (zero-frequency) Hookian response of the amorphous solid to a small applied shear strain y cr = Geo/ for y 0 the plateau can be seen in Fig. 3 and for intermediate times in Fig. 12. If steady flow is imposed on the system, however, the glass melts for any arbitrarily small shear rate. Particles are freed from their cages and diffusion perpendicular to the shear plane also becomes possible. Any finite shear rate, however small, sets a finite longest relaxation time, beyond which ergodicity is restored see Figs. 1 l(b,c) and 12. 

Most amorphous solids and many crystalline ones, particularly non-metals and polymers, exhibit a Coulomb-Mohr-type (Coulomb 1773 Mohr 1900) yield criterion or plastic-shear resistance such that this resistance on the best shear plane is dependent on the normal stress acting across the plane of shear, resulting in a dependence of the type... 

Most of the solid lubricants mentioned above owe their low-Mction characteristic primarily to a lamellar or layered crystal structure (see two of them in Figure 6.1 as typical examples). When present at a sliding contact interface, these solids shear easily along their atomic shear planes and thus provide low friction. Some of the solid lubricants do not have such layered crystal structures, but in applications, they too provide very low friction and wear. For example, certain soft metals (In, Pb, Ag, Sn, etc.), PTFE, a number of solid oxides and rare earth fluorides, diamond and diamondlike carbons, etc., can also provide fairly good lubrication despite the lack of a layered crystal structure like the ones shown in Figure 6.1 [1]. In fact, diamondlike carbon films are structurally amorphous but provide some of the lowest friction and wear coefficients among all other solid materials available today [8]. 

Tphe literature is replete with examples showing that the application of hydrostatic pressure enhances the ductile behavior of strained amorphous polymers. In this paper we present a possible explanation of this effect and two experiments demonstrating the enhanced ductility of polymers under compressive shear stresses applied orthogonally to the plane of shear. 

In contrast with the Takayanagi model, which considers only extensional strains, a major deformation process involves shear in the amorphous regions. Rigid lamellae move relative to each other by a shear process in a deformable matrix. The process is activated by the resolved shear stress a sin y cosy on the lamellar surfaces, where y is the angle between the applied tensile stress o and the lamellar plane normals, which reaches a maximum value for y = 45° (see Chapter 11 for discussion of resolved shear stress in plastic deformation processes). 

Fig. 9.12. (a) Atomic force microscope image of the impression created on a Zr— 17.9Cu-14.6Ni-10Al-5Ti (atomic percent) bulk metallic glass alloy which was subjected to nanoindentation at a maximum load of 60 mN. Discontinuous shear bands encompass the indent, (b) SAD patterns showing diffraction spots which were produced by the formation of nanocrystalline particles at the indents and in the shear bands. The inset schematically shows six diffraction spots which were associated with the (111) plane of tetragonal Zr2Ni particles, (c) A small distance away from the indent only halo ring patterns characteristic of a fully amorphous structure are seen. Reproduced with permission from Kim et al. (2002). 

In an isotropic polycrystalline polymer whose microstructure consists of stacked lamellae arranged in the form of spherolites, the slip systems activated depend on the local orientation of the lamellae with respect to the applied stress and, as deformation proceeds, these orientations are modified. To calculate the evolution of the crystalline texture, one can consider the polymer to behave as a crystalline aggregate. Although the entropic contribution of chain orientation in the amorphous regions may also need to be considered, the major contribution to work hardening in tension is rotation of the slip planes toward the tensile axis, so that the resolved shear stress in the slip direction diminishes. This results in a fiber texture in the limit of large deformations, such that the crystallites are oriented with their c axis (the chain axis) parallel to the stretch direction. Despite the relative success of such models, they do not explicitly address the micro-mechanisms involved in the transformation of the spherulitic texture into a fiber texture. One possibility is that the... 

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