Dislocation mobility model

From the early work of Taylor [63T01] connecting dislocation behavior to observed viscoplastic shock-compression response, numerous studies have attempted to relate conventional dislocation dynamics models to experimental observations. Theory and observations consistently require unusually large numbers of mobile dislocations. Although qualitatively descriptive, progress to date on dislocation models has not proven to provide quantitative descriptions to the observations in metals. 

With such clear evidence of anisotropic behavior within the plastic zone, it was natural to search for a new model that would predict correctly the pattern of slip. Three components in the model are necessary knowledge of the slip system combinations enabling the indenter to penetrate the surface by plastic flow, knowledge of the shear stresses acting under the indenter, and dislocation mobilities. 

Metals that have a compressibility of the same order of magnitude as covalent solids are much softer mechanically and more plastic than ceramics because the bonding electrons are in interstices and are much more easily displaced under stress than in ionic or covalent compounds. Owing to the mobility of the valence electrons, defects and dislocations have a different electronic behavior in metals than in rigid semiconductors. The barrier against plastic deformation is approximately proportional to the bandgap (which naturally follows from the model). 

As noted, an estimate of the tensile stress magnitude based on the Hoffman-Nix model often leads to a stress magnitude that is larger than any observed. However, as soon as the stress level reaches the yield stress of a polycrystalline material, glide dislocations can form to modulate the amplitude. This line of reasoning has been discussed in some detail by Machlin (1995) who pointed out that the mechanism as described is athermal except for the possible dependence of yield stress on temperature. At elevated temperatures, mechanisms associated with increased surface mobility of atoms can come into play to diminish the effectiveness of the Hoffman-Nix mechanism in generating stress, and evidence for the influence of such mechanisms is apparent in experimental data. 

This simple description only tests the fracture criterion at the crack tip. The CEPM brings into play the possibility of micro-de-cohesion at the head of the pile-up. A first simulation has been set up to discuss the possibility of forming a moving pile-up, due to a local softening effect and a mobile obstacle, as suggested in the model. This simulation is based on the theory of dislocations in the presence of the crack. It has to be compared to those used to study the brittle-to-ductile transition (BDT) (Roberts et al., 1993), in which the possible effects of corrosion on the dislocations is introduced. 

Figure 5.8 Atomistic models of supported thin films generated by simulating atom deposition onto a substrate, (a) Illustration of the process, (b) The mobility of the ions once deposited onto the surface, (c) Atomistic model of a CaO thin film supported on MgO(lOO) after the deposition of 1.8 equivalent monolayers onto the surface, (d) After 3.6 equivalent monolayers have been deposited onto the surface. Note in (d) the presence of a mixed screw-edge dislocation (arrow), which evolves in the supported CaO thin film to accommodate the lattice misfit. Reproduced from Sayle et aV with permission from the Royal Society of Chemistry.

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