Dislocations nucleation

In the sections that follow, illustrations of homogeneous and nonho-mogeneous dislocation nucleation are presented. The former case implies dislocation formation in a material system that is otherwise spatially uniform nucleation is equally likely at all locations. Nonhomogeneous nucleation, on the other hand, implies that spatial nonuniformity arising through configuration, material structure, or material defects renders certain sites in the structure far more susceptible to dislocation nucleation than other sites. 

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Introduction of the surface-nucleation mechanism in numerical computation of elastic-plastic wave evolution leads to enhanced precursor attenuation in thin specimens, but not in thicker ones. Inclusion of dislocation nucleation at subgrain boundaries indicates that a relatively low concentration of subgrain boundaries ( 2/mm) and nucleation density (10"-10 m ) is sufficient to obtain predicted precursor decay rates which are comparable to those obtained from the experiments. These experiments are only slightly above the threshold necessary to produce enhanced elastic-precursor decay. 

The Stonybrook group under Dudley has studied the behaviour of ice bicrystals and has shown that under certain conditions, grain boundaries can act as somces of dislocations. Grain boundary facets have been shown to act as dislocation nucleation sites and grain boundaries themselves have been observed to act as barriers to dislocation motion. 

The dislocation nucleation just discussed is a preyield phenomenon in any deformation experiment, it may occur (i) during any preconditioning treatment at temperature and pressure before the shear stress is applied, (ii) during the incubation period in a creep test, or (iii) during the nominally elastic region in a constant strain-rate experiment. Thus, the microstructure of the crystal immediately prior to the onset of deformation may not be the same as the microstructure of the as-grown crystal. 

Since Morrison-Smith et al. (1976) associated the strain features observed in these specimens (Figure 9.7) with acmite inclusions and not with high-pressure clusters of molecular water, they did not relate dislocation nucleation with the water in wet synthetic quartz. 

Nieminen et al. [152] observed a different mechanism of plastic deformation in essentially the same geometry, but at higher velocities (100 m/s versus 5 m/s) and with a different model for the potential between Cu atoms. Sliding took place between (100) layers inside the tip. This led to a reduction of the tip by two layers that was described as the climb of two successive edge dislocations under the action of the compressive load. Although wear covered more of the surface with material from the tip, the friction remained constant at constant normal load. The reason was that the portion of the surface where the tip advanced had a constant area. As in Sprensen et al. s work [63], dislocations nucleated at the comers of the contact and then propagated through it. 

What this result demonstrates is the presence of an enhanced stress in front of the pile up (x < 0). We forego a discussion of the implications of such stress enhancements for dislocation nucleation until section 11.5.3. 

The solution constructed above provides the necessary tools from elasticity theory in order to consider nucleation of a dislocation at a crack tip. The philosophical perspective adopted here is that due to Rice (1992) in which a comparison is made between the work needed to create new free surface and that needed to create a slip distribution corresponding ultimately to a dislocation. We present this model not so much with the hope that it will deliver quantitative insights but on the grounds that it is highly instructive concerning the atomic-level processes near a crack tip. In particular, the model is appealing because the treatment of dissipative processes such as dislocation nucleation is endowed with atomic-level realism, while still maintaining an overall continuum description. 

What we have learned is that dislocation nucleation will occur once 4>i np) reaches its maximum allowable value. This idea is depicted graphically in fig. 11.19 where it is seen that instability to dislocation nucleation occurs when (Siip) = Yus, where yus is a material parameter that Rice has christened the unstable stacking energy. This idea is intriguing since it posits that the competition between cleavage and dislocation nucleation has been reduced to consideration of the relative values of two simple material parameters, both of which admit of first-principles determination, and relevant geometrical factors. 

Later in the present chapter we will examine the application of these ideas to the study of fracture and dislocation nucleation at crack tips. For our present purposes, the key point to be made was the way in which several different modeling paradigms, namely, the use of bulk and planar constitutive models, are brought under the same roof, with the consequence that the resulting model is able to do things that neither of the constituent models can do by itself... 

Fig. 12.12. Illustration of dislocation nucleation due to nanoindentation as simulated using the quasicontinuum method (adapted from Shenoy et al. (1999)). Note the presence of a subsurface grain boundary encountered by dislocations after they are nucleated at the crystal surface and travel down the vertical slip planes.

Cohesive Surface Description of Crack Tip Dislocation Nucleation... 

Fig. 12.35. Schematic of the various crack tip geometries using the cohesive surface dislocation nucleation model (adapted from Xu et at. (1997)).

If the same level of spatial resolution is attained near a crack tip, we will see the nucleation of dislocations in its vicinity. An example of crack tip dislocation nucleation as evidenced in electron microscopy is given in fig. 13.3. Once the material fails, we can also subject it to post-mortem chemical and structural analysis. Using techniques such as Auger spectroscopy, the chemical profile of the failed material may be queried. Again, our main point is to note the diversity of the various geometric signatures of mechanical response. 

Fig. 13.3. Near vicinity of a crack tip indicating the presence of dislocations nucleated at the crack tip (courtesy of D. Clarke).

Kelchner C. L., Plimpton S. J. and Hamilton J. C., Dislocation Nucleation and Defect Structure during Surface Indentation, Phys. Rev. B58, 11 085 (1998). 

Rice J. R., Dislocation Nucleation from a Crack Tip An Analysis Based on the Peierls Concept, J. Mech. Phys. Solids 40, 239 (1992). 

Xu G., Argon A. S. and Ortiz M., Nucleation of Dislocations from Crack Tips under Mixes Moded of Loading Implications for Brittle vs Ductile Behavior of Crystals, Phil. Mag. 72, 415 (1995). Xu G., Argon A. S. and Ortiz M., Critical Configurations for Dislocation Nucleation, Phil. Mag. 75, 341 (1997). 

The mechanical interaction between the different epitaxial layers may result in the formation of misfit dislocations. Nucleation and propagation of cracks can ensue if the mismatch in thermal expansion coefficient is relatively large. The defects significantly influence the physical properties of the thin films. Examples from different material combinations and models of how to predict the numbers for critical thicknesses are provided in Section 14.4. 

Rice, J. R., Beltz, G. E., and Sun, Y. (1992) Peierls framework for analysis of dislocation nucleation from a crack tip, in Topics in Fracture and Fatigue, edited by Argon, A. S., New York Springer Verlag, pp. 1-58. 

Fig. 9.23 Predictions of the stress dependence of the normalized shear-activation volumes of modes A, B, and C of dislocation nucleation, compared with experimental measurements (from Argon et al. (2005) courtesy of Elsevier).

To probe the models for nucleation-controlled plastic flow we compare the predicted temperature dependence of the tensile plastic resistance with the tensile-yield-stress experimental results of Brooks and Mukhtar (2000). For comparison the polyethylene PE3 of average molecular weight = 131000 with a crystallinity of only 0.673 and lamella thickness of 34.3 nm is chosen. For the predictions of the temperature dependence, eqs. (9.26)-(9.28) of Section 9.4.3 are used, where we take in the denominator of eq. (9.25) the factor (1 + K), since the experiments were performed in tension. Noting that the lamella thickness of this polymer type is 1 = 34.3 nm, which is thicker than that for mode A of monolithic-screw-dislocation nucleation, we consider only modes B and C involving nucleation of screw-dislocation half loops and edge-dislocation half loops, and, together with the results of Fig. 9.21, we state the expected tensile yield stress Oy to be... 

Xu, G. and Zhang, C. (2003) Analysis of dislocation nucleation from a crystal surface based on the Peierls-Nabarro dislocation model, J. Mech. Phys. Solids, 51, 1371-1394. 

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