Dislocations Peierls stress

Perfect screw dislocation Peierls stress and energy 82... 

I. Perfect screw dislocation Peierls stress and energy. There were several early attempts to calculate the Peierls stress of the non-dissociated screw dislocation in silicon [92,98,99]. Empirical potential computations give values ranging from... 

Since some earlier work based on anisotropic elasticity theory had not been successful in describing the observed mechanical behaviour of NiAl (for an overview see [11]), several studies have addressed dislocation processes on the atomic length scale [6, 7, 8]. Their findings are encouraging for the use of atomistic methods, since they could explain several of the experimental observations. Nevertheless, most of the quantitative data they obtained are somewhat suspicious. For example, the Peierls stresses of the (100) and (111) dislocations are rather similar [6] and far too low to explain the measured yield stresses in hard oriented crystals. 

The objective of this work is to conduct molecular statics calculations of the core structure and the Peierls stresses of various dislocations in NiAl, using a recently developed embedded... 

The Burgers vectors, glide plane and ine direction of the dislocations studied in this paper are given in table 1. Included in this table are also the results for the Peierls stresses as calculated here and, for comparison, those determined previously [6] with a different interatomic interaction model [16]. In the following we give for each of the three Burgers vectors under consideration a short description of the results. 

The core structure of the (100) screw dislocation is planar and widely spread w = 2.66) on the 011 plane. In consequence, the screw dislocation only moves on the 011 glide plane and does so at a low Peierls stress of about 60 MPa. 

The edge dislocation on the 011 plane is again widely spread on the glide plane w = 2.9 6) and moves with similar ease. In contrast, the edge dislocation on the 001 plane is more compact w = 1.8 6) and significantly more difficult to move (see table 1). Mixed dislocations on the 011 plane have somewhat higher Peierls stresses than either edge or screw dislocations. 

Table 1 Summary of the calculated properties of the various dislocations in NiAl. Dislocations are grouped together for different glide planes. The dislocation character, edge (E), screw (S) or mixed type (M) is indicated together with Burgers vector and line direction. The Peierls stresses for the (111) dislocations on the 211 plane correspond to the asymmetry in twinning and antitwinning sense respectively.

For the deformation of NiAl in a soft orientation our calculations give by far the lowest Peierls barriers for the (100) 011 glide system. This glide system is also found in many experimental observations and generally accepted as the primary slip system in NiAl [18], Compared to previous atomistic modelling [6], we obtain Peierls stresses which are markedly lower. The calculated Peierls stresses (see table 1) are in the range of 40-150 MPa which is clearly at the lower end of the experimental low temperature deformation data [18]. This may either be attributed to an insufficiency of the interaction model used here or one may speculate that the low temperature deformation of NiAl is not limited by the Peierls stresses but by the interaction of the dislocations with other obstacles (possibly point defects and impurities). 

The (110) dislocations are from our calculations not expected to contribute significantly to the plastic deformation in hard oriented NiAl because of the very high Peierls stresses. Experimentally, these dislocations do not appear unless the temperature is raised to about 600 K [18]. At this temperature the experimental data strongly suggest a transition from (111) to (110) slip. 

Under the influence of the applied stress, a dislocation loop can grow by glide only as sufficient HOH diffuses to the growing segment to saturate the newly created core and develop a cloud of hydrolyzed Si—O bonds in the neighborhood of the dislocation in order to reduce the Peierls stress (the fundamental friction to the glide of a dislocation in a perfect crystal) to a very low value. 

Our next task is to use our newly found Peierls potential to estimate the stress to move a straight dislocation. The stress is essentially provided as the derivative of the energy profile with respect to the coordinate x, and is given by... 

Our analysis calls for a number of observations. First, we note that the formula for the Peierls stress leads to the expectation that the stress to move a dislocation will be lowest for those planes that have the largest interplanar spacing at fixed b. In the case of fee crystals, we note that the spacing between (001) planes is given by ao/2, while for (110) planes the spacing is V2ao/4, and finally for the (111) planes this value is ao/VS. A second observation to be made concerns... 

From a mechanistic perspective, what transpires in the context of all of these strengthening mechanisms when viewed from the microstructural level is the creation of obstacles to dislocation motion. These obstacles provide an additional resisting force above and beyond the intrinsic lattice friction (i.e. Peierls stress) and are revealed macroscopically through a larger flow stress than would be observed in the absence of such mechanisms. Our aim in this section is to examine how such disorder offers obstacles to the motion of dislocations, to review the phenomenology of particular mechanisms, and then to uncover the ways in which they can be understood on the basis of dislocation theory. 

Drag force, Bv, where B is the drag coefficient and v is the dislocation velocity. Peierls stress Fpeierb. 

For NaCl, the activation of the secondary slip systems at temperatures >200 C is required before ductility in polycrystals is obtained. A similar brittle to ductile transition occurs in KCl at 250 °C. For MgO, this transition occurs 1700 C. Some cubic materials, such as TiC, p-SiC and MgO.AljOj have sufficient independent primary systems but, unfortunately, the dislocations tend to be immobile in these materials. Thus, overall it is found that most ceramic polycrystals lack sufficient slip systems or have such a high Peierls stress that they are brittle except under extreme conditions of stress and temperature. 

The mechanical strength of hard materials is critical for load-bearing, structural applications. These brittle materials only deform plastically at high temperatures, or under severe hydrostatic constraint, since the Peierls stress for dislocation movement is high. Failure is usually by unstable crack propagation under a tensile stress that exceeds the tensile strength of the material. In terms of fracture mechanics, brittle failure occurs when the Mode I stress intensity factor Kj reaches the fracture toughness of the material, Kic (see below). 

On the other hand materials deform plastically only when subjected to shear stress. According to Frenkel analysis, strength (yield stress) of an ideal crystalline solid is proportional to its elastic shear modulus [28,29]. The strength of a real crystal is controlled by lattice defects, such as dislocations or point defects, and is significantly smaller then that of an ideal crystal. Nevertheless, the shear stress needed for dislocation motion (Peierls stress) or multiplication (Frank-Read source) and thus for plastic deformation is also proportional to the elastic shear modulus of a deformed material. Recently Teter argued that in many hardness tests one measures plastic deformation which is closely linked to deformation of a shear character [17]. He compared Vickers hardness data to the bulk and shear... 

Peterson, J. M. (1968) Peierls stress for screw dislocations in polyethylene, /. Appl. Phys., 39, 4920-4928. 

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