Peierls stresses

Dislocation mobility near and above the Peierls stress 

Dislocations and Plasticity in bcc Transition Metals at High Pressure 

As a practical matter, all computational dislocation dynamics methods require a robust analytic representation of the mobility of individual dislocation segments. 

In this section we first consider appropriate analytic forms to represent the atomistic results for a/2 111 screw dislocations discussed above in Section 4 within both the legacy lattice-based DD code [21,22] and the modern node-based ParaDiS code [27-30]. Using these analytic functions, we then discuss atomistically informed DD simulations of yield stress and plasticity for Ta and Mo as a function of pressure, temperature, and strain rate to complete our multiscale modeling of these materials. 

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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. 

Although the results of the present study and of the above mentioned previous study [6] are qualitatively almost identical, the calculated values for the Peierls stresses differ quite significantly. We find that the highest Peierls stresses in the (100) 011 glide system are as low as 170 MPa. 

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. 

Excellent agreement between experiment and onr calculations is obtained when considering the low temperature deformation in the hard orientation. Not only are the Peierls stresses almost exactly as large as the experimental critical resolved shear stresses at low temperatures, but the limiting role of the screw character can also be explained. Furthermore the transition from (111) to (110) slip at higher temperatures can be understood when combining the present results with a simple line tension model. 

J. J. Gilman, The Peierls Stress for Pure Metals (Evidence That It is Negligible), Phil. Mag., 87,5601 (2007). 

The lattice resistance of the two crystal forms of AIN is not known. However, some tentative conclusions can be made by assuming that the lattice resistance at room temperature is close to the Peierls stress (Peierls, 1940), which agrees with experimental observations of a wide range of materials to within a factor of 3 and is given by... 

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. 

In particular, to compute the Peierls stress, we make the transcription... 

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. 

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