Escaig Stress Research Articles

Screw dislocation cross slip at cross-slip plane jogs and screw dipole annihilation in FCC Cu and Ni investigated via atomistic simulations

Using atomistic simulations, the effect of jogs on the cross-slip of screw character dislocations and screw-dipole annihilation was examined for both FCC Cu and Ni. The stress-free activation energy for cross-slip at jogs is close to 0.4eV in Cu, determined using a nudged elastic band method. This value is a factor of 4-to-5 lower than the activation energy for cross-slip of screw dislocations in the absence of a jog. Similar results were obtained for Ni. Molecular dynamics simulations were used to study the annihilation of a jog-containing screw dipole. The critical Escaig stress on the glide plane for dipole annihilation drops quickly from the 0K value of ∼400MPa and, dipole annihilation is nearly athermal at room temperature. At 5K, Escaig stresses on the cross-slip plane are a factor of 1.5 less effective than Escaig stresses on the glide plane and, glide stresses on the cross-slip plane are a factor of 3 less effective for dipole annihilation by cross-slip. The activation volume for cross-slip of screw dislocations at jogs with respect to these three stress components range from 6 to 20b3. These results have been found to be useful in physics-based modeling of bulk cross-slip in higher length scale 3D dislocation dynamics simulations investigating dislocation pattern formation and fatigue structures in FCC crystals.

Stress dependence of cross slip energy barrier for face-centered cubic nickel

The energy barrier for the cross slip of screw dislocations in face-centered cubic (FCC) nickel as a function of multiple stress components is predicted by both continuum line tension and discrete atomistic models. Contrary to Escaig's claim that the Schmid stress component has a negligible effect on the energy barrier, we find that the line tension model, when solved numerically, predicts comparable effects from the Schmid stress and the Escaig stress on the cross slip plane. When the line tension model is compared against an atomistic model for FCC nickel, a good agreement is found for the effect of the Escaig stress on the glide plane. However, the atomistic model predicts a stronger effect than the line tension model for the two stress components on the cross slip plane. This discrepancy is larger at higher stresses and is also more severe for the Escaig stress component than for the Schmid stress component.

The cross-slip energy unresolved

Recent progress in dislocation dynamics modeling of work hardening has reawakened the interest in cross-slip, which can lead to dynamic recovery in fcc crystals. It is pointed out that neither continuum theory nor atomic modeling at present are able to reliably derive the reaction path and the activation energy of cross-slip. Classical continuum theory with the concept of Volterra dislocations fails, because during the nucleation process the effective Burgers vectors of the partials are not conserved and the specific atomic misfit energy changes. Atomistic modeling fails, because the ad hoc potentials used at present are unable to reliably predict the energies for atomic displacements far from equilibrium. It is, however, possible to derive the stress conditions necessary in order that cross-slip can spread. An important contribution to the driving force results from the ‘Escaig stress’ acting on the edge components of the partials forming a dissociated screw dislocation and changing their separation. Contrary to the widely held assumption, the driving force is however independent of whether the dislocation in the cross-slip plane will be expanded or compressed.

Atomistic simulations of Paidar–Pope–Vitek lock formation in Ni 3Al

The thermally activated process of Paidar–Pope–Vitek (PPV) lock formation in the L1 2 intermetallic Ni 3Al is simulated using the “nudged elastic band” method with an embedded atom potential. It is found that the one-step PPV lock is intrinsically unstable, but it can be stabilized by a large enough Escaig stress. The two-step PPV lock can be formed with a low activation energy when the one-step lock is involved as an intermediate step. In this case, the overall activation energy is about 1 eV, in reasonable agreement with the range of 0.5–0.9 eV expected from experimental observation of the flow stress anomaly in Ni 3Al. High Escaig stresses are required to stabilize the one-step lock, and the absence of such high stresses in the micro-strain regime is thought to be the underlying reason for the absence of the flow stress anomaly in micro-strain conditions.

Complex evolution of dislocation core structure in a process of motion: model analysis with ab-initio parameterization

We extend the Peierls–Nabarro (PN) model to eliminate the “continuum” approximation for the misfit energy, and use it to analyze features of the evolution of the dislocation core structure under various stress conditions (glide and Escaig stress). We show that the core may assume competing multiple structures with their marked dependence on the dislocation axis position. As we demonstrate for ordinary dislocations in fcc Ir and the ordered Ll 0 CuAu calculated using ab-initio generalized stacking fault energies, these lattice discreteness effects, missing in the original PN model, significantly affects the evolution of the dislocation under stress. In particular, these effects may result in the ladder-like dependence of the partial separation under Escaig stress conditions, and dramatic changes in the shape and amplitude of the Peierls barrier. Thus, we find that lattice discreteness effects can be significant not only in ordered alloys with a deep Peierls valley but also in fcc metals under stress and futher, these effects result in the evolution of dislocation structure which is more complex than previously thought.

Atomistic simulation of cross-slip processes in model fcc structures

Abstract Three-dimensional cross-slipped core structures of (a/2)[110] screw dislocations in model fcc structures are simulated using lattice statics within the embedded-atom method (EAM) formalism. Two parametric EAM potentials fitted to the elastic and structural properties of fcc Ni were used for the simulations. The two- and three-dimensional Green's function techniques newly developed by Rao et al, are used to relax the boundary forces in the simulations. Core structures and energetics of the constrictions occurring in the cross-slip process are studied. The core structure of the constrictions are diffuse, as opposed to a point constriction as envisaged by Stroh. The two constrictions formed by cross-slip onto a cross {111} plane have significantly different energy profiles, at variance with classical continuum theory of Stroh. This suggests that self-stress forces and atomistics dominate the energetics of the cross-slip process; the far-field elastic-energy contribution to cross-slip appears to be minimal. However, the Shockley partial separation distances near the constrictions as well as the variation in cross-slip energy with stacking-fault energy are in reasonable agreement with continuum predictions. Cross-slip energies estimated for Cu and Ni from these calculations show reasonable agreement with experimental data. The cross-slip energy shows a significantly weaker dependence on the Escaig stress compared with elasticity calculations. The activation volume for the cross-slip process is estimated to be of the order of 20b 3 at an applied Escaig stress of 10−3μ in Cu, an order of magnitude lower than experimental estimates and continuum predictions.

Atomistic Simulations of Cross-Slip Processes in Model FCC Structures and L10 TiAl

AbstractThree dimensional (3D) cross-slipped core structures of a/2[110] screw dislocations in model FCC structures are simulated using lattice statics within the Embedded Atom Method (EAM) formalism using potentials fitted to the elastic and structural properties of FCC Ni as well as L10TiAl. 2 and 3-D Green's function (GF) techniques are used to relax the boundary forces in the simulations. The core structure of the constrictions are diffuse. At large separation distances between Shockley partials in the unconstricted configuration, the two constrictions formed by cross-slip onto a cross {111} plane have significantly different energy profiles suggesting that self-stress forces dominate the energetics of the cross-slip process. The variation in cross-slip energy with stacking-fault energy is in reasonable agreement with continuum predictions, excepting at high fault energy values as in L10TiAl. Cross-slip energies estimated for Cu, Ni and γ-TiAl from these calculations show reasonable agreement with experimental data. The cross-slip energy shows a significantly weaker dependence on Escaig stress as compared to elasticity calculations, with the activation volume for the cross-slip process being approximately 20b3 at an applied Escaig stress of 10-3μ in Cu.