Cross-slip Energy Research Articles

High-performance ultra-lean biodegradable Mg–Ca alloys and guidelines for their processing

High-performance ultra-lean binary Mg–Ca alloys are engineered by intelligent alloying and thermo-mechanical processing using hot-extrusion. With Ca-alloying contents as low as 0.2-0.6 wt.%, remarkable room-temperature tensile properties are obtained with tensile strength values as high as 380–420 MPa, or ductility values reaching a maximum of 36 %. By means of multiscale structural and chemical analysis using electron microscopy and energy dispersive X-ray spectroscopy, we show that multimodal strengthening mechanisms can be activated by modifying the spatial distribution of Ca as secondary phase. Our results indicate that strong precipitation strengthening is achieved when Mg2Ca phase particles are dispersed within the grains. On the other hand, preferential distribution of the Mg2Ca precipitates along grain boundaries imparts substantial grain-boundary strengthening by the Hall-Petch effect. Apart from secondary-phase precipitation, the role of Ca as solute atoms is paramount in promoting homogeneous deformation. The presence of Ca directly alters the intrinsic stacking fault energies and modifies the cross-slip energy barriers such that the slip-transition probability from pyramidal-to-basal and vice-versa becomes comparable. Both effects ensure competitive activation of basal and non-basal slip, thereby reducing the mechanical anisotropy. The mechanical performance in the current work, when compared to earlier reported studies of Mg alloys with similar or higher alloying content, shows a 2 to 10-fold increase in tensile strength without compromising ductility.

First-principles calculations of the temperature dependence of stacking fault energies in Mg

Here, we calculate the Gibbs Free Energy of stacking faults relevant to 〈c+a〉 slip as well as the cross-slip energy barrier of the 〈c+a〉 screw dislocations in Mg, Mg-Al, and Mg-Ca alloys using density functional theory and the quasiharmonic approximation. While pyramidal II stacking fault energy is lower than pyramidal I in pure Mg for a large temperature range, the opposite is true at all temperatures in alloys. The addition of Al and Ca significantly reduce the pyramidal I stacking fault energy at room temperature working to assist in the stabilization of pyramidal I dislocations.

Prismatic-to-basal plastic slip transition in zirconium

We model three-dimensional dislocation ensembles in Zr pillars using newly developed mobility laws for dislocations on prismatic and basal planes. The effects of the loading orientation and temperature on the micro-scale mechanical response of single crystals are systematically explored. Easy dislocation glide is observed on prismatic planes, while hard glide occurs on basal planes. By selection of sample temperature and loading orientation, we show that the transition from prismatic to basal glide of dislocation ensembles can be controlled. We also show that the presence of dislocation cross-slip strongly promotes prismatic glide as a result of prismatic/basal cross-slip energy asymmetry. Cross-slip does not alter the occurrence of plastic slip transition but only induces a shift towards higher temperatures. The preponderance of plastic slip on basal or prismatic planes is found to be mediated by a transitional dislocation, which is composed of glissile segments on parallel prismatic planes connected by glissile super-jogs on basal planes. These findings provide a mechanistic understanding of experiments and highlight the significance of transitional prismatic-basal dislocations on the macroscopic characteristics of plasticity in HCP crystals.

Modeling the effect of short-range order on cross-slip in an FCC solid solution

Short-range ordering (SRO) in single-phase face-centered cubic solid solution alloys has been linked to changes in mechanical behavior that are correlated with pronounced changes in deformation microstructure. More specifically, it has been linked with the rise of localized planar slip, which is associated with a glide softening effect due to the destruction of SRO in a slip plane by lead dislocations in an array. While the glide softening effect has been well studied, what remains less clear is the effect of SRO on cross-slip. While it is apparently suppressed in the planar slip mode, the energetic factors governing this phenomenon have not been investigated in detail. In this study, cross-slip in a model Ni-10%Al alloy is studied through the use of atomistic simulations, comparing configurations with random configurational disorder and SRO. The resulting cross-slip activation barriers are found to depend not only on the overall state of SRO in the alloy, but also on the presence or absence of a diffuse anti-phase boundary in the slip plane. The results from this study demonstrate an increase in the cross-slip energy barrier due to an increase in energy per unit length of the final state for dislocations in a planar slip array, and the possibility of correlated cross-slip, and suggest also a reduction in dynamic recovery with the onset of SRO.

The effect of stress on the cross-slip energy in face-centered cubic metals: A study using dislocation dynamics simulations and line tension models

Dislocation dynamics simulations were used to calculate the energy barrier of cross-slip via Friedel–Escaig mechanism in face centered-cubic copper. The energy barrier in the unstressed case was found to be 1.9 eV, as reported by Ramírez et al. (2012). The energy barrier was reduced by applying an external stress. The most effective way of reducing it, was by applying a compressive stress on the glide plane. Furthermore, it was confirmed using dislocation dynamics simulations, that both the Schmid and Escaig stress have a comparable effect in reducing the energy barrier, in qualitative agreement with the atomistic simulations performed by Kang et al. (2014) in face-centered cubic nickel. Most of the energy barrier values for stressed cross-slip fell within the experimental error of 1.15 ± 0.37 eV measured by Bonneville et al. (1988). Moreover, the activation enthalpy obtained from the line tension model of Kang et al. (2014) and the general expression for the activation enthalpy proposed by Malka-Markovitz and Mordehai (2019) were in good quantitative agreement with the simulation results. Hence, both could be used to calculate the activation enthalpy of screw segments in dislocation dynamics simulations.

Stress effects on the energy barrier and mechanisms of cross-slip in FCC nickel

The energy barrier for homogeneous cross-slip of a screw dislocation in face-centered cubic (FCC) nickel is calculated using atomistic simulations as a function of the Escaig stress on the glide plane, the Escaig stress on the cross-slip plane, and the Schmid stress on the cross-slip plane. Two cross-slip mechanisms, Friedel-Escaig (FE) and Fleischer, are examined and their energy barriers are calculated for a large number of stress combinations. For each mechanism, the energy barrier as a function of three stress components can be reduced into a one-dimensional function of an effective stress. The stress domains in which FE and Fleischer mechanisms operate respectively are determined. The FE mechanism dominates when the Escaig stress on the glide plane (in the direction that reduces the stacking fault width) is the largest stress component. Increasing the Schmid stress and Escaig stress (in the direction that expands the stacking fault width) on the cross slip plane promotes the Fleischer mechanism. The cross slip energy barrier functions obtained here can be used as input functions for computing cross slip rates in mesoscale dislocation dynamics simulations.

A new variational line tension model for accurate evaluation of the stress effect on cross-slip energy barrier in face-centered cubic metals

The present work developed a new variational line tension model (LTM) that accounts for contributions from the local line energy, long-range interaction among dislocation segments, and interplay between dissociated partials. This new LTM has been shown to accurately predict cross-slip energy barriers under different stress states, verified through atomistic simulations on the face-centered cubic (FCC) nickel model system. We demonstrated that the line tension in general is not a constant, but varies with the local dislocation length and the separation distance between dissociated dislocations, and thus the constant line tension assumption is inherently inadequate.

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.

Ab initiocontinuum model for the influence of local stress on cross-slip of screw dislocations in fcc metals

We develop a model of cross-slip in face-centered cubic (fcc) metals based on an extension of the Peierls-Nabarro representation of the dislocation core. The dissociated core is described by a group of parametric fractional Volterra dislocations, subject to their mutual elastic interaction and a lattice-restoring force. The elastic interaction between them is computed from a nonsingular expression, while the lattice force is derived from the $\ensuremath{\gamma}$ surface obtained directly from ab initio calculations. Using a network-based formulation of dislocation dynamics, the dislocation core structure is not restricted to be planar, and the activation energy is determined for a path where the core has three-dimensional equilibrium configurations. We show that the activation energy for cross-slip in Cu is $1.9\phantom{\rule{4pt}{0ex}}\text{eV}$ when the core is represented by only two Shockley partials, while this value converges to $1.43\phantom{\rule{4pt}{0ex}}\text{eV}$ when the core is distributed over a bundle of 20 Volterra partial fractional dislocations. The results of the model compare favorably with the experimental value of $1.15\ifmmode\pm\else\textpm\fi{}0.37\phantom{\rule{4pt}{0ex}}\text{eV}$ [J. Bonneville and B. Escaig, Acta Metall. 27, 1477 (1979)]. We also show that the cross-slip activation energy decreases significantly when the core is in a particular local stress field. Results are given for a representative uniform ``Escaig'' stress and for the nonuniform stress field at the head of a dislocation pileup. A local homogeneous stress field is found to result in a significant reduction of the cross-slip energy. Additionally, for a nonhomogeneous stress field at the head of a five-dislocation pileup compressed against a Lomer-Cottrell junction, the cross-slip energy is found to decrease to $0.62\phantom{\rule{4pt}{0ex}}\text{eV}$. The relatively low values of the activation energy in local stress fields predicted by the proposed model suggest that cross-slip events are energetically more favorable in strained fcc crystals.

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.

Some basic aspects of electromagnetic radiation emission during plastic deformation and crack propagation in Cu–Zn alloys

This paper presents some basic aspects of electromagnetic radiation (EMR) emission during plastic deformation and crack propagation in Cu–Zn alloys. Six parameters, viz. stress intensity factor, elastic strain energy release rate, EMR amplitude (maximum and rms), EMR frequency, and electromagnetic energy release rate, at different percent of zinc content have been analyzed. Results show that EMR parameters increase with increase in zinc up to 30% and then they decrease with higher zinc percentage. Investigations showed that the electromagnetic energy release rate has a direct correlation with the elastic strain energy release rate, which can prove to be a novel technique for the evaluation of fracture toughness. It was further observed that the electromagnetic energy release rate bears a parabolic relation with the ratio of stress at crack tip instability, σ, to the stacking fault energy, U f, where cross-slip energy is also known to be only a function of ( σ/ U f).

A nonplanar Peierls–Nabarro model and its application to dislocation cross-slip

A novel semidiscrete Peierls–Nabarro model is introduced which can be used to study dislocation spreading at more than one slip plane, such as dislocation cross-slip and junctions. Within this essentially continuum model, the nonlinearity which arises from the atomic interaction across the slip plane is dealt with atomistic and/or ab initio calculations. As an example, we study the dislocation cross-slip and the constriction process in two contrasting fcc metals, Al and Ag. We find that the screw dislocation in Al can cross-slip spontaneously in contrast with the screw dislocation in Ag, which splits into two partials, and thus cannot cross-slip without first being constricted. The response of the dislocations to an external stress is examined in detail. The dislocation constriction energy and the critical stress for cross-slip are determined, and, from the latter, we estimate the cross-slip energy barrier for the straight screw dislocations.

On stress assisted dislocation constriction and cross-slip

A novel semidiscrete Peierls–Nabarro model is introduced which can be used to study dislocation spreading at more than one slip plane, such as dislocation cross-slip and junctions. The strength of the model, when combined with an atomistic simulation for dislocation core properties, is without suffering from the uncertainties associated with empirical potentials. Therefore, this method is particularly useful in providing insight into alloy design when empirical potentials are not available or not reliable for such multi-element systems. The model is applied to study the external stress assisted dislocation cross-slip and constriction process in two fcc metals, Al and Ag, exhibiting different deformation properties. We find that the screw dislocation in Al can cross-slip spontaneously in contrast with that in Ag, where the screw dislocation splits into two partials that cannot cross-slip without first being constricted. The dislocation response to an external stress is examined in detail. The dislocation constriction energy and the critical stress for cross-slip are determined, and from the latter, we estimate the cross-slip energy barrier for straight screw dislocations.

Dislocation constriction and cross-slip: Anab initiostudy

A novel model based on the Peierls framework of dislocations is developed. The new theory can deal with a dislocation spreading at more than one slip planes. As an example, we study dislocation cross-slip and constriction process of two fcc metals, Al and Ag. The energetic parameters entering the model are determined from ab initio calculations. We find that the screw dislocation in Al can cross-slip spontaneously in contrast with that in Ag, which splits into partials and cannot cross-slip without first being constricted. The dislocation response to an external stress is examined in detail. We determine dislocation constriction energy and critical stress for cross-slip, and from the latter, we estimate the cross-slip energy barrier for the straight screw dislocations.

Reply to comment on ‘atomistic simulation of cross-slip processes in model fcc structures’

Abstract The procedure used by Rao et al. (1999, Phil. Mag. A. 79, 1167) for evaluating the cross-slip energy in fcc Cu is explained in detail.

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.