Activation Energy For Cross-slip Research Articles

A data driven approach for cross-slip modelling in continuum dislocation dynamics

Cross-slip is a thermally activated process by which screw dislocation changes its glide plane to another slip plane sharing the same Burgers vector. The rate at which this process happens is determined by a Boltzmann type expression that is a function of the screw segment length and the stress acting on the dislocation. In continuum dislocation dynamics (CDD), the information regarding the length of the screw dislocation segment and local stress state on dislocations are lost due to the coarse-grained representation of the density. In this work, a data driven approach to characterize the lost information by analyzing the discrete dislocation configurations is proposed to enable cross-slip modeling in the CDD framework in terms of the coarse-grained dislocation density and stress fields. The analysis showed that the screw segment length follows an exponential distribution, and the stress fluctuations, defined as the difference between the stress on the dislocations and the mean field stress in CDD, follows a Lorentzian distribution. A novel approach for cross slip implementation in CDD employing the screw segment length and stress fluctuation statistics was proposed and rigorously tested by comparing the CDD cross-slip rates with discrete dislocation dynamics (DDD) rates. This approach has been applied in conjunction with three cross-slip models used in DDD simulations differing mainly in the functional form of cross slip activation energy. It was found that different cross-slip activation energy formulations yielded different cross-slip rates, yet the effect on mechanical stress-strain response and dislocation density evolution was minimal for the [001] type loading.

The effect of local chemical ordering on dislocation activity in multi-principle element alloys: A three-dimensional discrete dislocation dynamics study

The exceptional combination of strength and ductility in multi-component alloys is often attributed to the interaction of dislocations with the various solute atoms in the alloy. To study these effects on the mechanical properties of such alloys there is a need to develop a modeling framework capable of quantifying the effect of these solutes on the evolution of dislocation networks. Large scale three-dimensional (3D) Discrete dislocation dynamics (DDD) simulations can provide access to such studies but to date no relevant approaches are available that aim for a complete representation of real alloys with arbitrary chemical compositions. Here, we introduce a formulation of dislocation interaction with substitutional solute atoms in fcc alloys in 3D DDD simulations that accounts for solute strengthening induced by atomic misfit as well as fluctuations in the cross-slip activation energy. Using this model, we show that local fluctuations in the chemical composition of various CrFeCoNi-based multi-principal element alloys (MPEA) lead to sluggish dislocation motion, frequent cross-slip and alignment of dislocations with solute aggregation features, explaining experimental observations related to mechanical behavior and dislocation activity. It is also demonstrated, that this behavior observed for certain MPEAs cannot be reproduced by assuming a perfect solid solution. The developed method also provides a basis for further investigations of dislocation plasticity in any real arbitrary fcc alloy with substitutional solutes.

On the activation energy for plastic flow during tension test at room temperature and the anisotropy behaviour of Ti-6Al-4V alloy

The movement of dislocations inside of crystals during the tension test at constant crosshead velocity is related to activation energy for plastic flow in spatially extended polycrystalline systems. In this work, the main objectives are to establish the influence of the slip systems for α hexagonal compact packaging (hcp) titanium phase on the activation energy for plastic flow and the anisotropy influence on the plastic flow behaviour of Ti-6Al-4V alloy in sheet form under tension test at constant crosshead velocity of 1 mm/min in three in-plane orientations, namely in the rolling 0° (RD), 45° (DD) and transverse (TD) directions, respectively. By applying the quantum mechanics and relativistic model (QM-RM) proposed by Muñoz-Andrade, it is shown that for a <c+a> pyramidal type slip with a Burgers vector b=0.553 nm, the activation energy barrier for plastic flow at maximum stress in uniaxial tension in the sheet rolling direction, Q=115.115 kJ/mol is lower in comparison with Q=116,629 kJ/mol obtained by the <a> basal type slip with a Burgers vector b=0.295nm. These results are in accordance with the reduced cross-slip activation energy barrier for cross-slip onto pyramidal planes in an a hexagonal crystalline structure with compact packaging (hcp) titanium phase. Additionally, it was shown that transverse direction (TD) of Ti-6Al-4V alloy in sheet form has developed the maximum stress in uniaxial tension test and ductility.

Deformation modes and yield strength anomaly in L12 compounds

The synergy between various planar fault energies coupled with elastic anisotropy plays a major role in determining the deformation modes and thereby the yield strength anomaly in superalloys. The present work focuses on the feasibility of using planar fault energies and elastic moduli derived from density functional theory calculations and predicting thermodynamic viability of yield strength anomaly for elastically anisotropic compounds. Fault energies and elastic moduli in different binary (A3B) and pseudo-binary Ni3Al(1−x)Cx (C=Ta, Ti, and Ni) systems were estimated. It was observed that the alloying has a non-monotonic effect on the trends in fault energies and elastic moduli in Ni3Al(1−x)Cx. The addition of Ta and Ti to Ni3Al reduced the activation energy for cross-slip while Ni has the opposite effect. These predictions corroborate with the experimental results from literature that the peak shifts to lower temperatures in flow stress vs temperature curve. It was concluded that alloying elements that primarily affect fault energies influence yield anomaly in Ni3Al(1−x)Cx. Maps depicting the criteria for yield strength anomaly were developed for various combinations of critical fault energy ratios and elastic anisotropy. These results were discussed in the purview of alloy design and guidelines for screening complex precipitates compositions were proposed.

Cross-slip in face centred cubic metals: a general full stress-field dependent activation energy line-tension model

ABSTRACT Cross-slip is a thermally activated process by which a screw dislocation changes its slip plane. Understanding and modelling the activation barrier of the cross-slip process as a free-energy barrier that depends on the stress conditions at the vicinity of the dislocation is crucial. In this work, we employ the line-tension model for the cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier when both Escaig stresses are applied on the primary and cross-slip planes and Schmid stress is applied on the cross-slip plane. We propose a closed-form expression for the activation energy for cross-slip in a large range of stresses, without any fitting parameters. The results of the proposed model are in good agreement with previous numerical results and atomistic simulations. We also show that, when Schmid stress is applied on the cross-slip plane, the energy barrier is decreased, and in particular, cross-slip can occur even when the Escaig stress in the primary plane is smaller than that on the cross-slip plane. The proposed closed-form expression for the activation energy can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality. This will allow cross-slip to be more accurately related to macroscopic plasticity.

Cross-slip in face-centered cubic metals: a general Escaig stress-dependent activation energy line tension model

Cross-slip is a dislocation mechanism by which screw dislocations can change their glide plane. This thermally activated mechanism is an important mechanism in plasticity and understanding the energy barrier for cross-slip is essential to construct reliable cross-slip rules in dislocation models. In this work, we employ a line tension model for cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier under Escaig stresses. The analysis shows that the activation energy is proportional to the stacking fault energy, the unstressed dissociation width and a typical length for cross-slip along the dislocation line. Linearisation of the interaction forces between the partial dislocations yields that this typical length is related to the dislocation length that bows towards constriction during cross-slip. We show that the application of Escaig stresses on both the primary and the cross-slip planes varies the typical length for cross-slip and we propose a stress-dependent closed form expression for the activation energy for cross-slip in a large range of stresses. This analysis results in a stress-dependent activation volume, corresponding to the typical volume surrounding the stressed dislocation at constriction. The expression proposed here is shown to be in agreement with previous models, and to capture qualitatively the essentials found in atomistic simulations. The activation energy function can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality.

Atomistic simulations of dislocation behavior in a model FCC multicomponent concentrated solid solution alloy

In this work, molecular statics and molecular dynamics simulations of a/2<110> dislocation behavior for a model FCC Co30Fe16.67Ni36.67Ti16.67 alloy are discussed. It is shown that the single FCC phase is elastically stable in this alloy. Local stacking fault energies for the FCC alloy are determined as a function of average composition. The core structure of a/2<110> screw and edge dislocations in the FCC Co30Fe16.67Ni36.67Ti16.67 alloy is shown to be planar with significant variations in the Shockley partial splitting along the dislocation line (factor of ∼3) due to concentration fluctuations. The correlation lengths for dislocation line fluctuations in this alloy are determined and discussed. The critical stress to move both a/2<110> screw and edge dislocations at 0 K in the model FCC Co30Fe16.67Ni36.67Ti16.67 alloy is of the order of 0.0025–0.005μ, where μ is the (111) shear modulus, and is significantly higher than that of pure FCC Ni. Molecular dynamics simulation results on the critical stress to move a/2<110> screw and edge dislocations in the model FCC concentrated solid solution alloy show that it decreases with increasing temperature, similar to solid-solution strengthened FCC metals. These molecular dynamics simulation results are in reasonable agreement with experimental tensile yield strength data for an analogous FCC concentrated solid solution alloy. It is also shown that local fluctuations in the concentration of solutes has a strong effect on the effective cross-slip activation energy of screw dislocations in the random alloy.

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.

Atomistic simulations of surface cross-slip nucleation in face-centered cubic nickel and copper

In this manuscript, embedded atom potentials are used to determine the various core structures of glide screw-character dislocations intersecting free surfaces at right and inclined angles in face-centered cubic Ni and Cu. It is shown that the negative constriction forms at free surfaces under certain conditions. The role of various factors affecting the formation of negative constriction at the free surface, negative constriction energy, ledge annihilation and screw dislocation rotation due to Lothe’s forces are discussed. The activation energy for surface cross-slip nucleation when the screw dislocation intersects the free surfaces at right angles, in the absence of ledge annihilation forces, is shown to be 0.05eV in Ni and 0.09eV in Cu. The activation-energy values obtained via the nudged elastic band method are significantly lower than the activation energy for cross-slip at attractive forest dislocation intersections in these materials. The present results are expected to be useful in understanding the mechanical behavior of micron-sized pillars under pure tension and compression.

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.

Atomistic simulations of intersection cross-slip nucleation in L1 2 Ni 3Al

Using atomistic simulations, the authors evaluate the activation barrier for a screw superdislocation to form the Paidar–Pope–Vitek (PPV) locked configuration when intersecting a forest dislocation in L12 Ni3Al, as a function of the superpartial core width. It is shown that the PPV lock is stable at the intersection, unlike when formed along an isolated dislocation line, and that the activation energy for cross slip at the forest dislocation intersection is significantly lower than that for cross slip along an isolated dislocation.

Universal strain–temperature dependence of dislocation structures at the nanoscale

The universal topology of experimental strain–temperature maps of dislocation structures of face-centered cubic metals allows the ordering of dislocation structure forming processes in these metals, which is not consistent with the stacking fault energy or the melting temperature. Using dimensional analysis, it is shown that the metals can be ordered by the activation energy for cross slip. The experimental maps are scaled by the cross-slip activation energy to form a universal strain–temperature map. The implications for dislocation rearrangement mechanisms are discussed.

Calculations of intersection cross-slip activation energies in fcc metals using nudged elastic band method

The nudged elastic band (NEB) method is used to evaluate activation energies for dislocation intersection cross-slip in face-centered cubic (fcc) nickel and copper, to extend our prior work which used an approximate method. In this work we also extend the study by including Hirth locks (HL) in addition to Lomer–Cottrell locks and glide locks (GL). Using atomistic (molecular statics) simulations with embedded atom potentials we evaluated the activation barrier for a dislocation to transform from fully residing on the glide plane to fully residing on the cross-slip plane when intersecting a 120° forest dislocation in both Ni and Cu. The initial separation between the screw and the intersecting dislocation on the (111) glide plane is varied to find a minimum in the activation energy. The NEB method gives energies that are ∼10% lower than those reported in our prior work. It is estimated that the activation energies for cross-slip from the fully glide plane state to the partially cross-slipped state at the 120° intersection forming GL in Ni and Cu are ∼0.47 and ∼0.65eV, respectively, and from the fully cross-slip plane state to the partially cross-slipped state forming LC are ∼0.68 and ∼0.67eV. The activation energies for cross-slip from the fully glide plane state to the partially cross-slipped state at the 120° intersection forming HL in Ni and Cu are estimated to be ∼0.09 and ∼0.31eV, respectively. These values are a factor of 3–20 lower than the activation energy for bulk cross-slip in Ni and, a factor of 2–6 lower than the activation energy for cross-slip in Cu estimated by Friedel–Escaig analysis. These results suggest that cross-slip should nucleate preferentially at selected screw dislocation intersections in fcc materials and the activation energies for such mechanisms are also a function of stacking fault energy.

Activated states for cross-slip at screw dislocation intersections in face-centered cubic nickel and copper via atomistic simulation

We extend our recent simulation studies where a screw dislocation in face-centered cubic (fcc) Ni was found to spontaneously attain a low energy partially cross-slipped configuration upon intersecting a forest dislocation. Using atomistic (molecular statics) simulations with embedded atom potentials, we evaluated the activation barrier for a dislocation to transform from fully residing on the glide plane to fully residing on a cross-slip plane intersecting a forest dislocation in both Ni and Cu. The activation energies were obtained by determining equilibrium configurations (energies) when variable pure tensile or compressive stresses were applied along the [111] direction on the partially cross-slipped state. We show that the activation energy is a factor of 2–5 lower than that for cross-slip in isolation via the Escaig process. The cross-slip activation energies obtained at the intersection in Cu were in reasonable accord with the experimentally determined cross-slip activation energy for Cu. Further, the activation barrier for cross-slip at these intersections was shown to be linearly proportional to (d/b)[ln(3d/b)]1/2, as in the Escaig process, where d is the Shockley partial dislocation spacing and b is the Burgers vector of the screw dislocation. These results suggest that cross-slip should be preferentially observed at selected screw dislocation intersections in fcc materials.

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.

Evolution of dislocation patterns in fcc metals

The effect of strain on the microstructure and detailed internal structure of dislocation boundaries in pure polycrystalline fcc metals (aluminum, copper, nickel and gold) was systematically studied and compared as a function of strain following compression at room temperature. At low strains all metals form a cellular structure. The dislocations in the cell walls tend to rearrange themselves from tangles to ordered arrays of parallel dislocations as the strain is increased. However the rearrangement does not correlate well with the stacking fault energy. A good correlation is found with the cross-slip activation energy.

Predicting the stress–strain behaviour of carbon steels under hot working conditions: An irreversible thermodynamics model

An irreversible thermodynamics treatment of plastic deformation is re-formulated to include the effects of steel chemistry in austenite hot rolling. By relating the entropy to the relevant fluxes and forces, the assumption dS ∝ d τ / T is removed, where S and τ are the entropy and stress at temperature T. The effect of composition is incorporated in the activation energy for cross-slip, obtaining a good description of the stress–strain behaviour of various grades as a function of temperature and strain rate.

Cross-slip process in fcc nickel with hydrogen in a stacking fault: An atomistic study using the embedded-atom method

An atomistic study is conducted on the effect of H, which is homogeneously distributed in a stacking fault, on the activation energy of the cross slip of a screw dislocation in Ni using the embedded-atom method. The global minimum energy configurations with H in the stacking fault and the cross-slip processes are determined by the nudged elastic band method. It is revealed that H in the stacking fault increases the activation energy of cross slip significantly, due to the increase in the separation between partial dislocations induced by H. The increase in the activation energy induced by H in the stacking fault is much larger than that induced by H bound to dislocation cores during cross slip. The present study provides direct evidence that H in the stacking fault is the controlling mechanism for H-inhibited cross slip, and thus, H-induced slip planarity in common fcc materials where dislocations dissociate into partial dislocations.

Hydrogen-affected cross-slip process in fcc nickel

The effects of H on the cross-slip process of a dissociated screw dislocation in nickel are studied by atomistic simulations using a configuration-space-path technique. We find that H binding in the stacking fault exerts no effect on the activation energy of cross-slip. H that is bound to the cores of the partial dislocations and moves with the dislocations during cross-slip leads to an increase of the activation energy and thus induces slip planarity. Slip planarity is due only to a net decrease of the H-binding energy in the cross-slip process.

The activation energy for the fcc rolling-texture transition as related to the activation energy for cross slip

The determination of the activation energy for the rolling-texture transition in Cu–5%Zn is recapitulated, and the result is compared with the results of recent atomic-scale modelling of cross slip. It is concluded that the texture transition is governed by cross slip, and possible mechanisms are briefly discussed.