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.     

Dislocation cross-slip mechanisms in aluminum

We have systematically studied dislocation cross-slip in Al at zero temperature by atomistic simulations, focusing on the dependence of the transition paths and energy barriers on dislocation length and position. We find that for a short dislocation segment, the cross-slip follows the uniform Fleischer (FL) mechanism. For a longer dislocation segment, we have identified two different cross-slip mechanisms depending on the initial and final positions of the dislocation. If the initial and final positions are symmetric relative to the intersection of the primary and cross-slip planes, the dislocation cross-slips via the Friedel–Escaig (FE) mechanism. However, when the initial and final positions are asymmetric, the dislocation cross-slips via a combination of the FL and FE mechanisms. The leading partial folds over to the cross-slip plane first, forming a stair-rod dislocation at the intersection with which the trailing partial then merges via the FL mechanism. Afterwards, constrictions appear asymmetrically and move away from each other to complete the cross-slip via the FE mechanism.     

Explicit incorporation of cross-slip in a dislocation density-based crystal plasticity model

We present a crystal plasticity model that incorporates cross-slip of screw dislocations explicitly based on dislocation densities. The residence plane of screw dislocations is determined based on a probability function defined by activation energy and activation volume of cross-slip. This enables the redistribution of screw-dislocations and dislocation density patterning due to the effect of stacking fault energy. The formulation is employed for explaining the cross-slip phenomenon in aluminium during uniaxial tensile deformation of ?100? single crystal and a single slip orientation of single crystal, and compare the results with experimental observations. The effect of cross-slip on the stress–strain evolution is seen using this explicit treatment of cross-slip.     

Evaluating the effects of loading parameters on single-crystal slip in tantalum using molecular mechanics

This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension–compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.     

有限温度下位错环的脱体现象

在FCC单晶铜中构造了滑移面为（111）,伯格矢量为b=［112］/6的圆形不完全位错环．采用分子动力学方法模拟了该位错环在0—350 K温度区间内的自收缩过程．模拟结果发现：零温度下,位错不能跨越Peierls-Nabarro势垒运动,迁移速度为0;50　K温度下,螺型和刃型位错具有基本相同的迁移速度;随温度增加,刃型位错具有较大迁移速度;温度较高时,位错核宽度进一步增加;小位错环周围的局部应力,引起4个脱体位错环;脱体位错环在原位错的应力作用下逐渐生长,原位错消失后,在自相 关键词： 单晶铜 位错环 分子动力学 位错源     

A discussion of the structure and behaviour of dipole walls in cyclic plasticity

Assuming that cross-slip by thermally activated migration of jogs can cause annihilation of screw dislocation dipoles without macroscopic crystallographic confinement of cross-slip to the cross-slip plane, an attempt is made to re-derive earlier equations for the saturation stress and the plastic strain amplitude in persistent slip bands. These equations had been based on the assumption that cross-slip could occur only on a cross-slip plane making an obtuse angle with the slip plane, an assumption which limits the mean free path of screw dislocations. The key new assumption is that the walls of edge dislocation dipoles which dominate the structure of persistent slip bands are penetrable obstacles, which increases the mean free paths of the mobile dislocations. Agreement with experiment is obtained if the penetration probability in cyclic saturation is on average one third, a value for which there is a simple rationalization. Estimates can be made of the wall width, which is independent of temperature, in agreement with recent observations by Tippelt et al. However, the main unresolved difficulty is the role of the very fine dipoles, particularly the faulted dipoles, in the walls. A further weakness in the theory is that it ignores the cutting of dipoles by the cross-slipping screw dislocations. Despite these problems, the distribution of dipole heights can be worked out and is found to be in reasonable agreeement with experiment.     

Simulation of screw dislocation motion in iron by molecular dynamics simulations

Molecular dynamics (MD) simulations are used to investigate the response of a/2<111> screw dislocation in iron submitted to pure shear strain. The dislocation glides and remains in a (110) plane; the motion occurs exclusively through the nucleation and propagation of double kinks. The critical stress is calculated as a function of the temperature. A new method is developed and used to determine the activation energy of the double kink mechanism from MD simulations. It is shown that the differences between experimental and simulation conditions lead to a significant difference in activation energy. These differences are explained, and the method developed provides the link between MD and mesoscopic simulations.     

Atomic-scale plasticity in the presence of Frank loops

The different reactions between edge or screw dislocations and interstitial Frank loops were studied by means of molecular dynamics simulations. The calculations were performed at 600?K using an embedded atom method (EAM) potential describing a model FCC material with a low stacking fault energy. An interaction matrix that provides the corresponding interaction strength was determined. In an attempt to investigate the role of pile-ups, simulations with either one or two dislocations in the cell were performed. We find that screw and edge dislocations behave very differently. Edge dislocations shear Frank loops in two out of three cases, while screw dislocations systematically unfault Frank loops by mechanisms that involve cross-slip. After unfaulting, they are strongly pinned by the formation of extended helical turns. The simulations show an original unpinning effect that leads to clear band broadening. This process involves the junction of two screw dislocations around a helical turn (arm-exchange) and the transfer of a dislocation from its initial glide plane to an upper glide plane (elevator effect).     

Residual stress field in steel samples during plastic deformation and recovery processes

An X-ray diffraction method was applied to measure residual stresses and stored elastic energy in deformed and annealed polycrystalline ferritic and austenitic steel samples. The orientation distribution of plastic incompatibility second-order stresses created during elastoplastic deformation was determined and presented in Euler space. Using deformation models, these stresses were correlated with different types of intergranular interactions occurring in the studied materials. An important decrease of the first- and the second-order residual stresses was observed during recovery and recrystallisation processes. Diffraction peak widths, related to dislocation density, were studied and correlated with stress variation during annealing process. Differences in stress relaxation between ferritic and austenitic samples were explained by different values of the stacking fault energy, which influences dislocation climb and cross-slip.     

Which stresses affect the glide of screw dislocations in bcc metals?

By direct application of stress in molecular statics calculations we identify the stress components that affect the glide of 1/2?111? screw dislocations in bcc tungsten. These results prove that the hydrostatic stress and the normal stress parallel to the dislocation line do not play any role in the dislocation glide. Therefore, the Peierls stress of the dislocation cannot depend directly on the remaining two normal stresses that are perpendicular to the dislocation but, instead, on their combination that causes an equibiaxial tension-compression (and thus shear) in the plane perpendicular to the dislocation line. The Peierls stress of 1/2?111? screw dislocations then depends only on the orientation of the plane in which the shear stress parallel to the Burgers vector is applied and on the magnitude and orientation of the shear stress perpendicular to the slip direction.     

位错规范场对于位错芯区的应用

本文用位错连续分布方法分析了位错所产生的应变和应力场,用位错规范场表出了位错芯区的位错分布,并在一定规范条件下求解了位错规范场。得到了螺位错芯区内、外的应力场。在螺位错芯区外,其应力场与Volterra位错的应力场完全一样,而在芯区内,当ρ趋于零时,螺位错的应力场是有解的。最后计算了螺位错的能量。 关键词：     

Multiscale modelling of dislocation/grain boundary interactions. II. Screw dislocations impinging on tilt boundaries in Al

The interaction of dislocations with grain boundaries (GBs) determines a number of important aspects of the mechanical performance of materials, including strengthening and fatigue resistance. Here, the coupled atomistic/discrete-dislocation (CADD) multiscale method, which couples a discrete dislocation continuum region to a fully atomistic region, is used to study screw-dislocations interacting with Σ3, Σ11, and Σ9 symmetric tilt boundaries in Al. The low-energy Σ3 and Σ11 boundaries absorb lattice dislocations and generate extrinsic grain boundary dislocations (GBDs). As multiple screw dislocations impinge on the GB, the GBDs form a pile-up along the GB and provide a back stress that requires increasing applied load to push the lattice dislocations into the GB. Dislocation transmission is never observed, even with large GBD pile-ups near the dislocation/GB intersection. Results are compared with experiments and previous, related simulations. The Σ9 grain boundary, composed from a more complex set of structural units, absorbs screw dislocations that remain localized, with no GBD formation. With increasing applied stress, new screw dislocations are then nucleated into the opposite grain from structural units in the GB that are nearby but not at the location where the original dislocation intersected the boundary. The detailed behaviour depends on the precise location of the incident dislocations and the extent of the pile-up. Transmission can occur on both Schmid and non-Schmid planes and can depend on the shear stresses on the GB plane. A continuum yield locus for transmission is formulated. In general, the overall dissociation and/or transmission behaviour is also determined by the Burgers vectors and associated steps of the primitive vectors of the grain boundary, and the criteria for dislocation transmission formulated by Lee et al . [Scripta Metall. 23 799 (1989); Phil. Mag. A 62 131 (1990); Metall. Trans. A 21 2437 (1990)] are extended to account for these factors.     

Dislocation dynamic modelling of the brittle–ductile transition in tungsten

Brittle–ductile transitions in metals, ceramics and semiconductors are closely connected with dislocation activity emanating near to crack-tips. We have simulated the evolution of crack-tip plasticity using a two-dimensional dislocation dynamics model which has been developed to include two symmetric slip planes intersecting the crack-tip, and applied to single-crystal tungsten. The dislocation mobility law used was physically based on double-kink nucleation on screw dislocations, with an activation energy reduced by the local stress. Even in the strong stress gradients near a crack-tip, the dislocations are found to self-organise so that the internal stress in the array is effectively constant with time and position over a wide range of strain rates and temperatures. The resultant net activation energy for dislocation motion is found to be constant and close to the activation energy experimentally measured for the brittle–ductile transition. Use of a fracture criterion based on the local crack-tip stress intensity factor, as modified by the stresses from the emitted dislocations, allows explicit prediction of the form and temperature of the brittle–ductile transition. Predictions are found to be in very close agreement with experiment.     

Dislocation cross-slip in nanocrystalline fcc metals

Constant strain rate molecular dynamics simulations of nanocrystalline Al demonstrate that a significant amount of dislocations that have nucleated at the grain boundaries, exhibit cross-slip via the Fleischer mechanism as they propagate through the grain. The grain boundary structure is found to strongly influence when and where cross-slip occurs, allowing the dislocation to avoid local stress concentrations that otherwise can act as strong pinning sites for dislocation propagation.     

Slip band formation and mobile dislocation density generation in high rate deformation of single fcc crystals

The mechanisms for the nucleation, thickening, and growth of crystallographic slip bands from the sub-nanoscale to the microscale are studied using three-dimensional dislocation dynamics. In the simulations, a single fcc crystal is strained along the [111] direction at three different high strain rates: 10⁴, 10⁵, and 10⁶?s^??1. Dislocation inertia and drag are included and the simulations were conducted with and without cross-slip. With cross-slip, slip bands form parallel to active (111) planes as a result of double cross-slip onto fresh glide planes within localized regions of the crystal. In this manner, fine nanoscale slip bands nucleate throughout the crystal, and, with further straining, build up to larger bands by a proposed self-replicating mechanism. It is shown that slip bands are regions of concentrated glide, high dislocation multiplication rates, and high dislocation velocities. Cross-slip increases in activity proportionally with the product of the total dislocation density and the square root of the applied stress. Effects of cross-slip on work hardening are attributed to the role of cross-slip on mobile dislocation generation, rather than slip band formation. A new dislocation density evolution law is presented for high rates, which introduces the mobile density, a state variable that is missing in most constitutive laws.     

铝镁合金中位错的运动与交滑移

本文研究了在电子显微镜的照明电子束作用下,铝镁合金中位错运动与交互作用的行为。螺型位错往往单个运动,并且很容易改变运动方向,产生多次双交叉滑移。滑移和交滑移首先在与膜面接近45°的{111}面上进行,位错的柏氏矢量为接近膜面的α/2<110>,这是与照明电子束所产生的应力与膜面平行一事相符的。运动着的位错可以通过其应变场激活近邻的位错,使之发生运动;亦可能受到其它位错的排斥作用而受阻或改变运动方向。     

Power laws in dislocation plasticity

Starting from the idea that plastic flow produces dislocation structures in a state of self-organised criticality, it is shown that one expects power-law relationships between variables. If slip bands are modelled as avalanches of shear with an ellipsoidal shape, slightly tilted from the crystallographic slip plane, limited in size by interaction with secondary slip, the observed exponents of the power laws can be rationalised. In some cases, the constant of proportionality can also be estimated, and found to agree with experiment, even though the detailed mechanism of avalanche formation is not addressed. To analyse creep data and slip-band statistics, it is further assumed that the role of cross-slip is to eliminate screw dislocation dipoles, removing them entirely at stresses found in Stage III of work-hardening. If physical constants, such as the atomic vibration frequency, play a role, the dimensionless power-law relationships do not apply. One then finds creep rates linear in stress and absolute temperature, proportional to the logarithm of time, obeying an equation of state, as observed.     

Orientation effects in interaction of screw dislocation with interstitial impurity atom in b.c.c. lattice

The cross-slip and pinning of a 1/2a〈111〉 screw dislocation in b.c.c. metals in the vicinity of an interstitial impurity atom are studied in dependence on crystal orientation. To this purpose, the interaction energy between the dislocation and an interstitial atom is calculated in an anisotropic elastic continuum and it is assumed that the screw dislocation moves microscopically on {112} or {110} planes between its stable configuration positions in b.c.c. lattice. It is found that the probability of induced cross-slip is orientation dependent. This result is used for discussion of orientation dependence of the change of CRSS due to increased carbon content which was experimentally determined for Fe-3.2% Si alloy single crystals in a previous paper (Blahovec J., Kade?ková S.: Czech. J. Phys.B 21 (1971), 846).     

Effect of alloying element on dislocation cross-slip in γ′-Ni3Al: a first-principles study

The effects of alloying elements Re, Ru, Ta, Ti, and W on the activation enthalpy of dislocation cross-slip in γ′-Ni₃Al are studied combining density functional theory calculations with the classical theory of dislocations. The elements Re and W are found to effectively increase planar fault energies on the (111) plane and decrease the cross-slip activation enthalpy in Ni₃Al. The reduction of activation enthalpy will increase the probabilities of cross-slipping and forming sessile dislocation locks. Therefore, Re and W can inhibit the further motion of dislocations and raise the flow stress of Ni₃Al in the anomalous temperature regime. The underlying electronic mechanism is the strong bonding of Re–Ni and W–Ni and the weak bonding of Re–Al and W–Al in fault areas.