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

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.     

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.     

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.     

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.     

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。     

Ordinary dislocation configurations in high Nb-containing TiAl alloy deformed at high temperatures

Abstract

High Nb-containing TiAl (Nb–TiAl) alloys possess mechanical properties at elevated temperatures superior to conventional TiAl alloys. However, the strengthening mechanisms induced by Nb addition have been discussed controversial for a long time. In the present study, the dislocation structures in a polycrystalline high Nb–TiAl alloy after tensile tests at 700 and 900 °C were investigated by transmission electron microscope (TEM) observation. The results show that abundant double cross slip of ordinary dislocations is activated in the samples deformed at 700 °C. The dislocations are pinned at the jogs and numerous dipoles are observed. Debris can be commonly observed in the vicinity of screw dislocations. Trace analysis shows that the cross-slip plane is (1?1?0)γ at 700 °C but (1?1?1)γ octahedral plane at 900 °C. Three-dimensional (3D) dislocation structures, caused by cross-slip and annihilation of ordinary dislocations, were observed along the screw orientation. The dipoles and debris produced by high-temperature cross slip can be important for the strengthening of high Nb–TiAl alloys.     

Nucleation of kink pairs on partial dislocations: A new model for solution hardening and softening

Nucleation and motion of kink pairs on partial dislocations are examined by elasticity theory for materials with a high Peierls stress. Two approaches are used: one considers the change in average stacking-fault energy (SFE) due to alloying elements and the other considers the change in local SFE due to a nearby solute atom. Both approaches highlight the role of SFE on kink nucleation, propagation and annihilation and both furnish strain rate as a function of stress, temperature and SFE. Model predictions are compared with yield stress data for two systems: firstly, an intermetallic, MoSi₂, which softens for alloying elements (V, Nb, Cr and Al) that decrease the SFE and hardens for Re additions that increase the SFE; secondly, a ceramic oxide, MgO-Al₂O₃ spinel, which softens with increasing addition of excess alumina and at the same time exhibits a decrease in SFE. The average SFE approach agrees qualitatively with the data while quantitative agreement is obtained with the local SFE approach. The possibility is considered that the model applies to other materials, such as TiAl, HfV₂ and Fe₃Al, which show softening with certain alloying additions. One requirement is that the dislocations are dissociated more than a few atomic distances; otherwise kink nucleation occurs on the perfect dislocation (or simultaneously on both partials). Hence the model does not apply to materials such as bcc metals which only have a core dissociation. Normal hardening effects of solutes from size and modulus misfits are additive with any softening effects from a decrease in SFE and so may mask the latter, as occurs for W additions to MoSi₂.     

镍铬合金中的位错运动与位错反应

对镍铬合金中单一滑移面内和两个滑移面间的位错反应,特别是动态下的反应,进行了透射电子显微镜观察,并对其中的一些位错组态进行了衍衬分析。1.六角位错网络主要是单一滑移面内柏氏矢量相差120°的两组位错间反应的结果;2.与螺型位错一样,刃型或混合型位错也能在两个滑移面间交滑移;3.两个滑移面间的位错反应有时在其截线方向生成不滑动的位错(如L.C.位错锁)并不能完全阻挡住这两个滑移面上的位错运动;4.在含铝、钛的镍铬合金中,超点阵位错的反应与不含铝、钛的合金或无序固溶体中的位错反应相似。 关键词：     

Transmission electron microscopy observation of a deformation twin in TWIP steel by an ex situ tensile test

The formation of deformation twins in twinning-induced plasticity steels was observed in transmission electron microscope by an ex situ tensile test. The twinning process initially includes formation of extended dislocations at primary slip plane, then cross-slip to a conjugate slip plane with dissociation of the leading partial into a stair-rod dislocation and an emitted partial, and finally un-faulting of the original faults and formation of Frank partials. Repetition of the operation of the process on successive conjugate planes results in the formation of deformation twins. The formation mechanism of deformation twins can thus be explained by improving the stair-rod cross-slip model.     

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.     

Strain induced grain boundary premelting in bulk copper bicrystals

In bulk bicrystals strain induced grain boundary premelting (SIGBPM) occurs when heavy screw dislocation pileup can be held up to a certain high temperature, approximately 0.6T _M, where T _M is the melting point of bulk material in Kelvin. SIGBPM occurs at grain boundaries to which new twist component is added due to the rotation of both component crystals toward opposite direction about the axis perpendicular to the grain boundary plane. At the original grain boundary, grain boundary sliding takes place due to this relative rotation. In f.c.c. metals with relatively low stacking fault energies such as copper, nickel, brass(30Zn) and silver, dislocations dissociate into partials. Therefore high density tangled dislocations introduced during plastic deformation hardly loose. If these dislocations can be held to high temperatures, SIGBPM is promoted. Formation of static or dynamic recrystallized grains suppresses SIGBPM itself and the propagation of grain boundary cracks formed by SIGBPM.     

Nucleation of deformation twins in nanocrystalline fcc alloys

An earlier dislocation model for predicting the grain size effect on deformation twinning in nanocrystalline (nc) face-centred-cubic (fcc) metals has been found valid for pure metals but problematic for alloys. The problem arises from the assumption that the stacking-fault energy (γ_SF) is twice the coherent twin-boundary energy (γ_fcc), which is approximately correct for pure fcc metals, but not for alloys. Here we developed a modified dislocation model to explain the deformation twinning nucleation in fcc alloy systems, where γ_SF ≠ 2γ_twin. This model can explain the differences in the formations of deformation twins in pure metals and alloys, which is significant in low stacking-fault energy alloys. We also describe the procedure to calculate the optimum grain size for twinning in alloy systems and present a method to estimate γ_twin.     

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).     

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.     

Formation of misfit edge dislocations in Ge x Si1 ? x films ( x ～ 0.4–0.5) grown on tilted Si(001) → (111) substrates

The dislocation structure of Ge _x Si_{1 − x} films (x ∼ 0.4–0.5) grown by molecular epitaxy on Si(001) substrates tilted by 6° about the 〈011〉 axis was studied. It is shown that, in the tilt direction, edge misfit dislocations (MDs) arise only in the form of short segments lying on the intersections of 60° MDs. As a result, the total length of edge MDs along the substrate tilt direction is smaller than that along the tilt axis. The deviation of the substrate surface from the singular plane made it possible to detect a dislocation configuration that consists of a short segment of an edge MD and two diverging 60° MDs propagating from it in the tilt direction. The formation of the segment is assumed to begin with simultaneous nucleation of complementary dislocation half-loops that form a short edge MD on the interface and then propagate on one side as two diverging 60° MD lines. Original Russian Text ? Yu.B. Bolkhovityanov, A.K. Gutakovskii, A.S. Deryabin, L.V. Sokolov, 2008, published in Fizika Tverdogo Tela, 2008, Vol. 50, No. 10, pp. 1783–1787.     

Modelling and simulation of dynamic recrystallisation based on multi-phase-field and dislocation-based crystal plasticity models

ABSTRACT

The mechanical properties of metals used as structural materials are significantly affected by hot (or warm) plastic working. Therefore, it is industrially important to predict the microscopic behaviour of materials in the deformation process during heat treatment. In this process, a number of nuclei are generated in the vicinity of grain boundaries owing to thermal fluctuation or the coalescence of subgrains, and dynamic recrystallisation (DRX) occurs along with the deformation. In this paper, we develop a DRX model by coupling a dislocation-based crystal plasticity model and a multi-phase-field (MPF) model through the dislocation density. Then, the temperature dependence of the hardening tendency in the recrystallisation process is introduced into the DRX model. A multiphysics simulation for pure Ni is conducted, and then the validity of the DRX model is investigated by comparing the numerical results of microstructure formation and the nominal stress–strain curve during DRX with experimental results. The obtained results indicate that in the process of DRX, nucleation and grain growth occur mainly around grain boundaries with high dislocation density. As deformation progresses, new dislocations pile up and subsequent nucleation occurs in the recrystallised grains. The influence of such microstructural evolution appears as oscillation in the stress–strain curve. From the stress–strain curves, the temperature dependence in DRX is observed mainly in terms of the yield stress, the hardening ratio, and the change in the hardening tendency after nucleation occurs.     

Defect aggregates in neutron-irradiated β-Si3N4

Abstract

Microstructural analysis of the defect aggregates formed in bulk samples of polycrystalline β-Si₃N₄ neutron-irradiated to a dose of ～2.0 × 10²⁶n/m² at temperatures of 1100 K and 925 K has been carried out. This study has shown that the defect aggregates formed are faulted dislocation loops lying on the {1010} planes with a Burgers vector of b ? 1 /10<1125>. The vector is non-rational but corresponds to the insertion of an extra layer of [SiN4] tetrahedra on the {10l0} planes plus an additional shear in the loop plane. The formation of these loops is dependent upon the temperature of irradiation. In the sample irradiated at 1100 K their formation is additionally dependent upon whether or not a particular grain contains pre-existing c-axis dislocations. If no c-axis dislocations are present then independent nucleation of the loops is apparent; if there are pre-existing c-axis dislocations then the loops form from an apparent dissociation between the arcs of the irradiation-induced helical c-axis dislocation. In the sample irradiated at 925 K only independent nucleation of the loops occurs, regardless of whether or not there are any pre-existing c-axis dislocations in the grains.     

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.