Cross Slip Of Screw Dislocations Research Articles

Atomistic modeling of dislocation cross-slip in nickel using free-end nudged elastic band method

Cross-slip of screw dislocations plays an important role in the plastic deformation of face-centered cubic (FCC) metals and alloys. Here we use the free-end nudged elastic band (FENEB) method to determine the atomistic reaction pathways and energy barriers of cross-slip in an FCC single crystal of Ni. We focus on the cross-slip process mediated by an array of pinning vacancy clusters in the form of stacking fault tetrahedra. We also study a competing process of screw glide by direct cutting of those pinning obstacles on the original slip plane. The activation energies of both cross-slip and obstacle-cutting are determined for different stresses, obstacle spacings and sizes. Using FENEB-calculated energy barriers, we construct dislocation mechanism maps to reveal the effects of resolved shear stress, obstacle spacing and size on the rate-controlling dislocation process for plastic deformation. We further evaluate the activation volumes of cross-slip and obstacle-cutting. The latter result emphasizes the notion of finite strength of the atomically sized pinning obstacles to dislocation motion and also validates the Nabarro scaling law of the linear dependence of activation volume on obstacle spacing.

Fatigue behavior, microstructural evolution, and fatigue life model based on dislocation annihilation of an Fe-Ni-Cr alloy at 700 °C

Dislocation annihilation behavior of Sanicro 25 alloy was investigated based on various total strain amplitudes (Δεt/2). The slopes of cyclic stress response curves during stage ΙΙ were compared and showed that obvious stable cyclic behavior occurred at Δεt/2=0.3%. Microstructure analysis reveals that the number of slip plane increased with increasing Δεt/2. When Δεt/2=0.3%, dislocations can slip on the slip plane (111¯). When Δεt/2 increased to 0.4%, the slip planes included (1¯11) and (111¯). The fraction of substructured grains under Δεt/2=0.3% was obviously larger than that under Δεt/2=0.4%, which was attributed to the obvious dislocation annihilation. The deformed grains were dominant at Δεt/2=0.4%. The annihilation mechanisms of dislocations were analyzed during tensile and compressive loading based on the cyclic stress-time curves. The results showed that when Δεt/2=0.3%, during stage ΙΙ, dislocation annihilation mainly occurred during compressive loading. Dislocation annihilation included annihilation caused by cross-slip of screw dislocations and annihilation of adjacent edge dislocation dipoles. Furthermore, considering the critical annihilation distance between two adjacent edge dislocation dipoles, a modified dislocation annihilation model was presented. The dislocation annihilation model was verified based on the actual annihilation rate of dislocations. Further, the relationship of microstructure and fatigue properties was discussed. Based on the dislocation annihilation mechanisms, the fatigue life model considering dislocation annihilation was established. When the ratio of ρ¯− to ρ¯ increased, the fatigue life increased. Therefore, for cyclic hardening materials, obvious dislocation annihilation can increase fatigue life.

Screw dislocation interaction with irradiation defect-loops in α-iron: Evaluation of loop-induced stress field effect using dislocation dynamics simulations

Plastic strain spreading in post-irradiated Fe grains takes the form of wavy shear bands, where mobile dislocations interact with the radiation defect dispersions. In actual Fe grains, dislocation/loop interactions involve several contributing factors including: screw dislocation cross-slip and loop-induced stress. The loop-induced stress effect is here evaluated by systematic simulation case comparisons, using adapted dislocation dynamics simulations. Namely, dislocation/loop simulation cases are systematically compared with equivalent dislocation/facet simulation cases, under room temperature straining conditions. The facets have exactly the same size and orientation as in the reference loop cases, however; the facets have no associated stress field. It is thereby found that in presence of cross-slip the total reaction time and reaction strain associated with various dislocation/facet cases is close to their dislocation/loop counterparts (within 15% and 12%, respectively). In the present investigation context, loop-induced stress field contribution is thus a second order effect, regardless of the considered loop type and orientation. In this situation, the calculation-intensive dislocation/loop interaction description can be replaced by the much faster dislocation/facet approach, for computationally intensive grain-scale simulations.

Effects of second phases on deformation behavior and dynamic recrystallization of as-cast Mg-4.3Li-4.1Zn-1.4Y alloy during hot compression

Hot compression and dynamic recrystallization (DRX) behavior corresponding to the second phases of as-cast Mg-4.3Li-4.1Zn-1.4Y (wt.%) alloy was investigated in the range of 250–450 °C and 0.001–10 s−1. True strain-true stress curves showed typical characteristics DRX process. Constitutive relationship yielded an average activation energy (Q) and stress exponent (n) of 147.183 kJ/mol and 5.49, respectively. The hot deformation was mainly controlled by climb of edge dislocations, which turned into cross-slip of screw dislocations at ≥400 °C. The volume fraction of second phases changed the dislocation movement and resulted in the variation of the rate-controlling mechanism. The peak power dissipation efficiency (η) was observed at 450 °C/0.1 s−1 (32%), and the corresponding uniform and fine microstructure was attributed to the dynamic precipitation and complete DRX from uniformly distributed second phase particles. A wide flow instability region was observed at all temperatures and relatively high strain rates, corresponding to the non-uniform microstructure of the incomplete DRX and deformation band composed of ultrafine DRXed grains, which resulted from local distributed second phase particles. DRX process was attributed to the nucleation at second phase particles by the mechanism of particle stimulated nucleation (PSN), and the incomplete DRX process was accompanied by the dynamic recovery (DRV) process.

Cross-slip of long dislocations in FCC solid solutions

Cross-slip of screw dislocations is a dislocation process involved in dislocation structuring, work hardening, and fatigue. Cross-slip nucleation in FCC solid solution alloys has recently been shown to be strongly influenced by local fluctuations in spatial arrangement of solutes, leading to a statistical distribution of cross-slip nucleation barriers. For cross-slip to be effective macroscopically, however, small cross-slip nuclei (∼40b) must expand across the entire length of typical dislocation segments (102−103b). Here, a model is developed to compute the relevant activation energy distribution for cross-slip in a random FCC alloy over arbitrary lengths and under non-zero Escaig and Schmid stresses. The model considers cross-slip as a random walk of successive flips of adjacent 1b segments, with each flip having an energy consisting of a deterministic contribution due to constriction formation and stress effects, plus a stochastic contribution. The corresponding distribution is computed analytically from solute-dislocation and solute-solute binding energies. At zero stress, the probability of high activation energies increases with dislocation length. However, at stresses of just a few MPa, these barriers are eliminated and lower barriers are dominant. For increasing segment length, the effective energy barrier decreases according to a weak-link scaling relationship and good analytic predictions can be made using only known material properties. Overall, these results show that the effective cross-slip barrier in a random alloy is significantly lower than estimates based on average elastic and stacking fault properties of the alloy.

Nano-indentation used to study pyramidal slip in GaN single crystals

The nucleation and structure of dislocations created by the nano-indentation of GaN samples with dislocation densities ≈103, 106 or 109 ⊥/cm2 were studied in the interest of learning how dislocations can be created to relieve the mismatch strain in ternary nitride films grown on (0001) oriented binary nitride substrates. Using transmission electron microscopy and stress analyses to assist in interpreting the nano-indentation data, we determined that the pop-ins in the indenter load vs. penetration depth curves are created by an avalanche process at stresses well above the typical yield stress. The process begins by the homogeneous formation of a basal plane screw dislocation that triggers the formation of pyramidal and other basal plane dislocations that relieve the excess stored elastic energy. It appears that pyramidal slip can occur on either the {1122} or {0111} planes, as there is little resistance to the cross slip of screw dislocations.

Hydrogen-induced strain localisation in oxygen-free copper in the initial stage of plastic deformation

Single crystals of oxygen-free copper oriented to easy glide of dislocations were tensile tested in order to study the hydrogen effects on the strain localisation in the form of slip bands appearing on the polished specimen surface under tensile straining. It was found that hydrogen increases the plastic flow stress in Stage I of deformation. The dislocation slip localisation in the form of slip bands was observed and analysed using an online optical monitoring system and atomic force microscopy. The fine structure of the slip bands observed with AFM shows that they consist of a number of dislocation slip offsets which spacing in the presence of hydrogen is markedly reduced as compared to that in the hydrogen-free specimens. The tensile tests and AFM observations were accompanied with positron annihilation lifetime measurements showing that straining of pure copper in the presence of hydrogen results in free volume generation in the form of vacancy complexes. Hydrogen-enhanced free-volume generation is discussed in terms of hydrogen interactions with edge dislocation dipoles forming in double cross-slip of screw dislocations in the initial stage of plastic deformation of pure copper.

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.

Generation and interaction mechanisms of prismatic dislocation loops in FCC metals

We investigate the mechanisms of prismatic loop formation, motion, interactions, and large-scale patterning in fcc metals utilizing Discrete Dislocation Dynamics (DDD). We identify two main formation mechanisms; both enabled by cross-slip of screw dislocations. The first is termed Super-Jog-Drag-Truncation (SJDT), and the second is the Offset-Double-Cross-Slip (ODCS) mechanism. DDD simulations show that the ODCS mechanism is a precursor to the SJDT mechanism, which then leads to the formation of prismatic loop arrays. It is shown that successive SJDT events enable a knitting mechanism that can generate long strings of prismatic loop arrays, consistent with experiments. We show that fully sessile dislocation segments arise in several loop-loop interactions, leading to Frank-Read and single-arm type sources. A new stable butterfly configuration is found when two {11¯1}<011> prismatic loops interact to form glissile segments on conjugate glide planes, joined by one sessile segment that pins this structure. Absorption of prismatic loops by screw segments and the formation of helical turns is reproduced by DDD simulations, consistent with earlier MD results. An efficient new tripolar transport mechanism is found to contribute to the clustering of prismatic loops near Persistent Slip Band (PSB) channel walls during fatigue loading.

Shear stress- and line length-dependent screw dislocation cross-slip in FCC Ni

Screw dislocation cross-slip is important in dynamic recovery of deformed metals. A mobile screw dislocation segment can cross slip to annihilate an immobile screw dislocation segment with opposite Burgers vector, leaving excess dislocations of one kind in a crystal. Previous studies have found that the cross-slip process depends on both the local stress state and dislocation line length, yet a quantitative study of the combined effects of these two factors has not been conducted. In this work, we employ both dynamic concurrent atomistic-continuum (CAC) [L. Xiong, G. Tucker, D.L. McDowell, Y. Chen, J. Mech. Phys. Solids 59 (2011) 160–177] and molecular dynamics simulations to explore the shear stress- and line length-dependent screw dislocation cross-slip in face-centered cubic Ni. It is demonstrated that the CAC approach can accurately describe the 3-D cross-slip process at a significantly reduced computational cost, as a complement to other numerical methods. In particular, we show that the Fleischer (FL) [R.L. Fleischer, Acta Metall. 7 (1959) 134–135] type cross-slip, in which a stair-rod dislocation is involved, can be simulated in the coarse-grained domain. Our simulations show that as the applied shear stress increases, the cross-slip mechanism changes from the Friedel-Escaig (FE) [B. Escaig, J. Phys. 29 (1968) 225–239] type to the FL type. In addition, the critical shear stress for both cross-slip mechanisms depends on the dislocation line length. Moreover, the cross-slip of a screw dislocation with a length of 6.47 nm analyzed using periodic boundary conditions occurs via only the FL mechanism, whereas a longer dislocation with length of 12.94 nm can cross-slip via either the FE or FL process in Ni subject to different shear stresses.

Free-end adaptive nudged elastic band method for locating transition states in minimum energy path calculation.

A free-end adaptive nudged elastic band (FEA-NEB) method is presented for finding transition states on minimum energy paths, where the energy barrier is very narrow compared to the whole paths. The previously proposed free-end nudged elastic band method may suffer from convergence problems because of the kinks arising on the elastic band if the initial elastic band is far from the minimum energy path and weak springs are adopted. We analyze the origin of the formation of kinks and present an improved free-end algorithm to avoid the convergence problem. Moreover, by coupling the improved free-end algorithm and an adaptive strategy, we develop a FEA-NEB method to accurately locate the transition state with the elastic band cut off repeatedly and the density of images near the transition state increased. Several representative numerical examples, including the dislocation nucleation in a penta-twinned nanowire, the twin boundary migration under a shear stress, and the cross-slip of screw dislocation in face-centered cubic metals, are investigated by using the FEA-NEB method. Numerical results demonstrate both the stability and efficiency of the proposed method.

Atomistic simulation of < c + a > screw dislocation cross-slip in Mg

The core structure and glide behavior of a 〈c+a〉 screw dislocation in Mg is studied using molecular dynamics simulations at 0K, 70K and 300K. We find that slip on pyramidal II planes is preferred at 300K. At lower temperatures, the dislocation cross slips between pyramidal II and pyramidal I planes with sufficient applied stress. We find a metastable compact core structure, with an intermediate core energy between those of the dissociated dislocations on pyramidal II and pyramidal I planes. This compact core is observed in the cross slip from pyramidal II to pyramidal I planes at 0K and 70K.

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.

Dislocation cross-slip controlled creep in Zircaloy-4 at high stresses

Abstract Uniaxial creep tests were performed on Zircaloy-4 sheet in the temperature range of 500–600 °C at high stresses (>10−3E), to uncover the rate-controlling mechanism. A stress exponent of 9.3–11 and a stress-dependent activation energy in the range of 220–242 kJ/mol were obtained from the steady state creep data. TEM analyses revealed an extensive presence of hexagonal screw dislocation network on the basal planes indicating recovery of screw dislocations by cross-slip to be the dominant mechanism. The creep data was therefore analyzed in the light of Friedel׳s cross slip model for HCP metals according to which the stress-dependency of the activation energy determined from the creep data was written in the form, U = ( 150 ± 4 ) + ( 2236 ± 124 τ ) kJ / mol The constriction energy of screw dislocations of 150 kJ/mol is in agreement with the values reported in the literature for zirconium and other HCP metals. Further analysis of the yield strength and the activation volume data obtained from stress relaxation tests in the temperature range 500–600 °C favors cross-slip of screw dislocations as the rate controlling mechanism over the test conditions.

First principle predictions of anomalous yield strength in L12 materials

By using previous energy based arguments for screw dislocation cross-slip from (111) to (001) now combined with verifying antiphase boundary (111) stability and the width of subsegment complex stacking fault, we construct a simple plot that predicts the existence of yield strength anomaly and its relative strength. We construct the plot from calculating planar-fault energies, i.e. antiphase boundary (APB), complex and superlattice intrinsic stacking faults (CSF and SISF) and their stability for a range of L12 based intermetallics using ab initio electronic structure methods. Our plot reproduces the relative order of observed values of anomalous peak temperatures. The importance of determining the stability of APB(111) and the role of chemical (thermal antisite) disorder is also discussed.

Quasi-elastic strain fields in a lattice of SnSbCu alloy during creep

Apparent steady state creep of Sn0.65Sb0.25Cu0.10 alloy is studied under different constant stresses ranging from 19.27 to 21.67MPa near the transformation temperature ≅443K. Analysis creep data in the quasi-steady state regime at 443K reveals an anomalous creep behavior with a strain rate sensitivity parameter m changing from 0.15±0.01 to 0.33±0.01 which points to cross-slipping dislocation mechanism. The activation energy for creep deformation, Qst, was determined to be 45.47±5.96kJ/mole in the temperature region investigated. The experimental results obtained of Qst are compared with those predicted by Friedel–Jaffe–Dorn and Escaig cross-slip models. The results indicated that the rate controlling dominant mechanism for creep regime is cross-slip of screw dislocations. X-ray and microstructural analysis supports that the relaxation of the internal lattice strain fields takes place during apparent steady state creep.

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.

Hot deformation behavior and processing map of as-cast AZ61 magnesium alloy

Isothermal compression tests were performed to investigate the hot deformation behavior of as-cast AZ61 magnesium alloy. True stress–true strain curves were obtained for deformation at temperature from 220 to 380°C with the strain rate range from 10−3 to 1s−1. Based on the flow stress data, the processing map at a strain of 0.6 for AZ61 magnesium alloy was developed using the dynamic materials model (DMM) theory. The processing map was found to be characterized by three dynamic recrystallization (DRX) domains. The values of apparent activation energy for domains I and II, falling in the low strain rate regime, were estimated to be 200 and 178kJ/mol, respectively, suggesting that the cross-slip of screw dislocations may be the rate controlling process. At higher strain rates in domain III, dislocation climb is considered to be the rate controlling mechanism with the apparent activation energy being estimated as 152kJ/mol. Furthermore, both the mechanisms for DRX and the deformation/microstructure stability in three domains were discussed with reference to the characteristics of the stress–strain curves and the processing map.

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.

Dynamic Recrystallization in Zirconium Alloys

Abstract In this investigation, the characteristics of dynamic recrystallization (DRX) in five Zr-alloys, namely, commercial pure zirconium (CP-Zr), Zircaloy-2 (Zr–Sn), Zr-2.5Nb (Zr–Nb), Zr-2.5Nb-0.5Cu (Zr–Nb-Cu), and Zr-1Nb-1Sn-0.1Fe (Zr–Nb–Sn–Fe), have been examined. For this purpose, processing maps were constructed using strain rate sensitivity (m) data as a function of temperature and strain rate. This has been done using compression tests carried out at constant true strain rate. The processing maps revealed the bounds of DRX domain as iso-contour of m in strain rate–temperature plane. Optical microscopy and transmission electron microscopy (TEM) were used to analyze the evolution of the microstructure and to ascertain the nature of dislocation mechanisms in deformed and quenched samples from the DRX domain. For all the alloys studied, TEM revealed complete modification of β-transformed microstructure to an equiaxed morphology containing dislocation substructure within. The variation of grain size with strain rate and temperature, high ductility, and a linear variation of log(grain size) with log(Z) (where Z is the Zener–Hollomon parameter) are some important characteristic features associated with DRX domains of Zr-alloys. While Nb exhibited strong influence on lowering the strain rate for the occurrence of DRX of CP-Zr, Sn addition (Zr–Sn) did not alter DRX characteristics. TEM observations neither revealed the nature of nucleation event nor identified the dislocation mechanism involved in the DRX process. In order to ascertain the rate controlling dislocation mechanism, the flow stress data were analyzed using a model of thermally activated flow. On the basis of the magnitudes of activation energy and apparent activation area, the cross-slip of screw dislocation has been identified as the rate controlling mechanism involved in the DRX process. The activation energy has been found to increase by alloying elements, which is expected to lower stacking fault energy (SFE) and increase separation between the partials. Further analysis of the data using Friedel’s model revealed that the activation energy for the cross-slip process can be decomposed into two parts—one related to the process of forming a constriction in the dissociated dislocations and the other needed for recombining the dissociated dislocations. While the former component (related to SFE) is dominant in Nb containing Zr-alloys, both the components are involved in controlling the deformation behavior of CP-Zr and Zr–Sn alloys. The effects of alloying elements on DRX characteristics and on the evolution of dislocation structure have been rationalized on the basis of cross-slip as the rate controlling dislocation mechanism in a qualitative manner. The importance of dynamic recovery in DRX process has been emphasized in view of this.