Cross-slip Plane Research Articles

Analysis of deformation bands and cell structure in cyclically deformed near-[formula omitted]-oriented copper single crystals

In this study, we investigate the deformation bands (DBs), viz. DBI and DBII, and cell bands (CBs) in the near-1¯11-multiple-slip-oriented single crystals during cyclic deformation. Three different types each of DBIs [(111), (1¯1¯1), and (1¯11¯)] and DBIIs [(2¯11), (1¯21), and (1¯12)] can be summarized as the primarily activated slip plane and the combination of activated primary and coplanar slip systems, respectively. The formation planes of CBs [(121), (1¯1¯2), and (2¯11¯)] are perpendicular to the cross-slip plane and parallel to the primary slip direction. The highly symmetrical characteristics of multiple-slip-oriented single crystals can produce inconsistent correspondences between DBs and CBs.

Improving method for deterministic treatment of double cross-slip in FCC metals under low homologous temperatures

Despite its importance in crystal plasticity, cross-slip has not yet been completely understood. The widely accepted approach understands cross-slip as a thermally-activated stochastic process, especially at higher homologous temperatures. An alternative approach is based on an experimentally supported observation that, especially at lower homologous temperatures, cross-slip becomes a deterministic stress-driven process governed by the line tension, by the applied stress, and by the short-range interactions among dislocations. The current challenge remains in understanding how the tip of the screw dislocation segment of changes the primary slip plane for the secondary slip plane. We suggest an explanation of this problem available by the mathematical theory of moving parametrized curves. For the dynamical change between the primary plane and the cross-slip plane, two methods are introduced and compared. They are referred to as the tilting projection method (denoted as TPM) and the vertical projection method (denoted as VPM). Main difference between them is how they regularize the motion of the dislocation across the edge between the primary and the cross-slip plane. After the motion strategy is set, this article explains that dislocation motion laws can be treated numerically by means of the flowing finite-volume method, including the redistribution of the discretization points ensuring a long-term stability of the algorithm. Particular computational results of cross-slip obtained by both approaches are mutually compared and evaluated. For the considered material setup of the FCC copper and nickel crystals, good agreement has been observed.

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

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

An atomic-scale insight into Ni3Al slip traces

We examined at the atomic scale using in situ scanning tunnelling microscopy under ultra-high vacuum environment the slip traces left by dislocation movements at the free surface of Ni3(Al,Ta) single crystals deformed in compression at different temperatures, namely room temperature, 400 K and 600 K. The purpose is to extract from the slip traces, considered as direct signatures of dislocation movements in the bulk, the elementary dislocation mechanisms that could be at the origin of the so-called yield stress anomaly in this ordered crystallographic structure. The atomic surface structure has never been concomitantly observed with slip traces, but atomic scale resolution has been currently achieved allowing the imaging of a single lattice spacing deviation along a slip trace. Our atomic scale observations of slip traces do not permit to draw decisive conclusions regarding the various models that have been proposed to explain the yield stress anomaly, but they definitively bring new and unique insights in the understanding of this phenomenon. In particular, they show the formation and breaking of incomplete Kear–Wilsdorf configurations, which unambiguously supports interpretations of in situ TEM observations. They also prove that the so-called Kear–Wilsdorf locks are indeed early mobile on the cube cross slip plane, which is usually not accounted for in the models.

Influence of the stress state on the cross-slip free energy barrier in Al: An atomistic investigation

The influence of the stress state on the cross-slip rate in Al was analyzed by means of molecular dynamics simulations and transition state theory. The activation energy barrier in the absence of thermal energy was determined through the nudged elastic band method while the cross-slip rates were determined using molecular dynamics simulations for different magnitudes of the Schmid stress on the cross-slip plane, and of the Escaig stresses on the cross-slip and glide planes. The enthalpy barrier and the effective attempt frequency were determined from the average rates of cross-slip obtained from the molecular dynamics simulations. It was found that the different stress states influence the cross-slip rate assuming harmonic transition state theory. Moreover, the theoretical contributions to the enthalpy barrier (configurational and due to the interaction of the applied stress with the local stress field created by the defect) were identified from the atomistic simulations while the entropic contribution to the activation energy could be estimated by the Meyer-Neldel rule. Based on these results, an analytical expression of the activation enthalpy for cross-slip in Al as a function of the different combinations of Schmid and Escaig stress states was developed and validated. This expression can be easily used in dislocation dynamics simulations to evaluate the probability of cross-slip of screw dislocation segments.

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.

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

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.

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.

Evaluation of a-type screw dislocations in m-GaN film by means of X-ray diffractometry

Dislocations in an epitaxial GaN film with a surface (m-GaN) were investigated by means of X-ray diffractometry. It was clarified that a-type screw dislocations existed in the sample by evaluating diffraction contrast on X-ray topographs (XRTs). In addition, local lattice inclinations of the plane toward the [0001] direction were observed with spatial intervals similar to the separation distances of those a-type screw dislocations slipping on the (0001) basal plane and also on other cross-slip planes in the sample.

Automatic Control of the Electric Cross Sliding Welding Based on VC++

By controlling the electric cross sliding planes to achieve welding automation, Propose a VC++ based automatic control system. Based on electric electrical characteristics of cross slip planes, designed the hardware systems and control processes, use the VC++ software design a self-adjustment factor of Fuzzy-PID composite controller for control. Welding experiment had proved that the automatic tracking control result, and the result meets industry requirements.

What can be learnt on the yield stress anomaly of Ni3Al using AFM observations

We examined by in situ scanning probe microscopy the slip traces at the free surface of Ni3(Al,Ta) single crystals deformed in ultra high vacuum environment at various temperatures. It is evidenced that the mean free path of superdislocations in the primary octahedral planes strongly decreases with increasing temperatures. This is quantified by the decrease in the number of dislocations along slip traces corresponding to the primary (111) slip planes. Correlatively the number of cross-slip events increases with increasing temperature, together with a drastic increase of the distance travelled by the dislocations on the cube cross-slip plane. The experimental results are discussed in the frame of previous theoretical models that have been proposed to predict the yield stress anomaly of L12 intermetallic compounds.

Cross slip of dislocation loops in GaN under shear

AbstractThis work explores possible cross‐slip mechanisms of gliding type <a > = a /3[1 –2 1 0] dislocation loops in wurtzite gallium nitride (GaN) as a function of slip plane. A modified form of the dislocation dynamics code ParaDiS was employed using isotropic linear elasticity and dislocation mobilities estimated in part from molecular dynamics (MD) simulations. Under an externally applied uniform stress, the occurrence of cross slip events is highly dependent on the initial dislocation slip plane. The basal plane is the preferred active plane, owing to the greater mobility of <a > type segments on that plane, over the other planes considered including the prismatic (–1 0 1 0) and two equivalent pyramidal planes (–1 0 1 1) and (1 0 –1 1). For an applied stress state, cross slip processes are more readily seen from the prismatic‐to‐basal planes or the pyramidal‐to‐basal planes, and neither is found to occur in reverse. Cross slip by climb is not presently considered. In all cases, cross‐slip events occur after the loop expands until a greater number of screw‐oriented segments are able to access the cross slip plane and the resolved stresses on the plane become sufficiently large. In comparison to dislocations found in GaN previously, the calculations suggest that some threading dislocations along the [0001] direction that have edge character may have been formed from loops whose screw segments slip and escape on basal planes leaving only the edge segments.

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.

A dislocation dynamics analysis of the critical cross-slip annihilation distance and the cyclic saturation stress in fcc single crystals at different temperatures

Cross-slip is treated as a deterministic, mechanically activated process governed by the applied stress, by the interaction force between approaching screw dislocations of the opposite sign and by the line tension related to the persistent slip band channel width. The dislocations are modeled as moving polygons. In the evaluation of the critical cross-slip annihilation distance and the saturation stress in cycling, we accept two assumptions inspired by Brown [Brown L. Philos Mag A 2002;82:1691]: (i) the critical parameter associated with cross-slip is the spreading of the dislocation loop on the cross-slip plane, not the critical formation of a constriction in an extended screw dislocation core. (ii) The saturation stress in cycling is controlled by the stress required to separate two screw dislocations of opposite signs which are just on the point of mutual annihilation by cross-slip. The proposed model predicts the critical annihilation distance and the cyclic saturation stress in agreement with the available experimental data for Cu, Ni and Ag single crystals.

Expectable specific features of BCC crystal plastic flow and consistency with the Schmid law

When several types of slip systems participate in crystal plasticity, the critical shear stress (CSS) of each system can suffer load orientation and sign dependencies. Variations on the CSS can result from asymmetric slip planes contributing to the plastic straining, as is the case for {112} planes in BCC crystals, and from collaboratively involved slip planes in multi-planar dislocation motions. For BCC crystals, these planes are the in-zone, cross-slip planes of each slip direction. Strictly speaking, these expectable variations do not constitute a violation of the Schmid law and not even a deviation. In order to further account for crossed non-glide stress effects between slip planes, the existing regularized forms of the classical Schmid law which do not violate the fundamentals of the criterion seem adaptable for matching with typical experimental data of both BCC and FCC structures. This is discussed and exemplified here.

Spontaneous athermal cross-slip nucleation at screw dislocation intersections in FCC metals and L12 intermetallics investigated via atomistic simulations

In this manuscript, we extend on our prior work to show that under certain conditions cross-slip nucleation is athermal and spontaneous with zero activation energy in FCC elemental metals such as Ni and Cu, and L12 intermetallic compounds such as Ni3Al. Using atomistic simulations (molecular statics), we show that spontaneous cross-slip occurs at mildly repulsive intersections. Further, the local Shockley partial dislocation interactions at such repulsive intersections are found to be attractive leading to junction formation. The line orientation of the intersecting dislocation determines whether the spontaneous cross-slip nucleation occurs from either the glide plane to the cross-slip plane or vice versa. Collectively, these results suggest that cross-slip should be preferentially observed at selected screw dislocation intersections in FCC-derviative metals and alloys.

Dislocation dynamics simulations of slip systems interactions and forest strengthening in ice single crystal

The contribution of forest interactions to flow stress and strain hardening in ice single crystals is evaluated from dislocation dynamics simulations. The systematic mapping of dislocation–dislocation interactions and the calculation of the interaction strength between slip systems suggest an important contribution of collinear annihilation reactions. Comparison with experiment shows that the forest strengthening induced by a small density of collinear dislocation segments in cross-slip planes may have been underestimated in current models for ice plasticity.

Internal Stress Field of Double Cross-slip using Level Set Dislocation Dynamics

A three-dimensional level set method (LSM) was proposed for dislocation dynamics of which the dislocation curves were smoothly evolved, especially when topological changes of merging and breaking occur. The intersections of the zero levels of two level set functions are used to represent the dislocation lines in three dimensions. Fast marching method (FMM) or fast sweeping method (FSM) creating signed distance function (SDF) from the given interface can incorporate the existing different shapes into one level set function. Therefore, the dislocation lines can be represented by one set of level set functions. Within some specific restrictions, we succeeded to demonstrate some dislocation movements like cross-slip, double cross-slip and dislocation interactions on cross-slip plane, and discussed the internal stress field around such a complex topological dislocation configuration.

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.