Dislocation-dislocation Interactions Research Articles

High temperature dislocation processes in precipitation hardened crystals investigated by a 3D discrete dislocation dynamics

3D discrete dislocation dynamics is employed to investigate motion of general mixed dislocation segments subjected to high temperature loadings in microstructures with impenetrable particles. The implementations of the model first address several benchmark processes including shrinkage of a glissile dislocation loop driven by self-stresses and an annihilation of mutually interacting co-axial prismatic dislocation loops. In particular, we show that models of the microstructure with planar and/or translational symmetry improve efficiency, speed and stability of the calculations. Our simulations then focus on migration of low angle dislocation boundaries in an array of particles while taking into account all mutual dislocation-dislocation interactions and the action of an externally applied stress. The results show for the first time that the migration of tilt dislocation boundaries in crystals with particles can be associated with threshold stresses. The calculated thresholds are in a good agreement with experimental threshold stresses that characterize creep behaviour of precipitation hardened alloys.

Electronic structure study of screw dislocation core energetics in Aluminum and core energetics informed forces in a dislocation aggregate

We use a real-space formulation of orbital-free DFT to study the core energetics and core structure of an isolated screw dislocation in Aluminum. Using a direct energetics based approach, we estimate the core size of a perfect screw dislocation to be ≈ 7 |b|, which is considerably larger than previous estimates of 1–3 |b| based on displacement fields. The perfect screw upon structural relaxation dissociates into two Shockley partials with partial separation distances of 8.2 Å and 6.6 Å measured from the screw and edge component differential displacement plots, respectively. Similar to a previous electronic structure study on edge dislocation, we find that the core energy of the relaxed screw dislocation is not a constant, but strongly dependent on macroscopic deformations. Next, we use the edge and screw dislocation core energetics data with physically reasonable assumptions to develop a continuum energetics model for an aggregate of dislocations that accounts for the core energy dependence on macroscopic deformations. Further, we use this energetics model in a discrete dislocation network, and from the variations of the core energy with respect to the nodal positions of the network, we obtain the nodal core force which can directly be incorporated into discrete dislocation dynamics frameworks. We analyze and classify the nodal core force into three different contributions based on their decay behavior. Two of these contributions to the core force, both arising from the core energy dependence on macroscopic deformations, are not accounted for in currently used discrete dislocation dynamics models which assume the core energy to be a constant excepting for its dependence on the dislocation line orientation. Using case studies involving simple dislocation structures, we demonstrate that the contribution to the core force from the core energy dependence on macroscopic deformations can be significant in comparison to the elastic Peach–Koehler force even up to distances of 10–15 nm between dislocation structures. Thus, these core effects, whose origins are in the electronic structure of the dislocation core, can play an important role in influencing dislocation-dislocation interactions to much larger distances than considered heretofore.

Mechanical properties of Mg-Sc binary alloys under compression

The flow stress and work hardening behaviour during uniaxial compression of dilute binary Mg-Sc alloys have been studied at 4.2K, 78K and 298K. The influences of atomic misfit, chemical misfit, solute electronic properties and stacking fault energy (SFE) on strength and ductility have been examined. The results suggest that the small atomic misfit and the reduction of SFE due to Sc additions are decisive factors in determining the mechanical behaviour of the alloys. Mg-Sc alloys deform by basal, prismatic 〈a〉, pyramidal 〈c+a〉 slip and extension twinning. Sc exerts limited strengthening on these modes due to the small atomic size and weak solute-dislocation and solute-twin boundary interactions. Constitutive modelling of the flow stress permits for the evaluation of the critical resolved shear stress (CRSS) of slip and twinning systems and determination of their activity during deformation. Analysis of activation volume and activation distance suggests that dislocation-dislocation interactions determine the flow stress. The strain rate sensitivity parameter is unaffected by alloy composition, but it decreases sharply with decreasing temperature. Mg-Sc alloys show some improvement in strength and ductility in comparison to Mg, however not as much as demonstrated by common Mg-RE binary systems. The enhancement in ductility is attributed in part to the activity of twinning and non-basal slip.

Modeling plasticity of MgO by 2.5D dislocation dynamics simulations

In this study, we model the plasticity of MgO (periclase) using a 2.5-dimensional (2.5D) dislocation dynamics (DD) simulation approach. This model allows us to incorporate climb in DD simulations to model the creep behavior at high-temperature. Since a 2D formulation of DD cannot capture some important features of dislocation activity (e.g. those involving line tension), local rules are introduced to take these features into account (this is the 2.5D approach). To ensure the validity of such approach, the model is applied over a wide temperature range with a view in the lower temperature regimes where the newly introduced mechanism (climb) is not active, to benchmark our model against previous 3D simulations and experimental data. Thus we consider successfully a low temperature (T≤600K) regime where plasticity is dominated by dislocation glide in the thermally activated regime; an intermediate regime (T=1000K) where plasticity is dominated by dislocation-dislocation interactions; and a high-temperature regime (1500≤T≤1800K) which is the actual goal of the present study and where creep plasticity is governed by dislocation glide controlled by recovery (climb being considered here). We show that, taking into account the range of oxygen self-diffusion coefficients available in the literature, our simulations are able to describe properly the high-temperature creep behavior of MgO.

On the rapid hardening and exhaustion of twinning in magnesium alloy

We numerically study the rapid hardening and possible role of exhaustion of twinning in magnesium alloys under twinning dominated conditions, based on the large strain elastic visco-plastic self-consistent model. It is found that upon the exhaustion of the tensile twinning, further deformation requires the material to activate Prismatic and Pyramidal slips, which have relative high critical resolved shear stress (CRSS). However, the stress level at the exhaustion of the tensile twinning is not high enough to activate Prismatic and Pyramidal slips. Consequently, the imposed strain increments must mainly be accommodated by elastic deformations, and the strain hardening rate becomes a large fraction of the elastic modulus. Therefore, it can be concluded that the rapid hardening is a composite response more associated with elasticity of a large volume fraction of the material, than the dislocation-dislocation interactions normally held responsible for strain hardening of metals.

Size and orientation dependent mechanical behavior of body-centered tetragonal Sn at 0.6 of the melting temperature

Although, tin is one of the most prominent metals in soldering, very little is known about its mechanical behavior. In addition, possible size-effects of tin can become restricting for the ongoing miniaturization of microelectronic devices. Due to the low melting temperature of 505.15 K and the body-centered tetragonal crystal structure, differences in the mechanical behavior compared to face-centered cubic and body-centered cubic metals can be expected. Since Tin is especially interesting because of its multiple different slip systems, post mortem slip step analysis allowed to determine the activated slip systems and thus, to calculate size dependent critical resolved shear stresses. The measured size scaling exponent (−1.07 ± 0.06) is close to model-predictions of −1, irrespective of the activated families of slip systems in different orientations. Furthermore, an exceptional low scatter of the flow stress in various samples and no apparent hardening is found. It is concluded, that the activation of dislocation sources instead of dislocation-dislocation interactions are responsible for the observed behavior. This is in line with complementary μLaue diffraction experiments which indicate an unresolvable low density of geometrical necessary dislocations.

Role of W on the dislocation evolution in Ni-W alloy during tension followed by compression loading

In this paper, we report deformation behavior during tension followed by compression loading for Nickel and Nickel-Tungsten alloy (15 at% W) single crystals using molecular dynamics simulations to investigate the role of W on the dislocation evolution in Ni-W alloy. The stress-strain responses of single crystals under uniaxial tension followed by compression loading after different pre-strains (i.e. 0.10 and 0.20 true strains for pure Ni; 0.10 and 0.24 true strains for Ni-15 at% W alloy) are simulated at strain rate of 108 s−1 and at the temperature of 300 K. Dislocation mobility, dislocation-dislocation interaction and dislocation-twin interactions are thoroughly investigated to evaluate their influence on deformation behaviour during reverse loading. Slip dominated deformation mechanism prevails during forward loading but both twin and slip are found to be operative during reverse loading for Ni single crystal. It is observed that the dominant deformation mechanism is twin for both forward and reverse loading in case of Ni-15 at% W alloy single crystal.

Scale-Free Phase Field Theory of Dislocations

According to recent experimental and numerical investigations, if a characteristic length (such as grain size) of a specimen is in the submicron size regime, several new interesting phenomena emerge during the deformation. Since in such systems boundaries play a crucial role, to model the plastic response it is crucial to determine the dislocation distribution near the boundaries. In this Letter, a phase-field-type continuum theory of the time evolution of an ensemble of parallel edge dislocations with identical Burgers vectors, corresponding to the dislocation geometry near internal boundaries, is presented. Since the dislocation-dislocation interaction is scale free (1/r), apart from the average dislocation spacing the theory cannot contain any length scale parameter. As shown, the continuum theory suggested is able to recover the dislocation distribution near boundaries obtained by discrete dislocation dynamics simulations.

OS1331-282 高強度・高延性を有するナノ構造体の欠陥設計

When grain size decreases to the nanometer scale, dislocation structures hardly form in the grain; hence, it cannot be expected to obtain a large work hardening rate for nanostructured materials within the conventional framework of the theory based on the dislocation-dislocation interaction. However, the strength controlling mechanism of nanostructured materials could be different from that of coarse-grained materials; dislocation emission from grain boundaries must control the strength of nanostructured materials because of a shortage of intragranular dislocation sources. Therefore, if the resistance to following dislocation emissions from a site of grain boundaries can increase after the first dislocation emission from the site, we can expect that nanostructured materials can show large ductility due to the grain-boundary dislocation source hardening mechanism. In this paper, we first show the possibility of the grain-boundary dislocation source hardening mechanism to various Al <112> tilt grain boundaries and then consider the effect of the grain-boundary dislocation source hardening mechanism on ductility of nanostructured materials by performing tensile loading tests of nano-sized round-bar specimens.

Microstructure characterisation of an X70 grade pipeline steel and its dislocation development during Bauschinger testing

The microstructure of an X70 alloy and its dislocation development during one cycle of compression/tension strain has been analysed. The microstructure of the as received material and the dislocation arrangements before, during and after the Bauschinger test have been characterised. Results for this particular alloy show no evidence of grain boundary dislocation pile-ups or of precipitates pinning dislocations. A comparison between the dislocation arrangement in the as received, compressed and compressed-tensioned samples shows the formation of small dislocation cells, implying that the conception of the Bauschinger effect comes from dislocation-dislocation interactions.

Influence of hydrostatic compression on the sliding of a pair of edge dislocations in metals with a high impurity concentration

The dynamic drag of dislocations by point defects in hydrostatically compressed metals is theoretically investigated. Account is taken of the influence of a high pressure on dislocation-dislocation and dislocation-point defect interactions. It is shown that the pressure dependence of the force causing dynamic drag of dislocations is determined by competition between these interactions.

TEM and stress relaxation analysis of 99.1% aluminum processed by Equal Channel Angular Extrusion

Relaxation experiments were performed on 99.1% aluminum in addition to transmission electron microscopy and mechanical tests to follow the evolution of the microstructure and the mechanical properties changes after equal channel angular extrusion (ECAE). After deformation, weak beam investigations were conducted on selected specimens. The microstructure of deformed material shows the presence of almost parallel and elongated grains. Moreover, newly created subgrains separated by dislocation walls are observed. The tensile and Vickers hardness experiments for deformed samples showed an improvement of mechanical properties compared with the unextruded one. The activation volume, obtained from relaxation tests decreases with increasing the number of passes. This is due to change in mechanism from dislocation-dislocation interaction in coarse grains material (N = 0) to dislocation-grain boundary or grain deformation in ultra fine grains material (N≥1).

Micromechanics-based strain hardening model in consideration of dislocation-precipitate interactions

A micromechanics-based model to predict yield strength and plastic work hardening is proposed. To simplify the problem, additional strengthening by dislocation-dislocation interaction is assumed to be related only to the resistance to the motion of dislocations by uniformly distributed precipitates. The interaction between the mobile dislocations and precipitate particles is facilitated in a physically based approach. The main parameters of the proposed model are the size and strength of the precipitate under different aging conditions and microstructural parameters along with the stress state around the idealized precipitate. For verification purposes, the proposed hardening model was calibrated with previously published data and applied to the prediction of the yield stress and flow curve for precipitated alloys under different aging conditions. In particular, the existence of a transient region in the hardening rate from positive to negative could be reproduced well.

Cyclic Hardening Behavior of Polycrystals with Penetrable Grain Boundaries: Two-Dimensional Discrete Dislocation Dynamics Simulation

A two-dimensional discrete dislocation dynamics (DDD) technology by Giessen and Needleman (1995), which has been extended by integrating a dislocation-grain boundary interaction model, is used to computationally analyze the micro-cyclic plastic response of polycrystals containing micron-sized grains, with special attentions to significant influence of dislocation-penetrable grain boundaries (GBs) on the micro-plastic cyclic responses of polycrystals and underlying dislocation mechanism. Toward this end, a typical polycrystalline rectangular specimen under simple tension-compression loading is considered. Results show that, with the increase of cycle accumulative strain, continual dislocation accumulation and enhanced dislocation-dislocation interactions induce the cyclic hardening behavior; however, when a dynamic balance among dislocation nucleation, penetration through GB and dislocation annihilation is approximately established, cyclic stress gradually tends to saturate. In addition, other factors, including the grain size, cyclic strain amplitude and its history, also have considerable influences on the cyclic hardening and saturation.

Nano Effects of Helium-Plasma Treatment Nano-SiO&lt;sub&gt;2&lt;/sub&gt; Coating Vectran

The plasticity treatment of APPJ on microstructure and tensile deformation of Nano SiO2 coating Vectran in the dynamic states was investigated by specialized tensile testing at room temperature. With the addition of low-temperature Helium plasma treatment, Young's modulus and yield stress changed. It was found that micro structural parameter such as the activation volume was important to describe the Nano SiO2 coating Vectran and inter-phase strength between filaments and coating. The results of different APPJ treatments on the Nano SiO2 coating Vectran showed the change of the rate sensitivity of the filaments. The flow stress dependence of the strain rate sensitivity indicated that dynamical recover processes associated with the dislocation-dislocation interactions, which develop in the APPJ treatment Nano SiO2 coating Vectran and Vectran after small amount of deformation, leaded to strain localizations and early failure. Results revealed that APPJ treatment Nano SiO2 coating Vectran and the inter-phase would enhance the ductility of Vecetran at room temperature.

Atomic-scale analysis of defect dynamics and strain relaxation mechanisms in biaxially strained ultrathin films of face-centered cubic metals

We report results of a detailed systematic computational analysis of strain relaxation mechanisms and the associated defect dynamics in ultrathin, i.e., a few nanometers thick, Cu films subjected to a broad range of biaxial tensile strains. The analysis is based on isothermal-isostrain molecular-dynamics simulations of the response of Cu films that are oriented normal to the [111] crystallographic direction using an embedded-atom-method parametrization for Cu and multimillion-atom slab supercells. Our analysis reveals five regimes in the thin film’s mechanical response with increasing strain. Within the considered strain range, after an elastic response up to a biaxial strain level ε=5.5%, the strain in the metallic thin film is relaxed by plastic deformation. At low levels of the applied biaxial strain above the yield strain (ε∼6%), threading dislocation nucleation at the surface of the thin film in conjunction with vacancy cluster formation in the film leads eventually to the formation of voids that extend across the thickness of the film. For 6%&amp;lt;ε&amp;lt;8%, dislocations are emitted uniformly from the thin-film surface, inhibiting the nucleation of voids. For ε≥8%, in addition to nucleation of dislocations from the film surface, dislocation loops are generated in the bulk of the film and grow to intersect the thin-film surface. For ε≥10%, a high density of point defects in the film leads to nucleation of Frank partial dislocations that dissociate to form stacking fault tetrahedra. In addition, dislocation-dislocation interactions due to the high dislocation density lead to the formation of Lomer–Cottrell dislocation locks and complex stable dislocation junctions that act as obstacles to dislocation glide. As a result of these defect mechanisms, nanoscale domains are formed in the crystalline film with an average domain size of 1.5 nm and low-angle misorientations.

Effect of fine structure of Pb-In solid solutions on their deformation-induced strengthening at low temperatures

The specific features of low-temperature deformation-induced strengthening of Pb-In single crystals have been studied in a wide range of impurity concentrations. It was shown that a change in the strain-rate sensitivity of flow stress in the concentrated solid solution is connected with the inhomogeneous distribution of impurities. Based on the X-ray diffuse-scattering data, it was found that the short-range order of separation type was formed in these alloys; i.e., the lead atoms were randomly arranged and the indium atoms formed clusters whose characteristic size increased with concentration in a range of 1.0–1.9 nm. In the concentrated alloy, the appearance of coarse impurity clusters as strong obstacles for mobile dislocations in comparison with the impurity atoms and forest dislocations causes not only a sharp increase in the flow stress but also a change in the energy of dislocation-dislocation interaction.

Haasen Plot Activation Analysis of Constant-Force Indentation Creep in FCC Systems

AbstractAn analysis of the length-scale and temperature dependence of Haasen plots obtained from constant-force nano- and micro-indentation creep tests performed are reported here. The operative deformation mechanism for all the systems studied involved dislocation glide limited by dislocation-dislocation interactions. Our findings illustrate the potential usefulness of Haasen plot activation analysis for interpreting data from constant-force pyramidal indentation creep tests.

Investigation of high-temperature plastic deformation using instrumented microindentation tests. Part II: The deformation of Al-based particulate reinforced composites at 473 K to 833 K

Constant-load pyramidal indentation tests were performed from 473 K to 833 K on P/M fabricated 2024 aluminum reinforced with either SiO2, SiC, or Al2O3 particles to investigate the influence of particulate reinforcement on the high-temperature plastic deformation process during indentation. The composites all displayed larger apparent threshold stress σth than the previously reported unreinforced P/M 2024 aluminum alloy. SEM investigation of the indentations indicated that the indentation process is accompanied by considerable cracking and interfacial debonding of the reinforcing particles, the extent of which increases with increasing temperature. The magnitude of σth was largest for the Al2O3 reinforced composite and this is attributed to the load-transfer that occurs when the indenter contacts the reinforcing particles and the superior high-temperature interfacial strength of this composite. The apparent activation energy ΔG0 of the indentation strain rate increased from 0.25µb3 at 473 K to 0.60µb3 at 833 K. These values are within the expected range for weak particles and dislocation-dislocation interactions but are lower than the previously reported Δ0 of the unreinforced P/M 2024 alloy. We conclude that the low indentation strain rate of the particulate reinforced composites is the result of the load transfer due to the presence of the reinforcements and its affect on increasing the σth. The low values of ΔG0 are consistent with our observation that extensive particle cracking and interfacial debonding occur in the reinforced material during indentation.

Stability and Motion of Low Angle Dislocation Boundaries in Precipitation Hardened Crystals

The present study investigates stability and motion of low angle dislocation boundaries in an array of precipitates. The model considers discrete dislocations and precipitates that are treated as impenetrable particles. Peach-Koehler forces, which originate due to the combined effect of dislocation-dislocation interactions and the applied stress, act the individual dislocations on. Both, the dislocation glide and the dislocation climb at elevated temperatures are taken into account. Results of the numerical study suggest that a critical applied shear stress (CASS) always exists which separates stable and unstable low angle boundary configurations. Varying particle size, interparticle spacing and density of dislocations in the boundary cause changes of the CASS that are systematically investigated. It is shown that the CASSs can considerably differ from the standard Orowan stress controlling the equilibrium of an isolated dislocation in a given microstructure. This result underlines the importance of long-range dislocation interactions that influence the high temperature strength of the precipitation-hardened alloys.