Dislocation Assemblies Research Articles

Assessment of strain hardening in copper single crystals using in situ SEM microshear experiments

The effect of a pre-strain on the plasticity of copper single crystals subjected to in situ microshear deformation in a scanning electron microscope (SEM) is investigated. Pre-strains of 6.5 and 20% are imposed using [1 0 0] tensile testing. During tensile pre-deformation, several slip systems are activated and irregularly spaced slip bands form. A trace analysis revealed the presence of several slip bands on the tensile specimen near the grips while one family of slip bands parallel to the (1 1 1) crystallographic plane were detected in the middle of the tensile specimen. From the middle of the pre-deformed tensile specimens double microshear samples were prepared using focused ion beam (FIB) machining such that the [0 -1 -1] (1 -1 1) slip system could be directly activated. The results show how microshear behavior reacts to different levels of tensile pre-deformation. Sudden deformation events (SDEs) are observed during microshear testing. The critical stress associated with the first SDE is shown to increase with increasing pre-deformation as a result of an increasing number of slip bands introduced during pre-deformation per shear zone. The results allow also to obtain information on the interaction between dislocations activated during microshearing ([0 -1 -1] (1 -1 1)) and those which were introduced during tensile pre-deformation ([1 0 -1] (1 1 1) and [1 -1 0] (1 1 1)). When these slip systems interact glissile junctions and Lomer-Cottrell locks are likely to form. In the light of this analysis, we rationalize the occurrence of sudden deformation events based on piled up dislocation assemblies which overcome Lomer-Cottrell lock barriers.

Statistically motivated model of mechanisms controlling evolution of deformation band substructure

Deformation bands are interpreted as a spontaneously formed microstructure caused by anisotropy induced by the slip nature of plastic deformation. The gradient terms in the proposed constitutive equations have been derived by averaging the assembly of discrete dislocations. The rigid-plastic model points to the main constituents which control the fragmentation mechanism: anisotropy of the hardening matrix, anisotropic resistance of the boundaries to slip, and the bowing (Orowan) stress. For symmetric double slip compression, the model provides an explanation of the observed band orientation and band width, and of the significant change in structural morphology seen as the band reorientation occurs at large strains. The predictions are in favorable agreement with available observations.

Dynamic phases, pinning, and pattern formation for driven dislocation assemblies.

We examine driven dislocation assemblies and show that they can exhibit a set of dynamical phases remarkably similar to those of driven systems with quenched disorder such as vortices in superconductors, magnetic domain walls, and charge density wave materials. These phases include pinned-jammed, fluctuating, and dynamically ordered states, and each produces distinct dislocation patterns as well as specific features in the noise fluctuations and transport properties. Our work suggests that many of the results established for systems with quenched disorder undergoing plastic depinning transitions can be applied to dislocation systems, providing a new approach for understanding pattern formation and dynamics in these systems.

Random organization in periodically driven gliding dislocations

Abstract We numerically examine dynamical irreversible to reversible transitions and random organization for periodically driven gliding dislocation assemblies using the stroboscopic protocol developed to identify random organization in periodically driven dilute colloidal suspensions. We find that the gliding dislocations exhibit features associated with random organization and evolve into a dynamically reversible state after a transient time extending over a number of cycles. At a critical shearing amplitude, the transient time diverges. When the dislocations enter the reversible state they organize into patterns with fragmented domain wall type features.

A Modeling Approach to Evaluate Grain Interaction Induced by {111}^|^lt;011^|^gt; Planar Slips in Face-centered Cubic Polycrystalline Materials

An accommodation deformation model to relax incompatibility between soft (yielded) and hard (nonyielded) grains was proposed. Dislocation arrays were installed in the soft grain to investigate the effect of secondary slips on accommodating the displacement incompatibility due to the grain interaction at the grain boundary. When a secondary slip in the soft grain is active on the same plane as the dislocation arrays, it can accommodate the displacement incompatibility in almost all orientations. However, a dislocation reflection on the primary slip plane is difficult to adopt for accommodation deformation. When the secondary slip in the soft grain is restricted to a plane without the primary slip, accommodation deformation in the soft grain does not occur. To accommodate the displacement incompatibility at the grain boundary, slip systems in the adjacent grain are required in almost all orientations. Around the orientation at which the secondary plastic deformation is the hardest to achieve, three slip systems are operating in areas of accumulation with high displacement incompatibility. Thus, the three slip systems should operate on different octahedral slip planes. However, the displacement incompatibility is not fully accommodated, and a stress field remains near the normal to {111}. The combination of sufficient stress concentration to open the grain boundary and the assembly of dislocations on the three slip systems at the grain boundary may be the cause of intergranular cracking.

Numerical implementation of a 3D continuum theory of dislocation dynamics and application to micro-bending

Crystal plasticity is governed by the motion of lattice dislocations. Although continuum theories of static dislocation assemblies date back to the 1950s, the line-like character of these defects posed serious problems for the development of a continuum theory of plasticity which is based on the averaged dynamics of dislocation systems. Only recently the geometrical problem of performing meaningful averages over systems of moving, oriented lines has been solved. Such averaging leads to the definition of a dislocation density tensor of second order along with its evolution equation. This tensor can be envisaged as the analogue of the classical dislocation density tensor in an extended space which includes the line orientation as an independent variable. In the current work, we discuss the numerical implementation of a continuum theory of dislocation evolution that is based on this dislocation density measure and apply this to some simple benchmark problems as well as to plane-strain micro-bending.

Dynamical Correlations near Dislocation Jamming

Dislocation assemblies exhibit a jamming or yielding transition at a critical external shear stress value σ=σ{c}. Here we study the heterogeneous and collective nature of dislocation dynamics within a crystal plasticity model close to σ{c}, by considering the first-passage properties of the dislocation dynamics. As the transition is approached in the moving phase, the first-passage time distribution exhibits scaling, and a related peak dynamical susceptibility χ{4}{*} diverges as χ{4}{*}∼(σ-σ{c}){-α}, with α≈1.1. We relate this scaling to an avalanche description of the dynamics. While the static structural correlations are found to be independent of the external stress, we identify a diverging dynamical correlation length ξ{y} in the direction perpendicular to the dislocation glide motion.

Depinning and critical-current characteristics of topologically defected vortex lattices

We discuss the role of dislocation assemblies such as grain boundaries in the dynamic response of a driven vortex lattice. We simulate the depinning of a field-cooled vortex polycrystal and observe a general enhancement of the critical current as well as a distinct crossover in the characteristic of this quantity as a function of pinning density. The results agree with analytical predictions for grain-boundary depinning. The dynamics of grain boundaries thus proves an essential mechanism underlying the flow response of defected vortex lattices and the corresponding transport properties of the superconducting material. We emphasize the connection between the topological rearrangements of the lattice and its threshold dynamics. Our theory encompasses a variety of experimental observations in vortex matter as well as in colloidal crystals.

Material yielding and irreversible deformation mediated by dislocation motion

We study the collective behavior of dislocation assemblies in simplified models of plastic deformation. We first review several numerical results on long range dislocation interactions with simplified dislocation motion constraints. These typically give rise to a yielding transition separating stationary and moving dislocation phases. Furthermore, we discuss the intermittent relaxation of the plastic strain-rate observed around this transition at mesoscopic scales, and how this intermittent behavior gives rise to an average slow power law relaxation in time known in the literature as Andrade’s creep. We analyze the coherent dynamics and the average stress-strain relationship in the steady regime of plastic deformation. In this steady regime, plastic deformation proceeds in the form of plastic avalanches whose size and duration are broadly distributed and statistically characterized. One signature of the time correlations of this heterogeneous collective dislocation dynamics is a power spectrum scaling with frequency as f −a with an exponent α close to 1.5. This feature appears to be peculiar of dislocation and grain boundary motion as has been observed in other physical situations in the vicinity of a yielding transition.

Dislocation interactions mediated by grain boundaries

The dynamics of dislocation assemblies in deforming crystals indicates the emergence ofcollective phenomena, intermittent fluctuations and strain avalanches. In polycrystallinematerials, the understanding of plastic deformation mechanisms depends on grasping therole of grain boundaries on dislocation motion. Here the interaction of dislocations andelastic, low-angle grain boundaries is studied in the framework of a discrete dislocationrepresentation. We allow grain boundaries to deform under the effect of dislocation stressfields and compare the effect of such a perturbation to the case of rigid grain boundaries.We are able to determine, both analytically and numerically, corrections to dislocationstress fields acting on neighboring grains, as mediated by grain boundary deformation.Finally, we discuss conclusions and consequences for the avalanche statistics, as observed inpolycrystalline samples.

Statistical dynamics of dislocations in simple models of plastic deformation: Phase transitions and related phenomena

Dislocation assemblies in crystalline substrates are a beautiful example of the broad class of systems that are governed by the presence of kinematical constraints induced by interactions, geometry, and/or disorder. The interactions between dislocation lines of different type together with the dynamic constraints which tie the motion of the dislocations to their slip planes lead to the possibility of forming metastable jammed configurations even in the absence of any disorder in the material. However, general dislocation assemblies will also be affected by the presence of disorder-induced pinning forces. In this paper we study several aspects concerning the dynamics of dislocation assemblies in simple models of plastic deformation that we believe we can successfully address with the conceptual and technical tools provided by Statistical Mechanics. In particular, we discuss the yielding (or jamming) transition between stationary and moving states in these models, the intermittent and globally slow relaxations observed around this transition, and the stress–strain relationships measured in the steady regime of deformation. We also briefly describe the main implications of sample geometry and of quenched disorder in dislocation assemblies present in the vortex lattice of type II superconductors, where we obtain some of the statistical dynamic properties of experimental interest.

Depinning transition of dislocation assemblies: Pileups and low-angle grain boundaries

We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low-angle grain boundaries interacting with a disordered stress landscape provided by solute atoms, or by other immobile dislocations present in nonactive slip systems. Using linear elasticity, we compute the stress originated by small deformations of these assemblies and the corresponding energy cost in two and three dimensions. Contrary to the case of isolated dislocation lines, which are usually approximated as elastic strings with an effective line tension, the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness. A nonlocal elastic kernel results as a consequence of long-range interactions between dislocations. In light of this result, we revise statistical depinning theories of dislocation assemblies and compare the theoretical results with numerical simulations and experimental data.

Linking different scales: discrete, self-consistent field, and stochastic dislocation dynamics

The dynamics behavior of an assembly of parallel dislocations is investigated at different length scales. In the first part, it is shown that a discrete dislocation system is able to reproduce several important features of plastic deformation. Then, a self-consistent field continuum model is derived. Finally, a stochastic approach is outlined, which can be considered as an intermediate scale description between the discrete and the continuum models.

Investigation of Assemblies of Grain Boundary Dislocations in Nanostructured Copper by Computer Simulation

Computer simulation of X-ray diffraction patterns of nanostructured copper has been carried out on the basis of the kinematic theory of X-rays scattering, taking into account various configurations of extrinsic grain boundary dislocation assemblies. The conclusion based on comparison with experimental data about possible configurations of extrinsic grain boundary dislocation assemblies in nanostructured materials processed by severe plastic deformation has been done. The ways of further development of the suggested approach are shown.

Connecting atomistic and mesoscale simulations of crystal plasticity

A quantitative description of plastic deformation in crystalline solids requires a knowledge of how an assembly of dislocations — the defects responsible for crystal plasticity — evolves under stress1. In this context, molecular-dynamics simulations have been used to elucidate interatomic processes on microscopic (∼10−10 m) scales2, whereas ‘dislocation-dynamics’ simulations have explored the long-range elastic interactions between dislocations on mesoscopic (∼10−6 m) scales3. But a quantitative connection between interatomic processes and behaviour on mesoscopic scales has hitherto been lacking. Here we show how such a connection can be made using large-scale (100 million atoms) molecular-dynamics simulations to establish the local rules for mesoscopic simulations of interacting dislocations. In our molecular-dynamics simulations, we observe directly the formation and subsequent destruction of a junction (a Lomer–Cottrell lock) between two dislocations in the plastic zone near a crack tip: the formation of such junctions is an essential process in plastic deformation, as they act as an obstacle to dislocation motion. The force required to destroy this junction is then used to formulate the critical condition for junction destruction in a dislocation-dynamics simulation, the results of which compare well with previous deformation experiments4.

Long-ranged stress field produced by a planar assembly of edge dislocations: the effect of disorder

Abstract We consider the stress field induced by a planar assembly of edge dislocations. If these dislocations are periodically arranged, the stress field which they produce decreases exponentially with increasing distance from the wall. We show that in this case, disorder is a singular perturbation which leads to fluctuations of the stress field with a power-law dependence. Other physical examples where this mechanism operates are briefly mentioned.

Logarithmic Creep of Copper and Aluminium

Transient creep of polycrystalline OFHC copper and aluminium of 99·95 % purity was studied by the method of incremental loading, in tension at room temperature. All specimens were initially annealed, but some were also prestrained 10% either in tension or in compression before creep. The creep strain ε was expressed by ε = S log (1 + t/t o), and the dependence of the parameters s and to on the level of the applied tensile stress and on the sign of the prestrain was examined. The structure sensitivity of both parameters, indicated by the results, was discussed in terms of a simple stochastic model; the latter is based on the concepts of a spectrum of energy barriers to dislocation motion and the tendencyof dislocation assemblies to assume minimum-energy configurations.The observations point to the potential usefulness of such relatively simple investigations in assessing the creep resistance and studying structural detail of metals and alloys.

Interdomain and domain defect interactions in kdp

Abstract A synthesis is presented of interactions observable in the KDP domain structure below 100°K: interactions between domain tips, which follow the classical behavior of edge-type dislocations, and interactions between domain tips and certain mechanical imperfections (defects, sample boundaries). The Burgers vectors associated with the twinning dislocation assemblies lying at the domain tips is several thousand Angstroms in magnitude.