Dislocation Dynamics Simulations Research Articles

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.

Role of weakest links and system-size scaling in multiscale modeling of stochastic plasticity

Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where microstructural details are represented by a fluctuating local yielding threshold. In the present paper, we propose a method for determining this yield stress distribution by lower scale discrete dislocation dynamics simulations and using a weakest link argument. The success of scale-linking is demonstrated on the stress-strain curves obtained by the resulting mesoscopic and the discrete dislocation models. As shown by various scaling relations they are statistically equivalent and behave identically in the thermodynamic limit. The proposed technique is expected to be applicable for different microstructures and amorphous materials, too.

Influence of loading control on strain bursts and dislocation avalanches at the nanometer and micrometer scale

Through three-dimensional discrete dislocation dynamics simulations, we show that by tuning the mode of external loading, the collective dynamics of dislocations undergo a transition from driven avalanches under stress control to quasiperiodic oscillations under strain control. We directly correlate measured intermittent plastic events with internal dislocation activities and collective dynamics. Under different loading modes, the roles of the weakest dislocation source and the defect population trend are significantly different. This finding raises new possibilities of controlling correlated dislocation activities and obtaining a low defect density in nanostructured devices by tuning external constraints. In addition, the effect of machine stiffness comes to light. The statistical analysis of the burst magnitude is revisited and carefully discussed. Self-organized criticality and scale-free statistics of strain bursts are obeyed under stress control. However, this behavior is shown to break down under strain control. Rapid stress drops under pure strain control force truncation of dislocation avalanches, leading to a dynamical transition to quasiperiodic oscillations.

Initial dislocation density effect on strain hardening in FCC aluminium alloy under laser shock peening

The effect of initial dislocation density on subsequent dislocation evolution and strain hardening in FCC aluminium alloy under laser shock peening (LSP) was investigated by using three-dimension discrete dislocation dynamics (DD) simulation. Initial dislocations were randomly generated and distributed on slip planes for three different dislocation densities of 4.21 × 1012, 8.12 × 1012 and 1.26 × 1013 m−2. Besides, variable densities of prismatic loops were introduced into the DD cells as nanoprecipitates to study the dislocation pinning effect. The flow stresses as a function of strain rate obtained by DD simulation are compared with relevant experimental data. The results show a significant dislocation density accumulation in the form of dislocation band-like structures under LSP. The overall yield strength in FCC aluminium alloy decreases with increasing initial dislocation density and forest dislocation strengthening becomes negligible under laser induced ultra-high strain rate deformation. In addition, yield strength is enhanced by increasing the nanoprecipitate density due to dislocation pinning effect.

Atomistic-continuum hybrid analysis of dislocation behavior in spinodally decomposed Fe-Cr alloys

In this study, we first present the molecular dynamics (MD) simulation of dislocation behavior in a spinodally decomposed Fe-Cr alloy. The MD simulation is used for exploring the nature of the interaction between a dislocation and the spinodal decomposition without any specific assumptions. In order to classify the interaction mechanism, dislocation dynamics (DD) simulations of the interaction between a dislocation and the spinodal decomposition are performed. In the simulations, we controlled the interaction mechanism by adding and removing the atomistic mechanism. The simulation results clearly illustrate that the atomistic mechanism can be negligible in determining the critical resolved shear stress (CRSS) of spinodally decomposed Fe-Cr alloys, and the internal stress generated by the lattice constant mismatch is a dominant mechanism. These findings are very useful for simplifying the analysis of the mechanism of material strength change due to the spinodal decomposition. Particularly in the analysis using the DD simulations, the required computational effort for simulating the dislocation behavior is greatly reduced by taking into account only the internal stress without the atomistic dislocation core influence.

Dislocation dynamic simulation of dislocation pattern evolution in the early fatigue stages of aluminium single crystal

The two-dimensional discrete dislocation dynamics simulations under fully periodic boundary conditions has been employed to study the dislocation pattern evolution in the early stages of fatigue in aluminium single crystal. Long-range force among of dislocations is solved by line elasticity model, and short-range force is obtained by constitutive equations of dislocation nucleation, slip, pileup and annihilate. Dislocation movement mechanisms of single-slip-oriented and multi-slip systems are simulated and the evolution process of fatigue pattern is revealed. The result shows that dislocation quantity and microstructure strongly depend on external load and internal configuration. The dislocation pattern of single-slip-oriented generate matrix wall, and positive dislocations are vertical alignment and negative dislocations are at the angle of 45° with slip oriented in the initial stage. For multi-slip system, maze structure of dislocations is produced during dislocation multiplication, which eventually transforms into persistent slip band. The result is consistent with the existing experiment.

An Efficient High Order Method for Dislocation Climb in Two Dimensions

We present an efficient high order method for dislocation dynamics simulation of vacancy-assisted dislocation climb in two dimensions. The method is based on a second kind integral equation (SKIE) formulation that represents the vacancy concentration via the sum of double layer potentials and point sources located at each dislocation, where the climb velocity of each dislocation (or the strength of each point source) is proportional to the integral of the unknown density on the boundary of each dislocation. The method discretizes the interfaces only. Unlike previously used formulations, the proposed method avoids the need for introducing additional unknowns or integrating kernels with logarithmic singularity, and the boundary integrals in the formulation are easily discretized via the trapezoidal rule with spectral accuracy. Thus, the number of unknowns in the linear system to achieve certain accuracy is optimal for typical settings in dislocation dynamics. We compare three different methods for solving r...

Dislocation dynamic simulation of dislocation pattern evolution in the early fatigue stages of aluminium single crystal

Dislocation dynamic simulation of dislocation pattern evolution in the early fatigue stages of aluminium single crystal

Dislocation strengthening in FCC metals and in BCC metals at high temperatures

Till now, it was widely believed that the dislocation strengthening coefficients used in the Taylor-like relation were universal for a given crystallographic class of materials. In the present study, it is shown that this is actually untrue because of two effects that influence the strength of interactions between slip systems, namely the value of the Poisson ratio and the occurrence of doubly degenerated, asymmetric, junction configurations. New strengthening coefficient values for reactions between slip systems were determined using dislocation dynamics simulations on five representative FCC metals, plus germanium, and on five BCC transition metals for {110} and {112} slip systems at high homologous temperatures. The value of the Poisson ratio affects all the strengthening coefficients to various extents ranging from small to substantial. The effects of configuration asymmetry and Poisson's ratio are more marked in BCC metals than in FCC metals. These two major effects arise from a number of concurring dislocation mechanisms, which are discussed in some detail. It is expected that the use of accurate material-dependent coefficients will notably improve the predictive ability of current models for strain hardening.

Mobility law of dislocations with several character angles and temperatures in FCC aluminum

We study the mobility law of dislocations in aluminum as an important building block for the development of a multiscale method that couples an atomistic model with discrete dislocation dynamics in 3d (e.g., CADD3d). Straight dislocations of arbitrary character angles are modeled with classical molecular dynamics at several temperatures. The obtained mobility results are analyzed and validated by comparisons to theoretical models. A critical velocity parameter identified by the analytic models is correlated to the material dispersive nature. We revisit the interpretation of this constant by considering character angles that were not studied previously. Finally, the obtained mobility law is implemented and employed in the discrete dislocation dynamics simulation of a dislocation loop. Our results highlight the importance of including several angles when constructing the mobility law to produce consistent results.

Dislocation Dynamics Simulation of Interaction between Prismatic Dislocation Loops and Voids in Irradiated Thin Films

At the microscopic scale fast neutron irradiation brings about a high density of small point defect clusters in the form of dislocation loops and voids. And such radiation damage is of primary importance for materials used in nuclear energy production. In the present investigation emphasis is placed on the understanding of the mechanisms involved in the evolution of prismatic dislocation loops by glide in the presence of external free surfaces and those of the voids and in the interaction between dislocation loops and voids within irradiated thin films, so as to simulate in situ Transmission Electron Microscopy (TEM) images of dislocations, which is an indispensable tool for extracting information on radiation damage. By employing 3D dislocation dynamics based on isotropic elacticity and principle of superposition, the calculation results show that the image force is determined by the distance of the dislocation loop from the external and void surfaces and scales with the film thickness; the dislocation glide force is determined by the image stress as well as the loop–loop interaction stress which is in turn governed by the loop spacing. It is also shown that the presence of voids in the thin films has a strong influence on the behaviours of prismatic dislocations.

The stress statistics of the first pop-in or discrete plastic event in crystal plasticity

The stress at which the first discrete plastic event occurs is investigated using extreme value statistics. It is found that the average of this critical stress is inversely related to the deforming volume, via an exponentially truncated power-law. This is demonstrated for the first pop–in event observed in experimental nano-indentation data as a function of the indenter volume, and for the first discrete plastic event seen in a dislocation dynamics simulation. When the underlying master distribution of critical stresses is assumed to be a power-law, it becomes possible to extract the density of discrete plastic events available to the crystal, and to understand the exponential truncation as a break-down of the asymptotic Weibull limit.

Dislocation climb models from atomistic scheme to dislocation dynamics

We develop a mesoscopic dislocation dynamics model for vacancy-assisted dislocation climb by upscalings from a stochastic model on the atomistic scale. Our models incorporate microscopic mechanisms of (i) bulk diffusion of vacancies, (ii) vacancy exchange dynamics between bulk and dislocation core, (iii) vacancy pipe diffusion along the dislocation core, and (iv) vacancy attachment-detachment kinetics at jogs leading to the motion of jogs. Our mesoscopic model consists of the vacancy bulk diffusion equation and a dislocation climb velocity formula. The effects of these microscopic mechanisms are incorporated by a Robin boundary condition near the dislocations for the bulk diffusion equation and a new contribution in the dislocation climb velocity due to vacancy pipe diffusion driven by the stress variation along the dislocation. Our climb formulation is able to quantitatively describe the translation of prismatic loops at low temperatures when the bulk diffusion is negligible. Using this new formulation, we derive analytical formulas for the climb velocity of a straight edge dislocation and a prismatic circular loop. Our dislocation climb formulation can be implemented in dislocation dynamics simulations to incorporate all the above four microscopic mechanisms of dislocation climb.

Irreversibility of dislocation motion under cyclic loading due to strain gradients

Mechanisms that make dislocation motion irreversible are associated with the formation of dislocation junctions and cross-slip, leaving dislocations trapped inside the specimen. Using Discrete Dislocation Dynamics simulations, we identify another mechanism that produces irreversible plastic deformation and leaves no or only very few dislocations inside the sample: Under cyclic loading, dislocations which pass the neutral plane during loading (pile-up formation), generate a slip step upon unloading. The explanation is an intrinsic asymmetry between the backward and forward motion. An additional bias may be introduced by the geometry of the specimen due to the shortening of the line length of dislocations.

Fast Fourier transform discrete dislocation dynamics

Discrete dislocation dynamics simulations have been generally limited to modeling systems described by isotropic elasticity. Effects of anisotropy on dislocation interactions, which can be quite large, have generally been ignored because of the computational expense involved when including anisotropic elasticity. We present a different formalism of dislocation dynamics in which the dislocations are represented by the deformation tensor, which is a direct measure of the slip in the lattice caused by the dislocations and can be considered as an eigenstrain. The stresses arising from the dislocations are calculated with a fast Fourier transform (FFT) method, from which the forces are determined and the equations of motion are solved. Use of the FFTs means that the stress field is only available at the grid points, which requires some adjustments/regularizations to be made to the representation of the dislocations and the calculation of the force on individual segments, as is discussed hereinafter. A notable advantage of this approach is that there is no computational penalty for including anisotropic elasticity. We review the method and apply it in a simple dislocation dynamics calculation.

Controlling Strain Bursts and Avalanches at the Nano- to Micrometer Scale.

We demonstrate, through three-dimensional discrete dislocation dynamics simulations, that the complex dynamical response of nano- and microcrystals to external constraints can be tuned. Under load rate control, strain bursts are shown to exhibit scale-free avalanche statistics, similar to critical phenomena in many physical systems. For the other extreme of displacement rate control, strain burst response transitions to quasiperiodic oscillations, similar to stick-slip earthquakes. External load mode control is shown to enable a qualitative transition in the complex collective dynamics of dislocations from self-organized criticality to quasiperiodic oscillations.

The discrete-continuum connection in dislocation dynamics: I. Time coarse graining of cross slip

A recent continuum dislocation dynamics formalism (Xia and El-Azab 2015 Model. Simul. Mater. Sci. Eng. 23 055009) has been enriched by incorporating an improved cross slip model. 3D discrete dislocation dynamics simulations were used to collect cross slip rate data in the form of time series that were analysed to estimate the correlation time for cross slip, which was subsequently used as a time scale for local window averaging of the collected cross slip rate data. This time averaging filters out the cross slip rate fluctuations over time intervals less than the correlation time, thus resulting in relatively smoother time series for the cross slip rates. The coarse grained series were further cast in the form of smooth trends with superposed fluctuations and implemented in continuum dislocation dynamics simulations using a Monte Carlo scheme. This approach resulted in a significant improvement of the predicted stress–strain response and a more realistic dislocation cell structure evolution. The similitude law for the average cell size evolution with inverse of stress, however, remains unaffected by the cross slip rates used in continuum dislocation dynamics.

Critical stress statistics and a fold catastrophe in intermittent crystal plasticity.

The statistics and origin of the first discrete plastic event in a one-dimensional dislocation dynamics simulation are studied. This is done via a linear stability analysis of the evolving dislocation configuration up to the onset of irreversible plasticity. It is found that, via a fold catastrophe, the dislocation configuration prior to loading directly determines the stress at which the plastic event occurs and that between one and two trigger dislocations are involved. The resulting irreversible plastic strain arising from the instability is found to be highly correlated with these triggering dislocations.

Comparison of Dislocation Density Tensor Fields Derived from Discrete Dislocation Dynamics and Crystal Plasticity Simulations of Torsion

<p class="1Body">The importance of accurate simulation of the plastic deformation of ductile metals to the design of structures and components is well-known. Many techniques exist that address the length scales relevant to deformation processes, including dislocation dynamics (DD), which models the interaction and evolution of discrete dislocation line segments, and crystal plasticity (CP), which incorporates the crystalline nature and restricted motion of dislocations into a higher scale continuous field framework. While these two methods are conceptually related, there have been only nominal efforts focused on the system-level material response that use DD-generated information to enhance the fidelity of plasticity models. To ascertain to what degree the predictions of CP are consistent with those of DD, we compare their global and microstructural response in a number of deformation modes. After using nominally homogeneous compression and shear deformation dislocation dynamics simulations to calibrate crystal plasticity flow rule parameters, we compare not only the system-level stress-strain response of prismatic wires in torsion but also the resulting geometrically necessary dislocation density tensor fields. To establish a connection between explicit description of dislocations and the continuum assumed with crystal plasticity simulations, we ascertain the minimum length-scale at which meaningful dislocation density fields appear. Our results show that, for the case of torsion, the two material models can produce comparable spatial dislocation density distributions.</p>

Influence of coherent nanoinclusions on stress-driven migration of low-angle grain boundaries in nanocomposites

A theoretical model that effectively describes stress-driven migration of low-angle tilt grain boundaries in nanocomposites with nanocrystalline or ultrafine-grained metallic matrices containing ensembles of coherent nanoinclusions has been developed. Within this model, low-angle tilt boundaries have been considered as walls of edge dislocations that, under the influence of stress, slip in the metallic matrix and can penetrate into nanoinclusions. The dislocation dynamics simulation has revealed three main regimes of the stress-driven migration of low-angle grain boundaries. In the first regime, migrating grain boundaries are completely retarded by nanoinclusions and their migration is quickly terminated, while dislocations forming grain boundaries reach equilibrium positions. In the second regime, some segments of the migrating grain boundaries are pinned by nanoinclusions, whereas the other segments continue to migrate over long distances. In the third regime, all segments of grain boundaries (except for the segments located at the boundaries of inclusions) migrate over long distances. The characteristics of these regimes have been investigated, and the critical shear stresses for transitions between the regimes have been calculated.