Dislocation Dynamics Simulations Research Articles

Plastic anisotropy and composite slip: Application to uranium dioxide

The mechanical behaviour of UO2 single crystal is under debate due to the unexpected multi-slip observations in the experiments that involve dislocations in 12〈110〉{100} slip systems but also in 12〈110〉{110} and 12〈110〉{111}. We propose a multi-scale model based on a composite slip in which, under the effect of cross-slip, part of the dislocation density in primary slip systems can be transferred in secondary systems with a lower propensity to glide but a more favourable orientation regarding the shear stress. This approach allows to describe the anisotropic mechanical response of UO2 single crystal with an accuracy never reached up to now. After identifying the relevant slip systems depending on the orientation using a Schmid approach, dislocation dynamics simulations are used to assert if the cross-slip induces a composite slip and to quantify its effect on the flow stress which appears constrained by the activity of 12<110>{111} systems. In agreement with this result, the composite slip is adapted to couple the activity of slip systems with common Burger vectors in a crystal plasticity framework for a closer comparison to the experiment. This multi-scale approach significantly improves our current knowledge on the links between dislocation microstructures and mechanical properties in UO2. Composite slip mechanism appears as a candidate to explain unexpected plastic behaviours as often observed in complex materials with multiple slip modes underling that slip activation may be more complex than in usual constitutive laws.

Accelerating discrete dislocation dynamics simulations with graph neural networks

Discrete dislocation dynamics (DDD) is a widely employed computational method to study plasticity at the mesoscale that connects the motion of dislocation lines to the macroscopic response of crystalline materials. However, the computational cost of DDD simulations remains a bottleneck that limits its range of applicability. Here, we introduce a new DDD-GNN framework in which the expensive time-integration of dislocation motion is entirely substituted by a graph neural network (GNN) model trained on DDD trajectories. As a first application, we demonstrate the feasibility and potential of our method on a simple yet relevant model of a dislocation line gliding through an array of obstacles. We show that the DDD-GNN model is stable and reproduces very well unseen ground-truth DDD simulation responses for a range of straining rates and obstacle densities, without the need to explicitly compute nodal forces or dislocation mobilities during time-integration. Our approach opens new promising avenues to accelerate DDD simulations and to incorporate more complex dislocation motion behaviors.

The three-dimensional elastodynamic solution for dislocation plasticity and its implementation in discrete dislocation dynamics simulations

An analytical solution for the elastodynamic displacement field of non-uniformly moving Volterra dislocations is derived using the Green’s function approach. The elastodynamics strain and stress fields can then be evaluated by numerically differentiating the displacement field. Qualitative comparisons are made with molecular dynamic simulations, and the analytical solution is shown to capture the same features. The plane waves that emanate from, and are parallel to, the slip plane during the instantaneous injection process of edge or screw dislocations are captured by the analytical solution. This was not captured by previously proposed elastodynamic solutions. A computationally efficient swept-area-tracking algorithm is then developed and implemented into three-dimensional discrete dislocation dynamics simulations to compute the elastodynamic field induced by dislocation movements and interactions. This approach provides a way forward for modeling deformation of materials under shock loading or quantifying the dynamics effects that dominate during dislocation avalanches during deformation of metals.

Self-ion irradiation effects on nanoindentation-induced plasticity of crystalline iron: A joint experimental and computational study

In this paper, experimental work is supported by multi-scale numerical modeling to investigate nanomechanical response of pristine and ion irradiated with Fe2＋ ions with energy 5 MeV high purity iron specimens by nanoindentation and Electron Backscatter Diffraction. The appearance of a sudden displacement burst that is observed during the loading process in the load–displacement curves is connected with increased shear stress in a small subsurface volume due to dislocation slip activation and mobilization of pre-existing dislocations by irradiation. The molecular dynamics (MD) and 3D-discrete dislocation dynamics (3D-DDD) simulations are applied to model geometrically necessary dislocations (GNDs) nucleation mechanisms at early stages of nanoindentation test; providing an insight to the mechanical response of the material and its plastic instability and are in a qualitative agreement with GNDs density mapping images. Finally, we noted that dislocations and defects nucleated are responsible the material hardness increase, as observed in recorded load–displacement curves and pop-ins analysis.

Direct comparison between experiments and dislocation dynamics simulations of high rate deformation of single crystal copper

A long standing challenge in computational materials science is to establish a quantitative connection between the macroscopic properties of plastic deformation with the microscopic mechanisms of dislocations in crystalline materials. Although the discrete dislocation dynamics (DDD) simulation method has been developed for several decades with the goal of addressing this challenge, a one-to-one comparison between the DDD predictions on single crystal stress–strain curves and experimental measurements under identical conditions has not been possible to date. Such a comparison is an essential step towards establishing a dislocation-physics based theory of plasticity and a multiscale framework of the plastic behaviors of crystalline materials. Here we provide direct comparisons between the stress–strain curves of Cu single crystals under high strain rate loading in the [001] and [011] directions obtained from miniaturized desktop Kolsky bar experiments and those from DDD simulations under identical loading conditions. With an appropriate set of parameters, DDD simulations can produce stress–strain curves that are in reasonable agreement with the experimental results. However, the dislocation mobility values needed to achieve this agreement are an order of magnitude lower than expected based on previous measurements and atomistic simulations. We hypothesize that this discrepancy could be caused by drag forces from jogs and point defects produced during the plastic deformation. Cross-slip of screw dislocations is also found to be necessary to capture the experimental stress–strain behavior, especially for the [011] loading direction. This work provides an example of how direct comparisons between DDD simulations and experimental measurements can provide new insight into the fundamental mechanisms of plastic deformation.

Dislocation structures formation induced by thermal stress in additive manufacturing: Multiscale crystal plasticity modeling of dislocation transport

The motion of dislocations governs the plastic deformation of crystalline materials, which in turn determines the mechanical properties. The complex thermal history, large temperature gradients and high cooling rates during the process of additive manufacturing (AM) can induce high dislocation density and unique dislocation structures in the material. The origin of these dislocation structures and their stability during mechanical loading are debated. A novel temperature dependent continuum dislocation dynamics (CDD) model is developed, in which four state variables are used for each slip system representing the total dislocation density, edge and screw geometrically necessary dislocation densities and dislocation curvature. The CDD model is fully coupled with a crystal plasticity solver, which captures the plastic deformation induced by the dislocation motion. A hybrid continuous and discontinuous Galerkin formulation is developed to accurately reproduce the dynamics of highly discontinuous dislocation density fields that are typical of dislocation structures. A multiscale modeling approach is used, in which the thermally induced deformation in specific grains of a polycrystal is extracted from larger scale crystal plasticity simulations of the laser powder-bed fusion process, and is then used for single crystal scale dislocation dynamics simulations. Simulation results reveal the dynamics of dislocation structure formation in grains at different positions during laser scanning and cooling stages. The effect of the cyclic thermal stress during multi-layer AM fabrication is also investigated. The simulations provide a new perspective on the specific conditions that should be satisfied during AM process for the formation of stable dislocation structures.

Strengthening via Orowan Looping of Misfitting Plate-like Precipitates

Many common engineering alloys are strengthened by precipitates with plate-like geometries. The mechanics of precipitation strengthening, while well resolved with spherical precipitates, are less well understood for plate-like geometries. In this work, we employ discrete dislocation dynamics simulations to study precipitation strengthening by θ′ precipitates in AlCu. We show that Orowan looping with parallel plate-like precipitates can be fundamentally different from spheres because it is governed by a steady-state glide process rather than a single critical dislocation geometry. We develop a model based on the formation of a dislocation dipole across the precipitate thickness to explain the observed strengthening. Finally, we show that while the precipitate misfit field can lead to both strengthening and weakening, strengthening is more common because of the steady-state process by which Orowan loops form.

Mechanism of strain hardening of magnesium single-crystals: Discrete dislocation dynamics simulations

Poor ductility heavily limits the industrial application of magnesium (Mg) alloys, and pyramidal dislocations are an important deformation mode for ductility enhancement. In this work, discrete dislocation dynamics (DDD) simulations were performed to study the mechanical behavior and dislocation evolution of Mg single-crystals compressed along c-axis. Especially, basal-transition and cross-slip algorithms of pyramidal <c+a> dislocations were proposed and introduced in the DDD method. Simulation results show that basal-transition is an important mechanism for the strong strain hardening observed during c-axis compression of Mg single-crystals. Since the basal-transition events are thermally activated, increasing temperature leads to a high strain hardening rate. During the deformation, the <c+a> dislocations on first-order pyramidal planes mostly cross slip onto second-order pyramidal planes and few are transited onto basal planes, while <c+a> dislocations on second-order pyramidal planes are mostly transited onto basal planes directly. In addition, the basal-transition behavior is an important reason for the formation of dislocation loops and dislocation steps observed in experiments. The current work provides new mechanisms for the pyramidal dislocations, which are significant for understanding the behaviors of pyramidal dislocations and ductility enhancement of Mg alloys.

Irradiation hardening behavior of high entropy alloys using random field theory informed discrete dislocation dynamics simulation

High entropy alloys (HEAs) exhibit outstanding radiation resistance over traditional alloys owing to severe lattice distortion, and therefore, would be regarded as candidate materials for advanced reactors. However, the complex evolution of dislocation configurations in the irradiated HEAs subjected to the external loads has not been uncovered at the micron scale. To elucidate this key mechanism, we develop the random field theory informed discrete dislocation dynamics simulations based on high-resolution transmission electron microscopy, to systematically clarify the role of heterogeneous lattice strain on the complex interactions between the dislocation loop and dislocation in three-dimensional (3D) space. The results show that the lattice-strain-induced irradiation hardening decreases, in agreement with the excellent irradiation hardening resistance of the HEAs from the recent experiment. Based on the analysis of the micrometer-scale dislocation multiplication process, a new cross-slip mechanism through the collinear reaction between dislocations and rhombus perfect loops is revealed. The peaks and valleys of the heterogeneous lattice strains induced by severe lattice distortion are randomly distributed in a 3D space, reducing an aggregation of lattice point and dislocation density at the local region. The cross-slip process occurs by the joint action of the lattice distortion and rhombus-perfect-loop dislocation reaction, leading to the strong irradiation resistance attributed to a large number of narrow defect-free channel under a relatively random strain localization. The present study gives an insight into the fundamental irradiation damage behavior at the mesoscopic scale, thereby guiding the development of advanced HEA materials through the regulation of heterogeneous lattice strain for nuclear energy applications.

Modeling contact deformation of bare and coated rough metal bodies

The effect of the presence of a passivation layer on a metal rough surface during contact loading is investigated by means of dislocation dynamics simulations. The metal body is modeled as an FCC single crystal with a self-affine rough surface that is either bare, or covered by a thin coating, impenetrable to dislocations. This analysis permits to isolate the effect of surface roughening driven by dislocation motion: when the surface is bare the dislocations can glide out, leaving crystallographic steps at the surface that modify the local roughness; when the surface is passivated, dislocations are stopped by the interface.

Mg-3Al-1Zn alloy deformed along different strain paths: Role of latent hardening

The mechanical properties of magnesium alloy AZ31 were investigated experimentally with visco-plastic self-consistent modeling. Tension, compression and plane strain compression (PSC) tests were performed along 3 directions of a hot rolled plate, and the material parameters input in the model were fitted with the uniaxial stress-strain curves. The critical resolved shear stress (CRSS) for tension twinning was modeled with a modified Voce hardening law first decreasing, and then increasing with strain, that could reproduce better the flow stress for twin-predominant deformation. Such CRSS evolution may better model twin nucleation, propagation and growth. Firstly simulations were carried out assuming latent hardening coefficients for slip by other slip systems equal to self-hardening. Then different heterogeneous latent hardening were used, whose values were based on dislocation dynamics simulations from the literature. This study shows that equal self and latent hardening can reproduce the stress strain curves and plastic anisotropy as well as heterogeneous mode on mode latent hardening. Discrepancies between simulations and experimental results from PSC are explained by an under-estimation of twinning for some PSC strain paths.

Deformation, dislocation evolution and the non-Schmid effect in body-centered-cubic single- and polycrystal tantalum

A physically-informed continuum crystal plasticity model is presented to elucidate deformation mechanisms, dislocation evolution and the non-Schmid effect in body-centered-cubic (bcc) tantalum widely used as a key structural material for mechanical and thermal extremes. We show the unified structural modeling framework informed by mesoscopic dislocation dynamics simulations is capable of capturing salient features of the large inelastic behavior of tantalum at quasi-static (10−3 s−1) to extreme strain rates (5000 s−1) and at low (77 K) to high temperatures (873 K) at both single- and polycrystal levels. We also present predictive capabilities of the model for microstructural evolution in the material. To this end, we investigate the effects of dislocation interactions on slip activities, instability and the non-Schmid behavior at the single crystal level. Furthermore, ex situ measurements on crystallographic texture evolution and dislocation density growth are carried out for polycrystal tantalum specimens at increasing strains. Numerical simulation results also support that the modeling framework is capable of capturing the main features of the polycrystal behavior over a wide range of strains, strain rates and temperatures. The theoretical, experimental and numerical results at both single- and polycrystal levels provide critical insight into the underlying physical pictures for micro- and macroscopic responses and their relations in this important class of refractory bcc materials undergoing large inelastic deformations.

Avalanches and rate effects in strain-controlled discrete dislocation plasticity of Al single crystals

Three-dimensional discrete dislocation dynamics simulations are used to study strain-controlled plastic deformation of face-centered cubic aluminium single crystals. After describing the rate and size dependence of the average stress-strain curves, we study the power-law distributed strain bursts and the average avalanche shapes, and find a universal power-law exponent $\tau \approx 1.0$ for all imposed strain rates and system sizes, characterizing both the event sizes and their durations. We discuss the dependence of our results on loading rate and compare these with previous studies of strain-controlled two-dimensional systems of discrete dislocations as well as of quasistatic stress-controlled loading of aluminium single crystals.

Microscopic Mechanism of Void Nucleation at Dislocation Boundaries: A Discrete Dislocation Dynamics Simulation Study

Microscopic Mechanism of Void Nucleation at Dislocation Boundaries: A Discrete Dislocation Dynamics Simulation Study

Characterization of Lomer junctions based on the Lomer arm length distribution in dislocation networks

During the plastic deformation of crystalline materials, 3d dislocation networks form based on dislocation junctions. Particularly, immobile Lomer junctions are essential for the stability of dislocation networks. However, the formed Lomer junctions can unzip and dissolve again, if the linked mobile dislocations of the Lomer junction - the Lomer arms - experience sufficiently high resolved shear stresses. To generate a better understanding of the dislocation network stability and to pave the way to a general stability criterion of dislocation networks, we investigate the Lomer arm length distribution in dislocation networks by analyzing discrete dislocation dynamics simulation data of tensile-tested aluminum single crystals. We show that an exponential distribution fits best to the Lomer arm length distribution in the systems considered, which is independent of the crystal orientation. The influence of the slip system activity on the Lomer arm length distribution is discussed.

Machine learning of nonlocal micro-structural defect evolutions in crystalline materials

The presence and evolution of defects that appear in the manufacturing process play a vital role in the failure mechanisms of engineering materials. In particular, the collective behavior of dislocation dynamics at the mesoscale leads to avalanche, strain bursts, intermittent energy spikes, and nonlocal interactions producing anomalous features across different time- and length-scales, directly affecting plasticity, void and crack nucleation. Discrete Dislocation Dynamics (DDD) simulations are often used at the meso-level, but the cost and complexity increase dramatically with simulation time. To further understand how the anomalous features propagate to the continuum, we develop a probabilistic model for dislocation motion constructed from the position statistics obtained from DDD simulations. We obtain the continuous limit of discrete dislocation dynamics through a Probability Density Function for the dislocation motion, and propose a nonlocal transport model for the PDF. We develop a machine-learning framework to learn the parameters of the nonlocal operator with a power-law kernel, connecting the anomalous nature of DDD to the origin of its corresponding nonlocal operator at the continuum, facilitating the integration of dislocation dynamics into multi-scale, long-time material failure simulations.

Singularity-free theory and adaptive finite element computations of arbitrarily-shaped dislocation loop dynamics in 3D heterogeneous material structures

The long-standing problem of arbitrarily-shaped discrete dislocation loops in three-dimensional heterogeneous material structures is addressed by introducing novel singularity-free elastic field solutions as well as developing adaptive finite element computations for dislocation dynamics simulations. The first framework uses the Stroh formalism in combination with the biperiodic Fourier-transform and dual variable and position techniques to determine the finite-valued Peach–Koehler force acting on curved dislocation loops. On the other hand, the second versatile mixed-element method proposes to capture the driving forces through dissipative energy considerations with domain integrals by means of the virtual extension principle of the surfacial discontinuities. Excellent agreement between theoretical and numerical analyses is illustrated from simple circular shear dislocation loops to prismatic dislocations with complicated simply-connected contours in linear homogeneous isotropic solids and anisotropic elastic multimaterials, which also serves as improved benchmarks for dealing with more realistic boundary-value problems with evolving dislocations. Examples of sophisticated dislocation applications include the short-range core reaction between intersecting dislocation loops in interaction with a spherical cavity, as well as the Orowan dislocation-precipitate bypass mechanism in a compressed micropillar of polycrystalline copper. The latter multiscale investigation spans three orders of magnitude in size scale, and is thus enabled by computationally efficient and robust adaptive mesh generation procedures for explicit dislocation propagation, interaction, and coalescence in three-dimensional materials and material structures.

A model of thermal creep and annealing in finite domains based on coupled dislocation climb and vacancy diffusion

We develop a framework to investigate thermal creep and annealing in finite domains, where the climb motion of discrete dislocations is coupled to the diffusion of a continuum vacancy field. The model is first formulated in a continuum finite-deformation setting. All governing equations and boundary conditions are obtained from a unified irreversible thermodynamics principle. The resulting model couples a mechanical boundary value problem (BVP), a vacancy diffusion BVP, and the climb and glide motion of the discrete dislocation network within the crystal. The framework is then linearized for implementation in three-dimensional (3D) discrete dislocation dynamics (DDD) simulations for arbitrary anisotropic crystals. A solution scheme is developed based on the superposition principle, which is imposed weakly on the dislocation network to obtain a Galerkin solution for the nodal climb velocities. The framework includes diffusional (Nabarro–Herring) creep deformation as well as dislocation creep by climb-assisted-glide. The method is applied to simulate the annealing of vacancy loops in Al, with good agreement to experimental measurements by Silcox and Hirsch (1959). We further consider the effects of annealing under stress, and of the proximity of the vacancy loops to loaded and free boundaries Simulations in polycrystalline materials are carried out to highlight the effects of the grain size on dislocation climb and vacancy loop annealing. The method is also applied to estimate the creep rate due to climb-assisted glide of jogged-screw dislocations in γ-TiAl, and results are compared to experiments by Viswanathan et al. (1999). Finally, we discuss the effects of uniaxial and hydrostatic stresses on the two diffusive deformation pathways of the material, namely Nabarro–Herring creep and dislocation climb.

Toward selecting optimal predictive multiscale models

This work presents a systematic strategy for selecting an “optimal” predictive computational model among a set of possible mechanistic models of a physical system. To this end, the Occam-Plausibility Algorithm (Farrell-Maupin et al., 2015) is extended by introducing a method for the design of model-specific validation experiments to provide data that portray the features of the prediction quantities of interest. Leveraging Bayesian inference and model plausibility, the framework adaptively balances the trade-off between complexity and validity of the models while taking into account the uncertainty in data, model parameters, and the choice of the model itself for making reliable computational predictions. An application of this framework is demonstrated in discrete-continuum multiscale modeling of size-dependent plasticity in polycrystalline materials, involving dislocation dynamics simulations and strain gradient plasticity models.This study suggests that the effectiveness of validation experiments relies upon the choice of the model; thus, a validation data set that adequately informs a predictive computational model may not be effective for validating other models. Additionally, the multiscale modeling results show that, given the discrete dislocation dynamics data, the optimal strain gradient plasticity model for predicting the deformation of a microelectromechanical system is obtained by excluding the isotropic hardening mechanism.

Identification of dislocation reaction kinetics in complex dislocation networks for continuum modelling using data-driven methods

Plastic deformation of metals involves the complex evolution of dislocations forming strongly connected dislocation networks. These dislocation networks are based on dislocation reactions, which can form junctions during the interactions of different slip systems. Extracting the fundamentals of the network behaviour during plastic deformation by adequate physically based theories is essential for crystal plasticity models. In this work, we demonstrate how knowledge from discrete dislocation dynamics simulations to continuum-based formulations can be transferred by applying a physically based dislocation network evolution theory. By using data-driven methods, we validate a slip system dependent rate formulation of network evolution. We analyse different discrete dislocation dynamics simulation data sets of face-centred cubic single-crystals in high symmetric and non-high symmetric orientations under uniaxial tensile loading. Here, we focus on the reaction evolution during stage II plastic deformation. Our physically based model for network evolution depends on the plastic shear rate and the dislocation travel distance described by the dislocation density. We reveal a dependence of the reaction kinetics on the crystal orientation and the activity of the interacting slip systems, which can be described by the Schmid factor. It has been found, that the generation of new reaction density is mainly driven by active slip systems. However, the deposition of generated reaction density is not necessarily dependent on the slip system activity of the considered slip system, i.e. we observe a deposition of reaction density on inactive slip systems especially for glissile and coplanar reactions.