Dislocation Dynamics Simulations Research Articles

Defect dynamics modeling of mesoscale plasticity

The collective motion of defects and their interaction are the basic building blocks for plastic deformation and corresponding mechanical behaviors of crystalline metals. Especially, dislocations among various defects are the “carrier” of plastic deformation in many crystalline materials, particularly ductile materials. To get a fundamental understanding of plastic deformation mechanisms, it calls for an integrated computational platform to simultaneously capture detailed defects characteristics across several length scales together with corresponding macroscopic mechanical response. In this paper, we present a three-dimensional mesoscale defect dynamics model to directly couple the three dimensional discrete dislocation dynamics model with continuum finite element method, aiming at capturing both size dependent plasticity at micron-, and submicron scale and constitutive behaviors at larger scales where such size-dependence disappear. Using non-singular dislocation theories, our model could accurately consider both short- and long-range elastic interactions between multiple dislocation segments with even higher computational efficiency than traditional dislocation dynamics simulations, together with the careful consideration of crystal/material rotation in the coupled framework. In addition, our model could directly model dislocation nucleation from stress concentrators such as a void, crack and indentor tip, which could allow us to investigate various defects’ motion and their mutual interactions, predicting macroscopic mechanical response of complex structures. The developed concurrently coupled model could also consider multiphysical phenomena by solving coupled governing equations in finite element framework, which could shed light on complex defect behaviors under various physical environments.

Optimal Arrangements and Local Anisotropy of {100} Guinier-Preston (GP) Zones by Parametric Dislocation Dynamics (PDD) Simulations.

Stress-oriented precipitation and the resulting mechanical anisotropy have been widely studied over the decades. However, the local anisotropy of precipitates with specific orientations has been less thoroughly investigated. This study models the interaction between an edge dislocation source and {100} variants of Guinier-Preston (GP) zones in Al-Cu alloys using the parametric dislocation dynamics (PDD) method. Concentric geometrically necessary dislocation (GND) loops were employed to construct a line integral model for thin platelets. The simulations, conducted with our self-developed code based on Green's function method and Eshelby inclusion theory revealed distinct strengthening behavior along the strong and weak directions for 60° GP zones, demonstrating anisotropic strengthening from the perspective of elastic interactions. Furthermore, the optimal inclined arrangement of the GP zone array was determined through elastic energy calculations, and these results were corroborated by TEM observations.

On identifying dynamic length scales in crystal plasticity

Materials are often heterogeneous at various length scales, with variations in grain structure, defects, and composition which has a strong influence on the emergent macroscopic plastic behavior. In particular, heterogeneities lead to fluctuations in the plastic response in the form of jerky flow and ubiquitous strain bursts. One of the crucial aspects of plasticity modeling is scale bridging: In order to deliver physically correct crystal plasticity models, one needs to determine relevant microstructural length scales. In this paper we advance the idea that continuum descriptions of dislocation mediated plasticity cannot neglect dynamic correlations related to the avalanche behavior. We present an extensive weakest link analysis of crystal plasticity by means of three-dimensional discrete dislocation dynamics simulations with and without spherical precipitates. We investigate strain bursts and related length scales and conclude that while sufficiently strong obstacles to dislocation motion tend to confine the dislocation avalanches within well-defined sub-volumes, in pure dislocation systems the avalanches may span the system, implying that the dynamic length scale is, in fact, the size of the entire sample. Consequences of this finding on continuum modeling are thoroughly discussed.

Advanced modeling of higher-order kinematic hardening in strain gradient crystal plasticity based on discrete dislocation dynamics

An extensive study of size effects on the small-scale behavior of crystalline materials is carried out through discrete dislocation dynamics (DDD) simulations, intended to enrich strain gradient crystal plasticity (SGCP) theories. These simulations include cyclic shearing and tension-compression tests on two-dimensional (2D) constrained crystalline plates, with single- and double-slip systems. The results show significant material strengthening and pronounced kinematic hardening effects. DDD modeling allows for a detailed examination of the physical origin of the strengthening. The stress–strain responses show a two-stage behavior, starting with a micro-plasticity regime with a steep hardening slope leading to strengthening, and followed by a well-established hardening stage. The scaling exponent between the apparent (higher-order) yield stress and the geometrical size h varies depending on the test type. Scaling relationships of h−0.2 and h−0.3 are obtained for respectively constrained shearing and constrained tension-compression, aligning with some experimental observations. Notably, the DDD simulations reveal the occurrence of the uncommon type III (KIII) kinematic hardening of Asaro in both single- and double-slip cases, emphasizing the relevance of this hardening type in the realm of small-scale plasticity. Inspired by insights from DDD, two advanced SGCP models incorporating alternative descriptions of higher-order kinematic hardening mechanisms are proposed. The first model uses a Prager-type higher-order kinematic hardening formulation, and the second employs a Chaboche-type (multi-kinematic) formulation. Comparison of these models with DDD simulation results underscores their ability to effectively capture the observed strengthening and hardening effects. The multi-kinematic model, through the use of quadratic and non-quadratic higher-order potentials, shows a notably better qualitative congruence with DDD findings. This represents a significant step towards accurate modeling of small-scale material behaviors. However, it is noted that the proposed models still have limitations, especially in matching the DDD scaling exponents, with both models producing h−1 scaling relationships (i.e., Orowan relationship for precipitate size effects). This indicates the need for further improvements in gradient-enhanced theories in order to guarantee their suitability for practical engineering applications.

The Role of Dislocation Type in the Thermal Stability of Cellular Structures in Additively Manufactured Austenitic Stainless Steel.

The ultrafine cellular structure promotes the extraordinary mechanical performance of metals manufactured by laser powder-bed-fusion (L-PBF). An in-depth understanding of the mechanisms governing the thermal stability of such structures is crucial for designing reliable L-PBF components for high-temperature applications. Here, characterizations and 3D discrete dislocation dynamics simulations are performed to comprehensively understand the evolution of cellular structures in 316L stainless steel during annealing. The dominance of screw-type dislocation dipoles in the dislocation cells is reported. However, the majority of dislocations in sub-grain boundaries (SGBs) are geometrically necessary dislocations (GNDs) with varying types. The disparity in dislocation types can be attributed to the variation in local stacking fault energy (SFE) arising from chemical heterogeneity. The presence of screw-type dislocations facilitates the unpinning of dislocations from dislocation cells/SGBs, resulting in a high dislocation mobility. In contrast, the migration of SGBs with dominating edge-type GNDs requires collaborative motion of dislocations, leading to a sluggish migration rate and an enhanced thermal stability. This work emphasizes the significant role of dislocation type in the thermal stability of cellular structures. Furthermore, it sheds light on how to locally tune dislocation structures with desired dislocation types by adjusting local chemistry-dependent SFE and heat treatment.

A probabilistic coupled hardening model of double irradiation defects in iron

Irradiation hardening effect is of significance to the design and life extension of nuclear materials. Although various types of defects coexist under in-pile condition, most irradiation hardening models like the dispersed barrier hardening (DBH) model ignore their strength difference and treat them as a single defect type. In this work, the barrier strengths in presence of combined 〈111〉 and 〈100〉 loops in bcc iron are investigated using discrete dislocation dynamics simulations. Considering the coupling effect, the non-periodic distributed effect is preliminarily analyzed. A probabilistic model accounting for their coupled hardening effect is established based on dislocation depinning mechanism from simulation results, which can be also integrated into the modified DBH model using an effective barrier strength factor. The model presents good agreements with experimental results of iron alloy, and exhibits potential applicability in predicting the coupling effects of other defect types, including the dislocation loops and voids.

Combining simulation and experimental data via surrogate modelling of continuum dislocation dynamics simulations

Several computational models have been introduced in recent years to yield comprehensive insights into microstructural evolution analyses. However, the identification of the correct input parameters to a simulation that corresponds to a certain experimental result is a major challenge on this length scale. To complement simulation results with experimental data (and vice versa) is not trivial since, e.g. simulation model parameters might lack a physical understanding or uncertainties in the experimental data are neglected. Computational costs are another challenge mesoscale models always have to face, so comprehensive parameter studies can be costly. In this paper, we introduce a surrogate model to circumvent continuum dislocation dynamics simulation by a data-driven linkage between well-defined input parameters and output data and vice versa. We present meaningful results for a forward surrogate formulation that predicts simulation output based on the input parameter space, as well as for the inverse approach that derives the input parameter space based on simulation as well as experimental output quantities. This enables, e.g. a direct derivation of the input parameter space of a continuum dislocation dynamics simulation based on experimentally provided stress–strain data.

Crossed-state bowing and the strength of binary dislocation junctions

The strength of binary dislocation junctions in face-centered cubic metals is analyzed via a large set of discrete dislocation dynamics (DDD) simulations and an energy-based line tension model. The simulations reveal that, contrary to the prevailing wisdom, junctions often remain unbroken even after they have fully unzipped, a phenomenon which we call crossed-state bowing. After incorporating crossed-state bowing into the line tension model, we demonstrate that in some cases prior works severely underpredicted junction strength by neglecting crossed-state bowing. Using the line tension model we analyze the statistics of junction strength from a large population of junction geometries showing the influence of stress on the forest slip system and crossed-state bowing. Our results indicate that junction strengths under single-slip loading are not representative of multi-slip loading, and that crossed-state bowing controls junction strength about half of the time. The MATLAB code for our line tension model is available as an open-source code.

Junction formation rates, residence times, and the rate of plastic flow in FCC metals

During plastic flow in metals, dislocations from slip systems with different glide planes collide to form junctions. After being in-residence within the dislocation network for some period of time, these junctions then break, thereby liberating the attached dislocation lines. In this work we use random forest discrete dislocation dynamics simulations to quantify the junction formation rate and junction residence time as a function of stress for all junction types in face-centered cubic metals. We then relate these quantities to the dislocation link-length distribution, which is found to exhibit an exponential form. This enables us to quantify the mean junction strength and also the slip system interaction coefficients. Finally, using the link-length model we obtain a flow rule for our systems which is physics-based with all parameters determined from DDD simulations. The insights here provide a path forward for a dislocation network theory of plastic flow based on the link-length distribution.

Complex dislocation loop networks as natural extensions of the sink efficiency of saturated grain boundaries in irradiated metals.

The development of radiation-tolerant structural materials is an essential element for the success of advanced nuclear energy concepts. A proven strategy to increase radiation resistance is to create microstructures with a high density of internal defect sinks, such as grain boundaries (GBs). However, as GBs absorb defects, they undergo internal transformations that limit their ability to capture defects indefinitely. Here, we show that, as the sink efficiency of GBs becomes exhausted with increasing irradiation dose, networks of irradiation loops form in the vicinity of saturated or near-saturated GB, maintaining and even increasing their capacity to continue absorbing defects. The formation of these networks fundamentally changes the driving force for defect absorption at GB, from "chemical" to "elastic." Using thermally-activated dislocation dynamics simulations, we show that these networks are consistent with experimental measurements of defect densities near GB. Our results point to these networks as a natural continuation of the GB once they exhaust their internal defect absorption capacity.

Multiscale computational study to predict the irradiation-induced change in engineering properties of fusion reactor materials

In this study, we address the impact of irradiation conditions in a tokamak on the engineering properties of materials, leading to potential degradation of in-vessel components over their lifecycle. Our approach involves a predictive model for irradiation-induced damage, employing a multiscale computational framework. This framework integrates various simulation techniques, including Monte Carlo-based neutronics (OpenMC), dislocation dynamics (DD) using MoDELib, and finite element analysis (FEA) with Code_Aster. This integration offers a versatile solver capable of analysing tokamak components exposed to different irradiation doses and temperature conditions.To showcase the utility of this multiscale computational framework, we present a case study focused on tungsten monoblock designs. We assess the failure probabilities of these designs at different stages of their lifecycle. Neutron heating and damage energy values are obtained from OpenMC neutronics simulations. The neutron heating values serve as volumetric heat sources for the FEA thermal simulation. We calculate the displacement per atom (dpa) across the monoblock at various full power days (day 0, day 100, and day 1000) using the damage energy values. The irradiation-induced defect densities, dependent on temperature and dpa, are inputs to DD microstructural simulations performed on the representative volume element (RVE) using MoDELib. This allows us to obtain the yield stress of the material. Subsequently, the thermal fields from the FEA thermal simulation, along with the dpa and temperature-dependent yield stress from the DD simulation, are implemented for FEA mechanical simulations.To evaluate the failure probability of the monoblock designs at different stages of their lifecycle, we conduct an SDC-IC assessment, incorporating a plastic flow localization rule within the current framework. This comprehensive approach provides insights into the thermo-mechanical behaviour of in-vessel components subjected to neutron irradiation, offering a predictive capability for assessing their performance over time.

Couple-stress elasticity of intrinsic and extrinsic dislocations in three-dimensional multilayered materials

This work investigates the influence of couple stresses on intrinsic and extrinsic dislocations within three-dimensional heterogeneous multilayered structures. The materials consist of orthotropic and dissimilar layers with different elastic properties, incorporating the microstructural lengths from a special version of the anisotropic couple-stress elasticity. Double Fourier series expansions are used to describe extended displacements and tractions, considering rotation and couple-stress components and accounting for arbitrary displacement and rotation discontinuities associated with dislocation and disclination loops as well as periodic dislocation and disclination networks at semi-coherent interfaces. The dual-variable and position technique is used to recursively determine the field responses at any point in the multilayered laminate. The application examples focus on dislocation problems with couple stresses, revealing the effects of the core-spreading dislocation technique, free surfaces, anisotropic elasticity, and couple stresses on the field solutions. The analysis also uncovers pressure and von Mises stress amplitudes, non-zero rotation, and non-symmetric stress profiles due to couple stresses in copper/niobium bimaterials. Changes in the sign and magnitude of the Peach-Koehler forces are observed when couple stresses are introduced, which deviate from the classical theory of dislocations. The investigation finds a significant 29% reduction in energy per unit area at a semi-coherent interface between copper and niobium influenced by couple stresses. These results deepen our understanding of how couple stresses affect dislocation behavior in multilayered materials, and provide prospects for future discrete dislocation and disclination dynamics simulations with engineering applications in various nano- and micro-structured materials.

Unveiling deformation behavior and damage mechanism of irradiated high entropy alloys

The oxide dispersion strengthening (ODS) high entropy alloy (HEA) exhibits the high elevated temperature performance and radiation resistance due to severe atomic lattice distortion and oxide particles dispersed in matrix, which is expected to become the most promising structural material in the next generation of nuclear energy systems. However, microstructure and damage evolution of irradiated ODS HEA under loading remain elusive at submicron scale using the existing simulations owing to a lack of atomic-lattice-distortion information from a micromechanics description. Here, the random field theory informed discrete dislocation dynamics simulations based on the results of high-resolution transmission electron microscopy are developed to study the dislocation behavior and damage evolution in ODS HEA considering the influence of severe lattice distortion and nanoscale oxide particle. Noteworthy, the damage behavior shows an unusual trend of the decreasing-to-increasing transition with the continuous loading process. There are two main types of damage micromechanics generated in irradiated ODS HEA: the dislocation loop damage in which the damage is controlled by irradiation-induced dislocation loops and their evolution, the strain localization damage in which the damage comes from the dislocation multiplication in the local plastic region. The oxide particle hinders the dislocation movement in the main slip plane, and the lattice distortion induces the dislocation sliding to the secondary slip plane, which promotes the dislocation cross-slip and dislocation loop annihilation, and thus reduces the material damage in the elastic damage stage. These findings can deeply understand atomic-scale damage mechanism and guide the design of ODS HEA with high radiation resistance.

Role of interfaces on the mechanical response of accumulative roll bonded nanometallic laminates investigated via dislocation dynamics simulations

Unraveling the effects of continuous dislocation interactions with interfaces, particularly at the nanometer length scales, is key to a broader understanding of plasticity, to material design and to material certification. To this end, this work proposes a novel discrete dislocation dynamics-based model for dislocation interface interactions tracking the fate of residual dislocation on interfaces. This new approach is used to predict the impact of dislocation/interface reactions on the overall mechanical behavior of accumulative roll bonded nanometallic laminates. The framework considers the dynamic evolution of the interface concurrent with a large network of dislocations, thus, accounting for the local short and long range effects of the dislocations under the external boundary conditions. Specifically, this study focuses on two-phase Fe/Cu nanometallic laminates, and investigates the role of the underlying elastic and plastic contrast of the Fe and the Cu layers on the composite response of the material. Moreover, the role of initial microstructures, resulting from processing is also investigated. Subsequently, the model is used to examine the effect of layer thickness and interface orientation relationship on the residual stresses of the relaxed microstructure. The associated mechanical response of these laminates are compared when loaded under normal direction compression, as well as shear compression. Finally, this work predicts a dominant effect of the layer thickness, as compared to the interface orientation relationship, on the macroscopic response and on the residual stresses of these nanolaminates, while the local dislocation transmission propensity through the interface is significantly influenced by the corresponding orientation relationship.

Atomistically informed dislocation dynamics simulations: application to dislocation-loop interactions in zirconium

Neutron irradiation of zirconium alloys leads to the formation of high densities of small dislocation loops. Their interactions with gliding dislocations are responsible for hardening and early necking of the material. Multi-scale numerical simulations of the interactions between dislocations and loops are undertaken to predict the mechanical properties evolution of these materials due to irradiation. Molecular dynamics simulations are first performed to assess the critical ingredients needed for dislocation dynamics simulations. Appropriate models and associated coefficients are then introduced in dislocation dynamics simulations in order to reliably reproduce the dislocation line energy, the cross-slip process from basal to prismatic planes and the mobility of straight and jogged dislocations. Based on this parametrization, interactions between dislocations and loops are finally computed with the two numerical methods. Careful comparisons between the two types of simulations show qualitative and quantitative agreement, opening the path to investigations of irradiation effects at the grain scale through large scale dislocation dynamics simulations.

Prediction of yield surface of single crystal copper from discrete dislocation dynamics and geometric learning

The yield surface of a material is a criterion at which macroscopic plastic deformation begins. For crystalline solids, plastic deformation occurs through the motion of dislocations, which can be captured by discrete dislocation dynamics (DDD) simulations. In this paper, we predict the yield surfaces and strain-hardening behaviors using DDD simulations and a geometric manifold learning approach. The yield surfaces in the three-dimensional space of plane stress are constructed for single-crystal copper subjected to uniaxial loading along the [100] and [110] directions, respectively. With increasing plastic deformation under [100] loading, the yield surface expands nearly uniformly in all directions, corresponding to isotropic hardening. In contrast, under [110] loading, latent hardening is observed, where the yield surface remains nearly unchanged in the orientations in the vicinity of the loading direction itself but expands in other directions, resulting in an asymmetric shape. This difference in hardening behaviors is attributed to the different dislocation multiplication behaviors on various slip systems under the two loading conditions.

The interpretation of discrete dislocation dynamics simulation data: verification and validation (V&V) with application to size/scale effects and free surface effects

The interpretation of discrete dislocation dynamics simulation data: verification and validation (V&V) with application to size/scale effects and free surface effects

The effect of electric current on dislocation activity in pure aluminum: A 3D discrete dislocation dynamics study

Introducing electric current into metals and alloys to improve their ductility and to reduce the hardening tendency has been widely adopted. Nevertheless, how the electricity affects the plastic deformation of those materials remains a critical issue with controversial opinions. To clarify the material plastic deformation subjected to electric current, or the so-called electroplastic behavior, an in-depth understanding of the dislocation evolution during that process is vital. From that motivation, three-dimensional dislocation dynamics simulations were carried out to explore the dislocation behavior during the uniaxial tensile deformation of pure aluminum with the introduction of electric current. The scattering process between electrons and dislocations was first captured by a physical model. The electron wind force and local heat effect were quantitatively analyzed by figuring out the momentum and the energy transferred during the interaction of electrons and dislocations respectively. The dislocation density evolution, the activation of different slip systems and the dislocation distribution were further analyzed based on the simulations. The dislocation density in the [111] direction is revealed to increase more significantly than [101] and [001] directions with the introduction of electric current. The results show that the current can reduce the flow stress by promoting the activation of the difficult-to-move dislocations. The activation effect reduces the dislocation tangling tendency and leads to more uniform dislocation distribution. Therefore, a reduction of the flow stress can be observed in EAT comparing to TAT, via the discrete dislocation dynamics simulations even though the dislocation densities are similar. The simulation results are also confirmed by the EAT and TAT experiment results and TEM observations.

Micropillar compression using discrete dislocation dynamics and machine learning

Discrete dislocation dynamics (DDD) simulations reveal the evolution of dislocation structures and the interaction of dislocations. This study investigated the compression behavior of single-crystal copper micropillars using few-shot machine learning with data provided by DDD simulations. Two types of features are considered: external features comprising specimen size and loading orientation and internal features involving dislocation source length, Schmid factor, the orientation of the most easily activated dislocations and their distance from the free boundary. The yielding stress and stress-strain curves of single-crystal copper micropillar are predicted well by incorporating both external and internal features of the sample as separate or combined inputs. It is found that the machine learning accuracy predictions for single-crystal micropillar compression can be improved by incorporating easily activated dislocation features with external features. However, the effect of easily activated dislocation on yielding is less important compared to the effects of specimen size and Schmid factor which includes information of orientation but becomes more evident in small-sized micropillars. Overall, incorporating internal features, especially the information of most easily activated dislocations, improves predictive capabilities across diverse sample sizes and orientations.

Discrete dislocation dynamics simulations of [formula omitted]-type prismatic loops in zirconium

Neutron irradiation of zirconium alloys in light water nuclear reactors generates nano-scale defects in the form of vacancy and interstitial 〈a〉-type prismatic loops which lie in prismatic planes of the sample. The dynamics of idealised conservative square 〈a〉-type prismatic loops have been investigated for a range of loop lengths in the framework of linear isotropic elasticity. Three-dimensional dislocation dynamics (DD) simulations of a dislocation-loop interaction have been performed to investigate the dislocation-loop interaction mechanism. For this purpose, a mobility law developed for hexagonally close-packed materials has been implemented and described in detail. Analytical and numerical calculations have been performed to obtain expressions for the restoring force and angular stability of prismatic loops. These analyses have been used to inform a 2.5D discrete dislocation plasticity (DDP) model in order to emulate realistic prismatic loop physics and improve irradiation hardening simulations. From the 2.5D DDP prismatic loop analyses, it has been observed that the stable angle of smaller sized loops is less sensitive to external stresses compared to that of larger loops, which may have implications for the mechanisms of irradiation hardening. Furthermore, initial 2.5D single-slip simulations predict that prismatic loops cause significantly elevated flow stress that increases with increasing loop density in accord with experimental observations, and that the restraining effect of the out-of-plane loop segments (the restoring force) plays an important role in the strengthening caused by loops.