Dislocation Dynamics Simulations Research Articles

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.

Unravelling the mechanisms of copper precipitation-induced strengthening in austenitic stainless steels: An atomistic approach

Copper addition in austenitic stainless steel is known to provide good high-temperature strength through precipitation strengthening. However, the mechanism of such strengthening and its overall contribution to strength in austenitic stainless steels have not been adequately investigated. The present work employs molecular dynamics (MD) simulation to investigate the interaction between an edge dislocation and copper precipitate in austenitic stainless steel. The mechanism controlling the strength was found to be trailing partial detachment for smaller precipitates up to a maximum radius of 3 nm, whereas leading partial detachment controls the strength for larger precipitate sizes, irrespective of the inter-precipitate spacing. Besides, modulus strengthening was identified as the primary strengthening contributor for the coherent Cu precipitate in the present alloy, which was subsequently aligned with the theoretical predictions by the existing Russell-Brown (R-B) model, adopting some modifications. The discrepancy between the simulation results and the original R-B model is attributed to the interaction between the two partial dislocations in presence of the precipitate. The modified R-B model was then used in combination with Thermo-calc and DICTRA predictions to estimate the strength of Cu-added austenitic stainless steel. However, the predictions overestimated the experimental data due to the model's inability to account for the random distribution of precipitates. To address this limitation, a subsequent discrete dislocation dynamics (DDD) simulation was conducted, incorporating a random distribution of Cu precipitates. Finally, the DDD simulation results demonstrated a good match with the experimental results, which can be further extended to other alloy systems as well.

Simulation of intragranular plastic deformation localization in FCC polycrystals by Discrete Dislocation Dynamics

Strain localization mechanisms taking place in polycrystal grains are investigated using Discrete Dislocation Dynamics (DDDs) simulations. First, elastic Finite Element Method simulations are used to calculate the intragranular stress distribution linked to strain incompatibilities between grains. Many configurations are tested to evaluate the stress heterogeneity and constitute a database for DDD simulations. From the analysis of these microstructures, a criterion is proposed to identify the grains where the emergence of the localization of the deformation is the most likely. Then, DDD simulations are used to explore the plastic strain localization phenomenon at the grain scale. Those simulations show that stress concentrations close to a polycrystal quadruple node can play a fundamental role in plastic strain localization. This work paves the way for future investigations to be made thanks to DDD simulations regarding slip band initiation and strain relaxation phenomena.

The coupled effects of grain boundary strengthening and Orowan strengthening examined by dislocation dynamics simulations

DD simulations are performed to unravel the coupled effects between grain boundary strengthening and Orowan strengthening. With the simulations of a plastically-deformed grain embedded in elastic matrix, the internal stresses associated with inter- and intragranular obstacles are quantified. First, plastic yielding is controlled by the length of dislocation sources. Then, in plastic deformation, the stress contribution of bypassing mechanism increases significantly with the size and number of precipitates, while the stress contribution of geometrically necessary dislocations at grain boundaries slightly decreases. Compared with regular spatial distribution of precipitates, random distribution induces a higher strengthening effect by reducing the dislocation mobility. Simulations of four-grain aggregates involving grain refinement and precipitation are systematically investigated. The volume fraction of precipitates is the key factor controlling the Orowan strengthening in addition to the grain size effect. A generalized Hall–Petch equation based on the mean free path of dislocations is proposed. At low strain, a relatively uniform internal stress field is found inside the aggregates with weak stress concentrations around grain boundaries and precipitates. The underlying mechanisms identified in this work are essential for understanding the plastic behavior of precipitate-strengthened polycrystals.

A graph database for feature characterization of dislocation networks

Three-dimensional dislocation networks control the mechanical properties such as strain hardening of crystals. Due to the complexity of dislocation networks and their temporal evolution, analysis tools are needed that fully resolve the dynamic processes of the intrinsic dislocation graph structure. We propose the use of a graph database for the analysis of three-dimensional dislocation networks obtained from discrete dislocation dynamics simulations. This makes it possible to extract (sub-)graphs and their features with relative ease. That allows for a more holistic view of the evolution of dislocation networks and for the extraction of homogenized graph features to be incorporated into continuum formulation. As an illustration, we describe the static and dynamic analysis of spatio-temporal dislocation graphs as well as graph feature analysis.

Void nucleation at dislocation boundaries aided by the synergy of multiple dislocation pile-ups

Void nucleation is of great significance in understanding ductile fracture. Recent experiments have shown that voids are nucleated via vacancy condensation and dislocation boundaries are the main nucleation sites. However, it is unclear what role is played exactly by dislocation boundaries in promoting void nucleation. Here we propose a new mechanism for dislocation boundary-induced void nucleation and develop a corresponding model based on the classical nucleation theory and vacancy diffusion theory. The model suggests that void nucleation is mainly influenced by hydrostatic stress, temperature, and relative vacancy concentration, whose contributions are systematically studied. It is also suggested that the vacancy formation energy and the interaction energy of hydrostatic stress and vacancy, which are absent in the previous models and introduced in ours, exhibit a clear tendency to lower the activation free energy barrier. Analysis of the nucleation kinetic suggests that the growth rate of void depends on the vacancy diffusion coefficient and vacancy concentration; the higher the values of these parameters, the faster the growth rate of the void. The kinetic feasibility of the newly proposed mechanism is examined using three-dimensional discrete dislocation dynamics simulations. The results predict that the size of incipient voids nucleated at the dislocation boundary is ∼35 nm, which is consistent with the experimental characterization value of ∼50 nm. Finally, when the relaxation of the dislocation boundary is considered, the synergistic effect is weakened.

A data-based derivation of the internal stress in the discrete-continuum transition regime of dislocation based plasticity

Effectively homogenizing microstructure heterogeneity within the coarse-graining volume is a long-lasting challenge in crystal plasticity theories. In this paper, we propose a data-based homogenization method that utilizes discrete dislocation dynamic simulations to derive the nearfield correction stress (back stress) for continuum models. This stress accounts for the effective stress field induced by microstructure heterogeneity under the length scale of a coarse-graining volume, providing a physically based homogenization approach. To bridge the gap between discrete and continuous regimes, we introduce two versions of the nearfield correction stress, as well as a criterion based on microstructure and numerical parameters to determine the discrete and continuous transition. Moreover, by analyzing the mathematical connections with the work-conjugated gradient plasticity theory, we further provide a physical explanation for the observed material length scale in the thermodynamically consistent back stress term. This work presents a novel methodology for effectively addressing microstructure heterogeneity and advancing the understanding and modeling of material behavior bridging different length scales.

Size-dependent yield criterion for single crystals containing spherical voids

A micromechanics-based yield criterion is derived for a porous single crystal containing a random distribution of spherical voids, using homogenization and limit analysis of a hollow spherical representative volume element obeying a strain gradient crystal plasticity model. The criterion captures the effect of plastic anisotropy due to crystallographic slip on a set of discrete slip systems, as well as the void size dependence of yielding. The yield criterion is formally similar to the well known Gurson model for isotropic porous materials, and reduces to existing results in the literature in the limiting case of large void sizes relative to the length scale in the gradient plasticity model. The yield criterion is validated by comparison with rigorous upper bound yield loci obtained using a numerical limit analysis procedure. Predictions for the size dependence of void growth are obtained by integrating the porous plasticity model, and shown to be consistent with the observations from lower scale discrete dislocation dynamics simulations. The loading path dependence of void growth in the size-independent limit are compared with finite element simulations of void growth in a single crystal using the unit cell model.

Unraveling kinking: A plasticity enhancing failure mode in high strength nano metallic laminates

Kinking is an important and plasticity-enhancing deformation/failure mode in numerous mechanically anisotropic materials including high-strength nano metallic laminates (NMLs). However, our current limited understanding of the mechanics of kinking and its dependence on microstructural attributes is insufficient for thoroughly comprehending and eventually being able to control failure behaviors of materials. In this study, we investigate kinking dependencies on microstructural attributes in NMLs via in situ micropillar compression, multiscale microstructure characterization, dislocation dynamic simulations, and crystal plasticity modeling. By examining several NML systems (Cu/Fe, Ag/Fe, Al-4Mg/Fe), we demonstrate that the development of internal stresses during loading activates local layer-parallel glide triggering kinking in NMLs. Furthermore, this work reveals the effect of key microstructural features including layer thickness, layer waviness, interface barrier strength, and work hardening capacity on kink band formation in NMLs. More broadly, our efforts represent a generically applicable approach for probing large-strain deformation behavior of complex materials via synergetic modeling and experimental efforts.

Benchmarking discrete dislocation dynamics simulations with dark-field X-ray microscopy movies

Benchmarking discrete dislocation dynamics simulations with dark-field X-ray microscopy movies