Discrete Dislocation Dynamics Simulations Research Articles

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.

Predicting yield stress in a nano-precipitate strengthened austenitic steel by integrating multi length-scale simulations and experiments

A promising high-strength Fe – 17.7Mn – 4.7Cr – 0.48C – 10Ni – 5Al – 4Cu wt.% Austenitic steel was solutionized, then aged for 3 or 10 h at 580 °C producing a pronounced precipitation hardening response primarily due to the formation of nanoscale NiAl precipitates. Density functional theory (DFT), molecular dynamics (MD), and discrete dislocation dynamics (DDD) calculations were combined with microstructural data from atom-probe tomography (APT), informing theoretical strengthening models to predict yield strength at different stages of precipitation as a function of NiAl size, volume fraction, and composition. These yield strength predictions were compared with experimental microhardness measurements of the various ageing conditions, including the peak microhardness of 490 HV, which corresponds to an estimated alloy yield strength of 1200 MPa. Comparing MD calculations with theoretical models showed that anti-phase boundary (APB) formation was the predominant barrier to dislocation motion posed by the NiAl precipitates. Using single dislocation particle strengthening models with NiAl APB energies calculated from DFT, good agreement was observed between DDD calculations and the 10 h peak-aged experimental measurements, while agreement with the 3 h experimental measurements required reducing the NiAl APB energy. These results demonstrate the utility of the undertaken approach integrating simulations and experiments across multiple length-scales, particularly the presented coarse-grained DDD simulation method towards modeling materials strengthened by very fine precipitates. The results further suggest that the observed NiAl precipitates may adopt an alternate crystal structure early in their formation.

Enhanced mobility of dislocation network nodes and its effect on dislocation multiplication and strain hardening

Understanding plastic deformation of crystals in terms of the fundamental physics of dislocations has remained a grand challenge in materials science for decades. To overcome this, the Discrete Dislocation Dynamics (DDD) method has been developed, but its lack of atomistic resolution leaves open the possibility that certain key mechanisms may be overlooked. By comparing large-scale Molecular Dynamics (MD) with DDD simulations performed under identical conditions we uncover significant discrepancies in the predicted strength and microstructure evolution in BCC crystals under high-strain rate conditions. These are traced to unexpected behaviors of dislocation network nodes forming at dislocation intersections, that can move in ways not previously anticipated as revealed by MD. Once these newfound freedoms of nodal motion are incorporated, DDD simulations begin to closely match plastic evolution observed in MD. This additional mechanism of motion whereby non-screw dislocations can change their glide plane profoundly affects fundamental processes of dislocation multiplication, recovery and storage that define strength of metals.

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.

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.

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.

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.

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.

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.

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

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

Statistical analysis of discrete dislocation dynamics simulations: initial structures, cross-slip and microstructure evolution

Over the past decades, discrete dislocation dynamics simulations have been shown to reliably predict the evolution of dislocation microstructures for micrometer-sized metallic samples. Such simulations provide insight into the governing deformation mechanisms and the interplay between different physical phenomena such as dislocation reactions or cross-slip. This work is focused on a detailed analysis of the influence of the cross-slip on the evolution of dislocation systems. A tailored data mining strategy using the ‘discrete-to-continuous (D2C) framework’ allows to quantify differences and to quantitatively compare dislocation structures. We analyze the quantitative effects of the cross-slip on the microstructure in the course of a tensile test and a subsequent relaxation to present the role of cross-slip in the microstructure evolution. The precision of the extracted quantitative information using D2C strongly depends on the resolution of the domain averaging. We also analyze how the resolution of the averaging influences the distribution of total dislocation density and curvature fields of the specimen. Our analyzes are important approaches for interpreting the resulting structures calculated by dislocation dynamics simulations.

Parametric numerical study of dislocation density distribution in Czochralski-grown germanium crystals

Dislocations strongly affect the quality of Czochralski-grown germanium crystals used for various applications, however, the influence of different growth parameters on the dislocation distribution has not been extensively studied in the literature. In the present work, a simplified parametric crystal growth model is introduced which is suitable for large-scale numerical studies. The time-dependent temperature and dislocation density distributions in the crystal are calculated and analyzed. The Alexander–Haasen model is applied for dislocation modeling. Model parameters are taken from previously published discrete dislocation dynamics simulations, establishing a novel coupling between mesoscopic and macroscopic simulations. A W-shaped radial distribution of the dislocation density is obtained in the simulations. It is shown that the effective ambient temperature and crystallization front deflection have the strongest influence on the dislocation distribution. The results are compared to the experiment, showing a qualitative agreement, but also several deviations. Limitations of the considered dislocation modeling approach and the simplified thermal model are discussed.

An Investigation of Spiral Dislocation Sources Using Discrete Dislocation Dynamics (DDD) Simulations

Discrete Dislocation Dynamics (DDD) simulations are a powerful simulation methodology that can predict a crystalline material’s constitutive behavior based on its loading conditions and micro-constituent population/distribution. In this paper, a 3D DDD model with spiral dislocation sources is developed to study size-dependent plasticity in a pure metal material (taken here as Aluminum). It also shows, for the first time, multipole simulations of spirals and how they interact with one another. In addition, this paper also discusses how the free surface of a crystalline material affects the plasticity generation of the spiral dislocation. The surface effect is implemented using the Distributed Dislocation Method. One of the main results from this work, shown here for the first time, is that spiral dislocations can result in traditional Frank–Read sources (edge or screw character) in a crystal. Another important result from this paper is that with more dislocation sources, the plastic flow inside the material is more continuous, which results in a lowering of the flow stress. Lastly, the multipole interaction of the spiral dislocations resulted in a steady-state fan-shaped action for these dislocation sources.

Modeling the evolution of representative dislocation structures under high thermo-mechanical conditions during Additive Manufacturing of Alloys

Mesoscale simulations of discrete defects in metals provide an ideal framework to investigate the micro-scale mechanisms governing the plastic deformation under high thermal and mechanical loading conditions. To bridge size and time-scale while limiting computational effort, typically the concept of representative volume elements (RVEs) is employed. This approach considers the microstructure evolution in a volume that is representative of the overall material behavior. However, in settings with complex thermal and mechanical loading histories careful consideration of the impact of modeling constraints in terms of time scale and simulation domain on predicted results is required. We address the representation of heterogeneous dislocation structure formation in simulation volumes using the example of residual stress formation during cool-down of laser powder-bed fusion (LPBF) of AISI 316L stainless steel. This is achieved by a series of large-scale three-dimensional discrete dislocation dynamics (DDD) simulations assisted by thermo-mechanical finite element modeling of the LPBF process. Our results show that insufficient size of periodic simulation domains can result in dislocation patterns that reflect the boundaries of the primary cell. More pronounced dislocation interaction observed for larger domains highlight the significance of simulation domain constraints for predicting mechanical properties. We formulate criteria that characterize representative volume elements by capturing the conformity of the dislocation structure to the bulk material. This work provides a basis for future investigations of heterogeneous microstructure formation in mesoscale simulations of bulk material behavior.

Modeling of dislocation properties in Fe40Cr25Ni35 and Fe50Cr20Ni30 systems

Steels are used extensively in many industries due to their excellent balance of mechanical strength, manufacturability, costs, and acceptable corrosion resistance. Steels are being considered for structural components that are exposed to particularly challenging environments in advanced nuclear reactors. In this context, force-field molecular dynamics (MD) simulations were performed on austenitic steel surrogates with Fe40Cr25Ni35 and Fe50Cr20Ni30 compositions to compute the lattice parameter, elastic constants, bulk modulus, Poisson ratio, the dislocation velocity as a function of shear stress, and the phonon drag coefficient for use in discrete dislocation dynamics (DDD) simulations. The accurate computation of these parameters is essential to obtain correct results by the evolution of the dislocation network of the materials using DDD simulations. The dislocation velocity was extracted from the MD calculations for both steel compositions at 30 different values of stress. Because no significant migration of dislocations was observed at stresses below 200 MPa, the dislocation velocity and mobility were calculated at stresses of 200 MPa and higher. Subsequently, the dislocation density and strain–stress relationship were then computed using the DDD approach. The elastic and plastic deformations in the Fe40Cr25Ni35 system were found to be considerably larger than those of the Fe50Cr20Ni30 system. Our study illustrates the ability of atomistic and dislocation dynamics simulations to elucidate qualitative descriptions of the elasticity and plasticity in steel materials, and thus can assist experimental efforts to evaluate the impact of deformation in austenitic steels.