Discrete Dislocation Dynamics Research Articles

Research on microplastic deformation of Inconel718 under the conditions of high temperature and high strain rate

The compression experiments of the nickel-based superalloy Inconel718 were carried out with the help of split Hopkinson pressure bar device, and the microstructure evolution law in the compression deformation of the alloy was studied by means of optical microscopy, electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). Based on the dislocation theory, a three-dimensional discrete dislocation dynamics model is established. By simulating the dynamic evolution of the discrete dislocation, the interaction of the dislocation itself and the formation of the dislocation microstructure were captured, and further explore the microplastic deformation process of Inconel718. The results show that deformation conditions significantly affect the rheological behavior and dynamic recrystallization behaviour. The cross slip of dislocations is closely related to temperature and strain rate, which in turn affect the dislocation configuration. The deformation mechanism of Inconel718 under the conditions of high temperature and high strain rate is jointly dominated by dislocation slip and twin deformation. As the temperature increases, the average Schmidt factor increases, and more dislocation slip systems are activated. As the strain rate increases, the number of deformation twins increases, while the thickness of deformation twins decreases.

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.

A model for physical dislocation transmission through grain boundaries and its implementation in a discrete dislocation dynamics tool

The mechanical behavior of most metals in engineering applications is dominated by the grain size. Physics-based models of the interaction between dislocations and the grain boundary are important to correctly predict the plastic deformation behavior of polycrystalline materials. Dislocation-grain boundary interaction is complex and a challenge to model. We present a model for simulating the physical transmission of dislocations through grain boundaries within Discrete Dislocation Dynamics tools. The properties (glide plane, Burgers vector, initial length) of the transmitted dislocation are chosen based on geometric criteria as well as a maximization of the resolved shear stress of the transmitted dislocation. Additionally, stress and displacement transparency as well as the discontinuity are ensured via a grain boundary dislocation – a butterfly-like geometry in the general case – whose properties are selected to minimize the residual Burgers vector at the interface. This additional ‘grain boundary dislocation’ allows a direct comparison as well as a calibration of the model with experiments on the macroscale particularly for neighboring grains with a high dislocation density contrast. Two basic examples illustrate the model and an application to a 40-grain polycrystal demonstrates the scalability of the approach.

Enhanced toughness and ductility of T91 steel after exposure to liquid LBE saturated by oxygen at 350–500 °C

The mechanical tensile properties of T91 steel after being oxidized in liquid LBE saturated by oxygen at 350–500 °C for up to 1000 h are studied. Duplex oxide scales are found on T91 steels after the LBE exposure, and the thickness evolution is revealed. Oxidized T91 steels with surface oxide scale yield enhanced toughness and ductility, which is mainly attributed to the inner oxide layer. We show that the enhancing effect relies on the presence of the oxide scale, not its thickness. The possible enhancing effect of the oxide scale on the toughness of T91 steel by impeding the dislocation from emitting out of the steel surfaces is discussed and qualitatively verified by micro-scale elastoplastic simulations based on a newly proposed discrete dislocation dynamics and peridynamics superposition scheme.

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.

Dislocation flow turbulence simultaneously enhances strength and ductility

Multi-principal element alloys (MPEAs) exhibit outstanding strength attributed to the complex dislocation dynamics as compared to conventional alloys. Here, we develop an atomic-lattice-distortion-dependent discrete dislocation dynamics framework consisted of random field theory and phenomenological dislocation model to investigate the fundamental deformation mechanism underlying massive dislocation motions in body-centered cubic MPEA. Amazingly, the turbulence of dislocation speed is identified in light of strong heterogeneous lattice strain field caused by short-range ordering. Importantly, the vortex from dislocation flow turbulence not only acts as an effective source to initiate dislocation multiplication but also induces the strong local pinning trap to block dislocation movement, thus breaking the strength-ductility trade-off.

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.

Stress field and interaction forces between dislocations and precipitate distributions

AbstractA computational method is developed for calculation of the stress field and interaction forces between dislocations and precipitates of arbitrary shape and distribution. The internal stress generated by precipitates due to coherency strain is implemented within the discrete dislocation dynamics (DDD) framework. The s‐version finite element method (s‐FEM), which models a precipitate of arbitrary shape using a local mesh is used to calculate coherency stress fields. The method facilitates meshing precipitate volumes of arbitrary geometry, and multiple local meshes can be superimposed at various positions of the global mesh. Accuracy and convergence conditions of the method are established. For a single precipiate, the method is shown to be 3.5 times faster than a standard FEM calculation for the same accuracy, and the gain in speed increases with the number of precipitates. The CRSS of spherical precipitates is found to be higher than disk‐shaped precipitates of the same volume fraction.

Application of rigorous interface boundary conditions in mesoscale plasticity simulations

The interactions between dislocations and interface/grain boundaries, including dislocation absorption, transmission, and reflection, have garnered significant attention from the research community for their impact on the mechanical properties of materials. However, the traditional approaches used to simulate grain boundaries lack physical fidelity and are often incompatible across different simulation methods. We review a new mesoscale interface boundary condition based on Burgers vector conservation and kinetic dislocation reaction processes. The main focus of the paper is to demonstrate how to unify this boundary condition with different plasticity simulation approaches such as the crystal plasticity finite element (CPFEM), continuum dislocation dynamics (CDD), and discrete dislocation dynamics (DDD) methods. In DDD and CDD, plasticity is simulated based on dislocation activity; in the former, dislocations are described as discrete lines while in the latter in terms of dislocation density. CPFEM simulates plasticity in terms of slip on each slip system, without explicit treatment of dislocations; it is suitable for larger scale simulations. To validate our interface boundary condition, we implemented simulations using both the CPFEM method and a two-dimensional CDD model. Our results show that our compact and physically realistic interface boundary condition can be easily integrated into multiscale simulation methods and yield novel results consistent with experimental observations.

Dislocation descriptors of low and high angle grain boundaries with convolutional neural networks

Multiscale modeling of plasticity in polycrystalline metals is a long-standing challenge in part because of the lack of an accepted grain boundary descriptor, which has hindered the bridging of scales between atomistic simulations and meso-scale discrete dislocation dynamics (DDD) models. While grain boundary dislocations (GBDs) for low angle grain boundaries can be ascertained by Burgers circuit analyses, the dislocation structures of high angle grain boundaries have remained elusive because of overlapping dislocation core fields. Here, we use convolutional neural networks (CNNs) to establish the locations of GBDs responsible for the misorientations of <001> symmetrical-tilt Cu grain boundaries, from the local atomistic stress fields modeled with molecular dynamics (MD) simulations. We achieve accurate CNN predictions of GBDs with sub-angstrom resolution across an extensive set of low- to high-tilt-angle grain boundaries through a training dataset, generated from superposing continuum-representations of the MD stress fields of single dislocations that consider the contributions of both the Volterra and dislocation core fields. The approach paves the way for dislocation representations of the atomistic grain boundary structures modeled by MD simulations or density functional theory (DFT) calculations in mesoscale DDD models to elucidate multiscale plasticity effects.

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.

Mechanical properties and deformation mechanisms of single crystal Mg micropillars subjected to high-strain-rate C-axis compression

The mechanical properties and deformation mechanisms of single crystal magnesium under c-axis quasi-static and high-strain rate compressions are investigated through in situ scanning electron microscope (SEM) experiments and post-mortem transmission electron microscope (TEM) characterization. The findings revealed that ductility and high rates of hardening are preserved for pillars as large as 15 μm. Furthermore, rate effects result in a mild increase in flow stress with plastic deformations controlled primarily by the slip of <a+c> type dislocations. Importantly and in contrast to other literature reports, plastic deformation occurs in the absence of twining. As the strain increases and plastic deformation exceeds about 4%, crystal rotation activates basal slip, <a> type dislocations, resulting in a more rate independent flow stress. TEM observation on micropillars compressed at a strain rate of 250/s, revealed the activation of {112‾2‾}<1‾1‾23> slip systems and high mobility of screw dislocations as major contributors to plastic strains in excess of 10% without fracture. These findings are relevant to the design of lightweight materials used in transportation systems, e.g., selection of material grain size. Moreover, the experimental data here reported provides the materials science community with a unique opportunity to validate discrete dislocation dynamics (DDD) formulations employed in multiscale design of materials.

Discrete Dislocation Dynamics with Annihilation as the Limit of the Peierls–Nabarro Model in One Dimension

Discrete Dislocation Dynamics with Annihilation as the Limit of the Peierls–Nabarro Model in One Dimension

ON THE INFLUENCE OF NON-EQUILIBRIUM VACANCIES ON THE CHARACTERISTICS OF STRAIN INDUCED BROKEN DISLOCATION BOUNDARIES

The influence of material supersaturation with deformation vacancies on the characteristics of broken dislocation boundaries that appear near wedge disclinations as a result of accommodative plastic deformation is considered. An analysis is made for the elastic and osmotic forces acting on the dislocations of the broken boundary. Using discrete dislocation dynamics method, computer simulation of the nonconservative motion (climb) of dislocations in the boundary plane has been carried out. The broken boundary formed as a result of the splitting of the original disclination into two partial with equal strengths and the boundary with an inhomogeneous distribution of dislocations (with a linearly decreasing misorientation) were considered as initial ones. It is shown that in the case of broken dislocation boundary formed near a positive wedge disclination, dislocation climb leads to its unlimited growth through the model grain with a simultaneous decrease of misorientation. In the case of a boundary formed near a negative disclination, the osmotic forces acting on the dislocations of the broken boundary can, at sufficiently large super saturations of the material with nonequilibrium vacancies, lead to its significant compression with a simultaneous increase of the density of the Burgers vector. In this case, the choice of the initial configuration of the broken boundary has practically no effect on the characteristics of the equilibrium distribution of dislocations. The density distributions of the Burgers vector along the broken boundary are calculated for the case of small and large supersaturations of the material with nonequilibrium vacancies. The critical value of supersaturation above which the boundary compression occurs is calculated. The boundary compression leads to a significant increase in tensile stresses in its vicinity. In this case, the maximum tensile stresses in the plane coinciding with the plane of the boundary are reached at the boundary break point. The results obtained may be of interest in the analysis of possible mechanisms for the initiation of cracks and pores during ductile fracture of metals.

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

The interpretation of discrete dislocation dynamics simulation data: verification and validation (V&amp;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.