Prediction of yield surface of single crystal copper from discrete dislocation dynamics and geometric learning
Not provided.
Materials Science↗
SEARCH · Engineering Papers
Results for “Dislocation dynamics”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
On the implementation of dislocation reactions in continuum dislocation dynamics modeling of mesoscale plasticity
The continuum dislocation dynamics framework for mesoscale plasticity is intended to capture the dislocation density evolution and the deformation of crystals when subjected to mechanical loading. It does so by solving a set of transport equations for dislocations concurrently with crystal mechanics equations, with the latter being cast in the form of an eigenstrain problem. Incorporating dislocation reactions in the dislocation transport equations is essential for making such continuum dislocation dynamics predictive. A formulation is proposed to incorporate dislocation reactions in the transport equations of the vector density-based continuum dislocation dynamics. This formulation aims to rigorously enforce dislocation line continuity using the concept of virtual dislocations that close all dislocation loops involved in cross slip, annihilation, and glissile and sessile junction reactions. The addition of virtual dislocations enables us to accurately enforce the divergence free condition upon the numerical solution of the dislocation transport equations for all slip systems individually. A set of tests were performed to illustrate the accuracy of the formulation and the solution of the transport equations within the vector density-based continuum dislocation dynamics. Comparing the results from these tests with an earlier approach in which the divergence free constraint was enforced on the total dislocation density tensor or the sum of two densities when only cross slip is considered shows that the new approach yields highly accurate results. Bulk simulations were performed for a face centered cubic crystal based on the new formulation and the results were compared with discrete dislocation dynamics predictions of the same. The microstructural features obtained from continuum dislocation dynamics were also analyzed with reference to relevant experimental observations.
36 MATERIALS SCIENCE↗
Situating the Vector Density Approach Among Contemporary Continuum Theories of Dislocation Dynamics
Abstract For the past century, dislocations have been understood to be the carriers of plastic deformation in crystalline solids. However, their collective behavior is still poorly understood. Progress in understanding the collective behavior of dislocations has primarily come in one of two modes: the simulation of systems of interacting discrete dislocations and the treatment of density measures of varying complexity that are considered as continuum fields. A summary of contemporary models of continuum dislocation dynamics is presented. These include, in order of complexity, the two-dimensional statistical theory of dislocations, the field dislocation mechanics treating the total Kröner–Nye tensor, vector density approaches that treat geometrically necessary dislocations on each slip system of a crystal, and high-order theories that examine the effect of dislocation curvature and distribution over orientation. Each of theories contain common themes, including statistical closure of the kinetic dislocation transport equations and treatment of dislocation reactions such as junction formation. An emphasis is placed on how these common themes rely on closure relations obtained by analysis of discrete dislocation dynamics experiments. The outlook of these various continuum theories of dislocation motion is then discussed.
Engineering↗
Recent progress in the phase-field dislocation dynamics method
The phase-field dislocation dynamics (PFDD) method, originated in 2002, is a continuum dislocation model that uses order parameters to describe dislocation slips in crystalline materials. In the past two decades, and especially since it was last reviewed in 2016, PFDD was advanced significantly in terms of the mathematical formulation, numerical implementation, and applicability. The main purpose of this short review is to summarize recent progress made to improve the energy functional formulation and numerical techniques of PFDD as well as its recent applications. Additionally, some recommendations for future work to further extend the PFDD method are presented.
36 MATERIALS SCIENCE↗
Incorporating point defect generation due to jog formation into the vector density-based continuum dislocation dynamics approach
During plastic deformation of crystalline materials, point defects such as vacancies and interstitials are generated by jogs on moving dislocations. A detailed model for jog formation and transport during plastic deformation was developed within the vector density-based continuum dislocation dynamics framework. Here as a part of this model, point defect generation associated with jog transport was formulated in terms of the volume change due to the non-conservative motion of jogs. Balance equations for the vacancies and interstitials including their rate of generation due to jog transport were also formulated. A two-way coupling between point defects and dislocation dynamics was then completed by including the stress contributed by the eigen-strain of point defects. A jog drag stress was further introduced into the mobility law of dislocations to account for the energy dissipation during point defects generation. A number of test problems and a fully coupled simulation of dislocation dynamics and point defects generation and diffusion were performed. The results show that there is an asymmetry of vacancy and interstitial generation due to the different formation energies of the two types of defects. The results also show that a higher hardening rate and a higher dislocation density are obtained when the point defect generation mechanism is coupled to dislocation dynamics.
36 MATERIALS SCIENCE↗
On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms
Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its rate, as found from Orowan's law. In this work, we show that such a direct time integration scheme can suffer from accumulation of numerical errors. We introduce an alternative scheme based on field dislocation mechanics that ensures consistency between the plastic distortion and the dislocation content in the crystal. The new scheme is based on calculating the compatible and incompatible parts of the plastic distortion separately, and the incompatible part is calculated from the current dislocation density field. Stress field and dislocation transport calculations were implemented within a finite element based discretization of the governing equations, with the crystal mechanics part solved by a conventional Galerkin method and the dislocation transport equations by the least squares method. A simple test was first performed to show the accuracy of the two schemes for updating the plastic distortion, which shows that the solution method based on field dislocation mechanics is more accurate. This method then was used to simulate an austenitic steel crystal under uniaxial loading and multiple slip conditions. By considering dislocation interactions caused by junctions, a hardening rate similar to discrete dislocation dynamics simulation results was obtained. Finally, the simulations show that dislocations exhibit some self-organized structures as the strain is increased.
36 MATERIALS SCIENCE↗
A coupled vacancy diffusion-dislocation dynamics model for the climb-glide motion of jogged screw dislocations
Here, we develop a novel model to study the climb/glide motion of jogged screw dislocations within the discrete dislocation dynamics (DDD) framework. We present results for the dependence of the climb velocity on the applied stress and on the jog size and distribution statistics. We show that the model predictions are consistent with experimental data in both γ-TiAl and Zircaloy-4. The ranges of the applied stress and jog spacing that determine the dominance of one of three dislocation mechanisms are identified. These are the jog dragging, dipole dragging, and dipole bypass mechanisms, respectively. The overall dislocation motion in the jog dragging regime is composed of glide of screw segments and climb of jogs, controlling the plastic strain and the creep rate, respectively. Based on current simulations and on a detailed examination of the predicted jog heights compared to experiments, we advance the hypothesis that a combination of jog dragging and dipole bypass mechanisms is necessary to reproduce the high creep rate observed in some experiments.
36 MATERIALS SCIENCE↗
Accelerating discrete dislocation dynamics simulations with graph neural networks
Discrete dislocation dynamics (DDD) is a widely employed computational method to study plasticity at the mesoscale that connects the motion of dislocation lines to the macroscopic response of crystalline materials. However, the computational cost of DDD simulations remains a bottleneck that limits its range of applicability. Here, we introduce a new DDD-GNN framework in which the expensive time-integration of dislocation motion is entirely substituted by a graph neural network (GNN) model trained on DDD trajectories. As a first application, we demonstrate the feasibility and potential of our method on a simple yet relevant model of a dislocation line gliding through an array of obstacles. We show that the DDD-GNN model is stable and reproduces very well unseen ground-truth DDD simulation responses for a range of straining rates and obstacle densities, without the need to explicitly compute nodal forces or dislocation mobilities during time-integration. Our approach opens new promising avenues to accelerate DDD simulations and to incorporate more complex dislocation motion behaviors.
36 MATERIALS SCIENCE↗
Statistics of internal stress fluctuations in dislocated crystals and relevance to density-based dislocation dynamics models
A statistical analysis of internal stress fluctuations, defined as the difference between the local mean stress and stress on dislocations, is presented for deforming crystals with 3D discrete dislocation systems. Dislocation realizations are generated using dislocation dynamics simulations and the associated stress field is computed as a superposition of a regularized stress field of dislocation lines within the domain of the solution and a complementary stress field computed via a finite-element boundary value problem. The internal stress fluctuations of interest are defined by an ensemble of the difference between the stress on dislocation lines and the local mean field stress in the crystal. The latter is established in a piecewise fashion over small voxels in the crystal thus allowing the difference between the local average stress and stress on segments to be easily estimated. The results show that the Schmid stress (resolved shear stress) and Escaig stress fluctuations on various slip systems sampled over a random set of points follow a Cauchy (Lorentz) distribution at all strain levels, with the amplitude and width of the distribution being dependent on the strain. Finally, the implications of the Schmid and Escaig internal stress fluctuations are discussed from the points of view of dislocation cross-slip and the dislocation motion in continuum dislocation dynamics.
36 MATERIALS SCIENCE↗
A data driven approach for cross-slip modelling in continuum dislocation dynamics
Cross-slip is a thermally activated process by which screw dislocation changes its glide plane to another slip plane sharing the same Burgers vector. The rate at which this process happens is determined by a Boltzmann type expression that is a function of the screw segment length and the stress acting on the dislocation. In continuum dislocation dynamics (CDD), the information regarding the length of the screw dislocation segment and local stress state on dislocations are lost due to the coarse-grained representation of the density. Here, in this work, a data driven approach to characterize the lost information by analyzing the discrete dislocation configurations is proposed to enable cross-slip modeling in the CDD framework in terms of the coarse-grained dislocation density and stress fields. The analysis showed that the screw segment length follows an exponential distribution, and the stress fluctuations, defined as the difference between the stress on the dislocations and the mean field stress in CDD, follows a Lorentzian distribution. A novel approach for cross slip implementation in CDD employing the screw segment length and stress fluctuation statistics was proposed and rigorously tested by comparing the CDD cross-slip rates with discrete dislocation dynamics (DDD) rates. This approach has been applied in conjunction with three cross-slip models used in DDD simulations differing mainly in the functional form of cross slip activation energy. It was found that different cross-slip activation energy formulations yielded different cross-slip rates, yet the effect on mechanical stress-strain response and dislocation density evolution was minimal for the [001] type loading.
42 ENGINEERING↗
Dislocation dynamics in heterogeneous nanostructured materials
Crystalline materials can be strengthened by introducing dissimilar phases that impede dislocation glide. At the same time, the changes in microstructure and chemistry usually make the materials less ductile. One way to circumvent the strength–ductility dilemma is to take advantage of heterogeneous nanophases which simultaneously serve as dislocation barriers and sources. Owing to their superior mechanical properties, heterogeneous nanostructured materials (HNMs) have attracted a lot of attention worldwide. Nevertheless, it has been difficult to characterize dislocation dynamics in HNMs using classical continuum models, mainly due to the challenges in describing the elastic and plastic heterogeneity among the phases. Here, in this work, we advance a phase-field dislocation dynamics (PFDD) model to treat multi-phase materials, consisting of phases differing in composition, structural order, and size in the same system. We then apply the advanced PFDD model to exploring two important but divergent materials design problems in HNMs: dislocation/obstacle interactions and dislocation/interface interactions. Results show that the interactions between a dislocation and distribution of obstacles varying in structure and composition cannot be understood by simply interpolating from their individual interactions with a dislocation. It is also found that materials containing interfaces with nanoscale thicknesses and compositional gradients have a much higher dislocation bypass stress than those with sharp interfaces, providing an explanation for the simultaneous high strength and toughness of thick interface-containing nanolaminates as observed in recent experiments.
36 MATERIALS SCIENCE↗
Phase field dislocation dynamics formulation coupled with Fourier based micromechanics solver and its application to grain boundary–dislocation interactions
A new phase field dislocation dynamics (PFDD) formulation for homogeneous and heterogeneous materials is presented, which couples micromechanical solvers and the time-dependent Ginzburg–Landau equation. The strain fields are obtained from the micromechanical solver by solving the Lippmann–Schwinger equation and then used to define energy terms to model the evolution of the dislocations. Grain boundary (GB)–dislocation interactions are studied using the coupled PFDD formulation and by describing GBs as inclusions. GB energy and stiffness tensors are computed from molecular statics simulations, and a newly proposed lattice energy term that is dependent on the GB energy is considered in the calculations. Interaction of a screw dislocation with minimum energy and metastable states of low and high angle ⟨110⟩ symmetric tilt grain boundaries are studied. We show good agreement between predictions from our PFDD formulation and molecular dynamics simulations of grain boundary–dislocation interactions.
36 MATERIALS SCIENCE↗
Discrete dislocation dynamics for crystal RVEs. Part 1: Periodic network kinematics
A novel implementation of the dislocation flux boundary condition in discrete dislocation dynamics is presented. The continuity of the individual dislocation loops in a periodic representative crystal volume (RVE) is enforced across the boundary of the RVE with the help of a dual topological description for representing dislocation line kinematics in two equivalent spaces representing the deforming crystal, the RVE and the unbounded crystal spaces. The former describes the motion of the dislocations in the simulated crystal RVE whereas the latter represents the motion of dislocations in an infinite space containing all replicas of the RVE. A mapping between the two spaces forms the basis of the implementation of flux boundary condition. The implementation details are discussed in the context of statistical homogeneity of bulk crystals undergoing macroscopically homogeneous plastic deformation. In this case, the boundary nodes associated with dislocation segments bear no relevance in the motion of the dislocations. Finally, some test cases are presented and discussed to establish the proposed approach.
42 ENGINEERING↗
A discrete dislocation dynamics study of precipitate bypass mechanisms in nickel-based superalloys
Order strengthening in nickel-based superalloys is associated with the extra stress required for dislocations to bypass the $\gamma'$ precipitates distributed in the $\gamma$ matrix. Depending on the operating conditions and microstructure, a rich variety of bypass mechanism has been identified, with various shearing and Orowan looping processes gradually giving way to climb bypass as the operating conditions change from the low/intermediate temperatures and high stress regime, to the high temperature and low stress regime. When anti phase boundary (APB) shearing and Orowan looping mechanisms operate, the classical picture is that, at for a given volume fraction, the bypass mechanism changes from shearing to looping with increased particle size and within a broad coexistence size window. Another possibility, which is supported by indirect experimental evidence, is that a third “hybrid” transition mechanism may operate. Here, in this paper we use discrete dislocation dynamics (DDD) simulations to study dislocation bypass mechanisms in Ni-based superalloys. We develop a new method to compute generalized stacking fault forces in DDD simulations, based on a concept borrowed from complex analysis and known as the winding number of a closed curve about a point. We use this method to study the mechanisms of bypass of a square lattice of spherical $\gamma'$ precipitates by $a/2\langle110\rangle$ {111} edge dislocations, as a function of the precipitates volume fraction and size. We show that not only the hybrid mechanism is possible, but also that it operates as the transition mechanism between the shearing and looping regimes over a wide range of precipitates volume fraction and radii. Based on our simulation results, we propose a simple model for the strength of this mechanism. We also consider the effects of a $\gamma$/$\gamma'$ lattice misfit on the bypass mechanisms, which we approximate by an additional precipitate stress computed according to Eshelby’s inclusion theory. We show that in the shearing and hybrid looping-shearing regimes, a lattice misfit generally results in an increased bypass stress. For sufficiently high lattice misfit, the critical bypass configuration in attractive dislocation-precipitates interactions changes dramatically, and the bypass stress is controlled by the pinning of the trailing dislocation on the exit side of the precipitates, similar to what has been reported in the high-temperature creep literature.
36 MATERIALS SCIENCE↗
Plasticity in irradiated FeCrAl nanopillars investigated using discrete dislocation dynamics
Here, in this paper, we investigate plasticity in irradiated FeCrAl nanopillars using discrete dislocation dynamics simulations (DDD), with comparisons to transmission electron microscopic (TEM) in situ tensile tests of ion- and neutron-irradiated commercial C35M FeCrAl alloy. The effects of irradiation-induced defects, such as a/2<111> and a<100> type loops and composition fluctuations representative of phase separation in irradiated FeCrAl alloys, are investigated separately as well as superposed together in simulations. We explore the effects of defects on the stress-strain behavior, specifically yield strength and hardening response, of FeCrAl nanopillars. Our simulations confirm the widely accepted fact that irradiated alloys exhibit a stress-strain response with higher yield strength as compared to unirradiated alloys. However, our DDD calculations reveal an atypical superposition of the hardening contributions due to composition inhomogeneity and irradiation loops wherein composition inhomogeneity annihilates the hardening due to irradiation loops at small scales. As a result, we observe that the yield strength in irradiated alloys, after taking into consideration the effects of both composition inhomogeneity and irradiation loops, is smaller than the yield strength of the alloys with only irradiation loops and is approximately same for the alloy with composition inhomogeneity alone. This is referred to as “destructive interference” between the hardening contributions due to composition fluctuations and irradiation loops in the paper. We also identify this destructive interference in the superposition in our parallel TEM in situ tensile tests on unirradiated, ion-irradiated, and neutron-irradiated C35M FeCrAl alloy. This destructive interference in the hardening contributions contrasts with the dispersed barrier hardening (DBH) models widely utilized by the experimental community to model the hardening contributions due to different irradiation induced defects. The effects of the loading orientations on the yield strength and hardening are investigated and the mechanisms for the hardening in irradiated FeCrAl alloys are also reported.
36 MATERIALS SCIENCE↗
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.
36 MATERIALS SCIENCE↗
Active learning of a crystal plasticity flow rule from discrete dislocation dynamics simulations
Continuum-scale material deformation models, such as crystal plasticity (CP), can significantly enhance their predictive accuracy by incorporating input from lower-scale (i.e. mesoscale) models. The procedure to generate and extract the relevant information is however typically complex and ad hoc, involving decision and intervention by domain experts, leading to long development times. In this study, we develop a principled approach for calibration of continuum-scale models using lower scale information by representing a CP flow rule as a Gaussian process model. This representation allows for efficient parameter space exploration, guided by the uncertainty embedded in the model through a process known as Bayesian optimization (BO). We demonstrate a semi-autonomous BO loop which instantiates discrete dislocation dynamics simulations whose initial conditions are automatically chosen to optimize the uncertainty of a model CP flow rule. Our self-guided computational pipeline efficiently generated a dataset and corresponding model whose error, uncertainty, and physical feature sensitivities were validated with comparison to an independent dataset four times larger, demonstrating a valuable and efficient active learning implementation readily transferable to similar material systems.
36 MATERIALS SCIENCE↗
Coupled cluster and dislocation dynamics modeling of microstructure evolution in irradiated materials
We develop here a coupled cluster and dislocation dynamics framework to study the microstructure evolution of irradiated materials. The framework not only accounts for the three dimensional diffusion of radiation-generated clusters, but also their interaction with dislocation networks and the resultant climb motion of discrete dislocations within finite crystals. The framework is solved with a superposition solution scheme, and is applied to investigate the evolution of the irradiation-induced dislocation loops in zirconium (Zr), considering the effects of various bias factors including the diffusion anisotropy difference (DAD) of interstitials and interstitial clusters, the dislocation bias of defects to discrete dislocation segments, and the production bias of defects from the radiation cascade. We find that the DAD is the most critical factor influencing the kinetics of the loop evolution in Zr, while the recombination/interaction of mobile defects can induce a strong spatial dependence of the loop evolution together with the DAD. Here, the method is also adopted to study the evolution of interstitial $\langle$a$\rangle$ and vacancy $\langle$c$\rangle$ dislocation loop ensembles consistent with the microstructure observed during irradiation-induced growth of Zr. Our findings not only reveal the spatial dependence of the size and ellipticity of the dislocation loops, but also suggest a limit on the anisotropy factor of interstitials to reproduce the co-growth of $\langle$a$\rangle$ and $\langle$c$\rangle$ loops in zirconium, in good agreement with experimental observations and other simulation results.
Bias factors↗