Dislocation Dynamics Model Research Articles

Phase field dislocation dynamics modeling of shearing modes in Ni2(Cr,Mo,W)-containing HAYNES® 244® Superalloy

Density Functional Theory (DFT) calculations can determine planar defect energies and slip pathways that are present in ordered intermetallic systems used to strengthen Ni-based superalloys, but analytical models used to evaluate the strengthening effects of these phases often involve significant simplifying assumptions. Instead, Phase Field Dislocation Dynamics (PFDD) is a useful modeling tool that incorporates dislocation interactions with precipitates and slip pathways informed by DFT to determine how precipitate shearing might occur under applied stresses with improved accuracy over previous models. In this work, we apply PFDD to study precipitate shearing in HAYNES® 244®, a high strength Ni-based superalloy strengthened through a novel Ni2(Cr, Mo, W) phase that has a low symmetry Body Centered Orthorhombic (BCO) crystal structure which complicates analysis of slip pathways. Through our modeling, we show the formation of and evolution of extended dislocations in the matrix and in the precipitates, the interaction of dislocations with the precipitates, and the formation of planar faults in the precipitate. A key aspect of incorporating the DFT determined slip pathway is the influence of the unstable fault energy and the asymmetry of the energy pathway on the strengthening aspect of the precipitate. The resulting critical strengths are compared to analytical models. The size, orientation, particle distance, and calculated slip pathway for the different variants in this system are all shown to have an important effect on the critical stress to shear these precipitates.

From process to property: multi-physics modeling of dislocation dynamics and microscale damage in metal additive manufacturing

AbstractMetal additive manufacturing (AM) has the potential to tailor the mechanical performance of materials. Due to the complex thermal history and unique microstructure, AM materials are reported to contain distinct dislocation networks with a high dislocation density, which affect the plastic deformation behavior and fracture. However, it is challenging to experimentally observe the formation of such dislocation structures. In this work, a multi-scale multi-physics crystal plasticity modeling framework that integrates the process-structure-property relationship in metal AM is developed. The temperature field obtained from thermal-fluid flow simulations of the AM process and the microstructure from the phase field model of grain growth are combined into thermo-mechanical crystal plasticity simulations to obtain grain-scale thermal stresses. These stresses are used as input to simulate the evolution of dislocation structures within individual grains. Taking AM 316L stainless steel as the material of interest, the effect of initial dislocation configuration on the slip plane and cross-slip mechanism on the dislocation structure formation are investigated. Furthermore, a phase field damage model is implemented to study the initiation of microscale damage and their relationship with dislocation structures, which is a main novelty of this work. This modeling framework provides comprehensive simulations of all aspects of metal AM and offers insights into the dislocation mechanisms and damage formation at microscale in AM materials, which could be used to guide the manipulation of the mechanical properties of AM materials.

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.

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.

Does the Larkin length exist?

The yield stress of random solid solutions is a classic theme in physical metallurgy that currently attracts a renewed interest in connection to high entropy alloys. Here, we revisit this subject using a minimal dislocation dynamics model, where a dislocation is represented as an elastic line with a constant line tension embedded in the stochastic stress field of the solutes. Our exploration of size effects reveals that the so-called Larkin length (Lc ) is not a length scale over which a dislocation can be geometrically decomposed. Instead, Lc is a crossover length scale marking a transition in dislocation behavior identifiable in at least three properties: (1) below Lc , the dislocation is close to straight, aligned in a single energy valley, while above Lc , it roughens and traverses several valleys; (2) the yield stress exhibits pronounced size-dependence below Lc but becomes size-independent above Lc ; (3) the power-spectral density of the dislocation shape changes scaling at a critical wavelength directly proportional to Lc . We show that for white and correlated stress noises, Lc and the thermodynamic limit of the yield stress can be predicted using Larkin’s model, where the noise dependence in the glide direction is neglected. Moreover, we show that our analysis is relevant beyond the minimal line tension model by comparison with atomic-scale simulations. Finally, our work suggests a practical approach for predicting yield stresses in atomistic models of random solid solutions, which only involves small-scale atomistic simulations below Lc .

Mesoscale dislocation dynamics modeling of incipient plasticity under nanoindentation

A mesoscale dislocation dynamics model which couples three-dimensional dislocation dynamics (DD), and finite element method (FEM) was used to investigate the mechanical response of Aluminum (Al) single crystal under spherical nanoindentation. Together with an atomistically informed nucleation model, the dislocation dynamics model can capture both the dynamic evolution of dislocations under the complex stress state of indentation and the corresponding constitutive response of material. The resulting load-displacement curves and the evolution of dislocation microstructures were analyzed to provide insights into the underlying deformation mechanism for incipient plasticity under nanoindentation. Our model could show the transition of the governing mechanism for plasticity from nucleation-controlled plasticity to pre-existing source-driven plasticity with increasing indenter size, as shown in recent experiments. In addition, it could capture a clear picture on incipient plasticity including the formation of prismatic loops through successive cross-slips of nucleated dislocations, such as rhombus loop and prismatic helical structures, which agrees well with atomistic modeling results.

A combined kinetic Monte Carlo and phase field approach to model thermally activated dislocation motion

In this work, a kinetic Monte Carlo (KMC) scheme is integrated into a phase field dislocation dynamics (PFDD) model to account for thermal activation. While the implementation is general and could be applied to many different thermally activated processes, we apply the model to simulate a dislocation transmitting through an interface. Two cases are analyzed: a dislocation transmitting through a strong interface, and a dislocation transmitting through a more realistic grain boundary in tungsten. Results and trends for both cases are discussed in detail, and ultimately show that the combined KMC-PFDD algorithm is effective in capturing thermally activated dislocation processes.

Atomically-informed dislocation dynamics model for prediction of void hardening in irradiated tungsten

Nanometric voids are one of the fundamental defects generated by neutron irradiation in fusion environment, which impede dislocation motion and cause hardening of plasma facing tungsten. Accurate prediction of voids hardening is crucial for safety evaluation of irradiated tungsten. In this paper, we develop a void-dislocation interaction model within the framework of dislocation dynamics (DD) and implement it in open-source DD software ParaDiS. We use this model to study the hardening effects of randomly-distributed voids with different sizes and number densities. The model for short-range interaction during dislocation-void contact, especially the dislocation movement on void surface, is informed and calibrated by atomistic simulations. Meanwhile, the long-range elastic interaction between dislocation and void is efficiently computed by the approach developed in our recent work (Wu et al., 2022) with Eshelby's equivalent inclusion method. Our DD simulations show that the average resistance by voids with various sizes is proportional to the 2/3 power of total number density. We also find that a modified Friedel-Kroupa-Hirsch (MFKH) model can quantify the hardening effects of nanometric voids, where the hardening coefficient depends on an effective average void diameter that accounts for the size distribution of voids. This MFKH model extends our previous work (Wu et al., 2022) that addresses the hardening of small vacancy clusters where dislocations simply cut through them, which is essentially an elastic perturbation to the dislocation dynamics. The proposed MFKH model can predict both small vacancy clusters and nanometric voids hardening effects with only difference in size dependent hardening coefficient. We further verify the MFKH model by comparing its quick predictions of the hardening effects by randomly-distributed nanometric voids with experiments on twelve neutron-irradiated tungsten samples.

A discrete dislocation dynamics model of creep in polycrystals

The dislocation creep represents high temperature plastic deformation of metallic materials. However, the subject is usually approached with constitutive and phenomenological formulations. The notable exceptions are the recent use of numerical modeling. For example, single-crystal discrete dislocation dynamics (DDD) has been adopted to involve dislocation glide and climb together with diffusion of vacancies. This naturally provides a physics-based framework for dislocation creep. However, the existing model(s) are limited to single crystals and hence are limited in scope. This study extended a single crystal dislocation creep model into polycrystalline ensemble. This was then used to simulate steady state creep rate (ε˙) with respect to creep stress (σ), temperature (T) and grain size (d) in polycrystalline aluminum. Our virtual experiments showed an Arrhenius relationship between ε˙ and T, and a power law scaling with σ. Further, our simulations also revealed a power law increase in ε˙ with d. This is striking, as available experimental data indicate both grain size dependence as well as independence. The answer to this apparent contradiction also emerged from our numerical simulations. It was shown that ε˙ is controlled by interactions of dislocations with static obstacles and grain boundaries. Dominance of static obstacles, in particular, significantly diminished the grain size effect. The role of dislocation mean free path on the pinning and dislocation creep behavior of polycrystalline metallic material was thus mechanistically established.

Dislocation structures formation induced by thermal stress in additive manufacturing: Multiscale crystal plasticity modeling of dislocation transport

The motion of dislocations governs the plastic deformation of crystalline materials, which in turn determines the mechanical properties. The complex thermal history, large temperature gradients and high cooling rates during the process of additive manufacturing (AM) can induce high dislocation density and unique dislocation structures in the material. The origin of these dislocation structures and their stability during mechanical loading are debated. A novel temperature dependent continuum dislocation dynamics (CDD) model is developed, in which four state variables are used for each slip system representing the total dislocation density, edge and screw geometrically necessary dislocation densities and dislocation curvature. The CDD model is fully coupled with a crystal plasticity solver, which captures the plastic deformation induced by the dislocation motion. A hybrid continuous and discontinuous Galerkin formulation is developed to accurately reproduce the dynamics of highly discontinuous dislocation density fields that are typical of dislocation structures. A multiscale modeling approach is used, in which the thermally induced deformation in specific grains of a polycrystal is extracted from larger scale crystal plasticity simulations of the laser powder-bed fusion process, and is then used for single crystal scale dislocation dynamics simulations. Simulation results reveal the dynamics of dislocation structure formation in grains at different positions during laser scanning and cooling stages. The effect of the cyclic thermal stress during multi-layer AM fabrication is also investigated. The simulations provide a new perspective on the specific conditions that should be satisfied during AM process for the formation of stable dislocation structures.

Bayesian optimization of discrete dislocation plasticity of two-dimensional precipitation-hardened crystals

Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of microstructures, defined here by the size distribution of precipitates (fixed impurities or inclusions acting as obstacles for dislocation motion) within a simple two-dimensional discrete dislocation dynamics model. The aim is to design a microstructure optimizing a given mechanical property, e.g., maximizing the expected value of shear stress for a given strain. The problem of finding the optimal discretized shape for a distribution involves a norm constraint, and we find that sampling the space of possible solutions should be done in a specific way in order to avoid convergence problems. To this end, we propose a general mathematical approach that can be used to generate trial solutions uniformly at random while enforcing an Euclidean norm constraint. Both equality and inequality constraints are considered. A simple technique can then be used to convert between Euclidean and other Lebesgue $p$-norm (the 1-norm in particular) constrained representations. Considering different dislocation-precipitate interaction potentials, we demonstrate the convergence of the algorithm to the optimal solution and discuss its possible extensions to the more complex and realistic case of three-dimensional dislocation systems where also the optimization of precipitate shapes could be considered.

Dislocation Dynamics Model to Simulate Motion of Dislocation Loops in Metallic Materials

Dislocation dynamics has been an intensive research subject in materials science and engineering due to the significant roles it plays in plastic deformation and the hardening of metals, fracture mechanics, and the fabrication of semiconductor thin films. However, a long-standing problem from the three-dimensional dislocation dynamics is that the motion and interaction of dislocation loops heavily depend on the loop-segment sizes, which substantially reduces the accuracy of simulation. We herein propose a new three-dimensional dislocation dynamics model together with its physical background. The proposed model incorporates the inherent interactions among differential dislocation segments. The simulation results on motion of Frank–Read sources demonstrate that the proposed model can resolve the paradoxical segment-dependent phenomenon in dislocation dynamics.

Ultrahigh strength in lightweight steel via avalanche multiplication of intermetallic phases and dislocation

Lightweight high-strength steel has been an important topic for structural materials. Recent studies show that B2 intermetallic phase, nucleated around crystal defects such as grain boundaries and dislocations, can be used to further strengthen mechanical properties of metal alloys. Due to the limited density of nucleation sites, however, the current thermomechanical processing leads to formation of low density and coarse B2 phase. In this study, a lightweight steel Fe-Mn-Al-C (70 wt.% Fe) is processed by a thermal-controlled high strain rate plastic deformation process, warm laser shock peening (wLSP), in which high-density dislocations can be generated and high mobility of solute atoms at elevated temperature can facilitate the precipitation of B2 intermetallic phase. Simulations based on coupled phase-field and dislocation dynamics model are performed to investigate the intermetallic precipitation and dislocation formation during wLSP process. It is found that high density dislocations can be obtained in wLSP due to the pinning effect of B2 intermetallic phase on dislocations. The interaction between B2 intermetallic precipitates and shock wave facilitates the generation of high-density dislocations, which in turn serve as nucleation sites for B2 phase formation. This strong coupling effect results in avalanche multiplication of ultrahigh density and ultrafine B2 precipitates, and significant improvements in both strength and ductility. The yield strength of the lightweight steel reaches 2030Mpa with ultimate strength of 2850 MPa, among the highest for lightweight mid-carbon steel. This work provides a new insight to produce lightweight metals with ultrahigh density and ultrafine intermetallic phases for high strength and ductility.

Modeling of microscale internal stresses in additively manufactured stainless steel

Additively manufactured (AM) metallic materials often comprise as-printed dislocation cells inside grains. These dislocation cells can give rise to substantial microscale internal stresses in both initial undeformed and plastically deformed samples, thereby affecting the mechanical properties of AM metallic materials. Here we develop models of microscale internal stresses in AM stainless steel by focusing on their back stress components. Three sources of microscale back stresses are considered, including the printing and deformation-induced back stresses associated with as-printed dislocation cells as well as the deformation-induced back stresses associated with grain boundaries. We use a three-dimensional discrete dislocation dynamics model to demonstrate the manifestation of printing-induced back stresses. We adopt a dislocation pile-up model to evaluate the deformation-induced back stresses associated with as-printed dislocation cells. The extracted back stress relation from the pile-up model is incorporated into a crystal plasticity (CP) model that accounts for the other two sources of back stresses as well. The CP finite element simulation results agree with the experimentally measured tension–compression asymmetry and macroscopic back stress, the latter of which represents the effective resultant of microscale back stresses of different origins. Our results provide an in-depth understanding of the origins and evolution of microscale internal stresses in AM metallic materials.

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. 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.

Phase field modeling of dislocations and obstacles in InSb

We present a phase-field dislocation dynamics (PFDD) model informed by first-principle calculations to elucidate the competitive dislocation nucleation and propagation between the glide and shuffle sets in InSb diamond cubic crystal. The calculations are directly informed with generalized stacking fault energy curves on the (111) slip plane for both the “glide set,” with the smaller interplanar spacing, and the “shuffle set,” with the larger interplanar spacing. The formulation also includes elastic anisotropy and the gradient term associated with the dislocation core. The PFDD calculations show that under no stress the equilibrium structure of screw glide set dislocations dissociates into Shockley partials, while those of the shuffle set dislocations do not dissociate, remaining compact. The calculated dislocation core widths of these InSb dislocations agree well with the measured values for other semiconductor materials, such as Si and GaN. We find that a shuffle set dislocation emits from a dislocation source at an applied stress about three times smaller than that needed to emit leading and trailing partials successively on the glide set plane. Once the partial dislocations in the glide set are emitted, they propagate faster than the shuffle set perfect dislocation at the same stress level.

Microplasticity in inhomogeneous alloys

We report on a preliminary modelling effort to understand the influence of compositional inhomogeneity on alloy microplasticity from a dislocation dynamics perspective. We tackle this problem by multiscale simulations in three steps: (1) analysis of the 3D composition morphology in alloys with tendency to undergo spinodal instability both thermally and under irradiation, with bcc FeCrAl alloys as a model system, (2) atomistic simulation of the dislocation mobility as a function of the local alloy composition, and (3) using dislocation dynamics simulations to understand the impact of composition inhomogeneity on microplasticity. The dislocation dynamics model takes into consideration the coherency stress associated with composition inhomogeneity when computing the forces driving the dislocation motion and on cross slip. Our preliminary investigation shows that the stress-strain response of the alloy and the dislocation density evolution depend on the wavelength of the composition fluctuations. Our investigation also shows that the alloy inhomogeneity may alter the cross-slip activity, which, in turn, influences the dislocation density evolution. The dependence of the dislocation mobility and coherency stress on local composition and its variation, as well as the altered cross slip rates, cause the dislocation microstructure to differ relative to that in the homogeneous alloy of the same average composition.

Thick interface size effect on dislocation transmission in nanolaminates

Recent experimental studies have reported that thick interfaces in nanolaminates can lead to greater strengths than conventionally sharp interfaces without sacrificing deformability. Using a multi-phase phase-field dislocation dynamics model, dislocation transmission across a compositionally graded, nanoscale thick interface is investigated. Thicker interfaces over a finite range are found to lead to greater resistance to transmission. The limit interface thickness at which the peak resistance is reached, and the strengthening capacity of the interface are greater when the dislocation is dissociated, as in a face-centered cubic lattice, than when it is compact, as in a body-centered cubic lattice. The composition transitions within the interface are treated with multiple sublayers, and it is found that the interface transmission barrier is as strong as its most resistance composition.

Review of Sublimation Growth of SiC Bulk Crystals

The review on bulk growth of SiC includes a basic overview on the widely used physical vapor transport method for processing of 4H-SiC boules as well as the discussion of three current research topics: (a) Sublimation bulk growth of large area, freestanding cubic SiC, (b) in-situ Visualization of the PVT Process using 2D and 3D X-ray based imaging and (c) prediction of dislocation formation and motion in SiC using a continuum model of dislocation dynamics (CDD).