Stress Field Of Dislocation Research Articles

The hierarchical energy landscape of edge dislocation glide in refractory high-entropy alloys

Refractory high-entropy alloys (RHEAs) are considered as potential candidates for high-temperature applications, with the glide resistance of edge dislocations being a crucial factor in determining the high-temperature strength. However, the solid-solution strengthening mechanism of edge dislocations in RHEAs is not fully understood. The existing Labusch-type models mainly focus on the long-range interaction of solute atoms with the dislocation stress field, while there is little attention paid to the short-range interaction in the dislocation core region. Here, we conduct carefully designed atomic simulations to decouple the long-range and short-range interactions in a typical RHEA, NbMoTaW. Furthermore, the total change in solute-dislocation interaction energy is decomposed, and a hierarchical energy landscape is revealed, demonstrating that the short-range interaction at the core region gains more importance in the solid-solution strengthening of edge dislocations in NbMoTaW. Then, we determine the Larkin length, which signifies the transition from size-dependent to size-independent dislocation behavior. The activation barrier extracted from the simulation with the dislocation length above the Larkin length is incorporated into the crystal plasticity model, and the high-temperature yield strength is well predicted by the strengthening from edge dislocations. Our work provides deep insight into the solid-solution strengthening mechanism in random solution solids, elucidating the importance of the local atomic configuration around the dislocation core.

Intermitted 3D Diffraction Tomography Combined with In situ Laue Diffraction to Characterize Dislocation Structures and Stress Fields in Microbending Cantilevers

The mechanisms of plastic deformation are investigated using different characterization tools as scanning electron microscopy (SEM), transmission electron microscopy, or synchrotron‐based X‐ray techniques like Laue microdiffraction (μLaue). However, structural information can be limited to the specimen surface (SEM), to extremely thin samples (TEM), or depth averaging (μLaue). Until today, a nondestructive in situ investigation of a dislocation population, and de facto, the determination of the local stress tensor in bulk samples, remain challenging. To decompose the depth‐integrated μLaue signals, the so‐called “differential aperture X‐ray microscopy” (DAXM), allowing the 3D determination of the local structural crystal properties, is used. Using this approach, the local crystallographic phase, orientation, and the elastic strain tensor are obtained with 1 μm3 voxel size. In order to accomplish the experiment, a protocol and a new combined in situ mechanical testing rig with a DAXM microscope is created. The experiment is conducted on a severely bent focused ion beam copper single‐crystal microcantilever (10 × 10 × 25 μm3). The local deviatoric strain tensor and the local lattice curvature in the deformed sample are analyzed in 3D. The advantages and resolution limits of the technique are discussed in detail.

The Effect of Zr and Li on the Microstructure of AlMg5Si2Mn-Type Casting Alloys

AbstractIn the article, the authors present results of microstructural studies of Al-Mg-Si-Mn casting alloys with Zr, Li, and TiB2 additions on a broad scale. Zirconium content was set on two levels: 0.34 and 1.58 wt%, and Li was set 1.2 and 2.0 wt%. It was found that the addition of Zr shifts the eutectic melting temperature to a higher level, up to 611.3 °C at 1.6 wt% Zr. At the same time, Li addition leads to the depression of eutectic melting temperature: down to 587.2 °C at 2.0 wt% Li, what is a common effect of eutectic modification which was confirmed by means of structural examinations. The complex addition of Li and AlTi5B1 resulted in a eutectic melting temperature close to the equilibrium eutectic temperature for the Al-Mg-Si system (596.2 °C). The grain refinement effect of Zr is due to the nucleation of α-Al on the Zr(Al1−x, Six)3 phase. Crystals of this phase were detected in the grain centers of Zr-containing alloys. The Li addition does not affect α-Al grain size but changes the morphology of eutectic colonies from petal-like to fibrous. Observation of TiB2 particles inside the primary Mg2Si crystals gives direct experimental confirmation of nucleation of the primary phase on the surface of TiB2 in the alloy after adding Li and AlTi5B1. Natural aging of the alloys resulted in the formation of fine precipitates detected close to dislocations. The most apparent supposition is that the mechanism responsible for their formation is heterogeneous nucleation in the stress field of dislocations. Hardness tests showed adding 2.0 wt% of Li is very effective, increasing hardness up to 113 HV0.2 in naturally aged condition, which is nearly double that of commercial Al-Mg-Si die-casting alloy. Several effects were proposed which may synergistically contribute to the rise of hardness in Li-containing alloys, such as solid solution strengthening, formation of primary LiAlSi phase and natural aging.

Dislocation loop and irradiation-induced synergistic-competitive mechanism in Cu-rich precipitates: a phase-field study

Both irradiation and dislocations have been proposed as routes to rationally manipulate spatial distribution and micromorphology of precipitate. An interesting effect emerges in Fe–10at.%Cu–3at.%Mn–1.5at.%Ni–1.5at.%Al alloy due to the synergistic-competitive roles of dislocation loop and irradiation. Base on cascade mixing, vacancy-interstitial atoms and dislocation stress field model, we examine nucleation and growth dynamics of Cu-rich precipitates, where both dislocation loop and irradiation act in conjunction. Analytical treatments identify regimes, where the distribution of elements and point defects due to irradiation and dislocations are specific to the Cu-rich precipitates. Simulation results reveal that density, size and distribution of Cu-rich precipitates are a manifestation of the competing effects of the dislocation loop and the irradiation rate. More specifically, the dislocation loop preferentially assists the formation of precipitates and new dislocations at lower irradiation rates. Only the irradiation induces the formation of Cu-rich precipitates with the irradiation rate continues to increase. Equipped with molecular dynamics, where reproduces major interaction features of the solutes with point defects under displacement cascade, can verify multi-component morphologies of Cu-rich precipitates. This modeling framework provides an avenue to explore the role of dislocation loop and irradiation on the microstructural evolution of Cu-rich precipitates.

Application of laboratory micro X-ray fluorescence devices for X-ray topography

It is demonstrated that high-resolution energy-dispersive X-ray fluorescence mapping devices based on a micro-focused beam are not restricted to high-speed analyses of element distributions or to the detection of different grains, twins and subgrains in crystalline materials but can also be used for the detection of dislocations in high-quality single crystals. Si single crystals with low dislocation densities were selected as model materials to visualize the position of dislocations by the spatially resolved measurement of Bragg-peak intensity fluctuations. These originate from the most distorted planes caused by the stress fields of dislocations. The results obtained by this approach are compared with laboratory-based Lang X-ray topographs. The presented methodology yields comparable results and it is of particular interest in the field of crystal growth, where fast chemical and microstructural characterization feedback loops are indispensable for short and efficient development times. The beam divergence was reduced via an aperture management system to facilitate the visualization of dislocations for virtually as-grown, non-polished and non-planar samples with a very pronounced surface profile.

Dislocations in nonlocal simplified strain gradient elasticity: Eringen meets Aifantis

The nonlocal strain gradient elasticity theory is used to address mechanical problems at small scales where size effects and regularization cannot be neglected. In this work, dislocations are investigated in the framework of nonlocal simplified first strain gradient elasticity. It is shown that nonlocal simplified strain gradient elasticity is the unification of the theories of Eringen’s nonlocal elasticity of Helmholtz type and simplified first strain gradient elasticity. Nonlocal simplified strain gradient elasticity contains two characteristic lengths, namely the characteristic length of nonlocal elasticity of Helmholtz type and the characteristic length of simplified first strain gradient elasticity. The advantage of nonlocal simplified first strain gradient elasticity is that the displacement, elastic distortion, plastic distortion, total stress, Cauchy stress and double stress fields of screw and edge dislocations which are calculated here are nonsingular and finite everywhere. Moreover, the Peach-Koehler force of two screw dislocations and two edge dislocations is derived and it is shown that the Peach-Koehler force is also nonsingular. Numerical examples for all dislocation fields of screw and edge dislocations in aluminum are given.

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.

Influence of pre-existing configurations of dislocations on the initial pop-in load during nanoindentation in a CrCoNi medium-entropy alloy

ABSTRACT The origin and mechanisms responsible for incipient plasticity in metals are still poorly understood. Moreover, the reasons for the recently reported large scattering of the initial pop-in load remain unclear. Hence, this study addresses these issues through a combination of nanoindentation tests and electron channelling contrast imaging characterisation considering a CrCoNi medium-entropy alloy. Experimental findings were also supported by elastic calculations that consider both the indentation and dislocation stress fields. A wide scatter in the maximum shear stress underneath the indenter, as expected, was observed for the analysis based on dislocation density. As a consequence, the spatial arrangement of dislocations within the indented region or local dislocation configuration is introduced as a new parameter to overcome overly simple analysis based on the dislocation density. The maximum shear stress underneath the indenter increased from 6 GPa for dislocation closer to the indentation axis to 11 GPa at 600 nm for dislocation far away from it. Additionally, elastic calculations revealed that the response to the incoming nanoindenter was different for dislocations with different configurations. Thus, the complex interactions of stress fields due to configurations of dislocations and indentation account for the large scatter of the maximum shear stress beneath the indenter.

Misfit and the mechanism of high temperature and low stress creep of Ni-base single crystal superalloys

The present work proposes a new elementary deformation mechanism which governs high temperature and low stress creep of single crystal superalloys (SXs), where the misfit between the γ- and the γ′-phase plays a central role. In the coherent two phase SX microstructure, there is a tendency to minimize the overall elastic strain energy. This is accomplished by the formation of dislocation networks in the γ-phase close to the γ/γ’-interfaces. The stress fields of the network dislocations and misfit stresses accommodate each other to keep the overall strain energy of the system at a minimum. Previous work has shown that dynamic recovery is associated with knitting-out reactions, where dislocations from the network shear the γ’-phase and annihilate with dislocations of opposite sign on the other side of the γ’-phase region. Due to the presence of the misfit this results in an increase of elastic strain energy which is counteracted by coupled knitting-in reactions where newly arriving γ-channel dislocations re-establish the minimum energy configuration. Here we provide microstructural evidence for knitting-out and knitting-in reactions and show that while these reactions clearly occur, dislocation network spacings stay constant. The misfit between the γ- and the γ′-phase accounts for a constant network spacing. Dislocation networks are not static but represent dynamic steady state equilibrium structures in an evolving microstructure. Knitting regular networks requires climb processes which are suggested to be rate controlling. This new view of high temperature and low stress creep mechanism of SXs allows to rationalize previous results published in the literature.

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. 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.

Phase-field study of the effect of stress field and fission rate on intragranular Xe bubble evolution in U3Si2 nuclear fuel

Due to the superior thermal conductivity and high uranium density, U3Si2 is an excellent candidate for conventional UO2 nuclear fuel and shows great potential application in accident-tolerant fuel (ATF) assembly of light water reactors (LWRs). Currently, the behavior of Xe bubbles with internal or applied stress is rarely investigated, restricting further understanding of swelling in U3Si2. The mesoscopic phase-field method has been developed in this work to study the spatial and temporal Xe bubble evolution in U3Si2. The results show that the bubble density and its average size increase as the fission rate increases. Applied stress accelerates the nucleation and growth of gas bubbles, reshaping the bubbles’ morphology from spherical in a stress-free state into elongated along the applied direction in a stressed state. The gas bubbles in a local dislocation stress field nucleate preferentially at stress-concentrated sites and spread over the whole system in succession, and the bubble coarsening is controlled by the stress overlap of the dislocation pair. The results show a practical phase-field method for Xe bubble evolution study in U3Si2, which can be expanded into swelling behavior investigation in other fuels and lay a solid foundation for the development of ATF assembly.

Linear complexions directly modify dislocation motion in face-centered cubic alloys

Linear complexions are defect phases that form in the presence of dislocations and thus are promising for the direct control of plasticity. In this study, atomistic simulations are used to model the effect of linear complexions on dislocation-based mechanisms for plasticity, demonstrating unique behaviors that differ from classical dislocation glide mechanisms. Linear complexions impart higher resistance to the initiation and continuation of dislocation motion when compared to solid solution strengthening in all of the face-centered cubic alloys investigated here, with the exact strengthening level determined by the linear complexion type. Stacking fault linear complexions impart the most pronounced strengthening effect, as the dislocation core is delocalized, and initiation of plastic flow requires a dislocation nucleation event. The nanoparticle and platelet array linear complexions impart strengthening by acting as pinning sites for the dislocations, where the dislocations unpin one at a time through bowing mechanisms. For the nanoparticle arrays, this event occurs even though the obstacles do not cross the slip plane and instead only interact through modification of the dislocation's stress field. The bowing modes observed in the current work appear similar to traditional Orowan bowing around classical precipitates but differ in a number of important ways depending on the complexion type. As a whole, this study demonstrates that linear complexions are a unique tool for microstructure engineering that can allow for the creation of alloys with new plastic deformation mechanisms and extreme strength.

A model for redistribution of oppositely charged point defects under the stress field of dislocations in nonstoichiometric ionic solids: Implications in doped ceria

Point defect distribution in the vicinity of discontinuities plays important role in the transport properties of nonstoichiometric ionic solids. Here, considering dopants and oxygen vacancies as the major point defects in doped ceria, we develop a Monte Carlo model to examine how the stress field of edge dislocations affect point defect distribution in their surroundings. Point defects are considered to interact with the elastic stress field of dislocations due to their misfit volume, and the electrostatic interaction between the point defects is also taken into account. In contrast with a prevalent theory of chemo-mechanical equilibrium in solid solutions, the model developed here is consistent with classical elasticity in that the point defects do not interact through their self-stress fields. Stress effects both on the defect distribution, and on the electric potential, are examined for a single dislocation as well as a periodic array of like dislocations. In agreement with previous atomistic simulations, the model predicts that electrostatic interactions drive enrichment or depletion of defects of both types on either the compressive or tensile side of edge dislocations depending on the ionic radius of the dopant. The stress field of an array of like dislocations periodic in the direction of the Burgers vector is shown to result in different bulk defect concentrations and bulk electric potentials on the opposite sides of the array, whereas for an array with repeat direction normal to the Burgers vector, defect enrichment and depletion emerge in alternate regions limited to the vicinity of the dislocations.

Effect of Surface Dissolution on Dislocation Activation in Stressed FeSi6.5 Steel.

The effects of surface dissolution on dislocation activation in FeSi6.5 steel are quantitatively studied by analyzing the stress relaxation data using the thermal activation theory of dislocation. The stressed FeSi6.5 steel sample in acid solutions (H2SO4 or HCl) exhibits a much higher rate of stress reduction with time compared with that in air or deionized water. As the stress relaxation time is prolonged to 20 min, the relaxation rates are 0.055 MPa·min-1 in water and 0.074, 0.1, 0.11 MPa·min-1 in H2SO4 solutions with pH 4, 3, and 2, respectively. In a NaCl solution, a slight increase in the relaxation rate compared with air was found. Higher acidity (lower pH) of the solution inducing higher stress relaxation rate implies the softening is associated with the anodic dissolution of the surface layer and the accelerated (additional) flow of dislocations. The analyses using the thermal activation theory of dislocation during relaxation reveal the mechanism for the accelerated plastic flow induced by the corrosive medium. The variations of these parameters are related to the relaxation of the stress field of dislocations and the weakening of interaction between slip dislocations and short-range obstacles. The chemomechanical effect, including a reduction in apparent activation energy and a decrease in waiting time for dislocation to obtain sufficient thermal activation energy to cross obstacles, causes an increase in the stress relaxation rate (plastic strain rate). The study confirms that surface dissolution accelerates the plastic flow of metals and supports the view that surface dissolution facilitates dislocation slip. It is helpful to improve the formability of brittle metals.

Abnormal trapping of hydrogen in the elastic stress field of dislocations in body-centered cubic iron

It has been widely accepted that the tetrahedral interstitial site is the normal lattice trapping site for H atoms in the body-centered cubic iron. In this work, we found H trapped in a tetrahedral site is unstable in the dislocation elastic stress field. By contrast, the octahedral site is energetically preferred. This abnormal trapping phenomenon was rooted in the H-dislocation elastic interaction and zero-point quantum vibration of the H atom. At the abnormal trapping state, the interaction between H-edge dislocation and H-screw dislocation was identified to be at a similar level. As a result, the diffusivity of H around dislocation is enhanced by the abnormal trapping, and the local H content is much higher than the prediction with the assumption of normal trapping. Our results suggest that the dislocation motion can shuffle the trapping position of H atoms and assist the immature failure in the hydrogen environment.

Reduced strain gradient elasticity model with two characteristic lengths: fundamentals and application to straight dislocations

In this paper, the reduced strain gradient elasticity model with two characteristic lengths is proposed and presented. The reduced strain gradient elasticity model is a particular case of Mindlin’s first strain gradient elasticity theory with a reduced number of material parameters and is a generalization of the simplified first strain gradient elasticity model to include two different characteristic length scale parameters. The two characteristic lengths have the physical meaning of longitudinal and transverse length scales. The reduced strain gradient elasticity model is used to study screw and edge dislocations and to derive analytical solutions of the dislocation fields. The displacement, elastic distortion, plastic distortion and Cauchy stress fields of screw and edge dislocations are non-singular, finite and smooth. The dislocation fields of a screw dislocation depend on one characteristic length, whereas the dislocation fields of an edge dislocation depend on up to two characteristic lengths. For the numerical analysis of the dislocation fields, the material parameters including the characteristic lengths have been used, computed from a second nearest neighbor modified embedded-atom method (2NN MEAM) potential for aluminum.

Computational analysis of heterogeneous nucleation and precipitation in AA6005 Al-alloy during continuous cooling DSC experiments

A physically-based model for the computational evaluation of differential scanning calorimetry (DSC) curves during continuous cooling of Al alloys from solution annealing temperature is developed. The model is particularly suitable for predicting the nucleation and growth of quench induced precipitates at heterogeneous nucleation sites, such as grain boundaries, the stress field of dislocations or particles like primary phases or dispersoids. The thermokinetic model incorporates an extended formulation of the precipitate nucleation barrier and considers β-Mg2Si and B’-Al4Mg8Si7 phase precipitates. These are the dominating, experimentally observed quench induced phases in an aluminium AA6005 alloy within a wide range of cooling rates. The model is implemented in the thermokinetic software MatCalc, which simulates the precipitation processes and the evolution of excess specific heat capacities during the heat treatments. The Generalized Broken Bond model, incorporating the effects of interface curvature and diffuse interfaces, is used for interface energy prediction. Comparison of experiment and simulation demonstrates that the impact of heterogeneous nucleation sites must be adequately considered in the nucleation energy expression to obtain accurate predictions of the precipitate evolution, particularly for precipitation at low and very low undercooling as present during continuous cooling, particularly at slower cooling rates.

Dynamic torsional analysis of a functionally graded coated circular shafts weakened by multiple radial cracks

Analytical transient analysis of a functionally graded (FG) coated cylindrical bar weakened by multiple radial cracks under torsional transient loading is presented. The solution corresponding to a Volterra-type screw dislocation is achieved using the Fourier and Laplace transforms in the spatial and temporal domains, respectively. The obtained dislocation stress field is used to develop singular integral equations in terms of the unknown dislocation density function for the evaluation of multiple radial cracks. The resulting Cauchy integral equations are reduced to a set of algebraic equations and are solved numerically to determine the dislocation density functions. The achieved results are employed to evaluate the dynamic stress intensity factors (DSIFs) at the crack tips and the torsional rigidity of the FG coated circular cross-section bar with multiple embedded radial cracks. In addition, several numerical examples are presented to verify the results and to explore the effects of transient loading, FG coating layer, cracks position and interaction between them on the DSIFs and torsional rigidity of the FG coated cracked bars.

Exploring silicon [0 0 1] small angle symmetric tilt grain boundaries: Structures, energies and stress fields

A high efficient hybrid Monte Carlo and molecular dynamics (MC/MD) approach was carried out to reproduce silicon [001] small angle symmetric tilt grain boundaries at the atomic level. In the present paper, we concentrated on the variations of grain boundary properties under various misorientation angles, from which three critical misorientation angles were proposed and four grain boundary stages were divided to illustrate the structural transition of grain boundaries from small to large angle and the corresponding characteristics. The roles of dislocation stress fields in shaping some special grain boundary properties, such as dislocation structures and defect sink, were discussed. We also calculated three critical parameters (dislocation core radius, dislocation core energy and grain boundary width) about structures and energies of these studied grain boundaries, which would benefit the subsequent grain boundary engineering. Further investigations indicated that the three critical misorientation angles could be converted to the average distances of adjacent dislocations, which equalled to 6-, 2- and 1-times of dislocation core radius. Compared with the published literatures and classical theories, the simulations showed well accordance in structural units, stress fields and elastic strain energies.

Inversion of dislocation densities under mixed mode fracture

Mixed-mode crack growth is here investigated through experiments and computations for 34X and P2M steels, 7050 aluminium, and Ti-6Al-4V alloys in a compact tension shear (CTS) specimen. In this study, we use the mechanism-based strain gradient (MSG) plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on local stress distributions. The constitutive relations are based on Taylor’s dislocation model, which allows to gain insights into the role of the increased dislocation density associated with large gradients in plastic strain near cracks. The material model is implemented in a commercial finite element (FE) software package using a user subroutine, and the nonlinear stress intensity factors (SIFs) are evaluated as a function of the intrinsic material length. As a result of the FE calculations of dislocation density distributions, the effects of both the fracture mode and the stress–strain state are determined. Strain gradient effects associated with dislocation hardening mechanisms elevate crack tip stresses relative to conventional plasticity. Dislocation densities, stress fields and nonlinear SIF solutions are determined for experimental curvilinear crack paths by taking into account the transition from the initial Mode II crack to the mixed-mode fracture.