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Characterizing interface dislocations by atomically informed Frank-Bilby theory
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A dislocation dynamics model of the plastic flow of fcc polycrystals: dislocation intersection processes
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Atomistic Modeling of Dislocation Slip in Alpha-Iron towards the Development of a Multi-Scale Model of Dislocation Plasticity.
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Atomistically informed dislocation dynamics simulations on dislocation-interface interactions
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Quantitative microdiffraction from deformed crystals with unpaired dislocations and dislocation walls
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Atomistic Modeling of Dislocation Slip in Alpha-Iron towards the Development of a Multi-Scale Model of Dislocation Plasticity.
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Discrete dislocation dynamics-based prediction of dislocation density from diffraction line profiles of Ta
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Dislocation Patterning in Deforming Crystals: Theory, Computational Predictions and Validation (Final Technical Report)
This project was awarded for an initial period of three years, followed by a no-cost extension for one year and a funded one-year renewal. During the first four years, the project focused on investigating the role of dislocation reactions and dislocation correlation in dislocation patterning in FCC metals. During the fifth year, the scope of research was expanded to investigate the effects of composition inhomogeneity on the mesoscale plastic response of Body-Centered Cubic (BCC) alloys. In addition to its impact on metal hardening during deformation, dislocation patterning provides the microstructure information required to understand phenomena like fracture and recrystallization in metals. The Continuum Dislocation Dynamics (CDD) framework was the methodology used during the first four years, followed by the use of Discrete Dislocation Dynamics (DDD) during the fifth year. CDD is a density-based formalism of dislocation dynamics in which the plastic deformation of crystals is predicted together with the mesoscale dislocation patterns by tracking the space-time evolution of dislocations as driven by the applied stress, short-range and long-range interactions of dislocations, and cross slip. CDD is a crystal mechanics approach in which the plastic constitutive part is replaced with the equations of dislocation dynamics, which is driven by the internal stress via a mobility laws, while the evolution of the density gives the eigenstrain required to update the internal stress itself. The governing equations are thus those of crystal mechanics cast as an eigenstrain problem and those of dislocation transport and reactions. Our investigations during the first four years were driven by the hypothesis that that dislocation patterning is triggered by spatiotemporal dislocation density and internal stress fluctuations, and that such fluctuations influence the collective dislocation dynamic through their effects on the short-range reaction rates and the collective dislocation mobility. This hypothesis was tested by modeling the influence of the dislocation reactions and dislocation correlations on collective dislocation dynamics. The main research components during the first four years were: 1) Reformulation of the CDD framework to integrate the dislocation correlations and dislocation reactions. 2) Simulation of the dislocation correlations and quantifying their contribution to the long-range stress of complex dislocation systems. 3) Computational implementation of the updated CDD model for FCC single crystals and development of an efficient CDD code. 4) Investigation of dislocation patterning in FCC crystals based on the updated CDD model. Some key findings from these investigations were: 1) The patterning of dislocations is initiated by cross slip and internal stress fluctuations, and the refinement of the pattern results from junction formation. 2) Patterning is more prominent under high stress. 3) The correlation stress was found to be a significant part of the mean field stress in continuum representations of dislocation dynamics. During the last year of the project, we have established a method for performing dislocation dynamics in inhomogeneous alloys and demonstrated the impact of composition inhomogeneity on the characteristics of initial yielding and dislocation character in BCC alloys. We also tested this method using an irradiated ferritic alloy in which the composition and dislocation loops effects are both present. In doing so, we have considered two aspects of the role of inhomogeneity, the creation of internal coherency stress due to the dependence of the lattice parameter on the local composition, and the dependence of the dislocation mobility on the local composition. These two aspects resulted in an unexpected behavior of the dislocation system, and, in turn, the yielding behavior of BCC alloys. Key findings include: 1) The composition inhomogeneity in BCC alloys alters the well-known role of screw dislocations by forcing a level of waviness on the average dislocation character, thus destroying the screw character dominance in the yielding observed in pure or homogeneous BCC metals. 2) In the case of irradiated alloys, while composition inhomogeneity by itself and dislocation loops by themselves result in some hardening, the superposition of the two mechanisms does not result in the sum of the two contributions via any known rule. The latter result contradicts the classical works related hardening via multiple mechanisms, which state that various hardening mechanisms can be added linearly or using some Pythagorean additive rule. We were able to rationalize this unexpected result by a closer loop at the origin of the hardening mechanisms themselves, which both involved long-range elastic interactions with dislocations. We reached the conclusion that the hardening resulting from the total stress associated with these two mechanisms (current work) differs from the sum of the effects of the individual stress fields (classical literature). We have also found a major flaw in the classical theory of spinodal hardening. The latter theory never considered the impact of composition undulation on the solute hardening. We have built a new general theory accounting for the effect of solute friction together with the composition undulations on the dislocation configuration at Critical Resolved Shear Stress (CRSS), which is yielding a new definition of the spinodal hardening and new different results. This work is the first to recognize the lack of the role of solute in spinodal hardening theory of alloys.
Atomic-scale investigation of point defects and hydrogen-solute atmospheres on the edge dislocation mobility in alpha iron
In this study, we present atomistic mechanisms of 1/2 [111](11{sup ¯}0) edge dislocation interactions with point defects (hydrogen and vacancies) and hydrogen solute atmospheres in body centered cubic (bcc) iron. In metals such as iron, increases in hydrogen concentration can increase dislocation mobility and/or cleavage-type decohesion. Here, we first investigate the dislocation mobility in the presence of various point defects, i.e., change in the frictional stress as the edge dislocation interacts with (a) vacancy, (b) substitutional hydrogen, (c) one substitutional and one interstitial hydrogen, (d) interstitial hydrogen, (e) vacancy and interstitial hydrogen, and (f) two interstitial hydrogen. Second, we examine the role of a hydrogen-solute atmosphere on the rate of local dislocation velocity. The edge dislocation simulation with a vacancy in the compression side of the dislocation and an interstitial hydrogen atom at the tension side exhibit the strongest mechanical response, suggesting a higher potential barrier and hence, the higher frictional stress (i.e., ∼83% higher than the pure iron Peierls stress). In the case of a dislocation interacting with a vacancy on the compressive side, the vacancy binds with the edge dislocation, resulting in an increase in the friction stress of about 28% when compared with the Peierls stress of an edge dislocation in pure iron. Furthermore, as the applied strain increases, the vacancy migrates through a dislocation transportation mechanism by attaining a velocity of the same order as the dislocation velocity. For the case of the edge dislocation interacting with interstitial hydrogen on the tension side, the hydrogen atom jumps through one layer perpendicular to the glide plane during the pinning-unpinning process. Finally, our simulation of dislocation interactions with hydrogen show first an increase in the local dislocation velocity followed by a pinning of the dislocation core in the atmosphere, resulting in resistance to dislocation motion as the dislocation moves though the hydrogen-solute atmospheres. With this systematic, atomistic study of the edge dislocation with various point defects, we show significant increase in obstacle strengths in addition to an increase in the local dislocation velocity during interaction with solute atmospheres. The results have implications for constitutive development and modeling of the hydrogen effect on dislocation mobility and deformation in metals.
Dislocation evolution in 316 L stainless steel during multiaxial ratchetting deformation
Dislocation patterns and their evolutions in 316 L stainless steel during the multiaxial ratchetting deformation were observed by transmission electron microscopy (TEM). The microscopic observations indicate that the dislocation evolution presented during the multiaxial ratchetting with four kinds of multiaxial loading paths is similar to that in the uniaxial case [G. Z. Kang et al., Mater Sci Eng A 527 (2010) 5952]. That is, dislocation networks and dislocation tangles are formed quickly by the multiple-slip and cross-slip of dislocation activated by applied multiaxial stress; and then polarized patterns such as dislocation walls and elongated incipient dislocation cells are formed at the last stage of multiaxial ratchetting. The dislocation patterns evolve more quickly from the modes at low dislocation density to the ones at high density during the multiaxial ratchetting than that in the uniaxial case, and some traces of multiple-slip are observed in the multiaxial ones. The dislocation evolution during the multiaxial ratchetting deformation is summarized by comparing the observed dislocation patterns with those presented in the multiaxial strain-controlled and symmetrical stress-controlled cyclic tests. The multiaxial ratchetting of 316 L stainless steel can be microscopically and qualitatively explained by the observed evolution of dislocation patterns. - Highlights: Black-Right-Pointing-Pointer Dislocation patterns change from lines and nets to tangles, walls and cells. Black-Right-Pointing-Pointer Dislocation patterns evolve quicker in the multiaxial case. Black-Right-Pointing-Pointer Aligned dislocation arrays and some traces of multiple slips are observed. Black-Right-Pointing-Pointer Heterogeneous dislocation patterns result in the multiaxial ratchetting.
An interplay between a hydrogen atmosphere and dislocation characteristics in BCC Fe from time-averaged molecular dynamics
The interplay between hydrogen and dislocations (e.g., core and elastic energies, and dislocation–dislocation interactions) has implications on hydrogen embrittlement but is poorly understood. Continuum models of hydrogen enhanced local plasticity have not considered the effect of hydrogen on dislocation core energies. Energy minimization atomistic simulations can only resolve dislocation core energies in hydrogen-free systems because hydrogen motion is omitted so hydrogen atmosphere formation can’t occur. Additionally, previous studies focused more on face-centered-cubic than body-centered-cubic metals. Discrete dislocation dynamics studies of hydrogen–dislocation interactions assume isotropic elasticity, but the validity of this assumption isn’t understood. Here, we perform time-averaged molecular dynamics simulations to study the effect of hydrogen on dislocation energies in body-centered-cubic iron for several dislocation character angles. We see atmosphere formation and highly converged dislocation energies. We find that hydrogen reduces dislocation core energies but can increase or decrease elastic energies of isolated dislocations and dislocation–dislocation interaction energies depending on character angle. We also find that isotropic elasticity can be well fitted to dislocation energies obtained from simulations if the isotropic elastic constants are not constrained to their anisotropic counterparts. These results are relevant to ongoing efforts in understanding hydrogen embrittlement and provide a foundation for future work in this field.
Solute effects upon dislocation motion and recovery in Mg alloys (Final Report)
The objective the research was to develop a firmer understanding of the interactions between substitutional solute atoms and dislocations within Mg alloys. These interactions govern the absolute and relative mobilities of various types of dislocations in Mg (e.g., basal < a>, non-basal < a>, and pyramidal < c+a>). Furthermore, they have an impact on dislocation recovery processes (e.g., cross-glide, climb, rearrangement, and annihilation). Ultimately, solute-dislocation interactions strongly impact a) strain hardening, b) strain rate sensitivity, c) plastic anisotropy of textured polycrystals, d) texture evolution, e) dislocation substructures evolution, and even f) recrystallization behavior. It is broadly known that Mg alloys exhibit poor low temperature formability. Since formability is largely governed by properties (a) – (c) in this list, it is critical to develop a better understanding of solute-dislocation interactions, if one hopes to improve the situation. While the theory of static solute strengthening is well developed, especially for alloys with face centered cubic (FCC) crystal structures, there are outstanding questions related to applications to hexagonal close packed (HCP) crystal structures and dynamic strain aging (DSA) in materials of various structures. DSA has far-reaching implications for metal formability and, in the case of Mg alloys, appears to correlate with the so-called rare-earth (RE) texture which has been shown to benefit formability. The Portevin-Le Chatelier (PLC) effect, and associated negative strain rate sensitivity, occur at higher temperatures (>100℃) in Mg alloys as compared with similar Al alloys, even though they have similar melting points and solute diffusivities. Our preliminary research has shown that modern, physics-based models of DSA can be tuned to describe the behavior of Mg alloys if a rather higher activation enthalpy is assumed for cross-core diffusivity. While this partially explains the delay in DSA to higher temperatures, it is also hypothesized that this delay is due in part to the intrinsically more thermally activated (rate sensitive) nature of non-basal < a> dislocation motion which is required for macroscopic flow of Mg alloys, whereas octahedral slip in many FCC metals like aluminum is essentially athermal at room temperature. It was originally proposed to employ a combination of in-situ diffraction-based experimental characterization to validate existing theory. It was envisioned to perform in-situ transmission electron microscopy (TEM) to assess individual dislocation behavior and in-situ high-energy X-ray diffraction (HEXRD) techniques which were showing great promise for elucidating collective dislocation behavior, 2 including recovery, especially if the contributions to various forms of diffraction peak broadening (𝜂𝜂,𝜔𝜔,and 2𝜃𝜃) can be effectively integrated. Finally, it was envisioned to perform discrete dislocation dynamics (DDD) modeling approaches to aide in the interpretation of both TEM and HEXRD experiments. In the end, mechanical tests were performed on more complex Mg alloys which exhibited evidence of dynamic strain aging, and this led to the establishment of another project. Mechanical test data obtained at McMaster University served as the basis of an assessment of the applicability of Bazinski’s “stress equivalence” theory of solute strengthening to polycrystalline alloys of Mg. Although we did not succeed in applying the approach to Mg alloys, we did develop expertise with the HEXRD approach using a BCC, β-Ti alloy and demonstrated numerous new capabilities that may be applied to any polycrystalline material in collaboration with researchers at CHESS and around the world: (1) assessment of details of the elastoplastic transition (yielding) using a combination of HEXRD and full-field polycrystal plasticity modeling, (2) the first-ever experimental observation of strong stress rotation within the individual grains of a polycrystalline material, and (3) a comprehensive analysis of the grain-level dislocation density evolution based upon diffraction peak broadening along 𝜂𝜂,𝜔𝜔,and 2𝜃𝜃 directions. This final aspect allowed us to confirm that dislocations were gliding on multiple plane types and not restricted to {110} type planes, and it also provided clues as to why some grains were unloading during straining, with surprising implications for our understanding of the effects of geometrically necessary dislocations (GNDs). Finally, graduate student, Mohammed Shabana, developed a MATLAB code which confirmed the conclusions of Prof. Catalin Picu (Rensallear Polytechnic Institute, RPI) regarding the effect of solute-trapped, forest dislocations on the breaking stress of Lomer lock junctions in FCC metal alloys. He applied the same anisotropic line-tension model to a variety of dislocation junction configurations and found an inconsistency in the widely cited results of Dupuy and Fivel regarding the Hirth Lock, and he outlined an approach to extend these finding to HCP Mg alloys that we are still pursuing with discretionary fundings at UVA.
Tailoring Superconductivity with Quantum Dislocations
Despite the established knowledge that crystal dislocations can affect a material’s superconducting properties, the exact mechanism of the electron-dislocation interaction in a dislocated superconductor has long been missing. Being a type of defect, dislocations are expected to decrease a material’s superconducting transition temperature (T c ) by breaking the coherence. Yet experimentally, even in isotropic type I superconductors, dislocations can either decrease, increase, or have little influence on T c . These experimental findings have yet to be understood. Although the anisotropic pairing in dirty superconductors has explained impurity-induced T c reduction, no quantitative agreement has been reached in the case a dislocation given its complexity. By generalizing the one-dimensional quantized dislocation field to three dimensions, we reveal that there are indeed two distinct types of electron-dislocation interactions. Besides the usual electron-dislocation potential scattering, there is another interaction driving an effective attraction between electrons that is caused by dislons, which are quantized modes of a dislocation. The role of dislocations to superconductivity is thus clarified as the competition between the classical and quantum effects, showing excellent agreement with existing experimental data. In particular, the existence of both classical and quantum effects provides a plausible explanation for the illusive origin of dislocation-induced superconductivity in semiconducting PbS/PbTe superlattice nanostructures. A quantitative criterion has been derived, in which a dislocated superconductor with low elastic moduli and small electron effective mass and in a confined environment is inclined to enhance T c . This provides a new pathway for engineering a material’s superconducting properties by using dislocations as an additional degree of freedom.
< c+a > dislocations in {101 - 2} twins in Mg: A kinematic and energetic requirement
Consideration of published TEM and molecular dynamics studies of interactions between matrix dislocations and {101¯2} twin boundaries (TB) in hexagonal close packed metals inspires a hypothesis regarding the formation of dislocations with < c+a > Burgers vectors inside the twins. It was previously reported that when basal < a > dislocations from the matrix are swept by an advancing TB, they are converted into partial dislocations bounding basal I 1 stacking faults (SFs) within the twin. In the present work, we show that this dislocation configuration near TB renders it energetically favorable for a pair of partial dislocations to constrict into a dislocation within the twin. New in situ TEM observations confirm this hypothesis by revealing long < c+a > dislocation dipoles terminated by the TB at one end and by I1 SFs within the twin at the other end. Finally, the resulting near-screw < c+a > dislocation dipoles are observed to be glissile, enabling self-annihilation in some circumstances. Thus, rather than requiring a high energy dislocation pile-up to press two < a > dislocations through a TB into a single < c+a > dislocation, it is demonstrated that < c+a > dislocations naturally form, within {101¯2} twins in Mg, as TB migrates into a matrix, which inevitably contains dislocations with < a > Burgers vectors. Furthermore, these observations help to explain how the twins themselves may subsequently deform and why they may be particularly vulnerable to plastic, shear localization.
Resonant interaction between phonons and PbTe/PbSe (001) misfit dislocation networks
Here this work aims at a quantitative and mechanistic understanding of the dynamic process of the phonon-dislocation interaction in PbTe/PbSe (001) heterostructures using the Concurrent Atomistic-Continuum (CAC) method as the simulation tool. The misfit dislocation network and the atomic-scale dislocation core structure obtained in the simulations are found to agree reasonably well with the experimental observations of the PbTe/PbSe (001) interface. Through visualizing the dynamic interaction between phonons and dislocations, as well as quantifying the dislocation vibration amplitude, the phonon energy transmission, and the thermal resistance of the misfit interfaces, this work has illustrated and quantified two mechanisms for phonon-dislocation interaction: (1) phonon scattering by the strain field of dislocations, and (2) phonon scattering by dislocations that vibrate via the local modes of a dislocation network; the latter, leads to resonant phonon-dislocation interaction, which is manifested as local maxima of out-of-phase vibration of the atoms on the two sides of the slip plane, leading to local minima of the energy transmission in the heterostructure that contains one interface. The local vibrational modes are found to be excited only by shear stress induced by transverse phonons. Among various resonant modes, the one with the lowest frequency has the strongest effect. This work has also demonstrated the collective motion of dislocations under ultrafast phonon pulses. In addition, the dynamic properties of the misfit dislocation network localized within one interface are found to be significantly altered by the presence of misfit dislocations at other interfaces, thus further confirming the cooperative dynamic nature of the motion of dislocations and phonons.
Dislocation confinement in the growth of Na flux GaN on metalorganic chemical vapor deposition-GaN
We have demonstrated a GaN growth technique in the Na flux method to confine c-, (a+c)-, and a-type dislocations around the interface between a Na flux GaN crystal and a GaN layer grown by metalorganic chemical vapor deposition (MOCVD) on a (0001) sapphire substrate. Transmission electron microscopy (TEM) clearly revealed detailed interface structures and dislocation behaviors that reduced the density of vertically aligned dislocations threading to the Na flux GaN surface. Submicron-scale voids were formed at the interface above the dislocations with a c component in MOCVD-GaN, while no such voids were formed above the a-type dislocations. The penetration of the dislocations with a c component into Na flux GaN was, in most cases, effectively blocked by the presence of the voids. Although some dislocations with a c component in the MOCVD-GaN penetrated into the Na flux GaN, their propagation direction changed laterally through the voids. On the other hand, the a-type dislocations propagated laterally and collectively near the interface, when these dislocations in the MOCVD-GaN penetrated into the Na flux GaN. These results indicated that the dislocation propagation behavior was highly sensitive to the type of dislocation, but all types of dislocations were confined to within several micrometers region of the Na flux GaN from the interface. The cause of void formation, the role of voids in controlling the dislocation behavior, and the mechanism of lateral and collective dislocation propagation are discussed on the basis of TEM results.
Geometries of edge and mixed dislocations in bcc Fe from first principles calculations
We use density functional theory (DFT) to compute the core structures of $a_0[100](010)$ edge, $a_0[100](011)$ edge, $a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$ edge, and $a_0/2[111](1\bar{1}0)$ $71^{\circ}$ mixed dislocations in body-centered cubic (bcc) Fe. The calculations are performed using flexible boundary conditions (FBC), which effectively allow the dislocations to relax as isolated defects by coupling the DFT core to an infinite harmonic lattice through the lattice Green function (LGF). We use the LGFs of the dislocated geometries in contrast to most previous FBC-based dislocation calculations that use the LGF of the bulk crystal. The dislocation LGFs account for changes in the topology of the crystal in the core as well as local strain throughout the crystal lattice. A simple bulk-like approximation for the force constants in a dislocated geometry leads to dislocation LGFs that optimize the core structures of the $a_0[100](010)$ edge, $a_0[100](011)$ edge, and $a_0/2[111](1\bar{1}0)$ $71^{\circ}$ mixed dislocations. This approximation fails for the $a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$ dislocation however, so in this case we derive the LGF from more accurate force constants computed using a Gaussian approximation potential. The standard deviations of the dislocation Nye tensor distributions quantify the widths of the dislocation cores. The relaxed cores are compact, and the local magnetic moments on the Fe atoms closely follow the volumetric strain distributions in the cores. We also compute the core structures of these dislocations using eight different classical interatomic potentials, and quantify symmetry differences between the cores using the Fourier coefficients of their Nye tensor distributions. Most of the core structures computed using the classical potentials agree well with the DFT results. Furthermore the DFT core geometries provide benchmarking for classical potential studies of work-hardening, as well as substitutional and interstitial sites for computing solute-dislocation interactions that serve as inputs for mesoscale models of solute strengthening and solute diffusion near dislocations.