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At least 91 records · Page 5

Core energies of dislocations in bcc metals

Accurate methods and an efficient workflow for computing and documenting dislocation core energies are developed and applied to 1 2 ( 111 ) and ( 100 ) dislocations in five body-centered cubic (bcc) metals W, Ta, V, Mo, and α -Fe represented by 13 model interatomic potentials. For each dislocation type, dislocation core energies are extracted for a large number of dislocation characters thoroughly sampling the entire 2-space of crystallographic line orientations of the bcc lattice. Of particular interest, core energies of the 1 2 ( 111 ) { 110 } dislocations are found to be distinctly asymmetric with respect to the sign of the character angle, whereas core energies of ( 100 ) { 110 } junction dislocations exhibit marked cusps for line orientations vicinal to the closed-packed ( 111 ) directions. Overall, our findings furnish substantial insights for developing accurate models of dislocation core energies employed in mesoscale dislocation dynamics simulations of crystal plasticity.

36 MATERIALS SCIENCE↗

Dislocation transmission across Σ3{112} incoherent twin boundary: a combined atomistic and phase-field study

Grain boundaries (GBs) in polycrystalline materials act as impediments to dislocation motion and result in strengthening. Understanding slip transmission through GBs, specifically twin boundaries, is essential to understand the plastic deformation behavior of polycrystalline fcc materials. Here the interaction between a glide dislocation and Σ3{112} incoherent twin boundary (ITB) in copper is investigated using a combined atomistic and mesoscale approach. The material parameters and structure of the GB in the mesoscale phase field dislocation dynamics (PFDD) model are informed from Molecular Statics (MS) simulations. The structural unit of the ITB consists of an array of three partial dislocations. The interaction between a glide dislocation impinging on each of the GB partial dislocations is investigated using both PFDD and Molecular Dynamics (MD) with two boundary conditions. Transmission planes predicted by both PFDD and MD (NVT) are in agreement, and show that not all transmission events are direct. Critical transmission stresses predicted by PFDD are in the range of 276 MPa to 1380 MPa, while MD predictions are in the range from 100 MPa to 700 MPa. The PFDD and MD predictions of slip transmission are explained using dislocation theory based on isotropic linear elasticity.

36 MATERIALS SCIENCE↗

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.

36 MATERIALS SCIENCE↗

Asymmetric equilibrium core structures of pyramidal-II < c + a > dislocations in ten hexagonal-close-packed metals

The structures of pyramidal-II < c + a > dislocations, one of the most important defects in structural hexagonal-close-packed (HCP) metals, have not been fully characterized for many of the HCP metals in use today. Here, we employ ab initio informed phase-field dislocation dynamics to determine the minimum energy structure of pyramidal {1¯1¯22} < 11¯23 > dislocations in ten HCP metals, including Be, Co, Mg, Re, Ti, Zn, Cd, Hf, Y, and Zr. As input for the simulations, we calculate, using first-principles density functional theory, the {1¯1¯22} generalized stacking fault energy (GSFE) curves for all ten metals. From these calculations, it is found that magnetism in Co is necessary for achieving a local minimum in the GSFE curve. We observe in simulations that edge and screw character dislocations split into two partials separated by a low-energy intrinsic stacking fault. The splitting distance is shown to scale inversely with the local minimum energy normalized by the product of its shear modulus and Burgers vector. Interestingly, some HCP metals exhibit an asymmetric structure, with either unequal partial Burgers vectors or widths, in contrast to the symmetric configuration expected from linear elastic dislocation theory. We explain these structures by properties of the local maxima in their GSFE curves. Metals with larger degrees of elastic anisotropy result in dislocations with larger splitting distances than would be expected under the commonly used assumption of elastic isotropy. Furthermore, these findings on the sizes and asymmetry in the structures of pyramidal-II < c + a > dislocations are fundamental to understanding how these dislocations glide and interact or react with other defects when these metals are mechanically strained.

36 MATERIALS SCIENCE↗

Elastic interaction-induced anisotropic growth of dislocation loop arrays

The elastic interactions and reactions of dislocations lead to the formation of complex dislocation substructures, which is critical to the strain hardening and fatigue failure. Phase field dislocation dynamics simulations are conducted as a first step to understand the elastic interactions between dislocation loops. When the interloop spacing is small, the elastic interactions with neighboring loops become strong, rendering the edge segments strongly pinned, while allowing for the screw segments to propagate more easily. The interactions are found to result in an anisotropic stress distribution around the dislocation loops, leading to the formation of arrays of long, straight edge dislocations that could act as barriers to subsequent slip. Furthermore, the effect of initial loop size and applied strain rate on the elastic interaction-induced anisotropic pinning effect is investigated and discussed. Furthermore, the results are important for coarse-graining dislocation substructures formation into continuum level models of deformation in crystalline solids.

36 MATERIALS SCIENCE↗

Analytical integration of the tractions induced by non-singular dislocations on an arbitrary shaped triangular quadratic element

Here, an analytical model is proposed to evaluate the nodal force induced by a segment of dislocation upon an arbitrary shaped triangular element. This calculation is required in hybrid methods that associate dislocation dynamics to boundary or finite element to solve simultaneously the evolution of large ensembles of dislocations with complex boundary conditions. Nodal forces are defined as the triple integration of the unbalanced traction field induced by a straight dislocation upon the surface of the element. Following our previous approach (Queyreau et al 2014 Modelling Simul. Mater. Sci. Eng. 22 035004) on a simpler geometry and in the case of linear isotropic elasticity, triple integrals are solved by sequences of integration by parts that exhibit recurrence relations. The traction field is defined and finite everywhere even at the core of dislocations, thanks to the use of the non-singular stress expression formulated by Cai et al (2006 J. Mech. Phys. Solids 54 561–587). The nodal force expressions can be used when considering both a single convolution or double convolution of the Green's function with the core distribution. A solution is also proposed for the case of a semi-infinite segment through the study of the asymptotic behavior of the analytical expressions. The proposed approach is exact and very computationally efficient. The choice of an arbitrary shaped triangular element and quadratic shape functions allow the consideration of complex geometries and comply with automatic meshing procedures. These analytical expressions could also be employed to estimate dislocation interactions with interfaces.

42 ENGINEERING↗

Transitions in the morphology and critical stresses of gliding dislocations in multiprincipal element alloys

Refractory multiprincipal element alloys (MPEAs) are promising material candidates for high-temperature, high-strength applications. However, their deformation mechanisms, particularly at the dislocation scale, are unusual compared to those of conventional alloys, making it challenging to understand the origin of their high strength. Here, using an atomistically informed phase-field dislocation dynamics model, we study transitions in the morphology and critical stresses of long gliding screw dislocations over extended distances in a refractory MPEA. The model MPEA crystal accounts for the atomic-scale fluctuations in chemical composition across the glide planes via spatially correlated lattice energies and for the differences in glide resistances between screw and edge dislocations of unit length. Here, we show that the dislocation moves in a stop-start motion, alternating between wavy morphology in free flight and nearly recovered straight screw orientation in full arrest. The periods of wavy glide are due to variable kink-pair formation and migration rates along the length, where portions with higher rates glide more quickly. The critical stress to initiate motion corresponds to the stress required to form and migrate a kink pair at the weakest region along the length of the dislocation. Heterogeneity in lattice energy leads to variability in the local stress-strain response and to a strain hardening-like response, in which the critical stress to reactivate glide increases with glide distance. Statistical assessment of hundreds of realizations of dislocations indicates that the amount of hardening directly scales with the dispersion in underlying lattice energy.

3-dimensional systems↗

PyDislocDyn: A Python code for calculating dislocation drag and other crystal properties

PyDislocDyn is a suite of python programs designed to perform various calculations for dislocation dynamics in the continuum limit. In particular, one of its main purposes is to calculate dislocation drag from phonon wind. Additional features include the averaging of elastic constants for polycrystals, the calculation of the dislocation field including its limiting velocities, and the calculation of dislocation self-energy and line tension.

36 MATERIALS SCIENCE↗

The kinetics of static recovery by dislocation climb

Abstract The initial microstructure of a wide range of structural materials is conditioned by thermo-mechanical treatments such as hot-working, tempering, or solution annealing. At the elevated temperatures associated with these treatments the dislocation microstructure evolves, usually decreasing in density through a process known as static recovery. Despite its technological relevance, static recovery is not fully characterized from a theoretical standpoint, with even the controlling mechanisms subject to debate. In this study, a climb-enabled discrete dislocation dynamics (DDD) capability is leveraged to explore the kinetics of static recovery in pure Fe when controlled by dislocation climb. Quantitative data from these simulations is used to develop a revised static recovery law, and provides the parameters appropriate for predictive microstructure models in Fe. This law differs from previous analytical derivations invoking climb of dislocations, following the logarithmic trends typical of experimental observations where prior work did not. Direct comparison between the recovery law derived from DDD to experimental recovery data in alpha Fe shows strong agreement across a range of temperatures, and suggests that climb is the controlling mechanism for static recovery in pure metals.

36 MATERIALS SCIENCE↗

Simulation of dynamic crystal plasticity with a Lagrangian discontinuous Galerkin hydrodynamic method

Here we present a new Lagrangian modal discontinuous Galerkin (DG) hydrodynamic method that supports a dynamic dislocation based crystal plasticity model for simulating the mechanical behavior of crystallographic materials, both single crystal and polycrystalline, under dynamic conditions. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated by Taylor series polynomials of varying degree. These polynomials describe macro-scale hydrodynamic behavior while their evolution is determined by evaluating the dynamic crystal plasticity model at material points within the element. The dynamic crystal plasticity model is sensitive to the time increment size, with too large of time increments leading to instability in the model. To mitigate this, the temporal evolution of the dynamic crystal plasticity model is achieved with the combination of a sub-incrementing scheme with Heun’s third-order time integration scheme, which is also used to temporally evolve the governing equations. The implementation of the dynamic crystal plasticity model within the DG framework is tested using a 2D approximation of the Taylor impact test with a single crystal material, using quadratic elements that have faces that can bend. In addition to the standard continuous material modeling, we propose a new simulation method that would represent the heterogeneous behavior of polycrystalline microstructures within an element by varying the position and material properties of the material points within the element. This method is demonstrated using random orientation distributions on materials points that are arranged in both structured and random configurations.

42 ENGINEERING↗

Slip-free multiplication and complexity of dislocation networks in FCC metals

Abstract During plastic deformation of crystalline solids, intricate networks of dislocation lines form and evolve. To capture dislocation density evolution, prominent theories of crystal plasticity assume that 1) multiplication is driven by slip in active slip systems and 2) pair-wise slip system interactions dominate network evolution. In this work, we analyze a massive database of over 100 discrete dislocation dynamics simulations (with cross-slip suppressed), and our findings bring both of these assumptions into question. We demonstrate that dislocation multiplication is commonly observed on slip systems with no applied stress and no plastic strain rate, a phenomenon we refer to as slip-free multiplication. We show that while the formation of glissile junctions provides one mechanism for slip-free multiplication, additional mechanisms which account for the influence of coplanar interactions are needed to fully explain the observations. Unlike glissile junction formation which results from a binary reaction between a pair of slip systems, these new multiplication mechanisms require higher order reactions that lead to complex network configurations. While these complex configurations have not been given much attention previously, they account for about 50% of the line intersections in our database.

36 MATERIALS SCIENCE↗

Role of Chemical Disorder in High Temperature Dislocation Glide in Refractory Multi-principal Element Alloys

Refractory multi-principal element alloys (RMPEAs) combine a chemically disordered lattice with a structurally ordered, single‐phase body‐centered cubic (bcc) crystal structure. Chemical fluctuations in these alloys give rise to significant energy barriers that impede dislocation motion. In this study, we use phase field dislocation dynamics to examine how spatial temperature fluctuations compete with randomness in energy barriers to affect the motion of long screw dislocations in three equi-atomic MoNbTa‐based RMPEAs: MoNbTa, MoNbTaW, and MoNbTaVW. Over a wide range of homologous temperatures (T h ≈ 0–0.6), we determined a screw dislocation ‘flow stress’ as the minimum applied stress to sustain continuous motion over a long excursion distance within a fixed timeframe. All three RMPEAs exhibit temperature dependent flow stress with three characteristic glide regimes: at low homologous temperatures, flow stress drops sharply, and screw glide remains planar and rectilinear; at intermediate homologous temperatures, the flow stress levels off as glide becomes planar but wavy; and at high homologous temperatures, flow stress plateaus as screws exhibit nonplanar, three‐dimensional motion. Glide kinetics and transition temperatures are controlled by the chemically induced fluctuations in the energy landscape. The rectilinear to wavy transition temperature is controlled by statistically weakest local barriers in the glide plane, whereas the wavy to 3D transition temperature is governed by statistically strongest local barriers. At low and intermediate homologous temperatures, the relative spread in energy barriers governs glide behavior by controlling the local kinetics of kink pair formation and kink pinning. At high homologous temperatures, the average barrier height governs the glide behavior by controlling the number of out-of-plane excursions during 3D glide. These findings reveal how random chemical fluctuations determine screw‐driven plasticity in RMPEAs, providing critical insight for the design of high temperature structural alloys.

Defects↗

3D interface size effects on slip transfer in Ti/Nb nanolaminates

Two-phase nanolaminates are well-renowned for achieving extraordinarily high strengths but at the sacrifice of reduced toughness and strain to failure. Recently ”thick” interfaces, or so called 3D interfaces, in Cu/Nb nanolaminates were experimentally shown to improve both of these mechanical properties. Here, in this work, we study the effect of 3D interfaces in the hexagonal close packed (HCP)/body centered cubic (BCC) Ti/Nb nanolaminate system. Nanoindentation hardness testing suggests increased strength with the introduction of a 3D Ti–Nb interface and a positive size effect with increases in 3D interface thickness from 5 nm to 20 nm. To understand this effect from a single dislocation perspective, we present a phase-field dislocation dynamics (PFDD) model for multi-phase HCP/BCC systems. We employ the model to simulate stress-driven transfer of single dislocations across 3D Ti/Nb interfaces of various thicknesses. Our results show that the critical stress for slip transfer increases with the thickness of the interface. This positive size effect is stronger for transfer from basal or prismatic dislocations in the Ti layer to 110$\langle$111$\rangle$ dislocations in the Nb layer than the reverse. For this Ti/Nb system, a critical thickness of 2 nm is identified at which the asymmetry in slip transfer is minimized. This work showcases 3D interfaces as a beneficial microstructure modification to strengthen as well as reduce anisotropy in nanocrystalline materials containing HCP phases.

Dislocations↗

The Scattering of Phonons by Infinitely Long Quantum Dislocations Segments and the Generation of Thermal Transport Anisotropy in a Solid Threaded by Many Parallel Dislocations

A canonical quantization procedure is applied to the interaction of elastic waves—phonons—with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach–Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are pointed out. We compute the cross-section for phonons incident on the dislocation lines for an arbitrary angle of incidence. The consequences for thermal transport are explored, and we compare our results, involving a dynamic dislocation, with those of Klemens and Carruthers, involving a static dislocation. In our case, the relaxation time is inversely proportional to frequency, rather than directly proportional to frequency. As a consequence, the thermal transport anisotropy generated on a material by the presence of a highly-oriented array of dislocations is considerably more sensitive to the frequency of each propagating mode, and, therefore, to the temperature of the material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Low-temperature failure mechanism of [001] niobium micropillars under uniaxial tension

The plasticity of body-centered cubic (bcc) metals is dependent of temperature as well as sample dimension at the micrometer scale, but the effects of cryogenic temperature on the plasticity and the related failure process in micron-sized bcc metals have not been studied under uniaxial tension. In this work, we utilized in situ cryogenic micro-tensile tests, transmission electron microscopy, and dislocation dynamic simulations to examine the plasticity and failure processes of [001]-oriented bcc niobium micropillars. Our study reveals that a strong suppression of cross-slip at low temperatures prevents dislocation multiplication and leads to a dislocation starvation state, at which no mobile dislocation exists due to the rapid annihilation of dislocations at free surfaces. New dislocations are then nucleated until stress concentration at a slip step creates a micro-crack, the propagation of which leads to catastrophic failure. As a result, this unique failure process results from the combined effects of sample dimension and temperature.

36 MATERIALS SCIENCE↗

Stress effects on the energy barrier and mechanisms of cross-slip in FCC nickel

The energy barrier for homogeneous cross-slip of a screw dislocation in face-centered cubic (FCC) nickel is calculated using atomistic simulations as a function of the Escaig stress on the glide plane, the Escaig stress on the cross-slip plane, and the Schmid stress on the cross-slip plane. Two cross-slip mechanisms, Friedel-Escaig (FE) and Fleischer, are examined and their energy barriers are calculated for a large number of stress combinations. For each mechanism, the energy barrier as a function of three stress components can be reduced into a one-dimensional function of an effective stress. The stress domains in which FE and Fleischer mechanisms operate respectively are determined. Additionally, the FE mechanism dominates when the Escaig stress on the glide plane (in the direction that reduces the stacking fault width) is the largest stress component. Increasing the Schmid stress and Escaig stress (in the direction that expands the stacking fault width) on the cross slip plane promotes the Fleischer mechanism. The cross slip energy barrier functions obtained here can be used as input functions for computing cross slip rates in mesoscale dislocation dynamics simulations.

36 MATERIALS SCIENCE↗

Serrated Flow in Alloy Systems

This chapter presents the problem of the complexity of plastic flow in alloys, which is manifested by serrated deformation curves and transient plastic strain localizations. This phenomenon, which uncovers an inherently collective nature of the dynamics of crystal defects, is well known for conventional alloys. Surprisingly, despite the particular microstructure of HEAs, which strongly impacts the microscopic dynamics of defects, not only the HEAs are prone to the macroscopically jerky flow, but the serration patterns display many similar features, thus bearing evidence to similar laws for the collective dynamics. To provide a comprehensive approach to this problem, the chapter is subdivided into two parts. The first part presents the state-of-the art of this research under the angle of distinct regimes of collective dislocation dynamics found in conventional alloys, e.g., self-organized criticality, deterministic chaos, or synchronization. The second part summarizes recent investigations into serrated flows in HEAs, uncovering common and specific types of behaviors. Both parts conclude with the formulation of diverse open questions concerning these strongly coupled fields of research.

Lebyodkin, Mikhail↗

Phase-field dislocation modeling of cross-slip

The phase-field dislocation dynamics (PFDD) model is extended to simulate cross-slip in body-centered cubic materials. The model makes use of a non-orthogonal, body-centered cubic numerical grid such that all calculable points lie on dislocation glide planes. We demonstrate that the advanced PFDD model predicts a low-energy, non-planar core for screw dislocations and a planar core for edge dislocations. These core differences result in screw-edge character dependence in the critical stress to initiate glide and dislocation drag coefficients. Finally, we show that this model can be used to study the propensity of screw dislocations to cross-slip around or transmit through a coherent, crystallographic obstacle, depending on obstacle strength.

36 MATERIALS SCIENCE↗