We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented. The model is a minimal enhancement of classical crystal/$J_2$ plasticity that fundamentally accounts for polar/excess dislocations at the mesoscale. It has the ability to compute the static and dynamic finite deformation stress fields of arbitrary (evolving) dislocation distributions in finite bodies of arbitrary shape and elastic anisotropy under general boundary conditions. This capability is used to present a comparison of the static stress fields, at finite and small deformations, for screw and edge dislocations, revealing heretofore unexpected differences. The computational framework is verified against the sharply contrasting predictions of geometrically linear and nonlinear theories for the stress field of a spatially homogeneous dislocation distribution in the body, as well as against other exact results of the theory. Verification tests of the time-dependent numerics are also presented. Size effects in crystal and isotropic versions of the theory are shown to be a natural consequence of the model and are validated against available experimental data. With inertial effects incorporated, the development of an (asymmetric) propagating Mach cone is demonstrated in the finite deformation theory when a dislocation moves at speeds greater than the linear elastic shear wave speed of the material.
Stressed dislocation pattern formation in crystal plasticity at finite deformation is demonstrated for the first time. Size effects are also demonstrated within the same mathematical model. The model involves two extra material parameters beyond the requirements of standard classical crystal plasticity theory. The dislocation microstructures shown are decoupled from deformation microstructures, and emerge without any consideration of latent hardening or constitutive assumptions related to cross-slip. Crystal orientation effects on the pattern formation and mechanical response are also demonstr…
In the present study, molecular dynamics (MD) simulations have been performed to understand the effect of nanowire size, temperature and strain rate on the variations in dislocation density and deformation mechanisms in $<$100$>$ Cu nanowires. The nanowire size has been varied in the range 1.446-43.38 nm with a constant length of 21.69 nm. Different temperatures varying from 10 K to 700 K and strain rates in the range of $5 \times 10^7$ - $1 \times 10^9$ s$^{-1}$ have been considered. For all the conditions, the variations in dislocation density $(ρ)$ has been calculated as a function of strai…
Recent experiments by Kiritani et al. have revealed a surprisingly high rate of vacancy production during high-speed deformation of thin foils of fcc metals. Virtually no dislocations are seen after the deformation. This is interpreted as evidence for a dislocation-free deformation mechanism at very high strain rates. We have used molecular-dynamics simulations to investigate high-speed deformation of copper crystals. Even though no pre-existing dislocation sources are present in the initial system, dislocations are quickly nucleated and a very high dislocation density is reached during the de…
Recently, a dislocation free deformation mechanism was proposed by Kiritani et al., based on a series of experiments where thin foils of fcc metals were deformed at very high strain rates. In the experimental study, they observed a large density of stacking fault tetrahedra, but very low dislocation densities in the foils after deformation. This was interpreted as evidence for a new dislocation-free deformation mechanism, resulting in a very high vacancy production rate. In this paper we investigate this proposition using large-scale computer simulations of bulk and thin films of copper. To fa…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their fitting parameters. In this paper, we employ discrete dislocation dynamics to establish a continuum-based model for the evolution of the dislocation structure in polycrystalline thin films. Expressions are developed for the density of activated dislocation sources, as well as dislocation nucleation and annihilation rates. We demonstrate how size effect naturally…
In this paper, we present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in [1,2], that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. To this end, an analytical method to convert a discrete dislocation network to its continuous dislocation density tensor representation is first developed. From there, the mechanical fields are evaluated using a FDM-based spectral framework, while submesh resolution elastic interactions are accounted for via the introduction of a rigorous stress splitting proced…
Variational approach to determine the properties of dislocations at finite deformation
Institute for Solid State Physics and Optics, HUN-REN Wigner Research Centre for Physics（匈牙利科学院维格纳研究物理中心固体物理与光学研究所）；Department of Materials Physics, Eötvös Loránd University（厄特沃什·罗兰大学材料物理系）
Unlike the tensile mode, compressive deformation of a bcc metallic nanostructure is mediated by the glide of screw dislocation. Although the bcc screw dislocations are well known to possess unusual attributes, it is still unclear how these unique effects manifest in a nanoscale solid. In the present study, atomistic simulations render a close look at the dislocation activities underlying the compressive deformation of bcc iron nanopillars. It is found that instead of performing simple glide motion, the line defects exhibit a host of complex features. In this regard, the temperature is observed…
The present paper extends the thermodynamic dislocation theory developed by Langer, Bouchbinder, and Lookmann to non-uniform plastic deformations. The free energy density as well as the positive definite dissipation function are proposed. The governing equations are derived from the variational equation. As illustration, the problem of plane strain constrained shear of single crystal deforming in single slip is solved within the proposed theory.
The present paper extends the thermodynamic dislocation theory initiated by Langer, Bouchbinder and Lookman [2010] to non-uniform finite plastic deformations. The equations of motion are derived from the variational equation involving the free energy density and the positive definite dissipation function. We also consider the simplified theory by neglecting the excess dislocations. For illustration, the problem of finite strain constrained shear of single crystals with one active slip system is solved within the proposed theory.
Molecular dynamics (MD) is employed to investigate the plastic deformation mechanisms of single crystalline yttria-stabilized tetragonal zirconia (YSTZ) nanopillars under uniaxial compression. Simulation results show that the nanoscale plastic deformation of YSTZ is strongly dependent on the crystallographic orientation of zirconia nanopillars. For the first time, the experimental explored tetragonal to monoclinic phase transformation is reproduced by MD simulations in some particular loading directions. Three distinct mechanisms of dislocation, phase transformation, and a combination of dislo…
We employed a real-space formulation of orbital-free density functional theory using finite-element basis to study the defect-core and energetics of an edge dislocation in Aluminum. Our study shows that the core-size of a perfect edge dislocation is around ten times the magnitude of the Burgers vector. This finding is contrary to the widely accepted notion that continuum descriptions of dislocation energetics are accurate beyond 1-3 Burgers vector from the dislocation line. Consistent with prior electronic-structure studies, we find that the perfect edge dislocation dissociates into two Shockl…
We propose an explanation of anomalies observed in the behavior of deformation hardening of Invars. An extremely strong volume magnetostriction, typical of Invars, results in an enhancement of the exchange contribution to the energy of the dislocation system by about three orders of magnitude with respect to its value in conventional ferromagnetics. Both the self energy of individual dislocations and the interaction between them, determined usually only by the elastic deformation, in Invars is strongly diminished by the contribution of the exchange energy. This fact explains a strong suppressi…
A Phenomenological Mesoscopic Field Dislocation Mechanics (PMFDM) model is developed, extending continuum plasticity theory for studying initial-boundary value problems of small-scale plasticity. PMFDM results from an elementary space-time averaging of the equations of Field Dislocation Mechanics (FDM), followed by a closure assumption from any strain-gradient plasticity model that attempts to model effects of geometrically-necessary dislocations (GND) only in work-hardening.
We present a theory of deformation potential carrier scattering of two-dimensional electron gases from the strain fields surrounding dislocations. The results are applied to study the transport characteristics in III-V nitride two-dimensional electron gases in Al(Ga)N/GaN quantum wells. A hypothetical charged core has been associated as the {\em only} scattering potential for analyzing experimental results for transport studies of the nitrides; we critically examine this assumption in light of our results of strain field scattering. By computing the effect of all possible scattering mechanisms…
Predicting the behaviour of complex systems is one of the main goals of science. An important example is plastic deformation of micron-scale crystals, a process mediated by collective dynamics of dislocations, manifested as broadly distributed strain bursts and significant sample-to-sample variations in the response to applied loading. Here, by combining large-scale discrete dislocation dynamics simulations and machine learning, we study the problem of predicting the fluctuating stress-strain curves of individual small single crystals subject to strain-controlled loading using features of the …
The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the averaging procedure. This energy density is extrapolated to the cases of extremely small or large dislocation densities. By incorporating the configurational temperature and the density of redundant dislocations, we develop the thermodynamic dislocation theory for non-uniform plastic deformations and use it to predict the stress-strain curves and the disloc…
The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. Analytical methods and sophisticated `dislocation-dynamics' simulations have proved very effective in the study of dislocation patterning, and have led to macroscopic constitutive laws of plastic deformation. Yet, a statistical analysis of the dynamics of an assembly of interacting dislocations has not hitherto been performed. Here we report acoustic emission measurements on stressed ice single crystals, the results of which indicate that disloc…
We conduct dislocation dynamics (DD) simulations of Fe periodic single crystals under tensile load at several high strain rates and temperatures. The simulations are enabled by the recent development of temperature-dependent dislocation mobility relations obtained from atomistic calculations. The plastic evolution in the simulations is governed by rapid initial dislocation multiplication, followed by a saturation of the flow stress when the subpopulation of slow plastic carriers becomes stabilized by dislocation annihilation. Above 500 K, edge dislocations coexist with screw dislocations and c…
The nature of mechanically induced dislocations in SrTiO3 at low temperatures has been a disputed matter for a long time. Here we provide a systematic overview of the existing knowledge on dislocations in stoichiometric SrTiO3 complemented by computational models of several of the proposed dislocation types. Based on atomistic simulations we reveal their structure and mobility and put our focus on the splitting into partial dislocations, because this mechanism is held responsible for the good dislocation mobility in strontium titanate. Our results reveal that dislocations with a {1-10} glide p…
Molecular dynamics simulations are performed to investigate the role of a coherent Σ3 (111) twin boundary on the plastic deformation behavior of Cu nanopillars. Our work reveals that the mechanical response of pillars with and without the twin boundary is decisively driven by the characteristics of initial dislocation sources. In the condition of comparably large pillar size and abundant initial mobile dislocations, overall yield and flow stresses are controlled by the longest, available mobile dislocation. An inverse correlation of the yield and flow stresses with the length of the longest di…
The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of high-temperature deformation of aluminum and steel. Using physics-based parameters that we expect theoretically to be independent of strain rate and temperature, we are able to fit experimental stress-strain curves for three different strain rates and three different temperatures for each of these two materials. Our theoretical curves include yielding transitions at zero strain in agreement with experiment. We find that thermal softening effects are important even at the lowest temperat…
Alloying metals with other elements is often done to improve the material strength or hardness. A key microscopic mechanism is precipitation hardening, where precipitates impede dislocation motion, but the role of such obstacles in determining the nature of collective dislocation dynamics remains to be understood. Here, three-dimensional discrete dislocation dynamics simulations of FCC single crystals are performed with fully coherent spherical precipitates from zero precipitate density upto $ρ_p = 10^{21}\,\text{m}^{-3}$ and at various dislocation-precipitate interaction strengths. When the d…
Plastic deformation In crystalline materials is controlled by the motion and interactions of dislocations [AND 17]. Discrete Dislocation Dynamics (DDD) simulations have now existed for about 25 years to investigate plastic flow at the mesoscale, which lies at a critical position between two very different scales. At small scale, atomistic simulations are particularly adapted to investigate the core structure or mobility of individual dislocations, while continuous approaches can simulate the complete and continuous mechanical behaviour at the scale of the components. the purpose of DDD is to s…
Deformation twinning, which occurs in fcc metals only under particular conditions of intrinsic material properties, microstructure, and loading conditions, occupies an indispensable place in their deformation mechanism maps. Nonetheless, dedicated studies have seldom been carried out to explore the fundamental properties of twinning dislocations mediating this process. Here we employ a combination of atomistic computations and continuum modeling to investigate the nucleation of twinning dislocation loops in metals with fcc crystal structure. Besides the conventional layer-by-layer model of twi…
The importance of accurate simulation of the plastic deformation of ductile metals to the design of structures and components is well-known. Many techniques exist that address the length scales relevant to deformation pro- cesses, including dislocation dynamics (DD), which models the interaction and evolution of discrete dislocation line segments, and crystal plasticity (CP), which incorporates the crystalline nature and restricted motion of dis- locations into a higher scale continuous field framework. While these two methods are conceptually related, there have been only nominal efforts focu…
As a guide to constitutive specification, driving forces for dislocation velocity and nucleation rates are derived for a field theory of dislocation mechanics. A condition of closure for the theory in the form of a boundary condition for dislocation density is also derived. Kinematical features of dislocation evolution like initiation of bowing of a pinned screw segment, and initiation of cross-slip of a screw segment are discussed. An exact solution for the expansion of a polygonal loop as well as representation within the theory of dislocation level Schmid and non-Schmid behavior, and unload…
Owing to their non-planar cores 1/2<111> screw dislocations govern the plastic deformation of BCC metals. Atomistic studies of the glide of these dislocations at 0 K have been performed using Bond Order Potentials for molybdenum and tungsten that account for the mixed metallic and covalent bonding in transition metals. When applying pure shear stress in the slip direction it displays significant twinning-antitwinning asymmetry for molybdenum but not for tungsten. However, for tensile/compressive loading the Schmid law breaks down in both metals, principally due to the effect of shear stresses …
We present a framework which unifies classical phenomenological $J_2$ and crystal plasticity theories with quantitative dislocation mechanics. The theory allows the computation of stress fields of arbitrary dislocation distributions and, coupled with minimally modified classical ($J_2$ and crystal plasticity) models for the plastic strain rate of statistical dislocations, results in a versatile model of finite deformation mesoscale plasticity. We demonstrate some capabilities of the framework by solving two outstanding challenge problems in mesoscale plasticity: 1) recover the experimentally o…
Molecular dynamics simulations revealed significant difference in deformation behaviour of $<$100$>$ BCC Fe nanowires with and without twist boundary. The plastic deformation in perfect $<$100$>$ BCC Fe nanowire was dominated by twinning and reorientation to $<$110$>$ followed by further deformation by slip mode. On the contrary, $<$100$>$ BCC Fe nanowire with a twist boundary deformed by slip at low plastic strains followed by twinning at high strains and absence of full reorientation. The results suggest that the deformation in $<$100$>$ BCC Fe nanowire by dislocation slip is preferred over …
Despite decades of extensive research on mechanical properties of diamond, much remains to be understood in term of plastic deformation mechanisms due to the poor deformability at room temperature. In a recent work in Advanced Materials, it was claimed that room-temperature plasticity occurred in <001>-oriented single-crystal diamond nanopillars based on observation of unrecovered deformation inside scanning electron microscope. The plastic deformation was suggested to be mediated by a phase transition from sp3 carbon to an O8-carbon phase by molecular dynamics simulations. By comparison, our …
Using large-scale atomistic simulations, dislocation mechanics in the presence of linear complexions are investigated in an Fe-Ni alloy, where the complexions appear as nanoparticle arrays along edge dislocation lines. When mechanical shear stress is applied to drive dislocation motion, a strong pinning effect is observed where the defects are restricted by their own linear complexion structures. This pinning effect becomes weaker after the first dislocation break-away event, leading to a stress-strain curve with a profound initial yield point, similar to the static strain ageing behavior obse…
Deformation twinning is a form of permanent deformation that is commonly observed in low symmetry crystals such as hexagonal close-packed (hcp) metals. With recent increased interest in using hcp metals, such as magnesium, in structural, automotive, and armor applications due to their high strength to weight ratio, there is a need for a comprehensive understanding of deformation twinning and its interaction with dislocation slip. A great deal has been learned at the microscopic level where individual dislocations interact with twin boundaries through atomistic simulations, and at the macroscop…
Revealing Dislocation Interactions Controlling Mechanical Properties of Metals
Technical University of Denmark（丹麦技术大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；European Synchrotron Radiation Facility（欧洲同步辐射装置）；Univ. Grenoble Alps CEA IRIG MEM NRX（格勒诺布尔阿尔卑斯大学法国原子能和替代能源委员会IRIG MEM NRX）
Coarse-grained, metallic materials undergo microstructure refinement during tribological loading. This in turn results in changing tribological properties, so understanding deformation under tribological load is mandatory when designing tribological systems. Single-trace experiments were conducted to understand the initiation of deformation mechanisms acting in various tribological systems. The main scope of this work was to investigate the influence of normal and friction forces as well as crystal orientations on the dominating deformation mechanism in a face-centred cubic concentrated solid …
A physically-informed continuum crystal plasticity model is presented to elucidate the deformation mechanisms and dislocation evolution in body-centered-cubic (bcc) tantalum widely used as a key structural material for mechanical and thermal extremes. We show our unified structural modeling framework informed by mesoscopic dislocation dynamics simulations is capable of capturing salient features of the large inelastic behavior of tantalum at quasi-static (10$^{-3}$ s$^{-1}$) to extreme strain rates (5000 s$^{-1}$) and at room temperature and higher (873K) at both single- and polycrystal levels…
In this work, using the framework of (three-dimensional) Eshelbian dislocation mechanics, we derive the $J$-, $M$-, and $L$-integrals of a single (edge and screw) dislocation in isotropic elasticity as a limit of the $J$-, $M$-, and $L$-integrals between two straight dislocations as they have recently been derived by Agiasofitou and Lazar [Int. J. Eng. Sci. 114 (2017) 16-40]. Special attention is focused on the $M$-integral. The $M$-integral of a single dislocation in anisotropic elasticity is also derived. The obtained results reveal the physical interpretation of the $M$-integral (per unit l…
Multi-principal element alloys (MPEAs), commonly termed as medium- or high-entropy alloys containing three or more components in high concentrations, render a tunable chemical short-range order (SRO). Leveraging large-scale atomistic simulations, we probe the limit of Hall-Petch strengthening and deformation mechanisms in a model CrCoNi alloy and unravel chemical short-range ordering effects. It is found that, in the presence of SRO, the maximum strength is appreciably increased, and the strongest grain size drifts to a small value. Additionally, the propensity for faulting and deformation tra…
The sequence of deformation bursts during plastic deformation exhibits scale-free features. In addition to the burst or avalanche sizes and the rate of avalanches the process is characterized by correlations in the series which become manifest in the resulting shape of the stress-strain curve. We analyze such features of plastic deformation with 2D and 3D simulations of discrete dislocation dynamics models and we show, that only with severe plastic deformation the ensuing memory effects become negligible. The role of past deformation history and dislocation pinning by disorder are studied. In …
In Part I of this set of two papers, a model of mesoscopic plasticity is developed for studying initial-boundary value problems of small scale plasticity. Here we make qualitative, finite element method-based computational predictions of the theory. We demonstrate size effects and the development of strong inhomogeneity in simple shearing of plastically-constrained grains. Nonlocality in elastic straining leading to a strong Bauschinger effect is analyzed. Stability of the time dependent, spatially homogeneous, simple shearing solution of PMFDM is studied. Results from thermal cycling of small…
Implications of an analysis of the shear transformation of a zone of an oblate spheroid for dislocation theory, grain boundary sliding and superplasticity
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Anna University（安娜大学）
The dynamics of dislocation assemblies in deforming crystals indicate the emergence of collective phenomena, intermittent fluctuations and strain avalanches. In polycrystalline materials, the understanding of plastic deformation mechanisms depends on grasping the role of grain boundaries on dislocation motion. Here the interaction of dislocations and elastic, low angle grain boundaries is studied in the framework of a discrete dislocation representation. We allow grain boundaries to deform under the effect of dislocation stress fields and compare the effect of such a perturbation to the case o…
Based on the atomistic studies presented in Part I we develop analytical yield criteria for single crystals that capture the effect of shear stresses other than the Schmid stress (non-glide stresses) on the shear stress needed for dislocation glide (Peierls stress). These yield criteria characterize a non-associated plastic flow that originates owing to the complex response of 1/2<111> screw dislocations to an applied stress tensor. Employing these criteria we identify the operative slip systems for tensile/compressive loading along various axes within the standard stereographic triangle and d…
Crystal dislocations govern the plastic mechanical properties of materials but also affect the electrical and optical properties. However, a fundamental and quantitative quantum-mechanical theory of dislocation remains undiscovered for decades. Here we present an exactly solvable quantum field theory of dislocation, for both edge and screw dislocations in an isotropic medium by introducing a new quasiparticle "dislon". With this approach, the electron-dislocation relaxation time is studied from electron self-energy which can be reduced to classical results. Moreover, a fundamentally new type o…
The ability of a body-centered cubic metal to deform plastically is limited by the thermally activated glide motion of screw dislocations, which are line defects with a mobility exhibiting complex dependence on temperature, stress, and dislocation segment length. We derive an analytical expression for the velocity of dislocation glide, based on a statistical mechanics argument, and identify an apparent phase transition marked by a critical temperature above which the activation energy for glide effectively halves, changing from the formation energy of a double kink to that of a single kink. Th…
Compression experiments on micron-scale specimens and acoustic emission (AE) measurements on bulk samples revealed that the dislocation motion resembles a stick-slip process - a series of unpredictable local strain bursts with a scale-free size distribution. Here we present a unique experimental set-up, which detects weak AE waves of dislocation slip during the compression of Zn micropillars. Profound correlation is observed between the energies of deformation events and the emitted AE signals that, as we conclude, are induced by the collective dissipative motion of dislocations. The AE data a…
Plastic deformation of metals involves the complex evolution of dislocations forming strongly connected dislocation networks. These dislocation networks are based on dislocation reactions, which can form junctions during the interactions of different slip systems. Extracting the fundamentals of the network behaviour during plastic deformation by adequate physically based theories is essential for crystal plasticity models. In this work, we demonstrate how knowledge from discrete dislocation dynamics simulations to continuum-based formulations can be transferred by applying a physically based d…
The dynamical evolution of dislocations in plastically deformed metals is controlled by both deterministic factors arising out of applied loads and stochastic effects appearing due to fluctuations of internal stress. Such type of stochastic dislocation processes and the associated spatially inhomogeneous modes lead to randomness in the observed deformation structure. Previous studies have analyzed the role of randomness in such textural evolution but none of these models have considered the impact of a finite decay time (all previous models assumed instantaneous relaxation which is "unphysical…
