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 simulate the evolution of large dislocation ensembles in reaction to an external load and to assess the collective behaviour of dislocations.
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.
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…
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…
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）
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…
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…
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…
We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach-Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc i…
In this work, the so-called Eshelbian or configurational mechanics of quasicrystals is presented. Quasicrystals are considered as a prototype of novel materials. Material balance laws for quasicrystalline materials with dislocations are derived in the framework of generalized incompatible elasticity theory of quasicrystals. Translations, scaling transformations as well as rotations are examined; the latter presents particular interest due to the quasicrystalline structure. This derivation provides important quantities of the Eshelbian mechanics, as the Eshelby stress tensor, the scaling flux v…
Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its ra…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i) to represent dislocation kinematics in terms of a reasonable number of variables and (ii) to derive averaged descriptions of the dislocation dynamics (i.e. material laws) in terms of these variables. The kinematic problem (i) was recently solved through the introduction of continuum dislocation dynamics (CDD), which provides kinematically consistent evolutio…
The Discrete Dislocation (DD) analysis and its computional modeling have been advanced significantly over the past decade. This progress has been further magnified by the idea to couple DD with continuum mechanics analysis in association with computational algorithms such as finite elements. This coupling may pave the way to better understanding of the local response of materials at the micro scale and globally at the macroscale, increasing the potential for future applications in material, mechanical, structural and process engineering analyses.
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…
The influence of coherent interface on dissipations of mechanical energy of driven dislocations near to a point of martensite type phase transition is considered. The expressions for dynamic braking of dislocations, owing to losses of energy on excitation of deformations-type phase transition are received.
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase transformation, grain boundary, and plasticity-related phenomena at the level of individual line defects and domain walls. The continuously distributed defect approach is developed as a generalization of the discrete, isolated defect case. Constitutive guidance for equilibrium response and dissipative driving forces respecting frame-indifference and non-negative mechani…
The mechanisms of dislocation/precipitate interaction were studied by means of discrete dislocation dynamics within a multiscale approach. Simulations were carried out using the discrete continuous method in combination with a fast Fourier transform solver to compute the mechanical fields. The original simulation strategy was modified to include straight dislocation segments by means of the field dislocation mechanics method and was applied to simulate the interaction of an edge dislocation with a $θ'$ precipitate in an Al-Cu alloy. It was found that the elastic mismatch has a negligible influ…
From their birth in the manufacturing process, materials inherently contain defects that affect the mechanical behavior across multiple length and time-scales, including vacancies, dislocations, voids and cracks. Understanding, modeling, and real-time simulation of the underlying stochastic micro-structure defect evolution is therefore vital towards multi-scale coupling and propagating numerous sources of uncertainty from atomistic to eventually aging continuum mechanics. We develop a graph-based surrogate model of dislocation glide for computation of dislocation mobility. We model an edge dis…
The continuum dislocation dynamics framework for mesoscale plasticity is intended to capture the dislocation density evolution and the deformation of crystals when subjected to mechanical loading. It does so by solving a set of transport equations for dislocations concurrently with crystal mechanics equations, with the latter being cast in the form of an eigenstrain problem. Incorporating dislocation reactions in the dislocation transport equations is essential for making such continuum dislocation dynamics predictive. A formulation is proposed to incorporate dislocation reactions in the trans…
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 b…
A consistent, small scale description of plastic motion in a crystalline solid is presented based on a phase field description. By allowing for independent mass motion given by the phase field, and lattice distortion, the solid can remain in mechanical equilibrium on the timescale of plastic motion. Singular (incompatible) strains are determined by the phase field, to which smooth distortions are added to satisfy mechanical equilibrium. A numerical implementation of the model is presented, and used to study a benchmark problem: the motion of an edge dislocation dipole in a hexagonal lattice. T…
The mechanical behavior in compression of [111] LiF micropillars with diameters in the range 0.5 $μ$m to 2.0 $μ$m was analyzed by means of discrete dislocation dynamics at ambient and elevated temperature. The dislocation velocity was obtained from the Peach-Koehler force acting on the dislocation segments from a thermally-activated model that accounted for the influence of temperature on the lattice resistance. A size effect of the type "smaller is stronger" was predicted by the simulations, which was in quantitative agreement with previous experimental results by the authors \cite{SWC14}. Th…
High entropy alloys are a class of materials with many significant improvements in terms of mechanical properties as compared to ``classical'' alloys. The corresponding structure-property relations are not yet entirely clear, but it is commonly believed that the good mechanical performance is strongly related to dislocation interactions with the complex energy landscape formed due to alloying. Although in-situ Transmission Electron Microscopy (TEM) allows high-resolution studies of the structure and dynamics of moving dislocations and makes the local obstacle/energy ``landscape'' directly visi…
We derive a simple analytical line integral expression for the relaxation volume tensor of an arbitrary interconnected dislocation network. This quantity determines the magnitude of dislocation contribution to the dimensional changes and volumetric swelling of a material, and highlights the fundamental dual role of dislocations as sources of internal strain as well as carriers of plastic deformation. To illustrate applications of the method, we compute the relaxation volume of a stacking fault tetrahedron, a defect commonly occurring in fcc metals; the volume of an unusual tetrahedral configur…
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…
In this work, molecular dynamics (MD) simulations were used to investigate elementary dislocation properties in a Co-free high entropy (HEA) model alloy ($Cr_{15}Fe_{46}Mn_{17}Ni_{22}$ at. %) in comparison with a model alloy representative of Austenitic Stainless Steel (ASS) ($Cr_{20}Fe_{70}Ni_{10}$ at. %). Recently developed embedded-atom method (EAM) potentials were used to describe the atomic interactions in the alloys. Molecular Statics (MS) calculations were used to study the dislocation properties in terms of local stacking fault energy (SFE), dissociation distance while MD was used to i…
A clear understanding of the dynamic behavior of metals is critical for developing superior structural materials as well as for improving material processing techniques such as cold spray and shot peening. Using a high velocity (from 120 m/s to 700 m/s; strain rates >10^7 1/s) micro-projectile impact testing and quasistatic (strain rates: 10^-2 1/s) nanoindentation, we investigate the strain-rate-dependent mechanical behavior of single-crystal aluminum substrates with (001), (011), and (111) crystal orientations. For all three crystal orientations, the dynamic hardness initially increases with…
A new formulation of the Phase Field Crystal model is presented that is consistent with the necessary microscopic independence between the phase field, reflecting the broken symmetry of the phase, and both mass density and elastic distortion. Although these quantities are related in equilibrium through a macroscopic equation of state, they are independent variables in the free energy, and can be independently varied in evaluating the dissipation functional that leads to the model governing equations. The equations obtained describe dislocation motion in an elastically stressed solid, and serve…
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…
Recently, mechanical tests on ice as well as dislocation dynamics simulations have revealed that plastic flow displays a scale-free intermittent dynamics characterized by dislocation avalanches with a power law distribution of amplitudes. To further explore the complexity of dislocation dynamics during plastic flow, we present a statistical analysis of dislocation avalanche correlations and avalanche triggering. It is shown that the rate of avalanche triggering immediately after any avalanche is larger than the background activity due to uncorrelated events. This self-induced triggering increa…
We address the question of the observed pinning of 1/2 <110] ordinary screw dislocations in gamma-TiAl which leads to the characteristic trailing of dipoles in the microstructure. While it has been proposed that these may be variously intrinsic or extrinsic in nature, we are able to rule out the former mechanism. We do this by means of very large scale, three dimensional atomistic simulations using the quantum mechanical bond order potential. We find that the kink-pair formation energy is large: 6eV, while the single kink migration energy is conversely very small: 0.13eV. Using these, and othe…
The interaction of screw dislocations with an applied stress is studied using atomistic simulations in conjunction with a continuum treatment of the role played by the far field boundary condition. A finite cell of atoms is used to consider the response of dislocations to an applied stress and this introduces an additional force on the dislocation due to the presence of the boundary. Continuum mechanics is used to calculate the boundary force which is subsequently accounted for in the equilibrium condition for the dislocation. Using this formulation, the lattice resistance curve and the associ…
We report results of large-scale molecular-dynamics (MD) simulations of dynamic deformation under biaxial tensile strain of pre-strained single-crystalline nanometer-scale-thick face-centered cubic (fcc) copper films. Our results show that stacking faults, which are abundantly present in fcc metals, may play a significant role in the dissociation, cross-slip, and eventual annihilation of dislocations in small-volume structures of fcc metals. The underlying mechanisms are mediated by interactions within and between extended dislocations that lead to annihilation of Shockley partial dislocations…
The mechanisms of dislocation/precipitate interactions were analyzed in an Al-Cu alloy containing a homogeneous dispersion of $θ'$ precipitates by means of discrete dislocation dynamics simulations. The simulations were carried out within the framework of the discrete-continuous method and the precipitates were assumed to be impenetrable by dislocations. The main parameters that determine the dislocation/precipitate interactions (elastic mismatch, stress-free transformation strains, dislocation mobility and cross-slip rate) were obtained from atomistic simulations, while the size, shape, spati…
The stress-driven motion of dislocations in crystalline solids, and thus the ensuing plastic deformation process, is greatly influenced by the presence or absence of various point-like defects such as precipitates or solute atoms. These defects act as obstacles for dislocation motion and hence affect the mechanical properties of the material. Here we combine molecular dynamics studies with three-dimensional discrete dislocation dynamics simulations in order to model the interaction between different kinds of precipitates and a $\frac{1}{2}\langle 1 1 1\rangle$ $\{1 1 0\}$ edge dislocation in B…
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…
This paper discusses the free energy of complex dislocation microstructures, which is a fundamental property of continuum plasticity. In the past, multiple models of the self energy of dislocations have been proposed in the literature that partially contradict each other. In order to gain insight into the relationship between dislocation microstructures and the free energy associated with them, instead of deriving a model based on theoretical or phenomenological arguments, here, these quantities are directly measured using large scale molecular dynamics simulations. Plasticity is induced using…
We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model captures better than previous formulations the dynamics of complex interfaces and dislocations in single crystals as well as grain boundary migration in poly-crystals where the long-range elastic field is properly relaxed. The proposed model features a diffusivity that depends non-linearly on the local phase. It induces more localized interfaces between a disorder…
In small-scale metallic systems, collective dislocation activity has been correlated with size effects in strength and with a step-like plastic response under uniaxial compression and tension. Yielding and plastic flow in these samples is often accompanied by the emergence of multiple dislocation avalanches. Dislocations might be active pre-yield, but their activity typically cannot be discerned because of the inherent instrumental noise in detecting equipment. We apply Alternate Current (AC) load perturbations via Dynamic Mechanical Analysis (DMA) during quasi-static uniaxial compression expe…
Phase field dislocation dynamics formulation coupled with Fourier based micromechanics solver and its application to grain boundary-dislocation interactions
We present a methodology for the investigation of dislocation energetics in segregated alloys based on Monte Carlo simulations which equilibrate the topology and composition of the dislocation core and its surroundings. An environment-dependent partitioning of the system total energy into atomic contributions allows us to link the atomistic picture to continuum elasticity theory. The method is applied to extract core energies and radii of 60 degrees glide dislocations in segregated SiGe alloys which are inaccessible by other methods.
This paper presents PANIC, a 3D discrete mesoscale dislocation dynamics model which includes a fully quantitative treatment of both dislocation climb and dislocation glide, including climb driven by both osmotic and mechanical stresses and climb enabled by both bulk and pipe diffusion, including full elastic anisotropy for materials with hexagonal symmetry. Efficient calculations can be performed for epitaxial thin films, multilayers and device structures with free surfaces, including those with irregular geometries (e.g. islands). The model also includes the capability to simulate dislocation…
Computational analysis of short-range interactions between an edge dislocation and an array of equally-spaced identical shearable or non-shearable precipitates
Dislocation pileups directly impact the material properties of crystalline solids through the arrangement and collective motion of interacting dislocations. We study the statistical mechanics of these ordered defect structures embedded in two dimensional crystals, where the dislocations themselves form one-dimensional lattices. In particular, pileups exemplify a new class of inhomogeneous crystals characterized by spatially varying lattice spacings. By analytically formulating key statistical quantities and comparing our theory to numerical experiments using an intriguing mapping of dislocatio…
We develop a mesoscopic dislocation dynamics model for vacancy-assisted dislocation climb by upscalings from a stochastic model on the atomistic scale. Our models incorporate microscopic mechanisms of (i) bulk diffusion of vacancies, (ii) vacancy exchange dynamics between bulk and dislocation core, (iii) vacancy pipe diffusion along the dislocation core, and (iv) vacancy attachment-detachment kinetics at jogs leading to the motion of jogs. Our mesoscopic model consists of the vacancy bulk diffusion equation and a dislocation climb velocity formula. The effects of pipe diffusion and the jog str…
It has been shown in experiments that self-climb of prismatic dislocation loops by pipe diffusion plays important roles in their dynamical behaviors, e.g., coarsening of prismatic loops upon annealing, as well as the physical and mechanical properties of materials with irradiation. In this paper, we show that this dislocation dynamics self-climb formulation that we derived in Ref. [1] is able to quantitatively describe the properties of self-climb of prismatic loops that were observed in experiments and atomistic simulations. This dislocation dynamics formulation applies to self-climb by pipe …
