The dislocation core is an important region as it controls many important properties of materials. Elasticity breaks down in the core and the stress, force, and energy diverge at the dislocation line. We consider three commonest methods employed in Discrete Dislocation Dynamics (DDD) simulations to eliminate these singularities: (1) considering a cutoff parameter, (2) spreading the Burgers vector (CAWB theory), and (3) using gradient elasticity. Each of these methods includes an extra length parameter to regularize the elastic fields. In this article, we show that these regularization parameters can significantly influence the results of the DDD simulations. We use atomistic simulations for mixed dislocations to find the radius and energy of the dislocation core and find the regularization parameter and its variations with the dislocation character angle in each of the three methods. We have also considered if an arbitrary constant is chosen for the regularization parameter how the core energy should be added to the simulation codes. We have concluded that while the core energy in classical elasticity with a cutoff parameter can be described by one parameter, the other two methods need two energy parameters (core energy of edge and core energy of screw) for describing the variation of the core energy with the character angle. We have shown that no regularization parameter can be selected for the CAWB theory or gradient elasticity if no core energy is included.
Atomistic simulations were carried out to analyze the interaction between $< a>$ basal dislocations and precipitates in Mg-Al alloys and the associated strengthening mechanisms.
The classical modeling of dislocation climb based on a continuous description of vacancy diffusion is compared to recent atomistic simulations of dislocation climb in body-centered cubic iron under vacancy supersaturation [Phys. Rev. Lett. 105 095501 (2010)]. A quantitative agreement is obtained, showing the ability of the classical approach to describe dislocation climb. The analytical model is then used to extrapolate dislocation climb velocities to lower dislocation densities, in the range corresponding to experiments. This allows testing of the validity of the pure climb creep model propos…
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…
The interaction between edge basal dislocations and $β$-Mg$_{17}$Al$_{12}$ precipitates was studied using atomistic simulations. A strategy was developed to insert a lozenge-shaped Mg$_{17}$Al$_{12}$ precipitate with Burgers orientation relationship within the Mg matrix in an atomistic model ensuring that the matrix/precipitate interfaces were close to minimum energy configurations. It was found that the dislocation bypassed the precipitate by the formation of an Orowan loop, that entered the precipitate. Within the precipitate, the dislocation was not able to progress further until more dislo…
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…
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 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…
We present a combined study by Scanning Tunneling Microscopy and atomistic simulations of the emission of dissociated dislocation loops by nanoindentation on a (001) fcc surface. The latter consist of two stacking-fault ribbons bounded by Shockley partials and a stair-rod dislocation. These dissociated loops, which intersect the surface, are shown to originate from loops of interstitial character emitted along the <110> directions and are usually located at hundreds of angstroms away from the indentation point. Simulations reproduce the nucleation and glide of these dislocation loops.
The interaction between edge dislocations and Guinier-Preston zones in an Al-Cu alloy was analyzed by means of atomistic simulations. The different thermodynamic functions that determine the features of these obstacles for the dislocation glide were computed using molecular statics, molecular dynamics and the nudged elastic band method. It was found that Guinier-Preston zones are sheared by dislocations and the rate at which dislocations overcome the precipitate is controlled by the activation energy, $ΔU$, in agreement with the postulates of the harmonic transition state theory. Moreover, the…
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…
It is well known that grain boundaries (GBs) have a strong influence on mechanical properties of polycrystalline materials. Not as well-known is how different GBs interact with dislocations to influence dislocation movement. This work presents a molecular dynamics study of 33 different FCC Ni bicrystals, each subjected to four different strain states to induce incident dislocation-GB interactions for 132 unique configurations. The resulting simulations are analyzed to determine properties of the interaction that affect the likelihood of transmission of the dislocation through the GB in an effo…
The interaction between Mg edge basal dislocations and rod-shaped $β_1'$-MgZn$_2$ precipitates was studied by atomistic simulations using a new interatomic potential. The atomistic model was carefully built taking into account the experimental information about the orientation relationship between the matrix and the precipitate to ensure minimum energy interfaces. It was found that the dislocations initially overcame the precipitate by the formation of an Orowan loop that penetrated in the precipitate. The precipitate was finally sheared after several Orowan loops were piled-up. The number of …
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 …
Atomistic computations of the Peierls stress in fcc metals are relatively scarce. By way of contrast, there are many more atomistic computations for bcc metals, as well as mixed discrete-continuum computations of the Peierls-Nabarro type for fcc metals. One of the reasons for this is the low Peierls stresses in fcc metals. Because atomistic computations of the Peierls stress take place in finite simulation cells, image forces caused by boundaries must either be relaxed or corrected for if system size independent results are to be obtained. One of the approaches that has been developed for trea…
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…
Thermally-activated $\small{\nicefrac{1}{2}}<111>$ screw dislocation motion is the controlling plastic mechanism at low temperatures in body-centered cubic (bcc) crystals. Motion proceeds by the nucleation and propagation of atomic-sized kink pairs susceptible of being studied using molecular dynamics (MD). However, MD's natural inability to properly sample thermally-activated processes as well as to capture $\{110\}$ screw dislocation glide calls for the development of other methods capable of overcoming these limitations. Here we develop a kinetic Monte Carlo (kMC) approach to study single s…
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…
Although titanium nitride (TiN) is among the most extensively studied and thoroughly characterized thin-film ceramic materials, detailed knowledge of relevant dislocation core structures is lacking. By high-resolution scanning transmission electron microscopy (STEM) of epitaxial single crystal (001)-oriented TiN films, we identify different dislocation types and their core structures. These include, besides the expected primary full a/2{110}<1$\bar{1}$0> dislocation, Shockley partial dislocations a/6{111}<11$\bar{2}$> and sessile Lomer edge dislocations a/2{100}<011>. Density-functional theory…
Neutron irradiation progressively changes the properties of zirconium alloys: they harden and their average c/a lattice parameter ratio decreases with fluence. The bombardment by neutrons produces point defects, which evolve into dislocation loops that contribute to a non-uniform growth phenomenon called irradiation-induced growth (IIG). To gain insights into these dislocation loops in Zr we studied them using atomistic simulation. We constructed and relaxed dislocation loops of various types. We find that the energies of <a>-loops on different habit planes are similar, but our results indicat…
The mechanical properties of Mg-Al alloys are greatly influenced by the complex intermetallic phase Mg$_{17}$Al$_{12}$, which is the most dominant precipitate found in this alloy system. The interaction of basal edge and 30$^\text{o}$ dislocations with Mg$_{17}$Al$_{12}$ precipitates is studied by molecular dynamics and statics simulations, varying the inter-precipitate spacing ($L$), and size ($D$), shape and orientation of the precipitates. The critical resolved shear stress $τ_c$ to pass an array of precipitates follows the usual $\ln((1/D + 1/L)^{-1})$ proportionality. In all cases but the…
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 cross-slip process of a screw $<$a$>$ dislocation from the basal to the prismatic plane in magnesium was studied using the density functional theory and the molecular dynamics calculations. An atomistic method for calculating the total Peierls energy map has been devised to track the transition path of a dissociated and/or constricted screw $<$a$>$ dislocation in the cross-slip process. The barrier of a screw $<$a$>$ dislocation from the basal to the prismatic plane is estimated by the density functional theory for the first time to be $61.4\pm 2.0$ meV per Burgers vector length. The activ…
Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results that demonstrate the ability of phase field crystal (PFC) models to describe complex defect evolution phenomena on atomistic length scales and over long, diffusive time scales. Primary emphasis is given to the unification of conservative and non- conservative dislocation creation mechanisms in three-dimensional FCC and BCC materials. These include Frank-Read-ty…
Dislocation velocities and mobilities are studied by Molecular Dynamics simulations for edge and screw dislocations in pure aluminum and nickel, and edge dislocations in Al-2.5%Mg and Al-5.0%Mg random substitutional alloys using EAM potentials. In the pure materials, the velocities of all dislocations are close to linear with the ratio of (applied stress)/(temperature) at low velocities, consistent with phonon drag models and quantitative agreement with experiment is obtained for the mobility in Al. At higher velocities, different behavior is observed. The edge dislocation velocity remains dep…
A new approach for characterizing the dislocation microstructure obtained from atomistic simulations is introduced, which relies on converting properties of discrete lines to continuous data. This data is represented by a number of density and density-like field variables containing detailed information about properties of the dislocation microstructure. Applying this methodology to atomistic simulations of nanoscratching in iron reveals a pronounced "length scale effect": With increasing scratching length the number of dislocations increases but the density of geometrically necessary dislocat…
Functionally Graded Material (FGM) is a type of advanced material consisting of two (or more) distinct substances with a constantly changing composition profile. FGM technologies have moved from their traditional use to advanced micro and nanoscale electronics and energy conversion systems along with the advent of nanotechnology. MD simulations are used in this analysis to examine the effect of compressive load on Ag-Au FGM and Core-shell nanospheres. The plasticity process is often started by the nucleation of partial dislocations from the contact surfaces, and these dislocations spread towar…
The stress fields of dislocations predicted by classical elasticity are known to be unrealistically large approaching the dislocation core, due to the singular nature of the theory. While in many cases this is remedied with the approximation of an effective core radius, inside which ad hoc regularizations are implemented, such approximations lead to a compromise in the accuracy of the calculations. In this work, an anisotropic non-singular elastic representation of dislocation fields is developed to accurately represent the near-core stresses of dislocations in $α$-iron. The regularized stress…
This paper reports a study of the influence of the step at a silicon surface under an uniaxial tensile stress, using an empirical potential. Our aim was to find conditions leading to nucleation of dislocations from the step. We obtained that no dislocations could be generated with such conditions. This behaviour, different from the one predicted for metals, could be attributed either to the covalent bonding or to the cubic diamond structure.
In order to relieve the misfitting elastic energy, the hetero-interfaces become semicoherent by forming networks of dislocations. These microscopic structures strongly influence the materials properties associated with the development of advanced materials. We develop a continuum model for the dislocation structures of semicoherent interfaces. The classical Frank-Bilby equation that governs the dislocation structures on semicoherent interfaces is not able to determine a unique solution. The available methods in the literature either use further information from atomistic simulations or conside…
This paper evaluates qualitatively as well as quantitatively the accuracy of a recently proposed Peierls--Nabarro Finite Element (PN-FE) model for dislocations by a direct comparison with an equivalent molecular statics simulation. To this end, a two-dimensional microstructural specimen subjected to simple shear is considered, consisting of a central soft phase flanked by two hard-phase regions. A hexagonal atomic structure with equal lattice spacing is adopted, the interactions of which are described by the Lennard--Jones potential with phase specific depths of its energy well. During loading…
The fundamental dislocation processes of glide, climb, and annihilation are studied on diffusive time scales within the framework of a continuum field theory, the Phase Field Crystals (PFC) model. Glide and climb are examined for single edge dislocations subjected to shear and compressive strain, respectively, in a two dimensional hexagonal lattice. It is shown that the natural features of these processes are reproduced without any explicit consideration of elasticity theory or ad hoc construction of microscopic Peierls potentials. Particular attention is paid to the Peierls barrier for disloc…
The nonequilibrium dynamics of diffusion-mediated plasticity and creep in materials subjected to constant load at high homologous temperatures is studied atomistically using Phase Field Crystal (PFC) methods. Creep stress and grain size exponents obtained for nanopolycrystalline systems, $m \simeq 1.02$ and $p \simeq 1.98$, respectively, closely match those expected for idealized diffusional Nabarro-Herring creep. These exponents are observed in the presence of significant stress-assisted diffusive grain boundary migration, indicating that Nabarro-Herring creep and stress-assisted boundary mig…
Revisiting quantum effects on dislocation glide in bcc metals from DFT calculations and machine-learning potentials
ASNR/PSN-RES/SEMIA/LSMA Centre d’études de Cadarache（法国原子能和替代能源委员会卡达拉舍研究中心）；Université Paris-Saclay, CEA, Service de recherche en Corrosion et Comportement des Matériaux, SRMP（巴黎萨克雷大学，法国原子能和替代能源委员会材料腐蚀与行为研究服务处）；Univ. Lyon, UCBL, Institut Lumière Matière, UMR CNRS 5306（里昂大学，里昂第一大学，光物质研究所）
The population of dislocation defects in a crystalline material strongly influences its properties, so the ability to analyse this population in experimental samples is of great utility. As a complement to direct counting in the transmission electron microscope, quantitative analysis of x-ray diffraction line profiles is an important tool. This is an indirect approach to quantification and so requires careful validation of the physical models that underly the inferential process. Here we undertake to directly evaluate the ability of line profile analysis to quantify aspects of the dislocation …
Intermittent plastic deformation in crystals with power-law behaviors has been reported in previous experimental studies. The power-law behavior is reminiscent of self-organized criticality, and mesoscopic models have been proposed that describe this behavior in crystals. In this letter, we show that intermittent plasticity in metals under tensile deformation can be observed in molecular dynamics models, using embedded atom method potentials for Ni, Cu, and Al. Power-law behaviors of stress drop and waiting time of plastic deformation events are observed. It is shown that power-law behavior is…
Ferroelectric switching at edge dislocations in BaTiO$_3$ modelled at the atomic scale
Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-University Bochum（波鸿鲁尔大学先进材料模拟跨学科中心）；Center for Interface-Dominated High Performance Materials (ZGH), Ruhr-University Bochum（波鸿鲁尔大学界面主导高性能材料中心）；Faculty of Physics and Astronomy, Ruhr-University Bochum（波鸿鲁尔大学物理与天文学系）；Univ. Lille, CNRS, INRAE, Centrale Lille, UMR 8207 - UMET - Unité Matériaux et Transformations（里尔大学、法国国家科学研究中心、法国国家农业食品与环境研究院、里尔中央理工学院、UMR 8207 材料与转化单元）
Screw dislocations in bcc metals display non-planar cores at zero temperature which result in high lattice friction and thermally activated strain rate behavior. In bcc W, electronic structure molecular statics calculations reveal a compact, non-degenerate core with an associated Peierls stress between 1.7 and 2.8 GPa. However, a full picture of the dynamic behavior of dislocations can only be gained by using more efficient atomistic simulations based on semiempirical interatomic potentials. In this paper we assess the suitability of five different potentials in terms of static properties rele…
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…
Through millennia humans exploited the natural property of metals to get stronger or hardened when mechanically deformed. Ultimately rooted in the motion of dislocations, mechanisms of metal hardening remained in the crosshairs of physical metallurgists for over a century. Here, we performed atomistic simulations at the limits of supercomputing, which are sufficiently large to be statistically representative of macroscopic crystal plasticity yet fully resolved to examine the origins of metal hardening at its most fundamental level of atomic motion. We demonstrate that the notorious staged (inf…
Nanostructures have the immense potential to supplant the traditional metallic structure as they show enhanced mechanical properties through strain hardening. In this paper, the effect of grain size on the hardening mechanism of Al-Cu nanostructure is elucidated by molecular dynamics simulation. Al-Cu (50-54% Cu by weight) nanostructure having an average grain size of 4.57 to 7.26 nm are investigated for tensile simulation at different strain rate using embedded atom method (EAM) potential at a temperature of 50~500K. It is found that the failure mechanism of the nanostructure is governed by t…
High entropy alloys (HEAs) are single phase crystals that consist of random solid solutions of multiple elements in approximately equal proportions. This class of novel materials have exhibited superb mechanical properties, such as high strength combined with other desired features. The strength of crystalline materials is associated with the motion of dislocations. In this paper, we derive a stochastic continuum model based on the Peierls-Nabarro framework for inter-layer dislocations in a bilayer HEA from an atomistic model that incorporates the atomic level randomness. We use asymptotic ana…
The dislocation core field, which comes in addition to the Volterra elastic field, is studied for the <111> screw dislocation in alpha-iron. This core field, evidenced and characterized using ab initio calculations, corresponds to a biaxial dilatation, which we modeled within the anisotropic linear elasticity. We show that this core field needs to be considered when extracting quantitative information from atomistic simulations, such as dislocation core energies. Finally, we look at how dislocation properties are modified by this core field, by studying the interaction between two dislocations…
In this work we examine the driving force for edge dislocations to climb in $α$-Fe from atomistic and mesoscale viewpoints. We study the bias for the climb process depending on the dislocation orientation and the applied stress as coming from both the gradient of the chemical potential and the transport coefficients. Both terms are modified by the applied stress and therefore contribute to climb. Surprisingly, even though the vacancy migration barrier distribution is modified by the external stress as obtained by nudged-elastic band calculations, the mobilities resulting from a kinetic Monte C…
Ductile failure is studied in a bcc HfNbTaZr High Entropy Alloy (HEA) with a pre-existing void. Using molecular dynamics simulations of uniaxial tensile tests, we explore the effect of void radius on the elastic modulus and yield stress. The elastic modulus scales with porosity as in closed-cell foams. The critical stress for dislocation nucleation as a function of the void radius is very well described by a model designed after pure bcc metals, taking into account a larger core radius for the HEA. Twinning takes place as a complementary deformation mechanism, and some detwinning occurs at lar…
