This paper presents the thermodynamic dislocation theory containing several modifications over its first version which was originally proposed by Langer, Bouchbinder, and Lookman (2010). Employing a small set of physics-based material parameters identified by the large scale least squares analysis, we show that the theory can fit the stress-strain curves of bcc crystals niobium, tantalum, tungsten, and vanadium over a wide range of temperatures and strain rates.
We report the first ab initio density-functional study of <111> screw dislocations cores in the bcc transition metals Mo and Ta. Our results suggest a new picture of bcc plasticity with symmetric and compact dislocation cores, contrary to the presently accepted picture based on continuum and interatomic potentials. Core energy scales in this new picture are in much better agreement with the Peierls energy barriers to dislocation motion suggested by experiments.
Dislocation motion in body centered cubic (bcc) metals displays a number of specific features that result in a strong temperature dependence of the flow stress, and in shear deformation asymmetries relative to the loading direction as well as crystal orientation. Here we develop a generalized dislocation mobility law in bcc metals, and demonstrate its use in discrete Dislocation Dynamics (DD) simulations of plastic flow in tungsten (W) micro pillars. We present the theoretical background for dislocation mobility as a motivating basis for the developed law. Analytical theory, molecular dynamics…
We show here how density functional theory calculations can be used to predict the temperatureand orientation-dependence of the yield stress of body-centered cubic (BCC) metals in the thermallyactivated regime where plasticity is governed by the glide of screw dislocations with a 1/2 <111> Burgers vector. Our numerical model incorporates non-Schmid effects, both the twinning/antitwinning asymmetry and non-glide effects, characterized through ab initio calculations on straight dislocations. The model uses the stress-dependence of the kink-pair nucleation enthalpy predicted by a line tension mod…
By direct application of stress in molecular statics calculations we identify the stress components that affect the glide of 1/2<111> screw dislocations in bcc tungsten. These results prove that the hydrostatic stress and the normal stress parallel to the dislocation line do not play any role in the dislocation glide. Therefore, the Peierls stress of the dislocation cannot depend directly on the remaining two normal stresses that are perpendicular to the dislocation, as proposed by Koester A, Ma A, Hartmaier A. Acta Mater 2012;60:3894 but, instead, on their combination that causes an equibiaxi…
The validity of the structure-property relationships governing the deformation behavior of bcc metals was brought into question with recent {\it ab initio} density functional studies of isolated screw dislocations in Mo and Ta. These existing relationships were semiclassical in nature, having grown from atomistic investigations of the deformation properties of the groups V and VI transition metals. We find that the correct form for these structure-property relationships is fully quantum mechanical, involving the coupling of electronic states with the strain field at the core of long $a/2<111>$…
Body-centred cubic (BCC) transition metals tend to be brittle at low temperatures, posing significant challenges in processing and major concerns for damage tolerance. The brittleness is largely dictated by the screw dislocation core; the nature and control of which remain a puzzle after nearly a century. Here, we introduce a physics-based material index \{chi}, the energy difference between BCC and face-centred-cubic structures, that guides manipulation of core properties. The lattice friction and nucleation barrier have near-linear scaling with \{chi} and the core transforms from non-degener…
We simulate the dislocation core structure in bcc iron using the modified Molecular Static method. A feature of this method is the application of an iterative procedure in which the atomic structure in the vicinity of the defect and the constants that determine the displacements of atoms immersed in the elastic continuum are calculated in a self-consistent manner. Following the mentioned approach, we develop a model for calculating the atomic structure of edge dislocations, taking into account the anisotropy of the elastic medium surrounding the main calculation cell. Anisotropy is taken into …
Isolated kinks on thermally fluctuating (1/2)<111> screw, <100> edge and (1/2)<111> edge dislocations in bcc iron are simulated under zero stress conditions using molecular dynamics (MD). Kinks are seen to perform stochastic motion in a potential landscape that depends on the dislocation character and geometry, and their motion provides fresh insight into the coupling of dislocations to a heat bath. The kink formation energy, migration barrier and friction parameter are deduced from the simulations. A discrete Frenkel-Kontorova-Langevin (FKL) model is able to reproduce the coarse grained data …
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 …
We investigate the effect of hydrogen on the mobility of a screw dislocation in body-centered cubic (bcc) iron using first-principles calculations, and show that an increase of screw dislocation velocity is expected for a limited temperature range. The interaction energy between a screw dislocation and hydrogen atoms is calculated for various hydrogen positions and dislocation configurations with careful estimations of the finite size effects, and the strongest binding energy of a hydrogen atom to the stable screw dislocation configuration is estimated to be $256\pm32$ meV. These results are i…
The fully two-dimensional Peierls barrier map of screw dislocations in BCC iron has been calculated using the first principles method to identify the migration path of a dislocation core. An efficient method to correct the effect of the finite size cell used in the first principles method on the energy of a lattice defect was devised to determine the accurate barrier profile. We find that the migration path is close to a straight line which is confined in a $\{110\}$ plane and the Peierls barrier profile is single-humped. This result clarifies a reason that the existing empirical potentials of…
In an attempt to bridge the gap between atomistic and continuum plasticity simulations of hydrogen in iron, we present three dimensional discrete dislocation plasticity simulations incorporating the hydrogen elastic stress and a hydrogen dependent dislocation mobility law. The hydrogen induced stress is incorporated following the formulation derived by Gu and El-Awady (2018) which here we extend to a finite boundary value problem, a microcantilever beam, via the superposition principle. The hydrogen dependent mobility law is based on first principle calculations by Katzarov et al. (2017) and w…
The interplay of screw dislocations with carbon atoms is investigated in tungsten at high temperature using in situ straining experiments in a transmission electron microscope (TEM) and through ab initio calculations. When the temperature is high enough to activate carbon diffusion, above 1373 K, carbon segregates in the core of screw dislocations and modifies their mobility, even for a carbon concentration as low as 1 appm. TEM observations reveal the reappearance of a Peierls mechanism at these high temperatures, with screw dislocations gliding viscously through nucleation and propagation of…
The thermodynamic description of dislocation glide in crystals depends crucially on the shape of the Peierls barrier that the dislocation has to overcome when moving in the lattice. While the height of this barrier can be obtained unequivocally using saddle-point search algorithms such as the Nudged Elastic Band (NEB) method, its exact shape depends on the chosen approximation of the transition pathway of the system. The purpose of this paper is to formulate a procedure that allows to identify the position of the dislocation directly from the displacements of atoms in its core. We investigate …
The interaction between carbon and screw dislocations in tungsten is investigated using ab initio calculations. The presence of carbon atoms in the vicinity of the dislocation induces a reconstruction, with the dislocation relaxing to a configuration, the hard core structure, which is unstable in pure tungsten. The reconstruction corresponds to a strong binding of carbon in the prismatic sites created by the dislocation which is perfect for high concentrations of carbon segregated on the dislocation line. However, the reconstruction is only partial for lower atomic fractions, with the dislocat…
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…
We study the kinetics of the redistribution of impurity atoms in the elastic fields of dislocations by computer simulation methods. A work consists of several stages. The first is the simulation of a dislocation core structure with a Burgers vector along [100] direction by using the modified molecular static method. The second is obtaining the coefficients that determine the influence of the components of the strain tensor on the diagonal elements of the matrix of diffusion coefficients and in the equations for fluxes of carbon atoms in bcc iron. The third stage is associated with modeling the…
Temperature-activated dislocation avalanches signaling brittle-to-ductile transition in BCC micropillars
School of Mechanics & Engineering Science, Shanghai University（上海大学力学与工程科学学院）；Department of Mechanical & Aerospace Engineering, University of Miami（迈阿密大学机械与航空航天工程系）；School of Physics, Sun Yat-sen University（中山大学物理学院）；Department of Mechanical & Aerospace Engineering, University of California Los Angeles（加州大学洛杉矶分校机械与航空航天工程系）
Hydrogen segregation around a straight screw dislocation in bcc iron
Laboratoire des Sciences de l’Ingénieur pour l’Environnement (LaSIE) - UMR CNRS 7356（环境工程科学实验室）；Laboratoire des Sciences des Procédés et des Matériaux (LSPM) - UPR 3407（工艺与材料科学实验室）
In traditional body-centered cubic (bcc) metals, the core properties of screw dislocations play a critical role in plastic deformation at low temperatures. Recently, much attention has been focused on refractory high-entropy alloys (RHEAs), which also possess bcc crystal structures. However, unlike face-centered cubic high-entropy alloys (HEAs), there have been far fewer investigations on bcc HEAs, specifically on the possible effects of chemical short-range order (SRO) in these multiple principal element alloys on dislocation mobility. Here, using density functional theory, we investigate the…
The trigonal/bcc orientation relationships (ORs) and their likelihood of occurrence are extensively studied using dispersed Y4Zr3O12nano-precipitates in bcc Fe matrix by means of transmission electron microscopy, image simulations, and a crystallographic model. Two orientation relationships related by a rotation:[1-20]||[111] with (21-2)||(-110) and [1-20]||[111] with (00-3)||(-110), are established and periodic arrays of misfit dislocation doublets are identified at the strained interface in (110) for both ORs. Further eighteen energetically feasible ORs in Y4Zr3O12/bcc system are deduced by …
We use DFT to compute core structures of $a_0[100](010)$ edge, $a_0[100](011)$ edge, $a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$ edge, and $a_0/2[111](1\bar{1}0)$ $71^{\circ}$ mixed dislocations in bcc Fe. The calculations use flexible boundary conditions (FBC), which allow dislocations to relax as isolated defects by coupling the core to an infinite harmonic lattice through the lattice Green function (LGF). We use LGFs of dislocated geometries in contrast to previous FBC-based dislocation calculations that use the bulk crystal LGF. Dislocation LGFs account for changes in topology in the core as well …
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）
Molecular dynamics (MD) simulation of dislocation migration requires semi-empirical potentials of the interatomic interaction. While there are many reliable semi-empirical potentials for the bcc Fe, the number of the available potentials for the fcc is very limited. In the present study we tested three EAM potentials for the fcc Fe (ABCH97 [Phil. Mag. A, 75, 713-732 (1997)], BCT13 [MSMSE 21, 085004 (2013)] and ZFS18 [J. Comp. Chem. 39, 2420-2431 (2018)]) from literature. It was found that the ABCH97 potential does not provide that the fcc phase is the most stable at any temperature. On the oth…
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 …
Dimension reduction procedure is the recipe to represent defects in two dimensional dislocation dynamics according to the changes in the geometrical properties of the defects triggered by different conditions such as radiation, high temperature, or pressure. In the present study, this procedure is extended to incorporate further features related to the presence of defects with a special focus on face-centered cubic/body-centered cubic alloys used for diverse engineering purposes. In order to reflect the microstructural state of the alloy on the computational cell of two dimensional dislocation…
The body centered cubic (BCC) high entropy alloys MoNbTaW and MoNbTaVW show exceptional strength retention up to 1900K. The mechanistic origin of the retained strength is unknown yet is crucial for finding the best alloys across the immense space of BCC HEA compositions. Experiments on Nb-Mo, Fe-Si and Ti-Zr-Nb alloys report decreased mobility of edge dislocations, motivating a theory of strengthening of edge dislocations in BCC alloys. Unlike pure BCC metals and dilute alloys that are controlled by screw dislocation motion at low temperatures, the strength of BCC HEAs can be controlled by edg…
Hydrogen (H) induced damage in metals has been a long-standing woe for many industrial applications. One form of such damage is linked to H clustering, for which the atomic origin remains contended, particularly for non-hydride forming metals. In this work, we systematically studied H clustering behavior in bcc metals represented by W, Fe, Mo, and Cr, combining first-principles calculations, atomistic and Monte Carlo simulations. H clustering has been shown to be energetically favorable, and can be strongly facilitated by anisotropic stress field, dominated by the tensile component along one o…
Interpretation of thermal hardening phenomenon at high strain rate has recently become a critical problem in shock wave physics. In this letter, this problem is addressed from a viewpoint of dislocation generation, and a novel conclusion is gained that forest hardening induced by homogeneous nucleation (HN) results in thermal hardening behavior in a BCC metal significantly, apart from phonon drag mechanism. Through numerical simulations with a dislocation based crystal plasticity model, we have reproduced the experimental results quantitatively and predicted a thermal hardening behavior in oth…
The present paper is concerned with the development of a micromechanical model of the hardening, rate-sensitivity and thermal softening of bcc crystals. In formulating the model we specifically consider the following unit processes: double-kink formation and thermally activated motion of kinks; the close-range interactions between primary and forest dislocations, leading to the formation of jogs; the percolation motion of dislocations through a random array of forest dislocations introducing short-range obstacles of different strengths; dislocation multiplication due to breeding by double cros…
We investigate the lattice dynamics and thermodynamics of nonmagnetic bcc vanadium as a function of temperature and pressure, using the first principles linear response linear-muffin-tin-orbital method. The calculated phonon density of states (DOS) show strong temperature dependence, different from inelastic neutron scattering measurements where the phonon DOS show little change from room temperature up to 1273 K. We obtain the Helmholtz free energy including both electronic and phonon contributions and calculate various equation of state properties such as the bulk modulus and the thermal exp…
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 spintronics, one of the long standing questions is why the MgO-based magnetic tunnel junction (MTJ) is almost the only option to achieve a large tunnelling magnetoresistance (TMR) ratio at room temperature (RT) but not as large as the theoretical prediction. This study focuses on the development of an almost strain-free MTJ using metastable bcc CoxMn100-x ferromagnetic films. We have investigated the degree of crystallisation in MTJ consisting of CoxMn100-x/MgO/CoxMn100-x (x = 66, 75, 83 and 86) in relation to their TMR ratios. Cross-sectional high resolution transmission electron microscop…
We compute the lattice-dynamical and thermal equation of state properties of ferromagnetic bcc iron using the first principles linear response linear-muffin-tin-orbital method in the generalized-gradient approximation. The calculated phonon dispersion and phonon density of states, both at ambient and high pressures, show good agreement with inelastic neutron scattering data. We find the free energy as a function of volume and temperature, including both electronic excitations and phonon contributions, and we have derived various thermodynamic properties at high pressure and temperature. The th…
A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the Peierls stress. Explicit expressions are given for crystals with cubic symmetry: sc, fcc and bcc. Numerical simulations of this model with conservative or damped dynamics illustrate static and moving edge and screw dislocations and describe their co…
The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pile-up against, absorption by, and transfer through the grain boundary, is developed for nonuniform plastic deformations in polycrystals. The case study is carried out on the boundary conditions affecting work hardening of a bicrystal subjected to plane constrained shear for three types of grain boundaries: (i) impermeable hard grain boundary, (ii) grain boundary that allows dislocation transfer without absorption, (iii) grain boundary that absorbs dislocations and allows them to pass later.
Molecular dynamics simulations have been performed to understand the influence of temperature on the tensile deformation and fracture behavior of $<$111$>$ BCC Fe nanowires. The simulations have been carried out at different temperatures in the range 10-1000 K employing a constant strain rate of $1\times$ $10^8$ $s^{-1}$. The results indicate that at low temperatures (10-375 K), the nanowires yield through the nucleation of a sharp crack and fails in brittle manner. On the other hand, nucleation of multiple 1/2$<$111$>$ dislocations at yielding followed by significant plastic deformation leadi…
Within the harmonic approximation, the effects of lattice vibration on the thermodynamics of nano-sized coherent clusters in bcc-Fe consisting of vacancies and/or copper are investigated. A combination of on-lattice simulated annealing based on Metropolis Monte Carlo simulations and off-lattice relaxation by Molecular Dynamics is applied to obtain the most stable cluster configurations at T = 0 K. The most recent interatomic potential built within the framework of the embedded atom method for the Fe-Cu system is used. The vibrational part of the total free energy of defect clusters in bcc-Fe i…
Dislocations are the main carriers of plastic deformation in crystalline materials. Physically based constitutive equations of crystal plasticity typically incorporate dislocation mechanisms, using a dislocation density based description of dislocation microstructure evolution and plastic flow. Typically, such constitutive models are not formulated in a thermodynamic framework. Nevertheless, fundamental considerations of thermodynamic consistency impose constraints on the admissible range of model parameters and/or on the range of application of such models. In particular, it is mandatory to e…
In this paper, we developed a thermodynamically consistent approach to account for the Gibbs energy of pure metallic element with thermal vacancy over wide temperature range. Taking body centered cubic (bcc) W for a demonstration, the strong nonlinear increase for temperature dependence of heat capacities at high temperatures and a nonlinear Arrhenius plots of vacancy concentration in bcc W can be nicely reproduced by the obtained Gibbs energy. The successful description of thermal vacancy on abnormal thermodynamic behaviors in bcc W indicates that the presently proposed thermodynamically cons…
Twin boundaries (TBs) are assumed to be obstacles to dislocation motion and increase the strength of metals. Here, we report the abnormal phenomenon that TBs reduce the strength of body-centered cubic (BCC) tungsten (W). [1-11]-oriented W nanowires with (121) twin planes and free of dislocations were fabricated by chemical vapor deposition. In situ tensile tests within the transmission electron microscope were performed on single-crystal and twinned W nanowires. The fracture strength of the twinned W nanowire was 13.7 GPa, 16% lower than that of the single-crystal W nanowire (16.3 GPa). The we…
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…
The thermodynamic theory of dislocation-enabled plasticity is based on two unconventional hypotheses. The first of these is that a system of dislocations, driven by external forces and irreversibly exchanging heat with its environment, must be characterized by a thermodynamically defined effective temperature that is not the same as the ordinary temperature. The second hypothesis is that the overwhelmingly dominant mechanism controlling plastic deformation is thermally activated depinning of entangled pairs of dislocations. This paper consists of a systematic reformulation of this theory follo…
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.
The thermodynamic dislocation theory developed for non-uniform plastic deformations is used here for the analysis of twisted copper wires. With a small set of physical parameters that we expect to be independent of strain rate and temperature, we can simulate the torque-twist curves that match the experimental ones of Liu et al. (2012). It is shown that the size effect results from the accumulation and pile-up of excess dislocations.
