Multiscale modeling of plastic deformation of molybdenum and tungsten: II. Yield criterion for single crystals based on atomistic studies of glide of 1/2<111> screw dislocations
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 determine the ensuing tension-compression asymmetry. This result is in an excellent qualitative agreement with available experimental data. Moreover, using the constructed yield criteria within the Taylor homogenization procedure, we demonstrate that effects associated with non-planar cores of screw dislocations persist in random polycrystals. This affects significantly critical phenomena such as shear localization, which is demonstrated by analyzing the cavitation in a ductile plastic solid.
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…
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 …
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…
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…
Atomistic simulations, based either on an empirical interatomic potential or on ab initio calculations, are used to study the pyramidal glide of a 1/3 <1-210> screw dislocation in hexagonal close-packed zirconium. Generalized stacking fault calculations reveal a metastable stacking fault in the first order pyramidal {10-11} plane, which corresponds to an elementary pyramidal twin. This fault is at the origin of a metastable configuration of the screw dislocation in zirconium, which spontaneously appears when the dislocation glides in the pyramidal plane.
The stability of the perfect screw dislocation in silicon has been investigated using both classical potentials and first-principles calculations. Although a recent study by Koizumi et al . stated that the stable screw dislocation was located in both the 'shuffle' and the 'glide' sets of {111} planes, it is shown that this result depends on the classical potential used, and that the most stable configuration belongs to the 'shuffle' set only, in the centre of one hexagon. We also investigated the stability of an sp 2 hybridization in the core of the dislocation, obtained for one metastable con…
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 $a/2<111>$…
Pinning interaction between a screw dislocation and a void in fcc copper is investigated by means of molecular dynamics simulation. A screw dislocation bows out to undergo depinning on the original glide plane at low temperatures, where the behavior of the depinning stress is consistent with that obtained by a continuum model. If the temperature is higher than 300 K, the motion of a screw dislocation is no longer restricted to a single glide plane due to cross slip on the void surface. Several depinning mechanisms that involve multiple glide planes are found. In particular, a depinning mechani…
Plasticity in hexagonal close-packed zirconium is controlled by screw dislocations which easily glide in the prismatic planes where they are dissociated. At high enough temperatures, these dislocations can deviate out of the prism planes to also glide in the first order pyramidal and basal planes. To get a better understanding of these secondary slip systems, we have performed molecular dynamics (MD) simulations of a screw dislocation gliding in a basal plane. The gliding dislocation remains dissociated in the prism plane where it performs a random motion and occasionally cross-slips out of it…
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…
The properties of perfect screw dislocations have been investigated for several zinc-blende materials such as diamond, Si, $β$-SiC, Ge and GaAs, by performing first principles calculations. For almost all elements, a core configuration belonging to shuffle set planes is favored, in agreement with low temperature experiments. Only for diamond, a glide configuration has the lowest defect energy, thanks to an sp$^2$ hybridization in the core.
A high dimensional artificial neural network interatomic potential for Mo is developed. To train and validate the potential density functional theory calculations on structures and properties that correlate to fracture, such as elastic constants, surface energies, generalized stacking fault energies, and surface decohesion energies, have been employed. The potential provides total energies with a root mean square error less than 5\;meV per atom both in the training and validation data sets. The potential was applied to investigate screw dislocation core properties as well as to conduct large s…
Although the favored glide planes in hexagonal close-packed Zr are prismatic, screw dislocations can escape their habit plane to glide in either pyramidal or basal planes. Using abinitio calculations within the nudged elastic band method, we show that, surprisingly, both events share the same thermally activated process with an unusual conservative motion of the prismatic stacking fault perpendicularly to itself. Halfway through the migration, the screw dislocation adopts a nonplanar metastable configuration with stacking faults in adjacent prismatic planes joined by a two-layer pyramidal twin…
The influence of magnetism on the properties of screw dislocations in body-centered cubic chromium is investigated by means of ab initio calculations. Screw dislocations having Burgers vectors 1/2 111 and 100 are considered, following experimental observations showing activity for both slip systems. At low temperature, chromium has a magnetic order close to antiferromagnetism along 100 directions, for which 1/2 111 is not a periodicity vector. Hence, dislocations with Burgers vectors 1/2 111 generate magnetic faults when shearing the crystal, which constrain them to coexist and move pairwise, …
Interactions among dislocations and solute atoms are the basis of several important processes in metals plasticity. In body-centered cubic (bcc) metals and alloys, low-temperature plastic flow is controlled by screw dislocation glide, which is known to take place by the nucleation and sideward relaxation of kink pairs across two consecutive \emph{Peierls} valleys. In alloys, dislocations and solutes affect each other's kinetics via long-range stress field coupling and short-range inelastic interactions. It is known that in certain substitutional bcc alloys a transition from solute softening to…
The interaction between screw dislocations and oxygen interstitial atoms is studied with ab initio calculations in hexagonal close-packed titanium. Our calculations evidence a strong repulsion when the solute atoms are located in the dislocation glide plane, leading to spontaneous cross-slip, which allows the dislocation to bypass the atomic obstacle. This avoidance process explains several experimental observations in titanium in presence of oxygen: (1) a larger lattice friction against screw dislocation motion, (2) a reduction of the dislocation glide distance in prismatic planes and (3) an …
In this paper we develop a link between the atomic-level modeling of the glide of 1/2<111> screw dislocations at 0 K and the thermally activated motion of these dislocations via nucleation of pairs of kinks. For this purpose, we introduce the concept of a hypothetical Peierls barrier, which reproduces all the aspects of the dislocation glide at 0 K resulting from the complex response to non-glide stresses and is expressed in a compact form by the yield criteria advanced in Part II. To achieve this the barrier is dependent not only on the crystal symmetry and interatomic bonding but also on the…
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 propose a mesoscopic model that explains the factor of two to three discrepancy between experimentally measured yield stresses of BCC metals at low temperatures and typical Peierls stresses determined by atomistic simulations of isolated screw dislocations. The model involves a Frank-Read type source emitting dislocations that become pure screws at a certain distance from the source and, owing to their high Peierls stress, control its operation. However, due to the mutual interaction between emitted dislocations the group consisting of both non-screw and screw dislocations can move at an ap…
Plasticity in zirconium is controlled by 1/3<1-210> screw dislocations gliding in the prism planes of the hexagonal close-packed structure. This prismatic and not basal glide is observed for a given set of transition metals like zirconium and is known to be related to the number of valence electrons in the d band. We use ab initio calculations based on the density functional theory to study the core structure of screw dislocations in zirconium. Dislocations are found to dissociate in the prism plane in two partial dislocations, each with a pure screw character. Ab initio calculations also show…
Enhanced Elevated-Temperature Strength in Refractory Complex Concentrated Alloys via Temperature-Induced Transition from Screw-to-Edge Dislocation Control
University of California, Davis（加州大学戴维斯分校）；Oak Ridge National Laboratory（橡树岭国家实验室）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
The breakdown of the Schmid law in bcc metals has been known for a long time. The asymmetry of shearing in the slip direction <111> in the positive and negative sense, respectively, commonly identified with the twinning-antitwinning asymmetry, is undoubtedly one of the reasons. However, effect of stress components other than the shear stress in the slip direction may be important. In this paper we investigate by atomistic modeling the effect of shear stresses perpendicular to the Burgers vector on the glide of a/2<111> screw dislocations. We show that these shear stresses can significantly ele…
Basal slip acts as a secondary deformation mode in hexagonal close-packed titanium and becomes one of the primary mechanisms in titanium alloyed with simple metals. As these solute elements also lead to a pronounced reduction of the energy of the basal stacking fault, one can hypothesize that they promote basal dissociation of dislocations which can then easily glide in the basal planes. Here, we verify the validity of this hypothesis using ab initio calculations to model the interaction of a screw dislocation with indium (In) and tin (Sn). These calculations confirm that these simple metals a…
Dipolar dislocation loops, prevalent in fcc metals, are widely recognized as controlling many physical aspects of plastic deformation. We present results of 3D dislocation dynamics simulations that shed light on the mechanisms of their formation, motion, interactions, and large-scale patterning. We identify two main formation mechanisms, enabled by cross-slip, and show that arrays of dipoles can be easily formed as a result of the interaction between glide screw dislocations. We present a systematic analysis of the spectrum of possible junctions that can form as a result of mutual interaction …
The dynamic generalization of the Peierls-Nabarro equation for dislocations cores in an isotropic elastic medium is derived for screw, and edge dislocations of the `glide' and `climb' type, by means of Mura's eigenstrains method. These equations are of the integro-differential type and feature a non-local kernel in space and time. The equation for the screw differs by an instantaneous term from a previous attempt by Eshelby. Those for both types of edges involve in addition an unusual convolution with the second spatial derivative of the displacement jump. As a check, it is shown that these eq…
High-entropy alloys (HEAs) with concentrated solid solutions are conceived to possess a rugged atomic and energy landscape in which dislocation motion necessarily proceeds to accommodate mechanical deformation. Fundamental questions remain as to how rough the energy landscape is and to what extent it can be influenced by the local ordering of their constituent elements. Here, we construct and report the potential energy landscape (PEL) governing screw dislocation motion in refractory HEAs that reveals a hierarchical and multilevel structure with a collection of small basins nested in large met…
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…
Nonsymmoprhic symmetries, such as screw rotations or glide reflections, can enforce band crossings within high-symmetry lines or planes of the Brillouin zone. When these band degeneracies are close to the Fermi energy, they can give rise to a number of unusual phenomena: e.g., anomalous magnetoelectric responses, transverse Hall currents, and exotic surface states. In this paper, we present a comprehensive classification of such nonsymmorphic band crossings in trigonal materials with strong spin-orbit coupling. We find that in trigonal systems there are two different types of nonsymmorphic ban…
Cross-slip is a thermally activated process by which screw dislocation changes its glide plane to another slip plane sharing the same Burgers vector. The rate at which this process happens is determined by a Boltzmann type expression that is a function of the screw segment length and the stress acting on the dislocation. In continuum dislocation dynamics (CDD), the information regarding the length of the screw dislocation segment and local stress state on dislocations are lost due to the coarse-grained representation of the density. In this work, a data driven approach to characterize the lost…
The primary factors controlling defect stability in phase-field crystal (PFC) models are examined, with illustrative examples involving several existing variations of the model. Guidelines are presented for constructing models with stable defect structures that maintain high numerical efficiency. The general framework combines both long-range elastic fields and basic features of atomic-level core structures, with defect dynamics operable over diffusive time scales. Fundamental elements of the resulting defect physics are characterized for the case of fcc crystals. Stacking faults and split Sho…
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 …
Computational modeling is usually applied to aid experimental exploration of advanced materials to better understand the fundamental plasticity mechanisms during mechanical testing. In this work, we perform Molecular dynamics (MD) simulations to emulate experimental room temperature spherical-nanoindentation of crystalline W matrices by different interatomic potentials: EAM, modified EAM, and a recently developed machine learned based tabulated Gaussian approximation potential (tabGAP) for describing the interaction of W-W. Results show similarities between load displacements and stress-strain…
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 …
The influence of the stress state on the cross-slip rate in Al was analyzed by means of molecular dynamics simulations and transition state theory. The activation energy barrier in the absence of thermal energy was determined through the nudged elastic band method while the cross-slip rates were determined using molecular dynamics simulations for different magnitudes of the Schmid stress on the cross-slip plane, and of the Escaig stresses on the cross-slip and glide planes. The enthalpy barrier and the effective attempt frequency were determined from the average rates of cross-slip obtained fr…
We demonstrate that the straightforward application of the Nudged Elastic Band (NEB) method does not determine the correct Peierls barrier of 1/2<111> screw dislocations in BCC metals. Although this method guarantees that the states (images) of the system are distributed uniformly along the minimum energy path, it does not imply that the dislocation positions are distributed uniformly along this path. In fact, clustering of dislocation positions near potential minima occurs which leads to an overestimate of both the slope of the Peierls barrier and the Peierls stress. We propose a modification…
In this Thesis we first show how the shape of the Peierls barrier and its dependence on the applied loading can be extracted from the data obtained in atomistic studies at 0 K. We consider the Peierls barrier as a two-dimensional periodic function of the position of the intersection of the dislocation line with the perpendicular {111} plane, with adjustable terms dependent on the shear stresses parallel and perpendicular to the slip direction. The functional forms of these terms are based on the effective yield criterion recently developed on the basis of atomistic modeling of the glide of scr…
