Showing papers in "Modelling and Simulation in Materials Science and Engineering in 2010"

Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool

Abstract: The Open Visualization Tool (OVITO) is a new 3D visualization software designed for post-processing atomistic data obtained from molecular dynamics or Monte Carlo simulations. Unique analysis, editing and animations functions are integrated into its easy-to-use graphical user interface. The software is written in object-oriented C++, controllable via Python scripts and easily extendable through a plug-in interface. It is distributed as open-source software and can be downloaded from the website http://ovito.sourceforge.net/.

Extracting dislocations and non-dislocation crystal defects from atomistic simulation data

Abstract: We describe a novel method for extracting dislocation lines from atomistic simulation data in a fully automated way. The dislocation extraction algorithm (DXA) generates a geometric description of dislocation lines contained in an arbitrary crystalline model structure. Burgers vectors are determined reliably, and the extracted dislocation network fulfills the Burgers vector conservation rule at each node. All remaining crystal defects (grain boundaries, surfaces, etc), which cannot be represented by one-dimensional dislocation lines, are output as triangulated surfaces. This geometric representation is ideal for visualization of complex defect structures, even if they are not related to dislocation activity. In contrast to the recently proposed on-the-fly dislocation detection algorithm (ODDA) Stukowski (2010 Modelling Simul. Mater. Sci. Eng. 18 015012) the new method is extremely robust. While the ODDA was designed for a computationally efficient on-the-fly analysis, the DXA method enables a detailed analysis of dislocation lines even in highly distorted crystal regions, as they occur, for instance, close to grain boundaries or in dense dislocation networks.

Dislocation detection algorithm for atomistic simulations

Abstract: We present a novel computational method that makes it possible to directly extract dislocation lines and their associated Burgers vectors from three-dimensional atomistic simulations. The on-the-fly dislocation detection algorithm is based on a fully automated Burgers circuit analysis, which locates dislocation cores and determines their Burgers vector. Through a subsequent vectorization step, the transition from the atomistic system to a discrete dislocation representation is achieved. Using a parallelized implementation of the algorithm, the dislocation analysis can be efficiently performed on the fly within a molecular dynamics simulation. This enables the visualization and investigation of dislocation processes occurring on sub-picosecond time scales, whose observation is otherwise impeded by the presence of other crystal defects or simply by the huge amount of data produced by large-scale atomistic simulations. The presented method is able to identify individual segments as well as networks of perfect, partial and twinning dislocations. The dislocation density can be directly determined and even more sophisticated information is made accessible by our dislocation analysis, including dislocation reactions and junctions, as well as stacking fault and twin boundary densities.

Micromechanics prediction of the effective elastic moduli of graphene sheet-reinforced polymer nanocomposites

Abstract: We investigate the stiffening effect of graphene sheets dispersed in polymer nanocomposites using the Mori–Tanaka micromechanics method. The effective elastic moduli of graphene sheet-reinforced composites are first predicted by assuming that all the graphene sheets are either aligned or randomly oriented in the polymer matrix while maintaining their platelet-like shape. It is shown that a very low content of graphene sheets can considerably enhance the effective stiffness of the composite. The superiority of graphene sheets as a kind of reinforcement is further verified by a comparison with carbon nanotubes, another promising nanofiller in polymer composites. In addition, we analyze several critical physical mechanisms that may affect the reinforcing effects, including the agglomeration, stacking-up and rolling-up of graphene sheets. The results reveal the extent to which these factors will negatively influence the elastic moduli of graphene sheet-reinforced nanocomposites. This theoretical study may help to understand the relevant experimental results and facilitate the mechanical characterization and optimal synthesis of these kinds of novel and highly promising nanocomposites.

Dendritic solidification under natural and forced convection in binary alloys: 2D versus 3D simulation

Abstract: A model of both equiaxed and columnar dendritic growth was developed that incorporates thermal, solutal and fluid flow effects in either two or three dimensions. The model solves the momentum, mass and energy transport equations, including phase change. An imposed anisotropy algorithm, combined with a modified projection method solution of the Navier–Stokes equations, allows a relative coarse mesh and hence excellent computational efficiency. The model was used to study the effect of dimensionality (2D versus 3D) on dendritic growth with and without convection. The influence of forced convection on unconstrained equiaxed growth was studied first. In 3D, the upstream boundary layer is much thinner with a lower concentration than in 2D. This increases tip undercooling, accelerating upstream tip growth and promoting secondary branching. The influence of natural convection on constrained, columnar dendritic, growth was then studied. The 2D flow is blocked by the primary dendrite arms (which are effectively plates), while the 3D flow can wrap around the primaries. This change in flow strongly alters solute distribution and consequently the developing dendritic microstructure. 3D simulations are required to correctly predict unconstrained solidification microstructures.

A geometric approach to modeling microstructurally small fatigue crack formation: II. Physically based modeling of microstructure-dependent slip localization and actuation of the crack nucleation mechanism in AA 7075-T651

Abstract: The objective of this paper is to develop further a framework for computationally modeling microstructurally small fatigue crack growth in AA 7075-T651 (Bozek et al 2008 Modelling Simul. Mater. Sci. 16 065007). The focus is on the nucleation event, when a crack extends from within a second-phase particle into a surrounding grain, since this has been observed to be an initiating mechanism for fatigue crack growth in this alloy. It is hypothesized that nucleation can be predicted by computing a non-local nucleation metric near the crack front. The hypothesis is tested by employing a combination of experimentation and finite element modeling in which various slip-based and energy-based nucleation metrics are tested for validity, where each metric is derived from a continuum crystal plasticity formulation. To investigate each metric, a non-local procedure is developed for the calculation of nucleation metrics in the neighborhood of a crack front. Initially, an idealized baseline model consisting of a single grain containing a semi-ellipsoidal surface particle is studied to investigate the dependence of each nucleation metric on lattice orientation, number of load cycles and non-local regularization method. This is followed by a comparison of experimental observations and computational results for microstructural models constructed by replicating the observed microstructural geometry near second-phase particles in fatigue specimens. It is found that orientation strongly influences the direction of slip localization and, as a result, influences the nucleation mechanism. Also, the baseline models, replication models and past experimental observation consistently suggest that a set of particular grain orientations is most likely to nucleate fatigue cracks. It is found that a continuum crystal plasticity model and a non-local nucleation metric can be used to predict the nucleation event in AA 7075-T651. However, nucleation metric threshold values that correspond to various nucleation governing mechanisms must be calibrated.

Comparison of finite element and fast Fourier transform crystal plasticity solvers for texture prediction

Abstract: We compare two full-field formulations, i.e. a crystal plasticity fast Fourier transform-based (CPFFT) model and the crystal plasticity finite element model (CPFEM) in terms of the deformation textures predicted by both approaches. Plane-strain compression of a 1024-grain ensemble is simulated with CPFFT and CPFEM to assess the models in terms of their predictions of texture evolution for engineering applications. Different combinations of final textures and strain distributions are obtained with the CPFFT and CPFEM models for this 1024-grain polycrystal. To further understand these different predictions, the correlation between grain rotations and strain gradients is investigated through the simulation of plane-strain compression of bicrystals. Finally, a study of the influence of the initial crystal orientation and the crystallographic neighborhood on grain rotations and grain subdivisions is carried out by means of plane-strain compression simulations of a 64-grain cluster. (Some figures in this article are in colour only in the electronic version)

Determination of the crystal-melt interface kinetic coefficient from molecular dynamics simulations

Abstract: The generation and dissipation of latent heat at the moving solid–liquid boundary during non-equilibrium molecular dynamics (MD) simulations of crystallization can lead to significant underestimations of the interface mobility. In this work we examine the heat flow problem in detail for an embedded atom description of pure Ni and offer strategies to obtain an accurate value of the kinetic coefficient, μ. For free-solidification simulations in which the entire system is thermostated using a Nose–Hoover or velocity rescaling algorithm a non-uniform temperature profile is observed and a peak in the temperature is found at the interface position. It is shown that if the actual interface temperature, rather than the thermostat set point temperature, is used to compute the kinetic coefficient then μ is approximately a factor of 2 larger than previous estimates. In addition, we introduce a layered thermostat method in which several sub-regions, aligned normal to the crystallization direction, are indepently thermostated to a desired undercooling. We show that as the number of thermostats increases (i.e., as the width of each independently thermostated layer decreases) the kinetic coefficient converges to a value consistent with that obtained using a single thermostat and the calculated interface temperature. Also, the kinetic coefficient was determined from an analysis of the equilibrium fluctuations of the solid–liquid interface position. We demonstrate that the kinetic coefficient obtained from the relaxation times of the fluctuation spectrum is equivalent to the two values obtained from free-solidification simulations provided a simple correction is made for the contribution of heat flow controlled interface motion. Finally, a one-dimensional phase field model that captures the effect of thermostats has been developed. The mesoscale model reproduces qualitatively the results from MD simulations and thus allows for an a priori estimate of the accuracy of a kinetic coefficient determination for any given classical MD system. The model also elucidates that the magnitude of the temperature gradients obtained in simulations with a single thermostat depends on the length of the simulation system normal to the interface; the need for the corrections discussed in this paper can thus be gauged from a study of the dependence of the calculated kinetic coefficient on system size.

Molecular-dynamics study of solid–liquid interface migration in fcc metals

Abstract: In order to establish a link between various structural and kinetic properties of metals and the crystal–melt interfacial mobility, free-solidification molecular-dynamics simulations have been performed for a total of nine embedded atom method interatomic potentials describing pure Al, Cu and Ni. To fully explore the space of materials properties three new potentials have been developed. The new potentials are based on a previous description of Al, but in each case the liquid structure, the melting point and/or the latent heat are varied considerably. The kinetic coefficient, μ, for all systems has been compared with several theoretical predictions. It is found that at temperatures close to the melting point the magnitude of μ correlates well with the value of the diffusion coefficient in the liquid.

Screw dislocation mobility in BCC metals: the role of the compact core on double-kink nucleation

Abstract: In this work, we examine the kink-nucleation process in BCC screw dislocations using atomistic simulation and transition pathway analysis, with a particular focus on the compact core structure. We observe the existence of a threshold stress, which results in an abrupt change in the minimum energy path of the kink-nucleation process, and hence, a discontinuity in the activation energy versus stress for the process. The magnitude of the discontinuity is found to be related to the degree of metastability of an intermediate split-core structure. This feature appears to be a direct consequence of the so-called 'camel-hump' nature of the Peierls potential, which manifests itself in the existence of a metastable, intermediate split-core structure. The effect is observed in a number of empirical EAM potentials, including Fe, Ta, V, Nb and Mo, suggesting a generality to the observations.

Stress hot spots in viscoplastic deformation of polycrystals

Abstract: The viscoplastic deformation of polycrystals under uniaxial loading is investigated to determine the relationship between hot spots in stress and their location in relation to the microstructure. A 3D full-field formulation based on fast Fourier transforms for the prediction of the viscoplastic deformation of poly-crystals is used with rate-sensitive crystal plasticity. Two measured polycrystalline structures are used to instantiate the simulations, as well as a fully periodic synthetic polycrystal adapted from a simulation of grain growth. Application of (Euclidean) distance maps shows that hot spots in stress tend to occur close to grain boundaries. It is also found that low stress regions lie close to boundaries. The radial distribution function of the hot spots indicates clustering. Despite the lack of texture in the polycrystals, the hot spots are strongly concentrated in ! 110 " orientations, which can account for the observed clustering. All three microstructures yield similar results despite significant differences in topology. (Some figures in this article are in colour only in the electronic version)

A parallel reaction-transport model applied to cement hydration and microstructure development

Abstract: A recently described stochastic reaction-transport model on three-dimensional lattices is parallelized and is used to simulate the time-dependent structural and chemical evolution in multicomponent reactive systems. The model, called HydratiCA, uses probabilistic rules to simulate the kinetics of diffusion, homogeneous reactions and heterogeneous phenomena such as solid nucleation, growth and dissolution in complex three-dimensional systems. The algorithms require information only from each lattice site and its immediate neighbors, and this localization enables the parallelized model to exhibit near-linear scaling up to several hundred processors. Although applicable to a wide range of material systems, including sedimentary rock beds, reacting colloids and biochemical systems, validation is performed here on two minerals that are commonly found in Portland cement paste, calcium hydroxide and ettringite, by comparing their simulated dissolution or precipitation rates far from equilibrium to standard rate equations, and also by comparing simulated equilibrium states to thermodynamic calculations, as a function of temperature and pH. Finally, we demonstrate how HydratiCA can be used to investigate microstructure characteristics, such as spatial correlations between different condensed phases, in more complex microstructures.

The effect of cold spray impact velocity on deposit hardness

Abstract: The deposition and consolidation of metal powders by means of cold spray is a method where powder particles are accelerated to high velocity through entrainment in a gas undergoing expansion in a de Laval nozzle and are subsequently impacted upon a surface. The impacted powder particles form a consolidated structure which can be several centimeters thick. The characteristics of this structure depend on the initial characteristics of the metal powder and upon impact velocity. Initially soft particles are strain hardened during impact, resulting in a structure that can have a hardness value greater than that which can be achieved by conventional cold working. A materials model is proposed for these phenomena, and model calculation is compared with experimental data from cold sprayed copper and aluminum.

A generalized vertex dynamics model for grain growth in three dimensions

Abstract: A generalized three-dimensional (3D) vertex dynamics model for simulating grain growth is presented. In this approach, grain boundaries (GB) are triangulated and the microstructural evolution is driven by the minimization of the GB energy. The generalized model includes misorientation and inclination dependent GB energies and mobilities. The model systems considered are SrTiO3 ceramics.The paper describes the derivation of the equations for the dynamics and the algorithm for handling topological changes in the GB network in detail. For isotropic grain growth, the numerical results for the volume change rate of embedded grains are in excellent agreement with the MacPherson–Srolovitz relation which can be interpreted as the 3D analogue of the von Neumann–Mullins law. The inclination dependent GB energy yields a torque contribution on the GB shape. This is illustrated by means of 2D cross-sections of structures modelled with and without inclination dependence showing rather flat GBs for the energetically favourable GB inclinations.

Kinetics of AlN precipitation in microalloyed steel

Abstract: In this work, the thermodynamic information on AlN formation in steel and experimental data on AlN precipitation kinetics are reviewed. A revised expression for the Gibbs energy of AlN is presented with special emphasis on microalloyed steel. Using the software package MatCalc, computer simulations of AlN precipitation are performed and compared with independent experimental results from the literature. A new model for grain boundary precipitation is employed, which takes into account fast short-circuit diffusion along grain boundaries as well as slower bulk diffusion inside the grain, together with the classical treatment for randomly distributed precipitates with spherical diffusion fields. It is demonstrated that the precipitation of AlN can be modelled in a consistent way if precipitation at grain boundaries and dislocations is taken into account, dependent on chemical composition, grain size and annealing temperature. It is also demonstrated that, for consistent simulations, the influence of volumetric misfit stress must be taken into account for homogeneous precipitation of AlN in the bulk and heterogeneous precipitation at dislocations.

Toughening by nano-scaled twin boundaries in nanocrystals

Abstract: Joint enhancement on strength and toughness provides a cutting-edge research frontier for metals and alloys. Conventional strengthening methods typically lead to suppressed ductility and fracture toughness. In this study, large-scale atomic simulation on the fracture process is performed featuring nanocrystals embedded with nano-scaled twin boundaries (TBs). Four toughening mechanisms by nano-scaled TBs are identified: (i) crack blunting through dislocation accommodation along the nano-scaled TBs; (ii) crack deflection in a manner of intragranular propagation; (iii) daughter crack formation along the nano-scaled TBs that further enhances the toughness and (iv) curved TB planes owing to an excessive pileup of geometrically necessary dislocations. These toughening mechanisms jointly dictate the mechanical behavior of nano-structured materials, and provide insights into the application of nano-scaled TBs with an aim to simultaneously obtain enhanced strength and toughness. New approaches to introduce these coherent internal defects into the nanostructure of crystalline materials are also proposed.

Simulation of metal cutting using a physically based plasticity model

Abstract: Metal cutting is one of the most common metal shaping processes. Specified geometrical and surface properties are obtained by break-up of the material removed by the cutting edge into a chip. The c ...

Cube slip and non-Schmid effects in single crystal Ni-base superalloys

Abstract: An advanced constitutive model incorporating two specific aspects of Ni-base superalloy deformation behaviour is proposed. Several deformation mechanisms are active in these two-phase materials. In the matrix phase, cube slip plays an important role in the orientation dependence of the material. Moreover, inelastic deformation of the precipitate phase leads to non-Schmid effects in the material response. Macroscopic cube slip is modelled here by incorporating a zig-zag cross slip mechanism into the constitutive relations for the matrix phase. A cross slip factor is proposed that quantifies the amount of cross slip and consequently represents the orientation dependence of the cube slip. Further, a detailed precipitate phase constitutive model is proposed, which enables the simulation of non-Schmid effects, like the tension–compression asymmetry. The cross slip mechanism and the associated splitting of partial dislocations in the γ'-phase, which are responsible for the anomalous yield behaviour, are incorporated in the model. The proposed formulations are implemented in a recently developed crystal plasticity framework for single crystal Ni-base superalloys and a consistent set of model parameters for the commercial alloy CMSX-4 is determined. The model is shown to reasonably predict the material tensile response and creep behaviour for a range of temperatures and stress or strain rate levels. The incorporation of the cross slip mechanisms in the matrix and precipitate results in an adequate simulation of the material orientation dependence and the experimentally determined tension–compression asymmetry.

Finite-temperature extension of the quasicontinuum method using Langevin dynamics: entropy losses and analysis of errors

Abstract: The concurrent bridging of molecular dynamics and continuum thermodynamics presents a number of challenges, mostly associated with energy transmission and changes in the constitutive description of a material across domain boundaries. In this paper, we propose a framework for simulating coarse dynamic systems in the canonical ensemble using the quasicontinuum method (QC). The equations of motion are expressed in reduced QC coordinates and are strictly derived from dissipative Lagrangian mechanics. The derivation naturally leads to a classical Langevin implementation where the timescale is governed by vibrations emanating from the finest length scale occurring in the computational cell. The equations of motion are integrated explicitly via Newmark's (β = 0; γ = 1/2) method, which is parametrized to ensure overdamped dynamics. In this fashion, spurious heating due to reflected vibrations is suppressed, leading to stable canonical trajectories. To estimate the errors introduced by the QC reduction in the resulting dynamics, we have quantified the vibrational entropy losses in Al uniform meshes by calculating the thermal expansion coefficient for a number of conditions. We find that the entropic depletion introduced by coarsening varies linearly with the element size and is independent of the nodal cluster diameter. We rationalize the results in terms of the system, mesh and cluster sizes within the framework of the quasiharmonic approximation. The limitations of the method and alternatives to mitigate the errors introduced by coarsening are discussed. This work represents the first of a series of studies aimed at developing a fully non-equilibrium finite-temperature extension of QC.

Shear deformation kinematics of bicrystalline grain boundaries in atomistic simulations

Abstract: The shear deformation behavior of bicrystalline grain boundaries is analyzed using continuum mechanical metrics extracted from atomistic simulations. Calculating these quantities at this length-scale is premised on determining the atomic deformation gradient tensor using interatomic distances. Employing interatomic distance measurements in this manner permits extension of the deformation gradient formulation to estimate important continuum-scale quantities such as lattice curvature and vorticity. These continuum metrics are calculated from atomic deformation fields produced in 2D and thin 3D equilibrium bicrystalline grain boundary structures under shear at 10 K. Results from these simulations show that interface structure strongly influences the resulting accommodation mechanisms under shear and deformation fields produced in the surrounding lattice. Calculating these continuum quantities at the nanoscale lends insight into localized and collective atomic behavior during shear deformation for various mechanisms, and it is shown that different mechanisms lead to differing behavior. Additionally, the results of these calculations can perhaps serve as an intermediary form to inform continuum models seeking to explore larger-scaled grain boundary deformation behavior in 3D, and to evaluate the veracity of continuum models that overlap the nanoscale.

Atomistic study of multimechanism diffusion by self-interstitial defects in α-Fe

Abstract: We present the results of an extensive molecular dynamics study of self-interstitial atom (SIA) clusters containing up to 37 defects over a wide range of temperatures in iron. A long simulation time and high statistics of defect jumps allowed a detailed treatment of the data to be performed. Diffusion exhibits a change in mechanism from three-dimensional to one-dimensional for clusters of 4–7 SIAs. Stable sessile configurations present in the diffusion process are described and their influence on the diffusion parameters is discussed. Diffusion coefficients, correlation factors estimated, and mechanisms observed, are compared with previously published results, and the influence of the interatomic potential is considered.

Size effects in the torsion of thin metal wires

Abstract: The elasto-plastic torsional response of a thin metal wire is analysed using the phenomenological flow theory of strain-gradient plasticity proposed by Fleck and Willis (2009 Part I J. Mech. Phys. Solids 57 161, 2009 Part II J. Mech. Phys. Solids 57 1045). Numerical results are obtained via minimum principles, and closed-form expressions are derived in the limit of vanishing elasticity. An elevation of both initial yield and hardening rate is predicted with decreasing wire diameter. The role of the stored energy of cold work is investigated, and its implications for kinematic hardening are discussed.

A novel grain cluster-based homogenization scheme

Abstract: An efficient homogenization scheme, termed the relaxed grain cluster (RGC), for elasto-plastic deformations of polycrystals is presented. The scheme is based on a generalization of the grain cluster concept. A volume element consisting of eight (= 2 × 2 × 2) hexahedral grains is considered. The kinematics of the RGC scheme is formulated within a finite deformation framework, where the relaxation of the local deformation gradient of each individual grain is connected to the overall deformation gradient by the, so-called, interface relaxation vectors. The set of relaxation vectors is determined by the minimization of the constitutive energy (or work) density of the overall cluster. An additional energy density associated with the mismatch at the grain boundaries due to relaxations is incorporated as a penalty term into the energy minimization formulation. Effectively, this penalty term represents the kinematical condition of deformation compatibility at the grain boundaries.Simulations have been performed for a dual-phase grain cluster loaded in uniaxial tension. The results of the simulations are presented and discussed in terms of the effective stress–strain response and the overall deformation anisotropy as functions of the penalty energy parameters. In addition, the prediction of the RGC scheme is compared with predictions using other averaging schemes, as well as to the result of direct finite element (FE) simulation. The comparison indicates that the present RGC scheme is able to approximate FE simulation results of relatively fine discretization at about three orders of magnitude lower computational cost.

Interaction of dislocations with incoherent interfaces in nanoscale FCC–BCC metallic bi-layers

Abstract: Dislocation nucleation and propagation in a Cu–Nb bi-layer with an incoherent face-centered cubic (FCC)–body-centered cubic (BCC) interface are examined using atomistic simulations. The nanoindentation model is applied to generate dislocations at and near the surface in one of the layers and push them through the interface into the other layer. The reasons for high strength levels in multilayered metallic composites with incoherent interfaces are investigated. The interface acts as a very strong barrier to dislocation propagation. It is found that even under severe deformation at large indentation depths, no dislocations are transmitted across the interface from Cu into Nb. While dislocation transmission from Nb to Cu can be, in general, observed, it occurs under high loading forces. In both cases, the presence of the interface results in considerable strengthening of the bi-layer. Mechanisms of interactions between gliding dislocations and the incoherent interface have been studied in detail. In particular, interface shear at the interface under complex three-dimensional loading conditions is analyzed.

Testing continuum concepts for hydrogen embrittlement in metals using atomistics

Abstract: Hydrogen embrittlement is a pervasive mode of degradation in many metallic systems that can occur via several mechanisms. Here, the competition between dislocation emission and cleavage at a crack tip is evaluated in the presence of H. At this level, embrittlement is predicted when the critical stress intensity required for emission rises above that needed for cleavage, eliminating crack tip plasticity and blunting as toughening mechanisms. Continuum predictions for emission and cleavage are made using computed generalized stacking fault energies and surface energies in a model Ni-H system, and embrittlement is predicted at a critical H concentration. An atomistic model is then used to investigate actual crack tip behavior in the presence of controlled arrays of H atoms around the crack tip. The continuum models are accurate at low H concentrations, below the embrittlement point, but at higher H concentrations the models deviate from the atomistic behavior due to alternative dislocation emission modes. Additional H configurations are investigated to understand controlling features of the emission process. In no cases does crack propagation occur in preference to dislocation emission in geometries where emission is possible, indicating that embrittlement can be more complicated than envisioned by the basic brittle-ductile transition.

Three-dimensional shear transformation zone dynamics model for amorphous metals

Abstract: A fully three-dimensional (3D) mesoscale modeling framework for the mechanical behavior of amorphous metals is proposed. The model considers the coarse-grained action of shear transformation zones (STZs) as the fundamental deformation event. The simulations are controlled through the kinetic Monte Carlo algorithm and the mechanical response of the system is captured through finite-element analysis, where STZs are mapped onto a 3D finite-element mesh and are allowed to shear in any direction in three dimensions. Implementation of the technique in uniaxial creep tests over a wide range of conditions validates the model's ability to capture the expected behaviors of an amorphous metal, including high temperature flow conforming to the expected constitutive law and low temperature localization in the form of a nascent shear band. The simulation results are combined to construct a deformation map that is comparable to experimental deformation maps. The flexibility of the modeling framework is illustrated by performing a contact test (simulated nanoindentation) in which the model deforms through STZ activity in the region experiencing the highest shear stress.

Dislocation subgrain structures and modeling the plastic hardening of metallic single crystals

Abstract: A single crystal plasticity theory for insertion into finite element simulation is formulated using sequential laminates to model subgrain dislocation structures. It is known that local models do not adequately account for latent hardening, as latent hardening is not only a material property, but a nonlocal property (e.g. grain size and shape). The addition of the nonlocal energy from the formation of subgrain structure dislocation walls and the boundary layer misfits provide both latent and self-hardening of a crystal slip. Latent hardening occurs as the formation of new dislocation walls limits motion of new mobile dislocations, thus hardening future slip systems. Self-hardening is accomplished by an evolution of the subgrain structure length scale. The substructure length scale is computed by minimizing the nonlocal energy. The minimization of the nonlocal energy is a competition between the dislocation wall energy and the boundary layer energies. The nonlocal terms are also directly minimized within the subgrain model as they affect deformation response. The geometrical relationship between the dislocation walls and slip planes affecting the dislocation mean free path is taken into account, giving a first-order approximation to shape effects. A coplanar slip model is developed due to requirements while modeling the subgrain structure. This subgrain structure plasticity model is noteworthy as all material parameters are experimentally determined rather than fit. The model also has an inherit path dependence due to the formation of the subgrain structures. Validation is accomplished by comparison with single crystal tension test results.

Energetics and structure of lang0 0 1rang tilt grain boundaries in SiC

Abstract: We have developed a scheme, based on molecular dynamics, that allows finding minimum energy structures of grain boundaries (GBs) with relatively large cell of non-identical displacements. This scheme has been used to study symmetric 0?0?1 tilt GBs in cubic SiC. We analyze atomic configurations of dislocation cores found in low-angle GBs and we report structural units found in high-angle GBs. In contrast to what had been previously assumed we find that the lowest energy structures often do not favor perfect coordination of GB atoms and that most of the analyzed GBs contain 6- and 7-atom rings. We tested the applicability of existing empirical potentials to studies of high-symmetry GB structures in SiC and we found the Tersoff potential to be most appropriate. Knowledge of detailed atomic structures of GBs is essential for future studies of GB-controlled phenomena in SiC, such as diffusion of metallic fission product through this material or GB strengthening.

Efficient computation of forces on dislocation segments in anisotropic elasticity

Abstract: We compare several alternative approaches for computing the stress field of a straight dislocation segment and its forces on other segments in an anisotropic linear elastic medium. The Willis–Steeds–Lothe expression can be implemented faster than Brown's formula and the matrix formalism is only slightly faster than the integral formalism. Expressions for self-stress and self-force are also explicitly derived. As an example, the critical stress to activate a Frank–Read source is computed as a function of its length in both isotropic and anisotropic materials.