Fcc Bicrystals Research Articles

Intergranular fracture, grain-boundary structure, and dislocation-density interactions in FCC bicrystals

A dislocation-density based crystalline plasticity (DCP) and nonlinear finite element (FE) analysis were used to predict, and fundamentally understand how and why fracture nucleation and propagation are related to the interrelated microstructural mechanisms of dislocation-density pileups, GB structure, orientation, and total and partial dislocation density interactions within and adjacent for a random low angle grain boundary (LAGB) and a random high angle GB (HAGB). The GB orientations and structures were obtained from micropillar experiments, such that LAGBs and the HAGBs can be accurately represented and used for the modeling predictions. The normal stress, density of pileups, and dislocation-density accumulation along and within the GB were higher for the low angle GB bicrystal. These interrelated phenomena delineate how fracture for high angle GBs nucleate and propagate at lower nominal strains than the lower angle GB bicrystal case. These predictions underscore how fundamental mechanisms can be identified and used to understand how failure nucleates and propagates for different GB structures and orientations.

Effect of the grain boundary on the fatigue crack growth for aluminum bi-crystals

Grain boundaries (GBs) are relevant as structural barriers for deformations in nano-crystalline materials and their resistance against fatigue crack propagation. The overall behavior of the material's structure is the result of a complex confluence of multiple grains with a variety of relative orientations and their interaction with other structural defects. The effect of the grain boundary on cracked grains is an important factor in order to establish the mechanical behavior of nano-materials under static and dynamic loading conditions. For studying the effect of the grain boundary on the mechanical behavior of nano-crystalline solids a single boundary is placed as a defect that separates two miss-oriented crystals with a relative tilt or twist angle. The purpose of this study is to analyze the effect of the GB and the relative tilt and twist angles on the crack propagation under increasing cyclic loading of cracked FCC bi-crystals. Molecular dynamics simulations at room temperature of fatigue crack growth tests were performed to characterize the retardation effect of different grain miss-orientations on fatigue crack propagation. Al by-cristals with an initial edge crack and different miss-orientattion angles are simutalted, in the present research, under increasing cyclic loading condition. As a general trend high twist angles showed a greater effect on the resistance to crack propagation under single and compound grain miss-orientation.

Micro-beam bending of FCC bicrystals: A comparison between defect dynamics simulations and experiments

To understand the role of the grain boundary (GB) in plasticity at small scale, a concurrently coupled mesoscale plasticity model was developed to simulate micro-bending of bicrystalline micron-sized beams. By coupling dislocation dynamics (DD) with a finite element model (FEM), a novel defect dynamics model provides the means to investigate intricate interactions between dislocations and GBs under various loading conditions. Our simulations of micro-bending agree well with corresponding micro-bending experiments, and they show that mechanical response of bicrystals could have not only hardening but also softening depending on the characters of the GB. In addition, changing the location of the GB in the microbeams results in different mechanical responses; GBs located at the neutral plane show softening compared to single crystals, while inclined GBs located halfway along the length of the beam show little effect. Simulation results could provide a clear picture on detailed dislocation-GB interactions, and quantitative resolved shear stress analysis supplemented by dislocation density distribution is used to analyze the mechanical response of bicrystalline samples.

Influence of crystallographic orientation on the void growth at the grain boundaries in bi-crystals

Void growth and morphology evolution in fcc bi-crystals are investigated using crystal plasticity finite element method. For that purpose, representative volume element of bi-crystals with a void at the grain boundary are considered in the analysis. Grain boundary is assumed initially perpendicular/coaxial with the straight sides of the cell. Fully periodic boundary conditions are prescribed in the representative volume element and macroscopic stress triaxiality and Lode parameter are kept constant during the whole deformation process. Three different pairs of crystal orientations characterized as hard-hard, soft-soft and soft-hard have been employed for modelling the mechanical response of the bi-crystal. Simulations are performed to study the implications of triaxiality, Lode parameter and crystallographic orientation on slip mechanism, hardening and hence void evolution. The impact of void presence and its growth on the heterogeneity of lattice rotation and resulting grain fragmentation in neighbouring areas is also analysed and discussed.

Evolution pattern of collision cascades in bcc V with different grain boundary structures: an atomic scale study

In this paper, by means of atomic-scale simulations, we investigate modifications of the evolution pattern of collision cascades in bcc vanadium (V) with different grain boundary (GB) structures on picosecond (ps) timescale. In primary damage state, in agreement with previous results of bcc and fcc bi-crystals, we find that the GBs in V are biased towards interstitials. The biased absorption of interstitials over vacancies reduces the in-cascade annihilation of vacancy-interstitial pairs and leads to aggregation of more number of vacancies in the grains interiors. The sessile vacancies accumulate in the bulk and form immobile vacancy clusters; in contrast, the glissile interstitials disperse in the damage zone and mostly diffuse in the form of single self-interstitial atoms (SIAs)/di-interstitials towards the GB region. Moreover, meanwhile, as we discuss the mechanisms that reduce (or increase) the concentration of defects in bi-crystal structures on picosecond timescale, we study the energetics of defects in close vicinity of pristine GBs, as an alternative driving force that facilitates formation and accumulation of defects in the GB regions. Finally, in a prolonged irradiation, we examine stability and sink properties of the damaged GBs. The results reveal that, irrespective of GB structure, the presence of grain boundaries leads to aggregation of more number of vacancies in the grain interiors in continuous bombardment. Overall, based on the results obtained in the primary damage event and the prolonged irradiation, we conclude that the GBs in bcc V act as efficient defect sinks on the simulated time frame.

A Predictive Framework for Dislocation-Density Pile-Ups in Crystalline Systems With Coincident Site Lattice and Random Grain Boundaries

Evolving dislocation-density pile-ups at grain-boundaries (GBs) spanning a wide range of coincident site lattice (CSL) and random GB misorientations in face-centered cubic (fcc) bicrystals and polycrystalline aggregates has been investigated. A dislocation-density GB interaction scheme coupled to a dislocation-density-based crystalline plasticity formulation was used in a nonlinear finite element (FE) framework to understand how different GB orientations and GB-dislocation-density interactions affect local and overall behavior. An effective Burger's vector of residual dislocations was obtained for fcc bicrystals and compared with molecular dynamics (MDs) predictions of static GB energy, as well as dislocation-density transmission at GB interfaces. Dislocation-density pile-ups and accumulations of residual dislocations at GBs and triple junctions (TJs) were analyzed for a polycrystalline copper aggregate with Σ1, Σ3, Σ7, Σ13, and Σ21 CSLs and random high-angle GBs to understand and predict the effects of GB misorientation on pile-up formation and evolution. The predictions indicate that dislocation-density pile-ups occur at GBs with significantly misoriented slip systems and large residual Burger's vectors, such as Σ7, Σ13, and Σ21 CSLs and random high-angle GBs, and this resulted in heterogeneous inelastic deformations across the GB and local stress accumulations. GBs with low misorientations of slip systems had high transmission, no dislocation-density pile-ups, and lower stresses than the high-angle GBs. This investigation provides a fundamental understanding of how different representative GB orientations affect GB behavior, slip transmission, and dislocation-density pile-ups at a relevant microstructural scale.

Surface/interface effect on the scattered fields of an anti-plane shear wave in an infinite medium by a concentric multi-coated nanofiber/nanotube

Abstract In this paper, the scattering of anti-plane shear waves in an infinite matrix containing a multi-coated nanofiber/nanotube is studied. Based on the fact that the surface to volume ratio for nano-size objects increases, the usual classical theories which generally neglect the surface/interface effects fail to provide reasonable results. Therefore, to analyze the problem the wave-function expansion method is coupled with the surface/interface elasticity theory. In order to provide some quantitative results through consideration of several examples, the knowledge of the relevant surface and/or interface properties of the corresponding constituent materials are required. For this reason, part of this work is devoted to the development of the method of calculation of these properties. Subsequently, the surface shear modulus and residual stresses of several fcc materials as well as interface shear modulus and residual stresses of some fcc–fcc bicrystals are computed. For determination of these parameters a molecular dynamics program which uses Rafii-Tabar and Sutton interatomic potential function is addressed. In numerical calculations, the essential role of surfaces and interfaces in nano-scale is well approved.

Surface and Interface Effects on Torsion of Eccentrically Two-Phase fcc Circular Nanorods: Determination of the Surface/Interface Elastic Properties via an Atomistic Approach

The effect of surface and interface elasticity in the analysis of the Saint–Venant torsion problem of an eccentrically two-phase fcc circular nanorod is considered; description of the behavior of such a small structure via usual classical theories cease to hold. In this work, the problem is formulated in the context of the surface/interface elasticity. For a rigorous solution of the proposed problem, conformal mapping with a Laurent series expansion are employed together. The numerical results well illustrate that the torsional rigidity and stress distribution corresponding to such nanosized structural elements are significantly affected by the size. In order to employ surface and interface elasticity, several key properties such as surface energy, surface stresses, and surface elastic constants of several fcc materials as well as interface properties of the noncoherent fcc bicrystals are derived in terms of Rafii-Tabar and Sutton interatomic potential function. For determination of the surface/interface parameters a molecular dynamics program, which uses the above-mentioned potential function, is developed. The calculated surface and interface properties are in reasonable agreement with the corresponding results in literature. Some applications of the given results can be contemplated in the design of micro-/nano-electromechanical systems.

HCP双結晶の塑性すべりによって生ずる回位型変形場と応力集中(<小特集>M&M2009材料力学カンファレンス)

Plastic slip deformation of a HCP bicrystal is analyzed by a crystal plasticity FE code and distribution of plastic shear strain on the primary and secondary slip systems, as well as some stress components are examined. The constituent crystal are idealized ones and slip deformation on basal, prismatic and pyramidal slip systems can take place, but twin deformation cannot. After a deformation of 1% nominal tensile strain, sharp stress concentrations are developed at the junctions of the grain boundary plane and specimen surfaces even though the crystal orientations of the two grains differ only a few degree. Results are compared with the case for FCC bicrystals and effects of the activation of secondary slip systems are discussed.

Geometrically necessary dislocation structure organization in FCC bicrystal subjected to cyclic plasticity

Crystal plasticity finite element analysis of cyclic deformation of compatible type FCC bicrystals are performed. The model specimen used in the analysis is a virtual FCC bicrystal with an isotropic elastic property; therefore, the effect of constraint due to elastic incompatibility does not appear. The results of the analysis show the strain-amplitude-dependence of both the organization of the GND structure and the stress–strain behavior. The calculated stress–strain curve with the largest strain amplitude shows additional cyclic hardening. The microscopic mechanisms of the strain-amplitude-dependent organization of the GND structure and additional cyclic hardening behavior are discussed in terms of the activation of secondary slip system(s). Finally, the effects of the elastic anisotropy, the lattice friction stress and the interaction between dislocations are also argued.

Size and microstructure effects on the mechanical behavior of FCC bicrystals by quasicontinuum method

The effects of structure and size on the deformation of <110> tilt bicrystals in copper are investigated by concurrent multiscale simulations at zero temperature. In the simulation of eleven grain boundary (GB) structures, a direct relation is shown between structural units and sliding at GBs. We find that GB sliding operates by atom shuffling events localized on one particular type of structural units, which are present in the GB period. When this type of unit is absent, the GB deformation process occurs by migration, or GB-mediated nucleation of partial dislocations with no sliding, depending on the initial GB configuration. The elastic limit causing sliding is found to vary slightly at zero temperature, but no correlation was obtained with the GB energy at equilibrium. Additionally, both modulus of rigidity, and elastic limit remain constant as the bicrystal size varies from 1 nm up to 25 nm. However, differences in the stress relaxation after sliding are observed with respect to the size.

On the stress state at the yield point in symmetric bicrystals in (110) channel die compression

The stress state at the yield point in symmetric fcc bicrystals is analytically investigated for a range of crystal lattice orientations in (110) channel die compression. Although strain-rates and lattice-rotation rates necessarily are nonuniform, it is proved that the stress field satisfying both equilibrium and yield-locus constraints must lie on an edge of the locus and is thereby uniform.

Analytical and numerical investigation of non–uniform straining and subgrain initiation in bicrystals in channel die compression

Effects of the grain boundary (i.e. interface plane) on deformation and stress state in symmetric FCC bicrystals are investigated. The full range of lattice constraint directions for crystals compressed in a (110) direction within a rigid channel die is considered. The spatial non–uniformity is only two dimensional and in the plane transverse to the loading direction. Principal analytical results are that subgrains begin to form within each crystal and tangential velocity discontinuities extend from interface edges in characteristic directions which depend on crystal orientation. Numerical (finite element) results for several orientations at the end of the elastoplastic transition form purely elastic to fully plastic (multiple–slip) response are compared with the analytical rigid–plastic solutions. Both analytical and numerical results predict subranges of lattice orientations in which there is separation of crystal and channel wall.

Low angle grain boundary diffusion of Cr in Nb bicrystals

Abstract Grain boundary diffusion of Cr in [10]/[112] symmetrical bcc bicrystals of Nb has been investigated in the temperature range from 950 to 1197°C with tilt angles, θ, from 2 to 21°. For 0·17°, the activation energy is independent of θ, with an average value of 181-2kJ mol−1, which is about half of the activation energy of lattice diffusion. The grain boundary diffusion coefficients are greater than the lattice diffusion coefficients by five or six orders of magnitude and vary linearly with sin (θ/2), in agreement with the dislocation-pipe model. These conclusions are generally consistent with the findings in fcc bicrystals.

The Accommodation of Lattice Mismatch on the (111) Interphase Boundary Plane in FCC Metals

ABSTRACTUsing the embedded atom method we atomistically model the accommodation of the lattice nismatch and study the propertiesof the misfit dislocations in parallel oriented bicrystals. We calculate and analyze in detail the excess interfacial energies on the (100) and (111) boundary planes. The Ag/Ni system is chosen as a model system for metal/metal interfaces with a large lattice mismatch.Among the possible boundary planes in parallel oriented fcc bicrystals, the ones with terminating {111} planes arc energetically most favourable and are most often observed in experiments. This can be explained by a detailed analysis of the elastic strain fields in the interfaces, which correspond to networks of misfit dislocations. While the misfit dislocations on the (100) and (011) planes have a ½[01ī] Burgers vector, those on (111) can dissociate into misfit partials. The elastic strains connected with the misfit partials are, of course, much smaller than those for other types of misfit dislocations. The misfit partials form a triangular network within the boundary plane.

Finite crack on bimaterial and bicrystal interfaces

A Griffith crack lying along the interface between anisotropic elastic solids is analysed. Explicit solutions for the displacement and stress fields are obtained when the crack-tip fields are non-oscillatory ; i.e. the condition W = 0 is satisfied as derived by Qu and Bassani ( J. Mech. Phys. Solids 37, 417–433, 1989). In this case, the stress intensity factors are real and the three fracture modes are separable at the crack tip. For interfaces formed by misorienting identical anisotropic solids through a relative tilt, this condition is satisfied if the in-plane and anti-plane deformations decouple in the interface-crack coordinates. Complete crack-tip stress fields are calculated for FCC bicrystals satisfying the decoupling condition. Based on Schmid's law, the small-scale-yielding plastic zones surrounding the crack tip are also estimated.

Correlation Between the Structure, Energy, and Local Elastic Properties of Grain Boundaries in Metals

The zero-temperature energies and equilibrium volume expansions of point-defect free asymmetrical grain boundaries (GBs) involving the four densest planes in fcc bicrystals (with some higher-index plane on the other side of the interface) have been determined using an embedded-atom-method potential fitted to Au. It is found that the two asymmetrical tilt GBs at the endpoints of the related GB energy vs twist disorientation curves give rise to pronounced energy cusps. As for symmetrical GBs, a practically linear relationship between the GB energy and equilibrium volume expansion is observed. The volume expansion and the destruction of the perfect-crystal stacking at the GB are shown to cause a pronounced local decrease in the resistance toward shear parallel to the GB plane. 21 refs., 5 figs.

FCC双結晶に生ずる不均一多重すべりの計算機シミュレーション

FCC双結晶に生ずる不均一多重すべりの計算機シミュレーション