# Computational Materials Science

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Accurate ab-initio pseudopotential calculations within density functional theory in the LDA approximation have been performed for structural properties and stability of ZnSe/GaAs(001) defected heterostructures. There is a strong experimental evidence that ZnSe/GaAs heterostructures with minimum stacking fault density are related to the presence of a substantial concentration of Ga vacancies at interface. In order to gain insights into the still unknown microscopic maechanism governing their formation and stability, we compared the relative stability of some simple selected interface configurations, chosen taking into account charge neutrality prescription and allowing the presence of Ga vacancy next to the interface. Remarkably, our results show that, under particular thermodynamic conditions, some interfaces with vacancies are favoured over undefected ones.

Two different single crystals, Si with the diamond structure and Al with face-centered-cubic, are subjected to [0 0 1] tension in ab initio molecular dynamics (static) simulations based on Bachelet–Hammann–Schlüter (BHS) pseudopotential. Not only the ideal tensile strength under isotropic Poisson contraction, but also the crystal stability and bifurcation to anisotropic contraction are discussed in terms of the elastic stiffness matrix and the change in the charge density. The ideal tensile strengths are overestimated to as high as ε=0.18, σ=18.7 GPa for Si and ε=0.25, σ=23.5 GPa for Al, respectively. These values are inconsistent with the experimentally observed characteristics such as the hardness of Al being lower than that of Si. The elastic stiffness matrix reveals that the crystals become unstable at far lower strain and stress, ε=0.094, σ=10.7 GPa for Si and ε=0.055, σ=5.65 GPa for Al, and bifurcate to the lower energy pass of the anisotropic contraction. The change in the electronic structure suggests that nucleation/passage of a partial dislocation would take place in the bifurcated anisotropic contraction. Thus the instability point indicates the onset of the nonelastic deformation and is much more important than the ideal tensile strength.

Metal deposition of Zr an a Si(001) surface has been studied by state-of-the-art electronic structure calculations. The energy per Zr adatom as a function of the coverage shows, that Zr forms silicide islands even at low coverages. Adsorbed Zr is thermodynamically unstable against the formation of bulk silicide ZrSi2. The observation that the islands consist of structural elements of the bulk silicide is an indication that silicide grains will form spontaneously.

Systematic studies of O adsorption on clean and H-saturated Si-rich 3C–SiC(0 0 1) 3 × 2 surfaces within density functional theory are presented. We investigate the O binding energy for a variety of possible adsorption sites on the surface and in subsurface regions for both substrates. We find that the on-surface adsorption sites are preferred over deep adsorption for both substrates and that O is more strongly bound on the hydrogenated surface. We explore the dependence between the energy of the adsorption site and the surface relaxation accompanying it.

Phase transformations in steel under stress lead to transformation-induced plasticity (TRIP), and the phase transformations are influenced, too (“Stress-dependent transformation behaviour” = SDTB). These important phenomena are currently intensively investigated. Usually one performs tension and compression tests with small specimen undergoing phase transformation in special devices like dilatometer. Based on measured data for steel 100Cr6 (SAE52100), we investigate some proposals for TRIP and SDPB for the martensitic transformation. In particular, we discus the behaviour of the Greenwood–Johnson parameter under tension and compression, and proposals for the saturation function, using different optimisation strategies. We evaluate the Koistinen–Marburger formula and one of its modification by Wildau.

The significant creep anisotropy associated with crystallographic orientation in single crystal Ni-base superalloys in the temperature range 1023–1123 K has been well documented over the past 20 years. The mechanisms primarily responsible for this anisotropy are established and are related to proximity to symmetry boundaries and the rotation that occurs during creep in single slip orientations. However, quantification and modelling of this behaviour has not been sufficiently addressed. It is not yet possible to determine the effect of lower temperature anisotropy and transient behaviour in macroscopic models and component analysis. In this paper this situation is addressed through the development of a mechanism based slip system model capable of accounting for the major effects associated with lower temperature anisotropy, including transient behaviour and rupture life. The model has been fitted to the first and second-generation single crystal superalloys RR2000 and CMSX-4. The results of creep and rupture tests on these alloys in many crystallographic orientations at 1023 K are presented.

In analyzing microstructure evolution of material, study for the process of grain growth is both theoretically and practically significant. On (1 1 1) and (1 1 0) facets, the process of CVD–SiC film in two-dimension is simulated with Potts Monte Carlo method. The relationship between the microstructure morphology and growth rate, nucleating density is analyzed. The simulation result is given as the following. Both competitive growth and coarsening effect have been found in the growth process. The increase of nucleation density results in thinning of the grain size in SiC film. The grain size distribution is found to be self-similar, not differed with the corresponding growth parameter. The fitted result of Weibull and Louat function is better than that of lognormal function obviously. The result is in agreement with the corresponding theory and experiment conclusion well.

Under GGA, the cleavage energy, surface energy, surface grand potential, surface relaxation, and surface electronic structure have been calculated for five different terminations of PbTiO3 (1 1 0) surface by using PAW method implemented in VASP. Taking into account the results of two neutral PbTiO3 (1 0 0) surfaces, the favorable PbTiO3 (1 1 0) and (1 0 0) surfaces are the TiO2-terminated (1 0 0) surface, the PbO-terminated (1 0 0) surface, and the O-terminated (1 1 0) surface successively in view of surface energy minimization. The surface grand potential calculations show that two neutral PbO- and TiO2-terminated (1 0 0) surfaces are favored in the moderate Pb and O chemical potentials, two mutual complementary TiO- and Pb-(1 1 0) terminations are stable in Pb-poor environment and in O- and Pb-rich conditions, respectively. A non-negligible rumpling of O-terminated (1 1 0) surface is found in the third O2 layer and large lateral displacements between Ti and O atoms on the PbTiO layer lead to the initial O-Ti-O alignment broken. Different from the Fermi levels of the three nonstoichiometric TiO-, Pb- and O-terminations which are located in the band gap, the Fermi level of the PbTiO- termination is located at the bottom of the conduction band and that of the O2-termination is located at the top of the valence band due to increment and decrement of the occupation states for polarity compensation.

The roughening transition on the Pb (110) surface has been studied using a combination of lattice-gas Monte Carlo and molecular-dynamics methods in conjunction with a many-body glue potential. Lattice-gas Monte Carlo simulations yield a roughening transition temperature of approximately TRLGMC ≈ 1100 K. Molecular-dynamics simulations, which account for surface relaxation and lattice vibrations, detect the roughening transition at TRMD ≈ 545 K, above the high-resolution low-energy diffraction measurements of TREXP ≈ 415 K. The anisotropic body-centered solid-on-solid model is used in the interpretation of these results. The time scale of local roughening at 545 K is about 0.6 ns. The time evolution of the Pb (110) surface from an initially smooth to a rough configuration is illustrated by the use of modem visualization techniques. Means for improving the theoretical results are discussed.

Using multi-ion MGPT interatomic potentials derived from first-principles generalized pseudopotential theory, we have performed accurate atomistic simulations on the energetics of dislocation motion in the bcc transition metal Mo. Our calculated results include the (110) and (211) generalized stacking fault (γ) energy surfaces, the Peierls stress required to move an ideal straight 〈111〉 screw dislocation, and the kink-pair formation energy for nonstraight screw dislocations. Many-body angular forces, which are accounted for in the present theory through explicit three- and four-ion potentials, are quantitatively important to such properties for the bcc transition metals. This is demonstrated explicitly through the calculated y surfaces, which are found to be 10–50% higher in energy than those obtained with pure radial-force models. The Peierls stress for an applied shear is computed to be about 0.025μ, where μ is the bulk shear modulus. For zero applied stress, stable kink-pairs are predicted to form for kink lengths greater than 4b, where b is the magnitude of the Burgers vector. For long kinks greater than 15b, the calculated asymptotic value of the kink-pair formation energy is 2.0 eV.

Di-thiol–benzene (DTB) is one of the most intensively studied systems, both experimentally and theoretically, for electron transport in molecules. Despite this, there persists a gap of three orders of magnitude between the measured and most reliable calculated conductances. In this paper, we present state of the art calculations of the electron transport through DTB coupled to Au(1 1 1) surfaces using our newly developed method TranSIESTA. The method is based on density functional theory (DFT) and determines the self-consistent electronic structure of a nanostructure coupled to 3-dimensional electrodes with different electrochemical potentials, using a full atomistic description of both the electrodes and the nanostructure. We find qualitative differences with other more approximative theoretical approaches, although we confirm that the theoretical conductance for a perfectly contacted DTB molecule is several orders of magnitude higher than the value obtained in molecular break junction (MBJ) experiments. We discuss the formation of the molecular contact in the MBJ, and calculate the current–voltage (I–V) characteristics of DTB for geometries which do not include perfect thiolate bonds to one or both of the electrodes.

Using the tight-binding linear muffin-tin orbital (TB–LMTO) method, we study the magnetism of hexagonal V and Cr monolayers (MLs) either free-standing or epitaxially adsorbed on the Ag(1 1 1) surface, by spin-polarized ab initio electronic structure calculations. For free-standing MLs, we carried out calculations as a function of lattice parameter for various magnetic configurations. We found that for the lattice parameter of Ag(1 1 1) surface (5.45 a.u.), the ferrimagnetic and antiferromagnetic states are clearly more stable than the other solutions. This remains to be true for V and Cr MLs on a Ag(1 1 1) surface.

The Pb/Si(111) thin films were simulated within the density functional theory (DFT). The well-known Perdew-Burke-Ernzerhof (PBE) version of the generalized gradient approximation (GGA) and its recent nonempirical successor Wu-Cohen (WC) issue were used to estimate the exchange-correlation functional. Lattice parameters were calculated for Bulk of the Pb and Si compounds to obtain more reliable lattice mismatch at the interface to be consistent with our used full-potential method of calculations. The WC-GGA result predicts the lattice constants of the Pb and Si compounds better than the GGA when compared with experiment. We have found that the spin-orbit coupling (SOC) does not significantly influence the results. Our finding is in agreement with the recent observation of the Rashba-type spin-orbit splitting of quantum well states in ultrathin Pb/Si(111) films. Our result shows, in agreement with experiment, that the top site (T1) is the most stable phase. A combination of tight $\sigma$ and feeble $\pi$ bonds has been found at the interface, which results in a covalent Pb-Si bond. Our calculated electric field gradient (EFG) predicts quantum size effects (QSE) with respect to the number of deposited Pb layers on the Si substrate. The QSE prediction shows that the EFG dramatically drops on going from first to second layer. The EFG calculation shows that this system is not an ideal paradigm to freestanding films. Comment: 12 pages, 6 figures

We present calculations on energy- and time-resolved two-photon photoemission spectra of images states in Cu(100) and Cu(111) surfaces. The surface is modeled by a 1D effective potential and the states are propagated within a real-space, real-time method. To obtain the energy resolved spectra we employ a geometrical approach based on a subdivision of space into two regions. We treat electronic inelastic effects by taking into account the scattering rates calculated within a GW scheme. To get further insight into the decaying mechanism we have also studied the effect of the variation of the classical Hartree potential during the excitation. This effect turns out to be small.

We have studied the self-diffusion of single adatoms on Pd(1 1 1) surfaces using molecular-dynamics simulations along with a semi-empirical many-body interatomic potential for Pd, obtained within the second-moment approximation to the tight-binding model. The diffusion coefficient of Pd adatoms was computed, and was found to present Arrhenius behavior. The migration energy and pre-exponential factor were determined from the Arrhenius diagram and compared with recent scanning tunneling investigations of Pd/Pd(1 1 1) system. We conclude that our computed results are in better agreement with the experimental data, than those of previous computational works. The temperature dependence of the mean-square displacements and the relaxation of both surface atoms and adatoms in the normal to the surface direction were also obtained.

First-principles FLAPW-GGA band structure calculations were employed to examine the structural, electronic properties and the chemical bonding picture for four ZrCuSiAs-like Th-based quaternary pnictide oxides ThCuPO, ThCuAsO, ThAgPO, and ThAgAsO. These compounds were found to be semimetals and may be viewed as "intermediate" systems between two main isostructural groups of superconducting and semiconducting 1111 phases. The Th 5f states participate actively in the formation of valence bands and the Th 5f states for ThMPnO phases are itinerant and partially occupied. We found also that the bonding picture in ThMPnO phases can be classified as a high-anisotropic mixture of ionic and covalent contributions: inside [Th2O2] and [M2Pn2] blocks, mixed covalent-ionic bonds take place, whereas between the adjacent [Th2O2]/[M2Pn2] blocks, ionic bonds emerge owing to [Th2O2] \to [M2Pn2] charge transfer.

Under cyclic loading, the plasticized zone becomes complicated; it contains in particular a second plasticized zone, resulting from the local compression which occurs at the time of the closing of the crack to each cycle. The two plastic zones, monotonous (rm) and cyclic (rc), are proportional to (Kmax/Re)2 et (ΔK/Re)2, respectively. The objective of this work is to study the evolution of the fatigue crack grown rate (FCGR) and the influence of the plastic zone size (rc), which represents the seat of the residual stresses, on this evolution in the case of 12NC6 steel. Generally, the plastic zone size increases with the crack advance. The FCGR can be correlated with the energy absorptive in these plastic zones.

The problems in design of functionally graded materials (FGMs) are outlined and their modelling approaches are reviewed. Due to the concentrational or structural gradients in FGMs, the “normal” approximations and models, used for traditional composites, are not directly applicable to graded materials. The goal is to show the efficiency of the simplest models to provide the most accurate estimates of the properties and even to make simple elasto-plastic analysis of FGM components without vast computations by FEMs or an array of empirical fitting parameters. The development of a micromechanical model for FGMs with an arbitrary non-linear 3D-distribution of phases and corresponding properties is presented and the model application is discussed in comparison with other similar approaches. The model allows the prediction of basic properties of a 3-D FGM, computations of thermal stresses, and, in some limits, it may be used for pre-design evaluation of dynamic strain/stress distribution and inelastic behaviour. Since all equations of the model are expressed in a simple analytical form, the model is rather flexible for computations and may be easily implemented. As an example, results for W–Cu FGM are presented for application of upper divertor plates for the international experimental thermonuclear reactor (ITER).

Using the density-functional approach, the geometries, stabilities, electronic properties, and magnetism of the YnSi (n = 2–14) clusters have been systematically investigated. The growth pattern for the different-sized YnSi (n = 2–14) clusters is Si-substituting Yn+1 clusters and keeps the similar frameworks of the most stable Yn+1 clusters. The Si atom substitutes the surface atom of the Yn+1 clusters for n < 8. Starting from n = 8, the Si atom completely falls into the center of the Y-frame. The Si atom substitutes the center atom of the Yn+1 clusters to form the Si-encapsulated Yn geometries for n > 8. The calculated results show that doping of Si atom contributes to strengthening the stabilities of the yttrium framework. In addition, the relative stability of Y12Si is the strongest among the investigated YnSi clusters, which might stem from its highest symmetry. Mulliken population analysis shows that charges always transfer from Y atoms to Si atom in all the YnSi (n = 2–14) clusters. Doping of Si atom decreases the magnetic moments of the most Yn clusters. In particular, the magnetic moment does quench completely after doping Si in Y13, which is ascribed to the disappearance of the itinerant 4d electron spin exchange effect. Finally, the frontier orbitals properties of YnSi are also discussed.Highlights►This paper systematically studied the electronic properties of the YnSi clusters. ► The results show that Si atom contributes to strengthening the stabilities of Yn. ► Mulliken population analyses show that charges always transfer from Y to Si atom. ► Doping of Si atom decreases the magnetic moment of the most Yn clusters.

In this paper, we study the effect of normal and shear strains and oxygen vacancies on the structure of 180° ferroelectric domain walls in PbTiO3. It is known that oxygen vacancies move to the domain walls and pin them. Hence, we assume a periodic arrangement of oxygen vacancies on both Pb-centered and Ti-centered domain walls in PbTiO3. We use a semi-analytic anharmonic lattice statics method for obtaining the relaxed configurations using a shell potential. In agreement with recent ab initio calculations, we observe that a Pb-centered domain wall with oxygen vacancies is not stable even under strain. Our semi-analytic calculations for PbTiO3 show that oxygen vacancies affect the structure of 180° domain walls significantly but do not have a considerable effect on the thickness of domain walls; they broaden the domain walls by about 50%. We also study the effect of normal and shear strains on both perfect and defective 180° domain walls. We observe that normal and shear strains affect the structure but do not change the domain wall thickness.

This paper gives a bibliographical review of the finite element methods applied to the analysis and simulation of quenching and other heat treatment processes. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subjects that were published between 1976 and 2001. The following topics are included: quenching––quenching process in general, heat transfer and thermomechanical modelling, residual stresses in quenching, and other topics; hardening; annealing; tempering; and carburizing and nitriding. Three hundred and fifty references are listed.

The paper gives a bibliographical review of the finite element analyses and simulations of manufacturing processes of composite materials and their mechanical properties from the theoretical as well as practical points of view. Topics include: filament winding process; braiding, weaving and knitting; fiber preforms and resin injection; pultrusion; compression molding; injection molding; extrusion and other specific manufacturing processes and processes in general. The bibliography at the end of this paper contains 954 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1985 and 2003.

The objective of this paper is to investigate the influence of solid-state phase transformation on the evolution of residual stress distributions in butt-welded modified 9Cr–1Mo steel pipes. A thermal elastic plastic finite element model taking into account the metallurgical phase transformation was developed. Effects on welding residual stress of the volumetric change and the yield strength change due to austenite–martensite transformation were investigated by means of numerical analysis. The simulated results show that the volumetric change and the yield strength change due to martensite transformation have influences on the welding residual stress. The former not only changes the magnitude of residual stress, but also alters the sign of residual stress in the weld zone; and the later only changes the magnitude of residual stress. In the cases in which the volumetric change due to phase transformation is considered, the simulated results are generally in good agreement with the experimental measurements.

The article is devoted to the discussion of the high-throughput approach to band structures calculations. We present scientific and computational challenges as well as solutions relying on the developed framework (Automatic Flow, AFLOW/ACONVASP). The key factors of the method are the standardization and the robustness of the procedures. Two scenarios are relevant: 1) independent users generating databases in their own computational systems (off-line approach) and 2) teamed users sharing computational information based on a common ground (on-line approach). Both cases are integrated in the framework: for off-line approaches, the standardization is automatic and fully integrated for the 14 Bravais lattices, the primitive and conventional unit cells, and the coordinates of the high symmetry k-path in the Brillouin zones. For on-line tasks, the framework offers an expandable web interface where the user can prepare and set up calculations following the proposed standard. Few examples of band structures are included. LSDA+U parameters (U, J) are also presented for Nd, Sm, and Eu. Comment: 16 pages, 48 figures, http://materials.duke.edu/

This is a 2D cellular automaton simulation study on the evolution of the recrystallization texture in a 75% cold rolled interstitial free (IF) sheet steel. The model is applied to experimentally obtained high resolution microtexture EBSD data. The simulation is discrete in time and physical space. Orientation is treated as a continuous variable in Euler space. The dislocation density distribution is approximated from the Kikuchi pattern quality of the experimental EBSD data. It is used for the calculation of the scalar driving force field required for the recrystallization simulation. Different models for nucleation and for the influence of Zener-type particle pinning are presented and tested. Real time and space calibration of the simulation is obtained by using experimental input data for the grain boundary mobility, the driving forces, and the length scale of the deformed microstructure as mapped by the high resolution EBSD experiments. The simulations predict the kinetics and the evolution of microstructure and texture during recrystallization. Depending on the ratio of the precipitated volume fraction and the average radius of the particles the simulations reveal three different regimes for the influence of particle pinning on the resulting microstructures, kinetics and crystallographic textures.

In this paper a method for the estimation of the curvature along a condensed phase interface is presented. In a previous paper in this journal [J.W. Bullard, E.J. Garboczi, W.C. Carter, E.R. Fuller Jr., Computational Materials Science 4 (1995) 103–116] a mathematical relationship was established between this curvature and a template disk located at a given point along the interface. The portion of the computed area of the template disk covering one of the phases was shown to be asymptotically linear in the curvature. Instead of utilizing this relationship, an empirical approach was proposed in Bullard et al. in order to compensate for discrete uncertainties. In this paper, we show that this linear relationship can be used directly along the interface avoiding the empirical approach proposed earlier. Modifications of the algorithm are however needed, and with good data smoothing techniques, our method provides good quantitative curvature estimates.

The successful integration of the binary collision code Crystal-TRIM into the 2D-process simulator DIGS as an optional module is reported. The new module is applied to the simulation of the formation of LDD-like structures. The use of a trajectory split method in combination with a mechanism for the lateral duplication of ion trajectories enables the simulation of the implantation step in extended targets with good depth and lateral resolution within reasonable computation times. (C) 1998 Elsevier Science B.V.

The Monte Carlo (MC) simulation of 2D geometrical disordered multitunnel junction arrays becomes cumbersome, when both array dimensions and temperature increase. It is therefore difficult to get statistical information on electrical parameters in the high temperature range. We have shown that a fair estimation of the electrical response of 2D disordered arrays can be obtained by taking only its minimal resistance path (MRP). In order to get a fair agreement with the straightforward MC simulation of the real 2D array, we use the real capacitance matrix to compute the charging energy. The net gain factor on the simulation time amounts to more than 25 for 5×5 arrays.

Two-dimensional random cellular structures are generated by coupling Voronoi and Monte Carlo algorithms in order to study the effect of cell irregularities on the elasticity parameters of biopolymer cellular solids. Firstly, the Voronoi technique provides the tessellation of the 2D space without producing discontinuities. Secondly, Monte Carlo strategy allows cell curvature to be generated. The Voronoi/Monte Carlo technique is able to represent various structural effects: cell density, elongation, local concentration as well as cell gradient and presence of defects. These effects are discussed in this paper based on the theory of cellular solids and finite element calculation. These numerical results should provide quantitatively correlations between the studied structural effects and effective properties of several natural biopolymer systems.

A new hybrid lattice particle modeling (HLPM) scheme is proposed. The particle–particle interaction is derived from lattice modeling (LM) theory, whereas the computational scheme follows particle modeling (PM) technique. The newly proposed HLPM considers different particle interaction schemes, involving not only particles in the nearest neighborhood, but also the second nearest neighborhood. Different mesh structures with triangular or rectangular unit cells can be used. The current paper is concerned with the mathematical derivations of elastic interaction between contiguous particles in 2D lattice networks, accounting for different types of linkage mechanism and different shapes of lattice. Axial (α) and combined axial-angular (α − β) models are considered. Derivations are based on the equivalence of strain energy stored in a unit cell with its associated continuum structure in the case of in-plane elasticity. Conventional PM technique was restricted to a fixed Poisson’s ratio and had a strong bias in crack propagation direction, as a result of the geometry of the adopted lattice network. The current HLPM is free from the above-mentioned deficiencies and can be applied to a wide range of impact and dynamic fracture failure problems. Although the current analysis is based on the linear elastic spring model, inelastic considerations can be easily implemented, as HLPM has the same force interaction scheme as PM, based on the Lennard–Jones potential.

Based on high-resolution digital images of High Performance Concrete (HPC) microstructures, a two-dimensional mesoscopic lattice model which accounts for fatigue damage is proposed. Fatigue damage is introduced by considering the coupled effects of loading cycles and tensile strain on stiffness degradation of microstructural lattice elements under fatigue loading. The ultimate tensile strain is defined as the failure threshold value for microstructural lattice elements. Further, the effects of the lattice element properties (i.e. size and finite element type) and fatigue loading parameters (i.e. stress levels) on the damage mechanisms of the HPC microstructure are investigated and discussed. It is found that lattice truss elements 1 mm long are satisfactory, giving also their smaller computational requirements in comparison to beam counterparts, to investigate fatigue damage in the HPC microstructure. The numerical results of the present model are consistent with experimental observations.

This paper develops a comprehensive methodology for generating realistic 3D polycrystalline microstructures followed by discretization into a 3D tetrahedral mesh for finite element (FE) analysis. With input data on crystallographic orientations for a series of grain sections, created by a dual beam focused ion beam-scanning electron microscope (DB-FIB) system, the reconstruction method uses primitives in CAD modeling based on hierarchical geometrical representation. It involves steps of data cleanup, interface point identification, parametric polynomial and NURBS function based surface patch reconstruction, generalized cell-decomposition, geometric defeaturing and gap-overlap removal. The implementation of the entire procedure is done with the user-programming facilities of a commercial CAD package Unigraphics NX3. The reconstruction algorithms are validated with various error criteria. Subsequently, a finite mesh generator is developed to consistently discretize the reconstructed polycrystalline domain into a finite element mesh with resolution control that is necessary for meaningful computational analysis in microstructure–property evaluation. The mesh generator is enriched with mesh quality improvement and degree of freedom reduction tools.

In this work, we present a reduction procedure for 3D models describing phase transformations in copper-based shape memory alloys (SMAs) and develop a robust numerical algorithm for the computational analysis of thin single-crystal slabs of these alloys. Starting from a general Landau-type 3D model for the SMA dynamics we have developed a new mathematical “slow manifold” model that allows us to describe effectively the main features of the thermomechanical behaviour of CuAlNi alloys. Results of the mathematical modelling of the thermomechanical fields in CuAlNi SMAs are discussed with numerical examples.

From the meso-mechanical point of view, the internal structure of a material considerably influences its plastic deformation pattern at the meso-scale level. 2D calculations have shown that the consideration of an internal structure in an explicit form allows us to describe some experimentally observed phenomena, such as plastic strain localisation, material fragmentation, shear and rotation of grain conglomerates, etc. Real structural effects are three-dimensional by nature and in many cases can not be simulated in the framework of a 2D model. It is, therefore, a challenge to perform 3D-modelling for meso-volume behaviour under loading, taking into account material internal structure, and to investigate the phenomena caused by structural effects. In this paper, a special routine to generate a 3D heterogeneous structure is proposed. To calculate a 3D polycrystalline test-piece under plane shock wave as an example, we solve a dynamic problem and obtain numerical solutions using the finite-difference method. The results of 3D simulations are analysed and compared with those for a 2D set.

The present paper considers 3D grain size distributions and how they evolve during and after recrystallisation and grain growth as investigated by a 3D Potts Monte Carlo (MC) model. Two particular cases have been studied: (i) the effects of anisotropy in grain boundary energy and boundary mobility on grain size distributions after recrystallisation and (ii) the effects of second phase particles on the size distributions after both recrystallisation and grain growth. The present 3D MC simulations have shown that anisotropy has a strong effect on the size distributions of grains after recrystallisation, however, mainly in terms of a large and increasing fraction of small grains with increasing anisotropy. After “correcting” for the unrealistic large number of small grains, the differences between the different cases become quite small, but based on an evaluation of the skewness in these “corrected” grain size distributions, a small shift from a normal towards a log-normal-like distribution is still indicated. Concerning the effect of particles, simulations have shown that for an increasing volume fraction of particles, the coarsened microstructures show a clear shift from a Gaussian like towards a log-normal-like distribution. This behaviour is observed both for grain growth alone and for recrystallisation and subsequent coarsening.

The overall elastic properties of fiber reinforced composite are of primary importance for practical applications. In order to obtain the overall elastic properties, a homogenization procedure based on continuum micro-mechanics is usually applied to a representative volume element (RVE) representative of the whole composite. In this study, we first employ a modified random sequential adsorption algorithm to generate the complex geometry of a random fiber composite. Second, we investigate the effect of the interaction between two over-crossing fibers on the overall elastic properties of the composite. Third, we evaluate the overall elastic material properties of the composite using the finite element method for continuum micro-mechanical analysis.

A hybrid model is suggested to discretely consider self forces and non-conservative effects in 3D dislocation dynamics. The dislocations are idealized as line defects in a homogeneous linear elastic medium. Each dislocation line consists of interconnected straight segments. The displacement and stress fields associated with the segments are formulated for general anisotropy and arbitrary crystal symmetry using Brown's theorem and the integral formalism in the version of Asaro and Barnett. The stress field of each dislocation is then computed through a linear superposition of the stress contributions of all segments. The dynamics are described by solving Newton's equation of motion for each portion of dislocation. The differential equations of the individual segments are coupled through the line tension which is discretely considered by calculating the self interaction force among the segments that belong to the same dislocation according to the concept of Brown. Non-conservative dislocation motion is introduced by considering the osmotic force that arises from emitting or adsorbing point defects at the climbing segment. The influence of temperature is introduced by regarding the crystal as a canonical ensemble and by including a stochastic Langevin force as proposed by Rönnpagel.

The 3D flow around a rigid spherical particle suspended in a Newtonian fluid and submitted to simple shear is numerically studied using Rem3D® finite element code. The sphere motion is imposed by a sticking contact between the sphere and the fluid. The effect of the particle size as compared with the finite dimension of the shear cell was investigated. The direct calculations show that 3D modelling is necessary to correctly predict the sphere behaviour. The proximity of the particle and the cell walls strongly affects the flow velocities, the sphere motion (increase of the rotation period of the sphere) and the stress field (change of orientation angle and increase of maximal local stresses).

Recent discoveries of stress corrosion cracking (SCC) in weldments including penetration nozzles at pressurized water reactors (PWRs) and boiling water reactors (BWRs) have raised concerns about safety and integrity of plant components. It is well known that welding residual stress is an important factor resulting in SCC in weldments. In the present work, both experimental method and numerical simulation technology are used to investigate the characteristics of welding residual stress distribution in penetration nozzles welded by multi-pass J-groove joint. An experimental mock-up is fabricated to measure welding residual stress at first. In the experiment, each weld pass is performed using a semi-circle balanced welding procedure. Then, a corresponding finite element models with considering moving heat source, deposition sequence, inter-pass temperature, temperature-dependent thermal and mechanical properties, strain hardening and annealing effect is developed to simulate welding temperature and residual stress fields. The simulation results predicted by the 3D model are generally in good agreement with the measurements. Meanwhile, to clarify the influence of deposition sequence on the welding residual stress, the welding residual stress field in the same geometrical model induced by a continuous welding procedure is also calculated. Finally, the influence of a joint oblique angle on welding residual stress is investigated numerically. The numerical results suggest that both deposition sequence and oblique angles have effect on welding residual stress distribution.

Computational micromechanical analysis of the influence of moisture, density and microstructure of latewood on its hydroelastic and shrinkage properties is carried out. The elastic properties of cell sublayers have been determined using the unit cell models as for fiber reinforced composites (two covered cylinders representative volume element, for S1, S2 and S3 sublayers) and rectangular embedded unit cells (for isotropic M and P sublayers). 3D hierarchical finite element models of softwood cells as a hexagon-shape-tube with multilayered walls were generated using parametric techniques. The results for elastic properties of cell sublayers obtained from the unit cell models, from the self-consistent method and Halpin-Tsai equations are compared, and good agreement between these methods was observed. A computational technique, based on the representation of moisture effect as equivalent temperature-caused effects, has been developed and employed to the modeling of the moisture-related changes of the elastic properties of cell layers. A series of computational experiments have been carried out. In the simulations, it was observed that the shrinkage coefficients of longitudinal direction increase with increasing MFAs in layer S2, while the reverse is true in the transverse plane. The shrinkage coefficients of wood depend strongly on the shape of the hexagon-shaped cells. Wood density has a strong effect on both the Young’s modulus and the transverse Young’s modulus.

In this paper, laboratory scale extrusion experiments carried out on AA6063 billets are compared to numerical simulations. The numerical simulations are performed with a general solute-dependent elasto-viscoplastic constitutive model based on a hyperbolic sine law, allowing for the quantification of pressure levels, strain rates and stresses. The parameters for the material model were determined with compression tests. The extrusion trials were performed isothermally at temperatures of 623 and 723 K and with two distinct material conditions. The results of the numerical simulations show good agreement with the experimental results. It turns out that local high strain rates (>40 s−1) have a significant influence on the extrusion pressure. However adequate test methods to provide constitutive data at these strain rates are very limited. At high temperatures the difference between material conditions had a considerably smaller influence on the extrusion experiments compared to the simulations. It is argued that this effect can be attributed to dynamic precipitation that occurred during the experiments under high temperature, high strain rate conditions.

The implementation of a method for systematic analysis of local atomic structure in combination with 3D computer graphics is described. The method, Common Neighbor Analysis, is a decomposition of the radial distribution function according to the local environment of the pairs of atoms and can provide direct interpretation of various features of the radial distribution function in terms of atomic structure. It can also be used to identify atoms in particular environment, such as FCC, HCP, BCC or icosahedral. We describe an application of this program to a study of crystal nucleation in a molten Cu slab. While the majority of atoms in the resulting crystals are classified as being FCC, stacking faults are observed and can be traced back to the near-critical nuclei.

Distribution of magnetic moments in the low-dimensional metallic structures has been studied theoretically on the basis of periodic Anderson model. Calculation of noncollinear magnetic order was performed in the Hartree-Fock approximation using tight binding real space recursion method. Iteration process includes self-consistent determination of population numbers for the electrons with different directions of the magnetic moments at given atom relatively to the fixed axis. Energies of all states corresponding to the different directions of magnetic moments at the atom under consideration have been calculated, and the state with minimal energy being accepted for the next step.Analytical transformations based on the generalised “zeros and poles method” were performed for the Green function that allows to avoid some time-consuming numerical procedures. It gives the possibility to develop efficient algorithm for the calculation of noncollinear magnetic structure of complex space nonhomogeneous systems.Calculations performed for the parameters corresponding to Fe and Cr show the qualitatively different dependencies of the magnetic moment magnitude and the energies of d-electrons on the angles, which define the direction of magnetic moments.

A finite element analysis of the large deformation of three-dimensional polycrystals is presented using pixel-based finite elements as well as finite elements conforming with grain boundaries. The macroscopic response is obtained through volume-averaging laws. A constitutive framework for elasto-viscoplastic response of single crystals is utilized along with a fully-implicit Lagrangian finite element algorithm for modeling microstructure evolution. The effect of grain size is included by considering a physically motivated measure of lattice incompatibility which provides an updated shearing resistance within grains. A domain decomposition approach is adopted for parallel computation to allow efficient large scale simulations. Conforming grids are adopted to simulate flexible and complex shapes of grains. The computed mechanical properties of polycrystals are shown to be consistent with experimental results for different grain sizes.

The knowledge of the mechanical behaviour of dry woven fabrics is necessary in many applications. The aim of this study is to recall the specificity of the mechanical behaviour of dry fabrics and to understand the local phenomena that influence the macroscopic behaviour. For this, 3D finite element analyses of elementary patterns are performed. These calculations are not classical due to the constitution of the yarns made of a lot of small fibres. The possible motions of the yarns allow changes of undulation leading to nonlinear biaxial tensile behaviour and the lack of most of the other stiffnesses. The specificities of the calculation in order to reach this behaviour are described. The model is compared to biaxial tests on several fabrics. Such a model allows to understand the phenomena implicated in the behaviour and the main aspects that lead to the specific behaviour of woven media. It can also bring a help for the design of new fabrics in changing some mechanical and geometrical parameters in order to get prescribed properties.

Using thermal spraying various surface coatings consisting of different material compositions can be manufactured. Besides different solid phases the resulting coating microstructure often contains a non-negligible amount of pores altering their mechanical properties. A common practice to analyze the porosity and composition of a coating is to create cross section images using standard light microscopy equipment or a scanning electron microscope. In this paper a method is presented to construct a three-dimensional multiphase model of the coating from a number of such cross section images by means of an image morphing technique. The resulting model can then be used for visualization purposes or further analysis e.g. within a finite element simulation.The described method has been applied to the construction of a finite element model of a porous coating sample which is used in a compaction simulation to determine its behavior in a rolling process. The required cross section images were obtained using a successive grinding and microscopy procedure. The material behavior of the porous material is modeled by using a modified Johnson–Cook material model formulation for an elasto-viscoplastic material. Comparison of 2D and 3D-simulation results are shown.

Based on experimental results, the dynamic recrystallization mathematical models of 42CrMo steel were derived. The effects of strain rates on the strain/stress distribution and microstructural evolution in 42CrMo steel during hot upsetting process were simulated by integrating the thermo-mechanical coupled finite element model. The results show that the deformation of the specimen is inhomogeneous, and the degree of the deformation inhomogeneity decreases with the increase of strain rates. The distribution of the effective stress in the specimen is also inhomogeneous, and the locus of the maximum effective stress changes with the variations of strain rates. The dynamic recrystallization volume fraction decreases with the increase of strain rates. The distribution of the dynamic recrystallization grain is inhomogeneous in the deformed specimen, and the average dynamic recrystallization grain size decreases as the strain rate is increased. A good agreement between the predicted and experimental results confirmed that the derived dynamic recrystallization mathematical models can be successfully incorporated into the finite element model to predict the microstructural evolution in the hot upsetting process for 42CrMo steel.

In order to study the workability and establish the optimum hot formation processing parameters for 42CrMo steel, the compressive deformation behavior of 42CrMo steel was investigated at the temperatures from 850 to 1150 °C and strain rates from 0.01 to 50 s−1 on Gleeble-1500 thermo-simulation machine. The results show that the true stress–true strain curves exhibit a peak stress at a small strain, after which the flow stresses decrease monotonically until high strains, showing a dynamic flow softening. The flow stress obtained from experiments consists of four different stage, i.e., Stage I (Work hardening stage), Stage II (Stable stage), Stage III (Softening stage) and Stage IV (Steady stage). The stress level decreases with increasing deformation temperature and decreasing strain rate, which can be represented by a Zener–Hollomon parameter in an exponent-type equation. A revised model describing the relationships of the flow stress, strain rate and temperature of 42CrMo steel at elevated temperatures is proposed by compensation of strain and strain rate. The stress–strain values of 42CrMo steel predicted by the proposed model well agree with experimental results, which confirmed that the revised deformation constitutive equation gives an accurate and precise estimate for the flow stress of 42CrMo steel.

To predict the damage evolution of anisotropic plastic voided ductile materials, Gurson–Tvergaard–Needleman (GTN) yield criterion is developed based on Hill’s quadratic anisotropic yield criterion (1948) and isotropic hardening rule for matrix material. A user-defined subroutine is developed using the above model. An implicit stress integration procedure is modified to adapt the explicit dynamic solver. After performing a series of single element tests, cylindrical tension and thick plate tension are analyzed. Then a benchmark of NUMISHEET’2002, i.e. deep drawing of cylindrical cup, is taken as an example of sheet metal forming. Comparisons are made among the von Mises constitutive model, isotropic and anisotropic plastic GTN damage models. It is found that plastic anisotropy of the matrix in ductile sheet metal has influence on both deformation behavior and damage evolution of the material.

Top-cited authors
• Friedrich Schiller University Jena
• University of Iceland
• Lawrence Berkeley National Laboratory
• Université Catholique de Louvain - UCLouvain
• University of California, Berkeley