Elastic Anisotropy Of Crystal Research Articles

A new criterion for formation capability of annealing twin in face-centered cubic metals/alloys

Annealing twins (ATs) are prevalent in face-centered cubic (FCC) metals/alloys and significantly influence their mechanical properties. Therefore, understanding the formation capability of ATs is crucial for controlling the mechanical properties of FCC metals/alloys. Although the "Stacking Fault Energy" is a widely used factor to characterize AT formation capability, it doesn't comprehensively explain the observed experimental rankings of AT formation capability. In this study, through a combination of experiments and molecular dynamics simulations, we demonstrated that AT growth is primarily driven by the migration of the Σ3 incoherent twin boundary. This migration arises from the elastic strain energy imbalance between grains on either side of the twin boundary caused by the elastic anisotropy of crystal. Based on these findings, we propose a new criterion, defined as a ratio of the coherent twin boundary energy to the anisotropy factor, to represent the AT formation capability (inverse relationship). Such new criterion well explains the experimental observation, and can be generalized to the zero macroscopic strain deformation twin.

Numerical simulation of the effects of elastic anisotropy and grain size upon the machining of AA2024

ABSTRACTTurning modeling and simulation of different metallic materials using the commercially available Finite Element (FE) softwares is getting prime importance because of saving of time and money in comparison to the costly experiments. Mostly, the numerical analysis of machining process considers a purely isotropic behavior of metallic materials; however, the literature shows that the elastic crystal anisotropy is present in most of the ‘so-called’ isotropic materials. In the present work, the elastic anisotropy is incorporated in the FE simulations along with the effect of grain size. A modified Johnson-Cook ductile material model based on coupled plasticity and damage evolution has been proposed to model the cutting process. The simulation results were compared with experimental data on the turning process of Aluminum alloy (AA2024). It was found that the elastic anisotropy influences the average cutting force up to 5% as compared to the isotropic models while the effect of grain size was more pronounced up to 20%.

Density functional theory study of a new Bi-based (K1.00)(Ba1.00)3(Bi0.89Na0.11)4O12 double perovskite superconductor

A new single-phase double perovskite superconductor (K1.00)(Ba1.00)3(Bi0.89Na0.11)4O12 with a Tc∼31.5K has been recently synthesized via the hydrothermal route. In the present study, we employ DFT (density functional theory) calculations to investigate the properties (structural, mechanical, electronic, Fermi surface, charge density) of this new superconductor. The calculated lattice constant is in good agreement with the experimental result. The elastic constants, bulk modulus, shear modulus, Young’s modulus, elastic anisotropy of crystal, Peierls stress, and Debye temperature are calculated and used to explain the mechanical behavior of this newly synthesized perovskite. The calculated electron density of states (DOS) indicates strong ionic interactions that are present in the Na-O-Bi planes. Both the electron and hole like bands form the Fermi surface and exhibit the multi-band nature of the compound. The electron charge density map shows the isotropic nature of charge distribution.

Structural and elastic anisotropy of crystals at high pressures and temperatures from quantum mechanical methods: The case of Mg2SiO4 forsterite.

We report accurate ab initio theoretical predictions of the elastic, seismic, and structural anisotropy of the orthorhombic Mg2SiO4 forsterite crystal at high pressures (up to 20 GPa) and temperatures (up to its melting point, 2163 K), which constitute earth's upper mantle conditions. Single-crystal elastic stiffness constants are evaluated up to 20 GPa and their first- and second-order pressure derivatives reported. Christoffel's equation is solved at several pressures: directional seismic wave velocities and related properties (azimuthal and polarization seismic anisotropies) discussed. Thermal structural and average elastic properties, as computed within the quasi-harmonic approximation of the lattice potential, are predicted at high pressures and temperatures: directional thermal expansion coefficients, first- and second-order pressure derivatives of the isothermal bulk modulus, and P-V-T equation-of-state. The effect on computed properties of five different functionals, belonging to three different classes of approximations, of the density functional theory is explicitly investigated.

Pressure effect on elastic anisotropy of crystals from ab initio simulations: the case of silicate garnets.

A general methodology has been devised and implemented into the solid-state ab initio quantum-mechanical Crystal program for studying the evolution under geophysical pressure of the elastic anisotropy of crystalline materials. This scheme, which fully exploits both translational and point symmetry of the crystal, is developed within the formal frame of one-electron Hamiltonians and atom-centered basis functions. Six silicate garnet end-members, among the most important rock-forming minerals of the Earth's mantle, are considered, whose elastic anisotropy is fully characterized under high hydrostatic compressions, up to 60 GPa. The pressure dependence of azimuthal anisotropy and shear-wave birefringence of seismic wave velocities for these minerals are accurately simulated and compared with available single-crystal measurements.

On the influence of steel microstructure on short crack growth under cyclic loading

The fatigue behaviour of microstructurally short cracks in a structural steel was experimentally characterised. The so-called load increasing testing technique was applied on notched bending specimens and allowed for initiation of short micro cracks. Propagation of these cracks was observed and analysed using light optical and scanning electron microscopes in defined intervals of load cycles. A 2D mechanism-oriented model to simulate the fatigue growth of micro cracks is presented. The bulk material is discretised by extended finite elements which allow for crack initiation and propagation along an arbitrary, solution-dependent path. The two-phase microstructure morphology and the elastic crystal anisotropy in the neighbourhood of the crack are considered. An overview of the strategy for analysis of the influence of several microstructural features on fatigue damage development using the presented model is given.

A framework for numerical integration of crystal elasto-plastic constitutive equations compatible with explicit finite element codes

In this paper we summarize the elements of a numerical integration scheme for elasto-plastic response of single crystals. This is intended to be compatible with large-scale explicit finite element codes and therefore can be used for problems involving multiple crystals and also overall behavior of polycrystalline materials. The steps described here are general for anisotropic elastic and plastic response of crystals. The crystallographic axes of the lattice are explicitly stored and updated at each time step. A plastic predictor–elastic corrector scheme is used to calculate the plastic strain rates on all active slip systems based on a rate-dependent physics-based constitutive model without the need of further auxiliary assumptions. Finally we present the results of numerous calculations using a physics-based rate- and temperature-dependent model of copper and the effect of elastic unloading, elastic crystal anisotropy, and deformation-induced lattice rotation are emphasized.

Influence of Crystal Grain on Stress Intensity Factor of Microstructurally Small Cracks

If crack size is in the order of several grain diameters or smaller, the stress intensity factor (SIF), which brings about change in crack growth behavior, is affected by various factors caused by the grain. For example, kinks and bifurcations of cracks at grain boundary triple points vary the SIF when the crack runs along grain boundaries. The elastic anisotropy of crystals and inhomogeneous stress distribution at the microstructural level in a polycrystalline body also bring about changes in the SIF. In this paper, such influences of the crystal grain on the SIF are reviewed. Firstly, the SIF of kinked or branched cracks is outlined. Secondly, the SIF of cracks in an anisotropic body as well as inhomogeneous polycrystalline body is summarized. In particular, statistical changes in SIF are shown as a function of crack size. Finally, based on the results obtained, statistical changes in the SIF and their influence on the growth of the microstructurally-small-crack are discussed.

Analysis of Powder X-ray Diffraction Data Obtained under Uniaxial Stress Field.

High pressure in situ X-ray diffraction measurements have been carried out using Drickamer-type high pressure apparatus. Observations were made in two independent directions relative to the compression axis. Observed strains varied systematically in the two directions depending on the Miller indices of the diffraction lines. These systematic variations can be explained by the combined effect of uniaxial compression and the elastic anisotropy of crystals. Present results indicate that careful analysis is required to derive pressure value and equation of state from in situ X-ray diffraction study.

Driving force for grain boundary migration during electromigration: Effect of elastic anisotropy

Electromigration in thin metal films leads to internal stresses. Elastic crystal anisotropy may cause a distinct gradient of these stresses across the grain boundary if the adjacent grains have different orientations relative to the grain boundary and to the substrate. The stress gradient gives rise to a driving force for grain boundary migration. This driving force is proportional to the crystal anisotropy parameter and to the dilatation caused by electromigration. At typical values of the parameters the driving force is comparable to the driving force caused by the curvature when the radius of curvature is about 10{micro}m. The anisotropy driving force may cause low temperature recrystallization, especially in the regions where internal stresses are about the threshold value, or exceed it, and it may lead to an increase in the number of symmetrical grain boundaries during electromigration in the near-anode zone of interconnect lines.

The Voigt-Reuss-Hill Approximation and Elastic Moduli of Polycrystalline MgO, CaF2, β-ZnS, ZnSe, and CdTe

The Voigt-Reuss-Hill (VRH) approximation, a useful scheme by which anisotropic single-crystal elastic constants can be converted into isotropic polycrystalline elastic moduli, is shown to apply for moderately anisotropic cubic crystals like MgO, CaF2, β-ZnS, ZnSe, and CdTe. Experimental values of polycrystalline isotropic elastic moduli for these materials are presented here, and the validity of the VRH approximation is established. The VRH approximation is then discussed for these materials with respect to their elastic anisotropy of crystals. To provide further support to this work, a numerical confirmation on the VRH moduli is made with the use of a high-speed computer by calculating the mean velocity of sound in crystals and comparing this result with the corresponding quantity calculated from the actual polycrystalline elastic moduli. The general agreement is observed.