Anisotropic Elastic Constants Research Articles

Porous CrO[formula omitted]: A ferromagnetic half-metallic member in sparse hollandite oxide family

A stable polymorph of CrO2 is predicted using PBE+U method. The porous material is isostructural with α−MnO2 making it the second transition metal oxide in sparse hollandite group of materials. However, unlike the anti-ferromagnetic semiconducting character of the α−MnO2, it is found to be a ferromagnetic half-metal. At Fermi level, the hole pocket has ample contribution from O−2p orbital, though, the electron pocket is mostly contributed by Cr−3dxy and Cr−3dx2−y2. A combination of negative charge transfer through orbital mixing and extended anti-bonding state near Fermi level is responsible for the half-metallic ferromagnetic character of the structure. A comparative study of rutile and hollandite CrO2 and hollandite MnO2 structures delineate the interplay between structural, electronic and magnetic properties. The material shows a robust magnetic character under hydrothermal pressure, as well as, the band topology is conserved under uniaxial strain. Moderate magneto-crystalline anisotropy is observed and it shows a correspondence with the anisotropy of elastic constants. Occurrence of type−II Weyl nodes and their evolution under pressure is explored.

Direct ink writing of woodpile-kind alumina phononic crystals for MHz regime

We report comprehensive work on the fabrication of alumina-based phononic crystals (PhCs) using direct ink writing (DIW), measurement of anisotropic properties, and identification of acoustic bandgaps. Woodpile-structure-kind PhCs of characteristic size 1.1 mm and 10 periods were fabricated from alumina and polyvinyl alcohol (PVA) solution, and processed by freezing under vacuum. Next, the anisotropic elastic constants of alumina were obtained from bulk specimens using resonant ultrasound spectroscopy. Band diagrams and transmission loss were computed using the finite-element method and good correlations were found between the bandgaps estimated by these methods. Multiple partial bandgaps and several local resonances were observed in many directions for frequencies below 2 MHz. This work is the first step toward developing ceramic PhC using additive manufacturing methods for high-temperature applications.

Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes

In this study, a new anisotropic elastic shell model with a nonlocal strain gradient is developed to investigate the vibrations of simply supported single-walled carbon nanotubes (SWCNTs). The Sanders–Koiter shell theory is used to obtain strain–displacement relationships. Eringen’s nonlocal elasticity and Mindlin’s strain gradient theories are adopted to derive the constitutive equations, where the anisotropic elasticity constants are expressed via Chang’s molecular mechanics model. An analytical method is used to solve the equations of motion and to obtain the natural frequencies of SWCNTs. First, the anisotropic elastic shell model without size effects is validated through comparison with the results of molecular dynamics simulations reported in the literature. Then, the effects of the nonlocal and material parameters on the natural frequencies of SWCNTs with different geometries and wavenumbers are analyzed. From the numerical simulations, it is confirmed that the natural frequencies decrease as the nonlocal parameter increases, while they increase as the material parameter increases. As new results, the reduction in natural frequencies with increasing SWCNT radius and the increase in natural frequencies with increasing wavenumber are both amplified as the material parameter increases, while they are both attenuated as the nonlocal parameter increases.

A computational study of nematic core structure and disclination interactions in elastically anisotropic nematics.

A singular potential method in the Q tensor order parameter representation of a nematic liquid crystal is used to study the equilibrium configuration of a disclination dipole. Unlike the well studied isotropic limit (the so called one constant approximation), we focus on the case of anisotropic Frank elasticity (bend/splay elastic constant contrast). Prior research has established that the singular potential method provides an accurate description of the tensor order parameter profile in the vicinity of a disclination core of a highly anisotropic lyotropic chromonic liquid crystal. This research is extended here to two interacting disclinations forming a dipole configuration. The director angle is shown to decay in the far field inversely with distance to the dipole as is the case in the isotropic limit, but with a different angular dependence. Therefore elastic constant anisotropy modifies the elastic screening between disclinations, with implications for the study of ensembles of defects as seen, for example, in active matter in the extended system limit.

Sensitivity-matrix-based identification of anisotropic elastic constants and microstructure features in plasma sprayed coatings utilizing ultrasonic back-reflection

With the unique lamellar microstructure, macroscopic elasticity of plasma sprayed coatings shows either positive or inverse anisotropy due to complex microstructure of inter-layer pores and intra-layer cracks. It is extremely difficult to nondestructively evaluate anisotropic elastic constants of these coatings with thin thickness. Moreover, it is an absolute challenge to reveal the elastic anisotropy transitions between positive and inverse. It is also difficult to clarify the nonlinear relationship between macroscopic elasticity and microstructure, which is necessary for microstructural identification. In present work, a sensitivity-matrix-based method was developed to determine five independent elastic constants of plasma sprayed coating by ultrasonic back-reflection method, with the relative errors of inverted elastic constants less than 1.33 %. Then, an optimized physical-descriptor-based microstructure characterization and reconstruction method was proposed to model “pore and crack” coatings with different microstructural features, and relative errors of microstructural features between the reconstructed and preset values were less than 4.35 %. Based on above, the dependences between six microstructural features and elastic constants were established. The inverse elastic anisotropy was explained systematically as the increase of vertical crack content, the “roundness” of horizontal pore and its “weakening” preferred orientation. Finally, the sensitivity-matrix-based method was used to simultaneously identify the porosity, crack content, pore average aspect ratio, pore orientation factor, and crack orientation factor of plasma sprayed Al2O3 coating based on elastic constants inverted. The relative errors in these identifications were less than 14.85 %. This work provides a new sensitivity-matrix-based solving strategy for multi-parameter integrated quantitative identification of complex microstructural features in materials.

First-principles calculation of the electronic, optical, and photo-electrochemical properties of CaM2S4 (M = Sc, Y) compounds

The orthorhombic CaM2S4 (M = Sc, Y) structures were investigated in the present work by first-principles calculations. CaM2S4 (M = Sc, Y) compounds are found to be mechanically stable with the anisotropic elastic constants that make them to be stable with respect to uniaxial deformation (Young’s moduli are 73.724 and 57.441 GPa for CaSc2S4 and CaY2S4, respectively) but easy to be undergone to shear deformation (Poisson’s ratios are 0.352 and 0.371 for CaSc2S4 and CaY2S4, respectively). Due to their relatively small direct energy band gaps (1.89 eV for CaSc2S4 and 2.26 eV for CaY2S4), the two compounds are intriguing candidates for long-wave transparency applications. The high hybridization degree of Ca-d, Y/Sc-d and S-p orbitals results in a wide energy range between the valence highest band and the conduction lowest band enabling these compounds to interact actively with visible and ultra-violet waves. The high absorption rate of 12–18 × 105 cm−1 and good hole-electron separation make CaM2S4 (M = Sc, Y) compounds to consider them good candidates for optoelectronic materials. Moreover, CaM2S4 (M = Sc, Y) compounds show good ability in the process of photo-driven photocatalyst water splitting.

First-principles calculations to study the effect of pressure on the structural and elastic properties of Sc3TC4(T = Ni,Os,Ru)

The effects of pressure on structure, the density of states, mechanical properties and elastic anisotropy of Sc3TC4(T = Ni,Os,Ru) were investigated using the CASTEP modular that is based on density functional theory. The results show that Sc3TC4(T = Ni,Os,Ru) has relatively high compressibility under pressure, and are mechanically stable. As the pressure increases, the anisotropic elastic constants and elastic moduli of the three materials increase. The stability of the three compounds increases with increase of pressure and satisfies: Sc3NiC4>Sc3OsC4>Sc3RuC4.

Computation of the thermal elastic constants for arbitrary manybody potentials in LAMMPS using the stress-fluctuation formalism

This paper describes the implementation of the stress-fluctuation technique into the LAMMPS code to compute the anisotropic thermal elastic constants tensor of materials. The implementation provides both methods for computing the analytical fluctuation expressions and also a generic numerical derivative method. The former makes the extension to new potentials straightforward, as it requires writing code only for the second derivatives of each energy term w.r.t. distance, angle, etc. The latter provides a generic interface to compute an accurate approximation of the elastic constants for any potential already implemented in LAMMPS. We show how both methods compare with the direct deformation computation in several test cases and discuss the implementation advantages and limitations.

CRSS determination combining ab-initio framework and Surrogate Neural Networks

Critical Resolved Shear Stress (CRSS), fundamentally linked to the dislocation glide stress, is a crucial measure in dictating plastic deformation in metallic materials. A recent ab-initio predictive model for dislocation glide stress in Face-Centered Cubic (FCC) materials is developed which accurately predicts available experimental data, considering the anisotropic continuum energy, the atomistic misfit energy, and the minimum energy path for the intermittent motion of Shockley partials. The CRSS of a material is predominantly controlled by six parameters, namely, lattice constant, unstable/stable stacking-fault energies, and three anisotropic elastic constants for cubic materials, which are inputs to the predictive model. In this work, a large material dataset is produced incorporating properties of real materials and generating hypothetical combinations, subsequently calculating the CRSS for each combination using the predictive model. The hypothetical combinations of properties are employed to train a machine learning-based Surrogate Neural Network (SNN), and the ones of real materials are utilized to validate the SNN model yielding a 94% accuracy for 1,033 materials. The generated dataset is used to unravel the sensitivity of each material parameter to the predicted CRSS establishing a general trend for the FCC materials for the first time guiding the field in achieving superior mechanical properties.

Nondestructive measurement of anisotropic elastic constants of selective laser melted 316L based on a tri-mode ultrasonic method

Selective laser melting (SLM) technology can rapidly form metal parts with complex geometry, but the internal microstructure and material properties are significantly different from those of traditionally manufactured parts, such as obvious anisotropy and inhomogeneity. This paper proposed a tri-mode ultrasonic system to nondestructively measure the anisotropic elastic constants of 316L stainless steel prepared by SLM. Firstly, the quantitative relationship between ultrasonic wave velocities and anisotropic elastic constants was derived for elliptical anisotropic materials. The anisotropic elastic constants and Thomsen anisotropic parameters can be determined by measuring four ultrasonic wave velocities , , , and . Therefore, a tri-mode ultrasonic transducer was designed and fabricated to build the elastic constant ultrasonic measurement system. Then, the elastic constants and Thomsen anisotropic parameters of SLM samples were measured, and the key process parameters’ influence was discussed. The standard static tensile test validated the result of the ultrasonic test, and the maximum relative error was 6.94%. This study will provide a novel nondestructive measurement method and system of anisotropic elastic constants to ensure internal quality and improve the additive manufacturing process.

Frequency-domain probe beam deflection method for measurement of thermal conductivity of materials on micron length scale.

Time-domain thermoreflectance and frequency-domain thermoreflectance (FDTR) have been widely used for non-contact measurement of anisotropic thermal conductivity of materials with high spatial resolution. However, the requirement of a high thermoreflectance coefficient restricts the choice of metal coating and laser wavelength. The accuracy of the measurement is often limited by the high sensitivity to the radii of the laser beams. We describe an alternative frequency-domain pump-probe technique based on probe beam deflection. The beam deflection is primarily caused by thermoelastic deformation of the sample surface, with a magnitude determined by the thermal expansion coefficient of the bulk material to measure. We derive an analytical solution to the coupled elasticity and heat diffusion equations for periodic heating of a multilayer sample with anisotropic elastic constants, thermal conductivity, and thermal expansion coefficients. In most cases, a simplified model can reliably describe the frequency dependence of the beam deflection signal without knowledge of the elastic constants and thermal expansion coefficients of the material. The magnitude of the probe beam deflection signal is larger than the maximum magnitude achievable by thermoreflectance detection of surface temperatures if the thermal expansion coefficient is greater than 5 × 10-6K-1. The uncertainty propagated from laser beam radii is smaller than that in FDTR when using a large beam offset. We find a nearly perfect matching of the measured signal and model prediction, and measure thermal conductivities within 6% of accepted values for materials spanning the range of polymers to gold, 0.1-300 W/(m K).

Improved lightweight corrugated network design to auxetic perforated metamaterial

Auxetic metamaterials with peanut-shaped perforations are superior for durable morphing control applications due to its extremely low stress concentration level and controllable auxetic capability. However, there are some issues to be concerned for such metamaterials with complex cellular features, including (1) improving structure topology for higher material efficiency, (2) tunable Poisson's ratio from positive to negative, (3) characterization of full elastic properties. To this end, an improved lightweight design with orthogonal corrugated beams is proposed in this study to approximate the perforated auxetic structure and then its full anisotropic elastic constants are characterized by a distinctive computational homogenization model based on the eigenfunction expansion variational theory with simple implementation technique of periodic displacement constraints. The numerical model is verified by the experimental tests of three specimens with different geometrical topologies. Subsequently, the dependence of structural elastic responses on the microstructural configuration is highlighted towards an elevated understanding of cell-structure-property relationship. It is demonstrated that the local in-plane rotation of interconnected regions in unit cell under uniaxial loading contributes to the structural auxetic behavior. Also, it is feasible to achieve tailorable mechanical properties through flexible microstructural adjustment and a design criterion of the crucial zero Poisson's ratio is given by a polynomial in terms of the normalized amplitude and thickness of the curved beam. The results pave a way to the design and analysis of novel metamaterials with tunable mechanical properties.

Ab initio thermo-elasticity of [formula omitted]-MH[formula omitted] (M[formula omitted]Zr, Ti)

In the present work, we report the results of a systematic ab initio study of the thermo-elastic properties of δ-MH1.5 (M=Zr, Ti). This investigation serves three purposes: (i) Elucidate the fully anisotropic temperature dependent elastic constants of hydrides, (ii) address discrepancies in thermal expansion data reported in the literature and (iii) provide input data for thermodynamic-based phase-transformation modelling. Due to a reduced contribution from the vibrational free energy to the strain energy, in agreement with experimental observations we find that the temperature dependent stiffness of hydrides vary to a much lesser degree than the matrix. For δ-ZrH1.5, we further find that Zener’s anisotropy ratio varies with temperature. Regarding the linear thermal expansion, our results indicate that it is highly temperature dependent. With the exception of a few outliers, our DFT data concurs well with experimental data, if the temperature range over which it was measured is taken into account.

Comparing the impact of thermal stresses and bubble pressure on intergranular fracture in UO[formula omitted] using 2D phase field fracture simulations

UO2 fuel fragmentation and pulverization during loss-of-coolant accidents (LOCAs) is an ongoing safety concern that has gained importance due to recent interest in increasing burnup limits for light water reactor fuel. In this work, we investigate the importance of bubble pressure on fragmentation using 2D phase field fracture simulations of UO2 polycrystals. The model includes anisotropic single crystal elastic constants, encourages intergranular fracture, and includes bubble pressure and its impact on crack opening. An external stress is applied that is representative of the internal stresses observed in macroscale BISON simulations of LOCA tests. Cracks do not form under the external applied stress in UO2 polycrystals without porosity. Crack nucleation and propagation do occur under the external applied stress in polycrystals with unpressurized 1 μm radius intergranular voids, and crack propagation accelerates with increasing number of voids. Crack nucleation and propagation also occur in polycrystals without the external applied stress if the intergranular pores are pressurized, and crack propagation is faster with both pressurized pores and the external applied stress. Our 2D results indicate that bubble pressure may not be necessary to initiate fragmentation in polycrystals with intergranular porosity under LOCA conditions, though this should be verified using 3D simulations with fewer assumptions.

Lens-shaped nematic liquid crystal droplets with negative dielectric anisotropy in electric and magnetic fields

ABSTRACT Recently, plano-convex spherical lens-shaped liquid crystal (LC) sessile droplets with positive dielectric anisotropy were studied in magnetic and/or AC electric fields. Here, we present experimental observations in magnetic, AC electric, combined fields and theoretical considerations of plano-convex lens-shaped nematic LC droplets with negative dielectric anisotropy. In purely magnetic field, our results are the same as for positive materials, i.e. an inversion wall forms normal to the field that moves towards the periphery. In contrast to previous observations on nematic LCs with positive dielectric anisotropy, in electric fields applied normal to the base plane, we do not find any wall formation, but only a radial director structure with a central defect line along the field. Above a threshold electric field, the radial symmetry becomes twisted due to elastic constant anisotropy. Applying a magnetic field perpendicular to the vertical electric field, a twisted inversion wall forms together with a vertical central defect line. When the electric field is applied parallel to the base plane of the droplet, a homeotropic central region forms along the electric field. When this field is applied together with a magnetic field applied in the same direction, the homeotropic central region becomes perpendicular to the applied field.

Measurement of the Anisotropic Dynamic Elastic Constants of Additive Manufactured and Wrought Ti6Al4V Alloys.

Additively manufactured (AM) materials and hot rolled materials are typically orthotropic, and exhibit anisotropic elastic properties. This paper elucidates the anisotropic elastic properties (Young’s modulus, shear modulus, and Poisson’s ratio) of Ti6Al4V alloy in four different conditions: three AM (by selective laser melting, SLM, electron beam melting, EBM, and directed energy deposition, DED, processes) and one wrought alloy (for comparison). A specially designed polygon sample allowed measurement of 12 sound wave velocities (SWVs), employing the dynamic pulse-echo ultrasonic technique. In conjunction with the measured density values, these SWVs enabled deriving of the tensor of elastic constants (Cij) and the three-dimensional (3D) Young’s moduli maps. Electron backscatter diffraction (EBSD) and micro-computed tomography (μCT) were employed to characterize the grain size and orientation as well as porosity and other defects which could explain the difference in the measured elastic constants of the four materials. All three types of AM materials showed only minor anisotropy. The wrought (hot rolled) alloy exhibited the highest density, virtually pore-free μCT images, and the highest ultrasonic anisotropy and polarity behavior. EBSD analysis revealed that a thin β-phase layer that formed along the elongated grain boundaries caused the ultrasonic polarity behavior. The finding that the elastic properties depend on the manufacturing process and on the angle relative to either the rolling direction or the AM build direction should be taken into account in the design of products. The data reported herein is valuable for materials selection and finite element analyses in mechanical design. The pulse-echo measurement procedure employed in this study may be further adapted and used for quality control of AM materials and parts.

Determination of Constitutive Parameters of Crystal Plasticity using Micro-pillar Testing with Pure Aluminum

The uniaxial compression test using the micrometer-sized specimen is employed to evaluate elastic-plastic deformation behavior of the selective single crystal from polycrystalline materials. Through reflecting these properties into the crystal plasticity finite element method (CPFEM), elastic-plastic analyses of the polycrystalline materials can be performed based on the single crystalline properties of real materials. In this study, the micro-pillar compression tests were conducted in the some single crystals of recrystallized polycrystalline pure aluminum. A method identifying CRSS, work hardening parameters and anisotropic elastic constants was proposed. The predicted stress-strain curves of single crystals obtained by CPFEM agree well with the original experimental data.

Determination of anisotropic elastic parameters from morphological parameters of cancellous bone for osteoporotic lumbar spine

In biomechanics, large finite element models with macroscopic representation of several bones or joints are necessary to analyze implant failure mechanisms. In order to handle large simulation models of human bone, it is crucial to homogenize the trabecular structure regarding the mechanical behavior without losing information about the realistic material properties. Accordingly, morphology and fabric measurements of 60 vertebral cancellous bone samples from three osteoporotic lumbar spines were performed on the basis of X-ray microtomography (μCT) images to determine anisotropic elastic parameters as a function of bone density in the area of pedicle screw anchorage. The fabric tensor was mapped in cubic bone volumes by a 3D mean-intercept-length method. Fabric measurements resulted in a high degree of anisotropy (DA = 0.554). For the Young’s and shear moduli as a function of bone volume fraction (BV/TV, bone volume/total volume), an individually fit function was determined and high correlations were found (97.3 ≤ R2 ≤ 99.1,p < 0.005). The results suggest that the mathematical formulation for the relationship between anisotropic elastic constants and BV/TV is applicable to current μCT data of cancellous bone in the osteoporotic lumbar spine. In combination with the obtained results and findings, the developed routine allows determination of elastic constants of osteoporotic lumbar spine. Based on this, the elastic constants determined using homogenization theory can enable efficient investigation of human bone using finite element analysis (FEA).Graphical Cancellous Bone with Fabric Tensor Ellipsoid representing anisotropy and principal axis (colored coordinate system) of given trabecular structure

FEA-Based Ultrasonic Focusing Method in Anisotropic Media for Phased Array Systems

Traditional ultrasonic imaging methods have a low accuracy in the localization of defects in austenitic welds because the anisotropy and inhomogeneity of the welds cause distortion of the ultrasonic wave propagation paths in anisotropic media. The distribution of the grain orientation in the welds influences the ultrasonic wave velocity and ultrasonic wave propagation paths. To overcome this issue, a finite element analysis (FEA)-based ultrasonic imaging methodology for austenitic welds is proposed in this study. The proposed ultrasonic imaging method uses a wave propagation database to synthetically focus the inter-element signal recorded with a phased array system using a delay-and-sum strategy. The wave propagation database was constructed using FEA considering the grain orientation distribution and the anisotropic elastic constants in the welds. The grain orientation was extracted from a macrograph obtained from a dissimilar metal weld specimen, after which the elastic constants were optimized using FEA with grain orientation information. FEA was performed to calculate a full matrix of time-domain signals for all combinations of the transmitting and receiving elements in the phased array system. The proposed approach was assessed for an FEA-based simulated model embedded in a defect. The simulation results proved that the newly proposed ultrasonic imaging method can be used for defect localization in austenitic welds.

Bayesian inference of elastic constants and texture coefficients in additively manufactured cobalt-nickel superalloys using resonant ultrasound spectroscopy

Bayesian inference with sequential Monte Carlo is used to quantify the orientation distribution function coefficients and to calculate the fully anisotropic elastic constants of additively manufactured specimens from only the experimentally-measured resonant frequencies. The parallelizable and open-source SMCPy Python package enabled Bayesian inference within this new modeling framework, resulting in an order of magnitude reduction of the computation time for an 8-core machine. Residual stress-induced shifts on the resonant frequencies were explicitly accounted for during the Bayesian inference, enabling the estimation of their effect on the resonant frequencies without a stress-relief heat treatment. Additively manufactured cobalt-nickel-base superalloy (SB-CoNi-10C) specimens were sectioned at multiple inclinations relative to the build direction and scanned with resonant ultrasound spectroscopy to demonstrate characterization of any arbitrarily textured cubic microstructure through the resonant frequencies. The orientation distribution function coefficients of the textured polycrystalline microstructure were estimated in tensorial form to calculate both the 2nd order Hashin-Shtrikman bounds and the self-consistent estimate of the elastic constants, enabling accurate determination of all 21 possible independent elastic constants through the convergence constraints of the texture. Pole figures generated directly from the calculated texture coefficients showed good agreement with experimentally measured textures.