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Crystals 13(3), 419 (2023). doi:10.3390/cryst13030419, This work deals with non-linear d$^{hkl}$−sin$^2\psi$ distributions, often observed in X-ray residualstress analysis of plastically deformed metals. Two different alloys were examined: duplex stainlesssteel EN 1.4362 with an austenite:ferrite volume ratio of 50:50 and ferritic stainless steel EN 1.4016.By means of an in situ experiment with high-energy synchrotron X-ray diffraction, the phase-specificlattice strain response under increasing tensile deformation was analysed continuously with a samplingrate of 0.5 Hz. From Debye–Scherrer rings of nine different lattice planes {hkl}, the d$^{hkl}$−sin$^2\psi$ distributions were evaluated and the phase-specific stresses were calculated. For almost all latticeplanes investigated, oscillating courses in the d$^{hkl}$−sin$^2\psi$ distributions were observed, already occurringbelow the macro yield point and increasing in amplitude within the elasto-plastic region. Bycomparing the loaded and the unloaded state after deformation, the contribution of crystallographictexture and plastically induced intergranular strains to these oscillations could be separated. For thegiven material states, only a minor influence of crystallographic texture was observed. However, astrong dependence of the non-linearities on the respective lattice plane was found. In such cases, astress evaluation according to the sin$^2\psi$ method leads to errors, which increase significantly if only alimited y range is considered., Published by MDPI, Basel

The structural, mechanical, and thermodynamic properties of refractory metals Rh, Ir, W, Ta, Nb, Mo, Re, and Os have been systematically investigated by first-principles calculations based on density functional theory. Comparative studies reveal that Young's modulus (E = 636.42 GPa), shear modulus (G = 256.81 GPa), bulk modulus (B = 406.55 GPa), and microhardness (H = 44.69 GPa) of hexagonal Os are the highest, which reveals Os has the best overall mechanical properties. The body-centered cubic Nb has the smallest Young's modulus (E = 94.76 GPa), shear modulus (G = 33.62 GPa), bulk modulus (B = 174.50 GPa), and hardness (H = 2.04 GPa). Based on the ratio of bulk to shear modulus, it is judged that Rh, Ir, and Os are brittle materials (B/G < 1.75), and Nb, Ta, Mo, W, and Re exhibit ductile (B/G > 1.75). The elastic anisotropy has also been discussed by plotting both the 3D contours and the 2D planar projections of Young's modulus. For the face-centered cubic metals Rh and Ir and hexagonal close-packed metals Re and Os, the 3D contours of the Young's modulus are very similar, whereas body-centered cubic metals Ta, W, Nb, and Mo exhibit significant difference in elastic anisotropy. The thermodynamic calculations show that Debye temperature and minimum thermal conductivity decreases along Rh, Os, Mo, Ir, Re, W, Ta, Nb sequence. Furthermore, the results can be used as a general guidance for the design and development of high temperature refractory alloy system.

The paper analyzes Poisson’s ratios μ0=μ100,001=-s12/s11 and elastic anisotropy factor A'=s/s11 (s=s11-s12-s44/2) for single crystal materials of binary and three-component TiNi-TiFe alloys with gradually deteriorating resistance first to one B2-R and further to two martensite transformations B2-R-B19'. The study discusses a ratio H/E of TiNi-TiFe alloys both subject and not exposed to martensite transformations. Surprisingly, this ratio exceeds 0.035 for alloys with martensite transformations, being far higher than in the majority of metals and alloys.

Portlandite, Ca(OH)2, is a primary product in cement hydration, on which some biases or misconceptions persist, such as portlandite has inferior mechanical properties because of its layered microst...

Using first-principles calculations, we predict highly stable cubic bialkali bismuthides Cs(Na, K)2Bi with several technologically important mechanical and anisotropic elastic properties. We investigate the mechanical and anisotropic elastic properties under hydrostatic tension and compression. At zero pressure, CsK2Bi is characterized by elastic anisotropy with maximum and minimum stiffness along the directions of [111] and [100], respectively. Unlike CsK2Bi, CsNa2Bi exhibits almost isotropic elastic behavior at zero pressure. We found that hydrostatic tension and compression change the isotropic and anisotropic mechanical responses of these compounds. Moreover, the auxetic nature of the CsK2Bi compound is tunable under pressure. This compound transforms into a material with a positive Poisson’s ratio under hydrostatic compression, while it holds a large negative Poisson’s ratio of about −0.45 along the [111] direction under hydrostatic tension. An auxetic nature is not observed in CsNa2Bi, and Poisson’s ratio shows completely isotropic behavior under hydrostatic compression. A directional elastic wave velocity analysis shows that hydrostatic pressure effectively changes the propagation pattern of the elastic waves of both compounds and switches the directions of propagation. Cohesive energy, phonon dispersion, and Born–Huang conditions show that these compounds are thermodynamically, mechanically, and dynamically stable, confirming the practical feasibility of their synthesis. The identified mechanisms for controlling the auxetic and anisotropic elastic behavior of these compounds offer a vital feature for designing and developing high-performance nanoscale electromechanical devices.

The ionic transport and the mechanical properties in solids are intimately related. However, few studies have been done to elucidate the background of that relation. With the objective to fill this gap and gain further understanding on the fundamental properties of ion conducting materials, we are studying systematically the mechanical properties of different materials. In the present study, after showing briefly our previous results obtained in crystalline materials, results regarding the relation between ionic conduction and mechanical properties in superionic glasses is presented. All these results indicate the intimate relation between the mechanical and ionic conduction. The results also indicate that the Grüneisen parameter and the Anderson–Grüneisen parameter of ionic conductors exhibit large temperature dependence and increase with temperature.

The zone-center phonon frequencies and the elastic properties of six ternary chalcopyrite compounds represented by ABSe2 (A = Cu and Ag; B = Al, Ga and In) are systematically calculated by using the rigid ion model. In the present paper, we calculate four bond-stretching and three bond-bending interactions, along with three effective dynamical charges. The calculated results are compared and found to be in fairly good agreement with the available experimental and theoretical results. The elastic anisotropy of the studied compounds is analyzed and visualized by plotting three-dimensional surfaces representing the directional dependences of Young's modulus.

First-principles calculations were used to estimate the anisotropic elastic and thermal properties of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) M2AX phases. The crystals’ elastic properties were computed using the Voigt-Reuss-Hill approximation. Firstly, the material’s elastic anisotropy was explored, and its mechanical stability was assessed. According to the findings, Ti2lnC, Ti2lnN, Zr2lnC, and Zr2lnN are all brittle materials. Secondly, the elasticity of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) M2AX phase are anisotropic, and the elasticity of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) systems are different; the order of anisotropy is Ti2lnN > Ti2lnC, Zr2lnN > Zr2lnC. Finally, the elastic constants and moduli were used to determine the Debye temperature and sound velocity. Ti2lnC has the maximum Debye temperature and sound velocity, and Zr2lnN had the lowest Debye temperature and sound velocity. At the same time, Ti2lnC had the highest thermal conductivity.

A high-priority target in the design of new metallic materials for load-bearing implant applications is the reduction of Young's modulus approximating that of cortical bone in the predominant loading direction. Here, we explore how directionally preferential bulk elastic properties of implant materials are achieved by harnessing elastic anisotropy. Specifically focusing on recently proposed biocompatible refractory high-entropy alloys (RHEAs) in the body-centered cubic structure, we conduct systematic densityfunctional theory calculations to investigate the single-crystal elastic properties of 21 Ti-containing RHEAs. Our results provide evidence that the valence electron count has a dominant influence on elastic anisotropy and crystal directions of low Young's modulus and high torsion modulus in the RHEAs. By means of modeling the orientation distribution function for crystallographic texture, we examine the effect of non-random texture on the anisotropic poly-crystalline Young's modulus and torsion modulus with varying texture sharpness. We adopt fiber textures that can result from rolling and distinct texture orientations that can form during rapid directional solidification. We discuss the potential for lowering Young's modulus in the RHEAs by using single crystals or textured aggregates. Furthermore, we prepare four of the theoretically considered alloys by arc-melting and report their lattice parameters, quasi isotropic Young's moduli, and Wickers hardnesses. (c) 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

The aim of this study was to test the isotropic behavior hypothesis for concrete by means of wave propagation tests. The elastic properties of the concrete were determined using ultrasound ...

Three direct semiconductor materials and one indirect semiconductor material, Pm&minus, 3n XN (X = B, Al, Ga, In), are investigated in our work, employing density functional theory (DFT), where the structural properties, stability, elastic properties, elastic anisotropy properties and electronic properties are included. The shear modulus G and bulk modulus B of Pm&minus, 3n BN are 290 GPa and 244 GPa, respectively, which are slightly less than the values of B and G for c-BN and Pnma BN, while they are larger than those of C64 in the I41/amd phase. The shear modulus of Pm&minus, 3n BN is the greatest, and the shear modulus of C64 in the I41/amd phase is the smallest. The Debye temperatures of BN, AlN, GaN and InN are 1571, 793, 515 and 242 K, respectively, using the elastic modulus formula. AlN has the largest anisotropy in the Young&rsquo, s modulus, shear modulus, and Poisson&lsquo, s ratio, BN has the smallest elastic anisotropy in G, and InN has the smallest elastic anisotropy in the Poisson&rsquo, s ratio. Pm&minus, 3n BN, AlN, GaN and InN have the smallest elastic anisotropy along the (111) direction, and the elastic anisotropy of the E in the (100) (010) (001) planes and in the (011) (101) (110) planes is the same. The shear modulus and Poisson&rsquo, s ratio of BN, AlN, GaN and InN in the Pm&minus, 3n phase in the (001), (010), (100), (111), (101), (110), and (011) planes are the same. In addition, AlN, GaN and InN all have direct band-gaps and can be used as a semiconductor within the HSE06 hybrid functional.

The influence of plastic deformation of low-carbon steel on birefringence of the shear waves birefringence is examined. Acoustic measurements show that the birefringence changes monotonously, while the intensity of the change decreases with increasing strain. Significant reduction of the birefringence is found to indicate that the capability to plastic deformation has been largely used. In order to explain the experimental results, computer simulations of the crystallographic texture of a polycrystalline material, and its change during plastic deformation, have been carried out. It has been found that internal stresses due to the presence of mesodefects, accumulating at grain boundaries, have a significant effect on the crystallographic texture and the birefringence. Thus, this effect allows one condition monitoring of a plastically deformed low-carbon steels under plastic deformation.

The transformations of the shear (SH and SV) and longitudinal (L) acoustic waves at the twist boundary in piezoelectrics of 62m and 42m the and classes have been investigated. This boundary is formed at a hard contact between two identical crystal half-spaces rotated relative to each other around the Z||6||4 axis by an angle 2ϕ. Propagation occurs along the bisector of this angle (х axis) in the (x, y) twist plane. Situations have been established in which the shear modes are localized at the twist boundary exclusively due to the combination of the piezoelectric effect and half-space rotation, as well as the joint effect of the elastic anisotropy and rotation. The cases of independence of a bulk wave of the half-space rotation and occurrence of leaky waves are described.

A recent finite-element method (FEM)-based study from the present authors quantified the effect of elastic anisotropy of grains on stress intensification at potential intergranular stress corrosion cracking (IGSCC) initiation sites in austenitic stainless steels. In particular, it showed that the auxetic behavior of grains (negative Poisson's ratio) in some directions plays a very important role in IGSCC initiation, since it can induce local stress intensification factors of about 1.6. A similar effect is expected for other fcc alloys such as Ni-based alloys. The present article confirms those results and paves the way to the definition of an IGSCC susceptibility index by identifying grain configurations that are the most favorable for crack initiation. The index will rely on the probability to get those configurations on surface of specimens.

Turning 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 com...

Microtextured regions are known to have a detrimental effect on the fatigue performance of near α and α/β titanium alloys. Due to the elastic anisotropy of α titanium, stress heterogeneities are expected to result from such microstructural features. The present work is an assessment of their influence on the elastic stress field, using Fast Fourier Transform-based computations on a 2D extruded aggregate built from a real microstructure. The contribution of the microtextured regions was then isolated by comparing simulations obtained on a synthetic aggregate with similar grain morphology and texture but removed microtextured regions through a redistribution of crystalline orientations. The analysis of the computed fields revealed that the average stress experienced by α grains is only weakly affected by the neighborhood and mostly determined by the elastic anisotropy of α titanium. Nevertheless, complex mechanical interactions between microtextured regions were evidenced. Indeed, load partitioning and non-local influence on the stress field were found to result from the presence of microtextured regions. The implications on fatigue crack initiation are discussed in light of these results. Keywords: FFT, EBSD, Micromechanics, Titanium alloys, Microtextured regions, Macrozones

The anisotropy in elastic and thermal properties of the C40-type TMSi2 (TM = Ta, Nb, V) disilicides were calculated by DFT. The Voigt–Reuss–Hill approximation method was applied to analyze the elastic constants. The anisotropy in elastic of these TMSi2 disilicides were characterized by 3D surface constructions and 2D planar projections. The arrangement of anisotropy in elastic modulus is TaSi2 > NbSi2 > VSi2. Based on the directional sound velocities and Debye temperatures, they are also anisotropic. The minimum thermal conductivities of TMSi2 (TM = Ta, Nb, V) disilicides were calculated by Cahill’s model and Clarke’s model, and the anisotropy is sequenced as TaSi2 > NbSi2 > VSi2.

The elastic constants and the elastic anisotropy in hexagonal close-packed Fe–Ni alloys have been investigated at high pressures by plane-wave density functional calculations within the generalized gradient approximation and the Monte Carlo special quasi-random structure method. The comparisons with previous calculations and experiments are shown and discussed. We find that adding Ni to Fe has a certain influence on the structure and elasticity of hexagonal close-packed Fe–Ni alloys generally. In particular, the elastic constant C44 is seriously affected by the increasing Ni content. Furthermore, the elastic moduli and wave velocities yielded from disordered structures are slightly greater than those from the ordered structures in previous calculations at high pressures. Interestingly, the elastic anisotropies of the compressional wave are close to 1.1 and there are small changes with increasing pressure and Ni content, which indicates that the anisotropies are little affected by pressures and Ni content within disordered structure.

The understanding of the non-Schmid behavior in shape memory alloy NiTi is considered a significant breakthrough because this alloy still remains enigmatic. We utilize an Eshelby-Stroh formalism in conjunction with Molecular Statics-Peierls stress calculation to predict the experimental CRSS results for three different crystal orientations and tension-compression cases. These combination of tools incorporating elastic anisotropy and core displacements are necessary to develop a precise understanding of non-Schmid behavior. We note the different extents of core spreading produce a highly asymmetric tension-compression behavior and strong orientation dependence governed by the non-glide shear and normal stress components. The experimental results and empiricism free modeling produces excellent agreement, and most importantly enlisting scientific insight into the shape memory response.

Fe-Ga alloys show large magnetostriction, which strongly depends on crystal orientation. This phenomenon is associated to some degree with large elastic anisotropy. In this study, white X-ray diffraction with micro-beam synchrotron radiation was used to evaluate the microscopic stresses evolved in a polycrystalline Fe-Ga alloy under tensile loading. In the analysis, the large elastic anisotropy of the Fe-Ga alloy was focused. The stress distribution in the alloy microstructure under tensile loading was estimated using a finite element method (FEM) simulation that considered the dependence of the elasticity on the crystal orientation. The crystal orientation of grains in the polycrystalline Fe-Ga alloy was measured using electron backscatter diffraction. The FEM simulation showed that the stress distribution in the microstructure depended on the crystal orientation. The X-ray diffraction stress analysis indicated that under tensile loading, the stresses in the alloy depended on the crystal orientation. This finding is similar to the results obtained from the FEM simulation, although the absolute values of the stresses may have reflected the effects of heterogeneous deformation on the stress distribution.

We revisit the classical problem of the molecular orientation inside a hybrid cell filled with liquid-crystals with various elastic constant anisotropies by means of Monte Carlo simulations using t...

A coupling between diffusional and mechanical relaxation raised from composition-dependent elastic constants, and its effects on the evolution of precipitates with finite misfit strain are investigated. Inverse ripening has been observed where smaller precipitate grows at the expense of a larger one. This occurs due to fluxes generated under elastically-strained solute gradients around precipitates that scales with R r 6 where R and r are the precipitate radius and the radial coordinate, respectively. Both isotropic and anisotropic dependency of elastic constants on the composition were considered. The latter leads to the emergence of new patterns of elastic anisotropy and rearrangement of precipitates in the matrix.

Theoretical aspects of applying Lamb waves to nondestructive testing of layered anisotropic media are considered. Propagation of Lamb waves is analyzed using a six-dimensional complex Cauchy formalism that allows one to obtain a closed-form equation for determining the dispersion of Lamb waves in media with arbitrary elastic anisotropy. The possibility for applying the higher modes of Lamb waves to nondestructive testing is noted.

Thorium borocarbide compounds have fascinating physical properties and diverse structures, and hence have stimulated great interest. In this work, we determine the ground state structure of ThBC2 by the unbiased structure prediction method based on first-principles calculations. The dynamical and elastic stabilities of our proposed ThBC2 are verified by the calculations of phonon spectrum and elastic constants. To study the mechanical properties fundamentally, we estimated the elastic anisotropy of ThBC2. The results show that the Young&rsquo, s and shear moduli possess high degree of anisotropy. The ideal strength calculations reveal that ThBC2 readily collapses upon applied stress due to small ideal strengths. The cleavage fracture probably occurs along the [111] direction while slip may easily appear along the [ 1 &macr, 10 ] direction on the (111) plane for ThBC2. In addition, we provide an atomic explanation for the different characteristics of the strain&ndash, stress curves under different strains.

Zn2TiO4 spinel (Zn2TiO4-Sp) was synthesized by a solid-state reaction method (1573 K, room P and 72 h) and quasi-hydrostatically compressed to ~24 GPa using a DAC coupled with a synchrotron X-ray radiation (ambient T). We found that the Zn2TiO4-Sp was stable up to ~21 GPa and transformed to another phase at higher P. With some theoretical simulations, we revealed that this high-P phase adopted the CaTi2O4-type structure (Zn2TiO4-CT). Additionally, the isothermal bulk modulus (K T) of the Zn2TiO4-Sp was experimentally obtained as 156.0(44) GPa and theoretically obtained as 159.1(4) GPa, with its first pressure derivative $$K_{\text{T}}^{'}$$ as 3.8(6) and 4.37(4), respectively. The volumetric and axial isothermal bulk moduli of the Zn2TiO4-CT were theoretically obtained as K T = 150(2) GPa ( $$K_{\text{T}}^{'}$$ = 5.4(2); for the volume), K T-a = 173(2) GPa ( $$K_{{\text{T-}}a}^{'}$$ = 3.9(1); for the a-axis), K T-b = 74(2) GPa ( $$K_{{\text{T-}}b}^{'}$$ = 7.0(2); for the b-axis), and K T-c = 365(8) GPa ( $$K_{{\text{T-}}c}^{'}$$ = 1.5(4); for the c-axis), indicating a strong elastic anisotropy. The Zn2TiO4-CT was found as ~10.0 % denser than the Zn2TiO4-Sp at ambient conditions. The spinel and post-spinel phase assemblages for the Zn2TiO4 composition at high T have been deduced as Zn2TiO4-Sp, ZnTiO3-ilmenite + ZnO-wurtzite, ZnTiO3-ilmenite + ZnO-rock salt, ZnTiO3-perovskite + ZnO-rock salt, and Zn2TiO4-CT as P increases, which presumably implies a potential stability field for a CT-type Mg2SiO4 at very high P.

Rhenium diboride (ReB2) in its P 6 3 / mmc crystalline structure, is widely known as a super-hard material, and has been studied many times using the Density Functional Theory (DFT) approach. In this work the same chemical composition was studied in three additional unreported hypothetical crystallographic phases by means of DFT with the hybrid functional approach, and the elastic constants of each phase were calculated. The elastic behavior of ReB2 was analyzed by means of elastic moduli calculations. Additionally, the velocities of the elastic waves of each phase were calculated, along with the Debye’s temperatures, also elastic anisotropy is studied. Semi-empirical and empirical models of hardness were used to estimate qualitatively which phases are or are not hard. It has been determined that the elastic moduli of two out of the three hypothetical phases are desirable and the elastic waves move very slow ( 2 km/s) in one of them. These results and the analysis of the bond critical points (bcp) of each phase allow us to conclude that one of them is soft while the other two are hard. The synthesized phase of ReB2 P 6 3 / mmc was studied in order to compare and confirm the results.

Cast ASTM F75 femoral knee implant components distort during manufacture due to residual stress re-distribution or inducement. These castings pose a number of challenges for residual stress determination methods; they have a complex geometry, their microstructure is inhomogeneous, they work-harden rapidly and they have a coarse, elastically anisotropic grain structure. The contour method is anticipated to be the most promising residual stress determination technique. X-ray diffraction is feasible for components which have experienced plastic deformation on their surface which results in refined diffracting domains. Centre-hole drilling is feasible, but the influence of stress induced from drilling and the effect of coarse grain structure is unknown. Neutron diffraction is challenging also due to a coarse grain structure and difficult nuclear material properties.This paper is part of a Themed Issue on Measurement, modelling and mitigation of residual stress.

We present a new method for determining the unique reference state in which the Burgers vectors of misfit dislocations in semicoherent interfaces are defined. Similar to previous work, our method requires cancelation of coherency and dislocation stresses far from the interface as well as consistency of far-field rotations with a prescribed interface crystallographic character. We compute misfit dislocation elastic fields using Stroh’s formalism and the Sextic theory, accounting fully for elastic anisotropy. The method is applicable to all types of interfaces, including ones with three sets of dislocations, and does not require the definition of a transformation path between adjacent crystals. We examine the accuracy of our method by comparing it with previous results on interfaces with one or two sets of dislocations. We then use it to carry out the first calculations of the coherent reference state of an interface with three sets of dislocations.

The elastic properties of L1 2 -type Al 3 Sc at high temperature have been studied using the first-principles calculations combined with the quasi-harmonic approximation. The obtained elastic constants and polycrystalline elastic moduli exhibit a very gentle descent trend with increasing temperature. Elastic anisotropy of Al 3 Sc is slightly enhanced with increasing temperature, while the brittle nature is insensitive to temperature. The relevant important thermodynamic properties including thermal expansion coefficient and heat capacity are further derived and discussed. The moderate variation of elastic properties and the thermal properties may be attributed to the slightly weakened Al–Sc covalent bonding with temperature increasing. Our results would be valuable for further experimental study of high temperature mechanical properties of the relevant Al-based alloys.

The first-principles calculations based on density-functional theory were performed to investigate the structural properties, phase stability, and elastic properties of several selected Hf–Al intermetallics. The calculated formation enthalpies show that HfAl 2 is the most stable in these intermetallics. The predicted elastic moduli results indicate that the order in the degree of elastic anisotropy is HfAl > Hf 2 Al > D0 22 -HfAl 3 > Hf 3 Al 2 > Hf 5 Al 3 > Hf 2 Al 3 > D0 23 -HfAl 3 > L1 2 -HfAl 3 > Hf 4 Al 3 > HfAl 2 . By using the procedure of Brugger, the calculated sound velocities in different directions for the Hf–Al intermetallics are anisotropic. The Debye temperatures were also estimated from the elastic constant evaluations of Hf–Al intermetallics.

International audience; This works focused on the mechanical behavior of an 'as-forged' Ti-1023 alloy used in airframe forging applications. Its microstructure, characterized by SEM and EBSD, was composed by 15% of primary α p nodules (2-5 μm in size) embedded in millimeter long β grains partially fragmented into equiaxed β subgrains of 5-10 μm. Further neutron diffraction analysis indicated an almost random β texture. Tensile tests at different strain rates were performed. A very low strain rate sensitivity was observed. The contribution of each phase to the overall mechanical behavior was numerically investigated by a two-phase elasto-viscoplastic self-consistent (EVPSC) model with affine-type linearization. Internal stresses arising from elastic and plastic strain incompatibilities were analyzed. Throughout the mechanical loading, {100} β oriented grains were more deformed than {111} β grains and all the α nodules. The onset of plasticity occurred sequentially in the β phase, initially in {110} β grains followed by {111} β and then {100} β ones. The effect of the crystallographic texture on slip activity was also studied through simulations made with a synthetic rotated cube β texture, typical of β-working, while considering α textures in Burgers Orientation Relationship (BOR) with the β phase or being random.

The elastic properties, lattice wave propagation and phonon focusing of TiAl are studied in detail based on Bond matrices model and lattice-dynamical method. The results contain remarkably complex three-dimensional variations in the phonon flux with angular distribution. The feature of elastic waves and phonon distribution is affected by the elastic anisotropy of the lattice. The correspondence between these features and contours of Gaussian curvature on the slowness surface is explored and the phonon topology is discussed about the presence of caustics in the anistropic flux of phonons emanating from a localized phonon distribution. The topology slowness surface gives insights into the mixing of longitudinal and transverse modes and gives the origin of the phonon focusing. The elastic anisotropy not only affects lattice wave propagation but also influences phonon focusing.

Ni3Al-based superalloys have excellent mechanical properties which have been widely used in civilian and military fields. In this study, the mechanical properties of the face-centred cubic structure Ni3Al were investigated by a first principles study based on density functional theory (DFT), and the generalized gradient approximation (GGA) was used as the exchange-correlation function. The bulk modulus, Young&rsquo, s modulus, shear modulus and Poisson&rsquo, s ratio of Ni3Al polycrystal were calculated by Voigt-Reuss approximation method, which are in good agreement with the existing experimental values. Moreover, directional dependences of bulk modulus, Young&rsquo, s ratio of Ni3Al single crystal were explored. In addition, the thermodynamic properties (e.g., Debye temperature) of Ni3Al were investigated based on the calculated elastic constants, indicating an improved accuracy in this study, verified with a small deviation from the previous experimental value.

The lattice parameters and elastic constants of the tetragonal LiFeAs and NaFeAs under different pressures have been investigated by using the first-principles calculations. It is found that their lattice parameters at 0 GPa are in agreement with the available experimental data. By the elastic stability criteria under isotropic pressure, it is found that LiFeAs and NaFeAs with the tetragonal structure are not mechanically stable above 16 GPa and 18 GPa, respectively. Besides, Pugh’s modulus ratio, Poisson’s ratio, Vickers hardness, and elastic anisotropy factors of LiFeAs in the pressure range of 0–16 GPa and NaFeAs in the pressure range of 0–18 GPa are systematically investigated. It is shown that their ductilities increase with increasing pressure, and the ductility of NaFeAs is superior to that of LiFeAs under different pressures.

In this paper, we present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in [1,2], that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. To this end, an analytical method to convert a discrete dislocation network to its continuous dislocation density tensor representation is first developed. From there, the mechanical fields are evaluated using a FDM-based spectral framework, while submesh resolution elastic interactions are accounted for via the introduction of a rigorous stress splitting procedure that leverages properties of non-singular dislocation theories. The model results in a computationally efficient approach for DDD simulations that enables the use of elastic anisotropy and heterogeneities, while being fully compatible with recently developed subcycling time-integrators. As an example, the model is used to perform a work-hardening simulation, and potential applications that take advantage of the full-field nature of the method are explored, such as informing FDM models, and efficiently calculating virtual diffraction patterns., Comment: 27 pages, 8 figures

International audience; Near β-titanium alloys like Ti-5553 or Ti-1023 often exhibit bimodal phase constituents embedded in a retained β-phase matrix, which represents up to 40% of the volume. The highly elastic anisotropic β-phase may strongly influence the mechanical behavior of these alloys. The present work models the effect of the coupled role of β-phase elastic and plastic anisotropies on the local and overall responses of a fully β-phase polycrystalline aggregate like the Ti-17 alloy. The model is based on an advanced elasto-viscoplastic self-consistent (EVPSC) homogenization scheme solved by the "translated field" method together with an affine linearization of the viscoplastic flow rule. The effects of elastic anisotropy, crystallographic texture and grain morphology are theoretically studied during uniaxial tensile tests, tension-compression tests as well as multiaxial plastic yielding. First, it is shown that different sets of elastic constants taken from literature give rise to similar effective responses but to widely scattered incompatibility stresses. During uniaxial tensile loading, the highest local incompatibility stresses are achieved in oriented grains at the end of the elastic regime. Likewise, the effect of the β-grain morphology for realistic grain aspect ratios is seen to be weak on the overall behavior but strong on incompatibility stresses. In addition, the elastic anisotropy can have a significant influence on yield surfaces for β-forged textured polycrystals. Finally, the simulated Bauschinger stress monotonically increases with the elastic anisotropy coefficient for a random texture while it may be reduced in case of β-forged texture due to a competition between elastic and plastic sources of incompatibility stresses.

Very high cycle fatigue carried out on pure copper polycrystals promotes early slip markings, labelled as slip markings of types II and III, localized close to grain or twin boundaries. In this work, we focus on whether Schmid criterion can predict the preferential sites of slip markings of types II and III and identify the active slip systems. Combining observations of slip markings and polycrystalline modeling, it is shown that considering pure cubic elastic behavior, maximum resolved shear stress as a criterion for type II slip markings preferential sites is 70% reliable criterion. Concerning slip markings of type III, the reliability falls to 30%. The role of cross slip is highlighted and a scenario rationalizing the stress amplitude conditions and sites to observe early slip markings of type II or III for copper polycrystals is proposed.

The complete set of independent second- and third-order elastic constants of rare-earth hexaborides LaB 6 and CeB 6 are determined by the combination method of first-principles calculations and homogeneous deformation theory. The ground-state lattice parameters, second-order elastic constants, and bulk modulus are in reasonable agreement with the available experimental data. The third-order elastic constant of longitudinal mode C 111 has a larger absolute value than other shear modes, showing the contribution to lattice vibrations from longitudinal modes to be greater. The pressure derivatives of the second-order elastic constants related to the third-order elastic constants are calculated to be positive for the two hexaborides, which are consistent with those of their polycrystalline bulk modulus and shear modulus. Furthermore, the effect of pressure on the structural stability, mechanical property, and elastic anisotropy of the two hexaborides are investigated, showing a reduction in mechanical stability and an increase in ductility and anisotropy with increasing pressure.

The electromagnetic acoustic resonance method was applied to measure the elastic constants ( c 11 , c 12 , and c 44 ) of Fe–40, –43 and –46Al (at.%) single crystals from room temperature to 1173 K. The temperature dependence of the energy factor, K , and the elastic anisotropy factor, A , was obtained. A increased monotonously with increasing temperature and reached ∼7 at ∼1200 K. Therefore, it was confirmed that B2-type FeAl shows an anomalous temperature dependence of elasticity.

Springback prediction is necessary when applying high-strength steel sheets to automotive parts. The accuracy of springback prediction depends on the material model, which describes the deformation behavior of steel sheets. In this research, a material model which considers important material behaviors (Bauschinger effect, average Young’s modulus, elastic anisotropy and plastic anisotropy) was developed and implemented in FEM software. Springback analyses were performed for curved hat-shaped parts made of high-strength steel sheets. As a result, the effects of each material behavior on springback were clarified. It was found that not only the Bauschinger effect and average Young’s modulus but also elastic anisotropy and plastic anisotropy influenced the results of springback predictions, particularly in the case of anisotropic material. Springback analysis considering all four material behaviors yielded better springback prediction accuracy than those of conventional analyses.

We examine the effect of surface energy on an anisotropic elastic material weakened by an elliptical hole. A closed-form, full-field solution is derived using the standard Stroh formalism. In particular, explicit expressions for the hoop stress, normal, in-plane tangential and out-of-plane displacement components along the edge of the hole are obtained. These expressions clearly demonstrate the effect of elastic anisotropy of the bulk material on the corresponding field variables. When the material becomes isotropic, the hoop stress agrees with the well-known result in the literature while both the in-plane tangential and out-of-plane displacements vanish and the normal displacement is constant along the entire boundary of the elliptical hole.

A pressure-induced phase transition of Mg2Sr intermetallics from the low-pressure C14-type phase to an orthorhombic phase (space group Cmcm, Z = 4) at a high pressure of 21.0 GPa was firstly predicted using first-principles calculations combined with unbiased swarm structure searching techniques. The phase transition was identified as a first-order nature with a volume drop of 4.7%, driven by the softening of elastic behavior at high pressure. Further phonon calculations indicate that the newly predicted orthorhombic phase is dynamically stable at high pressure and ambient pressure. The mechanical properties including the elastic anisotropy of this orthorhombic phase were thus fully studied at ambient pressure. The elastic anisotropy behavior of this orthorhombic phase was investigated by the distributions of elastic moduli. The evidence of the bonding nature of Mg–Sr was also manifested by density of states (DOS) and electronic localization function (ELF) calculations.

A series of carbon-based superconductors XC6 with high Tc were reported recently. In this paper, based on the first-principles calculations, we studied the mechanical properties of these structures, and further explored the XC12 phases, where the X atoms are from elemental hydrogen to calcium, except noble gas atoms. The mechanically- and dynamically-stable structures include HC6, NC6, and SC6 in XC6 phases, and BC12, CC12, PC12, SC12, ClC12, and KC12 in XC12 phases. The doping leads to a weakening in mechanical properties and an increase in the elastic anisotropy. C6 has the lowest elastic anisotropy, and the anisotropy increases with the atomic number of doping atoms for both XC6 and XC12. Furthermore, the acoustic velocities, Debye temperatures, and the electronic properties are also studied.

The focused ion beam milling assisted digital image correlation (FIB-DIC) method has recently proven to be effective to measure residual stresses of coatings and in bulk materials. In this work, the effect of elastic anisotropy on residual stress measurements is studied for single crystalline materials. 3D elastic anisotropic finite element models of the double slot milling geometry were developed, which consider the crystallographic orientation of the samples. In order to verify the finite element analysis, FIB-DIC measurements were performed on bent samples of nanocrystalline nickel and single crystalline CMSX-6 alloy. A well-defined stress state was generated by deforming the samples elastically in an in-situ four-point bending device. The FIB-DIC double slot analysis was performed along the sample section to measure the applied bending stresses. The classical bending beam theory provides reference stress values and thus a validation of the measured stress and strain values is possible. It was found, that the theoretically calculated strains agree well with the measured strains, and a discussion on the limitations of the assumptions at the basis of the model is presented.

A novel phase field grain growth model combined with a micro-elasticity effect including elastic anisotropy and inhomogeneity is developed to investigate the effect of micro-elasticity on the grain growth. Due to the elastic anisotropy of each grain and the elastic interaction with its neighbors, an external elastic load affects strongly grain growth and texture evolution. A strong 〈1 0 0〉//ND fiber texture developed in poly-crystalline Cu with an initial random texture by biaxial external strain, whereas a 〈1 1 1〉//ND fiber texture evolved under the biaxial external stress condition. In contrast to the previously reported macro-elastic descriptions, there was a strong localization of strain energy density and inhomogeneous distribution even inside grains, and the elastically soft grains with a higher strain energy density grew at the expense of the elastically hard grains to reduce the total strain energy. The results suggest the possibility of tailoring the texture by controlling various external loads.

Ni3N was prepared by gaseous nitriding of nickel substrates using gas mixtures of high nitrogen activities, composed of NH3 and H2 at 1 atm and at temperatures between 175 °C and 550 °C. At least above 300 °C closed Ni3N layers developed, which possess distinct compressive macrostrain parallel to the surface. The observed hkl-anisotropy of the macrostrain could be ascribed to the elastic anisotropy as indicated by the single-crystal elastic constants of Ni3N obtained from firstprinciples calculations performed in this work. The macrostress originates from the thermal misfit between layer and substrate, developing upon cooling. The extent of macrostress is reduced by partial misfit accommodation by plastic deformation as well as by porosity.