Anisotropic Moduli Research Articles

Elastic anisotropies, thermal conductivities and tensile properties of MAX phases Zr2AlC and Zr2AlN: A first-principles calculation

In this study, the mechanical stability, elastic properties, including single-crystal elastic constants, polycrystalline elastic modulus and elastic anisotropy, Debye temperatures, electronic properties, minimum thermal conductivities and tensile character of Zr2AlC and Zr2AlN were calculated by first-principles calculations based on density functional theory. The results showed that Zr2AlX (X = C, N) are mechanically stable and anisotropic in elastic properties, and the degree of elastic anisotropy of Zr2AlN is slightly greater than Zr2AlC, and the sound velocities and minimum thermal conductivities of Zr2AlC and Zr2AlN along the [001] and [100] directions are also anisotropic. Moreover, the density of states (DOS) and charge density difference distributions showed that these Zr2AlX have metallic-covalent-ionic mixed bonds. Finally, the calculated tensile properties along the [001] and [110] directions of these MAX phases showed that the tensile strength along the [110] direction is greater than that along the [001] direction.

A Novel BN Polymorph in P4/mbm Phase with a (4,4) Nanotube

Herein, based on density functional theory, a new boron nitride structure derived from diamond is designed, and its stability is also proved. The new boron nitride structure is denoted as P4/mbm BN. The elastic moduli (bulk modulus, shear modulus, and Young's modulus) of P4/mbm BN are slightly greater than those of C72 and T carbon, and the shear modulus and Young's modulus are larger than those of P‐4m2 B7N7, B11N11, and B15N15. The shear modulus and Young's modulus of P4/mbm BN exhibit a smaller mechanical anisotropy than that of P‐4m2 B7N7, B11N11, and B15N15, where P‐4m2 B15N15 exhibits the greatest mechanical anisotropy of shear modulus and Young's modulus. The anisotropy of shear modulus in the (100), (010) plane of P‐4m2 B15N15 is 26.5 times that of P4/mbm BN, and the mechanical anisotropy of Young's modulus in (110) plane of P‐4m2 B15N15 is 35.6 times that of P4/mbm BN. P4/mbm BN is a wide and indirect bandgap semiconductor material with bandgap of 4.8 eV. Compared with silicon carbide and gallium nitride, P4/mbm BN has a wider bandgap, it might be more suitable for making high temperature, high frequency, radiation resistance, and high‐power devices.

Numerical analysis on fracture initiation from radial micro‐hole in anisotropy formation

AbstractThe radial jet drilling (RJD) technology is typically developed to open multiple lateral micro‐holes from a main wellbore to the formation. The multiple groups of 3D numerical models of radial micro‐holes through a main well are built by incorporating the pore hydro‐mechanical coupling effects. A number of sensitivity analyses were conducted on the effects of the radial jetting azimuth, the stress anisotropy, and the elastic anisotropy on the rock fracture initiation of the micro‐holes. As revealed from the results, the fracture initiation from the micro‐hole exhibited the diversified characteristics with the increase in the jetting azimuth of the micro‐hole. On the whole, the fracture initiation point was concentrated at the maximum principal stress. Thus, the jetting azimuth of the nozzle was recommended to be designed in the interval of 0°‐30°. A higher elastic modulus anisotropy ratio K and a lower Poisson's ratio anisotropy ratio K′ caused the significant rigidity characteristics of the rock, which increased the possibility of fracture initiation in the horizontal direction; a lower elastic modulus anisotropy ratio K and a higher Poisson's ratio anisotropy ratio K′ caused the strong rigidity characteristics, so the rock could not easily fracture in the vertical direction. Several suggestions were given that the rock is easy to be broken by selecting a smaller jetting azimuth angle and a more significant in‐situ stress difference. The numerical simulation results agree well with field experiment results, with an average accuracy of 97.17%. The proposed numerical model has a good performance in predicting the fracture initiation pressure of the radial micro‐hole in anisotropy formation.

Physical properties of group 14 elements in P2/m phase

Physical properties of J-carbon, J-silicon, and J-germanium (space group: P2/m) were studied by density functional theory calculations. J-germanium was found to be dynamically, mechanically and thermodynamically stable under ambient pressure. The bulk modulus B and the shear modulus G of J-germanium are 55 ​GPa and 41 ​GPa, respectively, slightly greater than those of P42/mnm Ge, hP12 Ge and oC12 Ge. J-carbon, J-silicon, and J-germanium exhibit a larger anisotropy in Young's modulus than do carbon, silicon, and germanium in the diamond phase and also exhibit larger anisotropy in bulk modulus and shear modulus than do the corresponding diamond phase allotropes. J-germanium is a quasi-direct band gap semiconductor material with the band gap of 0.943 ​eV that may be a candidate material for use in photovoltaic devices. The band gap and the minimum thermal conductivity κmin of J-carbon are both greater than those of diamond, and therefore, J-carbon may be a promising candidate material for deep ultraviolet photodetection.

Mechanical anisotropy of graphene nanocomposites induced by graphene alignment during stereolithography 3D printing

Stereolithographically 3D-printed graphene-PMMA nanocomposites were previously found to be mechanically stiffer and stronger in the print axis, suggesting that the graphene filler was selectively oriented. Here, using polarized light microscopy, we confirm experimentally for the first time the presence of aligned graphene platelets in these nanocomposites. The alignment appears to be weak, however, as anisotropy of the storage modulus and quasistatic failure strength was only ~ 10% – 30%, about 100 × lower than the maximum anisotropy possible and 10 × smaller than that of other 3D-printed anisotropic composites. The optimal graphene concentration for maximum anisotropy was 0.02wt%– 0.05wt%, as graphene agglomeration at higher concentrations reduced anisotropy and beyond 0.2wt% it prevented 3D printing altogether. Using finite element simulations, which were experimentally verified, it was also shown that the anisotropy of the bulk nanocomposites could be fully imparted to more complex 3D-printed parts such as Octet Truss structures.Graphic abstract

Effects of porosity, orientation and connectivity of microcracks on dispersion and attenuation of fluid-saturated rocks using an upscaling numerical modelling of the squirt flow mechanism

Squirt flow is a wave-induced fluid flow mechanism to account for the velocity dispersion and attenuation of fluid-saturated porous media. Theoretical models of squirt flow cannot deal with complex microcrack-pore networks and thus cannot give accurate dispersion and attenuation curves with respect to frequency. We adopt a numerical oscillatory compressibility test method, based on the quasi-static poroelastic equation of Biot, to model the squirt flow and calculate corresponding P-wave modulus dispersion and attenuation. We also designed nine porous medium models containing different crack-pore configurations and investigated the effects of microcrack porosity, orientation and connectivity on the elastic responses. Modelling results show that not only microcrack porosity but also their orientation has control on the magnitude of the P-wave modulus dispersion and attenuation. Preferentially aligned microcracks may cause frequency-dependent anisotropy in the P-wave modulus and attenuation. Microcrack connectivity has a negligible influence on the dispersion and attenuation magnitude but a large influence on the characteristic frequency of the squirt flow, which is not predicted by theoretical models based on simple representative element volume of crack-pore structure. Therefore, detailed geometry of crack-pore network, of which microcrack porosity, orientation, aspect ratio and connectivity are vital factors, dictates the unique variations in the elastic modulus and associated attenuation with frequency caused by the squirt flow. Pore structure obtained by CT scanning representative of that of the whole rock is needed to obtain more accurate poroelastic responses of the rock with the numerical oscillatory compressibility test method. In this regard, we provide a powerful tool for evaluating dispersion and attenuation of fluid-saturated rock media with complex crack-pore structure, which have potential applications in seismic exploration of hydrocarbon in the subsurface.

First-principles exploration of elastic anisotropy and thermal properties of the C40-type VSi2, NbSi2, and TaSi2 disilicides

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.

Anisotropic Resilient Modulus Model of Granular Materials Based on Particle Characteristics

Granular materials are widely used for bases or subbases in pavement structures. They typically exhibit strong anisotropic properties which relate to stress states and particle characteristics. The conventional design procedure for flexible pavements underestimates the anisotropy of resilient moduli. This study established an anisotropic resilient modulus model for granular materials that considered gradation and particle shape characteristics. Vertical and horizontal resilient moduli of certain granular materials were measured in self-developed triaxial tests to obtain corresponding model parameters and anisotropic coefficients. Gradation and particle shape models were established to quantify the granular material characteristics, and the parameters were regressed. Particle shapes were obtained via image processing, and the ratio ( η) of particle sphericity to roundness was chosen as a shape parameter. Results show that η increases with the decrease in particle size, and the average values of η for graded gravel and natural laterite are 0.54 and 0.63, respectively. The η distribution curves indicate that the proportion of relatively anisotropic particles, rather than extremely anisotropic particles, results in the differences in particle shape characteristics. The regression relationship between the anisotropic calculation parameters and the model parameters of vertical resilient modulus, gradation, and particle shape was established. Thus, the horizontal resilient modulus and the anisotropic coefficient can be predicted via conventional resilient modulus tests and gradation, and particle shape analysis. This study shows that the anisotropy of granular materials decreases with the increase in coarse particles and the uniformization of the particle size distribution, and it increases with the increase in anisotropic particles and the polarization of the η distribution.

BC2O in C2/m phase: Light element compound with direct band gaps

A novel ternary B–C–O compound, namely m-BC2O, is first proposed in this work. Based on density functional theory, the structural properties, electronic properties, mechanical anisotropy properties and stability of m-BC2O are investigated in this work. The m-BC2O is a potential superhard material due to the hardness of m-BC2O is 50.4 ​GPa utilizing the Lyakhov-Oganov model. The m-BC2O exhibits a larger mechanical anisotropy in Young's modulus. The ratio Emax/Emin of m-BC2O (Emax/Emin ​= ​3.24) is almost two times that of other B–C–O compounds, such as B2CO2 and B6C2O5. The Young's modulus for m-BC2O in (100) plane exhibits the largest anisotropy under ambient pressure than other (001) plane, (010) plane and (111) plane, while the (111) plane is the smallest one. The m-BC2O is a narrow and direct semiconductor materials with band gap of 0.48 ​eV, and the m-BC2O could be applied in optoelectronic devices.

Experimental Investigation on Anisotropic Strength and Deformation Behaviors of Columnar Jointed Rock Mass in Confined State

Columnar jointed rock mass (CJRM) has a special joint structure formed during the cooling of lava. The self-oriented joint structure can induce mechanical anisotropy of the rock mass, which poses a challenge for geotechnical engineering. To understand the mechanical properties of CJRM, conventional triaxial compression tests were conducted on the artificial CJRM specimens. It can be found from the experiment results that the orientation of columns has a distinct impact on the strength and deformation modulus. Four failure modes of CJRM specimens at different dip angles of columns under different confining pressures can be observed. The anisotropy degree in strength and deformation modulus is estimated, where it is found that the increase of confining pressure decreases the anisotropy in strength and increases the anisotropy in deformation modulus.

First-principles study on the elasticity and thermal properties of heavy Fermi compounds CePtSix (X=1,2,3)

Elastic constants, elastic anisotropy and thermal properties of heavy Fermi compounds CePtSix were computed by first-principles calculation based on density functional theory. We calculated the elastic constants of CePtSix compounds using the Viogt-Reuss-Hill approximation method. Vickers hardness is calculated by theoretical model. By introducing the 3D surface construction and its projection of the elastic modulus, we get the elastic anisotropy ranking of CePtSix. The arrangement of anisotropy in bulk modulus is CePtSi > CePt Si2>CePt Si3, meanwhile the sequence of Young's modulus is CePtSi > CePtSi3>CePtSi2. Moreover, the order of Debye temperature is CePtSi3>CePtSi2>CePtSi, indicating that CePtSi3 possesses the strongest bond strength and largest thermal conductivity.

Mechanical characterization of boron carbide single crystals

AbstractOut‐of‐plane anisotropy in the mechanical response of boron carbide was studied by performing nanoindentation experiments on four specific crystallographic orientations of single crystals, that is, , , , and . For each orientation of the single crystals, in‐plane variations of indentation modulus and hardness were also studied by monitoring the relative rotation between the crystal surface and a Berkovich indenter tip. A significant out‐of‐plane anisotropy in indentation modulus was observed with ~80 GPa difference between the highest and lowest values. A smaller but measurable out‐of‐plane anisotropy in indentation hardness was also observed. In‐plane anisotropy, on the other hand, was found to be significantly influenced by the scatter in the data and geometrical imperfections of the indenter tip. Investigations of indentation pop‐in events suggested that deformation is entirely elastic prior to the first pop‐in. Furthermore, quasi‐plastic flow along the orientation of the single crystals was found to be more homogeneous than the other tested orientations. For select indents, cross‐sectional transmission electron microscopy (TEM) of the indented regions showed formation of a quasi‐plastic zone in the form of lattice rotation and various microstructural defects. The quasi‐plastic zone grew in size with increasing the indentation depth. The TEM observations also suggested the crystal slip to be a potential mechanism of quasi‐plasticity and a precursor for formation of amorphous bands that could eventually lead to cracking and fragmentation. The proposed failure mechanism provides valuable insights for calibrating constitutive computational models of failure in boron carbide.

A porous nanotube network structure of metallic carbon

A porous nanotube network structure of carbon allotrope was designed, denoted as P4/mmm C96. Besides its structure similar to carbon nanotubes, the most interesting thing about P4/mmm C96 is that its band structure is metallic. The shear modulus G, Young’s modulus E, and bulk modulus B of P4/mmm C96 is 49.4 GPa, 128.6 GPa, and 107.8 GPa, respectively. Although the elastic modulus of P4/mmm C96 is low, it is still larger than other carbon allotropes, such as TY-II carbon, TY carbon, fcc-C10, Y carbon, Y-II carbon. The elastic anisotropy in shear modulus G, Poisson’s ratio v, and Young’s modulus E of P4/mmm C96 are larger than that of other C96 carbon allotropes, Finally, the elastic anisotropy of shear modulus of P4/mmm C96 in (100) plane is the greatest, the elastic anisotropy of E of P4/mmm C96 in (001) plane is the largest, while the elastic anisotropy in v in (001) plane is the greatest.

Influence of Interlayer Forced Air Cooling on Microstructure and Mechanical Properties of Wire Arc Additively Manufactured 304L Austenitic Stainless Steel

Wire‐and‐arc additive manufacturing (WAAM) is an innovative technology that involves deposition of subsequent layers of molten materials. Due to the high deposition rates, this technology is suitable for the production of large‐scale complex structures. Further enhancement in the productivity can be achieved by an interlayer cooling strategy that reduces idle time between depositions. However, the effect of the interlayer cooling on microstructure and mechanical properties has to be addressed. In this view, the present work compares microstructural features and mechanical properties of WAAM‐produced plates of austenitic AISI 304 L, focusing on the effect of both active interlayer air cooling and possible anisotropy induced by the additive process. Microstructural and mechanical characterization was conducted on samples extracted along the longitudinal, transverse, and diagonal directions to the deposition layers of WAAM plates, processed with and without interlayer active cooling. Results showed no remarkable influence of cooling conditions on the microstructure and mechanical properties of WAAM plates, which are indeed affected by the anisotropy induced by the additive process. The observed anisotropy in the elastic modulus, independent from different cooling conditions, was related to the crystallographic texture consequent to the highly oriented microstructure typically induced by the process.

Structural, electronic, dynamic, optic and elastic properties of MgScGa via density functional theory

The structural, electronic and phonon properties of the MgScGa compound were investigated by density functional theory using the generalized gradient approximation. Some basic structural properties of this compound, such as the lattice constants, bulk modulus and pressure derivative of the bulk module have been studied. Electronic properties were investigated by calculating and analyzing the electronic band structure and total density of states graphs for the MgScGa compound. Electronic band structure calculations showed that MgScGa compound has a semiconductor structure. Phonon spectra were calculated using a linear response method within the framework of the total predicted state density, density functional perturbation theory for the MgScGa compound. A factor group analysis has been performed in order to get the decomposition of whole representation of Γ of MgScGa compound into irreducible representation. For investigation of optic properties; real and imaginary components of complex dielectric function, reflectivity (R), refractive index (n), extinction coefficients (k), energy-loss functions for volume (LV) and surface (LS), the effective number of valence electrons per unit cell (Neff) were calculated. Elastic properties are revealed by calculating the elastic stiffness constants, Bulk, Shear and Young modulus, Poisson Ratio, Flexibility Coefficient and Zener anisotropy constant.

Impact of axisymmetric deformation on MR elastography of a nonlinear tissue-mimicking material and implications in peri-tumour stiffness quantification.

Solid tumour growth is often associated with the accumulation of mechanical stresses acting on the surrounding host tissue. Due to tissue nonlinearity, the shear modulus of the peri-tumoural region inherits a signature from the tumour expansion which depends on multiple factors, including the soft tissue constitutive behaviour and its stress/strain state. Shear waves used in MR-elastography (MRE) sense the apparent change in shear modulus along their propagation direction, thereby probing the anisotropic stiffness field around the tumour. We developed an analytical framework for a heterogeneous shear modulus distribution using a thick-shelled sphere approximation of the tumour and soft tissue ensemble. A hyperelastic material (plastisol) was identified to validate the proposed theory in a phantom setting. A balloon-catheter connected to a pressure sensor was used to replicate the stress generated from tumour pressure and growth while MRE data were acquired. The shear modulus anisotropy retrieved from the reconstructed elastography data confirmed the analytically predicted patterns at various levels of inflation. An alternative measure, combining the generated deformation and the local wave direction and independent of the reconstruction strategy, was also proposed to correlate the analytical findings with the stretch probed by the waves. Overall, this work demonstrates that MRE in combination with non-linear mechanics, is able to identify the apparent shear modulus variation arising from the strain generated by a growth within tissue, such as an idealised model of tumour. Investigation in real tissue represents the next step to further investigate the implications of endogenous forces in tissue characterisation through MRE.

Novel BCN2 and CN compounds in C2/m phase: First-principle calculations

A novel superhard CN (the stoichiometric ratio of carbon to nitrogen is 1:1) and BCN2 compound in C2/m phase are proposed and predicted according to density functional theory in this work. The physical properties, such as crystal structure, electronic properties, elastic properties, mechanical anisotropy properties and the stable of CN and BCN2 are investigated. The shear modulus G, Young's modulus E, and bulk modulus B of BCN2 and CN are 253 and 310 GPa; 448 and 719 GPa; and 186 and 323 GPa with GGA functional, respectively. Utilizing the Lyakhov-Oganov's model, CN and BCN2 are superhard materials, the hardness of CN and BCN2 is 60.99 GPa and 53.38 GPa, respectively. Compared with diamond and c-BN, although the hardness of CN and BCN2 is not as great as that of diamond, while they are both greater than that of c-BN. Using the Chen's model, CN also is a super-hard material with hardness is 58.63 GPa, while the hardness of BCN2 is only 26.67 GPa. C2/m CN is an indirect and wide band gap semiconductor material, while BCN2 is a metallic material. In addition, mechanical anisotropy of shear modulus G, Young's modulus E, and bulk modulus B of CN and BCN2 are also studied in detail.

Evaluating the hydromechanical responses of seabed–pipelines with rotated anisotropic heterogeneous seabed properties

Seabed sediments are inherently heterogeneous and present different fabric patterns including rotated anisotropy. This work aims to investigate the effects of rotated anisotropy in seabed properties on the hydromechanical responses of seabed and pipelines. Rotated anisotropic seabed property fields (e.g., hydraulic conductivity and shear modulus fields) are generated using the random field theory, and are then coupled with finite element models to simulate the hydromechanical responses of seabed–pipelines under dynamic nonlinear wave-induced loadings. Monte Carlo simulations are performed to approach a probabilistic analysis of the effects of heterogeneous seabed fields. The pore pressure, liquefaction, seabed displacement, and pipeline stress are analyzed for systematic varying rotation angles. The results show that the upper bounds of the liquefied area would decrease by about 15% and 8% with increasing rotated anisotropy in the hydraulic conductivity and shear modulus fields, respectively. For rotated anisotropic shear modulus fields, the von Mises stress is minimum when the rotation angle is 45∘. The transverse anisotropy in hydraulic conductivity or shear modulus is the most unfavorable situation, the results of which could be relied upon for a conservative design if the rotated anisotropy of a seabed property is unknown in a field project.

First-principles calculations to investigate the anisotropic elasticity and thermodynamic properties of FeAl3 under pressure effect

We have employed the first-principles calculations and quasi-harmonic Debye model to investigate the effect of the pressure on anisotropic elasticity and thermodynamic properties of FeAl3. According to Christoffel’s equation, the wave velocity anisotropy of FeAl3 as a function of pressure was also studied. Based on 3D surfaces and 2D projection contours, the anisotropy of shear modulus for FeAl3 changes significantly with the increasing pressure, and increases more obviously on [001] direction than that on [100] direction under high pressure. The thermodynamic properties calculations show that the volume of FeAl3 decreases with the increasing temperature and pressure. The bulk modulus decreases with the increasing temperature, and increases with the increasing pressure. Onthecontrary, the thermal expansion coefficient, the heat capacities, and Grüneisen constant increase with the increasing temperature, and decrease as pressure increases. It is found that the bulk modulus and Grüneisen constant display strong pressure dependence, while the heat capacities are sensitive to the temperature. And the thermal expansion coefficient is affected simultaneously by the pressure and temperature.

Exploration of D022-Type Al3TM(TM = Sc, Ti, V, Zr, Nb, Hf, Ta): Elastic Anisotropy, Electronic Structures, Work Function and Experimental Design.

The structural properties, elastic anisotropy, electronic structures and work function of D022-type Al3TM (TM = Sc, Ti, V, Y, Zr, Nb, La, Hf, Ta) are studied using the first-principles calculations. The results indicate that the obtained formation enthalpy and cohesive energy of these compounds are in accordance with the other calculated values. It is found that the Al3Zr is the most thermodynamic stable compound. The mechanical property indexes, such as elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, and Vickers hardness are systematically explored. Moreover, the calculated universal anisotropic index, percent anisotropy and shear anisotropic factors of D022-type Al3TM are analyzed carefully. It demonstrates that the shear modulus anisotropy of Al3La is the strongest, while that of Al3Ta is the weakest. In particular, the density of states at Fermi level is not zero, suggesting that these phases have metal properties and electrical conductivity. More importantly, the mechanisms of correlation between hardness and Young’s modulus are further explained by the work function. Finally, the experimental design proves that D022-Al3Ta has an excellent strengthening effect.