The relations between the shear modulus, the bulk modulus and Young's modulus for porous isotropic ceramic materials

2008 ◽  
Vol 490 (1-2) ◽  
pp. 305-312 ◽  
Author(s):  
K.K. Phani ◽  
Dipayan Sanyal
Keyword(s):  
Shear Modulus ◽  
Bulk Modulus ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Ceramic Materials

Mechanical and thermodynamics properties of Al2Ca and Mg2Ca under various pressure: A first principle study

2021 ◽  
Vol 11 (9) ◽  
pp. 1571-1578
Author(s):  
Zai Gao Huang
Keyword(s):  
Shear Modulus ◽  
Bulk Modulus ◽  
Young’S Modulus ◽  
Elastic Constants ◽  
Coefficient Of Thermal Expansion ◽  
Young's Modulus ◽  
Structural Parameters ◽  
Harmonic Approximation ◽  
Polycrystalline Materials ◽  
Ductile Phase

The mechanical and thermodynamic properties of Al2Ca and Mg2Ca in the pressure range of 0~100 Gpa were investigated using first-principles calculations. The structural parameters, such as lattice constant ratio, unit cell volume ratio, density, were investigated. The calculated elastic constants satisfy the born’s stability criterion, indicating that they are mechanically stable at normal and high pressure. Mechanical parameters such as bulk modulus, shear modulus, and Young’s modulus of polycrystalline materials have been derived from single-crystal elastic constants. The Poisson’s ratio and anisotropy were investigated. The results show that the B/G value of Mg2Ca is greater than 1.75, indicating it is a ductile phase under various pressures. When the pressure was equal to 40 Gpa, Al2Ca was transferred brittle to toughness, and the bulk modulus, shear modulus, and Young’s modulus of Al2Ca were all larger than those of Mg2Ca, indicating that the comprehensive mechanical properties of Al2Ca are better than those of Mg2Ca. The constant heat capacity obtained by the quasi-harmonic approximation indicates that the ability of Mg2Ca to release or store heat is greater than that of Al2Ca. Moreover, the coefficient of thermal expansion (α) increases exponentially at lower temperatures and linearly at higher temperatures for both alloys.

Lattice dynamical and elastic properties of BaFX (X = Cl, Br and I): Matlockite structure compounds

2019 ◽  
Vol 33 (20) ◽  
pp. 1950221 ◽  
Author(s):  
A. K. Kushwaha ◽  
S. Akbudak ◽  
A. C. Yadav ◽  
Ş. Uğur ◽  
G. Uğur
Keyword(s):  
Shear Modulus ◽  
Bulk Modulus ◽  
Young’S Modulus ◽  
Elastic Constants ◽  
Phonon Mode ◽  
Young's Modulus ◽  
Nearest Neighbors ◽  
Crystallographic Direction ◽  
Theoretical Results ◽  
Rigid Ion Model

In this study, an eleven-parameter rigid-ion model (RIM) is proposed for BaFX (X = Cl, Br and I) matlockite structure compounds. The interatomic interactions up to fourth nearest neighbors for the studied compounds are calculated. The zone-center raman and infrared phonon mode frequencies, elastic constants, bulk modulus B, shear modulus G, Young’s modulus E, Poisson’s coefficient, Debye temperature and sound velocity along [100], [110] and [001] directions have been calculated. It is observed that the studied BaFCl, BaFBr and BaFI compounds are stiffer in [100] direction than [001] crystallographic direction and the bulk modulus, shear modulus and Young’s modulus of the studied compounds decrease in the order of BaFCl [Formula: see text] BaFBr [Formula: see text] BaFI. The obtained results are compared with the theoretical and experimental results. It is observed that the obtained results agree very well with the experimental and theoretical results available in the literature.

Elastic Constants of Magnesium Thorium Alloy

1967 ◽  
Vol 89 (1) ◽  
pp. 93-97
Author(s):  
J. R. Asay
Keyword(s):  
Shear Modulus ◽  
Bulk Modulus ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Longitudinal Velocity ◽  
Shear Velocity ◽  
Polycrystalline Sample ◽  
Poisson's Ratio ◽  
Wave Measurements

The longitudinal and shear wave velocities in a polycrystalline sample of magnesium thorium alloy were measured by a pulse transmission technique as a function of temperature. Temperatures ranged from 25 C to about 350 deg C for longitudinal wave measurements and to about 220 deg C for shear measurements. The resulting velocity data were used to calculate various elastic properties of the material, including Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio. The resulting least squares fits for these data are: Longitudinal velocity, cl = 5.749 − 3.987 × 10−4T − 1.139 × 10−6T2mm/μsec; shear velocity, ct = 3.108 − 1.421 × 10−4T − 2.588 × 10−6T2mm/μsec; bulk modulus, B = 3.576 × 10″ − 2.744 × 107T + 1.187 × 105T2 dynes/cm2; Young’s modulus, E = 4.435 × 10″ − 1.415 × 107T = 6.037 × 105T2 dynes/cm2; shear modulus, G = 1.716 × 10″ − 7.994 × 106T − 2.619 × 105T2 dynes/cm2; Poisson’s ratio, σ = 0.293 − 6.459 × 10−6T + 3.392 × 10−7T2.

scholarly journals The Mechanical Properties and Elastic Anisotropies of Cubic Ni3Al from First Principles Calculations

Crystals ◽  
2018 ◽  
Vol 8 (8) ◽  
pp. 307 ◽  
Author(s):  
Xinghe Luan ◽  
Hongbo Qin ◽  
Fengmei Liu ◽  
Zongbei Dai ◽  
Yaoyong Yi ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Young’S Modulus ◽  
First Principles ◽  
Poisson’S Ratio ◽  
Density Functional ◽  
Young's Modulus ◽  
Small Deviation ◽  
Poisson's Ratio

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’s modulus, shear modulus and Poisson’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’s modulus, shear modulus and Poisson’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.

First-Principles Study of Structural, Mechanical, and Thermodynamic Properties of Refractory Metals (Rh, Ir, W, Ta, Nb, Mo, Re, and Os)

2020 ◽  
Vol 993 ◽  
pp. 1017-1030
Author(s):  
Ying Jie Sun ◽  
Kai Xiong ◽  
Zong Bo Li ◽  
Shun Meng Zhang ◽  
Yong Mao
Keyword(s):  
Thermodynamic Properties ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Young’S Modulus ◽  
First Principles ◽  
Elastic Anisotropy ◽  
Young's Modulus ◽  
Refractory Metals ◽  
Body Centered Cubic ◽  
Cubic Metals

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.

scholarly journals Anisotropies in Elasticity, Sound Velocity, and Minimum Thermal Conductivity of Low Borides VxBy Compounds

Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 577
Author(s):  
Jing Yu ◽  
Yongmei Zhang ◽  
Yuhong Zhao ◽  
Yue Ma
Keyword(s):  
Thermal Conductivity ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Sound Velocity ◽  
Young’S Modulus ◽  
Elastic Anisotropy ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Young’S Moduli ◽  
Crystallographic Planes

Anisotropies in the elasticity, sound velocity, and minimum thermal conductivity of low borides VB, V5B6, V3B4, and V2B3 are discussed using the first-principles calculations. The various elastic anisotropic indexes (AU, Acomp, and Ashear), three-dimensional (3D) surface contours, and their planar projections among different crystallographic planes of bulk modulus, shear modulus, and Young’s modulus are used to characterize elastic anisotropy. The bulk, shear, and Young’s moduli all show relatively strong degrees of anisotropy. With increased B content, the degree of anisotropy of the bulk modulus increases while those of the shear modulus and Young’s modulus decrease. The anisotropies of the sound velocity in the different planes show obvious differences. Meanwhile, the minimum thermal conductivity shows little dependence on crystallographic direction.

SIMULATION OF NONLINEAR MAGNETORHEOLOGICAL PARTICLE-FILLED ELASTOMERS

2013 ◽  
Vol 02 (03n04) ◽  
pp. 1350018
Author(s):  
SHULEI SUN ◽  
XIONGQI PENG ◽  
ZAOYANG GUO
Keyword(s):  
Magnetic Field ◽  
Shear Modulus ◽  
Young’S Modulus ◽  
Applied Magnetic Field ◽  
Smart Materials ◽  
Young's Modulus ◽  
Particle Volume ◽  
Magnetorheological Elastomers ◽  
Maxwell Stress Tensor ◽  
Element Simulation

Polymer matrix filled with ferromagnetic particles is a class of smart materials whose mechanical properties can be changed under different magnetic field. They are usually referred to as magnetorheological elastomers (MREs). A finite element simulation was presented to describe the mechanical behavior of MREs with the nonlinearity of the particle magnetization being incorporated. By introducing the Maxwell stress tensor, a representative volume element (RVE) was proposed to calculate the Young's modulus and shear modulus of MREs due to the applied magnetic field. The influences of the applied magnetic field and the particle volume fractions in the shear modulus and Young's modulus were studied. Results show that the shear modulus increases with the magnitude of the applied magnetic field, while the Young's modulus decreases.

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