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Molecular Origins of Toughness in Polymers
Published in Charles B. Arends, Polymer Toughening, 2020
Jozef Bicerano, Jerry T. Seitz
The modulus is the most important small-strain mechanical property. It is the key indicator of the “stiffness” or “rigidity” of specimens made from a material. It quantifies the resistance of the specimens to mechanical deformation, in the limit of infinitesimally small deformation. There are three major types of moduli. The bulk modulus B is the resistance of a specimen to isotropic compression (pressure). The Young’s modulus E is its resistance to uniaxial tension (being stretched). The shear modulus G is its resistance to simple shear deformation (being twisted).
Physical Properties of Infrared Optical Materials
Published in Paul Klocek, Handbook of Infrared Optical Materials, 2017
James Steve Browder, Stanley S. Ballard, Paul Klocek
Hooke’s law states that for small deformations the stress acting on a solid is proportional to the strain existing within it. The ratio of stress to strain is called the elastic modulus: the three common elastic moduli are Young’s, sometimes called the stretch modulus; bulk modulus, which is the reciprocal of compressibility; and shear or rigidity modulus. The names indicate the nature of the deformation that causes strain in the body.
Experimental assessment of the utilisation of corrugated cardboard as a core material for sandwich panels
Published in Alphose Zingoni, Insights and Innovations in Structural Engineering, Mechanics and Computation, 2016
Aaron von der Heyden, Jörg Lange
The material is characterised by three Young’s moduli (E1, E2, E3), three shear moduli (G12, G13, G23) and three Poisson’s ratios (ν12, ν13, ν23).
Mechanical and thermophysical properties of high-temperature IrxRe1−x alloys
Published in Phase Transitions, 2020
Navneet Yadav, Shakti Pratap Singh, A. K. Maddheshiya, P. K. Yadawa, R. R. Yadav
Young’s, shear, and bulk moduli of all alloys are found smaller than those of Ir0.7Re0.3 (Table 2). Thus, all the alloys comprise little stiffness and bonding with respect to Ir0.7Re0.3. Pugh’s ratio (B/G) and Poisson’s ratio (σ) define brittleness and ductility of a solid. A solid is usually brittle in nature with σ ≤ 0.26 and B/G ≤ 1.75; otherwise, it is ductile in nature [24,32]. In our evaluation, the low values of Poisson’s and Pugh’s ratio with respect to their critical values indicate that all the chosen alloys have brittle in nature at room temperature. The value of σ for stable and elastic materials should be less than 0.5. Our computed values of σ for the IrxRe1−x alloys are considerably smaller than its critical value. The smaller values of σ indicate that chosen alloys are stable against shear and a stronger degree of covalent bonding results in the higher hardness. The hardness of HCP structured material can be obtained using the relation. The evaluated value of hardness constant (HV) of Ir0.7Re0.3 is higher in magnitude than other alloys of the same group. Thus Ir0.7Re0.3 is comparatively harder material than other IrxRe1−x alloys at room temperature. Therefore, all the mechanical behaviour of a material can be described by the knowledge of these elastic moduli.
First principles study of the electronic, optical, elastic and thermoelectric properties of Nb2WNi alloy
Published in Molecular Physics, 2021
M. Güler, Ş. Uğur, G. Uğur, E. Güler
As well known, cubic crystals expose three individual elastic stiffness constants viz. C11, C12 and C44. These diverse constants provide detailed knowledge about the given crystal under external deformations. From them, the constant C11 explains the longitudinal attitude of the crystal. C12 constant describes the off-diagonal response while C44 conveys the shear behaviour of the related crystal [32–41]. The values of these stiffness constants also determine the validity of the Born mechanical stability. For Born mechanical stability C11 > 0, C44 > 0, C11 − C12 > 0, C11 + 2C12 > 0 and cubic stability C12 < B < C11 situations must be met. Meanwhile, B is the bulk modulus of the crystal. The bulk modulus characterises the compressibility of the crystal. Furthermore, the other two significant moduli are shear (G) and (E) moduli. The modulus G represents the elastic shear stiffness of a material and is also called the modulus of rigidity. The Young’s modulus sometimes referred to as elastic modulus, can be also defined as the ratio of applied stress to strain [32–41]. Table 1 inclines the numerical values of these briefly explained elastic and associated parameters. A quick check for the obtained elastic constants verifies the Born mechanical stability for both crystal structures of Nb2WNi alloy. Ductility and brittleness of materials play a key role in the production areas of mechanical engineering and sciences. Moreover, analysing the B/G ratio shows the ductile or brittle nature of the surveyed crystal. If the value of B/G arises higher than the numerical value of 1.75, the crystal can be accepted as ductile. If this value remains smaller than 1.75, then the crystal may be assumed as brittle [32–41]. From Table 1 the B/G ratio of Cu2MnAl type of Nb2WNi alloy appears at 3.21. The B/G ratio of Hg2CuTi type Nb2WNi alloy is 3.35. So, the B/G results for both crystal structures of Nb2WNi alloy are similar and prove the ductile mechanical behaviour of Nb2WNi alloy.