Hardness shear modulus ratio

The hardness shear modulus ratio in this case is similar to the one for metallic glasses. This suggests that the structure in the KCl-KBr solid solution is highly disordered i.e., glassy. 

Vickers Hardness 26.1 GPa Modulus of Elasticity 350-510 GPa Shear Modulus 193 GPa Bulk Modulus 241 GPa Poisson s Ratio 0.18... 

Vickers Hardness 19.65 GPa Modulus of Elasticity 338-580 GPa Shear Modulus 214 GPa Bulk Modulus 296 GPa Poisson s Ratio 0.21... 

Vickers Hardness 28-35 GPa Modulus of Elasticity 410-510 GPa Shear Modulus 186 GPa Bulk Modulus 240-390 GPa Poisson s Ratio 0.191... 

For interpreting indentation behavior, a useful parameter is the ratio of the hardness number, H to the shear modulus. For cubic crystals the latter is the elastic constant, C44. This ratio was used by Gilman (1973) and was used more generally by Chin (1975) who showed that it varies systematically with the type of chemical bonding in crystals. It has become known as the Chin-Gilman parameter (H/C44). Some average values for the three main classes of cubic crystals are given in Table 2.1. 

Ytterbium melts at 824°C vaporizes at 1,194°C electrical resistivity 25.0 microhm-cm Vickers hardness 21 kg/mm Young s modulus 0.182x10 kg/cm2 shear modulus 0.071x10 kg/cm Poisson s ratio 0.284 magnetic susceptibility 71x10 emu/mol thermal neutron absorption cross section 37 barns reacts slowly with water soluble in dilute acids and ammonia. 

The Physical Properties are listed next. Under this loose term a wide range of properties, including mechanical, electrical and magnetic properties of elements are presented. Such properties include color, odor, taste, refractive index, crystal structure, allotropic forms (if any), hardness, density, melting point, boiling point, vapor pressure, critical constants (temperature, pressure and vol-ume/density), electrical resistivity, viscosity, surface tension. Young s modulus, shear modulus, Poisson s ratio, magnetic susceptibility and the thermal neutron cross section data for many elements. Also, solubilities in water, acids, alkalies, and salt solutions (in certain cases) are presented in this section. 

Table 19.6 Mechanical properties (elastic modulus ( ), shear modulus (G), Poisson s ratio (v), hardness Hz), and fracture toughness Klc) of composites sintered by SPS...

In these equations, the subscripts h and s refer to the hard continuous phase and the soft rubbery phase, respectively, E = Young s modulus, G = shear modulus, vh = Poisson s ratio (— 0.35 for polystyrene and most rigid polymers), and cj>8 and h = volume fractions of the components. 

Fig. 4.26 Contours of tensile modulus (MPa) for a PU with hard segment volume fraction tpH = 0.354 and Poisson s ratio V = 0.5, according to the empirical log law for shear modulus of a two-phase composite material (equation (4.7)) [135]...

Vickers Hardness (GPa) 27.4-34.3 Modulus of Elasticity (GPa) 290-450 Shear Modulus (GPa) 165-200 Bulk Modulus (GPa) 190-250 Poisson s Ratio 0.18 Flexural Strength (MPa) 323-430 Compressive Strength (MPa) 2750... 

X10. The next three rows present the viscosity rj, the surface tension, and its tenqterature dependence, in the liquid state. The next properties are the coefficient of linear thermal expansion a and the sound velocity, both in the solid and in the liquid state. A number of quantities are tabulated for the presentation of the elastic properties. For isotropic materials, we list the volume compressihility k = —(l/V)(dV/dP), and in some cases also its reciprocal value, the bulk modulus (or compression modulus) the elastic modulus (or Young s modulus) E the shear modulus G and the Poisson number (or Poisson s ratio) fj,. Hooke s law, which expresses the linear relation between the strain s and the stress a in terms of Young s modulus, reads a = Ee. For monocrystalline materials, the components of the elastic compliance tensor s and the components of the elastic stiffness tensor c are given. The elastic compliance tensor s and the elastic stiffness tensor c are both defined by the generalized forms of Hooke s law, a = ce and e = sa. At the end of the list, the tensile strength, the Vickers hardness, and the Mohs hardness are given for some elements. 

Silvery-white lustrous metal face-centered cubic crystal structure ductile ferromagnetic density 8.908 g/cm at 20°C hardness 3.8 Mohs melts at 1,455°C vaporizes at 2,730°C electrical resistivity 6.97 microhm-cm at 20°C total emissivity 0.045, 0.060 and 0.190 erg/s.cm2 at 25, 100 and 1,000°C, respectively modulus of elasticity (tension) 206.0x10 MPa, modulus of elasticity (shear) 73.6x10 MPa Poisson s ratio 0.30 thermal neutron cross section (for neutron velocity of 2,200 m/s) absorption 4.5 barns, reaction cross section 17.5 barns insoluble in water dissolves in dilute nitric acid shghtly soluble in dilute HCl and H2SO4 insoluble in ammonia solution. Thermochemical Properties... 

The universal hardness , is obtained from the same formula if h is inserted instead of Aplastic- The universal hardness includes both the elastic and plastic deformation. The hnear part of the unloading curve corresponds to the elastic recovery when the diamond pyramid is in a constant area contact with the material. Therefore it represents Hooke s law and allows one to calculate the corresponding elastic modulus E/ — i/) which is a complicated function of the bulk, shear, and tensile moduli is the Poisson ratio). The details of the apparatus, the measuring procedure and possible errors are given in the relevant papers to which we refer here [25-28]. If done correctly, the plastic hardness measured by the indentation agrees within about 10-15% reasonably well with that from the classical Vickers method at least in the range H < 1500kgmm [25]. 

Here Geo is the equilibrium modulus of the unfilled polymer, is the volume fraction of filler, and , is a maximum volume fraction corresponding to close packing, which may be between 0.74 and 0.80. For < 0.70, this equation is equivalent to the result of a theoretical formulation by van dcr Pocl (which can be evaluated only numerically) relating the shear and bulk moduli of a composite with spherical particles to the shear and bulk moduli and Poisson s ratios of the two component materials. The derivation of van dcr Poel has been corrected and simplified by Smith.For a hard solid in a rubbery polymer, the ratio of the shear moduli is so large that the result is insensitive to its magnitude. An example is shown in Fig. 14-13 for data of Schwarzl, Brcc, and Nederveen for nearly monodisperse sodium chloride particles of several different sizes embedded in a cross-linked polypropylene ether. Extensive comparisons of data with equation 18 have been made by Landcl, -"- - who has also employed an alternative relation ... 

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