Metals shear moduli

Metal Shear modulus (10" dyncm ) Modulus of elasticity (10" dyncm" ) Poisson s ratio... 

Superabsorbents. Water-sweUable polymers are used extensively in consumer articles and for industrial appUcations. Most of these polymers are cross-linked acryUc copolymers of metal salts of acryUc acid and acrylamide or other monomers such as 2-acrylamido-2-methylpropanesulfonic acid. These hydrogel forming systems can have high gel strength as measured by the shear modulus (134). Sometimes inorganic water-insoluble powder is blended with the polymer to increase gel strength (135). Patents describe processes for making cross-linked polyurethane foams which contain superabsorbent polymers (136,137). 

Shear modulus, polyamide, 138 Sheet molding compounds (SMCs), 30 Shoe sole products, 205 Shore hardness gauge, 243 Side-chain liquid crystalline polymers, 49 Side reactions, in transition metal coupling, 477... 

In conclusion, one should choose an appropriate multilayer system for different application purposes. For the case of fatigue wear, multilayer films consisting of two hard materials with different shear modulus, such as DLCAVC multilayer film [115], would satisfy the requirement for wear resistance. While for abrasive wear, multilayer films consisting of hard ceramic layers and soft metal layers, such as TiN/Ti and CrN/Cr [116,117] multilayer films are more competent. 

A measure of shear strength is the shear modulus. For covalent crystals this correlates quite well with hardness (Gilman, 1973). It also correlates with the hardnesses of metals (Pugh, 1954), as well as with ionic crystals (Chin, 1975). Chin has pointed out that the proportionality number (VHN/C44) depends on the bonding type. This parameter has become known as the Chin-Gilman parameter. 

The dislocations in a tangle can lower their potential energy by aligning themselves to form dipoles and higher multipoles. The stress needed to push subsequent dislocations through a tangle (dipoles and multipoles) is proportional to the elastic shear modulus so it may be expected that the hardnesses of simple metals are proportional to their shear moduli. Figure 2.7 confirms this. 

Deformation-hardening in the 5-50% deformation range is known to be proportional to either the Young s modulus, Y, or the shear modulus, G, in metals. The Young s modulus depends strongly on the shear modulus since Y = 2(1+v) G where v = Poisson s ratio. For both fee and bcc pure metals data... 

Gerk showed that Equation (2.1) is followed not only for metals, but also for ionic and covalent crystals if two adjustments are made. For covalent crystals, the temperature must be raised to a level where dislocations glide readily, but below the level where they climb readily. For ionic crystals, G (an average shear modulus) must be adjusted for elastic anisotropy. Thus it becomes ... 

Figure 6.2 shows yield stress versus shear modulus data for face-centered cubic metals at about 78 K. The yield stresses were derived from Brinell Hardness Numbers (Gilman, 1960). The slope of the correlation line is tb = G/333, in good agreement with the theoretical estimate of the previous paragraph. 

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. 

A shear modulus of about 1 GPa has been measured for wet lysozyme. Thus its Chin-Gilman parameter is about 0.02 which is large compared with metals and small compared with covalent crystals. 

The temperature dependences of the isothermal elastic moduli of aluminium are given in Figure 5.2 [10]. Here the dashed lines represent extrapolations for T> 7fus. Tallon and Wolfenden found that the shear modulus of A1 would vanish at T = 1.677fus and interpreted this as the upper limit for the onset of instability of metastable superheated aluminium [10]. Experimental observations of the extent of superheating typically give 1.1 Tfus as the maximum temperature where a crystalline metallic element can be retained as a metastable state [11], This is considerably lower than the instability limits predicted from the thermodynamic arguments above. 

A test method to evaluate the shear stress capability of a seal material is reported [36], An electrolyte-anode-electrolyte trilayer was glass sealed to two metal interconnect plates as shown in Figure 5.11. Shear testing was done in two different modes, constant loading rate and constant displacement rate, to determine the shear modulus and viscosity. 

Silvery-gray metal hexagonal crystal structure malleable, ductile, and soft enough to be cut with a knife density 8.223 g/cm melts at 1,359°C vaporizes at 3,221°C resistivity llhxlCH ohm-cm at 25°C Young s modulus 5.75xl0n dynes/cm2 (from velocity of sound measurements) shear modulus 2.28 dynes/cm2 Poisson s ratio 0.261 thermal neutron absorption cross section, 46 barns insoluble in water soluble in acids. 

A bright white metal soft and ductile body-centered cubic structure index of refraction 3.03 density 5.96 g/cm melts at 1,910°C vaporizes at 3,407°C electrical resistivity, 18.1 microhm-cm at 0°C and 20.1 microhm-cm at 25°C magnetic susceptibility 1.4x10 cgs units modulus of elasticity 18-19x10 psi shear modulus 6.73xl0 psi Poisson s ratio 0.36 thermal neutron absorption cross section 5 barns/atom insoluble in water, dilute sulfuric acid, and hydrochloric acid at all concentrations soluble in nitric acid, aqua regia, and concentrated sulfuric acid insoluble in alkalies. 

There was previously a separate ISO standard for adhesion in shear but this was withdrawn in favour of extending the standard for shear modulus to allow the test to be continued to the failure point, i.e. the two methods have been combined. The composite method is contained in ISO 182715 and uses the same quadruple element test piece as did the separate adhesion standard. The double sandwich construction is intended to provide a very stiff test piece which will remain in alignment under high stresses. The present standard quadruple test piece uses rubber elements 4 1 mm thick and 20 5 mm long and these tolerances are much less tight than previously. The measured adhesion strength in shear is less affected by the test piece shape factor then tension tests8 and the wider tolerances should be perfectly satisfactory. The test piece is strained at a rate of 50 mm/min, in line with the speed for most other adhesion to metal tests, and the result expressed as the maximum force divided by the total bonded area of one of the double sandwiches. The British equivalent BS 903 Part A 1416 is identical. 

With metals, the modulus is stress divided by strain (Young s modulus) and is both a ratio and a constant. In the case of polyurethanes, the load defection curve is linear only over the first few percent. The Young s modulus is calculated in this area. As the curve passes through the origin, the modulus is the same in compression as in tension. Work has also shown that the Young s modulus is three times shear modulus (Wright and Cummins, 1969). 

To reduce the number of unknown parameters of the model, it was assumed [203] that the dependence (Jmm( h) can be determined from existing experimental data [200,212]. Fig. 8.13 compares the shear modulus for two limiting states of the membrane matrix equilibrium (rj) and nonequilibrium (77 ). The model proposed qualitatively agrees with few reliable experimental data on the effect of dissolved hydrogen on the mechanical modules. It correctly predicts the decrease in both Young s modulus and sheer modulus during the saturation of the metal with hydrogen in a wide... 

Fig. 4.4 Yield stress normalized by the elastic shear modulus plotted against a size scale parameter (volume per surface area) illustrating the six orders of magnitude of stress levels and ten orders of magnitude of size related to plastic behavior of single crystal metals [152]...

This approach correctly predicts the observed effective sound velocity, c, in the case of metal inclusions in a soft viscoelastic medium ), but cannot be applied when the medium has a large shear modulus. 

For crystals of reasonably pure, well-annealed metals at a given temperature, slip begins when the resolved shear stress reaches a certain critical value, which is characteristic of each metal. In the case of aluminum, for example, the observed critical shear stress Uco is usually about 4x10 N/m ( 4 bars = 0.4 MPa). Theoretically, for a perfect crystal, the resolved shear stress is expected to vary periodically as the lattice planes slide over each other and to have a maximum value that is simply related to the elastic shear modulus /t. This was first pointed out in 1926 by Frenkel who, on the basis of a simple model, estimated that the critical resolved shear stress was approximately equal to h/Itt (see Kittel 1968). In the case of aluminum (which is approximately elastically isotropic), = C44 = 2.7x10 N/m, so the theoretical critical resolved shear stress is about lO wco for the slip system <100>(100). 

FIGURE 1.10. Shear modulus G, bulk modulus K, Young s modulus E, and Poisson s ratio v of tungsten vs. temperature, as calculated fium single-crystal elastic constants (Gj, E, and v ) [1.31], and from measurements on polyciystalline tungsten (G, K, E, and Vj). [1.30] Taken from Metals Handbook [1.40]. o... 

For a typical metal, the shear modulus is measured in gigapascals, implying an ideal strength of the same order. This value is to be contrasted with typical... 

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