Relative tensile modulus

Poisson s ratio for the off-axis loaded lamina, v y, can also be derived. The relative tensile modulus, E jEi, shear modulus, Gj jGi2, and Poisson s ratio, v y, are plotted as a function of the angle of rotation, 9, for a glass-fiber-reinforced epoxy lamina and a graphite-fiber-reinforced epoxy lamina in Figures 5.120a and 5.120b, respectively. 

FIGURE 16.31 Relative storage vs. relative tensile modulus for PA, PP and their melt compounded CPNC at r = 25°C with different degree of clay dispersion. (From Sepehr and Utracki [2006].)... 

A number of micro-mechanical models have been developed over the years to predict the mechanical behavior of particulate composites [23-2. Halpin-Tsai model has received special attention owing to better prediction of the properties for a variety of reinforcement geometries. The relative tensile modulus is expressed as... 

Relative tensile modulus of OMMT-polypropylene nanocomposites as a function of inorganic volume fraction. The solid line represents the fitting by using unmodified Halpin-Tsai equation. (Reproduced from Mittal, V., /. Thermoplast. Compos. Mater., 22, 453, 2009. With permission from Sage Publishers.)... 

Figure 1.1 (a) Relative oxygen permeation and (b) relative tensile modulus of various polymer... 

Figure 12.32. Relative tensile modulus of pure HDPE, PET/HDPE conventional composite and MRC as a function of different exposure times where the relative tensile modulus is the ratio of the true modulus and the modulus of pure HDPE without exposure...

Based on the exact classical solution of the spherical-cavity problem (single spherical void embedded in an infinite elastic medium [Goodier 1933, Timoshenko Goodier 1951]), dilute-limit approximations to the problem of non-interacting spherical cavities (i.e. single pores or a dilute system of pores) in an elastic matrix have been obtained by Dewey [Dewey 1947] and Mackenzie [Mackenzie 1950], cf. also [Christensen 1979, Christensen 2000, Nemat-Nasser Hori 1999, Torquato 2002]. For the relative shear modulus, the relative bulk modulus, the relative tensile modulus and the relative Poisson ratio we have... 

Note that this exponential model results in a zero relative tensile modulus only in the limiting case of 100 % porosity. Without doubt, porosities close to 100 % can in principle be achieved, eg. in some aerogels [Gibson Ashby 1997]. However, the usual case encoimtered in practice will be a complete structural breakdown (loss of integrity) at significantly lower porosity levels. In order to allow for the possibility oi E =0 at porosities lower than 100 % (i.e. < 1), it is necessary to include a critical volume fraction (f)/ in the modulus-porosity relation, which is able to take the possible occurrence of a... 

In concluding this section we would like to emphasize that of course all semi-empirical relations presented for the relative tensile modulus can be used for fitting experimentally measured data for any kind of elastic modulus (and many other properties as well). Also it may be attempted to interpret the values obtained for the intrinsic properties by fitting in terms of a pore shape influence. However, the intrinsic value of 2 in the case of porous materials with spherical pores and Vq = 0.2 is specific to the tensile modulus (where... 

Figure 4. Voigt bound (solid straight line) and Hashin-Shtrikman upper bound (solid curve) for the relative tensile modulus of porous ceramics (e.g. alumina, zirconia or alumina-zirconia composites) the Reuss bound and the lower Hashin-Shtrikman bound (dashed lines along the axes) degenerate to zero...

Figure 7. Relative tensile modulus of porous ceramics (measured values, predictions and master fit) HS upper bound (thin solid curve), predictions for spherical pores (thin dotted special case of the Spriggs relation Eq. (110), thin dashed Coble-Kingeiy Eq. (117), thick solid modified exponential relation Eq. (114)), experimentally measured values (squares alumina, diamonds ZTA, triangles ATZ, circles zirconia, empty potato starch as a pore-forming agent, full com starch as a pore-forming agent) and master curve (thick dotted curve obtained by fitting with the Pabst-Gregorova relation, Eq. (121), critical porosity 0.729).

Accelerated Weathering xenon-arc Weather-Ometer 20.8 8 94 97 Relative tensile modulus strain calculated from grip separation Halar Ausimont Specimen 2 mm (0.08 in) nominal thickness, microtensile specimen to ASTM D1708... 

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