Experimental Young’s modulus

Figure 7. Correlation of experimental Young s modulus and molecular mechanics calculated (kcal/mol) interaction energies for low molecular weight hgnins with cellulose.

Calculated interaction energies of lignins with cellulose and experimental Young s modulus of Ugnins/ceUulose composites... 

Ln C02 lignin presented a somewhat anomalous behaviour it presented a stronger calculated attraction but the experimental Young s modulus value, although the second best of the four lignins tested, did not maintain the same expected trend and was lower than expected. 

Linear elasticity is the most basic of all material models. Only two material parameters need to be determined experimentally Young s modulus (E) and Poisson s ratio (v). Young s modulus can be obtained directly from uniaxial tension or compression experiments typical values (Kurtz et al. 2002) for a few select UHMWPEs at room temperature are presented in Table 14.3. 

Fig. 2.25 Experimental Young s modulus data of high purity alumina for three driferent green densities exjHessed by the theoretical ex nessions mentioned above [5]. With kind permission of John Wiley and Sons...

Using scanning force microscopy, Du et al. (4) determined Young s modulus of polyethylene single crystals in the chain direction to be 1.7 x 10" Pa. Ultra-drawn polyethylene fibers also have an experimental Young s modulus of... 

Use the equation, with the average A, to calculate the approximate Young s modulus of (a) diamond and (b) ice. Compare these with the experimental values of 1.0 X 10 Nm" and 7.7 X 10 Nm" respectively. Watch the units ... 

Obviously, the assumptions involved in the foregoing derivation are not entirely consistent. A transverse strain mismatch exists at the boundary between the fiber and the matrix by virtue of Equation (3.8). Moreover, the transverse stresses in the fiber and in the matrix are not likely to be the same because v, is not equal to Instead, a complete match of displacements across the boundary between the fiber and the matrix would constitute a rigorous solution for the apparent transverse Young s modulus. Such a solution can be found only by use of the theory of elasticity. The seriousness of such inconsistencies can be determined only by comparison with experimental results. 

The mechanics of materials approach to the estimation of stiffness of a composite material has been shown to be an upper bound on the actual stiffness. Paul [3-4] compared the upper and lower bound stiffness predictions with experimental data [3-24 and 3-25] for an alloy of tungsten carbide in cobalt. Tungsten carbide (WC) has a Young s modulus of 102 X 10 psi (703 GPa) and a Poisson s ratio of. 22. Cobalt (Co) has a Young s modulus of 30x 10 psi (207 GPa) and a Poisson s ratio of. 3. 

For a Hookian material, the concept of minimum strain energy states that a material fails, for example cell wall disruption occurs, when the total strain energy per unit volume attains a critical value. Such an approach has been used in the past to describe a number of experimental observations on the breakage of filamentous micro-organisms [78,79]. Unfortunately, little direct experimental data are available on the Young s modulus of elasticity, E, or shear modulus of elasticity G representing the wall properties of biomaterial. Few (natural) materials behave in an ideal Hookian manner and in the absence of any other information, it is not unreasonable to assume that the mechanical properties of the external walls of biomaterials will be anisotropic and anelastic. 

A glass fiber mat in which the fibers appear to be randomly oriented is impregnated with a thermosetting resin and cured. Strips are cut from the sheet in different directions, and their Young s modulus is measured. The Young s moduli are not the same in different directions. If the differences are much greater than the expected experimental errors, what is the most probable cause of the difference in moduli ... 

The left-hand side term represents the increment in matrix Young s modulus divided by the volume fraction (dE/dVf), all of which are experimentally determined. Additionally, since / Em and when q0 and q, are reasonably large, the equation can be rewritten as ... 

The increment in mechanical properties (tensile strength, 300% modulus, and Young s modulus) as a function of SAF is plotted in Fig. 39. In general, the higher level of SAF, which in turn indicates better exfoliation, results in high level of property enhancement. However, the level of increment with the increase in SAF is different in all three cases and follows a typical exponential growth pattern. The apparent nonlinear curve fitting of the experimental values presented in Fig. 39 is a measure of the dependence of mechanical properties on the proposed SAF function. 

Fig. 43 Fitting of composite models on introduction of IAF, for the sepiolite-filled NR nanocomposites symbols represent predicted values and the line indicates the best fit of the experimental data. YM Young s modulus...

Compared to other models (e.g., Voigt-Reuss, Halpin-Tsai, modified mixture law, and Cox), the dilute suspension of clusters model promulgated by Villoria and Miravete [255] could estimate the influence of the dispersion of nanofillers in nanocomposite Young s modulus with much improved theoretical-experimental correlation. 

In performing such experiments on isotropic materials, one is accustomed to express the elastic stiffness parameters in the experimentally more readily accessible technical parameters E (Young s modulus) and v (Poisson ratio). The relative change in length, in the direction of the tensile stress a is, by definition, given by (Al/t)i — a/E, whereas v = (Af/ )x/( A / )u. For several magnetostrictive films and substrates, E and v values are listed in table 1. Some useful relations are ... 

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