Longitudinal modulus calculation

The ultrasonic longitudinal and shear wave speeds were measured at room temperature for two fully oxidized samples of Ba2YCu307, as described above. From these values and the measured mass density, a longitudinal modulus,, and a shear modulus, Cs, can be calculated from Equation 3. The ordinary isotropic elastic moduli are related to these two moduli by ... 

High fibre volume is essential for good aircraft stmcture performance. It is also important that distribution of both fibre and resin is uniform throughout the component. To illustrate, the simple mle of mixtures (ROM) approach for calculation of longitudinal modulus falls into the mechanics of materials category the modulus of elasticity in the longitudinal direction ( l), which is the direction parallel fibres, is given as ... 

Examples of angle-ply and quasi-isotropic laminated T300/5208 (carbon/ epoxy) are analysed in terms of in-plane and flexural engineering constants. The lamina engineering constants were given in Table 11.1. Table 11.2 shows the longitudinal modulus and Poisson s ratio for different laminates experimentally measured [14]. The measured data compare quite well with calculated values from CLT. 

It may be seen from Fig. 3 that, as transverse crack density increases, all stiffness properties of the laminate are significantly reduced. Longitudinal and transverse moduli of the undamaged laminate, calculated from the classical lamination theory, are 166.5 GPa, shear modulus 44 GPa, Poisson s ratio 0.19. When transverse cracking in the 90° layer reaches saturation, the laminate longitudinal and shear moduli are predicted to lose more than 45% of their value. Inclusion of tensile residual stresses into the analysis would lead to even more significant reduction in the longitudinal modulus and Poisson s ratio, but reduction in shear modulus would remain the same. Predictions for a [O/OOi], SiC/CAS laminate are shown in Fig. 4. 

Calculate longitudinal modulus and longitudinal strength for an aligned and continuous fiber-reinforced composite. 

It is convenient to compare the actual modulus E with that calculated in the absence of thermal and longitudinal stresses, that is, from Eq. (17.202). From Eqs. (17.202) and (17.207), we find... 

In practice growth stresses are not measured directly (Archer, 1987). It is easier to release the stress and measure the strain relief (e), together with the elastic modulus or stiffness, E. The growth stress (a) is calculated assuming simple elastic theory, E = o/e. Where growth stresses are severe the longitudinal tensile strain at... 

Knowing the mass density p of the sample, the longitudinal elastic modulus c, related to the wave vector q, can be calculated according to Eq. (18). This equation is most important since it provides the key for the determination of the mechanical properties of materials at hypersonic frequencies from BriUouin spectra in a nondestructive manner. 

In order to illustrate the influence of the polymer modifications on the resulting tensile stresses 8, these can be calculated in approximation when the E-modulus E and the longitudinal change c are known. The results from the detection of these parameters were set in the following equation ... 

Fig. 40. (a) Temperature dependence of the longitudinal acoustic-phonon frequencies of Smo Y jsS in the [111] direction for four different values of the wavevector q (see Mook et al. 1981). (b) Temperature dependence of the bulk modulus Cg of Sm Y 25S measured by Bril-iouin scattering. Cg continues to soften upon cooling below 200 K, uniike the behavior of the phonon mode frequencies for qaO.l (flg. 40a). (c) Temperature dependence of the charge relaxation rate derived from the experimental data in figs. 40a and 40b (open circles) and calculated from theory (Schmidt and Miiller-Hartmann 1985) (solid line). The theoretical curve has been matched at 300 K to the experimental value. 

For unidirectionally reinforced composites, the elastic modulus of the composites along the longitudinal direction (in parallel mode) can be calculated by... 

Two methods are used for bend testing—three- and four-point bending tests. Here, the specimens are rectangular, without notches. It is obvious from Fig. 1.48 that the applied force (downward arrows) is compressive by nature, resisted by the tensional force (upward arrows). Thus, the longitudinal stresses at the lower surfaces (convex) in the specimens are tensile and compressive at their upper surfaces (concave). As a consequence, a calculable bending moment develops. The modulus of rupture is the stress of the specimen at its failure and represents the flexural strength of the specimen. 

---