Longitudinal moduli

Mechanical Properties. Although wool has a compHcated hierarchical stmcture (see Fig. 1), the mechanical properties of the fiber are largely understood in terms of a two-phase composite model (27—29). In these models, water-impenetrable crystalline regions (generally associated with the intermediate filaments) oriented parallel to the fiber axis are embedded in a water-sensitive matrix to form a semicrystalline biopolymer. The parallel arrangement of these filaments produces a fiber that is highly anisotropic. Whereas the longitudinal modulus of the fiber decreases by a factor of 3 from dry to wet, the torsional modulus, a measure of the matrix stiffness, decreases by a factor of 10 (30). 

Longitudinal modulus F = pocf Shear modulus G = pgcj... 

The transverse modulus, Ect, may be determined in a matmer similar to that described earlier for the longitudinal modulus. Consider a unidirectional fibre composite subjected to a transverse force, Fct, in the direction perpendicular to the fibre axis. 

From the relation (45) and by measuring in a tension test the longitudinal modulus of the composite Ec we can evaluate the Ef-modulus. The values of the Ef-modulus, together with the other moduli, are tabulated in Table 2, and they are plotted in Fig. 16. 

The transverse modulus (Mt) and many other properties of a long fiber resin composite may be estimated from the law of mixtures. The longitudinal modulus (Ml) may be estimated from the Kelly-Tyson equation (8.5), where the longitudinal modulus is proportional to the sum of the fiber modulus (Mp) and the resin matrix modulus (Mm)- Each modulus is based on a fractional volume (c). The constant k is equal to 1 for parallel continuous filaments and decreases for more randomly arranged shorter filaments. 

Since the contribution of the resin matrix is small in a strong composite, the second term in the Kelly-Tyson equation can be disregarded. Thus, the longitudinal modulus is dependent on the reinforcement modulus, which is independent of the diameter of the reinforcing fiber. 

The major Poisson s ratio is vl2 and E = E2/El is the ratio of the transverse to longitudinal modulus. Equation 8.24 gives the induced curvature for anticlastic deformation of an unsymmetric cross-ply laminate. The curvature is dependent on the thermal and chemical strain mismatch (e, — e2), lamina mechanical properties (v12, E) and the half-thickness, h. 

Sect. 6 a Aa T Do Fsh T X A M R De final radius of cylindrical gel after swelling displacement relaxation time for swelling collective diffusion constant shear energy trace of the strain tensor u,k swelling rate ratio total change of the radius of the gel longitudinal modulus ratio of the shear modulus to the longitudinal modulus effective collective diffusion constant... 

Here, E represents the longitudinal modulus only of the polymer network. The amplitude of the scattered light intensity from the gel is expressed by... 

Thus, the relaxation function observed by photon correlation spectroscopy will be a direct measure of the relaxational part of the longitudinal modulus. 

The orthogonal 3D woven laminate used in this work was elaborated and produced by the 3TEX Inc (USA). These laminates consist of unidirectional in-plane layers orientated in the 0 and 90° directions, The transverse reinforcing components are yarns orientated perpendicularly to the midplane, These yarns bind the material and hold the in-plane fibers together. This is achieved without interweaving the in-plane fibers, and hence the reduction in the in-plane stiffness caused by the fiber waviness is avoided. The amount of transverse yarns is about 3 percent of total fiber volume. The longitudinal modulus E of beams were 17.9 GPa and 56,3 GPa for glass and carbon fiber specimens respectively (measured in simple tension) The mechanical properties of the materials are described in detail in [5],... 

C22, C66 longitudinal modulus (along main fibrils), shear modulus of a craze... 

Figure 14.17. Longitudinal modulus vs. volume fraction of tungsten in epoxy. Tungsten having particle sizes from 0.5, 1, 5, and 10 xni is plotted on the graph. [Adapted, by pennission, from Nguyen T N, Lethiecq M, Levassort F, Patat F, Int. J. Polym. Analysis and Characterization, 1, No.4, 1995, 277-87.]...

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 ... 

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