Transversal modulus

The difference between the bounds defined by the simple models can be large, so that more advanced theories are needed to predict the transverse modulus of unidirectional composites from the constituent properties and fiber volume fractions (1). The Halpia-Tsai equations (50) provide one example of these advanced theories ia which the rule of mixtures expressions for the extensional modulus and Poisson s ratio are complemented by the equation... 

The transverse modulus is lower partly because the cell wall is less stiff in this direction, but partly because the foam structure is intrinsically anisotropic because of the cell shape. When wood is loaded across the grain, the cell walls bend (Fig. 26.5b,c). It behaves like a foam (Chapter 25) for which... 

The explanation is almost the same as that for the transverse modulus the cell walls bend like beams, and collapse occurs when these beams reach their plastic collapse load. As with the moduli, moisture and temperature influence the crushing... 

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. 

Fig. 3.7 Variation of longitudinal and transverse modulus in unidirectional composites...

Example 3.5 Calculate the transverse modulus of the PEEK/carbon fibre composite referred to in Example 3.2, using both the simplified solid mechanics approach and the empirical approach. For PEEK = 0.36. 

Predicted results for E2 are plotted in Figure 3-10 for three values of the fiber-to-matrix-modulus ratio. Note that if Vj = 1, the modulus predicted is that of the fibers. However, recognize that a perfect bond between fibers is then implied if a tensile <32 is applied. No such bond is implied if a compressive 02 is applied. Observe also that more than 50% by volume of fibers is required to raise the transverse modulus E2 to twice the matrix modulus even if E, = 10 x E ,l That is, the fibers do not contribute much to the transverse modulus unless the percentage of fibers is impractically high. Thus, the composite material property E2 is matrix-dominated. 

A unique but not yet widespread technique that may influence the interfacial bond quality relies on the localized variation in the polymer modulus normal to the polymer-substrate junction in the composite assembly, as illustrated schematically in Fig. 15 [41,52]. The transversal modulus variation may be accomplished by interposing a tertiary interphase between the substrate and... 

Evidently, the critical pressure to cause failure decreases with a stiffer interphase modulus, E, or a reduced interlayer thickness, h, or both. This hypothesis has been tested on several simulation systems, which confirm that increased adhesion is possible with a negative transversal modulus gradient at the material interface. 

Figure 15 Shematic representation of transversal modulus gradient at the material interface.

The moduli of elasticity, G for shear and E for tension, are ratios of stress to strain as measured within the proportional limits of the material. Thus the modulus is really a measure of the rigidity for shear of a material or its stiffness in tension and compression. For shear or torsion, the modulus analogous to that for tension is called the shear modulus or the modulus of rigidity, or sometimes the transverse modulus. 

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. 

We will see in Section 5.4.2 that the elastic modulus of a unidirectional, continuous-fiber-reinforced composite depends on whether the composite is tested along the direction of fiber orientation (parallel) or normal to the fiber direction (transverse). In fact, the elastic modulus parallel to the fibers, Ei, is given by Eq. (1.62), whereas the transverse modulus, 2, is given by Eq. (1.63). Consider a composite material that consists of 40% (by volume) continuous, uniaxially aligned, glass fibers (Ef =16 GPa) in a polyester matrix (Em = 3 GPa). 

Figure 8.11 Transverse modulus development during cure for IM6/3100...

Cure temperature (°C) a Degree of cure Et (GPa) transverse modulus [standard deviation] XT (MPa) transverse strength [standard deviation]... 

To ascertain the effect of increased transverse modulus after postcure, nine [90]8 254 mm x 152.4 mm postcured specimens were mechanically tested to obtain the transverse modulus after postcure. Once this data was obtained the increase in curvature due... 

This equation suggests that E, unlike Ed, is strongly influenced by the matrix modulus. Therefore, if the modulus of the matrix in practical cases decreases due to water absorption or creep relaxation, the transverse modulus will be seriously affected, in contrast to Ed ... 

Figure 4 shows the variation of the laminate axial modulus E, transverse modulus E., shear modulus, major Poisson s ratio (normalised by their undamaged value) as a function of the relative delamination area D " for the [Oj /30j /- 302], laminate Matrix crack density was... 

A recent analysis [5] has developed that used previously [4] and has included the lateral stress distribution in the beam beyond the crack tip. For anisotropic composites with a transverse modulus E2, a shear modulus /land Poisson s ratio v we have,... 

Rg. 11.7 A comparison between experimental moduli for low-density polyethylene filaments and values calculated using the pseudo-affine aggregate model E, extensional modulus Ei, transverse modulus and G, torsional modulus (a) experimental, (b) calculated and (c) experimental and calculated. (Reprinted by permission of Kluwer Academic Publishers.)... 

Fiber Axial modulus GPa (Msi) Transverse modulus GPa (Msi) Inplane shear modulus GPa (Msi) Poisson s Ratio Axial tensile strength MPa (Kslj Transverse tensile strength MPa (Ksij Axial compressive strength MPa (Ksi) Transverse compressive strength MPa (Ksi) Inplane shear strength MPa (Ksi)... 

High modulus melt-spun PE from Hoechst Celanese Certran has a modulus of about 40 GPa (common unreinforced engineering TPs have a modulus in the range 2.3 to 3 GPa) showed a longitudinal modulus of 37 GPa for imidirectional fiber and 110 MPa longitudinal strength, a transverse modulus of 3.9 GPa and transverse strength 28 MPa. The process continues to be applied to all melt-spun fibers. 

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