Transverse modulus, measurement

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. 

In Fig. 4 these experimental values based on X-ray measurement, are plotted against the cohesive energy density of the material. It might be expected that the more polar the polymer, the higher the transverse modulus. This hypothesis seems to be supported by the data. Two further values for polyethylene have not been included since they were obtained by other methods. Samuels, using the sound wave method obtained a... 

The effective adhesive transverse modulus Ea takes into account the fact that adhesive properties are different in bulk and film forms. In a bonded joint the adhesive layer is a film. When loaded using through thickness tensile or compressive loads the adherends restrict the deformations of the adhesive, unlike when the bulk form of the adhesive is being similarly loaded. These restrictions in deformations tend to increase the adhesive modulus measured between the relatively stiff adherends. This effective modulus is difficult to establish theoretically. 

There have been no similar attempts to determine comprehensive sets of elastic constants for oriented fibres or monofilaments. Kawabata [21] devised an apparatus that used a linear differential transformer to measure diametral changes of 0.05 iim in single fibres of diameter 5 fxm subjected to transverse compression. Equation (7.2) above was then used to calculate the transverse modulus El = l/ ii. Results were obtained for poly(p-phenylene terephthalamide) (Kevlar) and high-modulus polyethylene (Tekmilon) fibres. Values of E were in the range 2.31 -2.59 GPa for Kevlar and a value of 1 -2 GPa was found for Tekmilon. 

Longitudinal and transverse properties are applicable to unidirectionally reinforced composites. Suffix (F) to modulus and strength values indicates that tests were reported to have been performed in fiexure rather than tension Sonic modulus measurement method [87]... 

The transverse Poisson s ratio can be determined by measuring 2 the change in diameter parallel to the plane of contact in the compression of the monofilament under conditions of plane strain as described in the section on the transverse modulus above. 

In the above equations, is the tensile modulus measured in direction I, E2 is the transverse tensile modulus, Gi2 and G23 are shear moduli corresponding to shear stresses in directions 2 and 3 on planes perpendicular to 1 and 2 respectively, and v 2 = and V23 = —S2IC2 are Poisson s... 

The hardness of wood varies markedly from soft balsa to hard ironwood with pine, oak, and maple in between. It is measured either by determining the force needed to push a hard ball (diameter = 0.444 in) into the wood to a depth equal to half the ball s diameter (Janka hardness) or by the initial slope of the force vs. penetration-depth curve (Hardness modulus). Average values of Janka hardnesses for typical woods are listed in Table 13.1. The data are from Green et al., (2006), and are for penetration transverse to the tree axis. The values are for moisture contents of about ten percent. The first set of five items are hardwoods, while the second set are softwoods. To roughly convert Janka hardnesses to VHN multiply by 0.0045. 

---