Transverse shear modulus

The explicit formulae given by Rosen55 are also of value. They are derived from a model consisting of a random assemblage of composite cylinders (Hashin and Rosen56 ) and expressed in terms of the axial Young modulus E, the Poisson ratio for uniaxial stress in the fibre direction v, the transverse plane strain bulk modulus k, the axial shear modulus G and the transverse shear modulus G. ... 

For materials with a strong bond between the matrix and the fiber, models for steady transverse creep are available. The case of a linear matrix is represented exactly by the effect of rigid fibers in an incompressible linear elastic matrix and is covered in texts on elastic materials.7,11,12 For example, the transverse shear modulus, and therefore the shear viscosity, of a material containing up to about 60% rigid fibers in a square array is approximated well... 

Fig. 4.1 Dependences of the Young s moduli i ( (parallel to the c-axis), E, (parallel to the h-axis), and (parallel to the a-axis), and the axial-transverse elastic constants C55 and the transverse shear modulus Ju (= cgg) of a perfect orthorhombic polyethylene crystal on temperature as calculated by Karasawa et al. (1991).

The results of the Eshelby inclusion model of Chow (1978) are summarized in Figs. 4.4 and 4.5 for a prominent application in which the heterogeneities are much stiffer than the matrix and the results are evaluated for the special system of glass fiber or disks in an epoxy-resin polymer matrix where the shear modulus and bulk modulus of the glass are 30.6 GPa and 44.4 GPa, respectively, and those of the epoxy-resin matrix are 1.30 GPa and 3.90 GPa, respectively. For this system the dependence on volume fraction (p of filler of the normalized shear modulus of the heterogeneous composite is given in Fig. 4.4, with p being either the transverse shear modulus p 2 axial-radial shear modulus of the com-... 

Figure 14.19 Draw ratio dependence of the transverse shear modulus of PC + Vectra B blends, with same legend as Figure 14.16. (Adapted from [10] by permission of the Society of Plastic Engineers.)...

Hence, to define the elastic properties of the fiber, five independent components of elastic modulus are required—Axial Young s modulus En or ii ) Shear modulus (Gn or G ) Transverse Young s modulus (ii22 or Transverse Shear modulus (G22 or G ) and the Axial Poisson ratio (vi2 or v ). 

During load transfer, large shear stresses are transmitted by the adhesive layer to the adherend surfaces adjacent to the adhesive layer, which entails that shear stress equilibrium at the interface is maintained. These shear stresses trigger adherend shear deformations. Shear stresses are especially significant for adherends with relatively low transverse shear modulus, such as in the case of laminated FRP composites. This theory assumes a linear shear stress distribution through the thickness of the adherend, whereas... 

The engineering properties of interest are the elastic constants in the principal material coordinates. If we restrict ourselves to transversely isotropic materials, the elastic properties needed are Ei, Ei, v, and G23, i.e. the axial modulus, the transverse modulus, the major Poisson s ratio, the in-plane shear modulus and the transverse shear modulus, respectively. All the elastic properties can be obtained from these five elastic constants. Since experimental evaluation of these parameters is costly and time-consuming, it becomes important to have analytical models to compute these parameters based on the elastic constants of the individual constituents of the composite. The goal of micromechanics here is to find the elastic constants of the composite as functions of the elastic constants of its constituents, as... 

Kriz and Stinchcomb [32] published experimental data for unidirectional graphite/epoxy composites. These results illustrate the case when the fibres are transversely isotropic. The elastic properties of the matrix are = 5.28 GPa and T = 0.354, and for the fibres E = 232 GPa, E = 15 GPa, 0(2 = 24 GPa, v 2 = 0.279 and v 3 = 0.49. In Figs 11.21-11.25 are plotted the predictions against the experimental data for , , G12, G23 and V23, i.e. the longitudinal or axial modulus, the transverse modulus, the in-plane shear modulus, the transverse shear modulus and the transverse Poisson s ratio, respectively. 

For the transverse shear modulus, the approach designated self-consistent was based on the formula obtained by the self-consistent method for the plane-strain bulk modulus (11.61), on the transverse modulus calculated using the Chamis approach (11.49b) and the in-plane Poisson s ratio given by the rule of mixtures. Except when used to predict the axial modulus and the major Poisson s ratio, the rule of mixtures underestimates the remaining composite elastic properties. The Bridging Model proved to be a very effective theory to account for all five elastic properties for unidirectional composites that are transversely isotropic. 

In calculating the effect of the twisting torque, the transverse shear modulus of the unidirectional RP has been used. For an RP with... 

The BE theory is based on the assumption of pure bending. Consequently, it does not account for transverse shear deformation effects. These are known to increase with the ratio of the axial Young s modulus n) to the axial-transverse shear modulus (G12 or G23), the thickness to length ratio of the beam (tj /L or tj,/L), and the vibration mode number. 

In the ranges of 0.0081 < t/L < 0.0121 and 1 < n < 5 the corresponding equations of vibrating cantilever beams ("clamped-free" end conditions) have been applied successfully to a unidirectional graphite fibre reinforced epoxy composite revealing an E i to G12 ratio of 40 [5]. In the case of unidirectional on-axis specimens, however, 0 2 is the "longitudinal transverse shear modulus" and the terms "in-plane shear" and "interlaminar shear" are not defined. 

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