In-plane shear modulus

As in the case of the transverse tensile modulus, 2. the above analysis tends to underestimate the in-plane shear modulus. Therefore, once again it is common to resort to empirical relationships and the most popular is the Halpin-Tsai equation... 

The in-plane shear modulus of a lamina, G12. is determined in the mechanics of materials approach by presuming that the shearing stresses on the fiber and on the matrix are the same (clearly, the shear deformations cannot be the samel). The loading Is shown in the representative volume element of Figure 3-15. By virtue of the basic presumption,... 

ISO 14129 1997 Fibre-reinforced plastic composites - Determination of the in-plane shear stress/shear strain response, including the in-plane shear modulus and strength, by the plus or minus 45 degree tension test method... 

Therefore, the unidirectional translaminar (i.e. through-thickness) shear strength can be obtained for the maximum load and the in-plane shear modulus of elasticity, Gu, taken from the initial linear portion of the unidirectional shear stress-shear strain (ti2 - y 2) curve ... 

The plate-twist test for in-plane shear modulus requires only that a square plate be supported on two diagonal points and loaded on the other diagonal by tw=o further points. The test is similar to a flexure test and has the same benefits of low loads, large (linear) speeimen deflections, cheap specimens, and simple test equipment (sec Fig. 6). The test has been standardized for plywood for many years and has featured in many reviews over the last 25 years. 

ISO DIS 15,310, Reinforced plastic—Determination of in-plane shear modulus by the plate twist method. 

In this chapter, we use the term membrane to denote a thin film of one material that separates two similar (bilayer membrane) or dissimilar (mono-layer membrane) materials. We focus on fluid membranes (where there is no in-plane shear modulus and the only in-plane deformations are compres-sions/expansions), which are important in industrial applications such as encapsulation and cleaning. Furthermore, some fluid membranes are prototypes of biological systems, although it should be noted that true biological membranes often have several components and sometimes, even a solidlike underpinning that can give the membrane a shear rigidity. 

The four independent constants in the stress/strain equations are Ei, the modulus of elasticity in the fibre direction, E2, the modulus in the transverse direction, v, Poisson s ratio, and Gu, the in-plane shear modulus. The unidirectional lamina plays an essential role in structural engineering, for... 

Engineering constants for each multilayer laminate, axial and lateral E-moduli, Poisson s ratio, and the in-plane shear modulus (E, Ey, v y, G y) can be calculated from the inversion of eqn 4.8 (see Herakovich 1998). 

Coupling terms of laminate stiffness matrix Bending terms of laminate stiffness matrix Longitudinal Young s modulus of the lamina Transverse Young s modulus of the lamina In-plane shear modulus of the lamina Out-of-plane shear modulus of lamina (in the 1-3 plane) Out-of-plane shear modulus of lamina (in 2-3 plane) Moment stress resultants per unit width Force stress resultants per unit width Laminate reduced stiffness terms Transformed reduced stiffness terms... 

Longitudinal tension and compression moduU Shear modulus In-plane shear modulus Second moment of area Major and minor axis second moments of area Span of simply supported beam Longitudinal tension and compression strengths Longitudinal in-plane shear strength Mid-span deflection Point load Shear stiffness ratio... 

Gi2 = in plane shear modulus = shear modulus in 1-2 plane = 21 (J23 = shear modulus in 2-3 plane = G32 (5i3 = shear modulus in 1-3 plane = 31... 

Figure 22.2 Principal directions and stress components for an orthotropic material is the in-plane shear modulus as in plane No. 3 above.) Source Reprinted from University of London, Imperial College of Science, Technology and Medicine, Course entitled Mechanical Testing of Advanced Fibre Composites, 1995.

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... 

The effective in-plane shear modulus can be determined assuming that the composite is subjected to a uniform shear stress T12, as depicted in Fig. 11.12. In this case the shear stress is uniform across the composite the shear strains in the fibre and matrix are... 

Experimental data were obtained for the in-plane shear modulus G i of another unidirectional composite made of isotropic glass fibres and epoxy matrix with = 30.2 GPa and G = 1.8 GPa [31]. The predicted in-plane shear modulus G i is shown in Fig. 11.20. Again, in this case, the simple... 

In-plane shear modulus G12 of unidirectional glass/epoxy composite as a function of fibre volume fraction (G = 30.2 GPa, G" = 1.8 GPa). 

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