Cross-ply ratio

For the special cross-ply laminates, two geometrical parameters important N, the total number of layers, and M, the ratio of the total kness of odd-numbered layers to the total thickness of even-nbered layers (called the cross-ply ratio). Thus,... 

For both odd- and even-layered special cross-ply laminates, the extensional stiffnesses, Aj., are independent of N, the number of layers (although the N individual lamina thickneWs can be summed to get the total laminate thickness t, so N is implicit im quations (4.78) and (4.82)). However, A., and A22 depend on M, the cross-ply ratio, and on F, the lamina stiffness ratio, as shown in Figures 4-22 and 4-23. For a typical glass-fiber-reinforced lamina, F =. 3, so A, varies from. 65Q.nt to... 

Figure 4-22 Extensional Stiffness, A, versus Cross-Ply Ratio, M (After Tsai [4-6])...

The particular cross-ply laminate to be examined [4-10] has three layers, so is symmetric about its middle surface. Thus, no coupling exists between bending and extension. Under the condition N = N and all other loads and moments are zero, the stresses in the (symmetric) outer layers are identical. One outer layer is called the 1-layer and has fibers in the x-direction (see Figure 4-39). The inner layer is called the 2-layer and has fibers in the y-direction. The other outer layer is the 3-layer, but because of symmetry there is no need to refer to it. The cross-ply ratio, M, is, 2, so the thickness of the inner layer is ten times that of each of the outer layers (actually, the inner layer" is ten like-oriented lamina Each lamina is. 005 in (.1270 mm) thick, so the total laminate thickness is. 060 in (1.524 mm). 

Figure 4-43 Strength of a Cross-Ply Laminate with M =. 2 (After Tsai [4-10]) Strength and Stiffness for Other Cross-Ply Ratios...

Theoretical and measured strengths and stiffnesses of three-layer cross-ply laminates with cross-ply ratios ranging from. 2 to 4 are shown in Figure 4-44. The scatter in the data is partially due to the difficulty of making good tensile specimens the characteristic dog-bone shape is formed by routing that often damages the 90° layer. 

For two- and three-layered cross-ply and angle-ply laminates of E-glass-epoxy, Tsai [4-10] tabulates all the stiffnesses, inverse stiffnesses, thermal forces and moments, etc. Results are obtained for various cross-ply ratios and lamination angles, as appropriate, from a short computer program that could be used for other materials. 

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. 

The lamination scheme used is an antisymmetric cross-ply (0/90/.. . ) of eight layers. The adhesive Poisson s ratio is assumed to be a constant, v = 0.38. The material properties listed... 

Matrix cracking results in reduction in the laminate stiffness and strength. Stiffness reduction in CMCs is greater than that observed in polymer matrix composites due to lower ratio between fibre and matrix moduli. It also affects coefficients thermal expansion and vibration frequencies. A number of models have been suggested to estimate the effect of transverse macrocracks in the 90° plies and matrix cracks bridged by fibres in the 0° plies on the mechanical properties of cross-ply CMC laminates (Pryce and Smith, 1994 Daniel and Anastassopoulos, 1995 Lu and Hutchinson, 1995 Erdman and Weitsman, 1998 Birman and Byrd, 2001 Yasmin and Bowen, 2002 Birman and Weitsman, 2003). 

The presence of a cross-linked network again led to the development of good pressure-sensitive properties. A plot of peel strength vs. composition for the cured PVEE-MCEA system is shown in Pig. 4. In subsequent experiments, the pressure-sensitive properties were maximized at 3.8 pli/48 hour shear for the 55/45 ratio. 

With specimens of a cross section of breadth B = 9 mm and a width W = 4.3 mm, it was shown in /2/ that with the help of a "Stack Model", the shear failure near the neutral axis could be explained, even at high span/width ratios, S/W, where failure in pure tension/compression was expected.This model considered the relative ply thickness Aw/W in bending... 

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