EXAMPLE 7.1 FIGURE 7.6 we can use equation (7.9)for the flexural modulus in both cases.For the stacking sequences are different.Since the ply thicknesses are all the same, Solution.The total number of plies is N=6 in each case,and only the have the same thickness. 5x 106 psi (34.48 GPa).and E2=1.5 x 106 psi (10.34 GPa),and the plies all having stacking sequences of [0/90/0]and [90/0/901 The ply moduli are E= Determine the flexural and Young's moduli of E-glass/epoxy laminated beams stresses,will be discussed later. nated plates along with failure criteria,which include the interlaminar Both normal and shear components of the interlaminar stresses in lami- cussed in chapter 4 were based only on in-plane stresses in the lamina. composites known as delamination.Recall that the failure criteria dis- Interlaminar stresses are responsible for an important failure mode in stress distribution departs significantly from the parabolic distribution. (7.22).For a small number of plies,however,the laminated beam shear expected to approach the parabolic distribution described by equation increases,the shear stress distribution for the laminated beam can be B,is shown for both types of beams in figure 7.6.As the number of plies The shear stress distribution,as governed by the variation of the factor beams with a small number of plies and a large number of plies. homogeneous,isotropic beams and for laminated beams.Results are given for laminated Variation of shear stress,as governed by the factor B,across half the beam thickness for Many plies Laminated,large N Homogeneous isotropic : Few plies -Laminated,small N -Homogeneous isotropic Principles of Composite Material Mechanics and thickness is governed hy the EXAMPLE 7.2 distribution of normal and shear stresses through the thickness of the beam. Assume a ply thickness of 0.01 in (0.254 mm). For the [90/0/90],E-glass/epoxy beam described in example 7.1,sketch the result regardless of the ply-stacking sequence,as long as the number of longitudinal and transverse plies remains unchanged). depend on the stacking sequence (i.e.,the rule of mixtures gives the same not the same as the Young's modulus.The Young's modulus does not Note that the flexural modulus depends on the stacking sequence and is For the [90/0/901,beam E=1.5(+5(x10psi=2.66x10psi (18.34 GPa) fraction of transverse(90)plies.Therefore, (26.4GPa) where v1=volume fraction of longitudinal (0)plies and v2 volume The Young's modulus,or extensional modulus,can be estimated by using the rule of mixtures =4.09x10psi(28.2 GPa) xR-H+Oe一++—多交法 Analysis of Laminates