Composite modulus energy terms can be simplified as and strains are uniform over the RVE and using equations(3.20),the strain Again making the mechanics of materials assumption that the stresses energy in the matrix,U: FIGURE 3.6 sented as the sum of the strain energy in the fibers,U,and the strain stress,the total strain energy stored in the composite,U can be repre- is possible by using a strain energy approach.Under the given state of Composites,206-217.) Further insight into the micromechanics of the longitudinal loading case for B-glass/polyester.(From Adams,R.D.,1987.Engineered Materials Handbook,Vol.1, elementary mechanics of materials models,(b)Comparison of predicted and measured E Variation of composite moduli with fiber volume fraction(a)Predicted E and E2 from 包 Fiber volume fraction Y28a6 E.3.23 E,GPa Fiber volume fraction,vr 010203040.506 Rule of mixtures A3:504m A d=20 jm .d=30 um Principles of Composite Material Mechanics 0.5 8350 G355) 25a 3.2 E 105ps Thus,the assumption of equal strains,which led to equation (3.23).is valid we find that a=2.0884,b1=0.1093,a1/b1=Gn/Gm =19.1,and Ea/Em =1.00 equation(3.24)leads to Em =0.55x10 psi (3.79 GPa) En =Er2 =10.5x10 psi (72.4 GPa) E8-1.53X100P81G0.55GPa1:-04B E-5.05X100p614.82Gpa2n-D.55 measured properties of an E-glass/epoxy composite [9], fiber strain to the matrix strain can then be found.For example,using the when composite,fiber,and matrix properties are known.The ratio of the tion(3.27)and equation (3.28)can be solved simultaneously for a and b to derive these equations.To check the strain distribution,however,equa- Note that we did not assume equal strains in fibers and matrix in order Substitution of equation(3.26),equation (3.20),and equation (3.25)in avr+biVm =1 of mixtures for stress,equation (3.19),leads to where a and bi are constants.Substitution of equation(3.26)in the rule the matrix be defined in terms of the composite stress as follows: strains is not made?"In order to proceed,let the stresses in the fibers and approach also allows us to ask,"What happens if the assumption of equal the rule of mixtures given by equation (3.23).But the strain energy with the assumption of equal strains from equation(3.22),again leads to is easily shown that substitution of equation(3.25)in equation(3.24),along ratios of the fiber and the matrix,so the approximation is justified [8].It to be of the order of the square of the difference between the Poisson's tions leading to equations [3.201).This neglected term has been shown strains at the fiber/matrix interface has been neglected(recall the assump- In this approximation,the strain energy due to the mismatch in Poisson Effective Moduli of a Continuous Fiber-Reinforced Lamina 929 328 C26