= 3. You are given a high modulus carbon fiber (Ef = 380 GPa, vf = 0.19) and epoxy (Em: 3.2 GPa, vm = 0.42) to make into a unidirectional long fiber composite. Assume that the fibers and matrix are isotropic. a. Plot the Young's moduli and E2 as a function of volume fraction (V = 0 1). You can use either the Halpin-Tsai or Reuss models for calculating E2, just identify which you used. (5 points) b. Plot the Poisson's ratios V12 and V21 as a function of volume fraction (V = 0 1). (5 points) What are the absolute maximum stiffness and Poisson's ratios this composite can have? Hint: think of fiber packing volume fractions. (10 points) C. 4. You need to design a CFRP composite with a 1-direction stiffness of E = 200 GPa using the above materials from Problem 3. You are told to use a 0/90 layup in making this composite and that the volume fraction of the fibers after curing is V = 65%. a. What are the relative thicknesses of the 0 and 90 layers? Note: the 0 layer is oriented in the 1 direction. (10 points) b. What is the transverse stiffness (E2) of the composite with the above thicknesses? (5 points) Hint: this is technically a laminate question, but you can use a rule of mixtures to solve it.