Problem 4 (25%, 5 each) A uni-directional composite is made of an epoxy matrix and carbon fibers with a 50% fiber volume fraction. The properties of fiber and matrix materials are given in the table. Assume linear stress-strain relationship for all (strain=stress/modulus). ROM: Pc =P;V; +PmVm Material Diameter Density Tensile modulus Tensile strength Strain to failure (you calculate) Carbon Fiber 10um 1.8 g/cc 200 GPa 3 GPa=3000 MPa Epoxy 1.20 g/cc 5 GPa=5000MPa 100 MPa a. Write an expression and calculate its density. Comment on whether the estimate is reasonably reliable or rough estimate (state reasons if you have doubt about its accuracy) (Do indicate the unit of the result). b. Write an expression and calculate its longitudinal modulus. Comment on whether the estimate is reasonably reliable or rough estimate (state reasons if you have doubt about its accuracy) c. Calculate strains to failure for fiber and matrix (strain=stress/modulus; add result to table above) d. Write an expression and calculate its longitudinal strength. Comment on whether the estimate is reasonably reliable or rough estimate (state reasons if you have doubt about its accuracy) Stress (GPa) 3 e. Plot the stress-strain curves for the fiber and composite (longitudinal direction only) assuming linear relationship. Plot both curves on the same chart up to failure (draw directly on chart: "Insert, Shape", choose a line or curve). 2 1 Strain (%) 0 0 1 2 3