An aligned short-fiber carbon–epoxy composite is to be fabricated so that it behaves as a continuous fiber composite with a composite modulus of E1 = 80 GPa

An aligned short-fiber carbon–epoxy composite is to be fabricated so that it behaves as a continuous fiber composite with a composite modulus of E1 = 80 GPa. The 0.01-mm-diameter fibers have a modulus of elasticity Ef1 = 240 GPa and a tensile strength sf1 GPa ( ) . + = 2 5 . The epoxy matrix can be assumed to be a rigid plastic material with a yield strength of 20 MPa in shear. Determine (a) the fiber length necessary to just reach the “continuous fiber stress” at the midpoint for a composite stress of 50 MPa and (b) the fiber length and the composite stress necessary to develop the ultimate tensile strength in the fiber.