Q 4. (15p) A unidirectional discontinuous Kevlar-49 fiber-reinforced polyether ether ketone (PEEK)composite needs to be developed so that its longitudinal tensile modulus is at least 28 GPa and its longitudinal

tensile strength is at least 800 MPa. Through the use of proper coupling agent on the Kevlar fiber surface, it would be possible to control the inter facial shear strength between 12 and 35 MPa. The fiber bundle diameter is 0.28 mm and the fiber weight fraction is 56%. Determine the fiber length required for this composite. \text { The matrix properties are: } \rho_{m}=1.30 \mathrm{~g} / \mathrm{cm}^{3}, \mathrm{E}_{\mathrm{m}}=3.24 \mathrm{GPa}, \text { and } \mathrm{S}_{\mathrm{mu}}=170 \mathrm{MPa}