A casting grade of epoxy consists of 20 vol. % carbon fibers. When pulled in tension which phase fails first? Note that the tensile modulus of epoxy is 3.0 GPa and its tensile strength is 80 MPa. The tensile modulus of the carbon fiber used is 230 GPa and its tensile strength is 3200 MPa. Also, calculate the strength of this material when the fiber is completely oriented in the tensile direction and for the case where the fibers are randomly distributed in three dimensions. The critical interfacial shear strength between the epoxy matrix and carbon fiber is 40 MPa. Note that the carbon fibers in this problem are 6000 microns (6mm) in length and 7 microns in diameter.