A composite material is made from 45 vol % aramid (Kevlar) chopped fiber and 55 vol % polycarbonate matrix. The aramid fibers have a length of 6×10-4 m, a diameter of 12×10-6 m, an elastic modulus of 130×109 Pa, and a tensile strength of 3.6×109 Pa. The polycarbonate matrix has an elastic modulus of 2.4×109 Pa. Measurements have shown that the aramid-polycarbonate interface has a shear strength of 32×106 Pa. The tensile strength of the polycarbonate is 80 MPa. For safety, it is decided that the maximum stress in the matrix of this composite should be 60 MPa.
Assume that the aramid fibers are oriented along the tensile axis.
(a) What is the strain in the composite when the matrix is at a stress of 60 MPa? Use this as the design strain.
(b) What would be the fiber stress if this was a continuous-fiber composite, and is this fiber stress less than the tensile strength of the fibers?
(c) What is the critical fiber length?
(d) What is the average stress in the chopped aramid fiber?
(e) What is the composite-material stress?
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