A uniaxial composite material is made from 75 vol % continuous kevlar fibers and 25 vol % epoxy. The kevlar fibers have an elastic modulus of 131×109 Pa and a tensile strength of 4.0×109 Pa. The epoxy resin has an elastic modulus of 5×109 Pa and a tensile strength of 50×106 Pa. The composite must withstand an axial stress of 0.5×109 Pa and a transverse stress of 4×106 Pa. The axial and transverse stresses are not applied simultaneously. Assume that both the kevlar fibers and the epoxy matrix are elastic up to their failure.

Question

(a) Determine the elastic modulus in the axial direction of this composite material.
(b) Determine the elastic modulus in the transverse direction of this composite material.
(c) Determine the axial strain in the composite due to the axial stress alone.
(d) Determine the stresses in the fibers and in the matrix for the axial stress.
(e) Can each of the components of this composite withstand the axial stress, and if not, what is the fracture stress?
(f) What is the transverse fracture stress? Can the composite withstand the transverse stress applied alone?

Answer 1

(e) The stress in the fibers is less than the minimum of the tensile strength for Kevlar fibers of 4 GPa, thus the fibers should be sufficiently strong. The minimum tensile strength for epoxy resin is 50 MPa, thus the matrix also should be able to withstand this tensile stress.



(f) This transverse stress of 40 MPa is below the epoxy matrix tensile stress of 50 MPa; however, if we consider the fibers as holes, then the tensile strength is reduced to:







The composite cannot withstand the transverse stress.