Q. 1 A HMS-4 carbon fiber reinforced ( Vf = 60% ) epoxy matrix composite is fabricated by an injection molding process. Excellent fiber alignment is achieved but due to fiber breakage about 30 % of the aligned fibers end up with an average length of l'f = 1.5 mm and the remaining with an average length of l''f = 5.0 mm.
(a) Calculate the longitudinal tensile strength, σLtu, of the discontinuous fiber reinforced injection molded composite. Assume the matrix to behave like an elastic-perfectly plastic material. The fiber diameter df is 10 μm, and assume the interfacial shear strength τi = 5 MPa. The fiber and matrix properties are given as follows: Ef = 350 GPa, σfu= 2.5 GPa, Em = 3.5 GPa, σmy = 140 MPa.
(b) Suppose the above short fiber composite is to be fabricated so that it behaves like a continuous fiber composite. Determine (i) the fiber length necessary to just reach the "continuous fiber stress" at the midpoint for a composite stress of 500 MPa, and (ii) the fiber length and the composite stress necessary to develop ultimate tensile strength in the fiber. Assume the matrix yield strength in shear is 70 MPa.
Q. 2 Assume that the unit cell of a composite containing commingled filaments of E-glass and T-300 carbon fibers can be represented by a square array as shown below in the figure. The diameters of the E-glass filaments and T-300 carbon filaments are 7 x 10-6 m and 10 x 10-6 m , respectively.
1. Determine the unit cell dimension if the fiber volume fraction is 60%.
2. Determine the theoretical density of the composite. Assume the matrix material to be epoxy. The densities of the E-glass fiber, T-300 fiber , and the epoxy matrix are given as follows:
ρglass = 2.54 g/cc, ρcarbon = 1.76 g/cc, ρepoxy = 1.2 g/cc
