Compute the magnitude the load carried each the fiber and matrix phases

Strain Strain

(a) (b)

Fc � Fm � Ff (15.4)

From the definition of stress, Equation 7.1, F � �A; and thus expressions for Fc, Fm, and Ff in terms of their respective stresses (�c, �m, and �f ) and cross-sectional areas (Ac, Am, and Af ) are possible. Substitution of these into Equation 15.4 yields

where Am/Ac and Af /Ac are the area fractions of the matrix and fiber phases, respectively. If the composite, matrix, and fiber phase lengths are all equal, Am/Ac is equivalent to the volume fraction of the matrix, Vm; and likewise for the fibers, Vf � Af /Ac. Equation 15.6 now becomes

�c � �mVm � �f Vf (15.7)

Thus, Ecl is equal to the volume-fraction weighted average of the moduli of elasticity of the fiber and matrix phases. Other properties, including density, also have this dependence on volume fractions. Equation 15.10a is the fiber analogue of Equation 15.1, the upper bound for particle-reinforced composites.

It can also be shown, for longitudinal loading, that the ratio of the load carried by the fibers to that carried by the matrix is

(b) If the cross-sectional area is 250 mm2(0.4 in.2) and a stress of 50 MPa (7250 psi) is applied in this longitudinal direction, compute the magnitude of the load carried by each of the fiber and matrix phases.