the rule of mixtures

The simplest fair way to estimate a composite property: average the two materials, weighted by how much of each is present. If a composite is 60 percent fiber and 40 percent matrix by volume, weight the fiber property by 0.6 and the matrix by 0.4. It is like predicting a class's average height from the fractions of tall and short students.

How you average depends on the loading. Load along aligned fibers (isostrain, where both stretch the same amount) means stiffness adds in parallel: E_c = Vf times Ef + Vm times Em (the upper bound). Load across the fibers (isostress, where both feel the same stress) means the compliant matrix dominates: 1/E_c = Vf/Ef + Vm/Em (the lower bound). Numbers: Vf = 0.6, Ef = 230 GPa, Em = 3 GPa give longitudinal E_c = 0.6 times 230 + 0.4 times 3 = 139.2 GPa; transverse E_c = 1/(0.6/230 + 0.4/3) is about 7.4 GPa. Real composites lie between these bounds.

The rule of mixtures gives quick, honest first estimates and shows why aligned composites are so directional. For strength it is rougher: fibers and matrix fail at different strains, so the longitudinal-strength version uses the matrix stress at the fiber's breaking strain, and the transverse case is dominated by the weak interface. Treat it as bounds and trends, not a precise strength predictor.