Question

Q1) For a unidirectional carbon fiber reinforced lamina composites, fiber volume fraction 0.65, En-300 GPa, En = 30 G Pa, Gn2-40 G Pa while for matrix, Gm-10 GPa, Em-3 GPa Determine the longitudinal and transverse moduli of the composites, and the shear modulus of the composites.

Answer 1

Given that data, rightarrow A unidirectional carbon fibre reinforced lamina composites, fibre volume fraction = 0.65 rightarrow E_f_1 = 300 GPa rightarrow E_f_2 = 30 GPa rightarrow G_f12 = 40 GPa rightarrow G_m = 10 GPa rightarrow E_m = 3 GPa ast Longitudinal modulus: - E_f1 = E_F v_f + E_m v_m where, v_f = fiber volume fraction. = 0.65 E_f1 = 300 GPa v_m = matrix volume fraction = 1 - 0.65 = 0.35 E_11 = 300 times 0.65 + 3 times 0.35 E_11 = 196.05 GPa ast Transverse modulus: - E_22 = E_m/1 - squareroot v_f (1 - E_m/E_f2) = 3/1 - squareroot 0.65 (1 - 3/30) E_22 = 10.933 GPa ast shear modulus: - G_12 = G_m [Gf_12 (1 + v_f) + G_mv_m/G_f12 v_m + G_m (1 + v_f)] = 10 times [40(1 + 0.65) + 10 times 0.35/40m times 0.35 + 10 times (1 + 0.650] G_12 = 22.787 GPa