Acontinuous and aligned fibrous reinforced composite having a cross-sectional area of 970 mm2 (1.5 in.2) is subjected to an external tensile load. if the stresses sustained by the fibre and matrix phases are 215 mpa (31,300 psi) and 5.38 mpa (780 psi), respectively, the force sustained by the fibre phase is 76,800 n (17,265 lbf), and the total longitudinal composite strain is 1.56 × 10–3, determine the following:

(a) the force sustained by the matrix phase

(b) the modulus of elasticity of the composite material in the longitudinal direction

(c) the moduli of elasticity for fibre and matrix phases

(a) 3290 N

(b) 52.9 Gpa

(c) 3.45 Gpa and 1378 Gpa for matrix and fibre  phases respectively

Explanation:

(a)

The volume fraction of matrix is given by

where is volume fraction of matrix and is volume fraction of fibre

Moreover, the stress in matrix is given by

where is force on matrix and is the area of matrix, is cross-sectional area

Therefore,

Substituting the figures in the question

Therefore, force sustained by matrix is 3290 N

(b)

and also  

therefore we combine these two equations and say

Substituting the figures given

(c)

The moduli of elasticity of matrix and fibre are given by

Therefore,

Therefore, moduli of elasticity for fibre and matrix phases are 1378 Gpa and 3.45 Gpa respectively