Question

A biomaterial composite is made of a polymer matrix with aligned ceramic fibre reinforcement. The composite is deformed elastically under an applied stress of σapplied = 100 MPa along the longitudinal direction (i.e. parallel to the fibres). The elastic modulus of the fibre, Ef, is 200 GPa and that of the matrix, Em, is 5 GPa. The volume fraction of the fibre is Vf = 20%. Calculate the stress in the matrix.

a. 11 MPa

b. 100 MPa

c. 454 MPa

d. 20 MPa

Answer 1

Solution :

Vm = 0.8

Vf = 0.2

However, this total load is just the sum of the loads carried by fiber and matrix phases; that is,

Fc = Ff + Fm

Fc = Ac * c

Am = Vm * Ac = 0.8 Ac

Af = Vf * Ac = 0.2 Ac

first find the ratio of fiber load to matrix load, using Equation

so

Fc = Ff + Fm

Ac *  c = Af *  f + Am * m

Ac *  c = 0.2 Ac * f + 0.8 Ac * m

so

c = 0.2 f + 0.8 m

100 MPa   = 0.2 f + 0.8 (f /40)

so f = 454.5454 MPa

so m = f /40 = 11.36 MPa

summary :

stress in matrix = 11 MPa