Have you heard an ambulance, police car, or fire truck recently? Did you notice that the pitch of the siren changed as it approa
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(a) 23.4
The fiber-to-matrix load ratio is given by
where
is the fiber elasticity module
is the matrix elasticity module
is the fraction of volume of the fiber
is the fraction of volume of the matrix
Substituting,
(1)
(b) 44,594 N
The longitudinal load is
F = 46500 N
And it is sum of the loads carried by the fiber phase and the matrix phase:
(2)
We can rewrite (1) as
And inserting this into (2):
Solving the equation, we find the actual load carried by the fiber phase:
(c) 1,906 N
Since we know that the longitudinal load is the sum of the loads carried by the fiber phase and the matrix phase:
(2)
Using
F = 46500 N
We can immediately find the actual load carried by the matrix phase:
(d) 437 MPa
The cross-sectional area of the fiber phase is
where
is the total cross-sectional area
Substituting , we have
And the magnitude of the stress on the fiber phase is
(e) 8.0 MPa
The cross-sectional area of the matrix phase is
where
is the total cross-sectional area
Substituting , we have
And the magnitude of the stress on the matrix phase is
(f)
The longitudinal modulus of elasticity is
While the total stress experienced by the composite is
So, the strain experienced by the composite is