A continuous and aligned fiber-reinforced composite is to be produced consisting
ID: 507443 • Letter: A
Question
A continuous and aligned fiber-reinforced composite is to be produced consisting of 35 vol% aramid fibers and 65 vol% of a polycarbonate matrix; mechanical characteristics of these two materials are as follows:
Assume that this composite has a cross-sectional area of 330 mm2 (0.51 in.2) and is subjected to a longitudinal load of 40400 N (9080 lbf).
(a) Calculate the fiber-matrix load ratio.
(b) Calculate the actual load carried by fiber phase.
(c) Calculate the actual load carried by matrix phase.
(d) Compute the magnitude of the stress on the fiber phase.
(e) Compute the magnitude of the stress on the matrix phase.
(f) What strain is expected by the composite?
Modulus of Elasticity [GPa (psi)] Tensile Strength [MPa (psi)] Aramid fiber 131 (19 × 106) 3600 (520,000) Polycarbonate 2.4 (3.5 × 105) 65 (9425)Explanation / Answer
Given ,
Modulus of Elasticity of fiber, Ef= 131 GPa
Modulus of Elasticity of matrix, Em=2.4 GPa
Tensile Strength of fiber, f = 3600 MPa
Tensile Strength of fiber, m = 65 MPa
F= longitudinal load =40400N
A= cross-sectional area=330 mm2
Total stress = =F/A= 40400/330
F= longitudinal load =40400N
A= cross-sectional area=330 mm2
=F/A= 40400/330
=122.42 MPa
a) fiber-matrix load ratio=Ff/ Fm= EfVF/ EmVm
=131 x 0.35/2.4 x 0.65
=29.39
b) actual load carried by fiber phase,
Ff= (F x fiber-matrix load ratio) /(1+ fiber-matrix load ratio)
=(40400 x 29.39)/( 1+29.39)
=39070.61
So actual load carried by fiber phase = 39070.61 N
c) actual load carried by matrix phase, Fm= F/(1+ fiber-matrix load ratio)
=40400/(1+29.39)
=1329.38
So actual load carried by matrix phase =1329.38 N
d) magnitude of the stress on the fiber phase, f = Ef c
where c is strain experienced by composite,
c = Total stress / longitudinal modulus of elasticity
=/Ec
Ec=longitudinal modulus of elasticity= EmVm + EfVf
= 2.4 x 0.65 + 131 x 0.35
=47.41 GPa
Therefore, c = 122.42/ 47.41
strain experienced by composite, c =2.58 x 10-3
f = Ef c
=131 x 2.58 x 10-3
magnitude of the stress on the fiber phase, f =337.98 MPa
e) magnitude of the stress on the matrix phase, m = Em c
=2.4 x 2.58 x 10-3
=6.192 MPa
f) it has already solved in part (d)
strain is expected by the composite
c = Total stress / longitudinal modulus of elasticity
=/Ec
Ec=longitudinal modulus of elasticity= EmVm + EfVf
= 2.4 x 0.65 + 131 x 0.35
=47.41 GPa
Therefore, c = 122.42/ 47.41
strain experienced by composite, c =2.58 x 10-3
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