Page 231 - Mechanical Behavior of Materials

232 Chapter 5 Stress–Strain Relationships and Behavior

5.42 A sheet of epoxy reinforced with 60% unidirectional Kevlar 49 fibers has properties as
given in Table 5.3(b), where X is the fiber direction. The sheet is subjected to stresses σ X
= 160, σ Y = 10, and τ XY = 20 MPa. Determine the in-plane strains ε X , ε Y , and γ XY that
result.
5.43 A sheet of epoxy reinforced with 60% unidirectional E-glass fibers has properties as given
in Table 5.3(b), where X is the fiber direction. Strains ε X = 0.0030, ε Y =− 0.0020, and
γ XY = 0.0025 are measured. Estimate the applied stresses σ X , σ Y , and τ XY .
5.44 In a composite material, an epoxy matrix is reinforced with GY-70 type graphite fibers. The
volume percentage of fibers is 70%, and all are oriented in the same direction. For a sheet
of this material in the X-Y plane, with fibers in the X-direction, strains ε X = 0.0050 and
ε Y = 0.0010 are measured. Estimate the applied stresses σ X and σ Y . Reinforcement and
matrix properties are given in Table 5.3(a) and in the note below the table.
5.45 Graphite-epoxy material with 65% unidirectional fibers by volume was subjected to two
experiments: (1) A stress of 150 MPa was applied parallel to the fibers, as in Fig. 5.15(a).
The resulting strains parallel and transverse to this stress direction were measured from
strain gages as ε X = 1138 × 10 −6 and ε Y =−372 × 10 −6 . (2) A stress of 11.2 MPa was
applied transverse to the fibers, as in Fig. 5.15(c). The resulting strains parallel and transverse
to this stress direction were measured from strain gages as ε Y = 1165 × 10 −6 and ε X =
−22 × 10 −6 . However, the accuracy of the latter ε X measurement is compromised by the
very small value of strain involved.
(a) Estimate the constants E X , E Y , ν XY , and ν YX for this composite material.
(b) If the elastic modulus of the epoxy matrix is approximately 3.5 GPa, estimate the elastic
modulus of the graphite fibers.
5.46 A composite material is to be made from type E-glass fibers embedded in a matrix of ABS
plastic, with all fibers to be aligned in the same direction. For the composite, the elastic
modulus parallel to the reinforcement must be at least 48 GPa, and the elastic modulus
perpendicular to the reinforcement must be at least 5.0 GPa.
(a) What minimum volume fraction of fibers will satisfy both requirements?
(b) For the composite material with volume fraction of fibers chosen in (a), estimate the
elastic moduli in the parallel and perpendicular directions, the shear modulus, and the
major and minor Poisson’s ratios.
5.47 A composite material is to be made from silicon carbide (SiC) fibers embedded in a matrix
of an aluminum alloy, with all fibers to be aligned in the same direction. For the composite,
the elastic modulus parallel to the reinforcement must be at least 220 GPa, and the elastic
modulus perpendicular to the reinforcement must be at least 100 GPa. Proceed as in (a) and
(b) of Prob. 5.46.
5.48 A composite material is to be made of tungsten wire aligned in a single direction in an
aluminum alloy matrix. The elastic modulus parallel to the fibers must be at least 225 GPa,
and the elastic modulus perpendicular to the fibers must be at least 100 GPa. Proceed as in (a)
and (b) of Prob. 5.46.
5.49 A composite material is to be made by embedding unidirectional SiC fibers in a titanium
alloy metal matrix. For the composite, the elastic modulus in the fiber direction must be at
least 250 GPa, and the shear modulus must be at least 60 GPa. Proceed as in (a) and (b) of
Prob. 5.46.