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a center-to-center spacing of 100 m, the volume fraction of ﬁbers is 0.2 and the interface
area is approximately 157 cm2. Assume that the composite is a continuous ﬁber composite.
Calculate the volume fraction of ﬁbers and the interface area if the ﬁbers are arranged in a
hexagonal array and the nearest-neighbor distance is 50 m.
32. Explain how delamination at the ﬁber-matrix interface can enhance the fracture toughness of
33. Ceramic matrix and ﬁber materials often contain porosity levels on the order of 10%. How
will porosity inﬂuence the elastic modulus and the tensile strength of these materials?
34. What is ﬁber bridging, and how does it enhance the fracture toughness of ceramic-matrix
composites? Give an example of a composite system where ﬁber bridging is the dominant
mechanism for toughness.
35. In an epoxy/S-glass composite system, it is desired that the longitudinal elastic modulus be at
least twice the transverse elastic modulus. What volume fraction of ﬁbers is necessary to
achieve this condition?
36. Show that the critical volume fraction of ﬁbers necessary for ﬁber strengthening is given by
37. Explain why the rule of mixtures does not yield a reasonable estimate for the coefﬁcient of
38. E-glass and epoxy both exhibit isotropic thermal expansion. Do you expect that the
coefﬁcient of thermal expansion of an E-glass/epoxy composite will also be isotropic?
Explain your answer.
39. Explain why carbon ﬁbers have a modulus of elasticity that is so different along the ﬁber axis
compared with the value in the transverse direction. Do you expect the elastic modulus of a
diamond ﬁber to be different in different directions? Explain.
40. List and brieﬂy describe the three stages of fatigue failure in laminate composites.
41. Explain why the fracture toughness is high in composites with distributed damage.
42. A unidirectional ﬁber–reinforced composite has a modulus of 20 GPa in the longitudinal
direction and 3 GPa in the transverse direction. If the volume fraction of ﬁbers is 0.25, what
are the elastic moduli of the matrix and ﬁbers?
43. The pictures shown in Figure 14.5–1 and Figure 14.5–10a, b, and c belong to the same
Al-Li/alumina composite system. Construct a grid of test points and estimate the volume
fraction of the ﬁbers using all four pictures. Select one of the pictures and measure the area
of the composite and ﬁbers directly. Then compute the volume fraction. Compare the two
estimates and comment. Now double the test point spacing in the grid and make the same
measurements. Compare your answers.
44. Consider a unidirectional ﬁber-reinforced composite loaded p...
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