Question

CHAPTER 16 - COMPOSITES Prob. 1 - The below figure illustrates a rectangular array of elliptical-shaped fibers. Determine: a) The relationship between the fiber volume fraction and the specified geometrical parameters, and b) The maximum possible fiber volume fraction for this packing geometry. Prob. 2 - Homogeneous engineering materials are infrequent. Consider a composite which consists of a small spherical particle of one material that is embedded in a large matrix of another material. The particle has a radius of a. The composite is solidified at an elevated temperature Th, at which the composite is in a stress-free condition. The particle has a larger thermal expansion coefficient than the matrix, ?p > ?m. Upon cooling, the composite develops a residual stress field because of the thermal expansion mismatch. (a) At room temperature Tr, is the particle under tension or compression? (b) Because the particle is under [tension · compression] (circle one) the matrix is under [tension · compression] (circle one). Prob. 3 - As shown in Fig. 4, a unidirectional 45° off-axis E-glass/epoxy composite lamina is supported on frictionless rollers between two rigid walls. The lamina is fixed against displacements in the y direction and is free to move in the x direction. The lamina is heated from 20°F to 120°F. (a) What strain is expected in the x-direction? (b) What strain is expected in the y-direction?

          CHAPTER 16 - COMPOSITES
Prob. 1 - The below figure illustrates a rectangular array of elliptical-shaped fibers.
Determine:
a) The relationship between the fiber volume fraction and the specified
geometrical parameters, and
b) The maximum possible fiber volume fraction for this packing geometry.
Prob. 2 - Homogeneous engineering materials are infrequent. Consider a composite which
consists of a small spherical particle of one material that is embedded in a large
matrix of another material. The particle has a radius of a. The composite is solidified
at an elevated temperature Th, at which the composite is in a stress-free condition.
The particle has a larger thermal expansion coefficient than the matrix, ?p > ?m.
Upon cooling, the composite develops a residual stress field because of the thermal
expansion mismatch.
(a) At room temperature Tr, is the particle under tension or compression?
(b) Because the particle is under [tension · compression] (circle one) the matrix is
under [tension · compression] (circle one).
Prob. 3 - As shown in Fig. 4, a unidirectional 45° off-axis E-glass/epoxy composite lamina is
supported on frictionless rollers between two rigid walls. The lamina is fixed against
displacements in the y direction and is free to move in the x direction. The lamina is
heated from 20°F to 120°F.
(a) What strain is expected in the x-direction?
(b) What strain is expected in the y-direction?

$CHAPTER 16 - COMPOSITES Prob. 1 - The below figure illustrates a rectangular array of elliptical-shaped fibers. Determine: a) The relationship between the fiber volume fraction and the specified geometrical parameters, and b) The maximum possible fiber volume fraction for this packing geometry. Prob. 2 - Homogeneous engineering materials are infrequent. Consider a composite which consists of a small spherical particle of one material that is embedded in a large matrix of another material. The particle has a radius of a. The composite is solidified at an elevated temperature Th, at which the composite is in a stress-free condition. The particle has a larger thermal expansion coefficient than the matrix, ?p > ?m. Upon cooling, the composite develops a residual stress field because of the thermal expansion mismatch. (a) At room temperature Tr, is the particle under tension or compression? (b) Because the particle is under [tension · compression] (circle one) the matrix is under [tension · compression] (circle one). Prob. 3 - As shown in Fig. 4, a unidirectional 45° off-axis E-glass/epoxy composite lamina is supported on frictionless rollers between two rigid walls. The lamina is fixed against displacements in the y direction and is free to move in the x direction. The lamina is heated from 20°F to 120°F. (a) What strain is expected in the x-direction? (b) What strain is expected in the y-direction?$

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