
Concept explainers
(a)
The magnitude and direction of thermal stresses in matrix and fibers.
(a)

Answer to Problem 12.17P
The magnitude and direction of thermal stresses in matrix and fibers are
Explanation of Solution
Given:
Volume fraction of carbon fiberis
Volume fraction of epoxy resin is
Initial temperature is
Final temperature is
Elastic modulus of carbon fiber is
Ultimate tensile strength of carbon fiber is
Thermal expansion coefficient of carbon fiber is
Elastic modulus of Epoxy is
Ultimate tensile strength of epoxy resin is
Thermal expansion coefficient of Epoxy is
Concept used:
Write the expression for stress carried by composite.
Here,
Write the expression for strain in Fiber.
Here,
Write the expression for strain in Matrix.
Here,
Write the expression for the total strain in the composite.
Here,
Calculation:
The composite stress is zero because there is no application of stress to the composite material in the axial direction.
Substitute
Substitute
Substitute
Substitute
Simplify above expression for
Calculate the value of stress in matrix.
Conclusion:
Thus, the magnitude and direction of thermal stresses in matrix and fibers are
(b)
Composite strain in cooling the composite.
(b)

Answer to Problem 12.17P
Composite strain in cooling the composite is
Explanation of Solution
Given:
Initial temperature is
Final temperature is
Concept used:
Write the expression for stress in composite.
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, Composite strain in cooling the composite is
(c)
(c)

Answer to Problem 12.17P
The component of design which can cause problem and justify your answer.
Explanation of Solution
The tensile stress in the fiber is less than the ultimate tensile strength of fiber and the stress in matrix is compressive in nature whereas the tensile strength of epoxy matrix is
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Chapter 12 Solutions
Materials Science And Engineering Properties
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