(a)
The magnitude and direction of thermal stresses in matrix and fibers.
(a)
Answer to Problem 12.16P
The magnitude and direction of thermal stresses in matrix and fibers are
Explanation of Solution
Given:
Volume fraction of uniaxial glass fiber is
Volume fraction of epoxy resin is
Initial temperature is
Final temperature is
Elastic modulus of glass fiber is
Thermal expansion coefficientof glass fiberis
Elastic modulus of Epoxyis
Thermal expansion coefficientof 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 12.16P
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
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Chapter 12 Solutions
Materials Science And Engineering Properties
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- Materials Science And Engineering PropertiesCivil EngineeringISBN:9781111988609Author:Charles GilmorePublisher:Cengage Learning