
(a)
The strain in composite when stress in matrix is
(a)

Answer to Problem 12.14P
The strain in composite when stress in matrix reaches
Explanation of Solution
Given:
Elastic modulus of polycarbonate matrix is
Maximum allowable stress in matrix is
Concept used:
Write the expression for strain in composite.
Here,
Calculation:
Substitute
Conclusion:
Thus, the strain in composite when stress in matrix reaches
(b)
The fiber stress for continuous fiber composite and identify if this is less than tensile strength of fiber.
(b)

Answer to Problem 12.14P
The fiber stress for continuous fiber composite is
Explanation of Solution
Given:
Elastic modulus of Fiber is
Concept used:
Write the expression for fiber stress.
Here,
Calculation:
Substitute
Conclusion:
Thus, the fiber stress for continuous fiber composite is
(c)
Critical fiber length
(c)

Answer to Problem 12.14P
Critical fiber length is
Explanation of Solution
Given:
Diameter of aramid fiber is
Shear strength of Polycarbonate-aramid interface is
Concept used:
Write the expression for critical aspect ratio.
Here,
Calculation:
Substitute
Conclusion:
Thus, the Critical fiber length is
(d)
Average stress in chopped aramid fiber.
(d)

Answer to Problem 12.14P
Average stress in chopped aramid fiber is
Explanation of Solution
Given:
Length of aramid fiber is
Concept used:
Write the expression for average fiber stress.
Here,
Calculation:
Substitute
Conclusion:
Thus, the average stress in chopped aramid fiber is
(e)
Composite material stress.
(e)

Answer to Problem 12.14P
Composite material stress is
Explanation of Solution
Given:
Volume percentage of aramid chopped fiber is
Volume percent of polycarbonate matrix is
Tensile strength of aramid fiber is
Tensile strength of Polycarbonate is
Concept used:
Write the expression for composite material stress.
Here,
Calculation:
Substitute
Conclusion:
Thus, the composite material stress is
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Chapter 12 Solutions
Materials Science And Engineering Properties
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