Concept explainers
(a)
The strain where the first change in elastic modulus occurs in composite material.
(a)
Answer to Problem 12.12P
Matrix will rupture before the fiber at the strain of
Explanation of Solution
Given:
Elastic modulus of Boronis
Tensile strength of Boronis
Elastic modulus of Aluminumis
Yield strength of Aluminumis
Ultimate tensile strength of aluminum is
Concept used:
Write the expression for failure strain in Fiber.
Here,
Write the expression for failure strain in Matrix.
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, matrix will rupture before the fiber at the strain of
(b)
The composite stress where the change in elastic modulus occurs.
(b)
Answer to Problem 12.12P
The composite stress where the change in elastic modulus occurs is
Explanation of Solution
Given:
Volume percent of Boron fiber is
Volume percent of Aluminumis
Strain at fracture of Aluminumis
Concept used:
Write the expression for stress carried by composite.
Here,
Write the expression for stress in fiber by considering the iso-strain model for axial strain.
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, the composite stress where the change in elastic modulus occurs is
(c)
The elastic modulus at low strain and the elastic modulus after Aluminum yields, if Aluminum yields before fiber fails.
(c)
Answer to Problem 12.12P
The elastic modulus at low strain is
Explanation of Solution
Concept used:
Write the expression for modulus of elasticity of composite.
Here,
Calculation:
Substitute
After yielding of matrix the elastic modulus of composite is the elastic modulus of fiber in it. Therefore, the elastic modulus will be equal to 60% of
Conclusion:
Thus, the elastic modulus at low strain is
(d)
Fracture strength of composite.
(d)
Answer to Problem 12.12P
Fracture strength of composite is
Explanation of Solution
Concept used:
Write the expression for fracture strength.
Here,
Calculation:
Substitute
Conclusion:
Thus, the Fracture strength of 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