
Concept explainers
(a)
The elastic modulus of composite in axial direction.
(a)

Answer to Problem 12.8P
The elastic modulus of composite in axial direction is
Explanation of Solution
Given:
Volume percent of Kevlar fiber is
Volume percent of epoxy is
Elastic modulus of Kevlar is
Elastic modulus of epoxy is
Concept used:
Write the expression for elastic modulus of composite.
Here,
Calculation:
Substitute
Conclusion:
Thus, the elastic modulus of composite in axial direction is
(b)
The elastic modulus of composite in transverse direction.
(b)

Answer to Problem 12.8P
The elastic modulus of composite in transverse direction is
Explanation of Solution
Concept used:
Write the expression for elastic modulus of E-glass composite in the direction perpendicular to fiber axis.
Here,
Calculation:
Substitute
Conclusion:
Thus, the elastic modulus of composite in transverse direction is
(c)
The axial strainin composite due to axial stress.
(c)

Answer to Problem 12.8P
The axial strain in composite due to axial stress is
Explanation of Solution
Given:
Axial stress is
Concept used:
Write the expression for axial strain in composite.
Here,
Calculation:
Substitute
Conclusion:
Thus, the axial strain in composite due to axial stress is
(d)
The stresses in the fiber and in matrix of composite due to axial stress.
(d)

Answer to Problem 12.8P
The stresses in the fiber and in matrix of composite due to axial stress is
Explanation of Solution
Given:
Transverse stress is
Tensile strength of Kevlar is
Concept used:
Write the expression for stress in fiber by considering the iso-strain model for axial strain.
Here,
Write the expression for stress in matrix by considering the iso-strain model for axial strain.
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, the stresses in the fiber and in matrix of composite due to axial stress is
(e)
Whether each of the component can withstand the axial stress or not, if not what is the fracture stress.
(e)

Explanation of Solution
The calculated stress for fiber is very less than the minimum tensile strength of Kevlar. This indicates that the fiber is sufficiently string to withstand the stress.
Matrix can also hold the tensile stress as the minimum tensile strength of epoxy resin is larger than the calculate stress in it.
(f)
The transverse fracture stress.
(f)

Answer to Problem 12.8P
The transverse fracture stress is
Explanation of Solution
Given:
Tensile strength of epoxy is
Concept used:
Write the expression for transverse tensile strength of composite.
Here,
Calculation:
Substitute
Conclusion:
Thus, the transverse fracture stress is
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Chapter 12 Solutions
Materials Science And Engineering Properties
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