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
- In Example Problem 12.1, a uniaxial composite material is made into a circular rod Vbith a 1.27-cm diameter from 70 volume percent continuous carbon fibers and 30 volume percent epoxy. The rod is subject to an axial force of 100,000 N. The composite matcrial in Example Problem 12.1 is to be replaced with a less expensive composite made of 70 volume percent continuous E-glass fibers and 30 volume percent epoxy. The elastic moduli are 5 GPa for the epoxy resin and 72.4 GPa fos the E-glass. (a) Compare the elastic modulus, composite strain, fiber and matrix stresses, and density of this composite with the carbon epoxy composite in Example Problem 12.1. Usc the density of UHM carbon, and assume the density of the epoxy is 1.2g/cm3 . (b) Can both the E-glass fiber and matrix withstand the applied force?arrow_forwardComposite _________ is produced by laying fibers in random directions in a plane.arrow_forwardAn epoxy is randomly reinforced with E-Glass fibers with 0.0012 in. diameter, 0.5 in. length, 0.5 * 106 psi ultimate tensile strength, and 7.2 ksi shear strength. Does this fiber length fully strengthen the composite? What is the minimum fiber length that would make the composite continuously reinforced?arrow_forward
- Materials Science And Engineering PropertiesCivil EngineeringISBN:9781111988609Author:Charles GilmorePublisher:Cengage Learning