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_forwardA FRP composite includes 40% continuous and aligned Aramid fibers by vol-ume. The moduli of elasticity of the Aramid fibers and the epoxy resin matrix are 130 and 3.9 GPa, respectively. a. Compute the modulus of elasticity of the composite in the longitudinal and transverse directions. b. If the composite cross-sectional area is 150 mm' and a stress of 40 MPa is applied in the longitudinal direction, compute the load carried by the fibers and the matrix. c. Determine the strain sustained by each of the phases when stress in part (b) is applied.arrow_forwardA fiber-reinforced polymer composite under isostrain condition consists of 35% fibers and 65% polymer by volume. The moduli of elasticity of the filers and the polymer are 50 X 10 psi and 0.5 x 10® psi, respectively, and the Poison's ratios of the fibers and the polvmer are 0.25 and 0.41, respectively. Calculate the following: a. modulus of elasticitv of the composite. b. percentage of load carried by the fibers c. Poison's ratio of the compositearrow_forward
- IV- It is necessary to design a continuous and aligned glass fiber-reinforced polyester having a tensile strength of at least 1400 MPa in the longitudinal direction. The maximum possible specific gravity is 1.65. Using the following data, determine whether such a composite is possible. Justify. Assume a value of 15 MPa for the stress on the matrix when the fibers fail. Material Glass fiber Polyester Specific gravity 2.5 1.35 Tensile strength (MPa) 3500 50arrow_forwardBefore solve the problem please read the question carefully and give me right solution according to the questionarrow_forwardA FRP composite includes 47% continuous and aligned Aramid fibers by volume. The moduli of elasticity of the Aramid fibers and the epoxy resin matrix are 19 * 106 psi and 0.6 * 106 psi, respectively.a. Compute the modulus of elasticity of the composite in the longitudinal and transverse directions.b. If the composite cross-sectional area is 0.5 in.2 and a stress of 12 ksi is applied in the longitudinal direction, compute the load carried by the fibers and the matrix.c. Determine the strain sustained by each of the phases when stress in part(b) is applied.arrow_forward
- A composite sample of carbon reinforced epoxy has dimensions of in 20 in x 20 in x 0.135 in and mass of 3 lb. The carbon fibres have a modulus of elasticity of 80(106) lb/in2 and a density of 0.15 lb/in3. The epoxy matrix has modulus of elasticity of 0.90(106) lb/in2 and a density of 0.05 lb/in3. Assume there are no voids in the sample, calculate the volume fraction of: (i) The carbon fibres (ii) The epoxy matrix in the sample.arrow_forwardA continuous aligned fibre-reinforced composite is produced containing 33% aramid fibres of tensile strength 2.35GPA and the remainder of polycarbonate with tensile strength 78 MPa. What is the longitudinal strength of the composite in MPa? [Enter your answer as a real integer number - do not include the unit]arrow_forwardA 1500 mm long composite bar consists of aluminum and steel as shown. The cross-sectional area of the aluminum bar is twice that of the steel bar. If the assembly is exposed to an axial tensile load of 250 kN, determine the lengths of each of the components if the elongation of the aluminum is the same with that of the steel. The modulus of elasticity of steel E = 200 GPa and for the aluminum is one-third of the steel.arrow_forward
- A continuous and aligned fiber-reinforced composite is to be produced consisting of 37 vol% aramid fibers and 63 vol% of a polycarbonate matrix; mechanical characteristics of these two materials are as follows: Modulus of Elasticity [GPa(psi)] Tensile Strength [MPa(psi)] Aramid fiber 131 (19x106) 3600 (520,000) Polycarbonate 2.4 (3.5×105) 65 (9425) Also, the stress on the polycarbonate matrix when the aramid fibers fail is 45 MPa (6500 psi). For this composite, compute: (a) the longitudinal tensile strength i MPaarrow_forwardA composite containing carbon fibres in epoxy resin is loaded in a direction perpendicular to the reinforcing fibres. If there are 0.55 vol% fibres, modulus of the carbon fibres is 380 GPa and modulus of epoxy is 3 GPa, determine the modulus of the composite. What it the modulus of the composite? Select one: a. 6.1 GPa b. 5.4 GPa c. 6.6 GPa d. 7.2 GPaarrow_forwardA composite beam made of steel and bronze has the cross section shown. The cross-sectional dimensions are b, - 0.9 in, b2 - 2.7 in., and d- 1.8 in. The elastic modulus of the steel is E, - 30,000 ksi, and its allowable bending stress is 17 ksi. The elastic modulus of the bronze is E2 - 15,000 ksi, and its allowable bending stress is 14 ksi. Calculate the allowable bending moment that can be applied about the z centroidal axis. Bronze (2) d Steel (1) b2 Part 1 Your answer has been saved. See score details after the due date. Determine the modular ratio in order to transform the steel into an equivalent amount of bronze. Answer: n- Attempts: 1 of 1 used Part 2 Determine the area moment of inertia of the transformed section about the z-axis. Answer: in.4arrow_forward
- Materials Science And Engineering PropertiesCivil EngineeringISBN:9781111988609Author:Charles GilmorePublisher:Cengage Learning