Concept explainers
(a)
The magnitude and direction of thermal stresses in matrix and fibers.
(a)
Answer to Problem 12.17P
The magnitude and direction of thermal stresses in matrix and fibers are
Explanation of Solution
Given:
Volume fraction of carbon fiberis
Volume fraction of epoxy resin is
Initial temperature is
Final temperature is
Elastic modulus of carbon fiber is
Ultimate tensile strength of carbon fiber is
Thermal expansion coefficient of carbon fiber is
Elastic modulus of Epoxy is
Ultimate tensile strength of epoxy resin is
Thermal expansion coefficient of Epoxy is
Concept used:
Write the expression for stress carried by composite.
Here,
Write the expression for strain in Fiber.
Here,
Write the expression for strain in Matrix.
Here,
Write the expression for the total strain in the composite.
Here,
Calculation:
The composite stress is zero because there is no application of stress to the composite material in the axial direction.
Substitute
Substitute
Substitute
Substitute
Simplify above expression for
Calculate the value of stress in matrix.
Conclusion:
Thus, the magnitude and direction of thermal stresses in matrix and fibers are
(b)
Composite strain in cooling the composite.
(b)
Answer to Problem 12.17P
Composite strain in cooling the composite is
Explanation of Solution
Given:
Initial temperature is
Final temperature is
Concept used:
Write the expression for stress in composite.
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, Composite strain in cooling the composite is
(c)
(c)
Answer to Problem 12.17P
The component of design which can cause problem and justify your answer.
Explanation of Solution
The tensile stress in the fiber is less than the ultimate tensile strength of fiber and the stress in matrix is compressive in nature whereas the tensile strength of epoxy matrix is
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Chapter 12 Solutions
Materials Science And Engineering Properties
- Composite _________ is produced by laying fibers in random directions in a plane.arrow_forwardIn 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 fiberglass composite consists of epoxy matrix reinforced with glass fibers. The modulus of elasticity of the glass fibers and the epoxy is 65 GPa and 7 GPa, respectively. If the volume percentage of fibers is 33%, determine the modulus of elasticity of the fiberglass.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_forwardWhen looking up data for composite materials, it is important to: a.)Make sure the volume fraction of the fibres is specified b.)The orientation of each fibre layer is specified c.)The type of resin/matric is specified d.)All of the abovearrow_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
- A 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_forwardComposite materials can be reinforced with: a.)Fibres b.)Whiskers c.)Particles d.)All of the abovearrow_forwardA discontinuous fibre reinforced composite consists of 20mm long carbon fibres in a polymer matrix. The volume fraction of the composite is 0.5, interfacial shear strength 5MPa and the critical fibre length 2.5mm. The fibre modulus is 250GPA and strain to failure 1.5%. The matrix modulus is 3.5GPa and failure strain 10%. If the ultimate fibre strength = 3500MPa, calculate the average failure stress in the composite.arrow_forward
- Calculate the modulus of elasticity of fiberglass under isostrain condition if the fiberglass consists of 70% E-glass fibers and 30% epoxy by volume. Also, calculate the percentage of load carried by the glass fibers. The moduli of elasticity of the glass fibers and the epoxy are 70.5 and 6.9 GPa, respectively. If a longitudinal stress of 60 MPa is applied on the composite with a cross-sectional area of 300 mm2, what is the load carried by each of the fiber and the matrix phases?What is the strain sustained by each of the fiber and the matrix phases?arrow_forwardAn element representative of a composite comprising an isotropic fiber enveloped by the isotropic resin is shown in Figure 1. Note that the two materials stick together perfectly and that the external surface of the element is free of stress. Calculate the axial stress in the fiber (of) and that in the resin (om) in the middle of the axis longitudinal fiber (L/ 2) using the material strength approach in the case where the element is exposed to a change in temperature AT, depending on following variables The thermal expansion coefficients af and am • The Af and Am sections • The moduli of elasticity Ef and Em • AT Guide: There is no external force • Relations to consider: balance, geometric compatibility and relation stress-strain. Fibre : At, Er, Of, af Matrice : Am, Em, Ớm, đmarrow_forwardA bar having the cross section shown has been formed by securely bonding brass and aluminum stock. Taking h= 9 mm and using the data given below, determine the largest permissible bending moment when the composite bar is bent about a horizontal axis. Brass Aluminum 30 mm Modulus of elasticity Allowable stress h 30 mm h Aluminum 70 GPa 100 MPa The largest permissible bending moment is Brass 105 GPa 160 MPa 1.17 kN-m.arrow_forward
- Materials Science And Engineering PropertiesCivil EngineeringISBN:9781111988609Author:Charles GilmorePublisher:Cengage Learning