(a)
The magnitude and direction of thermal stresses in matrix and fibers.
(a)
Answer to Problem 12.16P
The magnitude and direction of thermal stresses in matrix and fibers are
Explanation of Solution
Given:
Volume fraction of uniaxial glass fiber is
Volume fraction of epoxy resin is
Initial temperature is
Final temperature is
Elastic modulus of glass fiber is
Thermal expansion coefficientof glass fiberis
Elastic modulus of Epoxyis
Thermal expansion coefficientof 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 12.16P
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
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Chapter 12 Solutions
Materials Science And Engineering Properties
- Two composite bars have the following composition. At an initial temperature of 5 degree C, there is an existing gap of 5mm. Bar 1 and 2 have coefficients of thermal expansion of a1 = 140 X106/°C and a2 = 67 X106/°C, respectively. Determine the temperature at which the 5mm gap is closed. GAP (1) (2) | B C A 540 mm 360 mm 75.20 degrees celsius 55.14 degrees celsius 95.25 degrees celsius 25.06 degrees celsius 50.11 degrees celsius O 5.02 degrees celsius 32.66 degrees celsiusarrow_forwardA composite beam is made of two brass [E - 111 GPa] bars bonded to two aluminum [E - 72 GPa] bars, as shown. The beam is subjected to a bending moment of 250 N-macting about the z axis. Using a - 10 mm, b- 65 mm, c- 20 mm, and d- 45 mm, calculate (a) the maximum bending stress in the aluminum bars. (b) the maximum bending stress in the brass bars. Aluminum Brass Brass Aluminum Answers: (a) Oa i MPa (b) Oer MPa Save for Later Attempts: 0 of 1 used Submit Answerarrow_forwardA composite column is formed by placing a steel bar, 20 mm in diameter and 200 mm long, inside an alloy cylinder of the same length whose internal and external diameters are 20 mm and 25 mm, respectively. The column is then subjected to an axial load of 50 kN. If E for steel is 200 OOO N/mm’ and E for the alloy is 70 000 N/mm’, calculate the stress in the cylinder and in the bar, the shortening of the column and the strain energy stored in the column.arrow_forward
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- Materials Science And Engineering PropertiesCivil EngineeringISBN:9781111988609Author:Charles GilmorePublisher:Cengage Learning