(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_forwardfor a fiber reinforced composite material, assume Fibre's volume fraction is 0.3. what is the effective tensile strength of the composite if the strength of fiber is 150GPa and that of matrix is 16GPaarrow_forwardA 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_forward
- A 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_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_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
- 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 ofm300 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_forwardIt is necessary to fabricate an aligned and discontinuous carbon fibre-epoxy matrix composite having a longitudinal tensile strength of 1900 MPa using 0.45 volume fraction of fibres. Compute the required fibre fracture strength assuming that the average fibre diameter and length are 8 × 10-3 mm and 3.5 mm, respectively. The fibre-matrix bond strength is 40 MPa, and the matrix stress at fibre failure is 12 MPa. Note that reasonable fibre fracture strength should normally be in the range of ~1.4 GPa – 20 GPa. (Hint: use equations 16.3 for critical fibre length and 16.18 for discontinuous and aligned fibre composites).arrow_forwardCalculate 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_forward
- 1. Three metal strips, each 40 mm height, are bonded together to form the composite beam shown. The modulus of elasticity is 210 GPa for the steel, 105 GPa for the brass, and 70 GPa for the aluminium. If the allowable bending stress for the aluminum (Gallow)al= 100 MPa, for the steel (Gallow)st 150 MPa and (Gallow)br=200 MPa for brass determine the maximum allowable intensit of w of the uniform distributed load. 2w 2m Aluminum Brass Steel 40 mm- 10 mm 10 mm 20 mmarrow_forward4. For the composite block shown, determine (a) the value of h if the portion of the load carried by the aluminum plates is half the portion of the load carried by the brass core, (b) the total load if the stress in the brass is 80 Mpa. P Rigid end plate Aluminum Plates (E=70 GPa) Brass Core (E=105 GPa) 40 mm I h 60 mm 300 mmarrow_forwardThe first parts of the stress-strain relationships of the components of a randomly oriented composite are shown in Figure P11.25. Estimate the volume percentage of fibers in the composite assuming a fiber efficiency parameter (K) of 0.2. 1400 1200 1000 - 800 E Fibers 600 - Composite 400 200 Matrix 0.002 0.004 0.006 Strain (m/m) FIGURE P11.25 Stress (MPa)arrow_forward
- Materials Science And Engineering PropertiesCivil EngineeringISBN:9781111988609Author:Charles GilmorePublisher:Cengage Learning