Mechanical Behavior of Materials Assignment-
Q1. Using the figure on the right, perform the following
a) Obtain approximate values of fracture toughness KIc and yield strength σo for A533B steel at temperatures of - 150oC and +10oC.
b) For each temperature, make a plot of stress versus crack length, showing the yielding line alone, and the fracture alone curve (similar to Figure 8.6 in the book, slide 20 in the notes).
c) Compare the two plots and comment on the engineering use of this steel at these two temperatures.
Q2. Consider a center-cracked plate in tension with the accurate values of F given in the table
a) Compare these values with the expression for F that is recommended for any α. What is its accuracy for α ≤ 0.9?
b) Two expressions that are sometimes used for F that are employed for center-cracked plates are
F = √(sec(πα/2)), F = √((2/απ)tan(πα/2)) (b, c)
Compare each of these with the numerical values, and characterize the accuracy of each for α ≤ 0.9
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α = a/b
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0
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0.1
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0.2
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0.3
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0.4
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0.5
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0.6
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0.7
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0.8
|
0.9
|
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F = F(α)
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1.000
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1.006
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1.025
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1.058
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1.109
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1.187
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1.303
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1.488
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1.816
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2.578
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Q3. A cylindrical pressure vessel has an inner diameter of 25 cm and wall thickness of 20 mm, contains a pressure of 50 MPa. The safety factor against yielding must be at least Xo = 3. Also a leak-before-break criterion must be met with a safety factor of Xa = 5 on crack length, requiring cc ≥ Xat
- Choose an appropriate material that can satisfy the leak-before-break condition and meets the safety factor in yielding (Use von-Mises theory)
Q4. AISI 4142 steel tempered at 205oC, used for airplane landing gears, has a Gc value of 10000 N/m. A nondestructive examination technique capable of detecting cracks that are 1 mm long is available.
Compute the stress level that the landing gear can support without failure. Assume the situation to be a single edge cracked member with relatively large width and height. Use units of K as MPa√m.