Me 475 mechanical behavior of materials assignment obtain

Question

Mechanical Behavior of Materials Assignment-

Q1. Using the figure on the right, perform the following

a) Obtain approximate values of fracture toughness K_Ic and yield strength σ_o for A533B steel at temperatures of - 150^oC and +10^oC.

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

α = a/b	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9
F = F(α)	1.000	1.006	1.025	1.058	1.109	1.187	1.303	1.488	1.816	2.578

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 X_o = 3. Also a leak-before-break criterion must be met with a safety factor of X_a = 5 on crack length, requiring c_c ≥ X_at

• 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 205^oC, used for airplane landing gears, has a G_c 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.