(Model answers will be posted shortly after the due date.)

Question 8.4

Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically-shaped surface crack of length 0.5 mm and having a tip radius of curvature of 5 x 10^-3 mm when a stress of 1035 MPa is applied.

Question 8.14

A specimen of 4340 steel alloy with a plane strain fracture toughness of 54.8 MPa m^0.5 is exposed to a stress of 1030 MPa. Will this specimen experience fracture if it is known that the largest surface crack is 0.5 mm long? Why, or why not? (Assume that the parameter Y has a value of 1.0.)

Question 8.26

A cylindrical 1045 steel bar is subjected to repeated compression-tension stress cycling along its axis. If the load amplitude is 66,700 N, compute the minimum allowable bar diameter to ensure that fatigue failure will not occur. Assume a safety factor of 2.0.

Question 8.49

Steady-state creep rate data are given here for some alloy taken at 200 C:

epsilons(h-1)	sigma (MPa)
2.5 x 10-3	55
2.4 x 10-2	69

If it is known that the activation energy for creep is 140,000 J/mol, compute the steady-state creep rate at a temperature of 250 C and a stress level of 48 MPa.

Question 9.6

For an alloy of composition 52 wt% zinc, 48 wt% copper, cite the phases present and their mass fractions at the following temperatures: 1000C, 800C, 500C and 300C.

Question 9.15

A magnesium-lead alloy of mass 7.5 kg consists of a solid alpha-phase that has a composition just slightly below the solubility limit at 300 C.

1. What mass of lead is in the alloy?
2. If the lead is heated to 400 C, how much more lead may be dissolved in the alpha phase without exceeding the solubility limit for this phase?

Question 9.28

For 5.7 kg of a magnesium-lead alloy of composition 50%wt Pb-50%wt Mg, is it possible, at equilibrium, to have alpha amd Mg₂Pb phases with respective masses of 5.13 and 0.57 kg? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why not.

Question 9.35

Consider the hypothetical eutectic phase diagram for metals A and B, which is similar to that for the lead-tin system (Figure 9.7 in Callister, 6th edition) Assume that:

1. alpha and beta phases exist at the A and B extremities of the phase diagram, respectively;
2. the eutectic composition is 36wt% A, 64wt% B and
3. the composition of the alpha phase at the eutectic temperature is 88 wt%A 12 wt% B.

Question 9.63

Compute the mass fraction of eutectoid cementite in an iron-carbon alloy that contains 1.00 wt% C.