Page 412 - Mechanical Behavior of Materials

Problems and Questions 413

fracture is needed. Some combinations of yield strength and fracture toughness from Fig. 8.32
are given in Table P8.42.
(a) For material heat treated to a yield strength of 800 MPa, what shaft diameter is
required to resist yielding if the possible crack is ignored? Also, what shaft diameter
is required to resist fracture due to the 1 mm crack, where the possibility of yielding is
ignored?
(b) Which value from (a) should be chosen to avoid failure by either cause?
(c) Repeat (a) for the additional combinations of yield strength and fracture toughness
given. What combination of yield strength and shaft diameter gives the most efficient
design, such that the diameter, and thus the weight, is minimized?
(d) Repeat the previous analysis for a = 0.50 mm and for a = 2.0 mm. Is the choice of a
yield strength sensitive to the crack size that might be present?

Table P8.42
σ o , MPa 800 1000 1200 1300 1400 1600 1800
√
K Ic ,MPa m 187 182 152 102 65 41 35

8.43 In Fig. 8.40, the fracture toughness of rolled plates of aluminum alloys is seen to vary with
orientation. Explain the physical reasons for this behavior and why the toughness for the L-T
orientation is the highest and that for S-L is the lowest.
8.44 Write a paragraph explaining the significance of the data for unirradiated and irradiated
A533B-1 steel of Fig. 8.41.
8.45 Consider the choice of a steel for an oil pipeline in a cold climate, such as Alaska or Siberia.
What are the desirable characteristics of a material for this application? What types of test
data should be available on candidate materials to serve as a basis for the decision?
8.46 A shaft of diameter 20 mm has a circumferential surface crack, as in Fig. 8.14, of depth
a = 1.5 mm. The shaft is made of the AISI 4130 steel of Table 8.1, and it is loaded with
a bending moment of 150 N·m, combined with a torque of 300 N·m. What is the safety
factor against brittle fracture? Noting that K IIIc is unknown, a reasonable and probably
conservative assumption is to employ a relationship of the same form as Eq. 8.34 and assume
that K IIIc = K Ic /2.

Sections 8.7, 8.8, and 8.9
8.47 For the situation of Ex. 8.4 under the applied stress given, do the following:
(a) Determine whether or not plane strain applies and whether or not LEFM is applicable.
(b) Estimate the plastic zone size, 2r oσ or 2r oε , whichever applies.
8.48 A double-edge-cracked plate of 7075-T651 aluminum has dimensions, as defined in
Fig. 8.12(b), of b = 15.9 mm, t = 6.35 mm, large h, and sharp precracks with a = 5.7 mm.
Under tension load, failure by sudden fracture occurred at a force of P max = 55.6kN. Prior to
this, there was a small amount of slow-stable crack growth, with the P-v curve being similar
to Fig. 8.28, Type I, and crossing the 5% slope deviation at P Q = 50.3kN.