Page 407 - Mechanical Behavior of Materials

408 Chapter 8 Fracture of Cracked Members

Section 8.5
8.23 A large part in a turbine-generator unit operates near room temperature and is made of
ASTM A470-8 steel. A surface crack has been found that is roughly a semi-ellipse, with
surface length 2c = 60 mm and depth a = 20 mm. The stress normal to the plane of the
crack is 200 MPa, and the member width and thickness are large compared with the crack
size. What is the safety factor against brittle fracture? Should the power plant continue
to operate if failure of this part is likely to cause costly damage to the remainder of the
unit?
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8.24 A solid circular shaft 40 mm in diameter is made of the steel 300-M (300 C temper). It is
subjected to a bending moment of 2 kN·m and may contain a half-circular surface crack,
as in Fig. 8.17(d).
(a) What crack size a c will cause brittle fracture?
(b) What crack size a must be found by inspection to achieve a safety factor in stress of
3.5 against brittle fracture?
(c) Calculate the ratio of the crack size from (a) to that from (b), and comment on the
significance of this value.
8.25 A beam with a rectangular cross section, as in Fig. 8.17(c), is made of 2219-T851 aluminum
and must withstand a bending moment of M = 150 N·m. The thickness is b = 20 mm, and
a quarter-circular corner crack as large as a = 1 mm may be present.
(a) What beam depth t is required for a safety factor 3.0 against brittle fracture?
(b) For the beam depth t as calculated in (a), is the design adequate with respect to possible
fully plastic failure? (Suggestion: Make a conservative estimate of M o by assuming that
the crack extends across the full thickness b.)
8.26 A round rod of silicon nitride ceramic is loaded as a simply supported beam under a uniformly
distributed force, as in Fig. A.4(b). The rod diameter is 10 mm, the length between supports is
120 mm, and the distributed force is w = 3.0 N/mm.
(a) If a half-circular surface crack as deep as 0.5 mm may be present, what is the safety
factor against brittle fracture?
(b) If a safety factor of 4.0 is required, what is the largest permissible depth for a half-
circular surface crack?
8.27 Solid circular shafts made of titanium 6Al-4V (annealed) are subjected in service to bending,
with a moment M = 6.0kN·m. Half-circular surface cracks, as in Fig. 8.17(d), may exist in
the part. From nondestructive inspection, it is expected that no cracks larger than a = 5.0mm
are present.
(a) What shaft diameter is required to resist yielding with a safety factor of 2.0 if no crack
is present?
(b) For an inspection-size crack, what shaft diameter is required to resist brittle fracture
with a safety factor of 3.0?
(c) What shaft diameter should actually be used?
8.28 A shaft of diameter 60 mm has a circumferential surface crack, as in Fig. 8.14, of depth
a = 10 mm. The shaft is made of the 18-Ni maraging steel (air melted) of Table 8.1.
(a) If the shaft is loaded with a bending moment of 2 kN·m, what is the safety factor against
brittle fracture?