Page 409 - Mechanical Behavior of Materials

410 Chapter 8 Fracture of Cracked Members

8.34 A cylindrical pressure vessel has an inner diameter of 150 mm and a wall thickness of 5 mm,
and it contains a pressure of 20 MPa. The safety factor against yielding must be at least
X o = 2. Also, a leak-before-break criterion must be met, with a safety factor of at least
X a = 9 on crack length, requiring c c ≥ X a t.
(a) Is the vessel safe if it is made from 300-M steel (300 C temper)?
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(b) From ASTM A517-F steel?
(c) What minimum fracture toughness is required for the material in this application?
(d) What is the safety factor on K relative to K Ic due to the X a = 9 requirement?
8.35 A thick-walled tube having inner radius r 1 = 30 mm and outer radius r 2 = 50 mm contains a
pressure of 200 MPa. It is made of the AISI 4130 steel of Table 8.1. As shown in Fig. P8.35,
a longitudinal crack is present, with width 2c = 10 mm and depth a = 3 mm. Estimate the
safety factors against brittle fracture and against yielding.

pressure

crack
r 1
2c
r 2
a

Figure P8.35

8.36 A disc having inner radius r 1 = 100 mm and outer radius r 2 = 400 mm rotates at 60
revolutions/sec. It is made of ASTM A470-8 steel. As shown in Fig. P8.36, the disc has a
quarter-circular corner crack of depth a = 10 mm at the inner radius. Estimate the safety
factors against brittle fracture and against yielding.

a
a
r 1 crack
r 2

ω

Figure P8.36