Page 411 - Mechanical Behavior of Materials

412 Chapter 8 Fracture of Cracked Members

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K Ic = 200 MPa m. The weld metal has similar properties to the plates. Then (c) comment
on the suitability of this steel for use at these two temperatures.
8.40 Consider 300-M steel with properties for 650 C and 300 C tempers as listed in Table 8.1.
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Solid circular shafts for an engineering application are currently being made from the
650 C temper material and have a diameter of 54 mm. The shafts are loaded with a
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bending moment of 8.0 kN·m, and nondestructive inspection assures that there are no cracks
deeper than a = 1.0 mm. Also, the design requires a safety factor of at least 2.0 against
yielding.
(a) Is the current design adequate? Assume that any cracks present are half-circular surface
cracks as in 8.17(d).
(b) It has been suggested that a weight and cost savings can be realized by chang-
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ing to the 300 C temper material with a higher yield strength, and then using a
smaller shaft diameter. What minimum shaft diameter would you recommend for
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the 300 C temper material? Would you recommend a change to the 300 C temper
material?
8.41 Consider rapid cooling (thermal shock) of the glass and ceramics listed in Table P8.41, with
additional data in Table 8.2. Sudden cooling of a thin surface layer of material causes a stress,
as given by Eq. 5.41.

Table P8.41
α E ν
Material 10 / C GPa
−6 ◦
Soda-lime glass 9.1 69 0.20
MgO 13.5 300 0.18
Al 2 O 3 8.0 400 0.22
SiC 4.5 396 0.22
Si 3 N 4 2.9 310 0.27
Sources: Tables 3.10, 5.2, P5.30, and [Creyke 82]
p. 50.

(a) Assume that a piece of each material contains a small half-circular surface crack of
depth a = 1.0 mm, and calculate the surface temperature change T necessary to
cause fracture for each. Which material is the most resistant to thermal shock? Which
is the least?
(b) Apply the method of Section 3.8.1 to determine the combination of materials properties
giving the function f 2 that controls the resistance to thermal shock. Rank the materials
according to f 2 . Comment on the effects of each of the properties K Ic , α, E, and ν,
and rationalize how each affects the resistance to thermal shock.
8.42 A solid round shaft is to be made from the AISI 4340 steel of Fig. 8.32. It must resist a bending
moment of M = 3.8kN·m, with a safety factor of two against yielding. Also, a half-circular
surface crack of depth a = 1.0 mm may be present, and a safety factor of three against brittle