Page 293 - Materials Science and Engineering An Introduction

8.6 Fracture Toughness Testing • 265

Table 8.3 Ranking of Several Metal Alloys Table 8.4 Ranking of Several Metal Alloys
Relative to Critical Crack Length (Yielding Relative to Maximum Allowable Pressure
Criterion) for a Thin-Walled Spherical (Leak-before-Break Criterion) for a
Pressure Vessel Thin-Walled Spherical Pressure Vessel
2 2
K Ic K Ic
a b (mm) (MPa . m)
Material Material
S y S y
Medium carbon (1040) steel 43.1 Medium carbon (1040) steel 11.2
AZ31B magnesium 19.6 4140 steel (tempered at 482 C) 6.1
2024 aluminum (T3) 16.3 Ti-5Al-2.5Sn titanium 5.8
Ti-5Al-2.5Sn titanium 6.6 2024 aluminum (T3) 5.6
4140 steel (tempered at 482 C) 5.3 4340 steel (tempered at 425 C) 5.4
4340 steel (tempered at 425 C) 3.8 17-7PH stainless steel 4.4
Ti-6Al-4V titanium 3.7 AZ31B magnesium 3.9
17-7PH stainless steel 3.4 Ti-6Al-4V titanium 3.3
7075 aluminum (T651) 2.4 4140 steel (tempered at 370 C) 2.4
4140 steel (tempered at 370 C) 1.6 4340 steel (tempered at 260 C) 1.5
4340 steel (tempered at 260 C) 0.93 7075 aluminum (T651) 1.2

and, from Equation 8.8,
pr
t = (8.12)
2s
The stress is replaced by the yield strength because the tank should be designed to contain the
pressure without yielding; furthermore, substitution of Equation 8.12 into Equation 8.11, after
some rearrangement, yields the following expression:

2 K Ic 2
p = a b (8.13)
2
Y pr s y
Hence, for some given spherical vessel of radius r, the maximum allowable pressure consist-
ent with this leak-before-break criterion is proportional to K Ic /s y . The same several materials
2
are ranked according to this ratio in Table 8.4; as may be noted, the medium carbon steel will
contain the greatest pressures.
Of the 11 metal alloys listed in Table B.5, the medium carbon steel ranks first according
to both yielding and leak-before-break criteria. For these reasons, many pressure vessels are con-
structed of medium carbon steels when temperature extremes and corrosion need not be considered.

8.6 FRACTURE TOUGHNESS TESTING
A number of different standardized tests have been devised to measure the fracture
toughness values for structural materials. 5 In the United States, these standard test
methods are developed by the ASTM. Procedures and specimen configurations for most

5 See, for example, ASTM Standard E399, “Standard Test Method for Linear–Elastic Plane–Strain Fracture Toughness
K Ic of Metallic Materials.” (This testing technique is described in Section M.6 of the Mechanical Engineering Online
Module.) Two other fracture toughness testing techniques are ASTM Standard E561-05E1, “Standard Test Method
for K–R Curve Determinations,” and ASTM Standard E1290-08, “Standard Test Method for Crack-Tip Opening
Displacement (CTOD) Fracture Toughness Measurement.”