Page 355 - Mechanical Behavior of Materials

356 Chapter 8 Fracture of Cracked Members

Figure E8.1

Comment For (c), an iterative or graphical solution is optional in this case, but is necessary
in other cases where a limit on α for 10% accuracy in K is exceeded.

8.4.3 Safety Factors

Where cracks may be present, safety factors against yielding, as examined in Chapter 7, need to be
supplemented by safety factors against brittle fracture. Depending on the particular situation, either
yielding or fracture might control the design.
√
Since stress S g and K are proportional according to K = FS g πa, a safety factor X against
fracture for stress can be accomplished by applying the same factor to K. Hence, if S g and a are
the stress and crack length that are expected to occur in actual service, the safety factor on K, and
thus on S g ,is
K Ic K Ic
X K = = √ (8.15)
K FS g πa
It may also be useful to compare the service crack length a with the crack length a c that is expected
to cause failure at the service stress S g .The valueof a c is available from
√
K Ic = F c S g πa c (8.16)
where F c is evaluated at a c . Combining the previous two equations leads to the following safety
factor on crack length:
2

a c F
X a = = X K (8.17)
a F c
Because X K is squared, safety factors on crack length must be rather large to achieve reasonable
safety factors on K and stress.