Crack growth rate taken the slope some point the curve
9.13 Crack Propagation Rate ● S57
FIGURE 9.32 Fatigue
Even though measures may be taken to minimize the possibility of fatigue failure, cracks and crack nucleation sites will always exist in structural components. Under the influence of cyclic stresses, cracks will inevitably form and grow; this process, if unabated, can ultimately lead to failure. The intent of the present discussion is to develop a criterion whereby fatigue life may be predicted on the basis of material and stress state parameters. Principles of fracture mechanics (Section 9.5) will be employed inasmuch as the treatment involves determination of a maximum crack length that may be tolerated without inducing failure. It should be noted that this discussion relates to the domain of highcycle fatigue, that is, for fatigue lives greater than about 104to 105cycles.
Results of fatigue studies have shown that the life of a structural component may be related to the rate of crack growth. During stage II propagation, cracks may grow from a barely perceivable size to some critical length. Experimental techniques are available which are employed to monitor crack length during the cyclic stressing. Data are recorded and then plotted as crack length a versus the number of cycles N.9A typical plot is shown in Figure 9.33, where curves are
S58  ●  Chapter 9 / Failure  �2  �1  a1,�1 
versus the number of cycles at 


Crack length a  

a0
(9.26) 

The parameters A and m are constants for the particular material, which will also depend on environment, frequency, and the stress ratio (R in Equation 9.24). The value of m normally ranges between 1 and 6.
Furthermore, �K is the stress intensity factor range at the crack tip, that is,
�K � Kmax � Kmin  (9.27a) 

�K � Y�� ��a � Y(�max � �min) ��a  (9.27b) 
