Fracture Mechanics Approach to Fatigue

During fatigue the stress amplitude usually remains constant and brittle failure occurs as a result of crack growth from a sub-critical to a critical size. Clearly the rate at which these cracks grow is the determining factor in the life of the component. It has been shown quite conclusively for many polymeric materials that the rate at which cracks grow is related to the stress intensity factor by a relation of the form 

AK is the alternating stress intensity factor corresponding to the stress range Act (i.e. AK — K ax — Kmin) and C2 and n are constants. 

Hence a graph of [og da/dN) against logfA/iT) will be a straight line of slope n as shown Fig. 2.77. Now, in Section 3.4 it was shown that the range of stress intensity factor could be represented by a general equation of the form 

Assuming that the geometry function, Y, does not change as the crack grows then this equation may be integrated to give the number of cycles, N/, which are necessary for the crack to grow from its initial size (2n,) to its critical size at fracture (lOc). 

The way in which this sort of approach may be used to design articles subjected to fatigue loading is illustrated in the following example. 

Exampk 2 A certain grade of acrylic has a Kc vidue of 1.6 MN m and the fatigue crack growth data as shown in Fig. 2.77. If a moulding in this material is subjected to a stress cycle which varies from 0 to IS MN/m, estimate the maximum internal flaw size which can be tolerated if the fatigue endurance is to be at least 10 cycles. 

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Fracture Mechanics Approach to Fatigue Crack Propagation Measurements and Observation... 

Paris, P.C. The Fracture Mechanics Approach to Fatigue. In Proceedings of the 10th Sagamore Conference, p. 107, Syracuse Press (1965)... 

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