Growing Cracks under a General Loading History

5 Growing Cracks under a General Loading History 

Consider a crack, open and growing at time t, after an arbitrary number of closures. Once again, we can regard it as having been open always under a stress history Z x, t), the normal component of which is not known until the problem is solved. Then (4.2.9, 15) hold so that the stress will have the same form as in the elastic case and is independent of material properties. This is a particular manifestation of the Generalized Partial Correspondence Principle, proved in Sect. 2.6. 

Expressions (4.2.16, 17) will hold for the stress intensity factor. Also, assume that while the crack is open, it is strictly growing at both ends, never stationary. 

using an argument similar to that in Sect. 4.3, we see that the dominant behaviour of the normal gap derivative 2(jc, t) given by (4.3.3), which may be deduced from (4.2.9), is 

These quantities can never be negative and since the crack is open, the stress intensity factors Ki(a t)) and /r,(6(t)). which in this case are given by (4.2.18, 23), must be positive. It follows that p(t) must be positive. 

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