Stress intensity factor weight functions

Figure 19.3 Crack speed in fatigue of sPS as a function of the amplitude of the stress intensity factor for different molecular weights...

Wu X.R. and Carlsson A.J. (1991). Weight Functions and Stress Intensity Factor Solutions. Pergamon Press, Oxford. 

In the previous section, the idea of surface tractions in obtaining a superposed K solution was used but the tractions were assumed constant over the whole crack. Clearly, if it was known how to weight the tractions, it would not be necessary to assume a constant stress. One approach to identify this weighting is to use functions derived from the point-force solutions (see Fig. 8.31). These are called Green s functions, g x). For example, the stress intensity factor can be written in terms of the stress along the crack site in the uncracked body. 

Two-dimensional problems concerning a crack of length L in an infinite body subjected to an arbitrary symmetrical loading stress o-(x) can be solved using a weight function approach. For this approach, the stress intensity factor K and the crack face displacements v (L, x) must be known for another symmetric case. The stress intensity factor fC for the unknown configuration is... 

Fig. 25. Master curve for FCP in polystyrene (10 Hz, sine wave) as a function of stress intensity factor (94). Curve includes data for 12 specimens varying greatly in molecular weight and its distribution, and encompasses both the threshold of crack growth and the approach to catastrophic fracture.

Th. Fett, D. Munz, Stress intensity factors and weight functions. Computational Mechanics Publ., Billerica, Massachusetts, 1997... 

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