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**Published:** Jan 2000

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**Source: **STP1389-EB

Fatigue cracks in shot-peened and case-hardened notched machine components are subjected to stress fields induced by the external load and residual stresses resulting from the surface treatment. Both stress fields are characterized by nonuniform distributions, and handbook stress intensity factor solutions are in such cases unavailable, especially in the case of planar nonelliptical cracks. The method presented here is based on the generalized weight function technique enabling the stress intensity factors to be calculated for any Mode I loading applied to arbitrary planar convex and embedded crack. The stress intensity factor can be determined at any point on the crack contour by using one general weight function discussed in the paper. The weight function, *mA*, can be sufficiently well described by two quantities, i.e., the distance, ρ, from the load point, *P(x, y)*, on the crack surface to the point, A, on the crack front where the stress intensity is to be calculated and the length, Γ*c*, of the inverted crack contour. The stress intensity factors are calculated by integrating the product of the stress field and the weight function over the entire crack area.

The general weight function and calculated stress intensity factors are validated against arious numerical and analytical data. The numerical procedure for calculating stress intensity factors for arbitrary nonlinear stress distributions is briefly discussed as well. Several examples of typical input data and stress intensity factor results are presented including embedded and edge cracks subjected to two-dimensional stress fields. The method is particularly suitable for modeling fatigue crack growth in the presence of complex stress fields.

**Keywords:**

stress intensity factor, weight function, nonlinear stress field

**Author Information:**

Glinka, G *University of Waterloo, Waterloo, Ontario*

Reinhardt, W *Babcock & Wilcox, Cambridge, Ontario*

**Committee/Subcommittee:** E08.06

**DOI:** 10.1520/STP14809S