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**Source: **STP34922S

The calculation of stress intensity factors in three-dimensional situations, under any stresses, is an engineering necessity. The authors presented at the 9th National Symposium on Fracture Mechanics, Pittsburgh, 1975, a method for calculating three-dimensional weight functions by finite elements. But the computer time was found to be too long for engineering applications.

In this study the three-dimensional problem is limited to symmetrical problems with applied stresses expressed by a polynomial in one coordinate. Calculations are performed on semi-elliptical cracks in the meridional plane of a cylinder, and the applied stress is expressed by a polynomial of the fourth degree in the coordinate in the radial direction (see nomenclature and Fig. 1). The method could be extended to other symmetrical geometries and loads.

So-called “polynomial influence functions” are defined and correspond to the terms of the polynomial. These functions depend on the radii ratio, the shape, and the depth of the crack; since these parameters are fixed, they are functions ofthe eccentric angle that defines a point on the crack front.

The polynomial influence functions are computed by the boundary integral equation method. The method was first tested on a penny-shaped crack for which the known weight function allowed a direct computation of the polynomial influence functions. The accuracy was found sufficient to apply the method to more difficult problems. These functions were then calculated for semi-elliptical cracks in cylinders.

The results are presented in the form of curves; they are discussed and compared with the results published by other authors.

**Keywords:**

crack propagation, fracture parameters, stress intensity factor, three-dimensional problems, semi-elliptical cracks, cylinders, boundary integral equation method, fatigue (materials)

**Author Information:**

Heliot, J *Research engineer and scientific manager, Creusot-Loire, Paris,*

Labbens, RC *Research engineer and scientific manager, Creusot-Loire, Paris,*

Pellissier-Tanon, A *Research consultant, France*

**Committee/Subcommittee:** E08.05

**DOI:** 10.1520/STP34922S