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    Semi-Elliptical Cracks in a Cylinder Subjected to Stress Gradients

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    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.


    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