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**Published:** Jan 1976

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**Source: **STP590-EB

The existence for a plane or axisymmetric cracked body of an influence or Green's function, depending on the geometry of the body, allows calculation by means of a simple integral of the stress intensity factor. In this way the respective influence of geometry and load in *K* calculation are separated. The relationship between this function and the compliance for a concentrated force applied on the crack is shown.

Starting from complex mathematical considerations, Bueckner defined weight functions equivalent to the influence functions and of particular advantage for analytic as well as numerical purposes. Moreover he showed that weight functions behave like *d*^{-½} at the distance *d* from the crack tip. In the sequel we shall refer to weight functions, since they are studied more deeply from a mathematical point of view and are known more widely than influence functions.

A practical calculation method of weight functions by finite elements is shown. This method can be used for any bidimensional cracked body, plane or axisymmetric. Curves of nondimensional weight functions are given for cylindrical geometries currently used in engineering.

It is pointed up that this method is more flexible than the use of handbooks which, in spite of their great interest, cannot foresee all the geometries and loads which are met in engineering problems.

**Keywords:**

crack propagation, fracture properties, stress intensity, stresses, elastic theory, weight function, plane problems, axisymmetric problems

**Author Information:**

Labbens, R *Société Creusot-Loire, Branche Mecanique et Entreprise, Paris,*

Pellissier-Tanon, A *Société Creusot-Loire, Branche Mecanique et Entreprise, Paris,*

Heliot, J *Société Creusot-Loire, Branche Mecanique et Entreprise, Paris,*

**Committee/Subcommittee:** E08.06

**DOI:** 10.1520/STP33957S