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.
The knowledge of weight functions would be of great help for the solution of three-dimensional crack problems. A numerical method of computation of these functions by finite elements is developed, starting from the simple consideration of concentrated forces applied to the crack and the energy released by local extensions of the crack.
Particular attention is paid to the consideration of the asymptotic value of the weight functions at the crack tip, which allows the definition of dimensionless weight functions and makes the numerical calculation easier.
Special weight functions are considered for the case when the applied stress depends on one coordinate only.
The method is checked by comparing the computed weight function for a penny-shaped crack in an infinite solid with the known closed form solution. It seems that the accuracy obtained could allow for solution of engineering problems; however this should be checked by other tests especially in the region of the singularity.
The computing time, however, is long because of the large number of nodes needed in three-dimensional bodies, and the calculation is costly. It seems advisable to investigate the possibilities of other methods of solution of elasticity problems, such as the method of boundary integral equations, for changing the order of magnitude of the computing time and the cost of the calculation.
On montre comment cette théorie peut être appliquée à des structures industrielles et non seulement à des géométries et des chargements simples, et comment les facteurs d'intensité de contrainte peuvent être définis dans tous les cas. On examine sous quelles conditions le facteur d'intensité de contrainte est un critère de rupture brutale, et les corrections et limitations qui résultent de la déformation plastique. On montre ensuite comment la connaissance des fonctions poids attachées à une géométrie ramène à une quadrature le calcul du facteur d'intensité de contrainte. On donne des fonctions de poids pour une longue fissure axiale et une fissure circonférentielle dans un cylindre de révolution.Abstract. 2014 The bases of Linear Elastic Fracture Mechanics are summed up. It is shown how this theory can be applied to industrial structures and not only to simple geometries and loads, and how stress intensity factors can always be defined. The conditions under which the stress intensity factor is a fast fracture criterion are examined, as well as corrections and limitations resulting from plastic deformation. It is shown how weight functions depending only on geometrical parameters make the calculation of the stress intensity factors possible by a simple integral, for any load applied to a given body. Such weight functions are given for a long axial crack and a circumferential crack in a cylinder of revolution.
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