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.
An experimental program has been conducted on Type 316 stainless steel uniaxial specimens to determine the main characteristics of their behavior under repeated loading. The cyclic stress-strain curve measured under constant repeated load, without high preloads, is independent of the level of the mean stress. Two different behaviors with respect to the occurrence of progressive deformation have been observed: (1) at room temperature, progressive deformation occurs when the maximum value of the tensile stress exceeds a critical value, and (2) at 320°C and for loading with temperature cycling between ambient temperature and 320°C, progressive deformation occurs when the amplitude of stress exceeds a critical value.
These results show that Section III of the ASME Code, which limits the range of variation of the primary plus secondary stress intensity to the value of 3 Sm, gives an effective guarantee against progressive deformation for operating conditions in the range of 20 to 320°C. It is recalled that the absence of progressive deformation is a necessary condition for the validity of conventional low-cycle fatigue analysis.
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.
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