Computation of 3-D stress singularities for multiple cracks and crack intersections by the scaled boundary finite element method

Among the various possible ways of dealing with notch and crack situations, the scaled boundary finite element method [SBFEM, (Wolf and Song in Finite element modelling of unbounded structures. Wiley, Chichester, 1996; Wolf in The scaled boundary finite element method. Wiley, Chichester, 2003)] has been adopted in this work. This method has been proved to be versatile, much less time consuming than the finite element method and generates highly accurate numerical predictions in cases of structures with notches and cracks. The SBFEM gives the advantage of boundary element method by reducing one dimension in modelling the structures but the mathematical formulations are more related to conventional displacement based finite element method. This method requires a certain scalability of the given structure with respect to a point called similarity center. Like in the case of the boundary element method, the structure needs to be discretized only at the surface where standard displacement based isoparametric finite element formulations are adequate. Unlike in the boundary element method, however, no fundamental solution is required by the scaled boundary finite element method. The similarity or scalability of the method requires separation of coordinates such that in the radial direction (i.e. scaling direction) it yields simple differential equations that can be solved analytically. So this approach can be considered as a semi-analytical method. Several two-dimensional examples have been analysed for crack and notch situations that are well known cases in fracture mechanics. A number of three-dimensional cases have been considered for different crack configurations that yield high order of singularity. The results, according to the authors’ knowledge are up to now unpublished in the open literature. Parametric studies are conducted for structures with bi-material interfaces.     

Oxidation of Silicon Carbide Fibers During Static Fatigue in Air at Intermediate Temperatures

The static fatigue of SiC-based fiber bundles and single fibers has been examined in previous papers, with emphasis placed on the analysis of the stress–rupture time data, and on the modelling of delayed failure from slow crack growth. The present paper investigates the oxidation of the fibers during static fatigue, at temperatures in the intermediate temperature range (500°–800°C). Two oxidation-induced phenomena have been evidenced: the formation of a thin silica film at the surface of fibers and the delayed failure of fiber bundles and single filaments. The stress–rupture time data are interpreted with respect to the chemical and structural characteristics of fibers, and to the oxide film growth rate. The structural analysis of the fibers was carried out using scanning electron microscopy and Auger electron spectroscopy. Delayed failure was found to result from slow crack propagation from surface defects, as a result of the consumption of the free carbon at grain boundaries and the local stresses induced by the SiC→SiO₂ transformation at the crack tip. The respective contributions of these phenomena to static fatigue are discussed.