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A predictor-corrector scheme capable of mixed-mode problems ispresented to optimize the shape of 3D crack fronts within the 3D simulation of fatiguecrack growth. It enables one to follow and/or predict crack paths as realistic aspossible. The whole procedure is embedded in an automatic incremental crack growthalgorithm for arbitrary three-dimensional problems with linear-elastic materialbehavior. The numerical simulation is based on the 3D dual boundary element method(Dual BEM) and on the optimized evaluation of very accurate stress intensity factors(SIFs) and T-stresses. As part of the proposed predictor-corrector scheme, 3Dsingularities along the crack front especially in the vicinity of the intersection of thecrack front and the boundary are considered. The knowledge about these singularitiesallows the specification of crack front shapes with bounded energy release rate.Additionally, it is assumed that the crack front shape ensures a constant energy releaserate along the whole crack front. A numerical example with a complex cross section ispresented to show the efficiency of the proposed crack growth criterion. A comparisonto recent experimental results shows good agreement.