Issue 33

M. Vormwald, Frattura ed Integrità Strutturale, 33 (2015) 253-261; DOI: 10.3221/IGF-ESIS.33.31 257 advance direction and the increment. In the crack initiation stage kinking in the critical plane is excluded and therefore only the increment must be calculated. It is not much more than a working hypothesis to simply add contributions of each mode according to m m m I,eff II,eff III,eff d / d a n C J C J C J          , (8) where m is the exponent of a power-law type crack growth rate formulation in terms of the  J -integral. TRANSFER OF MATERIAL DATA FOR DESCRIBING THE FATIGUE BEHAVIOR OF COMPONENTS he information gained by investigating material’s fatigue behavior under multiaxial fatigue must be made available for calculating fatigue lives of components. Several tasks have to be fulfilled before arriving at a result. Generally, a local stress or strain based approach is used. This implies the assumption that the life of a component can be determined from the failure life of a material element at the location of severest local stress and strain history. Challenge 6: Identification of critical locations It is not possible to identify the critical location only on the basis of quasi-static calculations of stresses and strains in the component, even after having gained the solutions for all loading cases. The fatigue live calculation for possibly very many locations has to be performed. The shortest of all lives obtained will determine the component’s life. Challenge 7: Calculation of local stress-strain time histories The method for calculating local stress and strain sequences might be the application of the finite element technology. However, the computational costs of such an approach are still too high for practical application. All actual software packages in the field heavily rely on approximations of the local elastic-plastic stress-strain histories on the basis of the knowledge of a hypothetical or pseudo linear elastic local stress histories,   e ij t  . For all unit load cases, L k =1, the transformation factors, ( c ij ) k , are calculated. The local pseudo-elastic stress time sequences are calculated by superposition,       1 l e ij ij k k k t c L t     (9) Köttgen et al. [25] suggested two approaches, the pseudo stress and the pseudo strain based approach. Both approaches are based on a two-step procedure. First, the relation between the loads and local stresses or plastic strains has to be established. Second, the latter are related to its local counterpart. The term “relation” means application of an incremental plasticity model. In the pseudo stress approach loads are expressed in terms of pseudo stresses according to Eq. (9), in the pseudo strain approach loads are expressed as pseudo strains. Buczynski and Glinka’s [26] extended Neuber’s rule to non-proportional loading. The authors assume that the total of the distortional strain energy in an increment of loading is equal for elastic-plastic and linear elastic deformation. More precisely, the assumed identity is formulated for each component of the deviatoric stress and strain tensors individually. Hertel et al. [27] compared the results of various approaches for a notched shaft under non-proportional tension- compression and torsion. The results for a butterfly-type loading are redrawn in Fig. 5. The accuracy of all approaches is comparable. The differences in predicted stress-strain paths are in the same order of magnitude as differences between measured and FE-calculated paths. Some more comparisons can be found in [28]. Challenge 8: Size effects In the literature on size effects in fatigue several types of size effect are distinguished [29]. Most important are the types taking into account the stress gradient and the highly stressed surface. Although fracture mechanics is the favorite method for describing the stress gradient effect, the required solutions for the crack driving forces in non-homogeneous stress fields have not yet been developed. In the uniaxial case, only very sharp gradients have a considerable effect on crack initiation lives [29]. Here, gradient effect has not yet been taken into account. Fatigue life calculations based on defect growth considerations require the definition of an initial defect size. The initial crack depth for starting the simulation, a 0 , has to be determined. It is chosen in such a way that the life calculation model provides a realistic strain life curve of the material under consideration. The initial crack depth is regarded as a Weibull- distributed random variable. The probability of finding an initial crack with a depth larger then a 0 is written as T