Issue 33

F. Morel et alii, Frattura ed Integrità Strutturale, 33 (2015) 404-414; DOI: 10.3221/IGF-ESIS.33.45 405 I NTRODUCTION raditionally, the fatigue design of components submitted to complex loading modes during service life is based on extensive material property databases. The relationship between microstructure and the resulting fatigue strength is primarily qualitative. This is all the more true in the presence of geometrical defects inducing stress and strain concentrations and hence affecting the strength. Several authors have established fatigue criteria taking into account accurately the detrimental influence of defects on the fatigue limits in tension [1], in torsion [2] and in combined tension and torsion [3]. However, although the practical interest of these approaches is undeniable, they often involve a material characteristic length whose physical meaning is unclear. Moreover, these methods neglect the variability of the microstructure in the vicinity of the defect and thus cannot correctly reflect the scatter observed in the HCF strength of metallic materials. This scatter is often explained by the anisotropic elasto-plastic behaviour of individual grains leading to a highly heterogeneous distribution of plastic slip. Since fatigue crack initiation is a local phenomenon, intimately related to the plastic activity at the crystal scale, it seems relevant to evaluate and use the mesoscopic mechanical quantities (i.e. the average mechanical quantities at the grain scale) to assess the macroscopic fatigue response. To get access to them, localization schemes are sometimes used, for instance by Dang Van [4], Papadopoulos [5], Monchiet [6] and Morel [7]. Despite the qualities of these criteria (ease of application, fairly accurate predictions), some simplifying assumptions (e.g. same elastic behaviour at the grain scale and the macroscopic scale) lead at most to a first order approximation of the fatigue problem. In particular, the free surface effects and the influence of the neighbouring grains are ignored. A promising approach, consisting in computing, by FE method, the mechanical response of explicitly modelled polycrystalline aggregates, allows to take into account microstructural details generally neglected in the homogenisation schemes and to deepen the analysis of the mesoscopic mechanical responses of metals under cyclic multiaxial loading. In recent years, several works have involved this kind of numerical simulations to contribute to the study of the HCF behaviour [8-12]. The present study falls within this framework and a specific effort is made to quantify the multiaxial fatigue performance of metals in the presence of defects through statistical modeling of the microstructure. The practical implications of such a work are numerous. Commercial alloys are indeed composed of various microstructural heterogeneities depending on the type of material and the manufacturing process used. For instance the shrinkage or gas pores which are most of the time present in cast alloys are known as the main source of crack initiation in such materials [13]. In some forged steels, the presence of non-metallic inclusions can be at the origin of a fatigue anisotropy caused by a change of fatigue damage mechanisms depending on the fibering orientation to the loading axis [14]. These two examples have one thing in common: the defects responsible for the crack initiation are often of the same size as the microstructure. This paper is hence focused on the specific case where the defect size is of the order of the grain size. More exactly, the purpose is to analyze the competition existing between the stress concentration induced, on one hand, by a small defect and, on the other hand, by the most highly stressed regions of the microstructure caused by the anisotropic behavior of the grains. This work contributes to a better understanding of the Kitagawa effect characterized by the existence of a critical defect size under which the fatigue strength is no more affected by the defect. M ODELLING APPROACH AND PROBABILISTIC FATIGUE CRITERION Finite Element modelling inite Element simulation of polycrystalline aggregate requires most of the time simplified geometries in particular to get reasonable computation time. In the present study, most of the FE models are of 2D type and the microstructure is explicitely modelled only in the immediate vicinity of the geometrical defect. A few 3D hemispherical notches are also modelled but only for the smallest defect size. For both 2D and 3D models, an homogeneous isotropic matrix embeds the polycrystal. The process used to generate the 2D polycrystalline geometries is described in [10]. Both smooth and notched microstructures are studied. The finite element mesh of the CAD of the microstructure is generated using Gmsh [15]. Three-node triangular finite elements with linear interpolation and generalised plane strain hypothesis are employed for the 2D simulations. Each crystal is distretized with an average of 75 elements. A finite element mesh illustration of a microstructure embedded in a matrix in shown in Fig. 1. In the absence T F