13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Numerical and analytical introduction to the prediction of grain boundary micro-crack initiation induced by slips bands impingement. Effect of material and microstructure parameters. Mohamed Ould Moussa1,*, Maxime Sauzay1 1 CEA, DEN, DANS, DMN, SRMA, F-91191Gif-sur-Yvette, France * Corresponding author: mohamed.ouldmoussa@cea.fr Abstract Micro-cracks are often observed at the intersections of thin slip bands (SB) and grain boundaries (GB) due to local stress concentration. Numerous models are based on the pile-up theory and the Griffith criterion, used since the pioneering work of Stroh. We have shown that the former underestimate strongly the macroscopic stress for GB micro crack nucleation. In fact, the key issue is that slip bands display finite thickness, observed to belong to [20nm 1000nm]. Therefore, one aims to account for the effect of SB thickness in crystalline finite element (FE) calculations performed using the Cast3M software. The simulations take into account the effects of isotropic elasticity parameters, cubic elasticity, GB orientation and crystallographic orientation of the considered grain. Following the theory of matching of asymptotic expansions, this leads to an analytical expression of the GB normal and shear stress, which show weaker stress singularities than the pile-up one. Keywords Micro-cracks, slip bands, pile-up theory, linear fracture mechanics, FE method, crystalline plasticity 1. Introduction Many issues are available dealing with the appearance and effects of either slip bands (SBs) or dislocation channels on the behavior of irradiated materials. Indeed, the intersection sites between SBs and grain boundaries (GBs) are prone to micro-crack nucleation because of strain localization. A series of papers [1 ; 2 ; 3 ; 4 ; 5 ; 6] highlight the presence of slip localization in Faced Centred Cubic (FCC) metals and alloys observed after post-irradiation tensile loading. Slip Bands were also observed in [7 ; 8 ; 9 ; 10 ; 11 ; 12 ; 13 ; 14] after cyclic loading. Such slip bands have been shown to be Persistent Slip Bands (PSBs) [9]. Some other works [15] have reported the formation of Slip Bands appearing during simple tensile loading. Whatever the loading conditions, such slip bands show a thickness lying between ten nanometers and a few micrometers, and a length about the grain size, usually varying from ten micrometers to a few hundred micrometers. Jiao et al. [5] have evidenced strong localization in austenitic stainless steels in post-irradiation tensile tests, using AFM measurements. Wejdemann and Pedersen [16] have applied the same techniques to observe such localization in the PSBs where plastic strain is shown to be fifty times larger than the macroscopic plastic strain. Sharp [1] and Edwards et al. [4] highlighted strain localization in single crystal and polycrystals of copper subjected to post-irradiation tensile loadings. Sauzay et al. [17] confirmed such localization in the case of irradiated austenitic stainless steels. In addition, several works attempted to model the stress concentration at grain boundaries. Besides, it is proved that the anisotropy character of crystalline elasticity induces stress concentration at grain boundaries according to Neumann [18]. Margolin and co-workers [19 ; 20] have carried out optical observations of slip traces and conclude that stresses are more concentrated near grain boundaries. The stress gradients around GBs, induced by plastic deformation incompatibilities between neighbor grains, can be tracked thanks to large-scale finite element (FE) computations [21].
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