13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- Such stress concentrations may allow to induce inter-granular crack initiation because they neglect plastic slip localization. Therefore, in the scope of the current contribution, one investigates the effect of localized slip on GB stress fields. An analytical approach, based on the well-known Stroh model [22], has been largely applied in order to evaluate GB stress. One recurrent issue has indeed been, since decades, the using of discrete or continuous dislocation pile-ups. The stress singularity, due to an edge or screw pile-up of length LPile-up has been shown to be the same as the one of a crack in the framework of linear elastic fracture mechanics (LEFM) [22 ; 23]. Therefore, an energy criterion has been proposed by [23], based on the Griffith criterion, for predicting micro-crack nucleation. The latter may be used for the case of a singularity exponent of 0.5 only and it fails when the exponent value is less than 0.5 because the energy release rate, G, becomes equal to zero [24 ; 25]. Cottrell [26] later suggested that the fracture process should be controlled by the critical crack growth stage under the applied tensile stress, which required higher stress than the crack nucleation itself as suggested by Stroh. Cottrell came with a modeling by supposing that slip occurs along two atomic planes which intersection shows pile-up dislocation. However, Sauzay and Evrard [17] recently have outcame with the limitation of such basic pile-up theory to more accurately predict micro-crack initiation. Following their work, the pile-up theory leads to an underestimation of macroscopic stresses with comparison to experimental data. Indeed, the pile-up approach postulates that slip localization occurs on one atomic plane only, but, experiments carried out using various materials and loading conditions show slip occurring on many slip atomic planes [8], [27], [5 ; 16], [28]. Therefore, because of the distribution of plastic slip through the slip band thickness [2 nm, 1000 nm], accounting for the SB thickness in the models may improve the predictions. The current contribution aims to validate an analytical model of GB stress fields in the case of SB impingement. Then, the first section presents the analytical modeling for close stress fields configuration which corresponds to points located near the intersection of the GB and the SB. The second section deals with finite element (FE) calculations in order to investigate numerically the effect of SB or GB geometry and material properties on GB stress fields. Besides, a final section is devoted, on one side, to adjust parameters and validate the analytical model and on the other side, to show the influence of GB and SB orientation on the adjusted model parameters and a conclusion will end the paper. 2. Analytical modeling The subsequent problem is to be solved: an elastoplastic slip band is embedded at the free surface of an elastic matrix, subjected to a displacement controlled tensile loading (Fig. 1a). a) b) Figure 1. a) Main grain, slip band and matrix b) SB-GB intersection and associated vectors SB GB n ρ m ρ GB n ρ θ x ρ y ρ
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