Issue 35

T. Auger et alii, Frattura ed Integrità Strutturale, 35 (2016) 250-259; DOI: 10.3221/IGF-ESIS.35.29 257 The approach is implemented in the Abaqus® finite element code, using a UMAT (User MATerial) subroutine [19]. The plasticity criterion is given by the Schmid law:    s s c where   .    s s s n g    is the reduced shear stress on the glide plane (s) and  s c is the local critical shear stress. At each time increment of the computation, we assume that the local critical shear stress is given by: 0 1,12            s s su u su u c u u b a h where µ is the isotropic shear modulus, b the norm of the Burgers vector, 0  c the lattice friction stress, su h the component of the hardening matrix. The critical shear stress is a function of the components a su of the interaction matrix (forest hardening) between the systems (s) and (u). The glide velocity  s  is expressed with a classical viscoplastic potential based on the resolved shear stress and the critical shear stress for glide activating on system (s): s s 0 sign ( ) if , 0 otherwise                    n s s s s c s c    where 0   is a reference shear rate and n is the rate exponent. The dislocation density evolution is governed by a dislocation production term, based on Orowan’s relationship, and is balanced by an annihilation dislocation term which takes into account the dynamic recovery during deformation: 2y c is a material parameter related to an annihilation distance of dislocations. The first term corresponds to the inverse of the average mean free path of the statistically stored dislocations on the system ( s ). K is a material parameter. Each material requires the identification of more than 20 parameters to be able to capture the plastic behavior shown in Fig. 6a. The modeling of such an aggregate allows the calculation of local strain and stress fields as well as the GB decohesion local stress. Figure 6: a. True stress versus true strain curve with 316LN parameters of the 3D aggregate Fig. 5b. b. S 22 on 2 matching grains after 15% deformation along the Y direction (each of them is rotated oppositely by 30° around the x axis to be able to display the interface loading).