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Journal Articles International Journal of Solids and Structures Year : 2008

Intra-granular plastic slip heterogeneities: Discrete vs. Mean Field approaches


In this paper, we derive the mechanical fields (internal stresses, elastic energy) arising from the presence of an inelastic distortion field representing a typical intra-granular “microstructure” as the one observed during the plastification of metallic polycrystals. This “microstructure” is due to the formation of discrete intra-granular plastic slip heterogeneities characterized by at least two internal lengths: the first one is the individual grain size which represents a stochastic parameter inherent to the processing route (prior working, annealing), and, the second one is the spatial distance between active slip lines or slip bands associated with inhomogeneous plastic slip in the interior of grains. These internal lengths can be observed and measured using conventional experimental techniques (EBSD, TEM, AFM). The micro-mechanical modeling of the mechanical fields associated with plastic slip events inside grains is performed with two different assumptions. The first one is based on the well-known Eshelby’s problem of plastic inclusion where only the grain diameter is considered as internal length scale. This classical method considers homogeneous plastic distortion in the grain and leads to a uniform and grain size independent total strain field in the grain. The second method accounts for a non-uniform plastic distortion in the grain characterized by its discrete nature and the two aforementioned internal lengths. Both methods consider grains as spherical inclusions with a given diameter embedded in a homogeneous medium. For the second method, plastic slip is constrained by grain boundaries seen as impenetrable obstacles to dislocations. Thus, plastic strain is embodied by distributions of discrete circular glide loops. After writing the field equations and the free energy of the medium, a micro-mechanical formulation based on the Fourier transform method is developed. It is then found that in contrast with the mean-field approach, the internal stress fields as well as the elastic energy corresponding to different dislocation configurations depend on internal lengths associated to the deformed medium. Different possible configurations associated with intra-granular plastic flow due to circular glide dislocation loops are analyzed. Finally, the results are discussed with respect to the grain size dependence of the flow strength and the Bauschinger effect for plastically deforming polycrystals and perspectives to develop new micro–macro transition schemes accounting for internal length scales are sketched out.

Dates and versions

hal-03038482 , version 1 (03-12-2020)



S. Berbenni, M. Berveiller, Thiebaud Richeton. Intra-granular plastic slip heterogeneities: Discrete vs. Mean Field approaches. International Journal of Solids and Structures, 2008, 45 (14-15), pp.4147-4172. ⟨10.1016/j.ijsolstr.2008.02.028⟩. ⟨hal-03038482⟩
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