Size effects on the hardening of channel-type microstructures: A field dislocation mechanics-based approach

Abstract A simple shear model based on the mechanical theory of dislocation fields is developed in order to predict in a straightforward way the effects of channel width on the kinematic hardening of a soft–hard periodic composite material with channel-type microstructures. The model uses a continuous description of the crystal incompatibility at channel–wall interfaces. A non-local tangential continuity condition on the plastic distortion rate is applied, accounting for the conservation of the Burgers vector at the interfaces. The constraints thus imposed on plasticity at the walls enhance kinematic hardening, which is found to be channel-size dependent for a fixed refined mesh size. The smaller the channel width becomes for a given volume fraction of walls (hard phase), the stronger the kinematic hardening and the Bauschinger effect. When the channel width is sufficiently large or when the continuous treatment of interfaces is overlooked, the model becomes equivalent to a size-independent isostrain mean field approach, which is only able to retrieve hard-phase volume fraction effects on composite hardening. Due to dislocation density transport, the incompatibility in the plastic distortion between phases is accommodated by the creation of a continuous layer of polar edge dislocation density through a gradual dynamic accumulation at the channel–wall interfaces. In contrast, the singular surface dislocations at the channel–wall interfaces commonly observed in Eshelby-type mean field approaches are shown to be unable to describe size-dependent hardening.