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Abstract

Our attempt to model the effect of strain gradients in the deformation behaviour of multiphase steels, with a ferritic matrix with retained austenite and martensitic regions is inspired by clssical works in the field of strain gradient plasticity [1-3]. Our study is based on a realistic microstructure adapted to microscopical material characterizations. A non local crystal plasticity finite element model has been used to describe plastic deformation in the ferrite and reveals a significant strengthening by virtue of strain gradients in the presence of hard martensitic regions. We have adopted the GND density as internal variable for plasticity to capture size effects in plastic deformation. Our model calculates the strain gradient as a first derivative of plastic deformation gradient and also takes into account higher order derivatives for the prediction of internal stresses which is very critical for these materials. Our simulations reveal that the amount of hardening depends on the size and distance of the martensitic regions. This strengthening via strain gradients was found to be particularly high at micron-level length scales due to high GND densities. We studied both isotropic hardening as well as kinematic hardening provided by strain gradients and pile up of dislocations and their role on the evolution of internal stresses during plastic deformation.

References:
[1] Fleck N A, Muller G M, Ashby M F, Hutchinson J W 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42, 475-487
[2] Nix W D, Gao H 1998 Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411-425
[3] Stolken J S, Evans A G 1998 A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109-5115