Micromorphic approach to crystal plasticity and phase transformation Samuel Forest *† , Kais Ammar * , Benoˆ ıt Appolaire ** , Nicolas Cordero * , and Ana¨ ıs Gaubert *** , * MINES ParisTech, Centre des mat´ eriaux, CNRS UMR 7633, Evry, France ** Laboratoire d’´ etude des microstructures, CNRS/ONERA, Chˆ atillon, France *** Dept. of Metallic Materials and Structures, ONERA, Chˆ atillon, France † Corresponding author: samuel.forest@mines-paristech.fr Abstract Continuum crystal plasticity models are extended to in- corporate the effect of the dislocation density tensor on material hardening. The approach is based on generalized continuum me- chanics including strain gradient plasticity, Cosserat and micromor- phic media. The applications deal with the effect of precipitate size in two–phase single crystals and to the Hall-Petch grain size effect in polycrystals. Some links between the micromorphic ap- proach and phase field models are established. A coupling between phase field approach and elastoviscoplasticity constitutive equations is then presented and applied to the prediction of the influence of viscoplasticity on the kinetics of diffusive precipitate growth and morphology changes. 1 Introduction Continuum crystal plasticity is a special class of anisotropic elastoviscoplas- tic behaviour of materials. It relies on the precise knowledge of the kine- matics of plastic slip according to crystallographic slip systems and of the driving force for activation of plastic slip, namely the corresponding resolved shear stress. When the number of dislocations inside the material volume element is high enough, a continuum description of plastic deformation and hardening can be formulated as settled in (Mandel, 1965, 1971, 1973) and (Teodosiu and Sidoroff, 1976). The objectives of this contribution is first to establish the continuum mechanical framework for the formulation of constitutive equations for sin- gle crystals including the effect of the dislocation density tensor. We show then than this model class can be used to predict size effects in the re- sponse of polycrystals. The considered plastic deformation mechanism is J. Schröder, K. Hackl (Eds.), Plasticity and Beyond, CISM International Centre for Mechanical Sciences, DOI 10.1007/978-3-7091-1625-8_3, © CISM, Udine 2014