ANR Project ELVIS

Micromechanical approach of nonlinear ELasto-VIScoplasticity in polycrystalline materials: theory, modeling, and experimental comparison

(# BLAN08-3_373405, 2009-2011)

Participants:

LPMTM : Renald Brenner, Olivier Castelnau

LGGE : Paul Duval, Fanny Grennerat, Maurine Montagnat

LMA : Alice Labé, Noel Lahellec, Hervé Moulinec, Pierre Suquet

Contact: olivier.castelnau(at)lpmtm.univ-paris13.fr

This project aims at a deeper understanding of the coupling between elasticity and viscoplasticity in polycrystalline materials, and the development of an improved modeling of their (nonlinear) elasto-viscoplastic behavior. Among the potential applications of this research program, one can evoke all situations in which the deformation history and the deformation path have significant impact on the actual mechanical response, such as the prediction of residual stress distribution, the response to complex (non-monotone, non-radial) loading paths, as well as life-time predictions in fatigue. Understanding this coupling requires better consideration of the intraphase (or intragranular) heterogeneities of strain in the material, which develop differently in the purely elastic and in the purely viscoplastic regimes. In transient regimes, the development of field heterogeneities and the coupling between elasticity and viscoplasticity are closely connected.

The project comprises four tasks:

(i) Theoretical models will be proposed to correctly (or at least better) take into account the coupling between elasticity and viscoplasticity, and associated hereditary effects. This issue will be addressed simultaneously in an integral and in the step-by-step mean-field homogenization methods, in order to compare the merits of both approaches. It will be of particular interest to integrate in those mean-field models the recent developments obtained for the homogenization of nonlinear composites governed by a single potential, such as the second-order procedure of Ponte Castañeda.

(ii) The accuracy of these homogenization methods will be estimated by comparison with "exact" results provided by full-field computations based on Fourier Transform (FFT), extended to deal with to elasto-viscoplastic polycrystals. These comparisons will be performed for 2D and 3D random microstructures.

(iii) A complete set of mechanical tests will be carried out on polycrystalline ice, under complex (non-monotone) deformation paths, in order to highlight transient effects and history effects. This particular material has been chosen for its high plastic anisotropy, leading to larger field heterogeneities, and its relative simplicity. It will be of particular interest to measure the intragranular strain distribution along the deformation path by means of an image correlation technique, taking further advantage of the unique possibility of elaborating real 2D ice specimens.

(iv) Finally, the intra- and inter-granular strain heterogeneities, and their effects on the effective behavior, will be investigated theoretically, numerically, and experimentally, by comparing predictions with experimental ones. This analysis will be performed both statistically, i.e. at the scale of sets of grains with similar crystal orientation, and locally, i.e. at some particular locations within given grains.

We expect the new models developed during the course of this project to be really predictive, in the sense that scale transitions and hereditary effects are correctly handled, so that they be used in the near future as predictive tools e.g. for the investigation of the mechanical response of new materials. Another outcome of this project should be the development of numerical codes, both for full-field and mean-field approaches, adapted to most types of elasto-viscoplastic polycrystalline materials. Existing numerical procedures will be tested and possibly improved, in order to reach efficient and accurate numerical resolutions.