Keywords: micro-macro modeling, self-consistent scheme, polycristalline plasticity, ductile crystallographic damage, finite element analysis.

The ductile damage often observed during the sheet or bulk metal forming has undoubtedly a micro-structural origin. For the modeling purpose it will be very interesting to take into account some micro-structural aspects of the ductile damage. Starting from a micromechanical model for elastoplastic polycristalline FCC metals developed for low cycle fatigue [1,2], a new model is proposed in order to describe the ductile crystallographic damage. First the theoretical background of the polycristalline plasticity including the mixed crystallographic nonlinear hardening fully coupled with damage is presented in the framework of the self-consistent micro-macro approach. This highly heterogeneous micro-damage is supposed to evolve on the activated slip systems and leads to an isotropic (homogeneous) macro damage at the representative volume element (RVE).

This model has been implemented into a general purpose finite element code Zebulon. Each Gauss point is then defined as an aggregate of grains (or single crystals) defined by their crystalline orientation. The initial and boundary value problem is then similar to classical macroscopic plasticity except the fact that the plastic flow and the damage are deduced at each integration point from the micromechanical model thanks to the self consistent scheme. Both the local integration of the constitutive equations and the global resolution strategy are discussed in details.

Application is made to the numerical simulation of some mechanical tests under various loading paths. The results at the macroscopic scale are compared with the classical polycrystalline plasticity without damage and to the available experimental results. Besides, many numerical results are shown at the lower scales for a some selected grains and crystallographic slip systems, in order to show the evolution of the heterogeneous fields as the stress, strain and the crystallographic damage.

The influence of many parameters are studied:

• Initial composition of the aggregate (number and orientation of grains) defining the intial texture of the material,
• The evolution of the texture with the plastic deformation and the ductile damage growth,
• The evolution of the local fields with respect to the damage effect;
• The localization of the mechanical fields at the macroscopic scale function of the lower scales;
• The sensitivity of the numerical solution to both time and space decartelization.

1

Saanouni K. and Abdul-Latif A., "Micromechanical modeling of low cycle fatigue under complex loadings. Part1:Theoretical formulation". Int. J. of Plasticity, Vol. 12, No9, pp:1111,1121, 1996. doi:10.1016/S0749-6419(96)00043-5

2

Abdul-Latif A. and Saanouni K., "Micromechanical modeling of low cycle fatigue under complex loadings. Part 2 : Applications". Int. J. of Plasticity, Vol. 12, No9, pp:1123-1149, 1996. doi:10.1016/S0749-6419(96)00044-7

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