Homogénéisation non linéaire des matériaux poreux monocristallins: Modélisation, implémentation numérique et applications au fluage et à la fatigue

Abstract : This study is concerned with the development of a rate-dependent constitutive model for porous single crystals with arbitrary crystal structure containing general ellipsoidal voids. The proposed model, called modified variational model (MVAR), is based on the nonlinear variational homogenization method, which makes use of a linear comparison porous single crystal material to estimate the response of the nonlinear porous single crystal. Thus, the main objective of this work is to propose a general constitutive model that accounts for the evolution of the microstructure and hence the induced anisotropy resulting when the initially anisotropic porous single crystal is subjected to finite deformations. Furthermore, periodic finite element simulations are used in order to validate the MVAR for a large number of parameters including cubic (FCC, BCC) and hexagonal (HCP) crystal anisotropy, various creep exponents (i.e., nonlinearity), several stress triaxiality ratios, Lode angle, general void shapes and orientations and various porosity levels. The MVAR model is found to be in good agreement with the finite element results for all cases considered in this study. The model is then used in a predictive manner to investigate the complex response of porous single crystals in several cases with strong coupling between the anisotropy of the crystal and the (morphological) anisotropy induced by the shape and orientation of the voids. In addition, an innovate way of calibrating the MVAR with just two adjustable parameters is depicted in the rate-independent context so that an excellent agreement related to simulation results is obtained. Moreover, a porous Tresca model is derived by an original approach starting from the novel porous single crystal model and considering the limiting case on infinite number of slip systems which leads to the Tresca criterion. Finally, the above-mentioned results are then extended to account for the evolution of microstructure when the material is subjected to finite deformations.
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https://pastel.archives-ouvertes.fr/tel-01235253
Contributor : Armel Mbiakop <>
Submitted on : Sunday, November 29, 2015 - 8:22:24 PM
Last modification on : Wednesday, March 27, 2019 - 4:16:24 PM
Long-term archiving on : Saturday, April 29, 2017 - 1:48:52 AM

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  • HAL Id : tel-01235253, version 1

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Mbiakop Armel. Homogénéisation non linéaire des matériaux poreux monocristallins: Modélisation, implémentation numérique et applications au fluage et à la fatigue. Mécanique [physics]. Ecole Doctorale Polytechnique, 2015. Français. ⟨tel-01235253⟩

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