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Reference : UMR7239-STEBER-001
Workplace : METZ
Date of publication : Wednesday, November 21, 2018
Scientific Responsible name : Stéphane BERBENNI
Type of Contract : PhD Student contract / Thesis offer
Contract Period : 36 months
Start date of the thesis : 7 January 2019
Proportion of work : Full time
Remuneration : 1 768,55 € gross monthly
Description of the thesis topic
Title of the PhD thesis:
Development and numerical implementation of a micromechanical homogenization elasto-viscoplastic model for aged duplex ferritic-austenitic stainless steels.
Context and objectives:
Duplex ferritic-austenitic stainless steels are widely used in the primary loop of the cooling system of nuclear pressurised water reactors. It is well established that at the service temperature (about 320°C) and after long periods of exposure (more than 10 000 hours), the ferritic phase of these duplex steels may be embrittled by a phenomenon known as ``475°C'' embrittlement (see Bugat et al. [1,2]). Then the damage mode in ferrite changes from ductile failure to cleavage cracking.
The issue addressed by the present PhD proposal is to develop a robust multiscale micromechanical approach based on both mean field homogenization scheme and full field calculations (FFT/ FEM) performed in LEM3 and EDF Research and Development. The homogenization schemes will consider both the bicrystal scale and the polycrystal scale and must be able to predict the complex mechanical behavior of aged duplex (austenite/ferrite) stainless steels. It should also feed FE structural calculations and damage models for EDF Research and Development. Cleavage in ferrite is primarily controlled by tensile (normal) stresses, which need to be well estimated by recent developed crystal plasticity homogenization schemes (finite strain translated field-based self-consistent model currently developed in LEM3). In addition, this PhD thesis will bring further scientific collaboration with another academic partner (S. Forest, J. Besson, Materials Centre, School of Mines) regarding damage initiation models and cleavage. The homogenization strategy will consider crystallographic slip at the scale of both crystalline phases and a homogenized bi-crystal model containing the imbrication (percolation) of ferritic and austenitic laths. The added value for EDF is to improve the mechanical description of two-phase lath structure and the mechanical interactions between phases in a more refined and physical homogenization scheme that can be further implemented in the FE code (aster) developed by EDF Research and Development. The main outcome of the project should permit to accurately identify the homogenized behavior for bi-crystal microstructure configurations in such duplex steels.
Work description and deliverables:
A homogenization model at the (ferrite + austenite) bi-crystal level will be developed and adapted. It will be based on recently developed translated fields (TF) method with affine formulation [3,4]. The model will take into account the single crystal elasto(visco)-plastic behavior at large strains [5,6] of both ferrite (BCC) and austenite (FCC) based on slip/strain-hardening rules developed by EDF Research and Development for this material. The case of ferrite (BCC phase) will be specifically studied as well as the orientation relationships between both phases. Local stress and strain fields especially normal stresses (useful for further damage initiation studies) will be calculated at the level of the bi-crystalline structure. As in Bugat et al. [1,2], the morphology of the different phases and ferrite variants with respect to austenite will be considered though relevant Eshelby-type tensors to approximate the lath morphologies with ellipsoidal heterogeneities. This homogenization model will be validated for different mechanical loadings by unit cell full field crystal plasticity FFT (as recently developed e.g. in ) / FE based simulations with EDF taking into bi-percolated structure. EBSD experiments combined with FIB at EDF/MAI will give a 3D description of the crystallographic/morphology of the two-phase microstructure, especially regarding the percolation of both phases. This essential feature will be taken into account in the homogenization model.
The deliverables of the PhD project are the following:
- Development of a homogenization model for two-phase grains (bi-crystal microstructure for duplex steels) including crystallographic slip, phase orientations, large deformation setting and lath morphologies.
-Fast Fourier Transform (FFT)-based unit cell calculations on bi-crystal microstructures (ferrite + austenite) taking into account crystal plasticity, local orientation relationships between phases and percolated structure.
- Development of new homogenized constitutive equations for duplex steels using EDF crystal plasticity models in finite strain framework and transfer via MFront to FE calculations in EDF Research and Development.
 S. Bugat, J. Besson, A.-F. Gourgues, F. N'Guyen, A. Pineau. Microstructure and damage initiation in duplex stainless steels. Mater. Sci. Eng. A317,32–36, 2001.
 S. Bugat, J. Besson, A. Pineau. Micromechanical modeling of the behavior of duplex stainless steels. Comp. Mater. Sci. 16, 158-166, 1999.
 C. Mareau, S. Berbenni, An Affine formulation for the Self-Consistent modeling of Elasto-Viscoplastic heterogeneous materials based on the Translated Field method, Int. J. Plast. 64, 134 150, 2015.
 S. Lhadi, S. Berbenni, N. Gey, T. Richeton, L. Germain, Micromechanical modeling of the effect of elastic and plastic anisotropies on the mechanical behavior of β-Ti alloy, Int J. Plast. 109, 88–107, 2018.
 J.P. Lorrain. Ductility criterion based on ellipticity loss of the elastic-plastic tangent modulus deduced from a self-consistent model. PhD Thesis, Arts et Métiers Paris Tech, Metz 2005.
 S. Forest, P. Pilvin, Modelling Finite deformation of polycrystals using Local Objective Frames. ZAMM 79, 199-202, 1999.
 K.S. Djaka, S. Berbenni, V. Taupin, R. A. Lebensohn. FFT-based numerical implementation of Mesoscale Field Dislocation Mechanics: application to two-phase laminates. 2018, submitted.
The PhD work will be mainly performed in LEM3, CNRS UMR 7239, Metz, France(Metz) (UMR CNRS 7239) in the department IMPACT in link with EDF R&D.
LEM3 (http://lem3.univ-lorraine.fr) is mixed research Unit n° 7239 between CNRS - University of Lorraine - Arts et Métiers ParisTech. The unit depends on the department INSIS in CNRS (Engineering Institute, CNRS).
The competence fields of LEM3are the following:
Materials Science, Mechanics of Materials, Microstructures and Process Studies, Micromechanics, Numerical Methods.
The graduate school is C2MP (Chemistry-Mechanics-Materials-Physics) -from the University of Lorraine, see the web site: http://doctorat.univ-lorraine.fr/fr/les-ecoles-doctorales/c2mp/presentation.
Constraints and risks
No particular risk.
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