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http://hdl.handle.net/10985/10846
Self-consistent modelling of heterogeneous materials with an elastic-viscoplastic behavior: Application to polycrystalline agregates
MAREAU, Charles; BERBENNI, Stéphane
The self-consistent scheme is a common homogenization method that was developed to connect local deformation mechanisms to the overall behavior of heterogeneous disordered materials. In the past decades, many efforts have been made to obtain extensions of the self-consistent approximation to the non-linear case. This work focuses on the specific case of heterogeneous materials with an elastic-viscoplastic behavior. For such materials, the overall behavior is strongly dependent on the space-time couplings originating from the differential form of the local constitutive law. Different approaches have thus been developed to describe the impact of such complex couplings on the overall behavior. (...)
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/108462015-01-01T00:00:00ZMAREAU, CharlesBERBENNI, StéphaneThe self-consistent scheme is a common homogenization method that was developed to connect local deformation mechanisms to the overall behavior of heterogeneous disordered materials. In the past decades, many efforts have been made to obtain extensions of the self-consistent approximation to the non-linear case. This work focuses on the specific case of heterogeneous materials with an elastic-viscoplastic behavior. For such materials, the overall behavior is strongly dependent on the space-time couplings originating from the differential form of the local constitutive law. Different approaches have thus been developed to describe the impact of such complex couplings on the overall behavior. (...)Modélisation autocohérente des matériaux hétérogènes élasto-viscoplastiques: une approche à champs translatés
http://hdl.handle.net/10985/10844
Modélisation autocohérente des matériaux hétérogènes élasto-viscoplastiques: une approche à champs translatés
MAREAU, Charles; BERBENNI, Stéphane
La méthode autocohérente [1] est un des outils permettant de faire le lien entre les mécanismes de déformation à l'échelle locale et le comportement macroscopique effectif. Si la méthode autocohérente a été initialement développée pour des comportements locaux linéaires, des extensions ont été proposées pour différentes classes de comportements non-linéaires : élastoplasticité [2] et viscoplasticité [3]. (...)
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/108442014-01-01T00:00:00ZMAREAU, CharlesBERBENNI, StéphaneLa méthode autocohérente [1] est un des outils permettant de faire le lien entre les mécanismes de déformation à l'échelle locale et le comportement macroscopique effectif. Si la méthode autocohérente a été initialement développée pour des comportements locaux linéaires, des extensions ont été proposées pour différentes classes de comportements non-linéaires : élastoplasticité [2] et viscoplasticité [3]. (...)An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method
http://hdl.handle.net/10985/9494
An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method
MAREAU, Charles; BERBENNI, Stéphane
The modeling of heterogeneous materials with an elasto-viscoplastic behavior is generally complex because of the differential nature of the local constitutive law. Indeed, the resolution of the heterogeneous problem involves space-time couplings which are generally difficult to estimate. In the present paper, a new homogenization model based on an affine linearization of the viscoplastic flow rule is proposed. First, the heterogeneous problem is written in the form of an integral equation. The purely thermoelastic and purely viscoplastic heterogeneous problems are solved independently using the self-consistent approximation. Using translated field techniques, the solutions of the above problems are combined to obtain the final self-consistent formulation. Then, some applications concerning two-phase fibre-reinforced composites and polycrystalline materials are presented. When compared to the reference solutions obtained from a FFT spectral method, a good description of the overall response of heterogeneous materials is obtained with the proposed model even when the viscoplastic flow rule is highly non-linear. Thanks to this approach, which is entirely formulated in the real-time space, the present model can be used for studying the response of heterogeneous materials submitted to complex thermomechanical loading paths with a good numerical efficiency.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/94942015-01-01T00:00:00ZMAREAU, CharlesBERBENNI, StéphaneThe modeling of heterogeneous materials with an elasto-viscoplastic behavior is generally complex because of the differential nature of the local constitutive law. Indeed, the resolution of the heterogeneous problem involves space-time couplings which are generally difficult to estimate. In the present paper, a new homogenization model based on an affine linearization of the viscoplastic flow rule is proposed. First, the heterogeneous problem is written in the form of an integral equation. The purely thermoelastic and purely viscoplastic heterogeneous problems are solved independently using the self-consistent approximation. Using translated field techniques, the solutions of the above problems are combined to obtain the final self-consistent formulation. Then, some applications concerning two-phase fibre-reinforced composites and polycrystalline materials are presented. When compared to the reference solutions obtained from a FFT spectral method, a good description of the overall response of heterogeneous materials is obtained with the proposed model even when the viscoplastic flow rule is highly non-linear. Thanks to this approach, which is entirely formulated in the real-time space, the present model can be used for studying the response of heterogeneous materials submitted to complex thermomechanical loading paths with a good numerical efficiency.Lattice strain measurements using synchrotron diffraction to calibrate a micromechanical modeling in a ferrite–cementite steel
http://hdl.handle.net/10985/7858
Lattice strain measurements using synchrotron diffraction to calibrate a micromechanical modeling in a ferrite–cementite steel
TAUPIN, Vincent; PESCI, Raphaël; BERBENNI, Stéphane; BERVEILLER, Sophie; OUAHAB, Razane; BOUAZIZ, Olivier
In situ tensile tests were performed at room temperature on a ferrite–cementite steel specifically designed for this study. The evolution of the average stress in ferrite during loading was analyzed by X-ray diffraction.Lattice strain measurements were performed with synchrotron ring diffraction in both ferrite and cementite.These in situ tests were complemented by macroscopic tensile and reversible tensile-compression tests to study the Bauschinger effect. In order to reproduce stresses in ferrite and cementite particles,a recently developed micromechanical Internal Length Mean Field (ILMF) model based on a generalized self-consistent scheme is applied. In this designed ferrite–cementite steel,the third ‘‘phase’’of the model represents finite intermediate‘‘layers’’in ferrite due to large geometrically necessary dislocation (GND) densities around cementite particles. The assumed constant thickness of the layers is calibrated thanks to the obtained experimental data.The ILMF model is validated by realistic estimates of the Bauschinger stress and the large difference between mean stresses in ferrite and in cementite phases.This difference cannot be reproduced by classic two-phase homogenization schemes without intermediate GND layers.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/78582013-01-01T00:00:00ZTAUPIN, VincentPESCI, RaphaëlBERBENNI, StéphaneBERVEILLER, SophieOUAHAB, RazaneBOUAZIZ, OlivierIn situ tensile tests were performed at room temperature on a ferrite–cementite steel specifically designed for this study. The evolution of the average stress in ferrite during loading was analyzed by X-ray diffraction.Lattice strain measurements were performed with synchrotron ring diffraction in both ferrite and cementite.These in situ tests were complemented by macroscopic tensile and reversible tensile-compression tests to study the Bauschinger effect. In order to reproduce stresses in ferrite and cementite particles,a recently developed micromechanical Internal Length Mean Field (ILMF) model based on a generalized self-consistent scheme is applied. In this designed ferrite–cementite steel,the third ‘‘phase’’of the model represents finite intermediate‘‘layers’’in ferrite due to large geometrically necessary dislocation (GND) densities around cementite particles. The assumed constant thickness of the layers is calibrated thanks to the obtained experimental data.The ILMF model is validated by realistic estimates of the Bauschinger stress and the large difference between mean stresses in ferrite and in cementite phases.This difference cannot be reproduced by classic two-phase homogenization schemes without intermediate GND layers.