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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 16 Jul 2024 07:08:39 GMT2024-07-16T07:08:39ZA comparison between different numerical methods for the modeling of polycrystalline materials with an elastic-viscoplastic behavior
http://hdl.handle.net/10985/9493
A comparison between different numerical methods for the modeling of polycrystalline materials with an elastic-viscoplastic behavior
ROBERT, Camille; MAREAU, Charles
The macroscopic behavior of polycrystalline materials is largely influenced by the shape, the arrangement and the orientation of crystallites. Different methods have thus been developed to determine the effective behavior of such materials as a function of their microstructural features. In this work, which focuses on polycrystalline materials with an elastic-viscoplastic behavior, the self-consistent, finite element and spectral methods are compared. These common methods are used to determine the effective behavior of \textit{different 316L polycrystalline aggregates} subjected to various loading conditions. Though no major difference is observed at the macroscopic scale, the hardening rate is found to be slightly overestimated with the finite element method. Indeed, spatial convergence cannot be guaranteed for finite element calculations, even when fine mesh resolutions, for which the computational cost is important, are used. Also, as the self-consistent method does not explicitly account for neighborhood effects, important discrepancies between the self-consistent method and the other methods exist regarding the mechanical response of a specific grain. The self-consistent method nevertheless provides a reasonable description of the average response obtained for a group of grains with identical features (e.g. shape, orientation).
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/94932015-01-01T00:00:00ZROBERT, CamilleMAREAU, CharlesThe macroscopic behavior of polycrystalline materials is largely influenced by the shape, the arrangement and the orientation of crystallites. Different methods have thus been developed to determine the effective behavior of such materials as a function of their microstructural features. In this work, which focuses on polycrystalline materials with an elastic-viscoplastic behavior, the self-consistent, finite element and spectral methods are compared. These common methods are used to determine the effective behavior of \textit{different 316L polycrystalline aggregates} subjected to various loading conditions. Though no major difference is observed at the macroscopic scale, the hardening rate is found to be slightly overestimated with the finite element method. Indeed, spatial convergence cannot be guaranteed for finite element calculations, even when fine mesh resolutions, for which the computational cost is important, are used. Also, as the self-consistent method does not explicitly account for neighborhood effects, important discrepancies between the self-consistent method and the other methods exist regarding the mechanical response of a specific grain. The self-consistent method nevertheless provides a reasonable description of the average response obtained for a group of grains with identical features (e.g. shape, orientation).Étude micromécanique de l’influence de défauts sur la tenue en fatigue à grand nombre de cycles
http://hdl.handle.net/10985/7418
Étude micromécanique de l’influence de défauts sur la tenue en fatigue à grand nombre de cycles
GUERCHAIS, Raphaël; ROBERT, Camille; MOREL, Franck; SAINTIER, Nicolas
The aim of this study is to analyse the influence of micro-notches on the fatigue behaviour of an electrolytic copper using finite element simulations of polycrystalline aggregates. In these simulations, in which the grains are explicitly modelled, the anisotropic behavior of each FCC crystal is described by the generalized Hooke’s law with a cubic elasticity tensor and by a single crystal visco-plastic model. The numerical analysis is done using several smooth and notched microstructures. The cyclic mechanical responses of the grains are then studied for different defect sizes and the ability of three fatigue criteria to predict the defect size effect on the fatigue strength is evaluated thanks to the comparison with experimental data.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/74182013-01-01T00:00:00ZGUERCHAIS, RaphaëlROBERT, CamilleMOREL, FranckSAINTIER, NicolasThe aim of this study is to analyse the influence of micro-notches on the fatigue behaviour of an electrolytic copper using finite element simulations of polycrystalline aggregates. In these simulations, in which the grains are explicitly modelled, the anisotropic behavior of each FCC crystal is described by the generalized Hooke’s law with a cubic elasticity tensor and by a single crystal visco-plastic model. The numerical analysis is done using several smooth and notched microstructures. The cyclic mechanical responses of the grains are then studied for different defect sizes and the ability of three fatigue criteria to predict the defect size effect on the fatigue strength is evaluated thanks to the comparison with experimental data.Micro-mechanical modelling of high cycle fatigue behaviour of metals under multiaxial loads
http://hdl.handle.net/10985/10518
Micro-mechanical modelling of high cycle fatigue behaviour of metals under multiaxial loads
ROBERT, Camille; SAINTIER, Nicolas; PALIN-LUC, Thierry; MOREL, Franck
An analysis of high cycle multiaxial fatigue behaviour is conducted through the numerical simulation of polycrystalline aggregates using the finite element method. The metallic material chosen for investigation is pure copper, which has a Face Centred Cubic (FCC) crystalline microstructure. The elementary volumes are modelled in 2D using an hypothesis of generalised plane strain and consist of 300 equi-probability, randomly oriented grains with equiaxed geometry. The aggregates are loaded at levels equivalent to the average macroscopic fatigue strength at 1E7 cycles. The goal is to compute the mechanical quantities at the mesoscopic scale (i.e., average within the grain) after stabilization of the local cyclic behaviour. The results show that the mesoscopic mechanical variables are characterised by high dispersion. A statistical analysis of the response of the aggregates is undertaken for different loading modes: fully reversed tensile loads, torsion and combined in-phase tension–torsion. Via the calculation of the local mechanical quantities for a sufficiently large number of different microstructures, a critical analysis of certain multiaxial endurance criteria (Crossland, Dang Van and Matake) is conducted. In terms of material behaviour models, it is shown that elastic anisotropy strongly affects the scatter of the mechanical parameters used in the different criteria and that its role is predominant compared to that of crystal plasticity. The analysis of multiaxial endurance criteria at both the macroscopic and mesoscopic scales clearly show that the critical plane type criteria (Dang Van and Matake) give an adequate estimation of the shear stress but badly reflect the scatter of the normal stress or the hydrostatic stress.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/105182012-01-01T00:00:00ZROBERT, CamilleSAINTIER, NicolasPALIN-LUC, ThierryMOREL, FranckAn analysis of high cycle multiaxial fatigue behaviour is conducted through the numerical simulation of polycrystalline aggregates using the finite element method. The metallic material chosen for investigation is pure copper, which has a Face Centred Cubic (FCC) crystalline microstructure. The elementary volumes are modelled in 2D using an hypothesis of generalised plane strain and consist of 300 equi-probability, randomly oriented grains with equiaxed geometry. The aggregates are loaded at levels equivalent to the average macroscopic fatigue strength at 1E7 cycles. The goal is to compute the mechanical quantities at the mesoscopic scale (i.e., average within the grain) after stabilization of the local cyclic behaviour. The results show that the mesoscopic mechanical variables are characterised by high dispersion. A statistical analysis of the response of the aggregates is undertaken for different loading modes: fully reversed tensile loads, torsion and combined in-phase tension–torsion. Via the calculation of the local mechanical quantities for a sufficiently large number of different microstructures, a critical analysis of certain multiaxial endurance criteria (Crossland, Dang Van and Matake) is conducted. In terms of material behaviour models, it is shown that elastic anisotropy strongly affects the scatter of the mechanical parameters used in the different criteria and that its role is predominant compared to that of crystal plasticity. The analysis of multiaxial endurance criteria at both the macroscopic and mesoscopic scales clearly show that the critical plane type criteria (Dang Van and Matake) give an adequate estimation of the shear stress but badly reflect the scatter of the normal stress or the hydrostatic stress.Influence of the microstructure and voids on the high-cycle fatigue strength of 316L stainless steel under multiaxial loading
http://hdl.handle.net/10985/10738
Influence of the microstructure and voids on the high-cycle fatigue strength of 316L stainless steel under multiaxial loading
GUERCHAIS, Raphaël; ROBERT, Camille; MOREL, Franck; SAINTIER, Nicolas
In the present study, the effects of both the microstructure and voids on the high-cycle fatigue behaviour of the 316L austenitic stainless steel are investigated by using finite element simulations of polycrystalline aggregates. The numerical analysis relies on a metallurgical and mechanical characterization. In particular, fatigue tests are carried out to estimate the fatigue limits at 2.106 cycles under uniaxial and multiaxial loading conditions (combined tension and torsion and biaxial tension) using both smooth specimens and specimens containing an artificial hemispherical defect. The simulations are carried out with several configurations of crystalline orientations in order to take into account the variability of the microstructure in the predictions of the macroscopic fatigue limits. These predictions are obtained, thanks to a probabilistic fatigue criterion using the finite element results. The capability of this criterion to predict the influence of voids on the average and the scatter of macroscopic fatigue limits is evaluated.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/107382015-01-01T00:00:00ZGUERCHAIS, RaphaëlROBERT, CamilleMOREL, FranckSAINTIER, NicolasIn the present study, the effects of both the microstructure and voids on the high-cycle fatigue behaviour of the 316L austenitic stainless steel are investigated by using finite element simulations of polycrystalline aggregates. The numerical analysis relies on a metallurgical and mechanical characterization. In particular, fatigue tests are carried out to estimate the fatigue limits at 2.106 cycles under uniaxial and multiaxial loading conditions (combined tension and torsion and biaxial tension) using both smooth specimens and specimens containing an artificial hemispherical defect. The simulations are carried out with several configurations of crystalline orientations in order to take into account the variability of the microstructure in the predictions of the macroscopic fatigue limits. These predictions are obtained, thanks to a probabilistic fatigue criterion using the finite element results. The capability of this criterion to predict the influence of voids on the average and the scatter of macroscopic fatigue limits is evaluated.Simulation of Metal Forming Processes with a 3D Adaptive Remeshing Procedure
http://hdl.handle.net/10985/10775
Simulation of Metal Forming Processes with a 3D Adaptive Remeshing Procedure
ZERAMDINI, Bessam; ROBERT, Camille; POTTIER, Thomas; GERMAIN, Guénaël
In this paper, a fully adaptive 3D numerical methodology based on a tetrahedral element was proposed in order to rove the finite element simulation of any metal forming process. This automatic methodology was implemented in a computational platform which integrates a finite element solver, 3D mesh generation and a field transfer algorithm. The proposed remeshing method was developed in order to solve problems associated with the severe distortion of elements subject to large deformations, to concentrate the elements where the error is large and to coarsen the mesh where the error is small. This leads to a significant reduction in the computation times while maintaining simulation accuracy . In addition, in order to enhance the contact conditions, this method has been coupled with a specific operator to maintain the initial contact between the workpiece nodes and the rigid tool after each remeshing step. In this paper special attention is paid to the data transfer methods and the necessary adaptive remeshing steps are given. Finally, a numerical example is detailed to demonstrate the efficiency of the approach and to compare the results for the different field transfer strategies
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/107752016-01-01T00:00:00ZZERAMDINI, BessamROBERT, CamillePOTTIER, ThomasGERMAIN, GuénaëlIn this paper, a fully adaptive 3D numerical methodology based on a tetrahedral element was proposed in order to rove the finite element simulation of any metal forming process. This automatic methodology was implemented in a computational platform which integrates a finite element solver, 3D mesh generation and a field transfer algorithm. The proposed remeshing method was developed in order to solve problems associated with the severe distortion of elements subject to large deformations, to concentrate the elements where the error is large and to coarsen the mesh where the error is small. This leads to a significant reduction in the computation times while maintaining simulation accuracy . In addition, in order to enhance the contact conditions, this method has been coupled with a specific operator to maintain the initial contact between the workpiece nodes and the rigid tool after each remeshing step. In this paper special attention is paid to the data transfer methods and the necessary adaptive remeshing steps are given. Finally, a numerical example is detailed to demonstrate the efficiency of the approach and to compare the results for the different field transfer strategiesProper Generalized Decomposition (PGD) for numerical calculation of polycrystalline aggregates under cyclic loading
http://hdl.handle.net/10985/10760
Proper Generalized Decomposition (PGD) for numerical calculation of polycrystalline aggregates under cyclic loading
NASRI, Mohamed Aziz; ROBERT, Camille; MOREL, Franck; EL AREM, Saber; AMMAR, Amine
none
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/107602015-01-01T00:00:00ZNASRI, Mohamed AzizROBERT, CamilleMOREL, FranckEL AREM, SaberAMMAR, AminenoneDifferent composite voxel methods for the numerical homogenization of heterogeneous inelastic materials with FFT-based techniques
http://hdl.handle.net/10985/11476
Different composite voxel methods for the numerical homogenization of heterogeneous inelastic materials with FFT-based techniques
MAREAU, Charles; ROBERT, Camille
FFT-based homogenization methods aim at calculating the effective behavior of heterogeneous materials with periodic microstructures. These methods operate on a regular grid of voxels, and hence require an appropriate spatial discretization of periodic microstructures. However, when different microstructural length scales are involved, it is not always possible to have sufficient spatial resolutions to explicitly consider the influence of fine microstructural features (e.g. voids, second-phase particles). To circumvent this difficulty, one solution consists of using composite voxel methods to define the effective properties and the effective internal variables of heterogeneous voxels. In this work, different composite voxel methods are proposed to deal with inelastic materials with mul- tiple length scales. These methods use simple homogenization rules to calculate the effective behavior of heterogeneous voxels. The first part of this paper is dedicated to the description of the composite voxel methods, which are based either on the Voigt, laminate structure or Mori–Tanaka approximations. In the second part, these methods are used to model the elasto-plastic behavior of a pearlitic steel poly- crystalline aggregate. According to the results, the Voigt approximation, which ignores morphological fea- tures, is not appropriate for treating heterogeneous voxels. When morphological information is accounted for, with either the laminate structure or Mori–Tanaka approximations, a better agreement with experi- mental observations is obtained. Though none of these methods is universal, they offer some possibilities to investigate the mechanical behavior of heterogeneous materials involving multiple length scales.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/114762017-01-01T00:00:00ZMAREAU, CharlesROBERT, CamilleFFT-based homogenization methods aim at calculating the effective behavior of heterogeneous materials with periodic microstructures. These methods operate on a regular grid of voxels, and hence require an appropriate spatial discretization of periodic microstructures. However, when different microstructural length scales are involved, it is not always possible to have sufficient spatial resolutions to explicitly consider the influence of fine microstructural features (e.g. voids, second-phase particles). To circumvent this difficulty, one solution consists of using composite voxel methods to define the effective properties and the effective internal variables of heterogeneous voxels. In this work, different composite voxel methods are proposed to deal with inelastic materials with mul- tiple length scales. These methods use simple homogenization rules to calculate the effective behavior of heterogeneous voxels. The first part of this paper is dedicated to the description of the composite voxel methods, which are based either on the Voigt, laminate structure or Mori–Tanaka approximations. In the second part, these methods are used to model the elasto-plastic behavior of a pearlitic steel poly- crystalline aggregate. According to the results, the Voigt approximation, which ignores morphological fea- tures, is not appropriate for treating heterogeneous voxels. When morphological information is accounted for, with either the laminate structure or Mori–Tanaka approximations, a better agreement with experi- mental observations is obtained. Though none of these methods is universal, they offer some possibilities to investigate the mechanical behavior of heterogeneous materials involving multiple length scales.Effet de surface libre dans les agrégats polycristallins en fatigue à grand nombre de cycles.
http://hdl.handle.net/10985/7383
Effet de surface libre dans les agrégats polycristallins en fatigue à grand nombre de cycles.
ROBERT, Camille; HOR, Anis; PALIN-LUC, Thierry; MOREL, Franck; SAINTIER, Nicolas
An analysis of high cycle fatigue behavior is done via the numerical simulation of polycrystalline aggregates. Different metallic materials with a FCC crystalline structure, but different cubic elastic coefficients, are investigated. Several statistical elementary volumes (SEV), consisting of 300 grains with isotropic texture and equiaxed geometries, are loaded at the median macroscopic fatigue limit for 107 cycles. Three different models are studied: 2D generalized plane strain, 3D periodic and 3D periodic with a free surface. Different mesoscopic variables are analyzed using extreme value statistics. The results show a detrimental e ect on the fatigue strength of the modeled aggregates with a free surface, if the crystalline elastic anisotropy is sufficient.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/73832013-01-01T00:00:00ZROBERT, CamilleHOR, AnisPALIN-LUC, ThierryMOREL, FranckSAINTIER, NicolasAn analysis of high cycle fatigue behavior is done via the numerical simulation of polycrystalline aggregates. Different metallic materials with a FCC crystalline structure, but different cubic elastic coefficients, are investigated. Several statistical elementary volumes (SEV), consisting of 300 grains with isotropic texture and equiaxed geometries, are loaded at the median macroscopic fatigue limit for 107 cycles. Three different models are studied: 2D generalized plane strain, 3D periodic and 3D periodic with a free surface. Different mesoscopic variables are analyzed using extreme value statistics. The results show a detrimental e ect on the fatigue strength of the modeled aggregates with a free surface, if the crystalline elastic anisotropy is sufficient.Simplified numerical approach for incremental sheet metal forming process
http://hdl.handle.net/10985/8600
Simplified numerical approach for incremental sheet metal forming process
BEN AYED, Lanouar; ROBERT, Camille; DELAMEZIERE, Arnaud; NOUARI, Mohammed; BATOZ, Jean-Louis
The current work presents a finite element approach for numerical simulation of the incremental sheet metal forming (ISF) process, called here ‘‘ISF-SAM’’ (for ISF-Simplified Analysis Modelling). The main goal of the study is to develop a simplified FE model sufficiently accurate to simulate the ISF process and quite efficient in terms of CPU time. Some assumptions have been adopted regarding the constitutive strains/stresses equations and the tool/sheet contact conditions. A simplified contact procedure was proposed to predict nodes in contact with the tool and to estimate their imposed displacements. A Discrete Kirchhoff Triangle shell element called DKT12, taking into account membrane and bending effects, has been used to mesh the sheet. An elasto-plastic constitutive model with isotropic hardening behaviour and a static scheme have been adopted to solve the nonlinear equilibrium equations. Satisfactory results have been obtained on two applications and a good correlation has been shown compared to experimental and numerical results, and at the same time a reduction of CPU time more than 60% has been observed. The bending phenomenon studied through the second application and the obtained results show the reliability of the DKT12 element.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/86002014-01-01T00:00:00ZBEN AYED, LanouarROBERT, CamilleDELAMEZIERE, ArnaudNOUARI, MohammedBATOZ, Jean-LouisThe current work presents a finite element approach for numerical simulation of the incremental sheet metal forming (ISF) process, called here ‘‘ISF-SAM’’ (for ISF-Simplified Analysis Modelling). The main goal of the study is to develop a simplified FE model sufficiently accurate to simulate the ISF process and quite efficient in terms of CPU time. Some assumptions have been adopted regarding the constitutive strains/stresses equations and the tool/sheet contact conditions. A simplified contact procedure was proposed to predict nodes in contact with the tool and to estimate their imposed displacements. A Discrete Kirchhoff Triangle shell element called DKT12, taking into account membrane and bending effects, has been used to mesh the sheet. An elasto-plastic constitutive model with isotropic hardening behaviour and a static scheme have been adopted to solve the nonlinear equilibrium equations. Satisfactory results have been obtained on two applications and a good correlation has been shown compared to experimental and numerical results, and at the same time a reduction of CPU time more than 60% has been observed. The bending phenomenon studied through the second application and the obtained results show the reliability of the DKT12 element.Étude numérique du comportement en fatigue à grand nombre de cycles d’agrégats polycristallins de cuivre
http://hdl.handle.net/10985/8269
Étude numérique du comportement en fatigue à grand nombre de cycles d’agrégats polycristallins de cuivre
ROBERT, Camille; SAINTIER, Nicolas; PALIN-LUC, Thierry; MOREL, Franck
Numerical study of high cycle fatigue behaviour of copper polycrystalline aggre- gates. An analysis of high cycle fatigue behaviour is undertaken via the numerical simulation of polycrystalline aggregates. The metallic material chosen for investigation is Copper, which has a FCC crystalline structure. The REV, which is composed of 300 randomly orientated equiaxed grains, is loaded at the fatigue limit determined at 10/7 cycles. The aim is to calculate the mechanical quantities at the mesoscopic scale (average quantities in the grains) after cyclic stabilisation has been achieved. The results highlight the fact that the mechanical quantities at this scale have a large scatter. A statistical analysis of the response of the aggregate for different loading conditions (tensile, torsion, and in-phase tension-torsion) is done. Thanks to the sufficiently large number of different microstructures investigated, a critical analysis of the Dang Van and Crossland multiaxial fatigue criteria has been undertaken, using the local mechanical quantities.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/82692011-01-01T00:00:00ZROBERT, CamilleSAINTIER, NicolasPALIN-LUC, ThierryMOREL, FranckNumerical study of high cycle fatigue behaviour of copper polycrystalline aggre- gates. An analysis of high cycle fatigue behaviour is undertaken via the numerical simulation of polycrystalline aggregates. The metallic material chosen for investigation is Copper, which has a FCC crystalline structure. The REV, which is composed of 300 randomly orientated equiaxed grains, is loaded at the fatigue limit determined at 10/7 cycles. The aim is to calculate the mechanical quantities at the mesoscopic scale (average quantities in the grains) after cyclic stabilisation has been achieved. The results highlight the fact that the mechanical quantities at this scale have a large scatter. A statistical analysis of the response of the aggregate for different loading conditions (tensile, torsion, and in-phase tension-torsion) is done. Thanks to the sufficiently large number of different microstructures investigated, a critical analysis of the Dang Van and Crossland multiaxial fatigue criteria has been undertaken, using the local mechanical quantities.