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http://hdl.handle.net/10985/13808
Void coalescence in porous ductile solids containing two populations of cavities
MORIN, Léo; MICHEL, Jean-Claude
A model of coalescence by internal necking of primary voids is developed which accounts for the presence of a second population of cavities. The derivation is based on a limit-analysis of a cylindrical cell containing a mesoscopic void and subjected to boundary conditions describing the kinematics of coalescence. The second population is accounted locally in the matrix surrounding the mesoscopic void through the microscopic potential of Michel and Suquet (1992) for spherical voids. The macroscopic criterion obtained is assessed through comparison of its predictions with the results of micromechanical finite element simulations on the same cell. A good agreement between model predictions and numerical results is found on the limit-load promoting coalescence.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/138082018-01-01T00:00:00ZMORIN, LéoMICHEL, Jean-ClaudeA model of coalescence by internal necking of primary voids is developed which accounts for the presence of a second population of cavities. The derivation is based on a limit-analysis of a cylindrical cell containing a mesoscopic void and subjected to boundary conditions describing the kinematics of coalescence. The second population is accounted locally in the matrix surrounding the mesoscopic void through the microscopic potential of Michel and Suquet (1992) for spherical voids. The macroscopic criterion obtained is assessed through comparison of its predictions with the results of micromechanical finite element simulations on the same cell. A good agreement between model predictions and numerical results is found on the limit-load promoting coalescence.A Gurson-type layer model for ductile porous solids with isotropic and kinematic hardening
http://hdl.handle.net/10985/12356
A Gurson-type layer model for ductile porous solids with isotropic and kinematic hardening
MORIN, Léo; MICHEL, Jean-Claude; LEBLOND, Jean-Baptiste
The aim of this work is to propose a Gurson-type model for ductile porous solids exhibiting isotropic and kinematic hardening. The derivation is based on a “sequential limit-analysis” of a hollow sphere made of a rigid-hardenable material. The heterogeneity of hardening is accounted for by discretizing the cell into a finite number of spherical layers in each of which the quantities characterizing hardening are considered as homogeneous. A simplified version of the model is also proposed, which permits to extend the previous works of Leblond et al. (1995) and Lacroix et al. (2016) for isotropic hardening to mixed isotropic/kinematic hardening. The model is finally assessed through comparison of its predictions with the results of some micromechanical finite element simulations of the same cell. First, the numerical and theoretical overall yield loci are compared for given distributions of isotropic and kinematic pre-hardening. Then the predictions of the model are investigated in evolution problems in which both isotropic and kinematic hardening parameters vary in time. A very good agreement between model predictions and numerical results is found in both cases.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/123562017-01-01T00:00:00ZMORIN, LéoMICHEL, Jean-ClaudeLEBLOND, Jean-BaptisteThe aim of this work is to propose a Gurson-type model for ductile porous solids exhibiting isotropic and kinematic hardening. The derivation is based on a “sequential limit-analysis” of a hollow sphere made of a rigid-hardenable material. The heterogeneity of hardening is accounted for by discretizing the cell into a finite number of spherical layers in each of which the quantities characterizing hardening are considered as homogeneous. A simplified version of the model is also proposed, which permits to extend the previous works of Leblond et al. (1995) and Lacroix et al. (2016) for isotropic hardening to mixed isotropic/kinematic hardening. The model is finally assessed through comparison of its predictions with the results of some micromechanical finite element simulations of the same cell. First, the numerical and theoretical overall yield loci are compared for given distributions of isotropic and kinematic pre-hardening. Then the predictions of the model are investigated in evolution problems in which both isotropic and kinematic hardening parameters vary in time. A very good agreement between model predictions and numerical results is found in both cases.A model of porous plastic single crystals based on fractal slip lines distribution
http://hdl.handle.net/10985/22240
A model of porous plastic single crystals based on fractal slip lines distribution
PAUX, Joseph; MORIN, Léo; BRENNER, Renald
The ductile failure of crystalline materials is strongly linked to the growth of intragranular voids. The estimation of the overall yield criterion thus requires to take into account the anisotropic plastic behavior of the single crystal. In the framework of the kinematic limit-analysis approach, this problem has been considered up to now with Gurson-type isotropic trial velocity fields. In the present work, a different class of piecewise constant velocity fields is proposed based on a detailed analysis of FFT numerical results on the strain localization in porous single crystals with periodic distributions of voids. This original approach is implemented for the model 2D problem of a square or hexagonal array of cylindrical voids in a hexagonal close-packed single crystal with in-plane prismatic slip systems. For equibiaxial loadings, the assumption of discontinuous velocity field provides a good approximation of the smooth jumps observed in the numerical results. Consistently, this new proposal leads to a significant improvement on the macroscopic yield stress with respect to the estimate based on an isotropic velocity field. Our theoretical estimate almost coincides with the FFT numerical results for all the unit-cells and crystalline orientations considered.
Sat, 01 Oct 2022 00:00:00 GMThttp://hdl.handle.net/10985/222402022-10-01T00:00:00ZPAUX, JosephMORIN, LéoBRENNER, RenaldThe ductile failure of crystalline materials is strongly linked to the growth of intragranular voids. The estimation of the overall yield criterion thus requires to take into account the anisotropic plastic behavior of the single crystal. In the framework of the kinematic limit-analysis approach, this problem has been considered up to now with Gurson-type isotropic trial velocity fields. In the present work, a different class of piecewise constant velocity fields is proposed based on a detailed analysis of FFT numerical results on the strain localization in porous single crystals with periodic distributions of voids. This original approach is implemented for the model 2D problem of a square or hexagonal array of cylindrical voids in a hexagonal close-packed single crystal with in-plane prismatic slip systems. For equibiaxial loadings, the assumption of discontinuous velocity field provides a good approximation of the smooth jumps observed in the numerical results. Consistently, this new proposal leads to a significant improvement on the macroscopic yield stress with respect to the estimate based on an isotropic velocity field. Our theoretical estimate almost coincides with the FFT numerical results for all the unit-cells and crystalline orientations considered.A model of porous plastic single crystals based on fractal slip lines distribution
http://hdl.handle.net/10985/22720
A model of porous plastic single crystals based on fractal slip lines distribution
PAUX, Joseph; MORIN, Léo; BRENNER, Renald
The ductile failure of crystalline materials is strongly linked to the growth of intragranular voids. The estimation of the overall yield criterion thus requires to take into account the anisotropic plastic behavior of the single crystal. In the framework of the kinematic limit-analysis approach, this problem has been considered up to now with Gurson-type isotropic trial velocity fields. In
the present work, a different class of piecewise constant velocity fields is proposed based on a detailed analysis of FFT numerical results on the strain localization in porous single crystals with periodic distributions of voids. This original approach is implemented for the model 2D problem of a square or hexagonal array of cylindrical voids in a hexagonal close-packed single crystal with in-plane prismatic slip systems. For equibiaxial loadings, the assumption of discontinuous velocity field provides a good approximation of the smooth jumps observed in the numerical results. Consistently, this new proposal leads to a significant improvement on the macroscopic yield stress with respect to the estimate based on an isotropic velocity field. Our theoretical
estimate almost coincides with the FFT numerical results for all the unit-cells and crystalline orientations considered.
Sat, 01 Oct 2022 00:00:00 GMThttp://hdl.handle.net/10985/227202022-10-01T00:00:00ZPAUX, JosephMORIN, LéoBRENNER, RenaldThe ductile failure of crystalline materials is strongly linked to the growth of intragranular voids. The estimation of the overall yield criterion thus requires to take into account the anisotropic plastic behavior of the single crystal. In the framework of the kinematic limit-analysis approach, this problem has been considered up to now with Gurson-type isotropic trial velocity fields. In
the present work, a different class of piecewise constant velocity fields is proposed based on a detailed analysis of FFT numerical results on the strain localization in porous single crystals with periodic distributions of voids. This original approach is implemented for the model 2D problem of a square or hexagonal array of cylindrical voids in a hexagonal close-packed single crystal with in-plane prismatic slip systems. For equibiaxial loadings, the assumption of discontinuous velocity field provides a good approximation of the smooth jumps observed in the numerical results. Consistently, this new proposal leads to a significant improvement on the macroscopic yield stress with respect to the estimate based on an isotropic velocity field. Our theoretical
estimate almost coincides with the FFT numerical results for all the unit-cells and crystalline orientations considered.Fast numerical estimation of residual stresses induced by laser shock peening
http://hdl.handle.net/10985/23050
Fast numerical estimation of residual stresses induced by laser shock peening
DERRIEN, Katell; BERTHE, Laurent; LAPOSTOLLE, Lucas; CASTELNAU, Olivier; MORIN, Léo
The aim of this paper is to develop a model allowing a fast first approximate estimation of the elastic–plastic stress wave propagation caused by a laser impact and the resulting residual stress field. We start by modeling the stress wave propagation, adopting a 1D uniaxial modeling, reducing the behavior of the specimen to the axis of the laser impact, excluding any edge effects caused by the edges of the laser spot. The plastic strain field resulting from this propagation can in turn be used to compute the residual stresses, by making use of an analytic modeling in the case of an infinite planar plate. The accuracy of the 1D model is assessed by comparing it to finite elements simulations, acting as a reference solution, for several materials and laser spot diameters. The results show that the stress wave propagation from the 1D model is close to identical to the reference solution. The residual plastic and stress fields from the finite elements model present a uniaxial distribution on a large portion of the laser spot, except for the very edge and spot center. The comparison between the 1D model and the reference solution shows a good match, indicating that the 1D model can be used for a fast approximation the mechanical fields created by a laser impact for laser spot diameters larger than 2 mm.
Tue, 01 Nov 2022 00:00:00 GMThttp://hdl.handle.net/10985/230502022-11-01T00:00:00ZDERRIEN, KatellBERTHE, LaurentLAPOSTOLLE, LucasCASTELNAU, OlivierMORIN, LéoThe aim of this paper is to develop a model allowing a fast first approximate estimation of the elastic–plastic stress wave propagation caused by a laser impact and the resulting residual stress field. We start by modeling the stress wave propagation, adopting a 1D uniaxial modeling, reducing the behavior of the specimen to the axis of the laser impact, excluding any edge effects caused by the edges of the laser spot. The plastic strain field resulting from this propagation can in turn be used to compute the residual stresses, by making use of an analytic modeling in the case of an infinite planar plate. The accuracy of the 1D model is assessed by comparing it to finite elements simulations, acting as a reference solution, for several materials and laser spot diameters. The results show that the stress wave propagation from the 1D model is close to identical to the reference solution. The residual plastic and stress fields from the finite elements model present a uniaxial distribution on a large portion of the laser spot, except for the very edge and spot center. The comparison between the 1D model and the reference solution shows a good match, indicating that the 1D model can be used for a fast approximation the mechanical fields created by a laser impact for laser spot diameters larger than 2 mm.Analysis of a model of field crack mechanics for brittle materials
http://hdl.handle.net/10985/20782
Analysis of a model of field crack mechanics for brittle materials
MORIN, Léo; ACHARYA, Amit
A computational model for arbitrary brittle crack propagation, in a fault-like layer within a 3-d elastic domain, and its associated quasi-static and dynamic fields is developed and analyzed. It uses a FFT-based solver for the balance of linear momentum and a Godunov-type projection-evolution method for the crack evolution equation. As applications, we explore the questions of equilibria and irreversibility for crack propagation with and without surface energy, existence of strength and toughness criteria, crack propagation under quasi-static and dynamic conditions, including Modes I, II and III, as well as multiaxial compressive loadings.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/207822021-01-01T00:00:00ZMORIN, LéoACHARYA, AmitA computational model for arbitrary brittle crack propagation, in a fault-like layer within a 3-d elastic domain, and its associated quasi-static and dynamic fields is developed and analyzed. It uses a FFT-based solver for the balance of linear momentum and a Godunov-type projection-evolution method for the crack evolution equation. As applications, we explore the questions of equilibria and irreversibility for crack propagation with and without surface energy, existence of strength and toughness criteria, crack propagation under quasi-static and dynamic conditions, including Modes I, II and III, as well as multiaxial compressive loadings.Characterization and modeling of the damage mechanisms in ductile steel metal-matrix composites: Application to virtual forming
http://hdl.handle.net/10985/24585
Characterization and modeling of the damage mechanisms in ductile steel metal-matrix composites: Application to virtual forming
TAJDARY, Pouya; DORHMI, Khaoula; MORIN, Léo; DERRIEN, Katell; HADJEM-HAMOUCHE, Zehoua; BRAHAM, Chedly; CHEVALIER, Jean-Pierre; CHEVALIER, Jean-Pierre
The aim of this work is to investigate the damage mechanisms and stiffness loss in Fe-TiB metal-matrix composites during plastic deformation. First, experimental results of interrupted tensile tests are performed to quantify the evolution of damage, using SEM observations, as well as the decrease of Young’s modulus as a function of the tensile strain. The experimental results are then used to calibrate a two-step homogenization model for metal-matrix composites in which the nucleation and growth of voids modify incrementally the overall elastic properties. The model is finally applied to the numerical prediction of stiffness loss in a problem of metal forming based on Nakazima tests. Overall, the stiffness loss predicted before the onset of coalescence is moderate and its distribution is homogeneous, emphasizing that Fe-TiB metal-matrix composites could be used in applications requiring metal forming.
Fri, 01 Sep 2023 00:00:00 GMThttp://hdl.handle.net/10985/245852023-09-01T00:00:00ZTAJDARY, PouyaDORHMI, KhaoulaMORIN, LéoDERRIEN, KatellHADJEM-HAMOUCHE, ZehouaBRAHAM, ChedlyCHEVALIER, Jean-PierreCHEVALIER, Jean-PierreThe aim of this work is to investigate the damage mechanisms and stiffness loss in Fe-TiB metal-matrix composites during plastic deformation. First, experimental results of interrupted tensile tests are performed to quantify the evolution of damage, using SEM observations, as well as the decrease of Young’s modulus as a function of the tensile strain. The experimental results are then used to calibrate a two-step homogenization model for metal-matrix composites in which the nucleation and growth of voids modify incrementally the overall elastic properties. The model is finally applied to the numerical prediction of stiffness loss in a problem of metal forming based on Nakazima tests. Overall, the stiffness loss predicted before the onset of coalescence is moderate and its distribution is homogeneous, emphasizing that Fe-TiB metal-matrix composites could be used in applications requiring metal forming.On the thermodynamics consistency of Gurson’s model and its computational implications
http://hdl.handle.net/10985/24621
On the thermodynamics consistency of Gurson’s model and its computational implications
BOUBY, Celine; MORIN, Léo; BIGNONNET, François; DORMIEUX, Luc; KONDO, Djimedo
The aim of this paper is to investigate the thermodynamics consistency of Gurson’s model and notably its relation to the class of standard generalized materials. First, we briefly recall Gurson’s model in its original format and reanalyzed it in the thermodynamic framework of poroplasticity of saturated media. This allows to properly define the coupling between elasticity and plasticity and to demonstrate that Gurson’s model fits into the framework of generalized standard materials model, provided that the internal variables being the plastic strain and the Lagrangian plastic porosity (and not the Eulerian porosity as in the original Gurson model). In particular, by construction, the porosity evolution law is proved to be a full part of the thermodynamic formulation of the model with a generalized normality rule. The implications in terms of numerical implementation of Gurson’s model are then investigated; a new numerical scheme based on the time-implicit discretization of the Lagrangian porosity is notably proposed and discussed with respect to available algorithms.
Sun, 01 Jan 2023 00:00:00 GMThttp://hdl.handle.net/10985/246212023-01-01T00:00:00ZBOUBY, CelineMORIN, LéoBIGNONNET, FrançoisDORMIEUX, LucKONDO, DjimedoThe aim of this paper is to investigate the thermodynamics consistency of Gurson’s model and notably its relation to the class of standard generalized materials. First, we briefly recall Gurson’s model in its original format and reanalyzed it in the thermodynamic framework of poroplasticity of saturated media. This allows to properly define the coupling between elasticity and plasticity and to demonstrate that Gurson’s model fits into the framework of generalized standard materials model, provided that the internal variables being the plastic strain and the Lagrangian plastic porosity (and not the Eulerian porosity as in the original Gurson model). In particular, by construction, the porosity evolution law is proved to be a full part of the thermodynamic formulation of the model with a generalized normality rule. The implications in terms of numerical implementation of Gurson’s model are then investigated; a new numerical scheme based on the time-implicit discretization of the Lagrangian porosity is notably proposed and discussed with respect to available algorithms.Classical and sequential limit analysis revisited
http://hdl.handle.net/10985/14080
Classical and sequential limit analysis revisited
LEBLOND, Jean-Baptiste; REMMAL, Almahdi; MORIN, Léo; KONDO, Djimedo
Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic–plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity – in the absence of hardening and within a linearized geometrical framework –, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity – although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic–plastic coupling in the specific case considered.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/140802018-01-01T00:00:00ZLEBLOND, Jean-BaptisteREMMAL, AlmahdiMORIN, LéoKONDO, DjimedoClassical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic–plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity – in the absence of hardening and within a linearized geometrical framework –, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity – although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic–plastic coupling in the specific case considered.Prediction of shear-dominated ductile fracture in a butterfly specimen using a model of plastic porous solids including void shape effects
http://hdl.handle.net/10985/12357
Prediction of shear-dominated ductile fracture in a butterfly specimen using a model of plastic porous solids including void shape effects
MORIN, Léo; LEBLOND, Jean-Baptiste; MOHR, Dirk; KONDO, Djimedo
The aim of this paper is to investigate ductile failure under shear-dominated loadings using a model of plastic porous solids incorporating void shape effects. We use the model proposed by (Madou and Leblond, 2012a,b; Madou et al., 2013; Madou and Leblond, 2013) to study the fracture of butterfly specimens subjected to combined tension and shear. This model is able to reproduce, for various loading conditions, the macroscopic softening behavior and the location of cracks observed in experiments performed by Dunand and Mohr (2011a,b). Void shape effects appear to have a very significant influence on ductile damage at low stress triaxiality
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/123572017-01-01T00:00:00ZMORIN, LéoLEBLOND, Jean-BaptisteMOHR, DirkKONDO, DjimedoThe aim of this paper is to investigate ductile failure under shear-dominated loadings using a model of plastic porous solids incorporating void shape effects. We use the model proposed by (Madou and Leblond, 2012a,b; Madou et al., 2013; Madou and Leblond, 2013) to study the fracture of butterfly specimens subjected to combined tension and shear. This model is able to reproduce, for various loading conditions, the macroscopic softening behavior and the location of cracks observed in experiments performed by Dunand and Mohr (2011a,b). Void shape effects appear to have a very significant influence on ductile damage at low stress triaxiality