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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 01 Feb 2023 00:40:32 GMT2023-02-01T00:40:32ZNumerical simulation of model problems in plasticity based on field dislocation mechanics
http://hdl.handle.net/10985/18365
Numerical simulation of model problems in plasticity based on field dislocation mechanics
MORIN, Léo; BRENNER, Rénald; SUQUET, Pierre M.
The aim of this paper is to investigate the numerical implementation of the field dislocation mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and Roy (2006 J. Mech. Phys. Solids 54 1687-710) is recalled which permits to express the set of equations under the form of a static problem, corresponding to the determination of the local stress field for a given dislocation density distribution, complemented by an evolution problem, corresponding to the transport of the dislocation density. The static problem is solved using FFT-based techniques (Brenner et al 2014 Phil. Mag. 94 1764-87). The main contribution of the present study is an efficient numerical scheme based on high resolution Godunov-type solvers to solve the evolution problem. Model problems of dislocation-mediated plasticity are finally considered in a simplified layer case. First, uncoupled problems with uniform velocity are considered, which permits to reproduce annihilation of dislocations and expansion of dislocation loops. Then, the FDM theory is applied to several problems of dislocation microstructures subjected to a mechanical loading.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/183652019-01-01T00:00:00ZMORIN, LéoBRENNER, RénaldSUQUET, Pierre M.The aim of this paper is to investigate the numerical implementation of the field dislocation mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and Roy (2006 J. Mech. Phys. Solids 54 1687-710) is recalled which permits to express the set of equations under the form of a static problem, corresponding to the determination of the local stress field for a given dislocation density distribution, complemented by an evolution problem, corresponding to the transport of the dislocation density. The static problem is solved using FFT-based techniques (Brenner et al 2014 Phil. Mag. 94 1764-87). The main contribution of the present study is an efficient numerical scheme based on high resolution Godunov-type solvers to solve the evolution problem. Model problems of dislocation-mediated plasticity are finally considered in a simplified layer case. First, uncoupled problems with uniform velocity are considered, which permits to reproduce annihilation of dislocations and expansion of dislocation loops. Then, the FDM theory is applied to several problems of dislocation microstructures subjected to a mechanical loading.Void coalescence in porous ductile solids containing two populations of cavities
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.Periodic smoothing splines for FFT-based solvers
http://hdl.handle.net/10985/19944
Periodic smoothing splines for FFT-based solvers
MORIN, Léo; BRENNER, Renald; DERRIEN, Katell; DORHMI, Khaoula
The aim of this paper is to develop a periodic smoother based on splines for FFT-based solvers. Spurious oscillations in FFT-based methods are shown to be due to pseudo-spectral differentiation of discontinuous fields. An automatic smoother based on polynomial splines is developed, which permits to add smoothness to initial material properties. The method, which is applied in various problems including conductivity, elasticity and field dislocation mechanics, improves significantly the local fields and reduces spurious oscillations.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/199442021-01-01T00:00:00ZMORIN, LéoBRENNER, RenaldDERRIEN, KatellDORHMI, KhaoulaThe aim of this paper is to develop a periodic smoother based on splines for FFT-based solvers. Spurious oscillations in FFT-based methods are shown to be due to pseudo-spectral differentiation of discontinuous fields. An automatic smoother based on polynomial splines is developed, which permits to add smoothness to initial material properties. The method, which is applied in various problems including conductivity, elasticity and field dislocation mechanics, improves significantly the local fields and reduces spurious oscillations.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, Djimédo
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, DjimédoThe 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 triaxialityDesigning isotropic composites reinforced by aligned transversely isotropic particles of spheroidal shape
http://hdl.handle.net/10985/14495
Designing isotropic composites reinforced by aligned transversely isotropic particles of spheroidal shape
DERRIEN, Katell; MORIN, Léo; GILORMINI, Pierre
The aim of this paper is to study the design of isotropic composites reinforced by aligned spheroidal particles made of a transversely isotropic material. The problem is investigated analytically using the framework of mean- eld homogenization. Conditions of macroscopic isotropy of particle-reinforced composites are derived for the dilute and Mori-Tanaka's schemes. This leads to a system of three nonlinear equations linking seven material constants and two geometrical constants. A design tool is finally proposed which permits to determine admissible particles achieving macroscopic isotropy for a given isotropic matrix behavior and a given particle aspect ratio. Correlations between transverse and longitudinal moduli of admissible particles are stud- ied for various particle shapes. Finally, the design of particles is investigated for aluminum and steel matrix composites.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/144952018-01-01T00:00:00ZDERRIEN, KatellMORIN, LéoGILORMINI, PierreThe aim of this paper is to study the design of isotropic composites reinforced by aligned spheroidal particles made of a transversely isotropic material. The problem is investigated analytically using the framework of mean- eld homogenization. Conditions of macroscopic isotropy of particle-reinforced composites are derived for the dilute and Mori-Tanaka's schemes. This leads to a system of three nonlinear equations linking seven material constants and two geometrical constants. A design tool is finally proposed which permits to determine admissible particles achieving macroscopic isotropy for a given isotropic matrix behavior and a given particle aspect ratio. Correlations between transverse and longitudinal moduli of admissible particles are stud- ied for various particle shapes. Finally, the design of particles is investigated for aluminum and steel matrix composites.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, Djimédo
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, DjimédoClassical 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.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.Analysis of shear ductile damage in forming processes using a micromechanical model with void shape effects
http://hdl.handle.net/10985/22205
Analysis of shear ductile damage in forming processes using a micromechanical model with void shape effects
TAJDARY, Pouya; MORIN, Léo; ROMERO-RESENDIZ, Liliana; GORJI, Maysam B.; BRAHAM, Chedly; GONZALEZ, Gonzalo
The aim of this work is to investigate and predict ductile failure in forming processes. Experimental results of deep drawing and corrugation processing on aluminum alloys suggest that in some cases failure can be due to shear-dominated loadings. In order to simulate numerically failure during forming, we use the micromechanical Madou–Leblond model, which permits to account for void shape effects that are important under shear loadings. In the case of deep drawing, the model is able to reproduce failure either due to bottom or shear cracks, depending on the processing conditions. In the case of corrugation processing, the model reproduces accurately the occurrence of failure as well as the crack shape. Comparisons with the GTN model show the importance of void shape effects upon failure.
Sat, 07 May 2022 00:00:00 GMThttp://hdl.handle.net/10985/222052022-05-07T00:00:00ZTAJDARY, PouyaMORIN, LéoROMERO-RESENDIZ, LilianaGORJI, Maysam B.BRAHAM, ChedlyGONZALEZ, GonzaloThe aim of this work is to investigate and predict ductile failure in forming processes. Experimental results of deep drawing and corrugation processing on aluminum alloys suggest that in some cases failure can be due to shear-dominated loadings. In order to simulate numerically failure during forming, we use the micromechanical Madou–Leblond model, which permits to account for void shape effects that are important under shear loadings. In the case of deep drawing, the model is able to reproduce failure either due to bottom or shear cracks, depending on the processing conditions. In the case of corrugation processing, the model reproduces accurately the occurrence of failure as well as the crack shape. Comparisons with the GTN model show the importance of void shape effects upon failure.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.