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http://hdl.handle.net/10985/23583
Coupled effects of crystallographic orientation and void shape on ductile failure initiation using a CPFE framework
ZHU, Jianchang; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid ; HUANG, M.S.; LI, Z.H.
Ductile failure reveals to be an anisotropic phenomenon, for which the proper mechanism has not been clearly addressed yet in the literature. In this paper, the effects of some key anisotropy factors on ductile failure initiation, detected by void coalescence and plastic strain localization, are investigated using unit-cell computations based on crystal plasticity finite element method.
The studied anisotropic effects are induced by the combination of initial crystallographic orientations and void shapes. Therefore, single crystals with three different initial orientations and polycrystalline aggregates with three different initial crystallographic textures are respectively considered. A single void with either spherical, prolate or oblate shape is assumed to be preexisting at the center of each unit cell. By contrast to previous analyses in the literature, plastic strain localization is predicted in the present study on the basis of bifurcation theory. To cover a wide range of stress states, the simulations are performed under two macroscopic loading configurations: proportional triaxial stressing, characterized by constant stress triaxiality and Lode parameter, and proportional in-plane straining, specified by constant strain-path ratio. The obtained results show that the combined anisotropic effects play an important role in the occurrence of void coalescence and plastic strain localization, as well as in the competition between them.
Wed, 01 Mar 2023 00:00:00 GMThttp://hdl.handle.net/10985/235832023-03-01T00:00:00ZZHU, JianchangBEN BETTAIEB, MohamedABED-MERAIM, Farid HUANG, M.S.LI, Z.H.Ductile failure reveals to be an anisotropic phenomenon, for which the proper mechanism has not been clearly addressed yet in the literature. In this paper, the effects of some key anisotropy factors on ductile failure initiation, detected by void coalescence and plastic strain localization, are investigated using unit-cell computations based on crystal plasticity finite element method.
The studied anisotropic effects are induced by the combination of initial crystallographic orientations and void shapes. Therefore, single crystals with three different initial orientations and polycrystalline aggregates with three different initial crystallographic textures are respectively considered. A single void with either spherical, prolate or oblate shape is assumed to be preexisting at the center of each unit cell. By contrast to previous analyses in the literature, plastic strain localization is predicted in the present study on the basis of bifurcation theory. To cover a wide range of stress states, the simulations are performed under two macroscopic loading configurations: proportional triaxial stressing, characterized by constant stress triaxiality and Lode parameter, and proportional in-plane straining, specified by constant strain-path ratio. The obtained results show that the combined anisotropic effects play an important role in the occurrence of void coalescence and plastic strain localization, as well as in the competition between them.On elastic gaps in strain gradient plasticity: 3D discrete dislocation dynamics investigation
http://hdl.handle.net/10985/23663
On elastic gaps in strain gradient plasticity: 3D discrete dislocation dynamics investigation
AMOUZOU-ADOUN, Yaovi Armand; JEBAHI, Mohamed; FIVEL, Marc; FOREST, Samuel; LECOMTE, Jean-Sebastien; SCHUMAN, Christophe; ABED-MERAIM, Farid
Although presenting attractive features in dealing with small-scale size effects, strain gradient plasticity (SGP) theories can lead to uncommon phenomena for some boundary value problems. Almost all non-incremental (Gurtin-type) SGP theories including thermodynamically-consistent higher-order dissipation predict elastic gaps under certain non-proportional loading conditions. An elastic gap is defined as a finite change in the equivalent yield stress after an infinitesimal change in the strain conditions, at the occurrence of the non-proportional loading source. The existence of such gaps in reality is largely questioned and represents a major source of uncertainty preventing the development of robust SGP theories for real small-scale applications. Using 3D discrete dislocation dynamics (3D-DDD), the present paper aims at investigating size effects within micron-scale single crystal structures under various non-proportional loading conditions, including tension-compression-passivation, bending-passivation and tension-bending. An in-depth investigation of the occurrence of elastic gaps under these conditions, which are known to entail such gaps when using classical non-incremental SGP theories, is conducted. The obtained 3D-DDD results reproduce well known experimentally confirmed size effects like Hall-Petch effect, Asaro’s type III kinematic hardening and reversible plasticity. However, no evidence of the phenomenon of elastic gaps is found, which constitutes a first indication that this phenomenon may not exist in reality. The simulations are performed on face-centered cubic (FCC) Nickel single grains with cuboid shapes ranging from 2 microns to 15 microns and different orientations.
Sat, 01 Apr 2023 00:00:00 GMThttp://hdl.handle.net/10985/236632023-04-01T00:00:00ZAMOUZOU-ADOUN, Yaovi ArmandJEBAHI, MohamedFIVEL, MarcFOREST, SamuelLECOMTE, Jean-SebastienSCHUMAN, ChristopheABED-MERAIM, Farid Although presenting attractive features in dealing with small-scale size effects, strain gradient plasticity (SGP) theories can lead to uncommon phenomena for some boundary value problems. Almost all non-incremental (Gurtin-type) SGP theories including thermodynamically-consistent higher-order dissipation predict elastic gaps under certain non-proportional loading conditions. An elastic gap is defined as a finite change in the equivalent yield stress after an infinitesimal change in the strain conditions, at the occurrence of the non-proportional loading source. The existence of such gaps in reality is largely questioned and represents a major source of uncertainty preventing the development of robust SGP theories for real small-scale applications. Using 3D discrete dislocation dynamics (3D-DDD), the present paper aims at investigating size effects within micron-scale single crystal structures under various non-proportional loading conditions, including tension-compression-passivation, bending-passivation and tension-bending. An in-depth investigation of the occurrence of elastic gaps under these conditions, which are known to entail such gaps when using classical non-incremental SGP theories, is conducted. The obtained 3D-DDD results reproduce well known experimentally confirmed size effects like Hall-Petch effect, Asaro’s type III kinematic hardening and reversible plasticity. However, no evidence of the phenomenon of elastic gaps is found, which constitutes a first indication that this phenomenon may not exist in reality. The simulations are performed on face-centered cubic (FCC) Nickel single grains with cuboid shapes ranging from 2 microns to 15 microns and different orientations.Strain localization analysis using a large deformation anisotropic elastic-plastic model coupled with damage
http://hdl.handle.net/10985/10208
Strain localization analysis using a large deformation anisotropic elastic-plastic model coupled with damage
HADDAG, Badis; ABED-MERAIM, Farid ; BALAN, Tudor
Sheet metal forming processes generally involve large deformations together with complex loading sequences. In order to improve numerical simulation predictions of sheet part forming, physically-based constitutive models are often required. The main objective of this paper is to analyze the strain localization phenomenon during the plastic deformation of sheet metals in the context of such advanced constitutive models. Most often, an accurate prediction of localization requires damage to be considered in the finite element simulation. For this purpose, an advanced, anisotropic elastic-plastic model, formulated within the large strain framework and taking strain-path changes into account, has been coupled with an isotropic damage model. This coupling is carried out within the framework of continuum damage mechanics. In order to detect the strain localization during sheet metal forming, Rice's localization criterion has been considered, thus predicting the limit strains at the occurrence of shear bands as well as their orientation. The coupled elastic-plastic-damage model has been implemented in Abaqus/implicit. The application of the model to the prediction of Forming Limit Diagrams (FLDs) provided results that are consistent with the literature and emphasized the impact of the hardening model on the strain-path dependency of the FLD. The fully three-dimensional formulation adopted in the numerical development allowed for some new results - e.g. the out-of-plane orientation of the normal to the localization band, as well as more realistic values for its in-plane orientation.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/102082009-01-01T00:00:00ZHADDAG, BadisABED-MERAIM, Farid BALAN, TudorSheet metal forming processes generally involve large deformations together with complex loading sequences. In order to improve numerical simulation predictions of sheet part forming, physically-based constitutive models are often required. The main objective of this paper is to analyze the strain localization phenomenon during the plastic deformation of sheet metals in the context of such advanced constitutive models. Most often, an accurate prediction of localization requires damage to be considered in the finite element simulation. For this purpose, an advanced, anisotropic elastic-plastic model, formulated within the large strain framework and taking strain-path changes into account, has been coupled with an isotropic damage model. This coupling is carried out within the framework of continuum damage mechanics. In order to detect the strain localization during sheet metal forming, Rice's localization criterion has been considered, thus predicting the limit strains at the occurrence of shear bands as well as their orientation. The coupled elastic-plastic-damage model has been implemented in Abaqus/implicit. The application of the model to the prediction of Forming Limit Diagrams (FLDs) provided results that are consistent with the literature and emphasized the impact of the hardening model on the strain-path dependency of the FLD. The fully three-dimensional formulation adopted in the numerical development allowed for some new results - e.g. the out-of-plane orientation of the normal to the localization band, as well as more realistic values for its in-plane orientation.Ductility limit prediction for polycrystalline aggregates using a CPFEM-based multiscale framework
http://hdl.handle.net/10985/23881
Ductility limit prediction for polycrystalline aggregates using a CPFEM-based multiscale framework
ZHU, Jianchang; BEN BETTAIEB, Mohamed; ZHOU, Shuai; ABED-MERAIM, Farid
The ductility of polycrystalline aggregates is usually limited by two main phenomena: plastic strain localization and void coalescence. The goal of this contribution is to develop a new multiscale framework, based on the crystal plasticity finite element method (CPFEM), for the prediction of ductility limits set by these two phenomena for porous and non-porous polycrystalline aggregates. This numerical framework is based on the combination of crystal plasticity constitutive modeling with the periodic homogenization scheme. Within this strategy, the single crystal constitutive modeling follows a finite strain rate-independent approach, where the plastic flow is governed by the classical Schmid law. Thereby, the competition between the two aforementioned phenomena, which limit ductility, is thoroughly analyzed using the bifurcation theory and a strain-based coalescence criterion. To cover a wide range of mechanical states in this analysis, two types of loadings are applied to the studied aggregates: proportional triaxial stress paths and proportional in-plane strain paths. The developed CPFEM-based framework is well suited to account for essential microstructural features: pre-existence of spherical voids, crystallographic and
morphological anisotropy, matrix polycrystallinity and interactions between grains and their surrounding medium. Extensive sensitivity studies are performed to analyze the impact of these microstructural features on the ductility limit predictions. The main trends obtained by classical phenomenological frameworks are extended here within the framework of crystal plasticity
constitutive modeling.
Tue, 01 Aug 2023 00:00:00 GMThttp://hdl.handle.net/10985/238812023-08-01T00:00:00ZZHU, JianchangBEN BETTAIEB, MohamedZHOU, ShuaiABED-MERAIM, Farid The ductility of polycrystalline aggregates is usually limited by two main phenomena: plastic strain localization and void coalescence. The goal of this contribution is to develop a new multiscale framework, based on the crystal plasticity finite element method (CPFEM), for the prediction of ductility limits set by these two phenomena for porous and non-porous polycrystalline aggregates. This numerical framework is based on the combination of crystal plasticity constitutive modeling with the periodic homogenization scheme. Within this strategy, the single crystal constitutive modeling follows a finite strain rate-independent approach, where the plastic flow is governed by the classical Schmid law. Thereby, the competition between the two aforementioned phenomena, which limit ductility, is thoroughly analyzed using the bifurcation theory and a strain-based coalescence criterion. To cover a wide range of mechanical states in this analysis, two types of loadings are applied to the studied aggregates: proportional triaxial stress paths and proportional in-plane strain paths. The developed CPFEM-based framework is well suited to account for essential microstructural features: pre-existence of spherical voids, crystallographic and
morphological anisotropy, matrix polycrystallinity and interactions between grains and their surrounding medium. Extensive sensitivity studies are performed to analyze the impact of these microstructural features on the ductility limit predictions. The main trends obtained by classical phenomenological frameworks are extended here within the framework of crystal plasticity
constitutive modeling.A physically-based mixed hardening model for the prediction of the ductility limits of thin metal sheets using a CPFE approach
http://hdl.handle.net/10985/25001
A physically-based mixed hardening model for the prediction of the ductility limits of thin metal sheets using a CPFE approach
ZHOU, Shuai; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
An advanced Crystal Plasticity Finite Element (CPFE) approach is developed to accurately predict the ductility limit strains of thin metal sheets. This method uses polycrystalline unit cells to represent the metal sheets at the macroscopic level. The macroscopic behavior of these unit cells is determined based on that of the constituent single crystals using the periodic
homogenization multiscale scheme. At the single crystal scale, the constitutive framework follows a finite strain rate-independent formulation, with the flow rule governed by the Schmid law. The evolution of the single crystal yield surface is described through a physically based mixed hardening model, where isotropic hardening is characterized by a dislocation density-based formulation, while kinematic hardening is described by the nonlinear Armstrong–Frederick model. The unit cell ductility limit strains are predicted by the Rice bifurcation criterion. The reliability of the mixed hardening model in accurately reproducing mechanical behavior is confirmed through simulations of uniaxial tension/compression loading. Then, the developed computational strategy is used to investigate the impact of key microstructural hardening parameters on the initiation of localized necking under linear strain paths. The numerical predictions reveal the significant influence of these parameters on the formability of thin metal sheets. Additionally, the analysis of ductility limits under non-linear strain paths demonstrates a strong dependency of the numerical predictions on strain path changes. The numerical predictions obtained by the developed CPFE multiscale strategy are compared with experimental results from the literature. In summary, the proposed approach provides a reliable tool for accurately predicting the ductility limits of thin metal sheets, offering valuable insights for engineering applications.
Thu, 21 Mar 2024 00:00:00 GMThttp://hdl.handle.net/10985/250012024-03-21T00:00:00ZZHOU, ShuaiBEN BETTAIEB, MohamedABED-MERAIM, Farid An advanced Crystal Plasticity Finite Element (CPFE) approach is developed to accurately predict the ductility limit strains of thin metal sheets. This method uses polycrystalline unit cells to represent the metal sheets at the macroscopic level. The macroscopic behavior of these unit cells is determined based on that of the constituent single crystals using the periodic
homogenization multiscale scheme. At the single crystal scale, the constitutive framework follows a finite strain rate-independent formulation, with the flow rule governed by the Schmid law. The evolution of the single crystal yield surface is described through a physically based mixed hardening model, where isotropic hardening is characterized by a dislocation density-based formulation, while kinematic hardening is described by the nonlinear Armstrong–Frederick model. The unit cell ductility limit strains are predicted by the Rice bifurcation criterion. The reliability of the mixed hardening model in accurately reproducing mechanical behavior is confirmed through simulations of uniaxial tension/compression loading. Then, the developed computational strategy is used to investigate the impact of key microstructural hardening parameters on the initiation of localized necking under linear strain paths. The numerical predictions reveal the significant influence of these parameters on the formability of thin metal sheets. Additionally, the analysis of ductility limits under non-linear strain paths demonstrates a strong dependency of the numerical predictions on strain path changes. The numerical predictions obtained by the developed CPFE multiscale strategy are compared with experimental results from the literature. In summary, the proposed approach provides a reliable tool for accurately predicting the ductility limits of thin metal sheets, offering valuable insights for engineering applications.Investigation of the effect of morphological and crystallographic textures on the ductility limits of thin metal sheets using a CPFEM-based approach
http://hdl.handle.net/10985/25002
Investigation of the effect of morphological and crystallographic textures on the ductility limits of thin metal sheets using a CPFEM-based approach
ZHOU, Shuai; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
The current contribution investigates the effect of some relevant microstructural parameters (specifically, morphological and crystallographic textures) on the ductility limits of polycrystalline aggregates using the Crystal Plasticity Finite Element Method (CPFEM). The polycrystalline aggregates are assumed to be representative of thin metal sheets and their macroscopic behavior is determined from that of their constituent single crystals on the basis of the periodic homogenization technique. The single crystal behavior is described by a finite strain elastoplastic framework in which the plastic flow rule obeys the classical Schmid law and plastic deformation is solely attributed to the slip on the crystallographic slip systems. The CPFEM is implemented within and in connection with ABAQUS/Standard finite element code. The ductility limits are predicted by the Rice bifurcation theory where strain localization is detected when the macroscopic acoustic tensor becomes singular. Three grain morphologies (namely, cube, random, and elongated morphology) and three initial crystallographic textures (namely, cube, random, and copper orientation) are considered to investigate the effect of morphological and crystallographic textures on the onset of plastic strain localization. The numerical results indicate that the effect of initial crystallographic texture is much more pronounced than that of grain morphology on the predicted ductility limits. In addition, the impact of grain size and sheet
thickness are thoroughly analyzed. The research reveals that the trends of the predicted ductility limits are strongly dependent on the size effects.
Mon, 01 Jul 2024 00:00:00 GMThttp://hdl.handle.net/10985/250022024-07-01T00:00:00ZZHOU, ShuaiBEN BETTAIEB, MohamedABED-MERAIM, Farid The current contribution investigates the effect of some relevant microstructural parameters (specifically, morphological and crystallographic textures) on the ductility limits of polycrystalline aggregates using the Crystal Plasticity Finite Element Method (CPFEM). The polycrystalline aggregates are assumed to be representative of thin metal sheets and their macroscopic behavior is determined from that of their constituent single crystals on the basis of the periodic homogenization technique. The single crystal behavior is described by a finite strain elastoplastic framework in which the plastic flow rule obeys the classical Schmid law and plastic deformation is solely attributed to the slip on the crystallographic slip systems. The CPFEM is implemented within and in connection with ABAQUS/Standard finite element code. The ductility limits are predicted by the Rice bifurcation theory where strain localization is detected when the macroscopic acoustic tensor becomes singular. Three grain morphologies (namely, cube, random, and elongated morphology) and three initial crystallographic textures (namely, cube, random, and copper orientation) are considered to investigate the effect of morphological and crystallographic textures on the onset of plastic strain localization. The numerical results indicate that the effect of initial crystallographic texture is much more pronounced than that of grain morphology on the predicted ductility limits. In addition, the impact of grain size and sheet
thickness are thoroughly analyzed. The research reveals that the trends of the predicted ductility limits are strongly dependent on the size effects.Ductility limit prediction using a GTN damage model coupled with localization bifurcation analysis
http://hdl.handle.net/10985/9973
Ductility limit prediction using a GTN damage model coupled with localization bifurcation analysis
MANSOURI, Lotfi; CHALAL, Hocine; ABED-MERAIM, Farid
Because the localization of deformation into narrow planar bands is often precursor to material failure, several approaches have been proposed to predict this phenomenon. In this paper, the Gurson–Tvergaard– Needleman (GTN) elastic–plastic–damage model for ductile materials is considered. A large-strain version of this constitutive model is coupled with the Rice localization criterion, which is based on bifurcation theory, to investigate strain localization. The resulting loss of ellipticity condition is then used to determine ellipticiy loss diagrams (ELDs) associated with strain paths that are those typically applied to metals under biaxial stretching. A sensitivity analysis is conducted with respect to the model parameters on a representative selection of ductile materials. The analysis shows that the damage parameters have a significant impact on the predicted ELDs, which confirms the predominant role of damage-induced softening in triggering plastic flow localization with the adopted constitutive description combined with the bifurcation approach. As a consequence of this high sensitivity, it appears that the proper identification of damage parameters is a key issue for accurate plastic flow localization predictions using the GTN model coupled with bifurcation theory. The effect of the dense matrix hardening parameters on the strain localization predictions of the voided aggregate, although found much smaller in the whole, is more noticeable for the plane strain tension loading path or, more generally, when the critical hardening modulus required for localization is not strongly negative.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/99732014-01-01T00:00:00ZMANSOURI, LotfiCHALAL, HocineABED-MERAIM, Farid Because the localization of deformation into narrow planar bands is often precursor to material failure, several approaches have been proposed to predict this phenomenon. In this paper, the Gurson–Tvergaard– Needleman (GTN) elastic–plastic–damage model for ductile materials is considered. A large-strain version of this constitutive model is coupled with the Rice localization criterion, which is based on bifurcation theory, to investigate strain localization. The resulting loss of ellipticity condition is then used to determine ellipticiy loss diagrams (ELDs) associated with strain paths that are those typically applied to metals under biaxial stretching. A sensitivity analysis is conducted with respect to the model parameters on a representative selection of ductile materials. The analysis shows that the damage parameters have a significant impact on the predicted ELDs, which confirms the predominant role of damage-induced softening in triggering plastic flow localization with the adopted constitutive description combined with the bifurcation approach. As a consequence of this high sensitivity, it appears that the proper identification of damage parameters is a key issue for accurate plastic flow localization predictions using the GTN model coupled with bifurcation theory. The effect of the dense matrix hardening parameters on the strain localization predictions of the voided aggregate, although found much smaller in the whole, is more noticeable for the plane strain tension loading path or, more generally, when the critical hardening modulus required for localization is not strongly negative.An advanced elastoplastic framework accounting for induced plastic anisotropy fully coupled with ductile damage
http://hdl.handle.net/10985/20500
An advanced elastoplastic framework accounting for induced plastic anisotropy fully coupled with ductile damage
PAUX, J.; BEN BETTAIEB, Mohamed; BADREDDINE, H.; LABERGERE, C.; SAANOUNI, K.; ABED-MERAIM, Farid
We present in this investigation an advanced phenomenological approach combining the computational efficiency of classical phenomenological plasticity models and the accuracy and high resolution of multiscale crystal plasticity schemes. Within this advanced approach, a new phenomenological constitutive framework has been developed and implemented into ABAQUS/Standard finite element (FE) code. Compared to classical approaches, this framework allows accounting for initial and induced plastic anisotropy, isotropic nonlinear hardening and the full coupling with isotropic ductile damage. Material parameters corresponding to this phenomenological constitutive framework are identified based on multiscale polycrystalline simulations, where the self-consistent scheme is used to ensure the transition between the single crystal and polycrystal scales. The single crystal mechanical behavior is assumed to be elastoplastic (rate-independent), and microscopic material degradation is well-considered by introducing a scalar damage variable at each crystallographic slip system for each individual grain. The evolution of polycrystalline yield surfaces, induced by the evolution of crystallographic texture, is accurately reproduced by the new constitutive modeling, where the anisotropy parameters are assumed to evolve during plastic deformation. Their evolution laws are identified based on multiscale simulations. The different identification procedures are presented and extensively discussed. The robustness and reliability of this advanced model are analyzed through some relevant numerical predictions obtained by applying a combined tensile/shear test.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/205002021-01-01T00:00:00ZPAUX, J.BEN BETTAIEB, MohamedBADREDDINE, H.LABERGERE, C.SAANOUNI, K.ABED-MERAIM, Farid We present in this investigation an advanced phenomenological approach combining the computational efficiency of classical phenomenological plasticity models and the accuracy and high resolution of multiscale crystal plasticity schemes. Within this advanced approach, a new phenomenological constitutive framework has been developed and implemented into ABAQUS/Standard finite element (FE) code. Compared to classical approaches, this framework allows accounting for initial and induced plastic anisotropy, isotropic nonlinear hardening and the full coupling with isotropic ductile damage. Material parameters corresponding to this phenomenological constitutive framework are identified based on multiscale polycrystalline simulations, where the self-consistent scheme is used to ensure the transition between the single crystal and polycrystal scales. The single crystal mechanical behavior is assumed to be elastoplastic (rate-independent), and microscopic material degradation is well-considered by introducing a scalar damage variable at each crystallographic slip system for each individual grain. The evolution of polycrystalline yield surfaces, induced by the evolution of crystallographic texture, is accurately reproduced by the new constitutive modeling, where the anisotropy parameters are assumed to evolve during plastic deformation. Their evolution laws are identified based on multiscale simulations. The different identification procedures are presented and extensively discussed. The robustness and reliability of this advanced model are analyzed through some relevant numerical predictions obtained by applying a combined tensile/shear test.Comparison between the Marciniak and Kuczyński imperfection approach and bifurcation theory in the prediction of localized necking for porous ductile materials
http://hdl.handle.net/10985/21455
Comparison between the Marciniak and Kuczyński imperfection approach and bifurcation theory in the prediction of localized necking for porous ductile materials
NASIR, Muhammad Waqar; CHALAL, Hocine; ABED-MERAIM, Farid
To prevent the occurrence of localized necking, the concept of forming limit diagram is often used, thus playing an important role in sheet metal forming processes. The aim of the present study is to develop a numerical tool for the theoretical prediction of forming limit diagrams, which would be a cost-efective procedure as compared to experimental measurements. The proposed numerical tool is based on the Marciniak and Kuczyński imperfection approach combined with the Gurson–Tvergaard–Needleman damage model, which is implemented into the MATLAB program within the framework of plane-stress conditions. Forming limit diagrams have been predicted by assuming both geometric (thickness) as well as material initial imperfections in the Marciniak and Kuczyński imperfection approach. These forming limit diagrams, for different sizes of geometric or material imperfections, are also compared with the forming limit diagram obtained by using the bifurcation theory. It is shown that the bifurcation-based forming limit diagram provides an upper bound as compared to the Marciniak and Kuczyński imperfection approach predictions. The results also reveal that irrespective of the imperfection type considered in the Marciniak and Kuczyński imperfection approach, the corresponding forming limit diagram tends to that predicted by bifurcation theory when the size of initial imperfection tends to zero. Additionally, the predicted ductility limits are lowered as the magnitude of initial imperfection increases; however, the decrease in the ductility limits at balanced biaxial tension is more signifcant than for the other strain-path ratios. The results for the forming limit diagrams indicate that the predicted ductility limits are more sensitive to the initial imperfection in the thickness and the isotropic hardening coefficient as compared to the other types of material imperfections. Moreover, the initial imperfection in the critical porosity is the most infuential one among the Gurson–Tvergaard–Needleman damage parameters.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/214552021-01-01T00:00:00ZNASIR, Muhammad WaqarCHALAL, HocineABED-MERAIM, Farid To prevent the occurrence of localized necking, the concept of forming limit diagram is often used, thus playing an important role in sheet metal forming processes. The aim of the present study is to develop a numerical tool for the theoretical prediction of forming limit diagrams, which would be a cost-efective procedure as compared to experimental measurements. The proposed numerical tool is based on the Marciniak and Kuczyński imperfection approach combined with the Gurson–Tvergaard–Needleman damage model, which is implemented into the MATLAB program within the framework of plane-stress conditions. Forming limit diagrams have been predicted by assuming both geometric (thickness) as well as material initial imperfections in the Marciniak and Kuczyński imperfection approach. These forming limit diagrams, for different sizes of geometric or material imperfections, are also compared with the forming limit diagram obtained by using the bifurcation theory. It is shown that the bifurcation-based forming limit diagram provides an upper bound as compared to the Marciniak and Kuczyński imperfection approach predictions. The results also reveal that irrespective of the imperfection type considered in the Marciniak and Kuczyński imperfection approach, the corresponding forming limit diagram tends to that predicted by bifurcation theory when the size of initial imperfection tends to zero. Additionally, the predicted ductility limits are lowered as the magnitude of initial imperfection increases; however, the decrease in the ductility limits at balanced biaxial tension is more signifcant than for the other strain-path ratios. The results for the forming limit diagrams indicate that the predicted ductility limits are more sensitive to the initial imperfection in the thickness and the isotropic hardening coefficient as compared to the other types of material imperfections. Moreover, the initial imperfection in the critical porosity is the most infuential one among the Gurson–Tvergaard–Needleman damage parameters.A quasi-static stability analysis for Biot’s equation and standard dissipative systems
http://hdl.handle.net/10985/10335
A quasi-static stability analysis for Biot’s equation and standard dissipative systems
NGUYEN, Quoc Son; ABED-MERAIM, Farid
In this paper, an extended version of Biot's differential equation is considered in order to discuss the quasi-static stability of a response for a solid in the framework of generalized standard materials. The same equation also holds for gradient theories since the gradients of arbitrary order of the state variables and of their rates can be introduced in the expression of the energy and of the dissipation potentials. The stability of a quasi-static response of a system governed by Biot's equations is discussed. Two approaches are considered, by direct estimates and by linearizations. The approach by direct estimates can be applied in visco-plasticity as well as in plasticity. A sufficient condition of stability is proposed and based upon the positivity of the second variation of energy along the considered response. This is an extension of the criterion of second variation, well known in elastic buckling, into the study of the stability of a response. The linearization approach is available only for smooth dissipation potentials, i.e. for the study of visco-elastic solids and leads to a result on asymptotic stability. The paper is illustrated by a simple example.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10985/103352007-01-01T00:00:00ZNGUYEN, Quoc SonABED-MERAIM, Farid In this paper, an extended version of Biot's differential equation is considered in order to discuss the quasi-static stability of a response for a solid in the framework of generalized standard materials. The same equation also holds for gradient theories since the gradients of arbitrary order of the state variables and of their rates can be introduced in the expression of the energy and of the dissipation potentials. The stability of a quasi-static response of a system governed by Biot's equations is discussed. Two approaches are considered, by direct estimates and by linearizations. The approach by direct estimates can be applied in visco-plasticity as well as in plasticity. A sufficient condition of stability is proposed and based upon the positivity of the second variation of energy along the considered response. This is an extension of the criterion of second variation, well known in elastic buckling, into the study of the stability of a response. The linearization approach is available only for smooth dissipation potentials, i.e. for the study of visco-elastic solids and leads to a result on asymptotic stability. The paper is illustrated by a simple example.