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http://hdl.handle.net/10985/11858
AKPAMA, Holanyo; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
Key Engineering Materials
In the present work, a powerful modeling tool is developed to predict and analyze the onset of strain localization in polycrystalline aggregates. The predictions of localized necking are based on two plastic instability criteria, namely the bifurcation theory and the initial imperfection approach. In this tool, a micromechanical model, based on the self-consistent scale-transition scheme, is used to accurately derive the mechanical behavior of polycrystalline aggregates from that of their microscopic constituents (the single crystals). The mechanical behavior of the single crystals is developed within a large strain rate-independent constitutive framework. This micromechanical constitutive modeling takes into account the essential microstructure-related features that are relevant at the microscale. These microstructural aspects include key physical mechanisms, such as initial and induced crystallographic textures, morphological anisotropy and interactions between the grains and their surrounding medium. The developed tool is used to predict sheet metal formability through the concept of forming limit diagrams (FLDs). The results obtained by the self-consistent averaging scheme, in terms of predicted FLDs, are compared with those given by the more classical
full-constraint Taylor model. Moreover, the predictions obtained by the imperfection approach are systematically compared with those given by the bifurcation analysis, and it is demonstrated that the former tend to the latter in the limit of a vanishing size for the initial imperfection.
Mon, 17 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10985/118582016-10-17T00:00:00ZAKPAMA, HolanyoBEN BETTAIEB, MohamedABED-MERAIM, FaridIn the present work, a powerful modeling tool is developed to predict and analyze the onset of strain localization in polycrystalline aggregates. The predictions of localized necking are based on two plastic instability criteria, namely the bifurcation theory and the initial imperfection approach. In this tool, a micromechanical model, based on the self-consistent scale-transition scheme, is used to accurately derive the mechanical behavior of polycrystalline aggregates from that of their microscopic constituents (the single crystals). The mechanical behavior of the single crystals is developed within a large strain rate-independent constitutive framework. This micromechanical constitutive modeling takes into account the essential microstructure-related features that are relevant at the microscale. These microstructural aspects include key physical mechanisms, such as initial and induced crystallographic textures, morphological anisotropy and interactions between the grains and their surrounding medium. The developed tool is used to predict sheet metal formability through the concept of forming limit diagrams (FLDs). The results obtained by the self-consistent averaging scheme, in terms of predicted FLDs, are compared with those given by the more classical
full-constraint Taylor model. Moreover, the predictions obtained by the imperfection approach are systematically compared with those given by the bifurcation analysis, and it is demonstrated that the former tend to the latter in the limit of a vanishing size for the initial imperfection.Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach
http://hdl.handle.net/10985/11915
AKPAMA, Holanyo; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
Latin American Journal of Solids and Structures
The prediction of plastic instability in sheet metals during forming processes represents nowadays an ambitious challenge. To reach this goal, a new numerical approach, based on the loss of ellipticity criterion, is proposed in the present contribution. A polycrystalline model is implemented as a user-material subroutine into the
ABAQUS/Implicit finite element (FE) code. The polycrystalline constitutive model is assigned to each integration point of the FE mesh. To derive the mechanical behavior of this polycrystalline aggregate from the behavior of its microscopic constituents, the
multiscale self-consistent scheme is used. The mechanical behavior of the single crystals is described by a finite strain rateindependent constitutive framework, where the Schmid law is used to model the plastic flow. The condition of loss of ellipticity at the
macroscale is used as plastic instability criterion in the FE modeling. This numerical approach, which couples the FE method with the self-consistent scheme, is used to simulate a deep drawing process, and the above criterion is used to predict the formability limit of the studied sheets during this operation.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/119152017-01-01T00:00:00ZAKPAMA, HolanyoBEN BETTAIEB, MohamedABED-MERAIM, FaridThe prediction of plastic instability in sheet metals during forming processes represents nowadays an ambitious challenge. To reach this goal, a new numerical approach, based on the loss of ellipticity criterion, is proposed in the present contribution. A polycrystalline model is implemented as a user-material subroutine into the
ABAQUS/Implicit finite element (FE) code. The polycrystalline constitutive model is assigned to each integration point of the FE mesh. To derive the mechanical behavior of this polycrystalline aggregate from the behavior of its microscopic constituents, the
multiscale self-consistent scheme is used. The mechanical behavior of the single crystals is described by a finite strain rateindependent constitutive framework, where the Schmid law is used to model the plastic flow. The condition of loss of ellipticity at the
macroscale is used as plastic instability criterion in the FE modeling. This numerical approach, which couples the FE method with the self-consistent scheme, is used to simulate a deep drawing process, and the above criterion is used to predict the formability limit of the studied sheets during this operation.Localized necking predictions based on rate-independent self-consistent polycrystal plasticity: Bifurcation analysis versus imperfection approach
http://hdl.handle.net/10985/11856
AKPAMA, Holanyo; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
International Journal of Plasticity
The present study focuses on the development of a relevant numerical tool for predicting
the onset of localized necking in polycrystalline aggregates. The latter are assumed to be representative of thin metal sheets. In this tool, a micromechanical model, based on the rate-independent self-consistent multi-scale scheme, is developed to accurately describe the mechanical behavior of polycrystalline aggregates from that of their single crystal constituents. In the current paper, the constitutive framework at the single crystal scale follows a finite strain formulation of the rate-independent theory of crystal elastoplasticity. To predict the occurrence of localized necking in polycrystalline aggregates, this micromechanical modeling is combined with two main strain localization approaches: the bifurcation analysis and the initial imperfection method. The formulation of both strain localization indicators takes into consideration the plane stress conditions to which thin metal sheets are subjected during deformation. From a numerical point of view, strain localization analysis with this crystal plasticity approach can be viewed as a strongly nonlinear problem. Hence, several numerical algorithms and techniques are developed and implemented in the aim of efficiently solving this non-linear problem. Various simulation results obtained by the application of the developed numerical tool are presented and extensively discussed. It is demonstrated from these results that the predictions obtained with the MarciniakeKuczynski procedure tend towards those yielded by the bifurcation theory, when the initial imperfection ratio tends towards zero. Furthermore, the above result is shown to be valid for both scale-transition schemes, namely the full-constraint Taylor model and self-consistent scheme.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/118562017-01-01T00:00:00ZAKPAMA, HolanyoBEN BETTAIEB, MohamedABED-MERAIM, FaridThe present study focuses on the development of a relevant numerical tool for predicting
the onset of localized necking in polycrystalline aggregates. The latter are assumed to be representative of thin metal sheets. In this tool, a micromechanical model, based on the rate-independent self-consistent multi-scale scheme, is developed to accurately describe the mechanical behavior of polycrystalline aggregates from that of their single crystal constituents. In the current paper, the constitutive framework at the single crystal scale follows a finite strain formulation of the rate-independent theory of crystal elastoplasticity. To predict the occurrence of localized necking in polycrystalline aggregates, this micromechanical modeling is combined with two main strain localization approaches: the bifurcation analysis and the initial imperfection method. The formulation of both strain localization indicators takes into consideration the plane stress conditions to which thin metal sheets are subjected during deformation. From a numerical point of view, strain localization analysis with this crystal plasticity approach can be viewed as a strongly nonlinear problem. Hence, several numerical algorithms and techniques are developed and implemented in the aim of efficiently solving this non-linear problem. Various simulation results obtained by the application of the developed numerical tool are presented and extensively discussed. It is demonstrated from these results that the predictions obtained with the MarciniakeKuczynski procedure tend towards those yielded by the bifurcation theory, when the initial imperfection ratio tends towards zero. Furthermore, the above result is shown to be valid for both scale-transition schemes, namely the full-constraint Taylor model and self-consistent scheme.Effect of kinematic hardening on localized necking in substrate-supported metal layers
http://hdl.handle.net/10985/11855
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
Effect of kinematic hardening on localized necking in substrate-supported metal layers
Prediction of necking limits in thin substrate-supported metal layers, which are typically used as functional components in electronic devices, represents nowadays an ambitious challenge. The specific purpose of the current work is, first, to numerically investigate the effect of kinematic hardening on localized necking in a
freestanding metal layer. Second, the impact of adding a substrate layer on the ductility evolution of the resulting elastomer/metal bilayer will be analyzed. The materials in the metal and substrate layers are assumed to be isotropic, incompressible and strain-rate independent. The behavior of the metal layer is described by a rigid–plastic model with mixed (isotropic and kinematic) hardening. The isotropic hardening contribution is
modeled by the Hollomon law, while kinematic hardening is modeled by the Armstrong–Frederick law. The substrate layer is made of elastomer material whose mechanical behavior is assumed to be hyperelastic and
modeled by a neo-Hookean constitutive law. The Marciniak–Kuczynski imperfection analysis is used to predict plastic flow localization. Through various numerical simulations, the influence of kinematic hardening on localized necking as well as the impact of the addition of an elastomer layer are specifically emphasized.
Comparisons with experimental results are also carried out to assess the relevance of incorporating kinematic hardening in the constitutive modeling of freestanding metal sheets.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/118552017-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, FaridPrediction of necking limits in thin substrate-supported metal layers, which are typically used as functional components in electronic devices, represents nowadays an ambitious challenge. The specific purpose of the current work is, first, to numerically investigate the effect of kinematic hardening on localized necking in a
freestanding metal layer. Second, the impact of adding a substrate layer on the ductility evolution of the resulting elastomer/metal bilayer will be analyzed. The materials in the metal and substrate layers are assumed to be isotropic, incompressible and strain-rate independent. The behavior of the metal layer is described by a rigid–plastic model with mixed (isotropic and kinematic) hardening. The isotropic hardening contribution is
modeled by the Hollomon law, while kinematic hardening is modeled by the Armstrong–Frederick law. The substrate layer is made of elastomer material whose mechanical behavior is assumed to be hyperelastic and
modeled by a neo-Hookean constitutive law. The Marciniak–Kuczynski imperfection analysis is used to predict plastic flow localization. Through various numerical simulations, the influence of kinematic hardening on localized necking as well as the impact of the addition of an elastomer layer are specifically emphasized.
Comparisons with experimental results are also carried out to assess the relevance of incorporating kinematic hardening in the constitutive modeling of freestanding metal sheets.Investigation of localized necking in substrate-supported metal layers: comparison of bifurcation and imperfection analyses
http://hdl.handle.net/10985/10047
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
International Journal of Plasticity
Localized necking is often considered as precursor to failure in metal components. In modern technologies, functional components (e.g., in flexible electronic devices) may be affected by this necking phenomenon, and to avoid the occurrence of strain localization, elastomer substrates are bonded to the metal layers. This paper proposes an investigation of the development of localized necking in both freestanding metal layers and elastomer/metal bilayers. Finite strain versions of both rigid–plastic flow theory and deformation theory of plasticity are employed to model the mechanical response of the metal layer. For the elastomer, a neo-Hookean constitutive law is considered. Localized necking is predicted using both bifurcation (whenever possible) and Marciniak–Kuczynski analyses. A variety of numerical results are presented, which pertain to the prediction of localized necking in freestanding metal layers and metal/substrate bilayers. The effects of the constitutive framework and the presence of an elastomer substrate on strain localization predictions have been specifically highlighted. It is demonstrated that the addition of an elastomer layer can retard significantly the occurrence of localized necking. It is also demonstrated that the results of the Marciniak–Kuczynski analysis tend towards the bifurcation predictions in the limit of a vanishing size for the geometric imperfection.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/100472015-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, FaridLocalized necking is often considered as precursor to failure in metal components. In modern technologies, functional components (e.g., in flexible electronic devices) may be affected by this necking phenomenon, and to avoid the occurrence of strain localization, elastomer substrates are bonded to the metal layers. This paper proposes an investigation of the development of localized necking in both freestanding metal layers and elastomer/metal bilayers. Finite strain versions of both rigid–plastic flow theory and deformation theory of plasticity are employed to model the mechanical response of the metal layer. For the elastomer, a neo-Hookean constitutive law is considered. Localized necking is predicted using both bifurcation (whenever possible) and Marciniak–Kuczynski analyses. A variety of numerical results are presented, which pertain to the prediction of localized necking in freestanding metal layers and metal/substrate bilayers. The effects of the constitutive framework and the presence of an elastomer substrate on strain localization predictions have been specifically highlighted. It is demonstrated that the addition of an elastomer layer can retard significantly the occurrence of localized necking. It is also demonstrated that the results of the Marciniak–Kuczynski analysis tend towards the bifurcation predictions in the limit of a vanishing size for the geometric imperfection.Theoretical and numerical investigation of the impact of out-of-plane compressive stress on sheet metal formability
http://hdl.handle.net/10985/11857
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
International Journal of Mechanical Sciences
In modern sheet metal forming processes, such as hydroforming and single point incremental forming, sheet metals are often subjected to out-of-plane compressive stresses in addition to traditional in-plane stresses. However, the effect of these out-of-plane stresses on the onset of plastic strain localization is not considered when classic necking criteria are used, as the latter are generally formulated based on the plane stress assumption. The main objective of the present investigation is to overcome this limitation by developing numerical tools and analytical relations that allow considering the influence of these compressive stresses on the prediction of localized necking. In the different tools developed, and for comparison purposes, finite strain versions of both the deformation theory of plasticity and the rigid-plastic flow theory are used to describe the mechanical behavior of the metal sheet. Furthermore, both the bifurcation theory and the initial imperfection approach are employed to predict the onset of strain localization. Various numerical predictions are reported to illustrate the effect of normal stress on the occurrence of localized necking in sheet metals. From these different results, it is clearly demonstrated that out-of-plane stresses may notably enhance sheet metal formability and, therefore, this property can be effectively used to avoid the initiation of early strain localization.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/118572017-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, FaridIn modern sheet metal forming processes, such as hydroforming and single point incremental forming, sheet metals are often subjected to out-of-plane compressive stresses in addition to traditional in-plane stresses. However, the effect of these out-of-plane stresses on the onset of plastic strain localization is not considered when classic necking criteria are used, as the latter are generally formulated based on the plane stress assumption. The main objective of the present investigation is to overcome this limitation by developing numerical tools and analytical relations that allow considering the influence of these compressive stresses on the prediction of localized necking. In the different tools developed, and for comparison purposes, finite strain versions of both the deformation theory of plasticity and the rigid-plastic flow theory are used to describe the mechanical behavior of the metal sheet. Furthermore, both the bifurcation theory and the initial imperfection approach are employed to predict the onset of strain localization. Various numerical predictions are reported to illustrate the effect of normal stress on the occurrence of localized necking in sheet metals. From these different results, it is clearly demonstrated that out-of-plane stresses may notably enhance sheet metal formability and, therefore, this property can be effectively used to avoid the initiation of early strain localization.Solidification sequence of Ni-Si-Cr ~3wt% B brazing alloys
http://hdl.handle.net/10985/12139
SIREDEY-SCHWALLER, Nathalie; HAMEL-AKRÉ, Johann; PELTIER, Laurent; HAZOTTE, Alain; BOCHER, Philippe
Welding in the World
Various Ni-Si-Cr-B brazing alloys with a similar boron content (3 wt%) are investigated. Alloy compositions cover a section of the quaternary phase diagram that connects BNi-3 to BNi-9 ternary alloys for industrial use. Samples were melted and solidified at low cooling rate (1 K/min) under secondary vacuum to minimize oxidation and the metastable phase formation. Transformation temperatures, microstructures, and chemical analyses are reported. Experimental conditions were found to play a significant role on the accuracy of obtained data. Thermodynamic data were collected upon heating. Before analyzing quaternary alloys, the results of investigated ternary alloys were compared with the literature and discussed.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/121392017-01-01T00:00:00ZSIREDEY-SCHWALLER, NathalieHAMEL-AKRÉ, JohannPELTIER, LaurentHAZOTTE, AlainBOCHER, PhilippeVarious Ni-Si-Cr-B brazing alloys with a similar boron content (3 wt%) are investigated. Alloy compositions cover a section of the quaternary phase diagram that connects BNi-3 to BNi-9 ternary alloys for industrial use. Samples were melted and solidified at low cooling rate (1 K/min) under secondary vacuum to minimize oxidation and the metastable phase formation. Transformation temperatures, microstructures, and chemical analyses are reported. Experimental conditions were found to play a significant role on the accuracy of obtained data. Thermodynamic data were collected upon heating. Before analyzing quaternary alloys, the results of investigated ternary alloys were compared with the literature and discussed.Analysis of primal and dual variables in structural shape control by piezoelectric patches using solid-shell finite elements
http://hdl.handle.net/10985/13034
KPEKY, Fessal; ABED-MERAIM, Farid; DAYA, El Mostafa
This paper presents an assessment of the performances of new piezoelectric solid−shell finite elements. Compared to conventional solid and shell elements, the solid–shell concept reveals to be very attractive, due to a number of well-established advantages and computational capabilities. This paper focuses on two element formulations, denoted SHB15E and SHB20E, which represent a quadratic prismatic solid−shell element and its hexahedral counterpart, respectively. The current analysis consists in an evaluation of primal and dual variables during the process of shape control of structures. The interest in this solid–shell approach is shown through a set of selective and representative plate and shell benchmark problems. The results obtained by the proposed formulations are compared with those given by state-of-the-art piezoelectric elements available in ABAQUS.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/130342017-01-01T00:00:00ZKPEKY, FessalABED-MERAIM, FaridDAYA, El MostafaThis paper presents an assessment of the performances of new piezoelectric solid−shell finite elements. Compared to conventional solid and shell elements, the solid–shell concept reveals to be very attractive, due to a number of well-established advantages and computational capabilities. This paper focuses on two element formulations, denoted SHB15E and SHB20E, which represent a quadratic prismatic solid−shell element and its hexahedral counterpart, respectively. The current analysis consists in an evaluation of primal and dual variables during the process of shape control of structures. The interest in this solid–shell approach is shown through a set of selective and representative plate and shell benchmark problems. The results obtained by the proposed formulations are compared with those given by state-of-the-art piezoelectric elements available in ABAQUS.Ductility prediction of substrate-supported metal layers based on rate-independent crystal plasticity theory
http://hdl.handle.net/10985/13135
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
International Journal of Material Forming
In several modern technological applications, the formability of functional metal components is often limited by the occurrence of localized necking. To retard the onset of such undesirable plastic instabilities and, hence, to improve formability, elastomer
substrates are sometimes adhered to these metal components. The current paper aims to numerically investigate the impact of such elastomer substrates on the formability enhancement of the resulting bilayer. To this end, both the bifurcation theory and the
initial imperfection approach are used to predict the inception of localized necking in substrate-supported metal layers. The fullconstraint Taylor scale-transition scheme is used to derive the mechanical behavior of a representative volume element of the
metal layer from the behavior of its microscopic constituents (the single crystals). The mechanical behavior of the elastomer substrate follows the neo-Hookean hyperelastic model. The adherence between the two layers is assumed to be perfect. Through
numerical simulations, it is shown that bonding an elastomer layer to a metal layer allows significant enhancement in formability, especially in the negative range of strain paths. These results highlight the benefits of adding elastomer substrates to thin metal
components in several technological applications. Also, it is shown that the limit strains predicted by the initial imperfection approach tend towards the bifurcation predictions as the size of the geometric imperfection in the metal layer reduces.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/131352018-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, FaridIn several modern technological applications, the formability of functional metal components is often limited by the occurrence of localized necking. To retard the onset of such undesirable plastic instabilities and, hence, to improve formability, elastomer
substrates are sometimes adhered to these metal components. The current paper aims to numerically investigate the impact of such elastomer substrates on the formability enhancement of the resulting bilayer. To this end, both the bifurcation theory and the
initial imperfection approach are used to predict the inception of localized necking in substrate-supported metal layers. The fullconstraint Taylor scale-transition scheme is used to derive the mechanical behavior of a representative volume element of the
metal layer from the behavior of its microscopic constituents (the single crystals). The mechanical behavior of the elastomer substrate follows the neo-Hookean hyperelastic model. The adherence between the two layers is assumed to be perfect. Through
numerical simulations, it is shown that bonding an elastomer layer to a metal layer allows significant enhancement in formability, especially in the negative range of strain paths. These results highlight the benefits of adding elastomer substrates to thin metal
components in several technological applications. Also, it is shown that the limit strains predicted by the initial imperfection approach tend towards the bifurcation predictions as the size of the geometric imperfection in the metal layer reduces.Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database
http://hdl.handle.net/10985/13136
GUPTA, Akash; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid; KALIDINDI, Surya
International Journal of Plasticity
The present investigation focuses on the development of a fast and robust numerical tool for the prediction of the forming limit diagrams (FLDs) for thin polycrystalline metal sheets using a Taylor-type (full constraints) crystal plasticity model. The incipience of localized necking is numerically determined by the well-known Marciniak–Kuczynski model. The crystal plasticity constitutive equations, on which these computations are based, are known to be highly nonlinear, thus involving computationally very expensive solutions. This presents a major impediment to the wider adoption of crystal plasticity theories in the computation of FLDs. In this work, this limitation is addressed by using a recently developed spectral database approach based on discrete Fourier transforms (DFTs). Significant improvements were made to the prior approach and a new database was created to address this challenge successfully. These extensions are detailed in the present paper. It is shown that the use of the database allows a significant reduction in the computational cost involved in crystal plasticity based FLD predictions (a reduction of about 96% in terms of CPU time).
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/131362018-01-01T00:00:00ZGUPTA, AkashBEN BETTAIEB, MohamedABED-MERAIM, FaridKALIDINDI, SuryaThe present investigation focuses on the development of a fast and robust numerical tool for the prediction of the forming limit diagrams (FLDs) for thin polycrystalline metal sheets using a Taylor-type (full constraints) crystal plasticity model. The incipience of localized necking is numerically determined by the well-known Marciniak–Kuczynski model. The crystal plasticity constitutive equations, on which these computations are based, are known to be highly nonlinear, thus involving computationally very expensive solutions. This presents a major impediment to the wider adoption of crystal plasticity theories in the computation of FLDs. In this work, this limitation is addressed by using a recently developed spectral database approach based on discrete Fourier transforms (DFTs). Significant improvements were made to the prior approach and a new database was created to address this challenge successfully. These extensions are detailed in the present paper. It is shown that the use of the database allows a significant reduction in the computational cost involved in crystal plasticity based FLD predictions (a reduction of about 96% in terms of CPU time).