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http://hdl.handle.net/10985/10654
Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP).
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/106542016-01-01T00:00:00ZAKPAMA, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, Farid In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP).Localized necking predictions based on rate-independent self-consistent polycrystal plasticity: Bifurcation analysis versus imperfection approach
http://hdl.handle.net/10985/11856
Localized necking predictions based on rate-independent self-consistent polycrystal plasticity: Bifurcation analysis versus imperfection approach
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
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, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, Farid 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.On the elasto-viscoplastic behavior of the Ti5553 alloy
http://hdl.handle.net/10985/11196
On the elasto-viscoplastic behavior of the Ti5553 alloy
BEN BETTAIEB, Mohamed; VAN HOOF, Thibaut; PARDOEN, Thomas; DUFOUR, Philippe; LENAIN, Astrid; JACQUES, Pascal J.; HABRAKEN, Anne-Marie
The elastoviscoplastic behavior of the Ti5553 alloy is characterized and compared to the classical Ti–6Al–4V alloy. The true stress–strain curves are determined based on tensile tests performed under different strain rates at room temperature and at 1501C, from which the elastic constants and the parameters of a Norton–Hoff viscoplastic model are identified. The strength of the Ti5553 alloy is 20–40% higher than the strength of the Ti–6Al–4V alloy. The Ti5553 alloy constitutes thus a promising candidate for advanced structural applications. In view of modeling structural applications of forming operations, the elastic and plastic initial anisotropy of the two alloys is investigated by combining compression on cylinders with elliptical sections, uniaxial tensile tests in different material directions, plane strain and shear tests. The initial anisotropy of the different alloys is very weak which justifies the modeling of the mechanical behavior with an isotropic yield surface. The identified elastoviscoplastic model is validated by comparing experimental results with FE predictions both on cylindrical notched specimens subjected to tensile tests and onflat specimens subjected to plane strain conditions.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/111962014-01-01T00:00:00ZBEN BETTAIEB, MohamedVAN HOOF, ThibautPARDOEN, ThomasDUFOUR, PhilippeLENAIN, AstridJACQUES, Pascal J.HABRAKEN, Anne-MarieThe elastoviscoplastic behavior of the Ti5553 alloy is characterized and compared to the classical Ti–6Al–4V alloy. The true stress–strain curves are determined based on tensile tests performed under different strain rates at room temperature and at 1501C, from which the elastic constants and the parameters of a Norton–Hoff viscoplastic model are identified. The strength of the Ti5553 alloy is 20–40% higher than the strength of the Ti–6Al–4V alloy. The Ti5553 alloy constitutes thus a promising candidate for advanced structural applications. In view of modeling structural applications of forming operations, the elastic and plastic initial anisotropy of the two alloys is investigated by combining compression on cylinders with elliptical sections, uniaxial tensile tests in different material directions, plane strain and shear tests. The initial anisotropy of the different alloys is very weak which justifies the modeling of the mechanical behavior with an isotropic yield surface. The identified elastoviscoplastic model is validated by comparing experimental results with FE predictions both on cylindrical notched specimens subjected to tensile tests and onflat specimens subjected to plane strain conditions.Investigation of localized necking in substrate-supported metal layers: comparison of bifurcation and imperfection analyses
http://hdl.handle.net/10985/10047
Investigation of localized necking in substrate-supported metal layers: comparison of bifurcation and imperfection analyses
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
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, Farid 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.Micromechanics-Based Damage Analysis of Fracture in Ti5553 Alloy with Application to Bolted Sectors
http://hdl.handle.net/10985/10046
Micromechanics-Based Damage Analysis of Fracture in Ti5553 Alloy with Application to Bolted Sectors
BEN BETTAIEB, Mohamed; VAN HOOF, Thibaut; MINNEBO, Hans; PARDOEN, Thomas; DUFOUR, Philippe; JACQUES, Pascal J.; HABRAKEN, Anne-Marie
A physics-based, uncoupled damage model is calibrated using cylindrical notched round tensile specimens made of Ti5553 and Ti-6Al-4V alloys. The fracture strain of Ti5553 is lower than for Ti-6Al-4V in the full range of stress triaxiality. This lower ductility originates from a higher volume fraction of damage sites. By proper heat treatment, the fracture strain of Ti5553 increases by almost a factor of two, as a result of a larger damage nucleation stress. This result proves the potential for further optimization of the damage resistance of the Ti5553 alloy. The damage model is combined with an elastoviscoplastic law in order to predict failure in a wide range of loading conditions. In particular, a specific application involving bolted sectors is addressed in order to determine the potential of replacing the Ti-6Al-4V by the Ti5553 alloy.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/100462015-01-01T00:00:00ZBEN BETTAIEB, MohamedVAN HOOF, ThibautMINNEBO, HansPARDOEN, ThomasDUFOUR, PhilippeJACQUES, Pascal J.HABRAKEN, Anne-MarieA physics-based, uncoupled damage model is calibrated using cylindrical notched round tensile specimens made of Ti5553 and Ti-6Al-4V alloys. The fracture strain of Ti5553 is lower than for Ti-6Al-4V in the full range of stress triaxiality. This lower ductility originates from a higher volume fraction of damage sites. By proper heat treatment, the fracture strain of Ti5553 increases by almost a factor of two, as a result of a larger damage nucleation stress. This result proves the potential for further optimization of the damage resistance of the Ti5553 alloy. The damage model is combined with an elastoviscoplastic law in order to predict failure in a wide range of loading conditions. In particular, a specific application involving bolted sectors is addressed in order to determine the potential of replacing the Ti-6Al-4V by the Ti5553 alloy.A comparative study of Forming Limit Diagrams predicted by two different plasticity theories involving vertex effects
http://hdl.handle.net/10985/10048
A comparative study of Forming Limit Diagrams predicted by two different plasticity theories involving vertex effects
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
The main objective of this contribution is to compare the Forming Limit Diagrams (FLDs) predicted by the use of two different vertex theories. The first theory is micromechanical and is based on the use of the Schmid law, within the framework of crystal plasticity coupled with the Taylor scale-transition scheme. The second theory is phenomenological and is based on the deformation theory of plasticity. For both theories, the mechanical behavior is formulated in the finite strain framework and is assumed to be isotropic and rate-independent. The theoretical framework of these approaches will be presented in details. In the micro-macro modeling, the isotropy is ensured by considering an isotropic initial texture. In the phenomenological modeling, the material parameters are identified on the basis of micro-macro simulations of tensile tests.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/100482015-01-01T00:00:00ZAKPAMA, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, Farid The main objective of this contribution is to compare the Forming Limit Diagrams (FLDs) predicted by the use of two different vertex theories. The first theory is micromechanical and is based on the use of the Schmid law, within the framework of crystal plasticity coupled with the Taylor scale-transition scheme. The second theory is phenomenological and is based on the deformation theory of plasticity. For both theories, the mechanical behavior is formulated in the finite strain framework and is assumed to be isotropic and rate-independent. The theoretical framework of these approaches will be presented in details. In the micro-macro modeling, the isotropy is ensured by considering an isotropic initial texture. In the phenomenological modeling, the material parameters are identified on the basis of micro-macro simulations of tensile tests.Localized necking in elastomer-supported metal layers: impact of kinematic hardening
http://hdl.handle.net/10985/13556
Localized necking in elastomer-supported metal layers: impact of kinematic hardening
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
The present paper deals with localized necking in stretched metal sheets using the initial imperfection approach. The first objective is to study the effect of kinematic hardening on the formability of a freestanding metal layer. To this end, the behavior of the metal layer is assumed to follow the rigid-plastic rate-independent flow theory. The isotropic (resp. kinematic) hardening of this metal is modeled by the Hollomon (resp. Prager) law. A parametric study is carried out in order to investigate the effect of kinematic hardening on the formability limits. It is shown that the effect of kinematic hardening on the ductility limit is noticeably different depending on the strain path considered. The second aim of the paper is to analyze the effect of an elastomer substrate, perfectly bonded to the metal layer, on the formability of the whole bilayer. It is found that the addition of an elastomer layer substantially enhances the formability of the bilayer, in agreement with earlier studies.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/135562017-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, Farid The present paper deals with localized necking in stretched metal sheets using the initial imperfection approach. The first objective is to study the effect of kinematic hardening on the formability of a freestanding metal layer. To this end, the behavior of the metal layer is assumed to follow the rigid-plastic rate-independent flow theory. The isotropic (resp. kinematic) hardening of this metal is modeled by the Hollomon (resp. Prager) law. A parametric study is carried out in order to investigate the effect of kinematic hardening on the formability limits. It is shown that the effect of kinematic hardening on the ductility limit is noticeably different depending on the strain path considered. The second aim of the paper is to analyze the effect of an elastomer substrate, perfectly bonded to the metal layer, on the formability of the whole bilayer. It is found that the addition of an elastomer layer substantially enhances the formability of the bilayer, in agreement with earlier studies.Strain rate effects on localized necking in substrate-supported metal layers
http://hdl.handle.net/10985/13154
Strain rate effects on localized necking in substrate-supported metal layers
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
Due to their good mechanical and technological performances, thin substrate-supported metal layers are increasingly used as functional components in flexible electronic devices. Consequently, the prediction of necking, and the associated limit strains, for such components is of major academic and industrial importance. The current contribution aims to numerically investigate the respective and combined effects of strain rate sensitivity of the metal layer and the addition of an elastomer layer on localized necking in substrate-supported metal layers. To this end, strain ratedependent forms for the flow theory of plasticity and the deformation theory counterpart are used to describe the mechanical behavior of the metal layer. As to the substrate layer, it is made of elastomer material whose mechanical response is described by a neo-Hookean hyperelastic model. The two layers are assumed to be perfectly adhered. Necking limit strains are predicted by the Marciniak–Kuczynski (M–K) imperfection approach. Various numerical results, corresponding to freestanding metal layers as well as substrate-supported metal layers, are presented and extensively discussed in this paper. The significant effect of strain rate sensitivity on the retardation of localized necking is first emphasized. Then, the combined and positive influence of strain rate sensitivity of the metal layer and characteristics of the elastomer layer (thickness and stiffness) on the enhancement of the ductility of the whole bilayer is analyzed and discussed.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/131542017-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, Farid Due to their good mechanical and technological performances, thin substrate-supported metal layers are increasingly used as functional components in flexible electronic devices. Consequently, the prediction of necking, and the associated limit strains, for such components is of major academic and industrial importance. The current contribution aims to numerically investigate the respective and combined effects of strain rate sensitivity of the metal layer and the addition of an elastomer layer on localized necking in substrate-supported metal layers. To this end, strain ratedependent forms for the flow theory of plasticity and the deformation theory counterpart are used to describe the mechanical behavior of the metal layer. As to the substrate layer, it is made of elastomer material whose mechanical response is described by a neo-Hookean hyperelastic model. The two layers are assumed to be perfectly adhered. Necking limit strains are predicted by the Marciniak–Kuczynski (M–K) imperfection approach. Various numerical results, corresponding to freestanding metal layers as well as substrate-supported metal layers, are presented and extensively discussed in this paper. The significant effect of strain rate sensitivity on the retardation of localized necking is first emphasized. Then, the combined and positive influence of strain rate sensitivity of the metal layer and characteristics of the elastomer layer (thickness and stiffness) on the enhancement of the ductility of the whole bilayer is analyzed and discussed.Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms
http://hdl.handle.net/10985/13535
Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP).
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/135352016-01-01T00:00:00ZAKPAMA, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, Farid In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP).Theoretical and numerical investigation of the impact of out-of-plane compressive stress on sheet metal formability
http://hdl.handle.net/10985/11857
Theoretical and numerical investigation of the impact of out-of-plane compressive stress on sheet metal formability
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
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, Farid 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.