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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, 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.Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach
http://hdl.handle.net/10985/11915
Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
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, Holanyo K.BEN 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.Influence of the Non-Schmid Effects on the Ductility Limit of Polycrystalline Sheet Metals
http://hdl.handle.net/10985/13534
Influence of the Non-Schmid Effects on the Ductility Limit of Polycrystalline Sheet Metals
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
The yield criterion in rate-independent single crystal plasticity is most often defined by the classical Schmid law. However, various experimental studies have shown that the plastic flow of several single crystals (especially with Body Centered Cubic crystallographic structure) often exhibits some non-Schmid effects. The main objective of the current contribution is to study the impact of these non-Schmid effects on the ductility limit of polycrystalline sheet metals. To this end, the Taylor multiscale scheme is used to determine the mechanical behavior of a volume element that is assumed to be representative of the sheet metal. The mechanical behavior of the single crystals is described by a finite strain rate-independent constitutive theory, where some non-Schmid effects are accounted for in the modeling of the plastic flow. The bifurcation theory is coupled with the Taylor multiscale scheme to predict the onset of localized necking in the polycrystalline aggregate. The impact of the considered non-Schmid effects on both the single crystal behavior and the polycrystal behavior is carefully analyzed. It is shown, in particular, that non-Schmid effects tend to precipitate the occurrence of localized necking in polycrystalline aggregates and they slightly influence the orientation of the localization band.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/135342018-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, FaridThe yield criterion in rate-independent single crystal plasticity is most often defined by the classical Schmid law. However, various experimental studies have shown that the plastic flow of several single crystals (especially with Body Centered Cubic crystallographic structure) often exhibits some non-Schmid effects. The main objective of the current contribution is to study the impact of these non-Schmid effects on the ductility limit of polycrystalline sheet metals. To this end, the Taylor multiscale scheme is used to determine the mechanical behavior of a volume element that is assumed to be representative of the sheet metal. The mechanical behavior of the single crystals is described by a finite strain rate-independent constitutive theory, where some non-Schmid effects are accounted for in the modeling of the plastic flow. The bifurcation theory is coupled with the Taylor multiscale scheme to predict the onset of localized necking in the polycrystalline aggregate. The impact of the considered non-Schmid effects on both the single crystal behavior and the polycrystal behavior is carefully analyzed. It is shown, in particular, that non-Schmid effects tend to precipitate the occurrence of localized necking in polycrystalline aggregates and they slightly influence the orientation of the localization band.Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database
http://hdl.handle.net/10985/13136
Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database
GUPTA, Akash; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid; KALIDINDI, Surya
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).Numerical investigation of the combined effects of curvature and normal stress on sheet metal formability
http://hdl.handle.net/10985/13175
Numerical investigation of the combined effects of curvature and normal stress on sheet metal formability
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid; LEMOINE, Xavier
A number of parts and components involved in the automotive industry are made of thin bent sheets, which are subjected to out-of-plane compressive stresses in addition to traditional in-plane stresses. Unfortunately, the classical predictions based on the conventional concept of Forming Limit Diagram (FLD) are no longer relevant when the strain distribution is heterogonous over the sheet thickness. Therefore, this conventional FLD concept is not capable of accounting for the effect of out-of-plane stresses on the onset of localized necking. The aim of the present contribution is to propose an extension of the well-known Marciniak–Kuczynski approach to simultaneously account for the effect of curvature and normal stress on formability prediction. The new developed tool allows predicting the limit strains for the whole range of strain paths. The mechanical behavior of the studied sheets follows the rigid–plastic flow theory. Through numerical results, it is shown that both curvature and normal stress tend to increase the formability limit of the sheet metal.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/131752017-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, FaridLEMOINE, XavierA number of parts and components involved in the automotive industry are made of thin bent sheets, which are subjected to out-of-plane compressive stresses in addition to traditional in-plane stresses. Unfortunately, the classical predictions based on the conventional concept of Forming Limit Diagram (FLD) are no longer relevant when the strain distribution is heterogonous over the sheet thickness. Therefore, this conventional FLD concept is not capable of accounting for the effect of out-of-plane stresses on the onset of localized necking. The aim of the present contribution is to propose an extension of the well-known Marciniak–Kuczynski approach to simultaneously account for the effect of curvature and normal stress on formability prediction. The new developed tool allows predicting the limit strains for the whole range of strain paths. The mechanical behavior of the studied sheets follows the rigid–plastic flow theory. Through numerical results, it is shown that both curvature and normal stress tend to increase the formability limit of the sheet metal.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, FaridIn 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).Influence of the Yield Surface Curvature on the Forming Limit Diagrams Predicted by Crystal Plasticity Theory
http://hdl.handle.net/10985/11189
Influence of the Yield Surface Curvature on the Forming Limit Diagrams Predicted by Crystal Plasticity Theory
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
The aim of this paper is to investigate the impact of the microscopic yield surface (i.e., at the single crystal scale) on the forming limit diagrams (FLDs) of face centred cubic (FCC) materials. To predict these FLDs, the bifurcation approach is used within the framework of rate-independent crystal plasticity theory. For this purpose, two micromechanical models are developed and implemented. The first one uses the classical Schmid law, which results in the formation of vertices (or corners) at the yield surface, while the second is based on regularization of the Schmid law, which induces rounded corners at the yield surface. In both cases, the overall macroscopic behavior is derived from the behavior of the microscopic constituents (the single crystals) by using two different scale-transition schemes: the selfconsistent approach and the Taylor model. The simulation results show that the use of the classical Schmid law allows predicting localized necking at realistic strain levels for the whole range of strain paths that span the FLD. However, the application of a regularized Schmid law results in much higher limit strains in the range of negative strain paths. Moreover, rounding the yield surface vertices through regularization of the Schmid law leads to unrealistically high limit strains in the range of positive strain paths.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/111892016-01-01T00:00:00ZAKPAMA, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, FaridThe aim of this paper is to investigate the impact of the microscopic yield surface (i.e., at the single crystal scale) on the forming limit diagrams (FLDs) of face centred cubic (FCC) materials. To predict these FLDs, the bifurcation approach is used within the framework of rate-independent crystal plasticity theory. For this purpose, two micromechanical models are developed and implemented. The first one uses the classical Schmid law, which results in the formation of vertices (or corners) at the yield surface, while the second is based on regularization of the Schmid law, which induces rounded corners at the yield surface. In both cases, the overall macroscopic behavior is derived from the behavior of the microscopic constituents (the single crystals) by using two different scale-transition schemes: the selfconsistent approach and the Taylor model. The simulation results show that the use of the classical Schmid law allows predicting localized necking at realistic strain levels for the whole range of strain paths that span the FLD. However, the application of a regularized Schmid law results in much higher limit strains in the range of negative strain paths. Moreover, rounding the yield surface vertices through regularization of the Schmid law leads to unrealistically high limit strains in the range of positive strain paths.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.Ductility prediction of substrate-supported metal layers based on rate-independent crystal plasticity theory
http://hdl.handle.net/10985/13135
Ductility prediction of substrate-supported metal layers based on rate-independent crystal plasticity theory
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
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.Combined effect of damage and plastic anisotropy on the ductility limit of thin metal sheets
http://hdl.handle.net/10985/11234
Combined effect of damage and plastic anisotropy on the ductility limit of thin metal sheets
MSOLLI, Sabeur; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
It is well known that both damage and plastic anisotropy strongly affect the ductility limit of thin metal sheets. Due to the manufacturing processes, initial defects, such as inclusions and voids, are commonly present in the produced sheet metals. Plastic anisotropy is a direct outcome of the rolling process, where the resulting metal sheets exhibit preferred crystallographic orientations or strong texture. In the present study, the combined effect of plastic anisotropy and damage on localized necking is numerically investigated and analyzed. To this aim, an improved version of the Gurson-Tvergaard-Needleman (GTN) constitutive framework is used to model the mechanical behavior of the studied sheet. This version, which is an extension of the original GTN model, incorporates Hill’s anisotropic yield function to take into account the plastic anisotropy of the matrix material. Particular attention is devoted to the derivation of the analytical tangent modulus associated with this constitutive model. This extended GTN model is successfully coupled with bifurcation theory to predict sheet metal ductility limits, which are represented in terms of forming limit diagrams (FLDs). The effect of some material parameters (e.g.,anisotropy parameters of the metallic matrix) on the shape and the location of the predicted FLDs is then investigated and discussed through numerical simulations.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/112342016-01-01T00:00:00ZMSOLLI, SabeurBEN BETTAIEB, MohamedABED-MERAIM, FaridIt is well known that both damage and plastic anisotropy strongly affect the ductility limit of thin metal sheets. Due to the manufacturing processes, initial defects, such as inclusions and voids, are commonly present in the produced sheet metals. Plastic anisotropy is a direct outcome of the rolling process, where the resulting metal sheets exhibit preferred crystallographic orientations or strong texture. In the present study, the combined effect of plastic anisotropy and damage on localized necking is numerically investigated and analyzed. To this aim, an improved version of the Gurson-Tvergaard-Needleman (GTN) constitutive framework is used to model the mechanical behavior of the studied sheet. This version, which is an extension of the original GTN model, incorporates Hill’s anisotropic yield function to take into account the plastic anisotropy of the matrix material. Particular attention is devoted to the derivation of the analytical tangent modulus associated with this constitutive model. This extended GTN model is successfully coupled with bifurcation theory to predict sheet metal ductility limits, which are represented in terms of forming limit diagrams (FLDs). The effect of some material parameters (e.g.,anisotropy parameters of the metallic matrix) on the shape and the location of the predicted FLDs is then investigated and discussed through numerical simulations.