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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 20 May 2024 15:54:49 GMT2024-05-20T15:54:49ZDuctility 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.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.Prediction of necking in thin sheet metals using an elastic‒plastic model coupled with ductile damage and bifurcation criteria
http://hdl.handle.net/10985/17483
Prediction of necking in thin sheet metals using an elastic‒plastic model coupled with ductile damage and bifurcation criteria
BOUKTIR, Yasser; CHALAL, Hocine; ABED-MERAIM, Farid
In this paper, the conditions for the occurrence of diffuse and localized necking in thin sheet metals are investigated. The prediction of these necking phenomena is undertaken using an elastic‒plastic model coupled with ductile damage, which is then combined with various plastic instability criteria based on bifurcation theory. The bifurcation criteria are first formulated within a general three-dimensional modeling framework, and then specialized to the particular case of plane-stress conditions. Some theoretical relationships or links between the different investigated bifurcation criteria are established, which allows a hierarchical classification in terms of their conservative character in predicting critical necking strains. The resulting numerical tool is implemented into the finite element code ABAQUS/Standard to predict forming limit diagrams (FLDs), in both situations of a fully three-dimensional formulation and a plane-stress framework. The proposed approach is then applied to the prediction of diffuse and localized necking for a DC06 mild steel material. The predicted FLDs confirm the above-established theoretical classification, revealing that the general bifurcation criterion provides a lower bound for diffuse necking prediction, while the loss of ellipticity criterion represents an upper bound for localized necking prediction. Some numerical aspects related to the prestrain effect on the development of necking are also investigated, which demonstrates the capability of the present approach in capturing the strain-path changes commonly encountered in complex sheet metal forming operations.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/174832018-01-01T00:00:00ZBOUKTIR, YasserCHALAL, HocineABED-MERAIM, Farid In this paper, the conditions for the occurrence of diffuse and localized necking in thin sheet metals are investigated. The prediction of these necking phenomena is undertaken using an elastic‒plastic model coupled with ductile damage, which is then combined with various plastic instability criteria based on bifurcation theory. The bifurcation criteria are first formulated within a general three-dimensional modeling framework, and then specialized to the particular case of plane-stress conditions. Some theoretical relationships or links between the different investigated bifurcation criteria are established, which allows a hierarchical classification in terms of their conservative character in predicting critical necking strains. The resulting numerical tool is implemented into the finite element code ABAQUS/Standard to predict forming limit diagrams (FLDs), in both situations of a fully three-dimensional formulation and a plane-stress framework. The proposed approach is then applied to the prediction of diffuse and localized necking for a DC06 mild steel material. The predicted FLDs confirm the above-established theoretical classification, revealing that the general bifurcation criterion provides a lower bound for diffuse necking prediction, while the loss of ellipticity criterion represents an upper bound for localized necking prediction. Some numerical aspects related to the prestrain effect on the development of necking are also investigated, which demonstrates the capability of the present approach in capturing the strain-path changes commonly encountered in complex sheet metal forming operations.Efficient solid–shell finite elements for quasi-static and dynamic analyses and their application to sheet metal forming simulation
http://hdl.handle.net/10985/10006
Efficient solid–shell finite elements for quasi-static and dynamic analyses and their application to sheet metal forming simulation
WANG, Peng; CHALAL, Hocine; ABED-MERAIM, Farid
Thin structures are commonly designed and employedin engineering industries to save material, reduce weight and improve the overall performance of products. The finite element (FE) simulation of such thin structural components has become a powerful and useful tool in this field. For the last few decades, much attention and effort have been paid to establish accurate and efficient FE. In this regard, the solid–shell concept proved to be very attractive due to its multiple advantages. Several treatments are additionally applied to the formulation of solid–shell elements to avoid all locking phenomena and to guarantee the accuracy and efficiency during the simulation of thin structures. The current contribution presents a family of prismatic and hexahedral assumed-strain based solid–shell elements, in which an arbitrary number of integration points are distributed along the thickness direction. Both linear and quadratic formulations of the solid–shell family elements are implemented into ABAQUS static/implicit and dynamic/explicit software to model thin 3D problems with only a single layer through the thickness. Twopopular benchmark tests are first conducted, in both static and dynamic analyses, for validation purposes. Then, attention is focused on a complex sheet metal forming process involving large strain,plasticity and contact.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/100062015-01-01T00:00:00ZWANG, PengCHALAL, HocineABED-MERAIM, Farid Thin structures are commonly designed and employedin engineering industries to save material, reduce weight and improve the overall performance of products. The finite element (FE) simulation of such thin structural components has become a powerful and useful tool in this field. For the last few decades, much attention and effort have been paid to establish accurate and efficient FE. In this regard, the solid–shell concept proved to be very attractive due to its multiple advantages. Several treatments are additionally applied to the formulation of solid–shell elements to avoid all locking phenomena and to guarantee the accuracy and efficiency during the simulation of thin structures. The current contribution presents a family of prismatic and hexahedral assumed-strain based solid–shell elements, in which an arbitrary number of integration points are distributed along the thickness direction. Both linear and quadratic formulations of the solid–shell family elements are implemented into ABAQUS static/implicit and dynamic/explicit software to model thin 3D problems with only a single layer through the thickness. Twopopular benchmark tests are first conducted, in both static and dynamic analyses, for validation purposes. Then, attention is focused on a complex sheet metal forming process involving large strain,plasticity and contact.Formability prediction using bifurcation criteria and GTN damage model
http://hdl.handle.net/10985/20267
Formability prediction using bifurcation criteria and GTN damage model
NASIR, Muhammad Waqar; CHALAL, Hocine; ABED-MERAIM, Farid
In this paper, four plastic instability criteria, which are based on the bifurcation theory, are coupled with the GTN damage model for the prediction of diffuse and localized necking. General bifurcation (GB) criterion and limit-point bifurcation (LPB) criterion are used to predict diffuse necking, while loss of ellipticity (LOE) criterion and loss of strong ellipticity (LOSE) criterion are used to predict localized necking. The resulting constitutive equations and instability criteria are implemented into the finite element code ABAQUS/Standard. The constitutive equations are formulated within the framework of large deformations and fully three-dimensional approach. Since the developed numerical tools have intended applications mainly for thin sheet metals; therefore, the plane-stress conditions are considered within the instability criteria. The present contribution focuses on the effect of destabilizing mechanisms, due to non-associative plasticity and non-normal plastic flow rule, on the prediction of forming limit diagrams (FLDs). Theoretical classification of the bifurcation criteria, in terms of their order of prediction of critical necking strains, is first presented. Then, several variants of the GTN model are combined with the bifurcation criteria for the prediction of FLDs for fictitious materials. It is shown that the hierarchical prediction order of the different instability criteria is consistent with the theoretical classification, for all the considered variants of the GTN model. More specifically, it is shown that the GB criterion provides a lower bound to all bifurcation criteria, in terms of necking prediction, while the LOE criterion represents an upper bound.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/202672021-01-01T00:00:00ZNASIR, Muhammad WaqarCHALAL, HocineABED-MERAIM, Farid In this paper, four plastic instability criteria, which are based on the bifurcation theory, are coupled with the GTN damage model for the prediction of diffuse and localized necking. General bifurcation (GB) criterion and limit-point bifurcation (LPB) criterion are used to predict diffuse necking, while loss of ellipticity (LOE) criterion and loss of strong ellipticity (LOSE) criterion are used to predict localized necking. The resulting constitutive equations and instability criteria are implemented into the finite element code ABAQUS/Standard. The constitutive equations are formulated within the framework of large deformations and fully three-dimensional approach. Since the developed numerical tools have intended applications mainly for thin sheet metals; therefore, the plane-stress conditions are considered within the instability criteria. The present contribution focuses on the effect of destabilizing mechanisms, due to non-associative plasticity and non-normal plastic flow rule, on the prediction of forming limit diagrams (FLDs). Theoretical classification of the bifurcation criteria, in terms of their order of prediction of critical necking strains, is first presented. Then, several variants of the GTN model are combined with the bifurcation criteria for the prediction of FLDs for fictitious materials. It is shown that the hierarchical prediction order of the different instability criteria is consistent with the theoretical classification, for all the considered variants of the GTN model. More specifically, it is shown that the GB criterion provides a lower bound to all bifurcation criteria, in terms of necking prediction, while the LOE criterion represents an upper bound.Numerical Predictions of the Occurrence of Necking in Deep Drawing Processes
http://hdl.handle.net/10985/17482
Numerical Predictions of the Occurrence of Necking in Deep Drawing Processes
CHALAL, Hocine; ABED-MERAIM, Farid
In this work, three numerical necking criteria based on finite element (FE) simulations are proposed for the prediction of forming limit diagrams (FLDs) for sheet metals. An elastic–plastic constitutive model coupled with the Lemaitre continuum damage theory has been implemented into the ABAQUS/Explicit software to simulate simple sheet stretching tests as well as Erichsen deep drawing tests with various sheet specimen geometries. Three numerical criteria have been investigated in order to establish an appropriate necking criterion for the prediction of formability limits. The first numerical criterion is based on the analysis of the thickness strain evolution in the central part of the specimens. The second numerical criterion is based on the analysis of the second time derivative of the thickness strain. As to the third numerical criterion, it relies on a damage threshold associated with the occurrence of necking. The FLDs thus predicted by numerical simulation of simple sheet stretching with various specimen geometries and Erichsen deep drawing tests are compared with the experimental results.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/174822017-01-01T00:00:00ZCHALAL, HocineABED-MERAIM, Farid In this work, three numerical necking criteria based on finite element (FE) simulations are proposed for the prediction of forming limit diagrams (FLDs) for sheet metals. An elastic–plastic constitutive model coupled with the Lemaitre continuum damage theory has been implemented into the ABAQUS/Explicit software to simulate simple sheet stretching tests as well as Erichsen deep drawing tests with various sheet specimen geometries. Three numerical criteria have been investigated in order to establish an appropriate necking criterion for the prediction of formability limits. The first numerical criterion is based on the analysis of the thickness strain evolution in the central part of the specimens. The second numerical criterion is based on the analysis of the second time derivative of the thickness strain. As to the third numerical criterion, it relies on a damage threshold associated with the occurrence of necking. The FLDs thus predicted by numerical simulation of simple sheet stretching with various specimen geometries and Erichsen deep drawing tests are compared with the experimental results.Vibration modeling of sandwich structures using solid-shell finite elements
http://hdl.handle.net/10985/10109
Vibration modeling of sandwich structures using solid-shell finite elements
KPEKY, Fessal; BOUDAOUD, Hakim; DAYA, El Mostafa; CHALAL, Hocine; ABED-MERAIM, Farid
The aim of this work is to propose a new finite element modeling for vibration of sandwich structures with soft core. Indeed, several approaches have been adopted in the literature to accurately model these types of structures, but show some limitations in certain configurations of high contrast of material properties or geometric aspect ratios between the different layers. In these situations, it is generally well-known that the use of higher-order or three-dimensional finite elements is more appropriate, but will generate a large number of degrees of freedom, and thereby, large CPU times. In this work, an alternative method is followed by considering the linear hexahedral solid-shell element previously developed by Abed-Meraim and Combescure [1]. This element is implemented into the commercial software ABAQUS Via a User Element (UEL) subroutine. Numerical tests on various cantilever sandwich beams are performed to show the efficiency of this approach.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/101092014-01-01T00:00:00ZKPEKY, FessalBOUDAOUD, HakimDAYA, El MostafaCHALAL, HocineABED-MERAIM, Farid The aim of this work is to propose a new finite element modeling for vibration of sandwich structures with soft core. Indeed, several approaches have been adopted in the literature to accurately model these types of structures, but show some limitations in certain configurations of high contrast of material properties or geometric aspect ratios between the different layers. In these situations, it is generally well-known that the use of higher-order or three-dimensional finite elements is more appropriate, but will generate a large number of degrees of freedom, and thereby, large CPU times. In this work, an alternative method is followed by considering the linear hexahedral solid-shell element previously developed by Abed-Meraim and Combescure [1]. This element is implemented into the commercial software ABAQUS Via a User Element (UEL) subroutine. Numerical tests on various cantilever sandwich beams are performed to show the efficiency of this approach.Determination of forming limit diagrams based on ductile damage models and necking criteria
http://hdl.handle.net/10985/17475
Determination of forming limit diagrams based on ductile damage models and necking criteria
CHALAL, Hocine; ABED-MERAIM, Farid
In this paper, forming limit diagrams (FLDs) for an aluminum alloy are predicted through numerical simulations using various localized necking criteria. A comparative study is conducted for the FLDs determined by using the Lemaitre damage approach and those obtained with the modified Gurson–Tvergaard–Needleman (GTN) damage model. To this end, both damage models coupled with elasto-plasticity and accounting for plastic anisotropy have been implemented into the ABAQUS/Explicit software, through the user-defined subroutine VUMAT, within the framework of large plastic strains and a fully three-dimensional formulation. The resulting constitutive frameworks are then combined with four localized necking criteria to predict the limit strains for an AA6016-T4 aluminum alloy. Three of these necking criteria are based on finite element (FE) simulations of the Nakazima deep drawing test with various specimen geometries, while the fourth criterion is based on bifurcation theory. The simulation results reveal that the limit strains predicted by local criteria, which are based on FE simulations of the Nakazima test, are in good agreement with the experiments for a number of strain paths, while those obtained with the bifurcation analysis provide an upper bound to the experimental FLD.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/174752017-01-01T00:00:00ZCHALAL, HocineABED-MERAIM, Farid In this paper, forming limit diagrams (FLDs) for an aluminum alloy are predicted through numerical simulations using various localized necking criteria. A comparative study is conducted for the FLDs determined by using the Lemaitre damage approach and those obtained with the modified Gurson–Tvergaard–Needleman (GTN) damage model. To this end, both damage models coupled with elasto-plasticity and accounting for plastic anisotropy have been implemented into the ABAQUS/Explicit software, through the user-defined subroutine VUMAT, within the framework of large plastic strains and a fully three-dimensional formulation. The resulting constitutive frameworks are then combined with four localized necking criteria to predict the limit strains for an AA6016-T4 aluminum alloy. Three of these necking criteria are based on finite element (FE) simulations of the Nakazima deep drawing test with various specimen geometries, while the fourth criterion is based on bifurcation theory. The simulation results reveal that the limit strains predicted by local criteria, which are based on FE simulations of the Nakazima test, are in good agreement with the experiments for a number of strain paths, while those obtained with the bifurcation analysis provide an upper bound to the experimental FLD.Finite element simulation of sheet metal forming processes using non-quadratic anisotropic plasticity models and solid-Shell finite elements
http://hdl.handle.net/10985/20268
Finite element simulation of sheet metal forming processes using non-quadratic anisotropic plasticity models and solid-Shell finite elements
YOUNAS, Nabeel; CHALAL, Hocine; ABED-MERAIM, Farid
During the last decades, a family of assumed-strain solid-shell finite elements has been developed with enriched benefits of solid and shell finite elements together with special treatments to avoid locking phenomena. These elements have been shown to be efficient in numerical simulation of thin 3D structures with various constitutive models. The current contribution consists in the combination of the developed linear and quadratic solid-shell elements with complex anisotropic plasticity models for aluminum alloys. Conventional quadratic anisotropic yield functions are associated with less accuracy in the simulation of forming processes with metallic materials involving strong anisotropy. For these materials, the plastic anisotropy can be modeled more accurately using advanced non-quadratic yield functions, such as the anisotropic yield criteria proposed by Barlat for aluminum alloys. In this work, various quadratic and non-quadratic anisotropic yield functions are combined with a linear eight-node hexahedral solid-shell element and a linear six-node prismatic solid-shell element, and their quadratic counterparts. The resulting solid-shell elements are implemented into the ABAQUS software for the simulation of benchmark deep drawing process of a cylindrical cup. The predicted results are assessed and compared to experimental ones taken from the literature. Compared to the use of conventional quadratic anisotropic yield functions, the results given by the combination of the developed solid-shell elements with non-quadratic anisotropic yield functions show good agreement with experiments.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/202682020-01-01T00:00:00ZYOUNAS, NabeelCHALAL, HocineABED-MERAIM, Farid During the last decades, a family of assumed-strain solid-shell finite elements has been developed with enriched benefits of solid and shell finite elements together with special treatments to avoid locking phenomena. These elements have been shown to be efficient in numerical simulation of thin 3D structures with various constitutive models. The current contribution consists in the combination of the developed linear and quadratic solid-shell elements with complex anisotropic plasticity models for aluminum alloys. Conventional quadratic anisotropic yield functions are associated with less accuracy in the simulation of forming processes with metallic materials involving strong anisotropy. For these materials, the plastic anisotropy can be modeled more accurately using advanced non-quadratic yield functions, such as the anisotropic yield criteria proposed by Barlat for aluminum alloys. In this work, various quadratic and non-quadratic anisotropic yield functions are combined with a linear eight-node hexahedral solid-shell element and a linear six-node prismatic solid-shell element, and their quadratic counterparts. The resulting solid-shell elements are implemented into the ABAQUS software for the simulation of benchmark deep drawing process of a cylindrical cup. The predicted results are assessed and compared to experimental ones taken from the literature. Compared to the use of conventional quadratic anisotropic yield functions, the results given by the combination of the developed solid-shell elements with non-quadratic anisotropic yield functions show good agreement with experiments.Formability prediction of ductile materials using a non-associative plasticity model and bifurcation-based criteria
http://hdl.handle.net/10985/20341
Formability prediction of ductile materials using a non-associative plasticity model and bifurcation-based criteria
BOUKTIR, Yasser; CHALAL, Hocine; ABED-MERAIM, Farid
Plastic instabilities such as diffuse or localized necking may occur during sheet metal forming processes, thus limiting sheet metal formability, which is detrimental to industry. The formability of sheet metals is usually characterized by the concept of forming limit diagram (FLD), which was first proposed by Keeler and Backofen and Goodwin . The FLD reports combinations of in-plane major and minor strains, thus delimiting the plane into two zones: a safe zone and a critical one located above the FLD. It remains however that the experimental determination of FLDs is difficult, time consuming and involving non-negligible costs. To overcome these drawbacks, significant efforts have been devoted in the literature to develop theoretical criteria able to predict the formability limits of sheet metals, which are associated with the occurrence of diffuse or localized necking. For reliable predictions of sheet metal formability, one of the requirements is to develop an integrated approach coupling advanced constitutive models, capable of accurately reproducing the key physical phenomena that occur during forming processes, with theoretically well-founded necking criteria. In this work, a non-associative elastic‒plastic model, with Hill'48 anisotropic plastic yield surface, is coupled with the continuum damage mechanics theory based on the Lemaitre isotropic damage model. The resulting constitutive model is then combined with four bifurcation-based criteria, namely: General Bifurcation (GB) and Limit-Point Bifurcation (LPB) , for the prediction of diffuse necking, and Loss of Ellipticity (LE) and Loss of Strong Ellipticity (LSE), for the prediction of localized necking. The complete approach is implemented into the finite element code ABAQUS/Standard, within the framework of large strains and plane-stress conditions. A comparative study of the above bifurcation criteria is carried out on a mild steel, in order to classify them with respect to their order of prediction of critical necking strains.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/203412016-01-01T00:00:00ZBOUKTIR, YasserCHALAL, HocineABED-MERAIM, Farid Plastic instabilities such as diffuse or localized necking may occur during sheet metal forming processes, thus limiting sheet metal formability, which is detrimental to industry. The formability of sheet metals is usually characterized by the concept of forming limit diagram (FLD), which was first proposed by Keeler and Backofen and Goodwin . The FLD reports combinations of in-plane major and minor strains, thus delimiting the plane into two zones: a safe zone and a critical one located above the FLD. It remains however that the experimental determination of FLDs is difficult, time consuming and involving non-negligible costs. To overcome these drawbacks, significant efforts have been devoted in the literature to develop theoretical criteria able to predict the formability limits of sheet metals, which are associated with the occurrence of diffuse or localized necking. For reliable predictions of sheet metal formability, one of the requirements is to develop an integrated approach coupling advanced constitutive models, capable of accurately reproducing the key physical phenomena that occur during forming processes, with theoretically well-founded necking criteria. In this work, a non-associative elastic‒plastic model, with Hill'48 anisotropic plastic yield surface, is coupled with the continuum damage mechanics theory based on the Lemaitre isotropic damage model. The resulting constitutive model is then combined with four bifurcation-based criteria, namely: General Bifurcation (GB) and Limit-Point Bifurcation (LPB) , for the prediction of diffuse necking, and Loss of Ellipticity (LE) and Loss of Strong Ellipticity (LSE), for the prediction of localized necking. The complete approach is implemented into the finite element code ABAQUS/Standard, within the framework of large strains and plane-stress conditions. A comparative study of the above bifurcation criteria is carried out on a mild steel, in order to classify them with respect to their order of prediction of critical necking strains.