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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 18 Aug 2022 07:19:08 GMT2022-08-18T07:19:08ZPrediction of forming limits for porous materials using void-size dependent model and bifurcation approach
http://hdl.handle.net/10985/19659
Prediction of forming limits for porous materials using void-size dependent model and bifurcation approach
NASIR, Muhammad Waqar; CHALAL, Hocine; ABED-MERAIM, Farid
The scientific literature has shown the strong effect of void size on material response. Several yield functions have been developed to incorporate the void size effects in ductile porous materials. Based on the interface stresses of the membrane around a spherical void, a Gurson-type yield function, which includes void size effects, is coupled with the bifurcation theory for the prediction of plastic strain localization. The constitutive equations as well as the bifurcation-based localization criterion are implemented into the finite element code ABAQUS/Standard within the framework of large plastic deformations. The resulting numerical tool is applied to the prediction of forming limit diagrams (FLDs) for an aluminum material. The effect of void size on the prediction of FLDs is investigated. It is shown that smaller void sizes lead to an increase in the ductility limits of the material. This effect on the FLDs becomes more significant for high initial porosity, due to the increase of void-matrix interface strength within the material.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/196592020-01-01T00:00:00ZNASIR, Muhammad WaqarCHALAL, HocineABED-MERAIM, FaridThe scientific literature has shown the strong effect of void size on material response. Several yield functions have been developed to incorporate the void size effects in ductile porous materials. Based on the interface stresses of the membrane around a spherical void, a Gurson-type yield function, which includes void size effects, is coupled with the bifurcation theory for the prediction of plastic strain localization. The constitutive equations as well as the bifurcation-based localization criterion are implemented into the finite element code ABAQUS/Standard within the framework of large plastic deformations. The resulting numerical tool is applied to the prediction of forming limit diagrams (FLDs) for an aluminum material. The effect of void size on the prediction of FLDs is investigated. It is shown that smaller void sizes lead to an increase in the ductility limits of the material. This effect on the FLDs becomes more significant for high initial porosity, due to the increase of void-matrix interface strength within the material.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, FaridIn 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.Formability limit prediction of TRIP780 steel sheet using lode angle dependent gurson-based models with Thomason coalescence criterion and bifurcation analysis
http://hdl.handle.net/10985/20337
Formability limit prediction of TRIP780 steel sheet using lode angle dependent gurson-based models with Thomason coalescence criterion and bifurcation analysis
NASIR, Muhammad Waqar; CHALAL, Hocine; ABED-MERAIM, Farid
For biaxial stretching strain paths, which are typically encountered in sheet metal forming, the stress triaxiality ranges from 0.33 to 0.67. At this low level of triaxiality, voids change their shape from spherical to general spheroidal shape. In the literature, unit cell studies show the dependency of void shape on the lode parameter, especially at low stress triaxiality. Several authors also pointed out the influence of lode parameter on ductile failure. In the current study, lode parameter dependent Gurson-based models are combined with bifurcation analysis for the prediction of formability limits of TRIP780 steel sheet. Moreover, Thomason’s coalescence criterion is considered for the prediction of critical porosity. For the anisotropic plastic behavior of the dense material, the quadratic Hill’48 yield surface is considered. Contribution to porosity evolution due to shear mechanism is also analyzed. In addition, the effect of lode parameter on the prediction of forming limit diagram (FLD) is investigated. It is observed that the accelerated evolution of porosity, due to the consideration of lode parameter, induces lower ductility limits for the modified Gurson-based model, as compared to the original Gurson model. The results also demonstrate that the use of the Thomason coalescence criterion for the determination of critical porosity plays an important role in the prediction of FLDs, as compared to fixed critical porosity used in the Gurson-Tvergaard-Needleman model.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/203372019-01-01T00:00:00ZNASIR, Muhammad WaqarCHALAL, HocineABED-MERAIM, FaridFor biaxial stretching strain paths, which are typically encountered in sheet metal forming, the stress triaxiality ranges from 0.33 to 0.67. At this low level of triaxiality, voids change their shape from spherical to general spheroidal shape. In the literature, unit cell studies show the dependency of void shape on the lode parameter, especially at low stress triaxiality. Several authors also pointed out the influence of lode parameter on ductile failure. In the current study, lode parameter dependent Gurson-based models are combined with bifurcation analysis for the prediction of formability limits of TRIP780 steel sheet. Moreover, Thomason’s coalescence criterion is considered for the prediction of critical porosity. For the anisotropic plastic behavior of the dense material, the quadratic Hill’48 yield surface is considered. Contribution to porosity evolution due to shear mechanism is also analyzed. In addition, the effect of lode parameter on the prediction of forming limit diagram (FLD) is investigated. It is observed that the accelerated evolution of porosity, due to the consideration of lode parameter, induces lower ductility limits for the modified Gurson-based model, as compared to the original Gurson model. The results also demonstrate that the use of the Thomason coalescence criterion for the determination of critical porosity plays an important role in the prediction of FLDs, as compared to fixed critical porosity used in the Gurson-Tvergaard-Needleman model.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, FaridTo 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.