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Farid Abed-meraim - One of the best experts on this subject based on the ideXlab platform.
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Formability prediction of substrate-supported metal layers using a non-associated plastic flow rule
Journal of Materials Processing Technology, 2020Co-Authors: Mohamed Ben Bettaieb, Farid Abed-meraimAbstract:When manufacturing flexible devices, it is quite common that Localized Necking appears due to the low ductility of the metal sheets used. To delay the inception of such Localized Necking, several industrial companies have proposed a promising technical solution based on the bonding of elastomer substrates to the metal sheets used in the manufacturing processes. In this context, the comprehensive numerical understanding of the impact of such substrate coating on the improvement of the ductility of elastomer-supported metal layers still remains a challenging goal. To achieve this goal, the bifurcation approach as well as the Marciniak and Kuczynski model are used to predict the occurrence of Localized Necking. The mechanical behavior of the metal layer is modeled by a non-associated anisotropic plasticity model. The adoption of non-associated plastic flow rule allows separating the description of the plastic potential from that of the yield function, which is essential to accurately model strong plastic anisotropy characterizing cold-rolled sheets. As to the elastomer substrate, its mechanical behavior is described by a neo-Hookean law. The paper presents a variety of numerical results relating to the prediction of plastic strain localization in both freestanding and elastomercoated metal layers. The effects of the non-associativity of the plastic flow rule for the metal layer and the addition of an elastomer substrate on the predictions of Localized Necking are especially underlined. It is shown that the ductility limits predicted by the non-associated elasto-plastic model are lower than their counterparts determined by an associated plasticity model. It is also proven that adhering an elastomer layer to the metal layer can substantially delay the initiation of plastic strain localization.
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Prediction of Necking in HCP sheet metals using a two-surface plasticity model
International Journal of Plasticity, 2019Co-Authors: Mohamed Yassine Jedidi, Farid Abed-meraim, Mohamed Ben Bettaieb, Mohamed Taoufik Khabou, Anas Bouguecha, Mohamed HaddarAbstract:In the present contribution, a two-surface plasticity model is coupled with several diffuse and Localized Necking criteria to predict the ductility limits of hexagonal closed packed sheet metals. The plastic strain is considered, in this two-surface constitutive framework, as the result of both slip and twinning deformation modes. This leads to a description of the plastic anisotropy by two separate yield functions: the Barlat yield function to model plastic anisotropy due to slip deformation modes, and the Cazacu yield function to model plastic anisotropy due to twinning deformation modes. Actually, the proposed two-surface model offers an accurate prediction of the plastic anisotropy as well as the tension–compression yield asymmetry for the material response. Furthermore, the current model allows incorporating the effect of distortional hardening resulting from the evolution of plastic anisotropy and tension–compression yield asymmetry. Diffuse Necking is predicted by the general bifurcation criterion. As to Localized Necking, it is determined by the Rice bifurcation criterion as well as by the Marciniak & Kuczynski imperfection approach. To apply both bifurcation criteria, the expression of the continuum tangent modulus associated with this constitutive framework is analytically derived. The set of equations resulting from the coupling between the Marciniak & Kuczynski approach and the constitutive relations is solved by developing an efficient implicit algorithm. The numerical implementation of the two-surface model is assessed and validated through a comparative study between our numerical predictions and several experimental results from the literature. A sensitivity study is presented to analyze the effect of some mechanical parameters on the prediction of diffuse and Localized Necking in thin sheet metals made of HCP materials. The effect of distortional hardening on the onset of plastic instability is also investigated.
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Prediction of Necking in thin sheet metals using an elastic‒plastic model coupled with ductile damage and bifurcation criteria
International Journal of Damage Mechanics, 2018Co-Authors: Yasser Bouktir, Hocine Chalal, Farid Abed-meraimAbstract: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.
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Ductility prediction of substrate-supported metal layers based on rate-independent crystal plasticity theory
International Journal of Material Forming, 2018Co-Authors: Mohamed Ben Bettaieb, Farid Abed-meraimAbstract: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.
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Influence of the Non-Schmid Effects on the Ductility Limit of Polycrystalline Sheet Metals
Materials, 2018Co-Authors: Mohamed Ben Bettaieb, Farid Abed-meraimAbstract: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.
Mohamed Ben Bettaieb - One of the best experts on this subject based on the ideXlab platform.
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Formability prediction of substrate-supported metal layers using a non-associated plastic flow rule
Journal of Materials Processing Technology, 2020Co-Authors: Mohamed Ben Bettaieb, Farid Abed-meraimAbstract:When manufacturing flexible devices, it is quite common that Localized Necking appears due to the low ductility of the metal sheets used. To delay the inception of such Localized Necking, several industrial companies have proposed a promising technical solution based on the bonding of elastomer substrates to the metal sheets used in the manufacturing processes. In this context, the comprehensive numerical understanding of the impact of such substrate coating on the improvement of the ductility of elastomer-supported metal layers still remains a challenging goal. To achieve this goal, the bifurcation approach as well as the Marciniak and Kuczynski model are used to predict the occurrence of Localized Necking. The mechanical behavior of the metal layer is modeled by a non-associated anisotropic plasticity model. The adoption of non-associated plastic flow rule allows separating the description of the plastic potential from that of the yield function, which is essential to accurately model strong plastic anisotropy characterizing cold-rolled sheets. As to the elastomer substrate, its mechanical behavior is described by a neo-Hookean law. The paper presents a variety of numerical results relating to the prediction of plastic strain localization in both freestanding and elastomercoated metal layers. The effects of the non-associativity of the plastic flow rule for the metal layer and the addition of an elastomer substrate on the predictions of Localized Necking are especially underlined. It is shown that the ductility limits predicted by the non-associated elasto-plastic model are lower than their counterparts determined by an associated plasticity model. It is also proven that adhering an elastomer layer to the metal layer can substantially delay the initiation of plastic strain localization.
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Prediction of Necking in HCP sheet metals using a two-surface plasticity model
International Journal of Plasticity, 2019Co-Authors: Mohamed Yassine Jedidi, Farid Abed-meraim, Mohamed Ben Bettaieb, Mohamed Taoufik Khabou, Anas Bouguecha, Mohamed HaddarAbstract:In the present contribution, a two-surface plasticity model is coupled with several diffuse and Localized Necking criteria to predict the ductility limits of hexagonal closed packed sheet metals. The plastic strain is considered, in this two-surface constitutive framework, as the result of both slip and twinning deformation modes. This leads to a description of the plastic anisotropy by two separate yield functions: the Barlat yield function to model plastic anisotropy due to slip deformation modes, and the Cazacu yield function to model plastic anisotropy due to twinning deformation modes. Actually, the proposed two-surface model offers an accurate prediction of the plastic anisotropy as well as the tension–compression yield asymmetry for the material response. Furthermore, the current model allows incorporating the effect of distortional hardening resulting from the evolution of plastic anisotropy and tension–compression yield asymmetry. Diffuse Necking is predicted by the general bifurcation criterion. As to Localized Necking, it is determined by the Rice bifurcation criterion as well as by the Marciniak & Kuczynski imperfection approach. To apply both bifurcation criteria, the expression of the continuum tangent modulus associated with this constitutive framework is analytically derived. The set of equations resulting from the coupling between the Marciniak & Kuczynski approach and the constitutive relations is solved by developing an efficient implicit algorithm. The numerical implementation of the two-surface model is assessed and validated through a comparative study between our numerical predictions and several experimental results from the literature. A sensitivity study is presented to analyze the effect of some mechanical parameters on the prediction of diffuse and Localized Necking in thin sheet metals made of HCP materials. The effect of distortional hardening on the onset of plastic instability is also investigated.
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Ductility prediction of substrate-supported metal layers based on rate-independent crystal plasticity theory
International Journal of Material Forming, 2018Co-Authors: Mohamed Ben Bettaieb, Farid Abed-meraimAbstract: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.
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Influence of the Non-Schmid Effects on the Ductility Limit of Polycrystalline Sheet Metals
Materials, 2018Co-Authors: Mohamed Ben Bettaieb, Farid Abed-meraimAbstract: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.
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Effect of kinematic hardening on Localized Necking in substrate-supported metal layers
International Journal of Mechanical Sciences, 2017Co-Authors: Mohamed Ben Bettaieb, Farid Abed-meraimAbstract:Prediction of Necking limits in thin substrate-supported metal layers, which are typically used as functional components in electronic devices, represents nowadays an ambitious challenge. The specific purpose of the current work is, first, to numerically investigate the effect of kinematic hardening on Localized Necking in a freestanding metal layer. Second, the impact of adding a substrate layer on the ductility evolution of the resulting elastomer/metal bilayer will be analyzed. The materials in the metal and substrate layers are assumed to be isotropic, incompressible and strain-rate independent. The behavior of the metal layer is described by a rigid–plastic model with mixed (isotropic and kinematic) hardening. The isotropic hardening contribution is modeled by the Hollomon law, while kinematic hardening is modeled by the Armstrong–Frederick law. The substrate layer is made of elastomer material whose mechanical behavior is assumed to be hyperelastic and modeled by a neo-Hookean constitutive law. The Marciniak–Kuczynski imperfection analysis is used to predict plastic flow localization. Through various numerical simulations, the influence of kinematic hardening on Localized Necking as well as the impact of the addition of an elastomer layer are specifically emphasized. Comparisons with experimental results are also carried out to assess the relevance of incorporating kinematic hardening in the constitutive modeling of freestanding metal sheets.
Holger Aretz - One of the best experts on this subject based on the ideXlab platform.
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efficient and robust prediction of Localized Necking in sheet metals
THE 8TH INTERNATIONAL CONFERENCE AND WORKSHOP ON NUMERICAL SIMULATION OF 3D SHEET METAL FORMING PROCESSES (NUMISHEET 2011), 2011Co-Authors: Holger Aretz, Olaf EnglerAbstract:The recently proposed Critical Specific Tension (CST) model is jointly used with the well‐known Marciniak and Kuczynski (M‐K) model to predict Localized Necking in anisotropic sheet metals in the regime of negative and positive minor in‐plane strains, respectively. A significantly simplified method is presented to calculate the critical tensile stress required in the CST model, without the need of iterative computations. In the present work the CST/M‐K model is used along with a rate‐independent phenomenological elasto‐plastic constitutive model as well as the known visco‐plastic self‐consistent (VPSC) crystal plasticity model developed by Tome and Lebensohn. A comparison between experimental data and the limit strains predicted by means of the phenomenological constitutive model reveals a very good agreement. In order to validate the correctness of the non‐trivial computational implementation of the VPSC‐based CST/M‐K model the predicted Necking strains are compared with results obtained by using the phe...
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an extension of hill s Localized Necking model
International Journal of Engineering Science, 2010Co-Authors: Holger AretzAbstract:Abstract An extension of the classical Localized Necking model according to Hill [25] is proposed, with special reference to forming limit strain prediction of orthotropic sheet metals. Due to its computational efficiency the proposed model is an appealing alternative to the popular and more advanced Marciniak–Kuczynski model [34] , [35] with variable imperfection orientation. The proposed model is expected of being very beneficial when computationally demanding constitutive models are used, for example deformation texture models. Application examples demonstrate the capabilities of the developed Localized Necking model.
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a simple isotropic distortional hardening model and its application in elastic plastic analysis of Localized Necking in orthotropic sheet metals
International Journal of Plasticity, 2008Co-Authors: Holger AretzAbstract:Abstract In the present work an elastic–plastic constitutive model including mixed isotropic-distortional hardening is presented. The approach is very simple and requires only experimental data that are part of the standard characterization of sheet metals. It is shown that the distortional hardening contribution can be of considerable importance for Localized Necking prediction in orthotropic sheet metals.
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numerical analysis of diffuse and Localized Necking in orthotropic sheet metals
International Journal of Plasticity, 2007Co-Authors: Holger AretzAbstract:Abstract In the present paper the diffuse and Localized Necking models according to Swift [Swift, H.W., 1952. Plastic instability under plane stress, Journal of the Mechanics and Physics of Solids, 11–18], Hill [Hill, R., 1952. On discontinuous plastic states, with special reference to Localized Necking in thin sheets. Journal of the Mechanics and Physics of Solids 1, 19–30] and Marciniak and Kuczynski [Marciniak, Z., Kuczynski, K., 1967. Limit strains in the process of stretch-forming sheet metal. International Journal of Mechanical Sciences 9, 609–620], respectively, are considered. A theoretical framework for the mentioned models is proposed that covers rigid–plastic as well as elastic–plastic constitutive modelling using various advanced phenomenological yield functions that are able to account very accurately for plastic anisotropy. The mentioned Necking models are applied to different orthotropic sheet metals in order to assess their predictive capabilities and to stress out some potential sources for discrepancies between simulations and experiments. In particular, the impact of the applied hardening curve and the equibiaxial r-value, which was recently introduced by Barlat [Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Choi, S.-H., Pourboghrat, F., Chu, E., Lege, D.J., 2003. Plane stress yield function for aluminium alloy sheets – part 1: theory. International Journal of Plasticity 19, 297–1319], on formability prediction is investigated. Furthermore, the impact of the Portevin–LeChatelier effect on the formability of aluminum sheet metals is discussed.
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A Comparison Between Geometrical and Material Imperfections in Localized Necking Prediction
AIP Conference Proceedings, 2007Co-Authors: Holger AretzAbstract:The Marciniak‐Kuczynski model is classically used in conjunction with the assumption of a pre‐existing thickness imperfection in form of a narrow groove. Alternatively, one may replace the thickness imperfection by a material imperfection. In the present work the material imperfection is realized by assuming an initially soft groove. Both imperfection concepts are compared to each other under linear and non‐linear strain‐paths. It turns out that the concepts are only equivalent under linear strain‐paths while the forming limit stresses are insensitive to the type of imperfection and the strain‐path.
Anil K Sachdev - One of the best experts on this subject based on the ideXlab platform.
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an analysis of Localized Necking in aluminium alloy tubes during hydroforming using a continuum damage model
International Journal of Mechanical Sciences, 2007Co-Authors: Siva Prasad N Varma, R Narasimhan, Alan A Luo, Anil K SachdevAbstract:In this work, Localized Necking in aluminium alloy tubes subjected to free hydroforming is analyzed. The main objective is to study the influence of loading conditions, such as prescribed fluid pressure or volume flow rate in conjunction with axial end feed, on the nature of the forming limit curve (FLC). To this end, the strain histories experienced at the tube mid-length, which were computed in an earlier investigation [14] [Varma NSP, Narasimhan R. A numerical study of the effect of loading conditions on tubular hydroforming, Journal of Materials Processing Technology 2005; [Submitted for publication]], are analyzed using the Marciniak–Kuczynski (M–K) method along with an anisotropic version of the Gurson model. The Gurson constitutive parameters are determined following an inverse approach using the sheet FLC for the chosen alloy. The predicted FLC for combined pressure and axial contraction corroborates well with the experimental data obtained in [12] [Kulkarni A, Biswas P, Narasimhan R, Luo A, Stoughton T, Mishra R, Sachdev AK. An experimental and numerical study of Necking initiation in aluminium alloy tubes during hydroforming. International Journal of Mechanical Sciences 46:2004;1727–46] and is almost flat, whereas it is akin to the sheet FLC and increases with negative minor strain when fluid volume is specified. The forming limit strains for loading with specified fluid volume are in general higher when compared to those with prescribed fluid pressure. Finally, it is demonstrated that a transition from axial to circumferential Necking occurs when high ratios of axial extension to volume flow rate are applied to the tube.
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the influence of particle distribution and volume fraction on the post Necking behaviour of aluminium alloys
Mechanics of Materials, 2006Co-Authors: Don R Metzger, Mukesh Jain, David Wilkinson, Sooho Kim, Xinjian Duan, Raja K Mishra, Anil K SachdevAbstract:Abstract Experimental observations show that the continuous cast (CC) Al–Mg alloy with 0.21 wt% Fe has a considerably lower fracture strain than that of a CC alloy with 0.08 wt% Fe and a direct chill cast (DC) alloy with 0.21% Fe. However, the forming limit strains are almost the same for the three alloys. The similarities and differences are thought to relate with the distribution of hard second-phase particles. In the present paper, the influence of particle distribution characteristics (random vs. stringer pattern) and volume fraction (1.2% vs. 3.5%) is examined in detail with the use of a simple plane stress finite element unit cell model. The model permits extension of the composite stress–strain curve beyond the diffuse Necking condition so that the nominally uniform response is followed directly by Localized Necking. The model results agree very well with tensile tests with respect to the differing behaviour of the three materials in the deformation range between the onset of diffuse Necking and that for Localized Necking.
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on the sequence of inhomogeneous deformation processes occurring during tensile deformation of strip cast aa5754
Acta Materialia, 2006Co-Authors: Jidong Kang, Mukesh Jain, David Wilkinson, J D Embury, Armand Joseph Beaudoin, Sooho Kim, R Mishira, Anil K SachdevAbstract:Abstract A variety of surface observational techniques including full-field strain mapping based on digital image correlation analysis, electron back-scatter diffraction and in situ field emission scanning electron microscopy have been used to follow the patterns of inhomogeneous flow which occur during tensile testing of AA5754. The observations permit the relationships between slip lines, dynamic strain aging, shear localization, diffuse and Localized Necking to be delineated. In addition, fracture observation and metallographic assessment of damage processes have been conducted to enable an understanding of the relationship between inhomogeneous deformation and ductility to be developed.
Jyhwen Wang - One of the best experts on this subject based on the ideXlab platform.
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modeling the Localized Necking in anisotropic sheet metals
International Journal of Plasticity, 2012Co-Authors: Liang Zhang, Jyhwen WangAbstract:Abstract Localized Necking is one of the most frequently observed failure mechanisms in sheet forming processes. The forming limit diagram (FLD) characterizes the sheet metal formability, and the prediction of FLD is of significant importance to industry. In this paper, the process of deformation and Localized Necking is modeled to predict the FLD of anisotropic sheet metals. The sheet is assumed to have no initial geometric defects and a Localized neck is assumed to develop in two stages. A Considere-type criterion is proposed to determine the critical strains for an initial neck to form. An energy-based hypothesis is proposed to quantify the defect ratio at the neck formation. The evolution of the initial neck is then considered in the second stage. It is demonstrated that, rather than the initial defects, Localized geometric softening at a certain stage of deformation can be the main cause of Localized Necking. As a result, the forming limit curves are found to exhibit different characteristics in different regions of FLD. The predicted forming limit curve for 2036-T4 aluminum is mostly in good agreement with experimental results. The sheet thickness, the strain hardening behavior, and plastic anisotropy are found to affect the sheet metal formability. The present work provides an alternative view of Localized Necking in anisotropic sheet metals. More realistic yield criteria and strain hardening models can be implemented to enhance the proposed model.
