Forming Limit Strains Research Articles

Forming Limits Prediction of Laminated SUS430/Al1050/SUS430 Composites and the Effect of Component Properties on Mechanical Performance

In this study, a constitutive model applied to predict the tensile properties and fracture behavior of well‐bonded multilayered metal composites is extended. The equivalent single‐layer model, as a convenient method, is introduced into finite‐element simulations by combining it with an improved Xue–Wierzbicki damage plasticity model that considers material anisotropy. The steel use stainless (SUS) 430/Al1050/SUS430 laminated sheet fabricated by cold rolling is selected as the research material. The quasistatic uniaxial tests and Nakazima tests are operated to verify the accuracy of the proposed method. The mean errors in tensile stress and fracture forming limit strains are 2% and 3%, respectively. A load‐sharing mixture rule is proposed to assess the effects of the volume fraction, strength coefficient, and hardening exponent of the constituent materials on the mechanical properties of the laminates. In the results, it is indicated that the laminate exhibits sufficient elongation and remains markedly enhanced in tensile strength, reaching 470 Mpa when the ductile Al layer is combined with the higher strength and hardenability steel layer. In this research, it is aimed to clarify the formability characteristics in laminated composites for optimal sheet configuration design and development.

AI-assisted prediction of St14 steel sheets formability: Neural-fuzzy systems and crystal plasticity assessments

We've introduced a new technique leveraging artificial intelligence to determine in-plane forming limit strains in St14 sheet metals. A neural-fuzzy AI system was devised to predict safe points on forming limit diagrams, considering aspects like crystal texture, metal sheet thickness, and spherical punch diameter. Neural-fuzzy systems could be utilized in prediction of forming limit curves using linguistic data description. To obtain the data required for training the AI network, in-depth tests, including XRD, metallography, tensile testing, and Nakazima's hemisphere evaluations, were carried out to detail the metallurgical and mechanical properties of St14 sheet metal. Data on texture, the tensile curves, and grain morphology were then incorporated in crystal plasticity models to find hardening constants for St14's single crystals. Using these determined values, Nakazima's tests were replicated through multi-crystal aggregate configurations. We then undertook a comprehensive parameter investigation via 324 crystal plasticity simulations to shed light on the effects of texture, sheet depth, and punch dimensions on St14's formability. This rich dataset paved the way for training an adaptive neural fuzzy inference system (ANFIS), leading to substantial reductions in time and computational needs. The results validate that the ANFIS model offers accurate and reliable predictions, highlighting its viability for wider use in determining forming limit diagrams.

Investigation of the influence of plane strain constrained anisotropic plastic flow on the localized necking prediction

PurposeThe purpose of this manuscript is to investigate the influence of the satisfying of plane strain conditions on the prediction of the localized necking and to evaluate this effect by the different hardening models.Design/methodology/approachHigh-order anisotropic Drucker yield function, two types of hardening models, namely Hollomon power and Voce saturated, and the modified maximum force criterion (MMFC) are employed to predict the forming limit strains of AA3104-H19 alloy. Two identification methods, namely conventional and plane strain constrained, are applied and forming limit diagrams of the material are predicted by the incorporation of the anisotropic Drucker criterion and the hardening models into the MMFC for both calibration methods.FindingsThe enhancement in the prediction accuracy of the forming limits provided by the implementation of the plane strain constrained method is strongly dependent upon the selected hardening model type in the MMFC. About 18% improvement in the prediction of the biaxial limit strains is provided via Hollomon power law hardening, whereas the opposite result is occurred in case that the Voce saturated hardening law is used, and the predictions match with the experimental data only in the plane strain point and its surroundings.Originality/valueThe plane strain constrained identification method precisely predicts the location of the plane strain point on the yield locus and also any yield stress or anisotropy coefficient in the plane strain state is not required during the calibration, therefore the method can reduce the number of the required experiments for the constitutive characterization, and it will be attractive for both academy and industry. Additionally, the improvement in the prediction of the biaxial forming limits can be provided by applying of this method along with the appropriate hardening law.

Influence of Temperature on the Forming Limits of High-Strength Low Alloy, and Dual-Phase Steels

High-strength steels (HSS) appear as a good alternative to common steels to reduce vehicle weight, thus reducing fuel consumption. Despite the excellent mechanical behavior towards its lower weight, its application in industry is still limited, as manufacturing such materials suffers from limitations, especially regarding formability. The literature shows springback to be the most common problem. Among the parameters that can be studied to minimize this problem, the temperature appears, according to the literature, to be one of the most influential parameters in minimizing springback. However, the consequence of the temperature increase on the forming limits of materials is not completely understood. This study proposes to determine the consequences of the use of the temperature rise technique in the forming limits of high-strength steels. Two different steels were studied (HSLA 350/440 and DP 350/600). To evaluate the formability, the Nakazima method was used (practical). Finite element models were made which describe the material as well as Nakazima experimental behavior. To predict the forming limit strains via the numerical method, the thickness gradient criterion was applied. The practical and computational results were compared to validate the finite element model. Four different temperature ranges were analyzed. In general, it was found that 400 °C has a negative impact on the forming limits of both steels. This negative effect was found to be due to the alloying elements, such as silicon and manganese, present in the alloy. These alloying elements take part in the increase and decrease in resistance coefficient at the elevated temperature. For HSLA 350/440 steel, the forming limit strain decreased with an increase in temperature up to 600 °C and then increased at 800 °C; whereas for DP 350/600 steel, the forming limit strain decreased till 400 °C and then increased for 600 °C and 800 °C. Another factor which might have contributed to the behavior of the DP steel is the interaction of hard martensite with soft ferrite phase.

Measurement and prediction methods for forming limit strain of stretch bending deformation in sheet metal forming

In this study, a new test method using protruding punch was proposed, that can separate bending and stretching deformations. In this test, the blank makes simultaneous contact with the punch head and shoulder to ensure a constant bending angle during the test. After the simultaneous contact, increasing the punch stroke increases the amount of stretch deformation without changing the bending deformation. In addition, this test method can control the inflow of materials by controlling the BHF, and it is possible to evaluate cracks during stretch bending deformation even for materials with low forming limits. This test can control the distribution of strain through the thickness. As a result, the measurable surface formation limit strain in this test was higher than FLC with uniform strain along the thickness. It is suggested that this is because the strain gradient through the thickness delayed the timing of necking occurrence. There is a linear relationship between this strain gradient and the maximum principal strain on the sheet surface, which can be applied to the prediction of stretch-bending cracks in FEM analysis.

Integral Hydro-Bulge Forming Method of Spherical Pressure Vessels Using a Triangle Patch Polyhedron

AbstractThis paper proposes an integral hydrobulge forming (IHBF) method using a triangular patch polyhedron as the closed preform shell. When triangular flat parts are welded along the edges in sequence, triangular patch polyhedra are naturally formed. From the radius of the spherical pressure vessel, a design formula was derived to calculate the side lengths of the triangular flat plate parts. The water pressure, water volume, average strain of molding, and amount of springback after molding, which are necessary for implementing the IHBF for practical use, were also formulated. To verify the forming performance of the spherical pressure vessel using IHBF method, the finite element method was carried out, and a stainless-steel spherical pressure vessel with a thickness of 1.0 mm and a diameter of approximately 500 mm was fabricated using the proposed IHBF method. As a result, the measured shape error expressed as roundness to diameter ratio was 0.52%, and the calculated average plastic strain was 0.02, which was approximately 1/19 times of the forming limit strain of the material. The amount of springback after forming by calculation was approximately 0.7 mm, indicating that the amount of water required for IHBF was 5.90% of the volume of the spherical pressure vessel, while the required water pressure was no bigger than 2.3 MPa. The process directly utilizes triangular flat plate parts, eliminating the need for molds to process closed preform shells resulting in a low average plastic strain during forming, thereby improving the quality of the formed spherical pressure vessels.

A novel triple-layer hot stamping process of titanium alloy TC4 sheet for enhancing formability and its application in a plug socket part

In this paper, a novel method was proposed to improve the production efficiency and formability of titanium alloy, which was named triple-layer sheet hot stamping with a cold die cooling (THF). The titanium alloy sheet was clamped by two steel sheets with no adhesive added, then heated, transferred and formed together. In order to verify the ability in enhancing formability of this process, spherical part forming tests were carried out to study the formability under the single-layer sheet hot stamping (SHF) and THF. Finally, a plug socket part was formed to verify the practicability of the novel forming process. The finite element (FE) model was established to analyze the forming process finding that the formability of the parts were significantly improved after using THF process. Comparing with SHF process, the stamping depth increases by 135.7% at 900 °C in the THF process. The forming limit strain increases from 0.18 of the single-layer sheet to 0.51 of the triple-layer sheet. The forming limit strain obtained by the THF process is close to that of isothermal forming. The friction state is one of the main reason for improving formability. Moreover, for plug socket parts, there is almost no thinning of the part in the THF process at 900 °C. In conclusion, it has great advantages in improving the formability of titanium alloy using the THF process.

Modeling anisotropic ductile fracture of AA7075-T6 sheet for sheet metal forming considering anisotropic stress state

Anisotropic ductile fracture is one of the critical issues in the precision plastic forming of lightweight sheet metals. In this work, a new anisotropic ductile fracture model is developed by introducing the anisotropic stress triaxiality into the weight equation of the shear-controlled ductile fracture criterion. In an attempt to consider the effect of material anisotropy on stress state, the proposed fracture model is constructed in the anisotropic stress state form. The proposed anisotropic fracture model is used to characterize the anisotropic ductile fracture behavior of the AA7075-T6 sheet with a thickness of 2.0 mm under various stress states at room temperature. A series of uniaxial tensile tests are conducted using the in-plane shear specimen, the specimen with a central hole, and the plane strain grooved specimen to experimentally investigate the ductile fracture of AA7075-T6 along rolling, diagonal, and transverse directions. The proposed fracture model is calibrated by fracture strains determined from the hybrid experimental–numerical approach. With the calibrated fracture model, the anisotropic ductile fracture behaviors of AA7075-T6 over a wide range of stress states are predicted and compared with experimental measurements. The results show that the proposed fracture model successfully captures the anisotropic ductile fracture behavior of AA7075-T6 under various stress states at room temperature. Furthermore, to further illustrate the fracture predictive capability of the proposed fracture model, the predicted anisotropic fracture forming limit diagram is compared with the experimental forming limit strains obtained from the literature. Reasonable agreement is shown between literature data points and predicted fracture forming limit diagram. Accordingly, the proposed model has a great advantage in quantitative characterizing the anisotropic ductile fracture of high-strength aluminum alloy sheets under various loading conditions.

A new ductile failure criterion for micro/meso scale forming limit prediction of metal foils considering size effect and free surface roughening

For the establishment of reliable micro/meso scale forming processes, it is essential to accurately predict the forming limits of metal foils under different deformation paths. However, existing uncoupled ductile failure criteria cannot accurately forecast the micro/meso scale forming limits of metal foils affected by size effect in the whole strain path range of forming limit curve (FLC). To deal with the issue, a new ductile failure criterion is proposed in this paper based on the theoretical analyses of size effect affected void nucleation, growth, and coalescence, as well as free surface roughening affected critical damage of metal foils. A method for identifying the material parameters of the proposed ductile failure criterion coupled with a modified Yld2000 yield criterion is provided, and the size effect on micro/meso scale FLCs forecasted by the proposed ductile failure criterion is discussed. In addition, the forming limit strains of SUS304 and pure copper foils with different thicknesses and grain sizes are employed to reveal the prediction capability of the new ductile failure criterion. Comparisons between the experimental results and the FLCs constructed by the proposed failure criterion demonstrate that the proposed failure criterion can accurately predict the forming limits of metal foils affected by size effect between uniaxial tension (UT) and equi-biaxial tension (EBT). To further show the prediction capability of the proposed failure criterion in actual micro/meso scale forming processes, the limit drawing ratio of a SUS304 foil and local maximum forming heights in micro-channel hydroforming for pure copper foils are predicted using the new failure criterion combined with the finite element method, and the predicted results are compared with experimental results. Comparative research demonstrates that the proposed ductile failure criterion can accurately forecast the forming limits of metal foils affected by size effect in actual micro/meso scale forming processes.

On the application of the forming limit diagrams for quality control of blanks for wheelbarrow of ASTM A1008 carbon steel

The effectivity of the forming limit diagrams in manufacturing wheelbarrow by deep-drawing is shown because of the high material scrap rate which reduces productivity. Several chemical, mechanical testing and microstructural analysis were performed to examine sheet quality and their impact on these diagrams. Chemical analysis revealed that Steel 1 and Steel 3 sheets fulfilled the specification without assuring adequate forming process. However, the higher titanium content of Steel 2 improved its formability since it promoted the formation of fine precipitates, thus refining the grain size. This steel had the highest ASTM grain size number G (9.11), which is the lowest average grain size (13 µm) compared to the other steels, which had G values in the range 8.7 to 9.11. Moreover, Steel 2 sheets had the greatest plastic strain ratio (rm = 1.80), the highest strain-hardening exponent (n = 0.250), the lowest anisotropy ∆r = 0.31), yielding better results in deep-drawing strain distribution, the highest forming limit strain (28%) and the highest uniform elongation zone, favoring that failure sites did not occur.

Effects of thickness reduction in cold rolling process on the formability of sheet metals using ANFIS

Cold rolling has detrimental effect on the formability of sheet metals. It is, however, inevitable in producing sheet high quality surfaces. The effects of cold rolling on the forming limits of stretch sheets are not investigated comprehensively in the literature. In this study, a through experimental study is conducted to observe the effect of different cold rolling thickness reduction on the formability of sheet metals. Since the experimental procedure of such tests are costly, an artificial intelligence is also adopted to predict effects of cold thickness reduction on the formability of the sheet metals. In this regard, St14 sheets are examined using tensile, metallography, cold rolling and Nakazima’s hemi-sphere punch experiments. The obtained data are further utilized to train and test an adaptive neural network fuzzy inference system (ANFIS) model. The results indicate that cold rolling reduces the formability of the sheet metals under stretch loading condition. Moreover, the tensile behavior of the sheet alters considerably due to cold thickness reduction of the same sheet metal. The trained ANFIS model also successfully trained and tested in prediction of forming limits diagrams. This model could be used to determine forming limit strains in other thickness reduction conditions. It is discussed that determination of forming limit diagrams is not an intrinsic property of a chemical composition of the sheet metals and many other factors must be taken into account.

Localized necking of sheet metal under the biaxial stretching condition

To account for the localized necking of sheet metal under the biaxial stretching condition, a theoretical model of localized necking was proposed. To develop the model, it was assumed that the deformation of sheet metal under biaxial stretching becomes locally inhomogeneous after the onset of diffuse necking due to the pre-existing imperfections, and thereby the local elements of the sheet undergo the transition of loading path. Based on the assumed condition, the onset condition of localized necking was identified. The proposed model was combined with particular constitutive equations to provide its application cases, where Hill's theory of localized necking was adopted together to cover non-biaxial stretching paths. Material properties and the forming limit strains of the aluminum alloy (Al6014-T4) sheet were characterized and compared with the limit strains obtained from the proposed model. Theoretical limit strains produced by the original M−K model and the MMFC were also compared with those of the proposed model and the experiments. With the advanced constitutive model, the proposed model well captured the distribution of experimental limit strains of the Al alloy sheet under biaxial stretching. The sheet instability was identified in terms of the instantaneous N-value of the work hardening model.

Crystal plasticity finite element analysis of size effect on the formability of ultra-thin ferritic stainless steel sheet for fuel cell bipolar plate

The present study investigated the size effect on the formability of ultra-thin metallic bipolar plate for proton exchange membrane (PEM) fuel cell by crystal plasticity finite element method (CPFEM) in conjunction with the Marciniak-Kuczynski (MK) model. Mechanical behavior and crystallographic texture of a 0.08 mm-thick ferritic stainless steel (FSS) sheet were characterized by uniaxial tensile test and electron backscatter diffraction (EBSD) measurement. Nakazima formability test was carried out to measure the forming limit diagram (FLD) of ultra-thin FSS sheet. A hybrid cellular automata–Monte Carlo (CA–MC) model was developed to generate a ‘realistic’ representative volume element (RVE) that accurately reconstructed the measured texture and grain boundary misorientation distribution (GBMD). The predicted FLD by the CPFEM–MK model with the realistic RVE shows a good agreement with the experimental results. In order to explore the size effect on the formability, the forming limit analyses were performed using RVEs with various thickness-to-grain size ratios (t/d = 2∼10). The results reveal a significant degradation of the formability of the ultra-thin FSS sheet as t/d decreases. With decreasing number of grains through the thickness, the stress and strain heterogeneities in the surface grains are noticeably increased due to the less constraint by the subsurface grains, which plays an important role in the size effect. Furthermore, it is found that the surface strain hot spots in the material with low t/d can act as the geometrical imperfection to accelerate the failure, together with the increased stress triaxiality in the surface grains as the results of the localized strains and premature necking during the deformation. This attributes the decrease of forming limit strains to the early plastic flow instability in the ultra-thin sheet material with low thickness-to-grain size ratio.

An improved Marciniak-Kuczynski approach for predicting sheet metal formability

The Marciniak-Kuczynski (M-K) approach is the most renowned numerical method for forming limit strain curve (FLC) determination. In the commonly used M-K model, the thickness imperfection orientation (ψ) in the sheet plane is variable and the analysis is looped for different initial imperfection orientations (ψ0) for each strain route (ρ), which causes enormous computational waste. In addition, the predicted necking angle may obviously deviate from the theoretical one. This paper investigates the initial imperfection orientation and the necking angles (ψ*) of the AA5182-O sheet by both Nakazima experiments and M-K analysis. The effects of anisotropy on the necking angles and forming limit strains are investigated numerically. The results indicate that the necking orientation at equibiaxial stretching corresponds to the direction of the maximum r-value. The reason of necking angle deviation is well explained. Furthermore, the theoretical equation of necking angle is modified by an empirical formula, which is related to the ratio of r0 to rmax near the equibiaxial expansion. In light of the constant orientation of the imperfection deformation band during stretching, an improved M-K method is proposed based on the pre-assigned and non-evolving groove orientation. Compared with the modified M-K approach, this improved method achieves a higher calculation efficiency with a 97.7% reduction in computing time while maintaining the same level of accuracy.

Effect of Strain-Rate on Forming Limit Strain of Aluminum Alloy and Mild Steel Sheets Under Strain Path Change

The aim of this study is to show the effect of the strain-rate on the forming limit strain of an aluminum alloy A5052 sheet and a mild steel sheet SPCC. Biaxial stretching test was carried out. The prescribed strain path was linear path or that with directional change in straining. The sheet was pre-strained by uniaxial tension in the latter path. The deformation speed was set to be quasi-static or high speed whose strain-rate was about 300 /s using the dedicated high speed stretching device. The forming limit strain of the A5052 sheet for the linear strain path was larger in the high speed stretching than that under the quasi-static condition. For the case with strain path change the forming limit strain was further large. This may be due to the softening phenomenon which occurs by aging treatment, because the stretching experiment was conducted about two weeks after the pre-straining operation. On the other hand, the forming limit strain of the SPCC under the high speed condition was smaller than that under the quasi-static condition in the linear strain path. This is attributed to the decreased strain hardening exponent when the strain-rate increases. Further, in the equi-biaxial stretching of the pre-strained specimen, large difference of the forming limit strain between the deformation speeds was found. It is concluded that A5052 aluminum alloy sheet has a good adaptability to high speed forming, on the other hand, attention should be paid in increasing the forming speed of SPCC.

Local One-Sided Rubber Bulging Test to Measure Various Strain Paths of Metal Tube

We proposed a local one-sided rubber bulging method of metal tubes to evaluate various strain paths at an aimed portion and measured the forming limit strains of metal tubes at the place of the occurrence of necking under biaxial deformation. Using this method, since rubber is used to give pressure from the inner side of the tube, no sealing mechanisms were necessary unlike during hydraulic pressure bulging. An opening was prepared in front of the die to locally bulge a tube at only the evaluation portion. To change the restriction conditions of the bulged region for biaxial deformation at the opening, a round or square cutout, or a slit was introduced. The test was conducted using a universal compression test machine and simple dies rather than a dedicated machine. Considering the experimental results, it was confirmed that the strain path was varied by changing the position and size of slits and cutouts. Using either a cutout or a slit, the strain path in the side of the metal tubes can be either equi-biaxial tension or simple tension, respectively. Additionally, by changing the size of the cuts or slits, the strain path can be varied.

Friction stir processing combined with incremental forming effect on AA2014-T6

ABSTRACT The present-study accustomed aluminum 2014-T6 alloy of 3 mm sheet as the work material for conducting the friction stir processing. The entire studies have been completed in two phases of work. In the first phase, the work material is subjected to single-pass and multi-pass friction stir processing for its structural embattlement. A multi-faceted tool called hexagonal tool pin profile was preferred to carry out the stir processing for both the single and multi-pass cases. An optimized stir processing parameters essentially tool-speed 1000 rpm, table-feed 60 mm/min and 2° pivot angle were selected to carry out the stir processing. In the second phase, the single-pass FSPed and multi-pass FSPed work samples along with an unprocessed base metal are subjected to single point incremental forming process for its performance assessment on formability. The effect of forming parameters on average thickness, wall angle, forming limit strains and surface roughness have been analyzed on the profile forming of a cylindrical cup. To characterize the nature of profile formed structures, metallurgical, grain analysis and micro-hardness studies have been carried out at different locations of the formed segments. Conforming to the results, multi-pass FSPed samples exhibit superior formability followed by single-pass and least in the unprocessed sample.

Investigations into Enhanced Formability of AA5083 Aluminum Alloy Sheet in Single-Point Incremental Forming

In this article, formability of aluminum alloy AA5083-sheet in single point incremental forming (SPIF) is investigated through forming limit curves (FLCs) and maximum formable wall angle considering different forming parameters and conditions. Theoretical FLCs were predicted for SPIF and conventional forming utilizing deformation instability and Marciniak-Kuczynski methods, respectively, and validated by experiments. SPIF was found to give better formability compared to the conventional one in terms of the limit strain values from varying plane strain to equi-biaxial stretching modes of deformations. Groove depth at the onset of fracture in incremental sheet forming test was observed to be more for higher forming speed, i.e., at higher tool rotational speed and feed and for lower incremental depth. The maximum formable wall angle was improved for lower step depth but not significantly increased for higher forming speed. The forming limit strains and maximum forming wall angle were found to increase for incremental forming at elevated temperature. Microstructure studies revealed grain refinement in the deformed sheet in SPIF forming, and microhardness values in the deformed sheets were observed to increase for incrementally formed parts compared to that of the as-received sheet.

A Novel Approach for Process and Tool Design During Manufacturing of Industrial Sheet Metal Components

Manufacturing of sheet metal components feeds into several domains such as automotive, aerospace and strategic applications. The optimum process and tool design are crucial in ensuring successful manufacturing of components without developing any defects. The current trend is to do it right the first time during the industrial stamping practice, so that the costly shop floor trials are eliminated or at least minimized. One of the common failures that are observed during manufacturing of industrial sheet metal components is the splitting/cracking. The present work focuses on addressing the design considerations for preventing development of such defects. Traditionally, the strain-based forming limit diagram (FLD) is used to assess if a proposed process and tool design will lead to splitting failures. The approach is to measure or predict the strains that will develop during the stamping process and to infer that splitting failures will occur if these strains are above the FLD. The optimum process and tool design should ensure that the strains developed in the component must be below the FLD. The approach of using the strain-based FLD has serious limitation, as it does not account for the influence of complex strain paths on the forming limit strains. As an alternative, stress-based FLDs have been proposed, which does address the effect of complex strain paths. But, the stress-based FLDs are not intuitive and therefore are not very suitable to use for analysis of industrial sheet metal components. In this work, a novel approach, based on monitoring development of local thickness gradients during manufacturing of sheet metal components, is proposed to assess a given process and tool design for developing splitting/cracking failures. The novel approach is validated for sheets of different metals and thicknesses. The effect of bilinear strains paths on the forming limits is captured and validated using this proposed novel approach. A new approach, based on the novel thickness gradient criteria, is proposed for quantifying the forming severity of industrial sheet metal components.

The roles of yield function and plastic potential under non-associated flow rule for formability prediction with perturbation approach

In this study, the perturbation approach for predicting material’s forming limit strains under non-associated flow rule (non-AFR) is proposed. The influence of yield function and plastic potential function on the forming limit curve (FLC) evaluated by the perturbation approach are discussed through analyzing the normalized growth rate of a perturbation. In the framework of non-AFR, Hill’48 and Yld2000-2d are chosen for AA5754-O. The results show that the left side of FLCs predicted with the different forms of yield function and plastic potential nearly overlap. Hence, it is concluded that the yield function and plastic potential have a negligible influence on the forming limit strain under a negative strain path. However, the FLC under a positive strain path is principally dependent on the relationship between strain ratio β and stress ratio α, which can be determined by the plastic potential. Additionally, in comparison to the FLC under AFR, an increase in the forming limits strain is observed near the plain strain region, when the derivative of the normalized yield function concerning α is positive and vice versa.