Modified Maximum Force Criterion Research Articles

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.

Enhancing/Improving Forming Limit Curve and Fracture Height Predictions in the Single-Point Incremental Forming of Al1050 Sheet Material

Single-point incremental forming (SPIF) has emerged as a cost-effective and rapid manufacturing method, especially suitable for small-batch production due to its minimal reliance on molds, swift production, and affordability. Nonetheless, SPIF’s effectiveness is closely tied to the specific characteristics of the employed sheet materials and the intricacies of the desired shapes. Immediate experimentation with SPIF often leads to numerous product defects. Therefore, the pre-emptive use of numerical simulations to predict these defects is of paramount importance. In this study, we focus on the critical role of the forming limit curve (FLC) in SPIF simulations, specifically in anticipating product fractures. To facilitate this, we first construct the forming limit curve for Al1050 sheet material, leveraging the modified maximum force criterion (MMFC). This criterion, well-established in the field, derives FLCs based on the theory of hardening laws in sheet metal yield curves. In conjunction with the MMFC, we introduce a graphical approach that simplifies the prediction of forming limit curves at fracture (FLCF). Within the context of the SPIF method, FLCF is established through both uniaxial tensile deformation (U.T) and simultaneous uniform tensile deformation in bi-axial tensile (B.T). Subsequently, the FLCF predictions are applied in simulations and experiments focused on forming truncated cone parts. Notably, a substantial deviation in fracture height, amounting to 15.97%, is observed between simulated and experimental samples. To enhance FLCF prediction accuracy in SPIF, we propose a novel method based on simulations of truncated cone parts with variable tool radii. A FLCF is then constructed by determining major/minor strains in simulated samples. To ascertain the validity of this enhanced FLCF model, our study includes simulations and tests of truncated cone samples with varying wall angles, revealing a substantial alignment in fracture height between corresponding samples. This research contributes to the advancement of SPIF by enhancing our ability to predict and mitigate product defects, ultimately expanding the applicability of SPIF in diverse industrial contexts.

A general instability framework for ductile metals in complex stress states from diffuse to acute localization

Adoption of stress-based forming limit curves (FLC) and their equivalent strain representations were introduced to overcome the path dependence of the conventional strain-based FLCs. The stress state and its instantaneous magnitude govern formability such that the triaxial stress state, induced through tool contact, can no longer be neglected. The present work reveals that in addition to the composition of the stress state, the boundary conditions of how the stress is applied to the material determine the onset of plastic instability. To this end, the relatively unknown generalized instability model of Hillier, derived from a stable bifurcation of the stress state under neutral stability, is revisited. Analytical solutions for instability in triaxial plane strain loading were derived for boundary conditions of a proportional, constant, or evolving contact pressure that enables critical evaluation of phenomenological plane stress mapping criteria proposed in the literature. As part of this work, the Hillier instability framework is extended to model the localization process under the constraint of quasi-stable plastic flow in arbitrary principal stress states to form the Generalized Incremental Stability Criterion (GISC). It is shown that the Modified Maximum Force Criterion (MMFC) emerges as one of many special cases of the GISC when restricted to plane stress proportional stressing with a prescribed minor load. Finally, the GISC is applied to Marciniak and Nakazima formability tests of a DP980 steel for identification of appropriate boundary conditions.

On the influence of tool contact stress on tensile instabilities in plane strain stretching and bending of sheet metals

It is well known that the widely used forming limit curve (FLC) based upon in-plane stretching fails to account for the delay in plastic instability in the presence of appreciable bending and tool contact pressure. The recently proposed General Incremental Stability Criterion (GISC) – a generalization of the Modified Maximum Force Criterion (MMFC) to triaxial loading – revealed the dependence of the boundary conditions on the formation of tensile instabilities. Nevertheless, it remains unclear how the combined effect of radial bending stresses and tool contact pressure affects the formation of an acute neck. It is shown in this study that a compressive normal stress causes a shift of the strain state from initial plane strain tension to positive minor strains for material layers within the cross-section. The convex (outer) layer remains in a state of plane strain-plane stress. Accounting for the shift in the strain state is key to capture the dependence of the contact pressure on necking. A simplified modelling approach, which enforces plane strain tension of the cross-section, was able to capture the formability gain due to bending but failed to account for the delay in plastic instability due to the contact pressure. An incremental multi-layer model was required to account for non-monotonic loading due to bending over the punch and the biaxial shift in the strain path caused by the contact pressure. The models were then applied to the experimental forming limits of a 3rd Gen 1180 advanced high strength steel to demonstrate the formability gains under triaxial loading due to the contact pressure.

Improvement of modified maximum force criterion for forming limit diagram prediction of sheet metal

This study presents a new criterion (MMFC2) for predicting the forming limit curve (FLC) of sheet metal. The strain path evolution of a critical element examined in a uniaxial tensile test is elaborated by incorporating the results of experimental measurement, finite element simulation, and theoretical prediction via the Modified Maximum Force Criterion (MMFC). A scaling factor is introduced to mimic the theoretical evaluation with the simulated one. It is believed that the rotation of the principal axes of the theoretically considering material point, which is initially co-axial with the external load coordinate, implicates the macro track of the strain path change. Furthermore, an optimal event of the second derivative of the axial rotations is proposed to indicate the strain localization and formulate the FLC. The performance of the proposed criterion is compared with that of the original MMFC in predicting the FLC of three automotive sheet metals, of which all related data were published in the Benchmark of Numisheet 2014 conference. The use of three different hardening laws and three yield functions is examined in the analogy. The comparison reveals that the results of MMFC2 are more sensitive to the employed constitutive model than that of MMFC. Furthermore, the proposed MMFC2 presents concordant results with the experimental data. Nakajima tests are conducted for CR4 mild steel sheets to validate the capacity of the proposed criterion. Well agreement between the experimentally measured data and theoretical prediction based on the Yld2k yield function verifies its usefulness in practice.

Simulation and experimental comparison study based on predicting forming limit curve of SUS304 sheet material

In this study, the modified maximum force criterion was used to ensure an accurate determination of the forming limit curve (FLC) for the SUS304 sheet metal. At first, the stress–strain curves according to Voce and Swift hardening models were verified using the experimental data and the stress function deduced by Hill in 1984 to predict FLCs. The accuracy of the FLCs was evaluated by analyzing the equivalent fracture strain data at three distinct locations: Biaxial tensile strain (BT, [Formula: see text]), uniaxial tensile strain (UT, [Formula: see text]), and plane strain (PS, [Formula: see text]), and then comparing them with the corresponding linear FLC experimental data. The accuracy of the predicted FLCs was further tested by comparing the fracture height of the samples according to the Nakazima model in the FEM simulation and the corresponding experiments.

Theoretical Forming Limit Diagram Based on Induced Stress in the Thickness Direction

The conventional theoretical forming limit diagram (FLD) based on the plane stress state has defects due to the neglect of the stress in the thickness direction of the sheet. It is urgent to study the FLD which considers the stress in the thickness direction. Through the finite element simulation, it is further confirmed that the stress in the thickness direction will be induced in the deformation process. At the same time, the effect of the induced stress in the thickness direction on FLD is not the same as that always applied stress in the thickness direction during the deformation process. Based on the Modified Maximum Force Criterion (MMFC) instability theory, C-H instability theory, Mises and Hill48 yield criterion, the effects of the two stresses on FLD are compared. The induced stress in the thickness direction also affects the sensitivity of the coefficient of normal anisotropy r, but does not significantly change the effect of the stress-strain index n on Forming Limit Curves (FLC). The theoretical calculations of the three materials TRIP780, AA5182, and 5754O are compared with the experimental data, which proves that the FLD which considers induced stress in the thickness direction is more accurate than the FLD of the plane stress.

A Comparative Evaluation of Third-Generation Advanced High-Strength Steels for Automotive Forming and Crash Applications.

While the third generation of advanced high-strength steels (3rd Gen AHSS) have increasingly gained attention for automotive lightweighting, it remains unclear to what extent the developed methodologies for the conventional dual-phase (DP) steels are applicable to this new class of steels. The present paper provides a comprehensive study on the constitutive, formability, tribology, and fracture behavior of three commercial 3rd Gen AHSS with an ultimate strength level ranging from 980 to 1180 MPa which are contrasted with two DP steels of the same strength levels and the 590R AHSS. The hardening response to large strain levels was determined experimentally using tensile and shear tests and then evaluated in 3D simulations of tensile tests. In general, the strain rate sensitivity of the two 3rd Gen 1180 AHSS was significantly different as one grade exhibited larger transformation-induced behavior. The in-plane formability of the three 1180 MPa steels was similar but with a stark contrast in the local formability whereas the opposite trend was observed for the 3rd Gen 980 and the DP980 steel. The forming limit curves could be accurately predicted using the experimentally measured hardening behavior and the deterministic modified Bressan–Williams through-thickness shear model or the linearized Modified Maximum Force Criterion. The resistance to sliding of the three 3rd Gen AHSS in the Twist Compression Test revealed a comparable coefficient of friction to the 590R except for the electro-galvanized 3rd Gen 1180 V1. An efficient experimental approach to fracture characterization for AHSS was developed that exploits tool contact and bending to obtain fracture strains on the surface of the specimen by suppressing necking. Miniature conical hole expansion, biaxial punch tests, and the VDA 238-100 bend test were performed to construct stress-state dependent fracture loci for use in forming and crash simulations. It is demonstrated that, the 3rd Gen 1180 V2 can potentially replace the DP980 steel in terms of both the global and local formability.

A simulation and experimental study on the deep drawing process of SPCC sheet using the graphical method

This study presents a method for finite element (FE) simulation of a deep drawing process of a cold-rolled carbon steel (SPCC) sheet material based on the graphical method. First, uniaxial tensile specimens were prepared and experimental tests were conducted to determine the flow stress curves. The calculation of the fracture points at special strain modes (plane strain, uniaxial tensile strain, and biaxial tensile strain) was presented using the modified maximum force criterion (MMFC). After that, the graphical method was adopted for the estimation of the forming limit curve (FLC) based on several hardening laws. FE models for a deep drawing process of the SPCC sheet were then built using the calculated FLCs. Using FE simulations, the fracture heights of cylinder cups formed by the deep drawing process were finally determined and compared with those from experiments. The results showed a good agreement between simulated and measured fracture height with a maximum of 3.6 % deviation. Additionally, simulations and corresponding experiments were performed to investigate the effects of the blank holder force, punch corner radius, and drawing ratio on the fracture height of cylinder cups.

Graphical method based on modified maximum force criterion to indicate forming limit curves of 22MnB5 boron steel sheets at elevated temperatures

A new approach for predicting forming limit curves (FLCs) at elevated temperatures was proposed herein. FLCs are often used to predict failure and determine the optimal forming parameters of automotive parts. First, a graphical method based on a modified maximum force criterion was applied to estimate the FLCs of 22MnB5 boron steel sheets at room temperature using various hardening laws. Subsequently, the predicted FLC data at room temperature were compared with corresponding data obtained from Nakazima’s tests to obtain the best prediction. To estimate the FLC at elevated temperatures, tensile tests were conducted at various temperatures to determine the ratios of equivalent fracture strains between the corresponding elevated temperatures and room temperature. FLCs at elevated temperatures could be established based on obtained ratios. However, the predicted FLCs at elevated temperatures did not agree well with the corresponding FLC experimental data of Zhou et al. A new method was proposed herein to improve the prediction of FLCs at elevated temperatures. An FLC calculated at room temperature was utilized to predict the failure of Nakazima’s samples via finite element simulation. Based on the simulation results at room temperature, the mathematical relationships between the equivalent ductile fracture strain versus stress triaxiality and strain ratio were established and then combined with ratios between elevated and room temperatures to calculate the FLCs at different temperatures. The predicted FLCs at elevated temperatures agree well with the corresponding experimental FLC data.

Prediction of limit strains during non-proportional load paths with a change in loading direction

Many different models have been published to predict failure after non-proportional load paths. Most of those models are phenomenological and heuristical models. They require a profound knowledge about the material. Examples are the enhanced Modified Maximum Force Criterion (eMMFC), the Polar Effective Plastic Strain-model (PEPS) or the Generalized Forming Limit Concept (GFLC). In addition to the load path, the loading direction has a significant influence on the formability of sheet metals. The mentioned models currently neglect this influence. By extending the GFLC-model by the parameter of loading direction, this influence is taken into account. By analyzing an acceptable number of bi-linear experiments, it is possible to calibrate the proposed model for a micro-alloyed steel HC340LA. Therewith an arbitrary load path with a change in loading direction can be evaluated. The results of this contribution show the effectiveness of this approach by different experiments.

On the experimental characterization of sheet metal formability and the consistent calibration of the MK model for biaxial stretching in plane stress

Analytical formability models based upon in-plane proportional plane stress loading such as the Marciniak–Kuczynski (MK) model are commonly evaluated against forming limit curves (FLCs) obtained using Nakazima tests with out-of-plane deformation, non-linear strain paths and tool contact. The present study has conducted a comprehensive experimental characterization of a DP1180 advanced high strength steel with relatively low formability to demonstrate that the use of Nakazima FLC data can lead to a physically inconsistent MK model. Although good agreement can be obtained using the MK model with Nakazima data, it is attributed to calibration bias in the hardening model and selection of the imperfection factor. Marciniak tests should be performed to characterize the FLC or process-corrections be applied to the Nakazima FLC to then calibrate the MK imperfection factor. An analysis of the MK framework reveals a false dependence of the imperfection factor on the hardening model due to artefacts in the hardening model calibration. When the Considère constraint for the uniform elongation is imposed during the hardening model calibration, the MK imperfection factor becomes nearly independent of the choice of hardening model. The accuracy of the FLC predicted by the MK model, when appropriately constrained and calibrated in a deterministic manner, was in a reasonable agreement with the experimental data only after accounting for material anisotropy. In contrast, the deterministic Modified Maximum Force Criterion (MMFC) model provided a very close estimate of the experimental forming limit strains of the mildly anisotropic DP1180 using both isotropic and anisotropic yield functions.

Experimental Characterization and Deterministic Prediction of In-Plane Formability of 3rd Generation Advanced High Strength Steels

The objective of the current study is to develop a practical, deterministic approach to the prediction of the in-plane formability of two third generation advanced high-strength steels (AHSS) of 980 and 1180 MPa ultimate tensile strength using only quasi-static mechanical property data. The hardening response to large strains was experimentally measured with the use of simple shear and tensile tests and validated in tensile simulations. The process-corrected limit strains in the Nakazima and Marciniak tests were compared to various analytical Forming Limit Curve (FLC) models for in-plane stretching. It was observed that the widely-used Marciniak–Kuczynski model can adequately predict the experimental FLC in biaxial stretching but significantly underestimated the limit strains in uniaxial stretching for both third generation AHSS. The observed through-thickness shear fracture mode in biaxial stretching was reasonably well-captured by the Bressan–Williams (BW) instability model for the 1180 MPa steel. A proposed extension of the BW model to uniaxial tension by adoption of the maximum in-plane shear stress criterion (BWx model) provided superior experimental correlation relative to the zero-extension model of Hill that was too conservative. Finally, a linearized version of the modified maximum force criterion (MMFC) was proposed that markedly improved the correlation with the process-corrected FLC for in-plane stretching of AHSS. The developed framework for FLC prediction was then applied to a DP980 AHSS and an AA5182 aluminum alloy from the literature. The DP980 corroborated the observed trend for the two third generation AHSS whereas the MK and the BWx models performed best for the AA5182 with its saturation-type hardening behavior and non-quadratic yield surface.

A theoretical prediction framework for the construction of a fracture forming limit curve accounting for fracture pattern transition

It has been accepted that the formability of a sheet metal with a moderate ductility can be limited by not only localized necking (LN), but also ductile fracture (DF). In this study, a theoretical prediction framework is developed for a comprehensive formability characterization, in which forming limit curves at LN (FLCN) and DF (FLCF) are elaborately correlated by considering strain path evolution. A dual-phase steel material (DP590 sheet metal) is selected with a series of DF and Nakajima tests performed. A newly proposed DF model (uncoupled type) is calibrated by implementing a hybrid experiment-simulation method in line with the DF tests, which are designed to achieve DF under distinct stress states, such as simple shear (SS), uniaxial tension (UT), plane strain tension (PST), and balanced biaxial tension (BBT). The resulting three dimensional (3D) fracture surface demonstrates a good agreement with the tested data. The modified maximum force criterion (MMFC) is selected for the theoretical identification of strain path evolution. The calibrated MMFC results in a FLCN exhibiting a certain level of underestimation as compared to the tested data in the range of positive minor strain. The MMFC is improved (iMMFC) by incorporating with an initial strain path-based function for a higher accuracy in characterizing evolutive strain paths; the resulting FLCN is observed to have a better performance than that of MMFC. Theoretical FLCFs are determined by the integral of ductile damage increment (defined by the DF model calibrated) over each identified strain path from UT to BBT. After considering strain path evolution, different deformation stages are added into the finalized forming limit diagrams including both FLCF and FLCN. It is found that the FLCF based on iMMFC model demonstrates acceptable deviations as compared to all the tested cracking data. Moreover, this FLCF intersects with the corresponding theoretical FLCN as load path approaches from UT to BBT, representing a fracture pattern transition from a LN band-accompanied DF to the one without LN band; this prediction is further validated by experimental observations. The FLCF based on MMFC fails to predict this transition behavior. The current study confirms the presence of a competition between LN-induced failure and DF-induced failure for sheet metals. Moreover, all of these findings advance the insight into the importance of performing a DF prediction aside of a FLCN prediction, especially for the case where a sheet metal with a moderate ductility shows a fracture pattern transition behavior.

Application of a Graphical Method on Estimating Forming Limit Curve of Automotive Sheet Metals

In the automotive engineering community, the modified maximum force criterion proposed by Hora and co-workers is considered acceptable for theoretically estimating the forming limit curve (FLC) of sheet metals. Based on this criterion, a graphical method is proposed to simplify evaluation of the FLC. This paper investigates the proposed graphical method in a special case by using a power-hardening law and the Mises yield function, which leads to an explicit expression of the critical strains according the strain paths. The FLC of a DP590 sheet estimated using the proposed method is compared with that estimated using existing analytical methods. The proposed method provides the best prediction of the FLC of the tested material. For verification, the calculated FLC is then adopted into the finite-element method to predict the punch stroke at fracture of several notched specimens subjected to Nakazima tests. The good agreement between the predicted and experimentally determined values of the punch strokes verifies the ability and potential of the proposed method in industrial engineering.

A comparative investigation into the influence of the constitutive model on the prediction of in-plane formability for Nakazima and Marciniak tests

The present study investigates the use of both Marciniak and Nakazima tests to generate the forming limit curves (FLCs) for a power-law hardening dual phase steel, DP980, and an aluminum-magnesium alloy, AA5182, that exhibits dynamic hardening and saturation-type behavior. The recently proposed methodology of Min et al. (2016) to compensate for the so-called process effects of non-linear strain paths (NLSP) and contact pressure was evaluated and applied to the Nakazima FLCs to enable comparison with the Marciniak FLCs and the formability predictions of the Modified Maximum Force Criterion (MMFC) of Hora et al. (1994, 2013) for in-plane stretching. An emphasis was placed upon the experimental determination of the constitutive model to plastic strains in excess of 0.5 using tensile and shear tests. A flexible variant of the Hockett-Sherby (1975) hardening model for large strain levels along with constraints upon the hardening model calibration are proposed. It is demonstrated that the choice of hardening model, test data, and the calibration procedure can have a marked influence on the Nakazima process corrections and the predicted FLC using the MMFC model. An extension to the Linear Best Fit (LBF) limit strain detection methodology by Volk and Hora (2011) was developed to account for bend severity and the material hardening response and is compared with the ISO 12004-2 limit strains. If the hardening model is accurately calibrated to large strain levels, the analytical MMFC predictions were in excellent agreement with the process-corrected Nakazima and Marciniak FLCs for DP980. The results for the AA5182 were found to be strongly dependent upon the choice of hardening model that influences both the MMFC and the contact pressure correction.

A Graphical Method to Estimate Forming Limit Curve of Sheet Metals

Since its foundation, the concept of forming limit diagram has been widely accepted in sheet metal forming community as a powerful tool for studying formability. There are pyramid models that were developed to estimate the forming limit curve theoretically, for example, Swift's diffuse necking criterion, Hill's localized necking criterion, Marciniak and Kuczynski model, Modified Maximum Force Criterion, etc.. Implement of these models, however, is a laborious task. To simply the task, this study presents a graphical method to estimate forming limit curve of sheet metal. Some new insights into the Modified Maximum Force Criterion, the Hora method, are discussed. The insights pertain to the use of a graphic tool to estimate limit strains at three critical forming modes in sheet metal forming that are the uniaxial tension, plane strain, and equi-biaxial tension. Connecting three points by linear lines yields to a simple graph of forming limit curve. Method validation is supported by comparing the estimated forming limit curve with experimentally measured data for several automotive sheet metals.

Considering fluctuations of material properties, stainless steel 1.4301, on manufacturability of kitchen sinks

In production of deep drawn sheet metal parts, it is often challenging to achieve a robust process. Especially in the production of kitchen sinks made out of stainless steel, the fluctuation of the process and material properties often lead to robustness problems. Therefore, numerical simulations are used to detect critical regions. To keep a constant product quality, process control is realised based on metamodels, which are computed by means of a series of finite element simulations. In order to enhance the forecast capability of the simulation model and to increase the reliability of quality features, the yield curve, the yield locus and the forming limit curve (FLC) of different suppliers are measured with tensile, bulge and Nakazima experiments. Because of the large deformation capability of stainless steels, large drawing depths can be achieved. However, the classic Nakazima geometries are not distributed homogenously in the forming limit diagram (FLD). To overcome this shortcoming, a shape optimization of the Nakazima specimen has been performed. Furthermore the influence of alloying elements on the hardening behaviour and on the FLC are analysed. In addition, the measured FLC-T (temperature dependent FLC) conducted with heated Nakazima tests is compared with the computed FLC-T with the modified maximum force criterion (MMFC).

A failure model for non-proportional loading under plane stress condition based on GFLC in comparison to eMMFC and PEPS

A mathematical model is presented for a forming limit for non-proportional loading under plane stress condition. The model results in an approach to reduce the number of experiments needed for the Generalized Forming Limit Concept (GFLC) and presents a numerical approach to calculate the linearized FLC from real Nakajima measurements. The mathematical model has been analyzed in comparison to Polar Effective Plastic Strain (PEPS) diagram and enhanced Modified Maximum Force Criterion (eMMFC), discussing both consistency with plasticity modeling and industrial applicability. An experimental setup based on Nakajima specimens is presented and DIC measurements are used to capture loading paths. The measured loading paths are used to validate predictions made by PEPS, eMMFC and the presented mathematical approach. The latter model shows promising results for prediction of failure for non-proportional loading.

Influence of the post-necking prediction of hardening law on the theoretical forming limit curve of aluminium sheets

This study clarified the influence of the post-necking prediction of the hardening law on the theoretical forming limit curve (FLC) of aluminium sheets subjected to punch-stretching tests. A procedure was developed to identify the parameters of a recently developed hardening model (Kim–Tuan hardening model) based on the curve fitting method. Subsequently, this model was used to capture the post-necking behaviours of two aluminium alloy sheets (AL5052-O and AL6016-T4), which were compared with those of various other hardening models, including the Swift model, Voce model, Hockett–Sherby model, Ghosh model, and a linear combination of the Swift and Voce models. These hardening models, with their extrapolations for post-necking prediction, were employed to analytically calculate the FLCs of the tested materials based on the modified maximum force criterion (MMFC). Furthermore, a simple and effective method was found to estimate the level of limited strain in the plane strain mode, namely FLC0. The proposed method was used to clarify the influence of the hardening law and yield function on the level of the computed FLC. The results indicated that the flow curves predicted by the Kim–Tuan hardening model effectively matched the experimental data obtained from uniaxial tensile tests, while their extrapolations provided intermediate predictions of the post-necking behaviour between the flow curves of the Swift and Voce models. In addition, the proposed hardening model improved the accuracy of the computed FLC for the studied materials.