Prediction Of Forming Limit Curves Research Articles

Forming limit of hot-rolled high-strength steels considering sheet thickness effect

The forming limit curve (FLC) has been commonly used tool to predict the metal forming cracking in engineering. Whereas, based on the assumption of plane stress state, the formability prediction of thick sheet of hot-rolled high-strength steels is quite different from the experimental measurement. Finite element simulation was used to study the effect of sheet thickness. It is found that extra stress along thickness is introduced between inside and outside the instability region, which become larger increased. Additionally, the visco-plastic self-consistent (VPSC) model and the M-K model are combined to establish the VPSC-MK model for investigating the influence of thickness difference. With reasonable capture of thickness stress, accurate prediction of FLC under different sheet thickness of hot rolled high-strength steel (HR-HSS) is well realized via VPSC-MK model. That is, it is revealed that the sheet thickness effect for HR-HSS mainly origins from normal stress induced during necking process.

Fracture forming limit curve prediction by ductile fracture models

The fracture forming limit curve is an essential tool giving information about fracture initiation in metal forming applications. In order to obtain a fracture-forming limit curve, the Nakajima test should be carried out. However, these tests are costly and time-consuming processes. Therefore, companies in the automotive industry tended to use non-expensive numerical approaches to determine the material's formability limits. In this work, an anisotropic polynomial yield criterion was implemented to calibrate the different ductile fracture models, including only or both the stress triaxiality and the Lode parameter's effect. Analyses of different uniaxial tensile test geometries were carried out, and the two-dimensional fracture loci were constructed by different ductile fracture models. Correspondingly, the fracture-forming limit curves were predicted by the two-dimensional fracture loci. The results showed that the ductile fracture models, including only the stress triaxiality effect, provide an acceptable performance covering the range from uniaxial tension and the plane strain tension lines, while the models, including the stress triaxiality and Lode parameter, provide a plausible prediction performance throughout the whole range for forming limit diagram.

Effect of temperature and strain rate fluctuation on forming limit curve of 5083 Al-Mg alloy sheet

The temperature and strain rate have significant effect on the formability of Al-Mg alloy sheet during warm forming process. Forming limit curve (FLC) is widely used for predicting sheet failure in warm forming simulation. However, the current simulation and optimization may lead to non-robust results, due to not considering the variation of FLC caused by the randomness of sheet temperature and deformation velocity, etc. In this study, a theoretical approach is developed to predict the temperature and strain rate dependent FLC. Backofen constitutive equation is extended, in which the material parameters are fitted as a function of temperature and strain rate by response surface method (RSM). Based on the M-K theory and Logan-Hosford yield criterion, the FLCs of 5083 Al-Mg sheet under different temperature and strain rate conditions are predicted and compared with the experimental results. By integrating the theoretical approach and Monte-Carlo simulation, the temperature and strain rate uncertainties are involved in FLC prediction to reflect manufacturing reality. The upper and lower margins of the FLC variation band are established, which covers the dispersion of the limit strains propagate from temperature and strain rate fluctuation. It is shown that under the combination of a higher temperature and a lower strain rate, the FLC of 5083 Al-Mg sheet is quite sensitive to small fluctuation of temperature or strain rate. In a particular temperature range (413 K–453 K), the FLC of 5083 Al-Mg alloy sheet becomes less sensitive to the fluctuation of temperature or strain rate. All these findings will advance the understanding of the design quality and robustness of the warm forming process.

Mechanical and micro-structural characterization of hot rolled brass foil

To assist the large-scale production of micro parts by micro sheet metal forming processes, mechanical and microstructural behaviors of metal foils are required. In the present study, an attempt has been made to characterize these properties of 100-μm thickness as-received brass foil. Mechanical characterization of foil has been done with tensile tests, bending tests and Nakazima tests. From the tensile test analysis, it has been observed that change in strain rate has a negligible impact on flow stress. However, serrations observed in flow stress are dependent on strain rate. The Electron backscatter diffraction (EBSD) analysis of as-received and post-deformed specimens shows the concentrated rise in Kernel average misorientation, high angle grain boundaries and low angle grain boundaries in deformed specimens. The fracture morphology study shows the presence of ductile fracture in the middle region of the fracture cross-section with shear lips in the edge region. Bending experiments show that the spring-back angle increases with the increase of bending angle up to 120°. After that, with an increase in bending angle, the spring-back angle decreases. The forming limit curve (FLC) obtained from the Nakazima test was compared to FLC obtained from different prediction criteria. From this study, it was observed that the FLC obtained from Marciniak-Kuczynski (M-K) criterion showed a good prediction of FLC for brass foil. However, FLCs obtained from Swift-Hill criterion, Abspoel empirical criterion and Pamstamp's Matwizard module over estimated foil's formability.

Prediction of Strain Path Changing Effect on Forming Limits of AA 6111-T4 Based on a Shear Ductile Fracture Criterion

Strain path changing is a phenomenon in the stamping of complex panels or multiple-step stamping processes. In this study, the influence of the strain path changing effect was investigated and assessed for an aluminum alloy of 6111-T4 with a shear ductile fracture criterion. Plastic deformation of the alloy was modeled by an anisotropic Drucker yield function with the assumption of normal anisotropy. Then the shear ductile fracture criterion was calibrated by the fracture strains at uniaxial tension, plane strain tension and equibiaxial tension under proportional loading conditions. The calibrated fracture criterion was utilized to predict forming limit curves (FLCs) of the alloy stretched under bilinear strain paths. The analyzed bilinear strain paths included biaxial tension after uniaxial tension, plane strain tension and equibiaxial tension. The predicted FLCs of bilinear strain paths were compared with experimental results. The comparison showed that the shear ductile fracture criterion could reasonably describe the effect of strain path changing on FLCs, but its accuracy was poor for some bilinear paths, such as uniaxial tension followed by equibiaxial tension and equibiaxial tension followed by plane strain tension. Kinematic hardening is suggested to substitute the isotropic hardening assumption for better prediction of FLCs with strain path changing effect.

A Modified M-K Method for Accurate Prediction of FLC of Aluminum Alloy

Forming limit curve (FLC) is an important failure criterion for sheet metals in sheet metal forming, while the M-K model is widely used for the prediction of the FLC. In the M-K model, such prediction is greatly influenced by the initial thickness imperfection factor and material properties, from which the original M-K model’s theoretical derivation is proposed as a solution to the above mentioned issue in this paper. Then the relationship between the M-K model and Keeler’s empirical formula is then studied, from which a new method to predict FLC is proposed that combines the M-K model with Keeler’s empirical formula according to the previous analyses. It turns out that this new method can simplify the calculation procedure. Finally, the experimental results of two kinds of aluminum alloys, AA6016 and AA5182, have verified the effectiveness of the proposed method.

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.

A comparison study of the yield surface exponent of the Barlat yield function on the forming limit curve prediction of zirconium alloys with M-K method

The forming limit curve (FLC) of zirconium alloys plays a significant role in the fabrications of spacer grid used for nuclear fuel assembly. The theoretical prediction of FLC has provided a convenient method to calculate the strain limit during the sheet forming process, but the prediction accuracy of zirconium alloy is still unsatisfactory due to its close-packed-hexagonal (HCP) structure. In this paper, to find a suitable yield surface exponent of zirconium alloys for improving the prediction accuracy, the theoretical FLCs of SZA6 zirconium alloy were calculated by self-programmed numerical codes with different exponent values and the results were compared with the experiments. To explain the mechanism of how the yield surface exponent affects the plastic behavior of SZA6 zirconium alloy, the strain distributions and element strain paths of Nakajima test were analyzed by finite element methods. At last, a suggested value of the yield surface exponent suitable for the FLC prediction of this zirconium alloy is acquired.

Experimental investigation of punch curvature influence in Nakazima test and numerical FLD prediction of AA5086

In this article, the influence of punch curvature on the forming limit curve (FLC) of AA5086 aluminum alloy sheet was studied by Nakazima test. Based on the digital image correlation (DIC) and the position-dependent method, the FLC of AA5086 aluminum alloy sheet was built, and the strain paths evolution during Nakazima test was analyzed. It was found that both the determined FLCs presented a phenomenon of shifting to the right side, and the FLCs with Φ44.45 mm punch was generally higher than that with Φ100 mm punch. The strain paths analyses show that the geometrical shape of the hemispherical punch leads to a biaxial pre-strain tension at the initial stage of the deformation. Furthermore, numerical simulation of Nakazima model was carried out to predict the FLC. For FE Nakazima model, the friction coefficient was calibrated according to strain path evolution. With a proper friction coefficient, the FE model presents a good FLC prediction compared to experimental results.

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.

An Investigation on Anisotropy Behavior and Forming Limit of 5182-H111 Aluminum Alloy

This paper studies the anisotropy behavior and forming limit of 5182-H111 aluminum alloy by experiments and theoretical analysis. The uniaxial tension tests for three different sheet directions were conducted to investigate the anisotropic properties of Al5182-H111 sheet. Moreover, the Nakajima tests for both rolling and transverse directions were performed to get the forming limit data. The experimental results show that the forming limit curves (FLCs) for rolling direction are much lower than that for transverse direction. In order to further investigate the influence of anisotropic properties on FLCs, the theoretical prediction of FLC was accomplished based on three different hardening laws. The results show that the theoretical FLC with Ghosh hardening law has much better agreement with experimental data. Furthermore, a new FLC was proposed by extending the forming limit from the strain state of uniaxial tension at transverse direction to the strain state of uniaxial tension at rolling direction. The adaptability of new FLC was verified in the Drawing test and Erichsen cupping test.

An Approach for Prediction of Coil Specific Forming Limit Curves

Forming limit curves (FLCs) are widely used for predicting failure in sheet metal forming operations. FLCs are determined in the laboratory according to ISO 12004‑2 using the Nakajima test. The testing procedure involves stretching a series of dog-bone shaped blanks with a hemispherical punch until failure occurs. This measurement procedure is extremely time-consuming. Consequently, a variety of statistical models have been proposed for predicting FLCs based on tensile test data. Unfortunately, practically all existing models are targeted for carbon and alloy steels, and thereby these models cannot be directly applied to stainless steels. In the present study, an approach for prediction of coil specific forming limit curves is developed. Predictive equations are derived based on statistical correlations between measured FLCs and steel properties. The application of the method to prediction of FLCs of stabilized ferritic stainless steels is described.

Combined numerical and experimental study to predict the forming limit curve of boron steel sheets at elevated temperatures

The aim of this study involved evaluating and predicting forming limit curves of boron steel 22MnB5 sheet at elevated temperatures. A finite-element method simulation was adopted based on ductile fracture criteria and simple experiments at elevated temperatures. First, tensile experimental data and ductile fracture criterions of Johnson–Cook and ductile void growth models were input to ABAQUS/Explicit software to predict and compare the same with fracture occurrence in experiments performed via Hecker’s punch stretching tests at room temperature. Subsequently, punch stretching test data at room temperature were added to correct the fracture strain locus in the space of the stress triaxiality and the equivalent strain following the ductile void growth model. After confirming the accuracy of the forming limit curve prediction at room temperature, fracture strain loci at high temperatures using ductile void growth model were determined based on the average ratio between the fracture equivalent plastic strains at room temperature as well as higher temperatures. Finally, Hecker’s punch stretching tests were numerically simulated to predict forming limit curve(s) of boron steel 22MnB5 sheet at high temperatures.

Influence of thickness and initial groove angle in M–K model on limit strain of 7B04 by considering through-thickness stress

Marciniack–Kuczinski (M–K) model is widely used to predict material’s forming limit curve (FLC). The prediction of FLC traditionally neglected through-thickness normal stress. However, it cannot be neglected in some forming processes. Much work has been done to study the effect of through-thickness normal stress on FLC with constant through-thickness normal stress or constant ratio of through-thickness normal stress and maximum principal stress. In addition, based on Nakazima test process, the ratio of through-thickness normal stress and maximum principal stress has been derived, which was a function of instantaneous thickness and loading path. Here, initial groove angle in M–K model was not considered. In this paper, uniaxial tension tests and Nakazima tests were performed on 7B04 aluminum alloy. Based on Hill 48 yield criterion and M–K model, the prediction model of FLC was established. The increase of thickness can enhance FLC. Meanwhile, it is necessary to consider through-thickness normal stress and initial groove angle in prediction model. On the left side of FLC, the effect of initial groove angle on FLC is weakened by increasing sheet thickness. On the right side of FLC, the effect of initial groove angle on FLC is strengthened by increasing sheet thickness. On the right side of FLC, the relation between limit strain points with different thicknesses is linear under one certain loading path. Thickness has decisive effect on through-thickness normal stress level and the changing trendy of through-thickness normal stress during calculation is different under different stress condition.

Limit Strains Analysis of Advanced High Strength Steels Sheets Based on Surface Roughness Measurements

The limit strains of dual-phase steels DP600 and 800 were evaluated in this work with a localization model formulated in plane-stress conditions using elasto-plastic constitutive equations. In this model, a geometrical imperfection parameter is defined from the sheet nominal thickness, initial ferrite grain size and average surface roughness. The proposed identification procedure provided a more physically meaning for this parameter and at best more conservative predictions in the drawing Forming Limit Curve (FLC) range of both investigated dual-phase steels. Nevertheless, the corresponding limit strains in the biaxial stretching region are underestimated with the present theoretical model. Thus, more detailed anisotropic yield function and hardening descriptions must be implemented to improve the accuracy of the FLC prediction of advanced high strength steels.

Evaluation of the forming limit curve of medium steel plate based on non-constant through-thickness normal stress

The forming limit curve (FLC) provides a convenient and useful way of presenting the necking or facture in sheet forming process. This work focused on determining the FLC of the medium steel plate with a thickness of 5 mm. The Nakazima test and uniaxial tension test were conducted to determine the limit strain pairs and the mechanical properties of the QSTE600TM medium plate, respectively. The M-K theory was extended under non-constant through-thickness normal stress condition to predict the FLC of the medium plate with higher accuracy. Meanwhile, the numerical Nakazima test was implemented to validate the non-constant through-thickness normal stress and determine the forming limit strains. The criterion for evaluating the limit strain pairs in simulation process was presented. The comparison showed that the experimental, theoretical and numerical FLCs well coincided, and demonstrated that the non-constant through-thickness normal stress was a critical factor in the FLC prediction of medium plate.

Novel Approach for Prediction of Localized Necking in Case of Nonlinear Strain Paths

Rising customer expectations regarding design complexity and weight reduction of sheet metal components alongside with further reduced time to market implicate increased demand for process validation using numerical forming simulation. Formability prediction though often is still based on the forming limit diagram first presented in the 1960s. Despite many drawbacks in case of nonlinear strain paths and major advances in research in the recent years, the forming limit curve (FLC) is still one of the most commonly used criteria for assessing formability of sheet metal materials. Especially when forming complex part geometries nonlinear strain paths may occur, which cannot be predicted using the conventional FLC-Concept. In this paper a novel approach for calculation of FLCs for nonlinear strain paths is presented. Combining an interesting approach for prediction of FLC using tensile test data and IFU-FLC-Criterion a model for prediction of localized necking for nonlinear strain paths can be derived. Presented model is purely based on experimental tensile test data making it easy to calibrate for any given material. Resulting prediction of localized necking is validated using an experimental deep drawing specimen made of AA6014 material having a sheet thickness of 1.04 mm. The results are compared to IFU-FLC-Criterion based on data of pre-stretched Nakajima specimen.

Accurate anisotropic material modelling using only tensile tests for hot and cold forming

Accurate material data for simulations require a lot of effort. Advanced yield loci require many different kinds of tests and a Forming Limit Curve (FLC) needs a large amount of samples. Many people use simple material models to reduce the effort of testing, however some models are either not accurate enough (i.e. Hill’48), or do not describe new types of materials (i.e. Keeler). Advanced yield loci describe the anisotropic materials behaviour accurately, but are not widely adopted because of the specialized tests, and data post-processing is a hurdle for many. To overcome these issues, correlations between the advanced yield locus points (biaxial, plane strain and shear) and mechanical properties have been investigated. This resulted in accurate prediction of the advanced stress points using only Rm, Ag and r-values in three directions from which a Vegter yield locus can be constructed with low effort. FLC’s can be predicted with the equations of Abspoel & Scholting depending on total elongation A80, r-value and thickness. Both predictive methods are initially developed for steel, aluminium and stainless steel (BCC and FCC materials). The validity of the predicted Vegter yield locus is investigated with simulation and measurements on both hot and cold formed parts and compared with Hill’48. An adapted specimen geometry, to ensure a homogeneous temperature distribution in the Gleeble hot tensile test, was used to measure the mechanical properties needed to predict a hot Vegter yield locus. Since for hot material, testing of stress states other than uniaxial is really challenging, the prediction for the yield locus adds a lot of value. For the hot FLC an A80 sample with a homogeneous temperature distribution is needed which is due to size limitations not possible in the Gleeble tensile tester. Heating the sample in an industrial type furnace and tensile testing it in a dedicated device is a good alternative to determine the necessary parameters for the FLC prediction.

Effect of yield criteria on the formability prediction of dual-phase steel sheets

The yield criterion is the basis of the material model that can describe the plastic behavior of the material under any possible stress states. The influence of diverse yield criteria on the formability prediction was explored via analyzing the hardening behavior and the forming limit of DP590 and DP780 sheets in this paper. The potential of the yield criterion to describe the hardening behavior of sheet metal was evaluated by comparing the equivalent stress-strain curves from the cruciform biaxial tensile tests with the uniaxial stress-strain curve. To characterize the hardening behaviors of dual-phase steel sheets under large strain condition, the hydraulic bulge tests were employed to obtain the equivalent stress-strain data based on different yield criteria. Accordingly, the material models including diverse yield criteria and hardening laws were used to calculate the theoretical forming limit curves (FLCs) based on the M-K model. Through comparing the predicted FLCs and the experimental ones from Nakazima tests, it was found that the theoretical FLCs based on the M-K model largely depend on the accurate yield criterion and hardening law. In addition, the numerical simulations of two stretch tests were carried out to verify the validity of the material models and the theoretical FLCs. The results indicated that the accurate yield criterion is of great significance to the description of hardening behavior and the prediction of FLCs.

Prediction and Experimental Validation of Forming Limit Curve of a Quenched and Partitioned Steel

Forming limit curve (FLC) is an effective tool to evaluate the formability of sheet metals. An accurate FLC prediction for a sheet metal is beneficial to its engineering application. A quenched and partitioned steel, known as QP980, is one of the 3rd generation advanced high strength steels and is composed of martensite, ferrite and a considerable amount of retained austenite (RA). Martensite transformation from RA induced by deformation, namely, transformation induced plasticity (TRIP), promotes the capability of work hardening and consequently formability. Nakazima tests were carried out to obtain the experimental forming limit strains with the aid of digital image correlation techniques. Scanning electron microscopy (SEM) was employed to examine the fracture morphologies of Nakazima specimens of the QP980 steel. The observed dimple pattern indicated that tensile stress was the predominant factor which led to failure of QP980 specimens. Therefore, maximum tensile stress criterion (MTSC) was adopted as the forming limit criterion. To predict the FLC of QP980 steel, Von-Mises yield criterion and power hardening law were adopted according to the tested mechanical properties of QP980 steel. Results were compared with those derived from other three representative instability theories, e. g. Hill criterion, Storen-Rice vertex theory and Bressan-Williams model, which shows that the MTSC based FLC is in better agreement with the experimental results.