Experimental Forming Limit Diagram Research Articles

Modeling the formability of aluminum alloys at elevated temperatures using a new thermo-elasto-viscoplastic crystal plasticity framework

Industrial processes often use high temperature forming of alloys such as aluminum that have unsatisfactory room temperature formability. Accurate forming models to integrate warm forming in production environment have been hampered by a lack of constitutive relations at elevated temperatures, forcing one to rely on experimental data for such integration. In this paper, the new thermo elasto-viscoplastic (TEV) crystal plasticity constitutive framework developed by Cyr et al. [1] is implemented in an Marciniak–Kuczynski [2] analysis to predict the forming limit diagrams (FLDs) of the AA5754 and AA3003 aluminum alloys at elevated temperatures. The model takes into account the temperature dependence of the single crystal elastic coefficients, single slip hardening parameters, thermal softening, slip rate sensitivity, and the total deformation. Temperature dependent hardening parameters have been determined through curve fitting the simulated stress–strain response with experiments during uniaxial tension at room and elevated temperatures. The calibration of the TEV model for the single slip parameters in uniaxial tension is shown to provide accurate predictions of the experimental forming limit diagrams (FLDs) without the need for further curve fitting. The effects of elastic constants and thermal softening on FLD prediction are discussed, and equations are developed to predict the temperature dependence of single-slip hardening parameters and so-called initial imperfection parameter employed in the Marciniak–Kuczynski (M–K) analysis. The predictive capability of the new model is then demonstrated by FLD simulations for various elevated temperatures.

Experimental Investigation on Forming Limit Diagram of the Commercially available AZ31B Magnesium Alloy

Forming of metal is a conventional technique used to manufacture most of the sheet metal products. Forming Limit Diagram (FLD) is an effective tool used to evaluate the formability of sheet metal, which is used to evaluate limiting strain in various strain condition. This work investigates the formability of commercially pure grades of magnesium sheet with different thickness, namely AZ31B alloy with 2 mm, 3 mm and 4 mm thickness with graphite as a lubricant. These cold-rolled magnesium sheets are stretch formed until fracture, hemispherical punch to evaluate the FLD. The formability test was conducted, using the punch and die set assembly. The experimental FLD were plotted based on the results of the formability test.

Numerical Investigation on Stress based Forming Limit Diagram for Ti-6Al-4V Alloy

Forming limit diagram (FLD) is an important tool in designing sheet metal forming processes. FLD is used to determine if a sheet metal forming process may induce necking in the material. However, these are only reliable for operations with linear strain paths. Stoughton [1] developed the stress based forming limit diagrams (FLSD) which are independent of strain path present in the material. This paper focuses on converting experimental FLD of Ti-6Al-4V at 400°Cpublished by Kotkunde et al. [2] to FLSDs. Various anisotropic yield criterion (Hill 48, Hosford 79, Barlat 89) and hardening rules (Hollomon Power Law, Swift Law and Modified Voce Law) are used.In addition, experimental FLDs and theoretical FLD curves obtained from Marciniak-Kuczynski (MK) analysis are converted to FLSDs and compared.

Forming limit diagrams of tailor rolled blank in hot stamping and its verification

The purpose of this study is to predict the rolling-orientation and temperature dependent forming limit diagrams (FLDs) of tailor rolled blank (TRB) in hot stamping process. The rolling orientation is defined by the angle of major loading direction and rolling direction and influences to hot formability of TRB. When forming take places at elevated temperature, the formability of TRB is greatly affected not only by the rolling orientation but also by inhomogeneous forming temperature. In this study, TRB of thickness ratio 1.43(1.5/1.05 mm) was employed to evaluate the formability at elevated temperature using stretch forming test which was performed according to various deformation modes. The experimental FLDs were determined by the second derivative Bragard method which was based on the analysis of strain distribution near failure. In order to obtain the rolling-orientation and temperature dependent FLDs, the experimental FLDs were used to establish interpolating equation using major loading direction, rolling direction and forming temperature. The determined equation was applied to predict failure by comparison of calculated major strain with the value of FE-simulation. The rolling-orientation and temperature dependent FLDs were also applied to FE-simulation for hot stamping of rectangular cup drawing to predict limit drawing height (LDH). The predicted LDH was verified by comparison with experimentally measured one. As a result, hot formability of TRB can be precisely predicted by the suggested FLDs compared to conventional FLDs considering thickness of TRB.

Stress based forming limit diagram for formability characterization of 6061 aluminum

Two numerical criteria of forming limit diagram (FLD) criterion and ductile fracture criterion (DFC) are presented for FLD prediction of 6061 aluminum. The numerical results are compared with the experimental FLD and also punch's load—displacement curve of experimental samples. Experimental FLD of this study is calculated using hemispherical punch test of Hecker. Experimental FLD is converted to FLSD and imported to the Abaqus software to predict necking of samples. Numerical results for FLSD prediction were compared with experimental FLSD. Results show that ductile fracture criterion has higher accuracy for FLD and FLSD prediction of 6061 aluminum. Comparison of numerical and experimental results for force—displacement curve of punch shows that numerical results have a good agreement with experiment.

Theoretical prediction of forming limit diagram of AZ31 magnesium alloy sheet at warm temperatures

A theoretical prediction on forming limit diagram (FLD) of AZ31 magnesium alloy sheet was developed at warm temperatures based on the M–K theory. Two different yield criteria of von Mises and Hill’48 were applied in this model. Mechanical properties of AZ31 magnesium alloy used in the prediction were obtained by uniaxial tensile tests and the Fields–Backofen equation was incorporated in the analysis. In addition, experimental FLDs of AZ31 were acquired by conducting rigid die swell test at different temperatures to verify the prediction. It is demonstrated from a comparison between the predicted and the experimental FLDs at 473 K and 523 K that the predicted results are influenced by the type of yield criterion used in the calculation, especially at lower temperatures. Furthermore, a better agreement between the predicted results and experimental data for AZ31 magnesium alloy sheet at warm temperatures was obtained when Hill’48 yield criterion was applied.

A New Thermo-Elasto-Viscoplastic Crystal Plasticity Framework to Predict the Formability of Aluminum Alloys at Elevated Temperatures

A new thermo-elasto-viscoplastic (TEV) crystal plasticity constitutive formulation is developed and implemented in the well-known Marciniak-Kuczynski analysis to predict the formability of aluminum alloys (AA) 5754 and 3003 at elevated temperatures. The model takes into account the temperature dependence of the single crystal elastic coefficients, single slip hardening parameters, thermal softening and slip rate sensitivity. Temperature dependent single slip hardening parameters are determined from uniaxial tension simulations at room and elevated temperatures. The new model is able to accurately predict the experimental forming limit diagrams (FLDs) without the need for further curve fitting. The effects of elastic constants and thermal softening on FLD predictions are discussed, and a new expression to represent the temperature dependence of the initial imperfection (for the M-K analysis) is developed to enable the model to successfully predict the FLDs for any temperature in the warm forming regime prior to recrystallization.

Analytical determination of forming limit curve for zirlo and its experimental validation

Zirconium alloy sheets used in the nuclear fuel assembly are subject to high temperature and stress, a corrosive and radiation environment and their performance has thus been of big concern. However, knowledge regarding the properties and the formability of zirconium alloys is still lacking. In this paper, strain-based forming limit diagrams (FLDs) are established for the zirconium alloy Zr1Sn1Nb0.1Fe (also called zirlo). The analytical forming limit curve (FLC) varies with forming limit model and yield criterion. To obtain the right hand side of the FLD, we apply the Swift's diffuse necking model, and for the left hand side, Hill's local necking model. Solutions from the analytical method are compared with experimental FLD established based on limit dome height (LDH) tests. Using the strain hardening exponent of a modified stress–strain relation, we could find excellent agreement of the analytical FLC with the LDH-based FLC.

Forming limit diagrams by including the M–K model in finite element simulation considering the effect of bending

Forming limit diagram is often used as a criterion to predict necking initiation in sheet metal forming processes. In this study, the forming limit diagram was obtained through the inclusion of the Marciniak–Kaczynski model in the Nakazima out-of-plane test finite element model and also a flat model. The effect of bending on the forming limit diagram was investigated numerically and experimentally. Data required for this simulation were determined through a simple tension test in three directions. After comparing the results of the flat and Nakazima finite element models with the experimental results, the forming limit diagram computed by the Nakazima finite element model was more convenient with less than 10% at the lower level of the experimental forming limit diagram.

Influence of material models on theoretical forming limit diagram prediction for Ti–6Al–4V alloy under warm condition

Forming limit diagram (FLD) is an important performance index to describe the maximum limit of principal strains that can be sustained by sheet metals till to the onset of localized necking. It offers a convenient and useful tool to predict the forming limit in the sheet metal forming processes. In the present study, FLD has been determined experimentally for Ti–6Al–4V alloy at 400 °C by conducting a Nakazima test with specimens of different widths. Additionally, for theoretical FLD prediction, various anisotropic yield criteria (Barlat 1989, Barlat 1996, Hill 1993) and different hardening models viz., Hollomon power law (HPL), Johnson–Cook (JC), modified Zerilli–Armstrong (m-ZA), modified Arrhenius (m-Arr) models have been developed. Theoretical FLDs have been determined using Marciniak and Kuczynski (M–K) theory incorporating the developed yield criteria and constitutive models. It has been observed that the effect of yield model is more pronounced than the effect of constitutive model for theoretical FLDs prediction. However, the value of thickness imperfection factor (f0) is solely dependent on hardening model. Hill (1993) yield criterion is best suited for FLD prediction in the right hand side region. Moreover, Barlat (1989) yield criterion is best suited for FLD prediction in left hand side region. Therefore, the proposed hybrid FLD in combination with Barlat (1989) and Hill (1993) yield models with m-Arr hardening model is in the best agreement with experimental FLD.

Experimental and theoretical investigation of forming limit diagram for Ti-6Al-4 V alloy at warm condition

Forming limit diagram (FLD) is an important performance index to describe the maximum limit of principal strains that can be sustained by sheet metals till to the onset of localized necking. It is useful tool to access the forming severity of a drawing or stamping processes. In the present work, FLD has been determined experimentally for Ti-6Al-4 V alloy at 400 °C by conducting a hemispherical dome test with specimens of different widths. Additionally, theoretical FLDs have been determined using Marciniak Kuczynski (M-K) model. Various yield criteria namely: Von Mises, Hill 1948, Hill 1993 and Cazacu Barlat in combination with different hardening models viz., Hollomon power law (HPL), Johnson-Cook (JC), modified Johnson-Cook (m-JC), modified Arrhenius (m-Arr.), modified Zerilli–Armstrong (m-ZA) have been used in M-K analysis for theoretical FLD prediction. The material properties required for determination of yield criteria and hardening models constants have been calculated using uniaxial tensile tests. The predicted theoretical FLDs results are compared with experimental FLD. It can be observed that influence of yield criterion in M-K analysis for theoretical FLD prediction is predominant than the hardening model. Based on the results; it is observed that the theoretical FLD using Cazacu Barlat and Hill 1993 yield criteria with m-Arr. hardening model has a very good agreement with experimental FLD.

Development of experimental and theoretical forming limit diagrams for warm forming of austenitic stainless steel 316

In sheet metal forming, the formability is limited by the onset of localized necking and it is important to know the limit up to which the material can be formed. Forming limit diagram (FLD) offers a convenient and useful tool to predict the forming behavior of the sheet metals, which can be enhanced by forming at elevated temperatures. This paper is focused on the development of FLD for austenitic stainless steel (ASS) 316 at 300°C, which has been experimentally determined to be the most suitable temperature for warm forming of ASS 316. Experimental FLD has been constructed by performing hemispherical dome punch tests on different width specimens. Theoretical FLDs have been developed using Marciniak–Kuczynski analysis based on Hill's and Barlat's yield criteria and compared with the experimental FLD. Theoretical FLD based on Barlat's yield criterion is found to be in a close agreement with the experimental FLD. These FLDs can be used for designing various warm forming processes on ASS 316.

Analysis of Forming Limit Diagram for Ti-6Al-4 V Alloy

Forming limit diagram (FLD) is aplotofthelimitingprincipalsurfacestrainsthatcanbesustainedby sheet metalspriortotheonsetoflocalized necking. It isusefulforcharacterizingtheformabilityofsheet metal and assessingtheformingseverityofvarious sheet metal processes. In this work, experimental FLD has been determined for Ti-6Al-4V alloy at 4000C using Nakajima test. Nakajima test has been conducted using spherical punch with specimens of different widths as per ASTM: E2218 – 02standard. In order to validate the experimental FLD results, theoretical forming limit diagram has been determined using MarciniakKuczynski (M-K) model. The accuracy of theoretical FLD is largely dependent on the selection yield criteria and hardening models. Here in M-K analysis, CazacuBarlat yield criterion with Hollomon power law (HPL) and Johnson-Cook (JC) hardening model has been considered. The material properties required for determination of yield criteria and hardening models have been calculated using uniaxial tensile tests. The predicted theoretical FLD results have been compared with experimental FLD. The influences of yield criteria and hardening models on the M-K theory parameters and the prediction itself have been investigated in the process. Based on the results; it can be observed that the theoretical FLD using CazacuBarlat with both hardening models has a better agreement with experimental FLD.

Finite Element Validation of Forming Limit Diagram of IN-718 Sheet Metal

The tensileanisotropy properties of Inconel-718 sheet metal were evaluated and the forming limit diagram (FLD) was established experimentally by deforming the material in different strain paths covering from tension-tension to tension-compression mode. Finite element model of the stretch forming process was developed successfully to predict limiting dome height (LDH) and strain distribution incorporating the Barlat-89 yield criterion and experimental FLD. It was found that the left side of FLD has higher forming limitscompared to right side. The IN-718 has encouraging stretch formability with uniform strain distribution in the cup compared to Ti6Al4V alloy reported in previous literature.

Analysis of forming limits based on a new ductile damage criterion in St14 steel sheets

Abstract Analytical and numerical analyses of forming limit in sheet metal hydraulic bulging test under combined internal pressure and independent axial feeding are researched in this paper. To predict the initiation of fracture, a new normalized ductile damage criterion based on strain hardening exponent, stress triaxiality and strain lode parameters are adopted. Eventually, elastic modulus is chosen as a characterization parameter to measure the ductile damage during the process of plastic deformation of the material. In addition, the explicit expressions of elastoplastic constitutive equations related to this damage criterion are compiled and implemented in ABAQUS/CAE software as the user subroutines. After compared against the analytical and the experimental forming limit diagrams (FLDs), the simulative FLDs demonstrate to be reasonable so that this model can be extended to predict a wide range of sheet metals’ forming processes.

A pragmatic approach to accommodate in-plane anisotropy in forming limit diagrams

The traditionally used forming limit diagram (FLD), a locus of limit strain states under different linear strain paths is usually determined from the blanks along the rolling direction. The effect of in-plane anisotropy on the forming limit diagram is neglected for engineering applications. However, the in-plane anisotropy effect is significant when the FLD is used to estimate forming limit stress diagram (FLSD). The available models to account for the in-plane anisotropy are reviewed and their limitations are discussed. A simpler and more pragmatic approach to account for the in-plane anisotropy in forming limit diagrams is proposed. The new method calculates the change in the plane strain limit using constitutive models of plasticity theory. The orientation specific FLD is then calculated by interpolating between the limit strains along the uniaxial, plane and biaxial strain paths. The proposed methodology is discussed by comparing the experimental FLDs for three different grades of low carbon steels and an aluminum alloy. The calculation of FLSD using the predicted anisotropic FLD, assuming Hill48 yield criterion is illustrated for one of the materials.

초기 형상 불안정성 기반 성형한계선도의 이론적 변수에 따른 성형 한계영역 평가

The current study examines the effect of the analytical parameter values on the theoretical forming limit diagram (FLD) based on the Marciniak-Kuczynski model (M-K model). Tensile tests were performed to obtain stress-strain curves and determine the anisotropic properties in the rolling, transverse and diagonal direction of SPCC sheet materials. The experimental forming limit curve for SPCC sheet material was obtained by limiting dome stretching tests. To predict the theoretical FLD based on the M-K model, the Hosford 79 yield function was employed. The effects of three analytical parameters - the exponent of the yield function, the initial imperfection parameter and the fracture criterion parameter - on the M-K model, were examined and the results of the theoretical FLD were compared to the experimentally measured FLD. It was found that the various analytical parameters should be carefully considered to reasonably predict the theoretical FLD. The comparison of the acceptable forming limit area between the theoretical and experimental FLD is used to compare the two diagrams.

Experimental Detection of the Onset of Local Necking in an Aluminium Sheet

Forming limit diagrams (FLDs) are widely used to assess metal sheet formability. Experimental FLDs are obtained by performing formability tests and determining failure strains. The standard method for detection of forming limits is based on the spatial distribution of the strains and requires formation of a single local neck. Some aluminium alloys, such as AA6016, have a tendency to form multiple strain localizations in formability tests, which can be interpreted as multiple local necks. Thus, use of the standard method is questionable for these aluminium alloys. The present paper presents an alternative, digital-image-correlation-based method for experimental detection of the onset of local necking in an aluminium sheet. The method is based on monitoring the sheet-thickness evolution, and is developed to be user independent and resistant to noise in the measurements. The method can be used in combination with different types of formability tests. The main requirement is that digital image correlation is used for strain measurements. Here, the method is initially tested on uniaxial tension tests of AA6016 aluminium alloy sheets and then extended to formability tests.

A comparative study of forming limit diagram prediction of tailor welded blanks

The Forming Limit Diagram (FLD) is a useful method for characterizing the formability of sheet metals. In this paper, different numerical models were used to investigate the FLD of Tailor Welded Blanks (TWB). TWB were CO2 laser-welded of interstitial-free (IF) steel sheets with difference in thickness. Numerical approaches of Muschenborn-Sonne Forming Limit Diagram (MSFLD), Forming Limit Diagram criterion (FLDcrt) and Ductile Fracture Criterion (DFCcrt), as well as new numerical method of Second Derivative of Thinning (SDT) were used for FLD prediction. The results of numerical models were compared with the experimental FLD, Limit Dome Height (LDH) and also load–displacement of samples. The emphasis of this investigation is to determine the performance of these different approaches in predicting the FLD. Results show that previous approaches are successful for the left side of FLD (drawing), but not so successful for the right side of the FLD (stretching). Influence of anisotropy on the forming behavior of TWB is investigated in this study and its results are compared with isotropic models and experimental data.

Digital speckle based strain measurement system for forming limit diagram prediction

A digital speckle based strain measurement system is developed to investigate the forming limit diagram (FLD) of sheet metal. A stochastic speckle pattern is sprayed on the surface of flat sheet metal before forming. A series of images are recorded by two cameras during the forming process. The strain field is then calculated for FLD determination, which involves the following key issues. First, to solve the problem of large deformation and strain measurement in sheet metal forming, a fractionized matching algorithm using deformation continuity of adjacent images is proposed. Second, an algorithm for three-dimensional (3-D) strain calculation is discussed, and a spline model is specially used to calculate the strain of the sheet metal in deep drawing. Third, a limit strain determination algorithm is proposed for forming limit curve (FLC) calculation by creating sections in the measured strain fields. Finally, a forming limit strain measurement system (also called Xi'an Jiaotong University Forming Limit Curve measurement system, XJTUFLC) is developed on the Visual Studio 2010 platform. With our self-developed image acquisition instrument and sheet metal bulging setup, FLD determination tests are conducted to validate the performance of the system. And the measured FLD is compared with the traditional experimental FLD as well as with that predicted by the empirical model. From the analysis of the experimental results, it can be concluded that the proposed system is feasible to measure the full-field strain during sheet metal forming processes and provides a better solution for forming limit diagram prediction.