Conventional Forming Limit Diagram Research Articles

A method and apparatus for determination of the ultrasonic-assisted forming limit diagram

It was recently demonstrated that ultrasonic vibrations could result in lower forming forces and a better surface finish in a wide range of metal forming processes. The Nakazima stretch-forming test is a long-established experimental procedure for the formability evaluation of sheet metals. Today, the development of a standard test is critical for assessing sheet metals’ formability enhancement due to ultrasonic vibrations, which can potentially unlock the material selection limit in various manufacturing applications. This study aims to present a method and apparatus for effectuating the forming limit diagram (FLD). At the same time, high-frequency ultrasonic vibrations are combined with the movement of the forming tool. Taking St14 steel as an example, the mechanical and microstructural properties such as formability, Micro-Vickers hardness, and grain sizes were systematically investigated. Furthermore, the conventional FLD, as well as the novel “Ultrasonic-Assisted Forming Limit Diagram” (UA-FLD), were attained and compared with a nonlinear regression-based approach. The results have indicated that superimposing ultrasonic vibrations with the amplitude of 15µm at the frequency of 20 kHz to the tool would cause a notable enhancement in forming limit diagram, a maximum of 28% increase in hardness, and a 23% reduction in average grain size of the specimens.

Effect of magnetic field on tension–tension side of forming limit diagram in sheet metal forming using a magnetorheological fluid

Sheet flexible-die forming using a magnetorheological (MR) fluid, which can change the mechanical property of flexible-die during the forming process, has become an innovative technology with great application potential in manufacturing thin-walled complex components. Although it has been proved that using an MR fluid as a flexible-die can improve the sheet formability, there is still a lack of in-depth understanding and systematic research. In this paper, the bulging process using elliptical dies with six kinds of ellipticities was adopted to achieve different strain paths and obtain the tension-tension side of forming limit diagram (FLD). Experiments using three kinds of MR fluids and four magnetic field conditions were conducted to systematically study their effects on the tension–tension side of FLD. The effect of the magnetic field on the fracture pattern of the specimen and its mechanism were also discussed. Results showed that magnetic particle content and magnetic field condition have a comprehensive impact on the forming limit diagram. When an MR fluid with a magnetic particle content of 20% is used, the forming limit under different magnetic field conditions has little difference. When the magnetic particle content increases to 30%, the forming limit curve gradually increases with increasing magnetic flux density. But when it reaches 43%, the forming limit curve increased first and then decreased with the increase of magnetic flux density. Besides, the extended FLD of the Al1060-O sheet was established, in which the conventional forming limit diagram is expanded to consider the influence of the magnetic field condition. These results can provide guidance in the parameter selection of magnetic flux density and magnetic particle content in sheet flexible-die forming using an MR fluid.

Prediction of edge fracture during hole-flanging of advanced high-strength steel considering blanking pre-damage

The stretch-flangeability of advanced high-strength steel (AHSS) sheets after blanking highly depends on the stress states as well as the edge pre-damage inherited from the initial blanking process. It cannot be predicted by using conventional forming limit diagram methods. To solve this issue, in this study, a numerical simulation model of the two-step hole cutting-hole expansion tests for the TRIP800 sheet was established by considering the initial surface irregularities induced by hole fabrication into the hole expansion process. Two methods, punching and wire-cut electrical discharge machining with low speed were adopted to cut holes. The modified Mohr–Coulomb fracture model together with post-failure softening was utilized to predict the fracture initiation and crack propagation during two forming processes. The results manifested that the WEDM-LS cutting method brought negligible damage to the hole edge and the sheet edge fabricated by this method can be assumed without pre-damage. Multiple finer notches were detected at the surface of the punched hole. These features triggered stress states with higher stress triaxiality up to 0.6 and thus accelerated the edge fracture occurrence during the hole expansion deformation. The measured hole expansion ratio of the punched hole was 26.1%, which was correctly predicted by the proposed model by considering edge pre-damage. As a comparison, the ideal model without pre-damage overestimated the value by about 100%.

A novel specimen design to establish the forming limit diagram (FLD) for GFRP through stamping test

Inspired by metal forming tests, the conventional forming limit diagram (FLD) was employed to characterize the forming properties of the Glass Fiber Reinforced Polypropylene (GFRP) composite in this study. The strain history of GFRP specimens was captured by using a 3D digital image correlation (DIC) system. Since the conventional metal FLD is established by major and minor strains only, which is inadequate to characterize the formability of different components in the pre-consolidated woven composites. Therefore, this study proposes a new notch design, where the specimens have two long notches with different aspect ratios on the both sides, to ensure that the failure is dominated by fiber breakage mode while retaining the fiber continuity in specimens. For comparison, the conventional hourglass specimens and the newly-proposed notch specimens with different widths were both tested through a series of stamping experiments to investigate the formability of the GFRP materials. The equivalent fiber strains based FLD from the conventional narrow hourglass specimens with 45°,-45° shows an abnormal value of equivalent fiber strain around 40% in the shear deformation region, which was far beyond the tensile limit of glass fibers. On contrary, the FLD from the proposed notch specimens presented a limiting strains around 5%, involving all possible deformation modes. Thus, the FLD of the notch specimens was established in the form of parallel line here, which can be used as a criterion to characterize the formability of GFRP in which the fiber breakage was a dominant failure mode. Note that this criterion takes into account the influence of different components on the formability of GFRP and combined deformation history with failure mechanism, implying more suitable for GFRP. This study provided an effective way to establish the design criteria and FLD for other woven pre-consolidated GFRP materials.

Investigation of Crack Prediction Method Using Limiting Surface Strain in High-Strength Steel Sheets

To study cracks, which are affected by bending forming, a hat-shape forming experiment was conducted. Then, a prediction method using limiting surface strain for bending crack was investigated. In the case of high bendability steel, breakage occurred after necking, which grew from the front and rear surface with obvious thickness reduction. In this type of breakage, it was found that the forming limit could be predicted by using a conventional forming limit diagram (FLD), which means that there is a limiting strain at the middle of the thickness direction. On the other hand, in the case of low bendability steel, cracks outside the bending surface occurred and grew, followed by breaking without the necking with obvious thickness reduction. In this case, the forming limit could not be predicted by using FLD, and it was found that the forming limit could be predicted by using limiting surface strain for bending crack, which could be obtained by finite element analysis (FEA) and an experiment by a V-shape bending test.

Prediction of FLD for sheet metal by considering through-thickness shear stresses

In this study, the effect of through-thickness shear (TTS) stress has been examined on the prediction of forming limit diagrams (FLDs). Determination of the FLD is based on the Marciniak–Kuczynski (M–K) model with some modifications on the stress states for consideration of the TTS stress effects. For solving the equations, the Newton–Raphson method has been used. Furthermore, the Nakazima test has been simulated to investigate the stress state which occurs in the sheet during the test. Results showed that the formability of sheet metal could be better as the through-thickness stress increased. Also, implementation of TTS stress in the present model, the corresponding FLD has better agreement than the conventional FLD with the experimental test result.

Analysis of formability in conventional hole flanging of AA7075-O sheets: punch edge radius effect and limitations of the FLC

Hole flanges are commonly manufactured in mass production by conventional press-working. In an industrial context, the process limits are usually evaluated by means of the Limiting Forming Ratio (LFR), which defines the maximum attainable diameter of the flange related to the initial pre-cut hole. Nevertheless, the LFR does not provide enough information about material deformation, thickness distribution or the expected onset and type of failure. In this sense, a systematic investigation using the Forming Limit Diagram (FLD) is needed. Under these circumstances, the aim of this work is to provide a better understanding of the deformation process in conventional hole flanging, analysing the effect of the punch edge radius as well as the influence of the strain distribution along the hole flange on formability. An experimental campaign on 1.6 mm thickness AA7075 annealed sheet was completed using cylindrical punches with different profile radii. In addition, numerical modelling of the process using finite elements was developed. The results allow better understanding of the physical mechanisms governing material deformation and process formability in very ductile materials. In this regard, this research work contributes to the current state of the art in conventional hole flanging by establishing the modes of failure that prevail in the process and the influence of the bending induced by the tool radius in the flange formability. In addition, the limitations of using conventional FLD for providing a limiting threshold for the strain states attained in the flanges deformed with different punch profiles are also identified.

A comparative study of the extended forming limit diagrams considering strain path, through-thickness normal and shear stress

The substitute presentations of the conventional forming limit diagram (FLD) are stress-based forming limit diagram (FLSD), extended stress forming limit diagram (XSFLD), and polar effective plastic strain forming limit diagram (PEPS-FLD). These diagrams have already been proposed as alternative criteria to the conventional FLD for predicting forming limits in processes that sheet does not experience proportional or in-plane loading conditions. The present study provides a complete comparison of different forms of forming limit diagrams. For this purpose, FLD and extended FLDs are predicted based on the modified Marciniak and Kuczynski (M-K) model with Yld2011 anisotropic yield function while various factors that cause a change in the FLD of a specific alloy including initial imperfection coefficient (f0), non-linear strain path, through-thickness normal and shear stresses are considered. The results indicate that all forms of extended diagrams are independent of strain path and the diagrams in stress space (i.e., FLSD and XSFLD) are less sensitive to the strain path than PEPS-FLD. In this regard, the main weakness of XSFLD, especially on the right-hand side, is that the safety margin cannot be visualized easily. By increasing the initial imperfection coefficient, the level of all forms of diagram increases. However, the effect of through thickness stresses on different diagrams is not the same. Increase in normal and shear stresses results in a downward shift in FLSD and an upward shift in other types of forming limit diagrams.

Numerical investigation of the combined effects of curvature and normal stress on sheet metal formability

A number of parts and components involved in the automotive industry are made of thin bent sheets, which are subjected to out-of-plane compressive stresses in addition to traditional in-plane stresses. Unfortunately, the classical predictions based on the conventional concept of Forming Limit Diagram (FLD) are no longer relevant when the strain distribution is heterogonous over the sheet thickness. Therefore, this conventional FLD concept is not capable of accounting for the effect of out-of-plane stresses on the onset of localized necking. The aim of the present contribution is to propose an extension of the well-known Marciniak–Kuczynski approach to simultaneously account for the effect of curvature and normal stress on formability prediction. The new developed tool allows predicting the limit strains for the whole range of strain paths. The mechanical behavior of the studied sheets follows the rigid–plastic flow theory. Through numerical results, it is shown that both curvature and normal stress tend to increase the formability limit of the sheet metal.

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.

다양한 하중경로에서의 DP980 강판의 파단변형률 예측에 관한 연구

Abstract The current study is concerned with the prediction of fracture strains for DP980 steel sheets over a wide range of loading paths. The use of DP980 steel is increasing significantly in automotive industries for enhanced safety and higher fuel efficiency. The material behavior of advanced high-strength steels (AHSSs) sheets sometimes show unpredictable and sudden fracture during sheet metal forming. A modified Lou–Huh ductile fracture criterion is utilized to predict the formability of AHSSs because the conventional forming limit diagram (FLD) constructed based on necking is unable to evaluate the formability of AHSSs sheets. Fracture loci were extracted from three dimensional fracture envelopes by assuming the plane-stress condition to evaluate equivalent plastic strains at the onset of fracture for a wide range of loading paths. Three different types of specimens -- pure shear, dog-bone and plane strain grooved -- were utilized for tensile testing to calibrate the fracture model of DP980 steel sheets. Fracture strains of each loading path were evaluated such that there shows little deviation between fracture strains predicted from the fracture model and the experimental measurements. From the comparison, it is clearly shown that the three dimensional fracture envelopes can accurately predict the onset of the fracture of DP980 steel sheets for complicated loading conditions from compressive loading to shear loading and to equi-biaxial tensile loading.

Enhancement of Lemaitre Model to Predict Cracks at Low and Negative Triaxialities in Sheet Metal Forming

Advanced high strength steels are still one of the best alternatives for light weight design in the automotive industry. Due to their good performances like high strength and high energy absorption, those steel grades are excellent for body in white components. Because of their restricted ductility, which sometimes leads to the formation of cracks without or low necking during forming operations, conventional forming limit diagrams may fall short. As a remedy, an enhanced variant of the Lemaitre continuum mechanical damage model (CDM) is presented in this work.Previous model extensions of the Lemaitre model improved the damage prediction for the shear and compression dominated stress states by introducing an additional weighting factor for the influence of compression on damage evolution, the so called crack closure parameter h. However, the possible range of the fracture behavior predicted by such models for low and negative stress triaxialities is limited. In this work, the Lemaitre CDM has been enhanced by considering the maximal shear stress to predict the fracture occurrence under shear. Previous models for the effect of void closure on damage evolution are reviewed and a novel model enhancement taking into account the maximal shear stresses is described. The determination of the damage model parameters is presented for a dual phase steel. For this particular material, the response of model enhancement on the failure prediction is discussed for a test part.

Formability prediction of AL7020 with experimental and numerical failure criteria

The formability of aluminum alloy sheet metal is a key issue in its design, analysis and operation of manufacturing processes. The conventional forming limit diagram (FLD) which evaluates the principal strains at failure is often used to quantify the formability limits. Due to the sensitivity of the FLD to the strain paths, the forming limit stress diagram (FLSD) based on principal stresses is shown to be more efficient. In contrast, a fully coupled behavior-damage models are recently proposed, which allow to predict the strain localization and the failure occurrence based on appropriates fully coupled constitutive equations describing the main physical phenomena involved. In this work a fully coupled constitutive equations taking into account the mixed nonlinear isotropic and kinematic hardenings fully coupled with the isotropic ductile damage is used. The microcracks closure is added to affect the equivalent plastic strain at fracture in a large range of stress states. Various tests are conducted to test the formability of aluminum alloy AL7020. The three different methods (FLD, FLSD and the fully coupled model) are identified and validated separately. With the help of Nakazima tests and cross-section deep drawing tests, the quality of the three failure criteria for AL7020 are compared and demonstrated with the investigations of the simulation results.

A different approach to estimate the process parameters in tube hydroforming

An enhanced unfolding inverse finite element method (IFEM) has been used together with an extended strain-based forming limit diagram (FLD) to develop a fast approach to predict the feasibility of tube hydroforming process of concept part and determine where the failure or defects can occur. In tube hydroforming, the inverse IFEM has been used for estimating the initial length of tube, axial feeding and fluid pressure. The already developed IFEM algorithm used in this study is based on the total deformation theory of plasticity. Although the nature of tube hydroforming is three-dimensional deformation, in this article a modeling technique has been used to perform the computations in two-dimensional space. Therefore, compared with conventional forward finite element methods, the present computations are quite fast with no trial and error process. In addition, the solution provides all the components of strain. Using the extended strain-based forming limit diagram, the components of strain can lead us to measure the potentials for failures during the deformation. The extended strain-based FLD based on the Marciniak and Kuczynski (M-K) model has been computed and used to predict the onset of necking during tube hydroforming. The extended strain-based FLD is built based on equivalent plastic strains and material flow direction at the end of forming. This new forming limit diagram is much less strain path dependent than the conventional forming limit diagram. Furthermore, the use and interpretation of this new diagram is easier than the stress-based forming limit diagram. The results of analysis for free bulging and square bulging have been compared with some published experimental data and the results obtained by conventional commercial software. The results indicate that the fluid pressure estimated by this method is 2.7 % greater than the results obtained by the experiment in the square bulging sample. In addition, the fluid pressure estimated in the free bulge sample is 5.6 % greater than the experimental results.

Hydroformability assessment of AA6063 tubes using the polar effective plastic strain diagram

Conventional forming limit diagram concept to determine the forming severity in tube hydroformed products might be restrictive because materials experience complex stress and strain path changes during the shaping process. In this study, a polar effective plastic strain diagram approach was adopted as a strain path–insensitive measurement to establish a criterion for evaluation of necking and, consequently, bursting failures in the tube hydroforming process. The polar effective plastic strain–based failure prediction uses information of the effective plastic strain and the direction defined by the arctangent of the current strain-rate ratio. These values were measured and calculated from free-expansion tests of straight AA6063 tubes for various combinations of axial feed and internal pressure using a stereo vision-based surface strain measurement system. The polar effective plastic strain diagram was constructed and applied to finite element analysis to predict the forming limit of AA6063 tubes. The effect of pretensions was also considered.

Comparison of FLD and Thickness Distribution on AA5052 Aluminium alloy Formed parts by Incremental Forming Process

Incremental forming process is one of the most promising newer techniques in metal forming process. Formability of analysis has to be carried out in order to obtain successful forming process. This paper aims to study the forming behavior of AA5052 aluminium alloy through incremental forming process. Truncated square pyramid and cone are formed to study the formability of AA5052 aluminium alloy at room temperature. A computer controlled numerical machine was used for forming. Forming limit diagram (FLD) is used to study the behavior of sheet metal. FLD and thickness distribution has been predicted and compared for both the shapes. The forming limit diagram obtained through incremental forming very much varies from conventional forming limit diagram. Comparison of FLD and thickness distribution shows that cone has higher forming limit than square cup and the thickness after forming is better in cone shapes than in square cups.

Effect of nonlinear strain paths on forming limits under isotropic and anisotropic hardening

The path-dependence of the conventional Forming Limit Diagram (FLD) is an important issue for its applications in industry. Great efforts have been made to understand the nature of the path-dependence with both experimental and theoretical approaches, many of them attempting to find a path-independent way for the application of forming limits. In this paper, we focus on the nonlinear strain path effect on forming limit predictions using both isotropic and anisotropic hardening models. The Forming Limit Diagram (FLD), Forming Limit Stress Diagram (FLSD) and Forming Limit Effective Strain Diagram (epFLD) of sheet metals subject to linear and nonlinear strain paths are analyzed and compared using the Marciniak–Kuczynski approach. An anisotropic hardening model based on Yoshida and Uemori development is adopted in this study, and it is coupled with the traditional Hill’48 yield surface. This model is capable of describing the complex Bauschinger phenomenon after the material undergoes the reverse loading process such as the early re-yielding, work-hardening stagnation and permanent softening. Two different scenarios for the change of strain paths are also investigated. In the first scenario, the sheet material is initially loaded with a fixed strain increment ratio, unloaded to the free stress state, and then reloaded with a different strain increment ratio until the forming limit is reached. In the second scenario, the material does not undergo elastic unloading. Instead, the strain path is abruptly changed to a different strain increment ratio and the material undergoes continuous loading until the forming limit is reached. It is found that the work-hardening behavior after the pre-straining and the loading scenario plays an important role in the path dependent behavior of forming limits. Detailed analysis reveals that the M–K approach may have contributed to the significance of path-dependence observed in this study, especially at high pre-strain levels.

Experimental investigations on microstructure and formability of cryorolled AA 5052 sheets

In this paper the effect of cryorolling on tensile and forming behaviour of aluminium alloy (AA) 5052 sheets has been investigated and compared with room temperature rolling of the same. These sheets were rolled up to 50% reduction in thickness at two different temperatures, namely, room and cryogenic temperatures, and compared. The combined forming and fracture limit diagram has been drawn and compared for AA 5052 alloy sheets of both rolling conditions. The formability results obtained for the room temperature rolled (RTR) and cryorolled (CR) conditions have been correlated with tensile properties. Cryorolled AA 5052 alloy with an elongated microstructure exhibited a very high percentage of necking strain during forming compared to the conventional forming limit diagram. This is due to the excessive cross-slip formed during deformation.

Influence of Different Pre-Stretching Modes on the Forming Limit Diagram of AA6014

In order to evaluate the formability of sheet materials forming limit diagrams (FLD) are recorded which represent the values of major and minor strain when necking occurs. FLDs are recorded based on the assumption that exclusively linear strain paths occur. In real forming parts, however, particularly in those with complex shapes, predominantly non-linear strain paths occur which reduce the accuracy of the failure prediction according to a conventional FLD. For this reason forming limits after loading with non-linear strain paths have to be investigated. In this contribution a systematic analysis of the forming limits of a conventional AA6014 alloy after loading with non-linear strain paths is presented. This material is pre-stretched in uniaxial, plane strain and biaxial direction up to several levels before performing Nakajima experiments in order to determine FLDs. During the pre-stretching process as well as during the Nakajima experiment the strain distribution can be measured online very precisely with the optical deformation measurement systems GOM Aramis or VIALUX. The gained curves are compared to the FLD of the as-received material. The results prove a significant influence of the pre-stretching condition on the forming limits of the used aluminum alloy. For a low pre-stretching in uniaxial as well as in biaxial direction the FLDs show a slightly reduced formability while after higher pre-stretching levels the forming limit can be improved such as for biaxial loading after uniaxial pre-stretching. The formability after pre-stretching in plane strain direction was changed. Also, a shift of the FLD depending on the direction of pre-stretching can be observed.

세탁기용 VCM 강판 성형시 PET 코팅층 찢김 저감방법

A VCM sheet is a metal sheet on which PET/PVC is coated for outer panels of home appliances. The purpose of this study is to obtain methods for suppressing PET tearing that occurs during the press forming of the VCM sheet. In order to identity the factors that minimize PET tearing, an FE analysis was performed. The occurrence of PET tearing cannot be predicted using the conventional forming limit diagram. PET is torn by friction between a die and sheet, which is caused by the thickening of material at a die corner. To reduce the thickening of material, the blank shape was re-designed and the thickened material at a flange was removed by a trimming process. The results of the FE-analysis involving modified process parameters showed that the thickness of the product at a die corner is distributed within the clearance of drawing and flangeforming process. A forming experiment was conducted to verify the proposed process parameters. A good final product was obtained without PET tearing of the VCM sheet.