Experimental Forming Limit Diagram Research Articles

Numerical and analytical analyses of the formability and fracture of AA7075-O aluminum sheets in hemispherical punch tests

In this study, numerical simulations and experimental validations of the simulation of hemispherical punch tests for AA7075-O aluminum sheets with various sample widths are presented. It is convincingly believed in literature that a finite element (FE) based forming limit diagram (FLD) can be predicted very well using various time-dependent criteria. This matter has been investigated and securitized deeply and the FE-based FLD was predicted using three time-dependent criteria and compared with the experimental FLD. Results show that two of the three criteria could predict the relatively appropriate shape of the FLD while one of them has failed to match. Aside from using FE simulation to predict the FLD, an analytical method, namely, Marciniak-Kuczynski (M-K) was also used to make a better evaluation about the capability of the finite element method (FEM) to predict FLD. Among the FE-based FLDs, the one predicted using the Martinez-Donaire et al., 2014 was found to be close to the one predicted using the M-K method. Although, the main objective of this paper is to investigate the capability of the FEM to predict an FLD for AA7075-O aluminum sheets, the fracture behavior for each case was predicted using a unified fracture model. Several computer runs were executed to perform the tests and reproduce the experimental results. The aim of this study was to discuss the simulation of hemispherical punch tests and analyze the numerical results and compare them with the experimental and analytical methods. It was observed that the experimental FLD can be reproduced using various time-dependent criteria in a relatively appropriate manner but with limitations especially at the equibiaxial stress state. These limitations were scrutinized and discussed in detail by comparing the results with experimental and analytical calculations.

Evaluation of forming limit diagram and bending stiffness of SS316L/polyurethane/SS316L sandwich sheets

Abstract In this study, SS316L/polyurethane/SS316L was produced by warm roll bonding and direct adhesion without using any adhesive. By changing the polymer core thickness in the sandwich sheet, its mechanical properties, such as tensile behavior and flexural bending strength, were investigated. Also, by performing the Erichsen test and getting the experimental forming limit diagram, the forming behavior of the sandwich sheets in various thicknesses was investigated and compared with that of the monolithic steel sheet. The experimental results showed that by increasing the thickness of the sandwich sheets with polymeric core thickness of 2 mm to 2.5 and 3 mm, the bending stiffness was raised by 111% and 288%; also, the displacement in the second region of the bending test diagram, indicating the bending ability without delamination, was increased from 100% to 109%. Forming limit diagrams of the sandwich sheets were higher than those of the steel sheet, which indicates that the forming behavior of them are higher than that of the monolithic steel sheet.

Formability evaluation based on a constitutive model with stress rate direction dependency considering bifurcation modes

Accurately predicting the fractures that occur in materials during forming not only improves quality, but also reduces the amount of material that is discarded. Therefore, as a key technology for digital transformation to achieve carbon neutrality, it is necessary to improve the accuracy of forming analysis and establish an efficient method for predicting forming limits. Formability assessment is typically performed using ductile fracture criteria or experimental forming limit diagrams (FLDs), which require prior fracture testing. The authors have established a forming evaluation method based on three-dimensional local bifurcation theory as a versatile method that does not require destructive testing. This method can follow abrupt changes in the stress field, such as localized necking, by using a flow rule that takes into account the directionality of the stress rate. In this study, the proposed method is applied to the tensile testing and the forming analysis of a square cup drawing to analytically verify the location and onset time of local bifurcation modes that may lead to fracture.

Predicting the forming limit diagram of the fine-grained AA 1050 sheet using GTN damage model with experimental verifications

In this research, forming limit diagram (FLD) of aluminum alloy 1050 (AA 1050) sheet produced by Accumulative Roll Bonding (ARB) is investigated numerically and experimentally. The Gurson-Tvergaard-Needleman (GTN) ductile damage model is used to predict sheet failure and obtain its FLD using numerical simulation in Abaqus/Explicit. Nucleation and growth of voids in the material during the deformation is the basic concept of the GTN damage model. This damage model has nine basic parameters that obtaining through experimental tests is time-consuming and costly, and in some cases, impossible. Thus, the present study tries to obtain the above parameters for fine-grained aluminum 1050 fabricated by ARB using the finite element method. Therefore, after considering each parameter’s interval, numerical simulation and the anti-inference method are used in the uniaxial tensile test to identify GTN parameters for the AA 1050 sheet using FEM. The optimum parameters of the GTN model are used in the FEM of the Nakazima test for FLD prediction. Also, The FLD of the fine-grained aluminum sheet is obtained experimentally using the Nakazima test. Finally, the numerical and experimental FLDs are compared for validation.

Study on the Effect of Anisotropy on Plastic Flow Localization of Third Generation Advanced High Strength Steel

The aim of this work is to analyze the effect of the anisotropy on the formability of the third generation of advanced high strength steel (3genAHSS) from experimental and theoretical point of view. The reference material is the USS CR980XG3TM️ AHSS, a 3genAHSS 980T/600Y-retained austenite bearing-high elongation steel grade. A careful experimental work on the selected 3genAHSS characterization has been performed. The anisotropy factors and the yield stresses have been identified from tensile tests at several orientations with respect to the rolling direction. The experimental forming limit diagram under linear strain paths has been determined using Nakajima tests and the Erichson test for the equibiaxial stretching, respectively. The Marciniak-Kuczynski analysis is used to simulate the onset of localized necking through an advanced sheet metal forming limit model. YLD00-2d yield condition gives the initial shape of the yield locus. Swift strain–hardening power law is used to describe the strain hardening of the material. The effect of the anisotropy on the forming limits of 3genAHSS steel is analyzed. It was achieved proper reproducibility of the experimental tendencies of anisotropic factor distribution and the yield stress as a function of the tensile loading axis by the selected constitutive equations. A good accuracy of the FLDmodel on the prediction of the experimental results is found.

Deformation behaviour and formability analysis of thin brass sheet: experiments and modelling

ABSTRACT In this study, the hot deformation and formability behaviour of commercially Brass sheet under uniaxial and multiaxial loading conditions at a wide range of temperatures (room temperature −773 K) have been investigated by experiments and theoretical modelling. Uniaxial tensile test and Nakazima test at different test temperatures have been conducted. Different constitutive models, namely, Johnson-Cook (JC) model, modified Zerilli–Armstrong (m-ZA) model, modified JC model, integrated Johnson Cook and Zerilli–Armstrong (JC-ZA) model, have been used to understand the prediction behaviour of flow stress of Brass. Further anisotropic yield criteria, namely, Hill’48 and Barlat’89 yield functions have been utilised for yield loci prediction. From Nakazima test, the experimental forming limit diagram has been plotted. Other formability parameters, namely, limit dome height, thickness distribution, and strain distribution have been analysed. The theoretical FLD by Marciniak Kuczynski (MK) model. By employing the uniaxial constitutive models, anisotropic yield criteria have been investigated. The predicted MK-FLD coupled with the JC-ZA model and Barlat’89 yield criteria shows good agreement with measured experimental FLD.

Investigation of material failure in micro-stamping of metallic bipolar plates

Micro-stamping is a promising process for the low-cost manufacture of micro-channels from thin metal sheet for fuel cell bipolar plates. Most previous studies numerically analysed micro-stamping processes by assuming a perfect tool profile and position. In this work, thin 316 L stainless steel sheet is stamped with a micro-stamping tool to produce micro-channels and the initiation of fracture is experimentally investigated. Severe material thinning and fracture were observed in locations where the sheet contacts the tool and related to tool misalignment and profile inaccuracies that only could be identified with a 3D profilometer and an optical microscope. A 2D finite element model of the process was then developed and showed that, to accurately represent material thinning and forming limits in the micro-stamping of the stainless steel sheet, the scanned tool profile shape and position need to be accounted for. Comparison with the experimental Forming Limit Diagram (FLD) suggests that in the stamping of micro-channels from thin stainless steel sheet, material failure is governed by the development of a neck and therefore can be successfully assessed by the FLD.

Prediction of forming limit diagrams from tensile tests of automotive grade steels by a machine learning approach

Steels’ formability is extremely important to the automotive industry. This property is usually assessed through the Forming Limit Diagrams (FLDs), which comprise the regions of maximum strains, where neither necking nor fracture of the material is observed. In this work, the use of Machine Learning algorithms was evaluated for the FLDs’ construction, based on the tensile properties of a group of steels. A set of historical data, consisting of tensile tests values and measured FLDs, based on Nakajima method of various AHSS, HSLA and IF steels, was used to build the model. In order to evaluate the predictive capacity of the model, experimental and Keeler-Brazier FLDs were compared. The proposed method was able to predict with great correlation and low mean error the FLDs of those materials. The results show a viable route for predicting FLDs based on tensile properties.

Effect of localization criteria and yield criteria in predicting the forming limit diagram (FLD) of DP590 steel sheets

ABSTRACT The main objective of the present work is to study the effect of different localisation criteria and yield criteria in predicting the forming limit diagram (FLD) of dual phase (DP) 590 steel sheets. DP590 steel is used in automotive applications for structural and safety parts such as cross members, longitudinal beams, B-pillar reinforcements and bumper reinforcements. Limit dome height (LDH) tests were performed for DP590 steel sheets and experimental FLD is plotted. Tensile tests and plastic strain ratio ‘r’ tests were performed at different rolling directions to evaluate the mechanical properties The evaluated mechanical properties were used in finite element (FE) simulations to predict the FLD of DP590 steel sheet. Three material models namely Transversely anisotropic elastic plastic, 3 parameter Barlat yield law and Hill 3 R which includes diverse yield criteria Hill 48, Barlat 89 and Hill 3 R, respectively, were used in FE analysis. Three different localisation criteria namely equivalent plastic strain criterion, thickness criterion and localisation criterion based on true strain gradient were used to predict the FLD of DP590 steel sheets. It was found that predicted FLD is close to experimental FLD when localisation criterion proposed, based on true strain gradient and Hill 48 yield criterion is used.

Comparative study of Dual-Phase -590 steel on formability at superplastic region and room temperature

A steel alloy DP590 is commonly used for automobile applications because of its outstanding mechanical characteristics. One crucial limitation of this steel forming is that it has limited malleability and ductility. In this study, we compared the experimental forming limit diagram (FLD) for DP590 at RT and 800°C using stretching. An experiment with a strain rate of 0.01/s is carried out with samples cut in four different directions (0°,30°,60°& 90°) as seen from the rolling direction. Rolling direction specimens have been found to be among the stronger samples. FLD can be applied as a method for studying temperature differences in formability characteristics of DP590. Scanning electron microscopy was used for the analysis deformation pattern. Based on these results, it shows that the material has become significantly more formable.

Crystal plasticity finite element–Marciniak-Kuczynski approach with surface roughening effect in predicting formability of ultra-thin ferritic stainless steel sheets

Forming Limit Diagrams (FLDs) of 0.1 and 1 mm thick ultra-thin ferritic stainless steel (FSS) sheets are predicted using a combination of the crystal plasticity finite element (CPFE) approach and the Marciniak-Kuczynski (M-K) model. In a scale of few microns, especially for thin materials, surface roughness significantly affects sheet formability; therefore, the M-K model is further modified to address the surface roughening effect. The CPFE combined M-K model with the surface roughening effect can reproduce experimental FLDs of two FSS sheets, unlike the method without considering the surface roughening effect. The results highlight the importance of surface roughening, particularly in thinner sheets, where the portion of surface roughness is an order higher than that in the thicker sheets. The evolution of the deformation texture under various loading paths is further investigated and discussed. The findings coincide with reports of previous studies.

Experimental Determination and Theoretical Prediction of Limiting Strains for ASS 316L at Hot Forming Conditions

In the present work, the austenitic stainless steel 316L is used for determining the forming limit diagrams (FLDs) at hot forming conditions. Firstly, the theoretical prediction of flow stress was done using Johnson-Cook and modified Zerilli-Armstrong (m-ZA) constitutive equations at three test temperatures (750, 825 and 900 °C). It was found that the m-ZA model displayed better predictability of flow stress. Additionally, Hill 1948 and Barlat 1989 yielding functions have been formulated, and it was found that Barlat 1989 displays better-yielding behavior predictability at all considered temperatures. Further, the Nakazima test has been used to find the experimental FLD. The limiting strains of the material displayed an improvement of approximately 57% with an increase in temperature from 750 °C to 900 °C. The Marciniak-Kuczynski (M-K) model has been used for theoretical prediction of FLD and it was found that the combination of Barlat 1989 function with m-ZA model displayed the best FLD prediction ability at all the considered temperatures with an error of approximately 5%. Further, the limiting dome height, surface strain and thickness distribution have been found at all the testing temperatures. The fractographic study revealed a ductile type of failure for all the specimens at all the temperatures.

Study on Plastic Response Under Biaxial Tension and Its Correlation with Formability for Wrought Magnesium Alloys

The mechanical response and microstructural changes under biaxial tension of two magnesium alloy sheets, ZE10 and AZ31, have been investigated. The forming limit diagram (FLD) of the two alloys was further assessed using the Marciniak–Kuczynski (M–K) model combined with two constitutive models: (a) crystal plasticity finite element (CPFE), and (b) phenomenological yield. The FLDs predicted by the combined CPFE and M–K model were in excellent agreement with the experimental data. The phenomenological yield models using the mechanical data at small plastic work led to poor prediction results. However, these could well reproduce the experimental FLDs when the mechanical data at larger plastic work were used for parameter identification. In-depth analyses revealed that the evolution of the anisotropic strain hardening during biaxial tension and significant evolution of the r-value during uniaxial tension were the main sources of the error in the predictions by the phenomenological models using the material data at smaller plastic work.

Comparative study of ASS 316L on formability at room temperature and super plastic region

ABSTRACT In the sheet metal industry, hot forming of high strength sheet metal alloys such as austenitic stainless steels (ASSs) are in great demand. Identifying the safe strain region is essential to avoid failures and reduce the wastage. Forming limit diagram (FLD) is a vital tool which is used to describe the maximum limit of principal strains that can be sustained by sheet metals till the onset of localised necking. These diagrams are also useful in comparing the changes in forming characteristics of the material with changes in process parameters like temperature, orientation and speed of deformation. The present study aimed at comparing the experimental FLD for ASS 316L at room temperature and 900°C by stretch forming. These specimens are cut in three different orientations (0°, 45° & 90°) to the rolling direction and experiments are conducted at a strain rate of 0.1/s. It is reported that, the specimens from rolling direction are among the stronger samples. The change in formability characteristics of ASS 316L with changes in temperatures using FLD has been observed. The optical microscopy and scanning electron microscopy is analysed to understand the fracture morphologies. The comparison between these set of results indicates that there is significant increase in formability of material. Abbreviations ASS: Austenitic Stainless Steel; RT: Room Temperature; FLD: Forming Limit Diagram; FFLD: Fracture Forming Limit Diagram; SEM: Scanning Electronic Microscopy; LDH: Limiting Dome Height; UTS: Ultimate Tensile Strength; YTS: Yield Tensile Strength; K: Strength Factor; n: Strain Hardening Exponent

Finite element and experimental method for analyzing the effects of martensite morphologies on the formability of DP steels

In this article, we investigated the effect of martensite morphology on the mechanical properties and formability of dual phase steels. At first, three heat treatment cycles were subjected to a low-carbon steel to produce ferrite–martensite microstructure with martensite morphology of blocky-shaped, continuous, and fibrous. Tensile tests were then carried out so as to study mechanical properties, particularly the strength and strain hardening behavior of dual phase steels. In order to study the formability of dual phase samples, Forming Limit Diagram was obtained experimentally and numerically. Experimental forming limit diagram was obtained using Nakazima forming test, while Finite Element Method was utilized to numerically predict the forming limit diagram. The results indicated that the dual phase samples with fibrous martensite morphology had the highest tensile properties and strain rate hardening out of the three different microstructures. Blocky-shaped martensite morphology, on the other hand, had the worst mechanical properties. The study of the strain hardening behavior of dual phase sample by Kocks–Mecking-type plots, evinced two stages of strain hardening for all specimens with different microstructures: stages III and IV. The forming limit diagram of dual phase steels also proved that samples with fibrous martensite morphology had the best formability compared to other two microstructures. The simulated forming limit diagram manifested that there is a good agreement between experimental results and those obtained by FEM.

Investigations into Improvement in Formability of AA5754 and AA6082 Sheets at Elevated Temperatures

Warm forming is an attractive formability improvement technique which can be utilized to intensify the usage of aluminum alloy sheets in autobody constructions. In the present work, laboratory-scale stretch forming and deep drawing experiments were performed to demonstrate the comparative formability improvement in AA6082-O and AA5754-H22 aluminum alloy sheets at elevated temperatures. Significant enhancement of limiting dome height and forming limit diagram (FLD) was observed when stretch forming was performed at 200 °C. Warm deep drawing under both isothermal and nonisothermal conditions was carried out, and drastic improvement in drawability was found only under nonisothermal condition with an initial temperature gradient of 93 °C across the blank. Thermomechanical finite element (FE) models of the warm forming processes were developed using temperature-dependent Barlat-89 yield model coupled with Cowper–Symonds strain rate sensitivity model. The limiting dome heights, failure locations and strain distributions were well predicted by implementing experimental FLD as the failure criterion. Further, the effect of evolution of nonisothermal temperature gradient on the improvement in drawability of both the materials was analyzed in terms of cup height, earing profile, thickness distribution and surface strain evolution.

Prediction of Forming Limit Diagram (FLD) of Al 5182 by using different hardening laws and different localization criteria and comparing with experimental FLD

ABSTRACTAluminium alloys play a key role in automotive applications in present days. The main reason for using Al alloys is due to its light weight and high strength to weight ratio. The main objective of this paper is to predict Forming Limit Diagram (FLD) of Al 5182 by using different hardening laws and different localization criteria and comparing with the experimental results. Tensile tests were performed for different rolling directions and mechanical properties were evaluated. These mechanical properties were used in Finite Element Method (FEM) simulations to predict the FLD of Al 5182. Different hardening laws like Load curve, Voce law and Hockey Sherby law were used and different localization criteria like Bhargava et al., equivalent plastic strain criterion, thickness criterion, maximum punch load, transition strain path were used to predict FLD. It was observed that FLD of Al 5182 predicted by localization criterion proposed by Bhargava et al. is coming closer to experimental results in all hardening laws and in among the three hardening laws used Load curve and Voce hardening law, the simulated FLD was coming closer to experimental results.

Comparative study on theoretical and experimental evaluation of forming limit diagrams

Forming limit diagrams (FLDs) are generally used to reflect the strain limits of sheet metal materials. These diagrams contain essential information for planning of high series stamping processes, however the experimental definition is still a difficult and time-consuming procedure. Five or more samples are needed to cover the different strain paths sufficiently, from pure shear (ε1 = -2ε2) up to biaxial stretch forming (ε1 = ε2), moreover the experimental detection of the onset of local necking depends on the capability of the measuring equipment and person. The determination of the measurement results is further complicated by the material and other influencing conditions, like strain path (deformation history), rolling direction, sheet thickness, temperature, measuring grid size, tool surfaces, friction and vibrations. All these things supports the development of clearly theoretical and semi-empirical models for defining FLDs. This paper presents a comparative study of some kind of well-known theoretical models and experimental FLDs of automotive dual phase (DP) thin sheets. The experimental determination was carried out by Nakajima tests on five different sample geometries. We used follow-up strain analysis on the cracked samples. The results highlighted that most of the theoretical and semi-empirical models can be appropriately used in the negative quadrant of the FLD despite of the effect of the friction. However, in the positive quadrant, there are some more visible deviations due to outer conditions like lubricant.

Measurement of directional anisotropy coefficients for AA7020-T6 tubes and prediction of forming limit curve

The mechanical properties of tubes in hoop directions can be measured with ring hoop tensile test (RHTT). This test involves placing a ring sample of tube over the two D-shaped mandrels which can be parted with a testing machine. In this article, the goal was measuring the directional anisotropy coefficients of hydroformed AA7020-T6 tubes (r0, r45, and r90) to predict forming limit diagram (FLD). Due to deriving anisotropy coefficients in different directions, various tensile tests should be performed for the tube. For longitudinal and circumferential samples, a simple tensile test and ring hoop tensile test were applied to obtain r0 and r90, respectively. Additionally, for testing in 45° to the rolling direction, a new testing method which is inspired by RHTT was used to find r45. Afterwards, forming limit diagram of this aluminum alloy was predicted theoretically based on the Marciniak-Kuczynski (M-K) model and Voce hardening law. Since, one of the important factors in gaining accurate FLDs is yield function. Two advanced yield functions, BBC2008 and YLd2011, were selected. These advanced yield functions can describe material’s anisotropy behavior better than the classical ones. The importance of the directional anisotropy coefficients and other data obtained by tensile tests was in calibration of yield functions. Good agreement between the FLD derived under the influence of a calibrated yield function and the experimental FLD supports the present calibration.

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.