Experimental Forming Limit Curve Research Articles

Formability prediction of high‐strength steel sheet using experimental, analytical and theoretical analysis based on strain and stress forming limit curves and its application to automotive forming parts

AbstractIn this work, the high‐strength steel (HSS) sheet dual‐phase 440 (DP440) were conducted to establish the forming limit curve (FLC) and analytical forming limit stress curve (FLSC) obtained from experimental forming limit curve. First, the Nakajima stretch forming examination was carried out to obtain forming limit curve of investigated sheet. Afterwards, the theoretical Marciniak–Kuczinsky (M–K) model was developed and calculated to evaluate localized necking limits both in strain and stress spaces combination with anisotropic yield criteria. Then, the analytical forming limit stress curves were plastically calculated by using experimental forming limit curve data combination with Swift hardening model and anisotropic yield criteria namely, Hill’48 and Yld2000‐2d for representing anisotropic plastic deformation behavior on examined steel sheet. Finally, automotive stamping parts were performed in order to verify an applicability of all developed curves. It was observed that the analytical forming limit stress curves could more precisely predict the formability of automotive parts better than the forming limit curve based on strain. Particularly, the one based on Yld2000‐2d predict better than the one based on Hill’48. Simultaneously, the experimental forming limit curve and analytical forming limit stress curve were also evaluated comparing with the theoretical calculated forming limit curve and forming limit stress curve using the Marciniak–Kuczinsky model. It should be noted again that the experimental forming limit curve and analytical forming limit stress curve are the best one. Therefore, the Yld2000‐2d yield function better represented the anisotropic behavior of the high‐strength steel sheet dual‐phase 440 than Hill′ 48 yield function, and can suitable be used for the analysis prediction and design of bumper automotive parts under forming processes.

A novel integrated framework for reproducible formability predictions using virtual materials testing

Background: Formed aluminium alloy sheet materials are increasingly adopted in production processes such as vehicle manufacturing, due to the potential for weight-saving and improved recyclability when compared to more traditional steel alloys. To maximise these benefits whilst maintaining sufficient mechanical properties, the link between formability and microstructure must be better understood. Virtual materials testing is a cost-effective strategy for generating microstructure-informed formability predictions. Methods: We developed an open-source hybrid framework, combining experimental and computational tasks, for generating reproducible formability predictions. Starting with experimental texture measurements and stress-strain curves, we calibrated crystal plasticity (CP) model parameters. The framework used these parameters to perform a large set of multiaxial full-field CP simulations, from which various anisotropic yield functions were fitted. With these anisotropy parameters, we then employed a Marciniak-Kuczyński finite-element model to predict forming limit curves, which we compared with those from experimental Nakazima tests. Results: We executed the workflow with the aluminium alloy Surfalex HF (AA6016A) as a case study material. The 18-parameter Barlat yield function provided the best fit, compared to six-parameter functions. Predicted forming limits depended strongly on the chosen hardening law, and good agreement with the experimental forming limit curve was found. All of the generated data have been uploaded to the Zenodo repository. A set of Jupyter notebooks to allow interactive inspection of our methods and data are also available. Conclusions: We demonstrated a robust methodology for replicable virtual materials testing, which enables cheaper and faster formability analyses. This complete workflow is encoded within a simple yet highly customisable computational pipeline that can be applied to any material. To maximise reproducibility, our approach takes care to ensure our methods and data — and the ways in which that data is processed — are unambiguously defined during all steps of the workflow.

Forming limit analysis of AA5052 sheet under bilinear strain path by designing a novel large-scale gripping fixture

The combined strain paths have significant effects on the formability on the sheet metal. In this work, aiming at a widely-used AA5052-O sheet metal, the uniaxial tension and the Nakazima tests were conducted on the large-scale specimens subjected to the pre-tension deformation. First, a novel gripping fixture was designed and manufactured to achieve the uniform pre-strains of the large specimen. Then, two types of strain paths of the tension - tension and tension - bulging were implemented to reveal the evolutions of the mechanical properties and forming limit curves (FLCs), respectively. Moreover, the forming limit stress curves (FLSCs), which are more insensitive to the changes of strain paths, are calculated from the experimental FLCs to improve the prediction accuracy of finite element (FE) simulations. Compared to the conventional necking criterion of path transition and the FLC criterion, the FLSC criterion can effectively enhance the simulation precision in the biaxial tension region.

Polar effective plastic strain - forming limit diagram of DP 440 steel sheet with application to two-step forming test

In this work, experimental forming limit curve (FLC) and polar effective plastic strain -forming limit diagram (PEPS-FLD) are developed in order to predict the formability of dual phase (DP) steel grade 440. The Forming Limit Diagrams (FLD) of the examined steel are first obtained using the Nakajima stretch-forming test with a decreased hemispherical punch diameter of 50 mm in combination with Auto-Grid Vialux strain measurement system. To achieve a PEPS-FLD, an experimental FLC data must be completely projected onto the polar space using the results of FLC, Hill's 48 anisotropic yield criterion, and PEPS algorithm through plasticity calculation. Finally, a two-step forming test is conducted both experiments and simulation to demonstrate the practical applicability of the PEPS-FLD. It really would appear that the PEPS-FLD could predict the formability in non-linear strain path and can be utilized to enhance formability by creating non-linear strain path of DP440 more accurately than FLD.

Forming limit of AZ31B magnesium alloy under in-plane complex biaxial loading paths with cruciform specimens

This paper focused on the forming limit curves (FLC) of the AZ31B magnesium alloy sheet metal under different complex loading paths in-plane. Compared with simple loading paths, the study of forming limit of sheet metal under complex loading paths was more practical. In this study, biaxial tensile test of the cruciform specimen was utilized to acquire the FLC after the cruciform specimen was subjected to uniaxial pre-tensile process along rolling direction, which experimentally characterize the forming limits under different pre-strain values of 1.15%, 2.34%, 4.0%, and 5.4%. Subsequently, based on the constitutive model, Hill48 yield criterion and shear failure criterion, the theoretical FLCs of AZ31B magnesium alloy sheet metal was be calculated. Meanwhile, the normal biaxial tensile tests were also simulated by Abaqus to obtain the limit strains by Finite Element Analysis (FEA). Extracting limit strains from the fracture region in FEA model when the first derivative of the strain difference with respect to time reached the maximum value between the first principal strain of necked element and the first principal strain of the element adjacent to the necked zone. As a result, the experimental FLCs was qualitatively consistent with the result of theoretical model and FEA model. In addition, the FLCs of AZ31B magnesium alloy sheet moved to the upper left of forming limit diagram with the increase of the pre-strain, which indicated that the pre-strain process along the rolling direction could significantly improve the formability of the sheet metal.

Formability Assessment with Microstructural Investigations for Zirconium 702 Thin Foils: Bio-Material Applications

ABSTRACT Application of Zirconium alloys for biomedical applications have received increasing attention. Unique properties like formation of an internal bone-like apatite layer and also the interaction with magnetic resonance imaging (MRI) diagnostics with better compatibility, low magnetic susceptibility and overall excellent biocompatibility, mechanical properties and resistance to biocorrosion. Forming process is plastic deformation process wherein material undergoes permanent deformation in die cavity without fracture. Local necking, wrinkling, cracking, earing etc are few of observed errors. Due to miniaturization, manufacturing at micro level is essential. Micro forming is difficult to control as thickness of foil is below 100 microns. Hence, investigation and prediction of mechanical properties of the material at micro-level plays a very vital role. The current research focusses on the forming limit curves (FLC), which is one of the way of investigation performed to predict the formability of the material Zirconium 702 (Zr702) with the sheet thickness 100 microns. Nakajima test as per the ASTM 2218–14 standards was applied. Numerical and Experimental FLCs arrived at shows good concordance. Micro-structural study is also performed on the test specimen before and after forming to analyse the behaviour of the material.

Comparison of Constitutive Models for Predicting the Formability of SS 304 by Tubular Hydroforming Process

Finite Element (FE) simulation of sheet/tube forming precision depends mainly on the accuracy of the constitutive modeling. The present paper aim is to compare the constitutive models to fit the stress-strain curves. The accurate deformation behavior of the SS 304 tubes depends on the constitutive modeling of hardening behavior. Deformation data of the tensile specimens cut from tubular sample were collected by conducting Uniaxial tensile tests (UTT) at three different rolling directions. Five constitutive relationships were then recognized by fitting the true stress and strain data with the constitutive models of Hollomon, Power, Krupowsky, Voce and Ghosh, and the fitting accuracy were analyzed and compared. Effects of hardening models on Forming Limit Curves (FLC), pressure loading and bulge height of the hydroformed tube were then studied. The obtained FLC from the simulations were compared with experimental FLC to predict the accuracy of the hardening models.

Experimental determination of forming limit diagram for α + β brass at hot forming conditions

Brass is an alloy of copper and zinc; it has a composition of 60% and 40% respectively. It plays a major role in manufacturing of musical instruments, electrical applicants like electrical sockets and household articles like kitchen utensils, keys, door knobs, etc. It has unique properties like malleability, corrosion resistance, low melting point and formability characteristics. Forming limit diagrams is significant performance indexes for evaluating the formability of a material. In the present study comparative experimental investigation of forming behaviour of brass has been performed at two different temperatures (500 °C and 600 °C) and strain rates (0.001,0.01 & 0.1 s−1). Subsequently, experimental forming limit curve, thickness distribution curves and limiting dome height curves have been plotted at different temperatures and strain rates using Nakazima test samples. Comparison between these set of results shows significant variations in formability of material. Furthermore, scanning electron microscope is used to observe the fractured specimens and SEM images are taken. The scanning electron microscope, however, it is much more substantial in failure analysis of over load fractures.

Influence of heat treatments on the formability of the 6061 Al alloy sheets: experiments and GTN damage model

The research mainly focused on the forming limit curves (FLC) of the 6061 Al alloy subjected to heat treatments with various (1 mm, 1.6 mm, 2 mm, and 2.5 mm) sheet metal thicknesses. Five peculiar heat treatments, including natural aging temper (T4) and highest-strength (T6) temper, were devised to study the influence of heat treatments on the formability of 6061 Al alloy sheets. Tensile tests were executed to determine the plastic behavior of the alloy under specific heat treatments. Laser marked FLC specimens were deep-drawn with the proposed spring-attached Nakajima deep drawing test setup. A finite element model (FEM) of the deep drawing experiment was constructed to investigate the nucleation and growth mechanism of the voids. The developed model was compared and verified with the experimental FLC, fracture locations, and dome height. The FEM results were differed from the experimental FLC by less than 5% considering all heat treatments and sheet thicknesses. The results declared that sheet metal thickness has a positive effect on the effective strain up to failure. On the other hand, the duration of artificial aging time reduced effective strain to failure controlled by nucleation and growth of voids.

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.

Modeling anisotropic ductile fracture behavior of Ti-6Al-4V titanium alloy for sheet forming applications at room temperature

An anisotropic modified Mohr–Coulomb (MMC) ductile fracture criterion was developed to characterize the ductile fracture behavior of the Ti-6Al-4V titanium alloy at room temperature. The stress triaxiality is inherently coupled within the ductile fracture criterion and shows an exponential effect on the material ductility decay. The effect of the Lode angle is considered as well, considering a parabolic trend. The fracture criterion was developed based on the direction-independent plastic strain-rate increment called isotropic equivalent plastic strain-rate increment. To incorporate the influence of directionality on the ductile fracture behavior, the fourth order linear transformation tensor was successfully introduced. The Ti-6Al-4V fracture behavior under uniaxial tension, in-plane shear, plane strain along various loading orientations, and equi-biaxial tension states of stress was successfully predicted using the newly developed fracture criterion. Furthermore, the theoretical Fracture Forming Limit Curve (FFLC) predicted by the anisotropic ductile fracture criterion was compared with experimental forming limit curves from literature. The results show that the developed phenomenological anisotropic MMC ductile fracture criterion has a great advantage to predict the ductile failure of sheet metals characterized by strong anisotropy.

Efficacy of semi-empirical models for prediction of forming limit curve of IN718 alloy at elevated temperatures

ABSTRACT Inconel 718 alloy (IN718) is a high-strength material and is widely used in aerospace and nuclear applications for extreme working conditions. IN718 alloy is difficult to form at room temperature (RT) conditions. Warm/hot forming is used as an alternative approach for forming of complex shape components for IN718 alloy. The present study is focused on the influence of processing temperatures (RT, 400°C and 700°C) on the formability of IN718 alloy. Experimental forming limit curves (FLCs) have been plotted at different temperatures using standard Nakazima test. Improvement in maximum major safe strain values for T-C (tension–compression) and T-T (equi-biaxial tension) region is found to be 54.35% and 66.16%, respectively, at 700ºC. Further, the effect of processing temperatures on surface strain distribution, thickness distribution and limiting dome height (LDH) is also analysed. Surface strain distribution at test temperature mainly depends on strain path throughout stretching. LDH is increased by approximately 33–44% at 700ºC. FLCs are predicted based on Paul and Chow semi-empirical models based on uniaxial anisotropic properties and Hosford’s constants. The predicted FLCs are validated with experimental FLCs based on average absolute error (AAE). Predicted FLCs by Paul method show good agreement with experimental limiting strains.

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.

Influence of Pre-Stretching Levels on the Forming Limit Strain and Stress Curves of High Strength Steel Sheet

In this work, Forming Limit Curves (FLCs) of the conventional and pre-stretched High Strength Steel (HSS) sheet grade 440 (SCGA440-45) were investigated. The conventional forming limit curve was experimentally determined by using the Nakajima stretching test. Subsequently, the non-linear strain path FLCs were precisely developed through the Nakajima stretching test after the specimens were pre-stretched in biaxial direction up to several levels on the Marciniak In-plane stretching test. The gained non-linear strain path FLCs were compared with the conventional FLC.Additionally, the experimental Forming Limit Stress Curve (FLSCs) were calculated using the experimental FLC and non-linear strain path FLCs data from investigated steel sheet. The yield criterion Hill’48 was employed in combination with the Swift strain hardening law to describe anisotropic deformation and plastic flow behavior of the HSS sheet, respectively. Hereby, the influence of pre-stretching levels on the experimentally determined the FLCs and FLSCs were examined. The results prove a significant influence of the pre-stretching levels on the both FLCs and FLSCs of the investigated HSS sheet. For a low pre-stretching in biaxial loading the FLCs demonstrated a reduced formability and the FLSCs exhibited the limited stress levels depending on the experimental FLC data.

Modelling strategies and FEM approaches to characterize micro-sandwich sheets with unknown core properties

The micro-sandwich sheets with metallic/polymer fibrous core have been pointed out as one of the most promising technological solutions to the automotive industry. However, due to the lack of understanding of certain fundamentals related with the mechanical behavior of micro-sandwich sheets during forming processes, the transfer and scale-up of this promising technology to industry has been limited. A challenging aspect in the experimental characterization of these materials is related with the unknow properties of the composition of the core which consist of metallic (polymer) fibers and adhesive. In general, the suppliers of monolithic metal sheets also make available the respective datasheets with the mechanical and chemical properties. These datasheets use to refer the minimum, maximum or a specific tolerance range (dependent of the grade material) to the mechanical properties. However, the micro-sandwich sheets are not provided with this mechanical and chemical data, at least, for all layers. Therefore, it is missing a simple and robust methodology to supply the mechanical properties of the total micro-sandwich sheet to the industry. Furthermore, there is no study about the different numerical approaches available in the commercial stamping softwares to modelling and simulate micro-sandwich materials. In this work, a strategy to deduce the unknown mechanical properties of the fibrous core from symmetric or asymmetric micro-sandwich sheets, i.e., with the same or different skin thickness, is presented. For true stress-strain curves and anisotropy purposes, uniaxial tensile tests in 3 different directions, according ISO 6892-1:2009 standard, were performed. Total micro-sandwich specimens and skin specimens were tested. The mechanical properties of the core were deduced from micro-sandwich and skin’s mechanical properties. Based on this data, the constitutive model was established. Additionally, 6 different Nakazima geometries were punched according to ISO 12004 for formability assessment. Experimental Forming Limit Curves (FLC) and principal strains data were recorded during the tests thanks to a high-resolution cameras and software GOM ARAMIS. Finally, the experimental mechanical tests were virtually reproduced with both commercial codes AutoForm R5.2 and PAM-STAMP 2G 2015.1. Thus, different modelling strategies and Finite Element Method (FEM) approaches were compared. The excellent agreement between numerical and experimental results demonstrate the accuracy of the applied methodology.

Experimental Investigation of Forming Limit Curve for AA5754-O

The Forming Limit Curve (FLC) is a line that is consisted of the major and minor strain pairs for different kinds of strain paths. It is widely adopted for the quantitative description of the sheet metal formability. In this paper, a stand-alone servo-motor apparatus associated with the high-accuracy measurement system was developed, based on which the FLC of AA5754-O with the thickness of 3.0mm was investigated. Firstly, the material properties of metal sheet were explored and the anisotropic coefficients in the constitutive law were calculated to describe the yield behaviour. Secondly, in order to increase the strain level of cruciform specimens, various simulations with different shapes of specimens were performed with ABAQUS/Explicit. Finally, the biaxial tensile tests with the optimized shape of cruciform specimens were performed under different loading ratio conditions. The experimental FLC of AA5754-O was obtained. The fracture zone of each specimen was occurred in the central region without premature arm fracture, which verified the feasibility of the cruciform specimen purposed.

Experimental and numerical investigations on determination of strain localization in sheet forming

This work presents results of investigations on the determination of strain localization in sheet forming. Nakajima formability test has been chosen for the experimental studies and numerical analysis. The onset of localized necking has been determined using the criteria studied in the authors’ earlier works, based on the analysis of the principal strains evolution in time. The first criterion is based on the analysis of the through-thickness thinning (through–thickness strain) and its first time derivative in the most strained zone. The limit strain in the second method is determined by the maximum of the strain acceleration. Limit strains obtained from these criteria have been confronted with the experimental forming limit curve (FLC) evaluated according to modified Bragard method used in the ISO standard. The comparison shows that the first criterion predicts formability limits closer to the experimental FLC and second method predicts values of strains higher than FLC. These values are closer to the maximum strains measured before fracture appears in experiment. These investigations show that criteria based on the analysis of strain evolution used in numerical simulation and experimental studies allow us to determine strain localization.

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.

Developing a Zener–Hollomon Based Forming Limit Surface for Warm Sheet Forming of Magnesium Alloy

The concept of Zener–Hollomon (Z) based Forming Limit Surface (Z-FLS)—which has minor strain, major strain, and ln(Z) as its three axes—was initially proposed in a previous study. In the Z-FLS diagram, strain rate and temperature effects on the major limit strain are reflected by ln(Z). In the current study, the concept of Z-FLS is revisited to provide a practical approach to construct Z-FLS. A Z-FLS then is constructed for magnesium alloy AZ31B sheet material using available experimental forming limit curves. The constructed Z-FLS is used to identify fracture in a non-isothermal warm cup forming process, which was modeled as a coupled thermo-mechanical process. Based on the Z-FLS, the determined limiting draw ratio (LDR) matches well with the published experimental results.

Formability Prediction for Tube Hydroforming of Stainless Steel 304 Using Damage Mechanics Model

Tube hydroforming (THF) is an important manufacturing technology for producing tube components by means of fluid pressure. In comparison to other basic forming processes like deep drawing, forming steps can be reduced and more complex shape is allowed. In this work, it was aimed to establish the forming limit curve (FLC) of stainless steel tube grade 304 for the THF process by using finite element (FE) simulations coupled with the Gurson–Tvergaard–Needleman (GTN) damage model as failure criterion. The parameters of the GTN model were obtained by metallography analysis, tensile test, plane strain test of the examined steel in combination with the direct current potential drop (DCPD) and digital image correlation (DIC) techniques. These parameters were well verified by comparing the predicted FLC of steel sheet with the experimental FLC gathered from the Nakazima test. Then, the FLC of steel tube 304 was established by FE simulations coupled with the damage model of tube bulging tests. During the bulge tests, pressure and axial feed were properly controlled in order to generate the left-hand FLC, while pressure and external force needed to be simultaneously incorporated for the right-hand FLC. Finally, the FLC was applied to evaluate material formability in an industrial THF process of the steel tube.