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

In 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.     

薄板成形极限图(FLD)的多项式拟合分析

基于多项式拟合的基本原理以及相关性与方差的综合分析，探讨了成形极限散点与高次多项式之间的相关特性以及表面工程主应变极值点FLD0与拟合曲线的关系。在所得的拟合曲线基础上配合数理统计与概率理论分析，拟合曲线的上下置信函数可以成为描绘成形极限曲线(FLC)的重要依据，也可以为FLD0值的区间估计提供可靠科学的置信分析。     

Constitutive modeling and the effects of strain-rate and temperature on the formability of Ti–6Al–4V alloy sheet

The constitutive model considering the strain-rate and temperature effects was presented by fitting the true stress–strain curves of Ti–6Al–4V alloy over a wide range of strain-rates (0.0005–0.05 s⁻¹) and temperatures (923–1023 K). The Forming Limit Curve (FLC) of Ti–6Al–4V alloy at 973 K was measured by conducting the hemispherical dome test with specimens of different widths. The forming limit prediction model of Ti–6Al–4V alloy, which takes strain-rate and temperature sensitivity into account, was predicted based on Marciniak and Kuczynski (M–K) theory along with Von Mises yield criterion. The comparison shows that the limit strain decreases with temperature lowering but strain-rate increasing. The comparison between theoretical analysis and experiment of FLC verifies the accuracy and reliability of the proposed methodology, which considers the strain-rate and temperature effects, to predict limit strains in the positive minor strain region of Forming Limit Diagram (FLD).     

Formability analysis of thin press hardening steel sheets under isothermal and non-isothermal conditions

Aiming at the enhancement of the lightweight potential of press hardening steels, investigations on the formability of thin, boron alloyed, hot dip aluminized steel sheets are carried out. The material formability is described through Forming Limit Diagram (FLD), determined by means of Nakajima formability test of thin 22MnB5 sheets (0.50 mm, 0.80 mm, 1.25 mm) at elevated temperatures. The influence of sheet thickness on forming limits is evaluated under both isothermal and non-isothermal conditions. The effect of different deformation start temperatures is examined. The non-isothermal behavior is further investigated via microstructural analysis and a study on temperature profile during Nakajima test. The results show a significant difference regarding the influence of sheet thickness under isothermal and non-isothermal conditions. Increasing the sheet thickness results, as expected, in higher forming limits for isothermal conditions, whereas for non-isothermal conditions the opposite effect on formability is observed. The obtained Forming Limit Curves (FLCs) are validated through hot stamping simulation and subsequent analysis of different thin components, concluding that in case of thin sheets the isothermal FLC constitutes a more conservative approach, while the non-isothermal one reaches the formability limits with higher accuracy.     

Modelling the correlation between the geometrical features and the forming limit strains of perforated Al 8011 sheets using artificial neural network

In the recent years, sheet metals are produced with perforations in various shapes and patterns to improve the appearance of sheet and to save weight of components. As in conventional metal sheets, it is important to form the perforated sheet metals also within their safe strain regions to avoid the forming failures like necking, fracture and wrinkling. The Forming Limit Diagram (FLD) is an appropriate tool to determine the forming limit strains. The limiting strains of perforated sheet metals mainly depend on the geometry of the perforations and forming variables. This leads to large increase in number of test to be conducted with various geometry and forming variables for determining the forming limit strain for perforated sheets. Aiming to reduce the number of experiments needed, in this work, an Artificial Neural Network (ANN) model has been developed for forming limit diagram of perforated Al 8011 sheets based on experimental results and correlated with the geometrical features of the perforated sheets. This model is a feed forward back propagation neural network (BPNN) with a set of geometrical variables as its inputs and the safe true strains as its output. This ANN model can be applied for prediction of FLD of perforated sheet having any geometry.     

An experimental and theoretical study on the prediction of forming limit diagrams using new BBC yield criteria and M–K analysis

In the present paper, a comprehensive study on the prediction of forming limit diagrams (FLDs) for an AA3003-O aluminium alloy is developed theoretically and experimentally. For obtaining the experimental FLDs, an out-of-plane formability test was performed based on the technique proposed by Ozturk and Lee [F. Ozturk, D. Lee, J. Mater. Process. Technol. 170 (2005) 247–253]. The classical Marciniak–Kuczynski (M–K) model and some new yield criteria are utilized to simulate the necking phenomenon and calculate the limit strains theoretically. The employed yield functions are: the BBC2000, BBC2002, and BBC2003 yield criteria proposed by Banabic et al. [D. Banabic, S.D. Comsa, T. Balan, in: Proceedings of the Cold Metal Forming 2000 Conference, Cluj-Napoca, 2000, p. 217; D. Banabic, T. Kuwabara, T. Balan, D.S. Comsa, D. Julean, Int. J. Mech. Sci. 45 (2003) 797–811; D. Banabic, H. Aretz, D.S. Comsa, L. Paraianu, Int. J. Plast. 21 (2005) 493–512]. To calibrate and determine each particular coefficients of performed yield functions an appropriate error-function is defined and minimized by a Newton algorithm. To compare the calculated yield stresses and r-values with experimental data a relative root mean square deviation method presented by Leacock [Alan G. Leacock, J. Mech. Phys. Solids 54 (2006) 425–444] is used. Work-hardening effects on the FLD are analyzed by using Swift and Voce hardening laws. The effect of yield surface on the prediction of numerical FLDs and the number of experimental anisotropy parameters on the accuracy of yield functions are also studied.     

坐标网分析技术与成形极限图的应用

用网格自动应变测试分析系统ASAME测试了11炉批冷轧薄板的成形极限，对实际测量的成形极限与模拟计算的成形极限进行了比较。对冲压的摩托车油箱进行应变分析，根据成形极限图（FLD）确定冲压零件的安全裕度，评价材料的适用性。     

Forming limit diagram for Indian interstitial free steels

In this work, the suitability of interstitial free steel sheets of thickness 0.6 and 1.6 mm for press forming operations were examined by obtaining the forming limit diagram. The microstructural aspects, tensile properties and formability parameters were studied. Forming limit diagrams (FLD) were evaluated for the above sheet metals of two different thicknesses and they were compared. Strain distribution profiles were obtained from the forming experiment. The fracture surfaces of the formed samples were observed using scanning electron microscope. Using the fractography, the fracture behaviour and formability were analyzed. The tensile properties and formability parameters were correlated with the FLD. It was found that the formability of both sheets is good and the sheet with 1.6 mm thickness was superior.     

Evaluation of non-linear strain paths using Generalized Forming Limit Concept and a modification of the Time Dependent Evaluation Method

The prediction of formability is one of the most important tasks in sheet metal forming process simulation. The common criterion for ductile fracture in industrial applications is the Forming Limit Diagram (FLD). This is only applicable for linear strain paths. However, in most industrial simulation cases non-linear strain paths occur. To resolve this problem, a phenomenological approach is introduced, the so-called Generalized Forming Limit Concept (GFLC). The GFLC enables prediction of localized necking on arbitrary non-linear strain paths. Another possibility is the use of the Time Dependent Evaluation Method (TDEM) within the simulation as a failure criteria. During the Numisheet Benchmark 1 (2014) a two-stage forming process was performed with three typical sheet materials (AA5182, DP600 and TRIP 780) and three different blank shapes. The task was to determinate the point in time and space of local instability. Therefore the strain path for the point of maximum local thinning is evaluated. To predict the start of local necking the Generalized Forming Limit Concept (GFLC), the Time Dependent Evaluation Method (TDEM) and the modified TDEM were applied. The results of the simulation are compared with the results of the Benchmark experiment.     

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.     

Stress and strain based fracture forming limit curves for advanced high strength steel sheet

In this work, strain based fracture forming limit curve (FFLC) of advanced high strength (AHS) steel grade 980 was determined by means of experimental Nakajima stretch-forming test and tensile tests of samples under shear deformation. During the tests, a digital image correlation (DIC) technique was applied to capture the developed strain histories of deformed samples up to failure. The gathered fracture strains from different stress states were used to construct the FFLC. Subsequently, the FFLC in the strain space was transformed to a principal stress space by using plasticity theories. As a result, the fracture forming limit stress curve (FFLSC) of examined steel was obtained. Furthermore, fracture locus (FL) as a relationship between stress triaxialities and critical plastic strains was determined. Hereby, two anisotropic yield functions, namely, the Hill’48 and Yld89 model were taken into account and their effects on the calculated curves were investigated. To verify the applicability of the obtained limit curves, rectangular cup drawing test and forming tests of so-called Diabolo and mini-tunnel samples were performed. Obviously, the FFLSCs and FLs more accurately described the failure occurrences of 980 steel sheets than the FFLCs. In addition, it was found that the drawing depths predicted by the FLs and the Yld89 yield criterion slightly better agreed with the experimental results than those from the FFLSCs and the Hill’48 model, respectively.     

Inverse identification of the Swift law parameters using the bulge test

An inverse methodology is proposed for determining the work hardening law of metal sheets, from the results of pressure vs. pole height, obtained from the bulge test. This involves the identification of the parameters of the Swift law. The influence of these parameters as well as the sheet anisotropy and the sheet thickness on the results of pressure with pole height is studied following a forward analysis, based on finite element simulation. This allows understanding that the overlapping of the pressure vs. pole height curves of different metal sheets is possible, provided that the hardening coefficient has the same value, whatever the values of the remaining parameters of the Swift law, the sheet anisotropy and the initial sheet thickness. The overlapping of the curves is performed by multiplying the values of the pressure and the pole height using appropriate factors, which depend on the ratios between the yield stresses and the thicknesses of the sheets, and also on their anisotropy. Afterwards, an inverse methodology is established, consisting of the search for the best coincidence between pressure vs. pole height of experimental and reference curves, the latter being obtained by numerical simulation assuming isotropic behaviour with various values of the Swift hardening coefficient in the range of the material under study. This methodology is compared with a classical strategy and proves to be an efficient alternative for determining the parameters of the Swift law. It aims to be simple from an experimental point of view and, for that purpose, only uses results of the load evolution during the test. The methodology is limited to materials with the hardening behaviour adequately described by the Swift law.     

Experimental strain-hardening behaviors and associated computational models with anisotropic sheet metals

Several anisotropic hardening models with simple loading conditions are proposed, including exponential hardening model, linear hardening model and multi-linear hardening model (which also suits for using the experimental data directly). Three special hardening curves, in the 0°, 45° and 90° angles, respectively, measured against the rolling direction, are the special cases of the proposed hardening models. These models make sense to be applied for simulating forming processes of the planar anisotropic hardening sheet metals, in particular for determining the springback and FLD of formed parts. In order to describe this view further, the constitutive relations of stress and strain, based on the plastic potential flow rule with isotropic hardening and kinematic hardening assumptions, have been discussed briefly. And then, the corresponding results of constitutive relations dependent on the proposed hardening models of materials will be represented, respectively.     

Experimental prediction of sheet metal formability of AW-5754 for non-linear strain paths by using a cruciform specimen and a blank holder with adjustable draw beads on a sheet metal testing machine

The main objective to guarantee a high efficiency in the press shop is to produce sheet metal parts without failure. The feasibility of sheet metal parts is nowadays ensured during the development process by a comparison of the occurring strains in the simulation with the Forming Limit Diagram (FLD). The principle of the experimental procedure to determine the FLD is standardized in ISO 12004–2 [1]. This procedure is only valid with high accuracy for proportional unbroken strain paths. However, in most industrial forming operations non-linear strain paths occur. To resolve this problem, a phenomenological approach was introduced by Volk [2], the so-called Generalized Forming Limit Concept (GFLC). Localized necking and the remaining formability for any arbitrary non-linear strain path can be predicted with the GFLC. Furthermore, experimental investigation of multi-linear strain paths appears highly complex in practice and involves a range of testing equipment, e.g. different specimens, testing machines and tools. In this paper an alternative method is introduced by using a cruciform specimen and a draw bead tool on a sheet metal testing machine. The different draw bead heights allow the creation of arbitrary strain states, which can be changed at different height of the punch. Conventionally cruciform specimens are used to determine the yield loci in the first quadrant of the stress space at low strain values. To enable a cruciform specimen for the evaluation of strain limits comparable to the conventional Nakajima test, an optimization of the geometry regarding the maximum achievable strains in the specimen center takes place. The developed specimen and tool allow testing of materials under multi-axial strain states with a reduced testing effort.     

Forming and fracture limits of aluminium alloy

Abstract

Forming and fracture limits of an AA 3104-H19 aluminium alloy sheet were studied by hydraulic bulging and Marciniak type deep drawing and tensile tests. The alloy appeared to be highly anisotropic, exhibiting distinctly different fracture patterns in the rolling and transverse directions. The preferred fracture direction was transverse to the rolling direction. In the tensile test, samples loaded in the rolling direction failed transverse to the rolling direction, but in the transverse direction, the fracture was inclined at ～55° to the tensile axis. In some cases, two such competing fractures in the characteristic directions could be observed. Scanning electron microscopy studies revealed a typical ductile fracture pattern. The fracture occurred by shearing in the through thickness direction, and typical alternating shear lips in a direction inclined at ～45° to the through thickness direction could be observed. Forming limit diagrams for both rolling and transverse directions were determined from the experiments. The measured limit strains in uniaxial tension were predicted well by the modified Rice–Tracey theory, but in equibiaxial tension, the theory overestimated the fracture limit strains.     

Fracture limit prediction for roller hemming of aluminum alloy sheet

Roller hemming limit is predicted based on ductile fracture criterion in this approach. Plastic deformation in sheets made of aluminum alloy 6061-T6 is studied experimentally. Combined isotropic and kinematic hardening rule is considered in roller hemming numerical analysis. Forming limit stress curve at fracture (FLSCF) is derived from Cockcroft–Latham ductile damage criterion to determine fracture during roller hemming simulation. Serrated strain paths are detected along hemline. The zones where fracture takes place obtained by experiments and FE simulations are compared. It is demonstrated that FLSCF, which is on the basis of ductile damage criteria and basically irrelevant to linearity of strain path could be used to predict fracture of roller hemming correctly.     

Forming limit evaluation of adhesive bonded sandwich steel sheets and numerical prediction

In the present work, the effect of hardener to resin ratio of epoxy adhesive on the formability of adhesive bonded steel sheets has been studied. Forming limit curve has been evaluated by hemispherical dome tests at predefined strain-paths. They are predicted by finite element simulations using strain mapping method. Cohesive zone model has been used to model the interface between skin and adhesive core. An improvement in the forming limit of sandwich steel sheets has been observed when the hardener to resin ratio is changed from 0.6 : 1 to 1 : 1 due to the improved plasticity of adhesive core layer at 1 : 1 ratio as compared to others. The forming limit of sandwich sheet made at 1 : 1 ratio is equivalent to base steel sheet of same thickness and grade. This shows the potential use of sandwich sheet in place of base steel sheet. The forming limit curve predictions agree well with experimental data for base sheet, while reasonable agreement is observed in case of sandwich sheet. Numerical prediction of interface delamination show insignificant influence of hardener to resin ratio on the onset of delamination and significant effect of strain-paths.     

Modeling of localization and fracture phenomena in strain and stress space for sheet metal forming

In this study, a model based on a strain localization level to overcome the shortcomings of the well-established Forming Limit Diagram (FLD) in predicting the physical phenomenon of necking is introduced. An optical measurement system was used to capture the strain history of the Nakazima experiment until rupture occurred. In order to measure the fracture strain more accurately, a further method is introduced, which is based on the microscopic measurements of ruptured regions. This model is validated using a 3-point bending test. The results show the ability of the method to predict failure under bending conditions as well. Additionally, failure is investigated based on the pressure sensitivity and the Lode dependency. The results show that the triaxiality at the failure point is independent of the loading path.