Nakazima Test Research Articles

Compensation for process-dependent effects in the determination of localized necking limits

This work describes a new procedure to remove the differences in measured forming limits obtained from Marciniak and Nakazima tests, which are the two most frequently used testing methods to obtain necking limits for forming limit diagrams (FLD) used in formability analysis of sheet metal stamping processes. The procedure compensates for the combined effects of curvature and nonlinear strain path that occur during these tests, using measurements recorded by digital image correlation (DIC) throughout the deformation history of the point on the test specimen that eventually necks. The severity of forming is then determined by presenting the critical forming conditions in a stress diagram in order to account for the effects of through-thickness pressure that influences the onset of localized necking in the Nakazima test. These stress-based forming limits are then transformed back to the familiar strain limits (or FLD), but now representing the limits under the restriction of in-plane perfectly linear stretching and plane-stress conditions. Accounting for the effects of nonlinear strain path is particularly sensitive to the detection of the actual onset of localized necking, so this work also recommends the use of realistic methods to detect the actual onset of localized necking. The method adopted in this work is based on a new method described by Min et al. [13,14], in which a change in the surface curvature is used to detect a geometric effect associated with the onset of localized necking. In addition to demonstrating that the standard Marciniak and Nakazima tests (punch diameter of 101.6mm) produce essentially identical limit curves for a 980MPa grade multi-phase high strength steel after correction for curvature, nonlinear strain path, and pressure, the method is also applied to the analysis of data from a non-standard Nakazima test with a smaller punch diameter of 50.8mm, where the severity of these processing conditions are significantly enhanced. This additional test is further proof of the validity and comprehensive coverage of the corrections for the different processing conditions involved in measurement of forming limit curves.

The effect of yield surface curvature change by cross hardening on forming limit diagrams of sheets

The paper aims at clarification of the role of reduction in yield locus curvature on forming limit diagrams. To this end, a cross-hardening model showing a reduction of yield surface curvature is used which accounts for dynamic and latent hardening effects associated with dislocation motion during loading. The model's three-dimensional tensorial as well as reduced plane-stress vector formulations are given. The first quadrants of forming limit diagrams are numerically produced using finite element models of the Marciniak-Kuczyński test with spatially correlated random defect distribution as localization triggering mechanism. The effect of cross hardening is investigated in detail. It is demonstrated that for plane strain loading path there occurs no difference in localization predictions of the models with and without cross hardening whereas for biaxial strain paths a delayed localization is observed in the cross hardening model as compared to the one without cross hardening effects. This is in accordance with the relative bluntness of the yield surface at the points of load path change towards localization. These results are complemented by Nakazima test simulations where similar observations are made.

Prediction of limit strains in hot forming of aluminium alloy sheets

Theoretical analysis for the prediction of the limit strains of AA5083 aluminium alloy sheets deformed at room and elevated temperatures are presented and discussed in relation to experimental limit strains. The AA5083 forming limit strain curves, FLC, were predicted by employing D-Bressan and Marciniak–Kuczynski macroscopic concept models and were compared with the experimental FLC from Nakazima tests performed at room and high temperatures. In order to calibrate the models, tensile tests on specimens cut at 0°, 45° and 90° with respect to the rolling direction were carried out in a wide rage of temperatures and strain rates in order to obtain the coefficients of plastic anisotropy as well as material strain and strain rate hardening behaviour at different temperatures. The applied critical shear stress rupture criterion and strain gradient evolution models showed to give a satisfactory agreement with the forming limit strain curves of AA5083 aluminium sheet, proving the suitability of a novel concept of shear stress rupture and local necking evolution in sheet metals deformed at room and elevated temperatures. The correlation of M–K predicted FLC-N curve with the experimental points for room and high temperatures was also fairly good.

Experimental Verification of the Strain Non-Uniformity Index (SNI) based Failure Prediction

Formability of the sheet metal depends upon the uniformity of strain distribution, which depends on material properties, tooling and process parameters. Nakazima Test was conducted to study the strain distribution and establish the forming limits of AA 6016. The experimental conditions were simulated using AUTOFORM 5.2 Plus software and the failure predicted using the SNI based methodology. The failure predictions were correlated with the state of the experimentally deformed Nakazima samples, and also with the FLD based forming limits. The failure prediction from the SNI based methodology was found to correlate well with the state of the experimental Nakazima sample.

Forming limit diagrams of fine-grained Al 5083 produced by equal channel angular rolling process

The objective of this research is to study the strain forming limits of Al–Mg alloy (5083) sheet, fabricated by equal channel angular rolling process at room temperature. For this purpose, the equal channel angular rolling process was executed at room temperature in three passes. Mechanical properties, microhardness, and microstructure were investigated after the equal channel angular rolling process. Uniaxial tensile tests of the equal channel angular rolling process produced samples and showed that yield and ultimate stresses increase, while the uniform elongation to fracture decreases in comparison with the annealed state. There was a continuous hardness enhancement by increasing the number of the equal channel angular rolling passes. After the third pass, the amount of hardness raised by 73% in comparison with the annealed sample. In the fourth pass, the hardness reduced slightly, that was attributed to the strain saturation in room temperature and was followed by high surface cracks. In the annealed condition, the average grain size was 45 µm, and after the third equal channel angular rolling pass, this amount was reduced to 10 µm. Furthermore, the forming limit diagrams were determined experimentally, using the Nakazima test. The obtained results show that after the third pass, the forming limit diagrams’ level move downward, meaning that a reduction occurred in the forming limits of equal channel angular rolled samples.

Prediction and Experimental Validation of Forming Limit Curve of a Quenched and Partitioned Steel

Forming limit curve (FLC) is an effective tool to evaluate the formability of sheet metals. An accurate FLC prediction for a sheet metal is beneficial to its engineering application. A quenched and partitioned steel, known as QP980, is one of the 3rd generation advanced high strength steels and is composed of martensite, ferrite and a considerable amount of retained austenite (RA). Martensite transformation from RA induced by deformation, namely, transformation induced plasticity (TRIP), promotes the capability of work hardening and consequently formability. Nakazima tests were carried out to obtain the experimental forming limit strains with the aid of digital image correlation techniques. Scanning electron microscopy (SEM) was employed to examine the fracture morphologies of Nakazima specimens of the QP980 steel. The observed dimple pattern indicated that tensile stress was the predominant factor which led to failure of QP980 specimens. Therefore, maximum tensile stress criterion (MTSC) was adopted as the forming limit criterion. To predict the FLC of QP980 steel, Von-Mises yield criterion and power hardening law were adopted according to the tested mechanical properties of QP980 steel. Results were compared with those derived from other three representative instability theories, e. g. Hill criterion, Storen-Rice vertex theory and Bressan-Williams model, which shows that the MTSC based FLC is in better agreement with the experimental results.

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

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

Investigation on the hot formability of TA15 titanium alloy sheet

The hot formability of TA15 titanium alloy sheet was studied experimentally and theoretically. The hot uniaxial tensile tests were conducted for further investigation on hot formability. Based on the finite element models in different thermal conditions, the punch displacement-force curves were compared to test data to investigate the influence of sheet temperature distribution on limit strain. The simulation results indicated that the hot punch was essential for keeping the temperature of sheet center region. Meanwhile, the non-uniform sheet temperature distribution that the temperature of central sheet was higher than the one at sheet edge, was positive for making the damage occur at an appropriate region due to the good deformability of central sheet with higher temperature. The theoretical FLCs of TA15 titanium alloy sheet were predicted by introducing Hill48 yield criterion and temperature path into M-K model. The results proved that the monotonic decreasing temperature path had no effect on sheet formability, and the Nakazima test results depended on the final temperature of region at where the fracture or necking occurred. The comparison results also indicated that the test data agreed well with the theoretical FLC at 810°C.

Forming Limit Diagram Generation of Aluminum Alloy AA2014 Using Nakazima Test Simulation Tool

Plastic instability is a commonly observed problem, in sheet metal forming operation, which leads to defective products. Forming Limit Diagram (FLD) is an important parameter to be considered in the manufacturing process of non-defective sheet products. This paper focuses on FLD prediction based on simulation of Nakazima test using finite element software Pam-Stamp 2G. Finite Element Model (FEM) for Nakazima test is established in this work. Then the experimental values are compared with the simulation results in order to establish the credibility of Nakazima test simulation tool. Then the simulation is extended to predict the FLD of AA2014 aluminium alloy.

Determination of Forming Limit Diagrams for Thin Foil Materials Based on Scaled Nakajima Test

For a better process understanding of micro deep drawing processes and reliable prediction of component failure in FE simulations, it requires the most accurate knowledge of actual material behaviour. However, it is not sufficient to describe material failure for a multi axial stress state in deep drawing using a mechanical parameter as the elongation from tensile test. A forming limit diagram and a forming limit curve are more suited to describe the limit of formability under deep drawing stress state conditions. Methods like hydraulic or pneumatic bulge tests are available to determine forming limit curves even for thin metal foil materials. Nevertheless, using these methods only positive minor strains can be achieved. Especially for a deep drawing process negative minor strains and the left side of a forming limit diagram are more important. Therefore, in this study, experiments based on scaled Nakazima tests were performed to determine complete forming limit diagrams for different foil materials with a thickness range of 20 µm to 25 µm. Scaling the test setup improves the handling of thin specimens. Results with a higher local resolution and the specimens’ size is much closer to the actual size of a micro deep drawn component. Using this testing method forming limit diagrams for the materials Al99.5, E-Cu58, stainless austenitic nickel-chromium steel X5CrNi18-10 (1.4301 / AISI 304), all produced by rolling, and an Al-Zr-foil, produced by a PVD sputtering process, were determined for the micro range.

Formability of coated vinyl on sheet metal during deep drawing process

In this study, the formability of vinyl coated metal (VCM) which is sheet metal coated with PET and PVC was studied. VCM has excellent appearances because of the artificial pattern named hairline and is used in home appliances such as washing machines and refrigerators. However, there are problems in the formability of VCM because PET film fracture or delamination occurs when VCM is formed (in particular, in drawing processes) in some cases. To predict the formability of VCM, a finite element numerical model that expressed material damage was established using GTN (Gurson–Tvergaard–Needleman) damage model. Individual materials that would constitute VCM were determined through tensile test based reverse engineering. The numerical model was verified using the results of VCM tensile tests and rectangular deep drawing tests and a good congruence between the results obtained from the numerical model and actual phenomena was identified. In addition, the mechanism for PET films to reach fracture early compared to their elongation in VCM forming was identified. Furthermore, bending processes were simulated using the verified numerical model to examine damage behaviors of VCM according to process variables and Nakazima test was simulated to draw forming limit curves and evaluate the formability of VCM.

Predictive Performances of FLC Using Marciniak-Kuczynski Model and Modified Maximum Force Criterion

This paper is focused on the performance evaluation of two theoretical models that can be used to predict the Forming Limit Curve (FLC) for an AA6016-T4 aluminium alloy sheet. The FLC is calculated based on the Marciniak-Kuczynski (M-K) model and the Modified Maximum Force Criterion (MMFC) using the Hill '48, Barlat '89 and BBC 2005 yield criteria, the latter identified in three variants, namely with 6, 7, and 8 material parameters. The performance assessment of the M-K and MMFC models combined with different yield functions is based on the comparison between the theoretical predictions and the experimental data provided by the Nakazima test (ISO 12004: 2008) as well as by an experimental procedure recently developed by the authors for the FLC determination.

Curvature Based Forming Limit Prediction of High-Strength Steel Components with Superimposed Stretching and Bending in the Deep Drawing Process

The state of deformation in deep drawing operations is characterized by superimposed stretching and bending (i.e. stretch-bending). Bending effects, especially for Advanced High Strength Steels (AHSS) are known to influence the material formability. Traditional formability measures such as the Forming Limit Curve (FLC) fail to reliably predict stretch-bending formability. Consequently, to ensure an efficient and economical use of AHSS in the industrial application, current research work is focusing on the reliable numerical prediction of stretch-bending formability of AHSS sheets.Within this work, a phenomenological concept to predict the forming limit (e.g. the onset of necking) in deep drawing processes taking bending effects into account is presented. The proposed concept is based on curvature-dependent (i.e. regarding the principle curvatures κ1 and κ2 of the stretch-bend (convex) sheet surface) forming limit surfaces representing the probability of failure and is calibrated with experimental results from stretch-bending tests and conventional forming test such as a Nakazima test. The results of the phenomenological forming limit criterion are promising and show a more accurate prediction of the drawing depth at failure than the conventional FLC approach. The method contributes also to a probabilistic view on the forming limit of deep drawing parts.

Study on temperature distribution of HSS in hot FLD test

In this paper, we study forming limit diagram (FLD) of high strength steel (HSS) under high temperature condition to simulate the hot stamping process. We investigate the sheet specimen temperature distribution in hot FLD test. First, we propose a simple model of heat transfer process in sheet specimen, in which the sheet specimen is separated into two sections due to different mechanism. In thermal radiation, the convection and thermal contact conductance are included in two partial differential equations (PDEs) to express the temperature distribution in these two sections (S1 and S2 sections). Second, hot FLD experiments (Nakazima test) are performed and temperature distributions of sheet specimen are investigated by thermal infrared imager. Furthermore, the experimental temperature distributions are compared with theoretical ones, and these two measurements make good agreement between each other. This conclusion validates the feasibility of proposed thermal model in hot stamping process. In addition, an uneven sheet temperature distribution is examined in expansion process experiment, we observe that the temperature of specimen increases from center to edge until it reaches the temperature of punch. The further theoretical analysis proves that this phenomenon is mainly caused by the punch through thermal contact conductance between punch and S1 section, which indicates that a hot punch is indispensable to sustain the temperature of the deforming sheet. Third, the theoretical temperature distribution on S1 section under different die height is calculated. The radiation heat flux of the sheet decreases as the die height is increasing, but the sheet temperature increment is small, which implies that the height of die affects the sheet temperature slightly.

Hot formability of DIN 27MnCrB5 steel sheets under controlled thinning

Hot stamping has been widely studied and increasingly applied in the automotive industry. This process is characterized by its ability to stamp high strength steels, yielding products with high mechanical strength, thus reducing the weight of stamped components and therefore the vehicles weight. It also demands less energy because steel sheets can be heated by induction, more efficient than electric furnaces. With controlled thinning, it is possible to manufacture thinner stamped parts with high mechanical strength, therefore it is necessary to know the formability limits to prevent failure and achieve the largest possible thickness reduction. In this work the hot formability of DIN 27MnCrB5 steel sheets 4mm thick, under thinning conditions was evaluated by numerical simulation with the finite element (FEM) software Forge2008. Tensile tests were carried out at 500, 600, 700, and 800°C and with strain rates from 0.1 to 4s−1. With the results of tensile tests, it was possible to calculate Hensel–Spittel coefficients to model the steel sheet and simulate the hot Nakazima test to evaluate the highest dome which could be formed without failure risks caused by sheet thinning. Simulation results obtained with specimens 200mm long and 125, 150 or 200mm wide that were stamped at 930°C, showed the radial position and dome height associated to plastic instability as well provided the thickness distribution along the specimen. The numerical results were compared to experimental tests and showed a good agreement in terms of failure initiation and localization. As a result, a new numerical and experimental strategy was elaborated to define the hot formability based on the plastic instability and necking localization as a function of stamping temperature and blank dimensions. This strategy proved to be useful to define the safe formability region and therefore the larger thickness reduction that can be done during hot stamping to reduce vehicular components weight and to avoid cracks and failures usually observed in components like clutch covers.

Experimental and Numerical Method for the Analysis of Warm Titanium Sheet Stamping of an Automotive Component

Product design involves many aspects as geometry and material or mechanical requirements that have to be chosen on the base of the part requirements. Manufacturing process is the link between them representing a fundamental aspect of the product design process. Designers and technicians have a consolidated set of tools and knowledge based on long time experience, but the request of more new performing products characterized by more complex geometries or harder to form materials as Titanium alloys stimulated the use of numerical models. They allow us to study the product feasibility but they require reliable inputs for their development and validation. The present research focuses on sheet stamping processes and proposes a methodology that uses the Nakazima test to characterize the formability of the material and to develop and validate the model. In particular, the method is applied to cold (20°C) and warm (300°C) stamping of a complex automotive component made of CP Titanium. After characterizing the material and validating the model at the different temperatures, the stamping process is studied and results are compared. In particular, this approach allowed joining the experimental tests required to develop and validate the model, therefore reducing the resources required for the product design.

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.

핫스탬핑 공정에서 Tailor Rolled Blank 의 성형 특성을 고려한 성형한계 예측

The current study aims to predict the forming limits considering the deformation characteristics of tailor rolled blank(TRB) during hot stamping. The formability of TRB is affected by the TRB line orientation because elongations change due to the intrinsic geometry within the sheet. To evaluate the forming limits, Nakazima tests were conducted at elevated temperatures with different TRB line orientations. Forming limit diagrams(FLD) of TRB can be predicted by an interpolating equation based on the Nakazima test. Predicted FLDs were used in FE-simulations of a rectangular drawing. The predicted limit drawing height was compared with experimental results. The simulation results show good agreement with the experimental ones with an error range of 3%.

Application of the Warm Hydroforming Process to the Manufacturing of Pre-Aged 6xxx Series Components Using a Numerical/Experimental Approach

In this work the Warm Hydroforming (WHF) process for the production of a 6xxx series Al alloy component has been investigated using a numerical/experimental approach: both experimental and numerical hydroforming tests were carried out using the alloy AC170PX, a pre aged (T4 condition) Al alloy often adopted for automotive applications. In order to evaluate both the mechanical and strain behaviour of the material, tensile tests were carried out at different temperature and strain rate levels using the Gleeble system 3180, keeping also into account the ageing effect; in addition, formability (Nakazima) tests in warm conditions were performed by means of a specific equipment and the Forming Limit Curves at different temperature levels were evaluated according to the ISO standard 12004-2. Hydroforming experiments were carried out using a prototypal press machine specifically designed for WHF and SuperPlastic Forming tests. Such tests, scheduled by a DoE approach, were aimed at investigating the suitability of using the investigated Al alloy in the WHF process: attention was thus focused on those parameters mainly affecting the aging phenomenon (temperature, heating time and cycle time). In order to overcome the actual physical limitation of the hydroforming facilities, a Finite Element (FE) model of the WHF process was also created implementing experimental data (flow stress curves and FLCs) and tuned using data from preliminary WHF tests. In particular, after setting the Coefficient Of Friction (COF) according to temperature and verifying the robustness of numerical simulations, the FE model was used for investigating: (i) the influence of the Blank Holder Force (neglected in the experimental campaign); (ii) the adoption of quite smaller values of the parameter cycle time (being the aim to determine higher strain rates in the material). Through the definition of proper response variables (Flatness, Bursting Pressure and Thickness Ratio) both experimental and numerical results were analyzed by means of polynomial Response Surfaces in order to evaluate the optimal process conditions.

Analysis of Failure in Dual Phase Steel Sheets Subject to Electrohydraulic Forming

In previous work, the formability of dual phase steel sheets formed under quasi-static and high strain rate conditions was investigated in macroscale (Golovashchenko et al., 2013, “Formability of Dual Phase Steels in Electrohydraulic Forming,” J. Mater. Process. Technol., 213, pp. 1191–1212) and microscale (Samei et al., 2013, “Quantitative Microstructural Analysis of Formability Enhancement in Dual Phase Steels Subject to Electrohydraulic Forming,” J. Mater. Eng. Perform., 22(7), pp. 2080–2088). The Nakazima test and electrohydraulic forming (EHF) were used for quasi-static and high strain rate forming, respectively. It was shown that dual phase steel sheets exhibit hyperplastic behavior when subject to EHF into a conical die and the micromechanisms of formability improvement were discussed (Samei et al., 2014, “Metallurgical Investigations on Hyperplasticity in Dual Phase Steel Sheets,” ASME J. Manuf. Sci. Eng. (in press)). In this paper, mechanisms of failure in dual phase steels formed under quasi-static and EHF conditions are discussed. For this purpose, the nucleation, growth, and volume fraction of voids were studied. Also, fractography was carried out to understand the different types of fractures in the three grades of dual phase steels. The main objective of this work was to determine how failure was suppressed in the EHF specimens formed in the conical die compared to the Nakazima specimens. The impact of the sheet against the die was found to be the major reason for the delay in failure in the EHF specimens.