Nakazima Test Research Articles

Deep drawing of coated aluminium sheets: Experimental and numerical study

AbstractFor years, coated metal sheets have been used in cookware manufacturing. This paper focuses on employing experimental and numerical analyses to determine the quality and formability of commercially available polytetrafluoroethylene (PTFE)‐coated aluminium sheets. For this purpose, examinations of the coating‘s microstructure, hardness, and friction coefficient through nano‐indentation and scratch tests, were investigated. Tensile test was performed to obtain some mechanical characteristics of the coated aluminium sheets. Moreover, the forming limit curve for the studied material was established by conducting Nakazima test, covering both negative and positive domains of minor strain. The influence of sheet thickness on formability was investigated since using 2 mm and 1 mm thick sheets in this work. Finally, the limits of deep drawing process using the finite element method with Abaqus software was studied.

Formability Characterization Using Curvature and Strain-Rate-Based Limit Strain Detection Methods Applied to Marciniak, Nakazima, and Stretch-Bend Tests

Despite advancements in the characterization of forming limit curves (FLCs) with the development of stereoscopic digital image correlation (DIC), there is still uncertainty in the accuracy of the limit strains, especially in forming operations with out-of-plane bending. The ISO12004-2:2008 standard offers a standardized approach to FLC determination but is not without limitations and is not always applicable to new materials and forming processes (e.g., warm forming, hot stamping). In the present work, a physically based limit strain detection technique is developed, termed the Enhanced Curvature Method (ECM), based on the sheet surface curvature evolution at the onset of necking in sheet formability testing. The ECM is applied to the characterization of 1.1 mm AA5182-O sheet using Marciniak, Nakazima, and stretch–bend characterization tests, and its limit strains are compared with those from the linear best-fit (LBF) local strain-rate approach and the ISO-12004 standard. The ECM considers the physical nature of necking in sheet forming with the aid of thresholds defined in terms of an imperfection metric analogous to the well-known Marciniak–Kuczynski (MK) imperfection factor. By quantifying the evolution of necking, FLCs of different safety margins can be readily generated, enabling a more intuitive selection for the factor of safety. For lower and upper ECM thresholds, the Marciniak plane strain limiting strain was determined to lie between 0.173 and 0.198, respectively, which is comparable to the analytical prediction of 0.194 and in general agreement with the published literature for AA5182-O. Similar plane strain limits were obtained using the ISO and LBF methods with values of 0.188 and 0.208, respectively. The same rankings in limit strain values between methods were observed for plane strain loading in Nakazima and stretch–bend tests.

Numerical Analysis and Application of Marciniak and Nakazima Experimental Model on the Formability of 304L Sheet

Abstract The comprehensive strength, ductility and high work hardening rate of 304L stainless steel contribute to its excellent mechanical and forming properties. This steel alloy is further distinguished by its notable corrosion resistance, high and low temperature capabilities, and excellent welding performance, making it a widely utilized material in industries such as petroleum, chemical, and nuclear power. In this study, we developed a simulation model based on the testing methods of Marciniak and Nakazima. By incorporating a constitutive model for ductile damage into our simulations, we made predictions regarding strain damage and failure under three different types of strain paths: uniaxial tension, biaxial tension, and plane strain. The results obtained from our finite element analysis were then utilized to generate the Forming Limit Diagram (FLD), which provided valuable insights into the material’s behavior under various forming conditions. Highlighting key differences in the simulation results between the Marciniak and Nakazima test methods. Additionally, the study included a comprehensive simulation verification in the context of bending forming analysis. Notably, the results of the bending analysis fell within the safe range, establishing a solid theoretical foundation for subsequent plate forming and risk assessment.

Forming Limits Prediction of Laminated SUS430/Al1050/SUS430 Composites and the Effect of Component Properties on Mechanical Performance

In this study, a constitutive model applied to predict the tensile properties and fracture behavior of well‐bonded multilayered metal composites is extended. The equivalent single‐layer model, as a convenient method, is introduced into finite‐element simulations by combining it with an improved Xue–Wierzbicki damage plasticity model that considers material anisotropy. The steel use stainless (SUS) 430/Al1050/SUS430 laminated sheet fabricated by cold rolling is selected as the research material. The quasistatic uniaxial tests and Nakazima tests are operated to verify the accuracy of the proposed method. The mean errors in tensile stress and fracture forming limit strains are 2% and 3%, respectively. A load‐sharing mixture rule is proposed to assess the effects of the volume fraction, strength coefficient, and hardening exponent of the constituent materials on the mechanical properties of the laminates. In the results, it is indicated that the laminate exhibits sufficient elongation and remains markedly enhanced in tensile strength, reaching 470 Mpa when the ductile Al layer is combined with the higher strength and hardenability steel layer. In this research, it is aimed to clarify the formability characteristics in laminated composites for optimal sheet configuration design and development.

Investigation and optimization on the formability of aluminum 1050/stainless steel 304L bilayer sheets fabricated by cold roll bonding considering the Box-Behnken method

Composite metal sheets have found extensive applications thanks to their high corrosion and wear resistance, as well as greater strength, stiffness, and formability relative to the base sheets. Stainless steel composite sheets account for over 80% of the metallic composite sheets. Their higher performance and lower costs have increased their applications in the food and automotive industries. This study experimentally addressed the formability of the Al 1050/Stainless Steel 304 L bilayer sheets prepared through the cold rolling process. After designing the experiment using the response surface method, considering the layer thickness and reduction ratio of the rolling process, the bilayer sheets were prepared using the cold roll bonding process. Formability included the forming limit diagram, the magnitude of FLD0, and elongation, which were derived by Nakazima and tensile tests. Then, the formability was optimized as a function of input parameters considering the Box-Behnken method. To this end, a new criterion was presented to compare the formability of the sheets. This criterion can be used to assess the formability of a sheet considering various loading modes. Microstructural observations justified the variations in the formability of the bilayer sheets against the input parameters, i.e., thickness ratio and reduction ratio. The results indicated that the formability of the Al 1050/Stainless Steel 304 L bilayer sheet (i.e., safe forming region) reached its maximum value at tAl=4mm;tSS=0.8mm;andr=45%.

AI-assisted prediction of St14 steel sheets formability: Neural-fuzzy systems and crystal plasticity assessments

We've introduced a new technique leveraging artificial intelligence to determine in-plane forming limit strains in St14 sheet metals. A neural-fuzzy AI system was devised to predict safe points on forming limit diagrams, considering aspects like crystal texture, metal sheet thickness, and spherical punch diameter. Neural-fuzzy systems could be utilized in prediction of forming limit curves using linguistic data description. To obtain the data required for training the AI network, in-depth tests, including XRD, metallography, tensile testing, and Nakazima's hemisphere evaluations, were carried out to detail the metallurgical and mechanical properties of St14 sheet metal. Data on texture, the tensile curves, and grain morphology were then incorporated in crystal plasticity models to find hardening constants for St14's single crystals. Using these determined values, Nakazima's tests were replicated through multi-crystal aggregate configurations. We then undertook a comprehensive parameter investigation via 324 crystal plasticity simulations to shed light on the effects of texture, sheet depth, and punch dimensions on St14's formability. This rich dataset paved the way for training an adaptive neural fuzzy inference system (ANFIS), leading to substantial reductions in time and computational needs. The results validate that the ANFIS model offers accurate and reliable predictions, highlighting its viability for wider use in determining forming limit diagrams.

Crystal Plasticity Finite Element Analyses on the Formability of AA6061 Aluminum Alloy with Different Ageing Treatments

Different ageing treatments have been developed to achieve targeted properties in aluminum alloys through altering microstructures. However, there is a lack of understanding regarding the effect of ageing treatments on the formability of these alloys. In this study, we employed crystal plasticity finite element (CPFE) modeling, in conjunction with the Marciniak-Kuczynski (M-K) approach, to investigate the effects of ageing treatments on the mechanical properties and formability of AA6061 aluminum alloy. The as-received sheet was in the T6 heat treatment state, which was subjected to artificial ageing and pre-ageing, respectively, to achieve two age-hardened alloys with modified precipitation states. The microstructures and crystallographic textures of the three alloys were measured using the electron backscattering diffraction (EBSD) technique, and uniaxial tensile tests were performed along the rolling direction (RD), transverse direction (TD), and diagonal direction (DD, 45° to the RD) for each alloy. The forming limit curve (FLC) of the as-received alloy was determined using the Nakazima test. The dependence of mechanical strength, tensile ductility, and work-hardening behavior on the ageing treatments was clarified. Then, the tensile test results were utilized to calibrate the modeling parameters used in the CPFE model, whereas the FLC predictability of the developed model was validated with the experimental one. In the formability analysis, the effects of the ageing treatment on the FLC exhibit a notable dependency on loading paths, and the pre-aged alloy exhibits better formability than the other two at the plane strain tension state, thanks to its high work-hardening levels. In addition, the deformed textures along the different loading paths and the effects of the initial texture on the FLC are also discussed.

A novel mechanical attachment for biaxial tensile test: Application to formability evaluation for DP590 at different temperatures

A novel mechanical attachment for conducting in-plane biaxial tensile test is provided in this paper. In this attachment, the conversion of force from an external actuator into two pairs of orthogonal forces is achieved by specially designed trapezoidal blocks. By using trapezoidal blocks with different inclination angles, biaxial tensile tests of six different tensile ratios can be performed. A heating device is designed for the attachment to conduct thermal biaxial tensile tests. The heating device adopts a combination of the induction heating technology and the conduction heating method. With the developed mechanical attachment and the heating device, the forming limit curves (FLC) of DP590 sheets at ambient temperature, 300 °C, 400 °C and 500 °C are determined using biaxial tensile tests. A classical Nakazima test procedure at ambient temperature is carried out to establish a reference FLC for the material, and the reference FLC is further used to evaluate the results from biaxial tensile tests. Furthermore, an anisotropic GTN model based on Yld2000-3d yield criterion is calibrated by inverse identification procedures and applied to predict the localized necking and fracture for DP590 sheets under biaxial tensions.

Effect of strain rates on the forming properties of DP Steel at high-temperature

Dual Phase steel grade, with its remarkable combination of features including formability and resistance to high temperatures, has been a revolutionary alloy in modern industry. It is a useful material that may be applied to many different tasks. It presents us with the task of examining its characteristics in response to changes in critical parameters such as temperature and loading rate during stretching operations. Understanding the formability behavior of DP steel sheets, which have a thickness of 1 mm, at various increased temperatures and strain rates was the main goal of the investigation. We investigated and examined the tensile characteristics at 650 and 750 degrees Celsius in the first investigation. On the other hand, because of flow stresses in the material at higher temperatures, elongation has decreased in value as deformation rates have increased. In addition, we plotted the FLDs experimentally and examined the formation behavior while performing the Nakazima Test on specimens with a thickness of 1 mm. Furthermore, a limiting dome height (LDH) study was conducted on a laboratory scale. In terms of temperature, the LDH was shown to be higher at 750 and at 0.001/s

Application of artificial neural networks for characterisation of formability properties of sheet metals

Artificial neural network models were developed to estimate forming limit diagrams from tensile test results based on our own experiments and data from the literature for steel and aluminium sheet metals. Experimental data were obtained from tensile tests and Nakazima tests. The input parameters used in the models were yield strength, ultimate tensile strength, uniform elongation, elongation at fracture, anisotropy coefficient and hardening exponent or combinations of these. The forming limit curves were defined by the measured minor and major strains using seven standard test specimens. After training the artificial neural network, the difference between measured and predicted results was evaluated by linear regression parameters and by the absolute errors. For steel sheet data taken from the literature, the estimated outputs of ANN models were compared with the results of empirical formulae developed by different authors. It was found that there was a high correlation coefficient between predicted and measured values for models using neural networks, which gave better approximations than other linear and non-linear models.

Characterization and modeling of the damage mechanisms in ductile steel metal-matrix composites: Application to virtual forming

The aim of this work is to investigate the damage mechanisms and stiffness loss in Fe-TiB2 metal-matrix composites during plastic deformation. First, experimental results of interrupted tensile tests are performed to quantify the evolution of damage, using SEM observations, as well as the decrease of Young’s modulus as a function of the tensile strain. The experimental results are then used to calibrate a two-step homogenization model for metal-matrix composites in which the nucleation and growth of voids modify incrementally the overall elastic properties. The model is finally applied to the numerical prediction of stiffness loss in a problem of metal forming based on Nakazima tests. Overall, the stiffness loss predicted before the onset of coalescence is moderate and its distribution is homogeneous, emphasizing that Fe-TiB2 metal-matrix composites could be used in applications requiring metal forming.

On the Measurement of Nakazima Testing Based Out-of-Plane Forming Limit Curves using 2D Digital Image Correlation

The strain compensation method for measuring in-plane forming limit curves (FLCs) using 2D digital image correlation developed previously [A method of measuring in-plane forming limit curves using 2D Digital Image Correlation, SAE Int. J. Mater. Manf., 2023] was modified and extended to more versatile and popular out-of-plane FLCs. The current study introduces a straightforward strain compensation technique for measuring Nakazima testing based out-of-plane FLCs utilizing an affordable single-camera (2D) DIC system. In this study, forming tests are performed on two automotive-grade sheet metal alloys: DP980 steel and a 6xxx series aluminum alloy using the Nakazima test method. The experiments are conducted on a customized setup that allows for simultaneous optical strain measurements using both a stereo DIC and a 2D DIC system. The FLCs are obtained by applying a temporal FLC computation approach to the two measurement sets. The results show that 2D DIC FLC points match those obtained by stereo DIC for both the materials after applying the proposed strain correction method.

Experimental characterization of forming behavior of 3rd GEN AHSS

Third generation of Advanced High Strength Steels (3rd GEN AHSS) for cold stamping combine superior formability and ductility at higher strengths. Their combination with the Laser Welded Blanks (LWB) technology is one answer to improve safety and weight reduction of vehicules for automakers. In this study, a Nakazima test is used to evaluate the forming behavior of LWB based 3rd GEN AHSS and to estimate their Forming Limit. Tests equipped with a Digital Image Correlation (DIC) system are carried out for several materials combinations in order to understand the influence of the weld on LWB formability. The experimental results are used to determine the critical area during this forming test and a dedicated FLC for each material combination. The location of the onset of failure is investigated, from optical observations, DIC data as well as modeling. It appears that different failure locations are obtained depending on both AHSS combination and strain paths. In order to improve the accuracy of the determination of the onset of the failure, a method is proposed to evaluate the failure risk in base metal and in the vicinity of the weld. The improvement of failure prediction will be very helpful to analyze part formability and provide design recommendations.

Experimental investigation to determine necking of commercially pure titanium sheets using a time-of-flight camera and Heaviside-digital image correlation

The plastic instability evolution in polycrystalline metallic materials is a key to understanding the deformation processes during mechanical loading. Plasticity assessments of commercially pure titanium (CP-Ti) can be performed to enhance its mechanical properties. The aim of the present investigation is to determine the plastic deformation during the metal forming processes of CP-Ti sheets at room temperature. This localized deformation might affect the ductility of the sheets’ materials during the forming processes due to their complex strain paths. Therefore, this study is focused on the determination of Forming Limit Diagrams (FLDs) of CP-Ti sheets in different strain paths based on experimental Nakazima test. The latter is employed to determine the complete FLD using several specimens with various geometries to achieve different strain paths in tensile tests. For this purpose, the strain field measurements before cracking are carried out by the Digital Image Correlation (DIC) procedure. The detection of macroscopic cracks is determined by the Heaviside-DIC (H-DIC). During experimental tests, several images are taken with an integrated camera. The captured images are analyzed by DIC and H-DIC. In this work, a second depth camera is accurately calibrated. Thus, depth and standard cameras address most error sources inherent in the time-of-flight (ToF) technology within a unified calibration framework. Therefore, the automatic calibration method of the consumer ToF camera is used and developed for the first time with H-DIC technique, in the framework of material formability, to better determine the ductility limit of CP-Ti.

Numerical comparison of advanced high strength steels forming limit curve using Banabic and Nakazima tests

Numerical comparison of advanced high strength steels forming limit curve using Banabic and Nakazima tests

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.

Experimental and numerical study of microstructure, mechanical characteristics, and forming limit curve for Al 1050/ Mg-AZ31B two-layer sheets manufactured via roll bonding technique

In this article, Al 1050/ Mg-AZ31B two-layer sheets were fabricated by the roll bonding technique. Then, forming limit diagrams and mechanical characteristics were studied experimentally and numerically. Interface modeling by applying the traction-separation rule, and cohesive zone model (CZM) was performed to improve the accuracy of finite element simulations for the first time. First, the interface behavior of the bilayer sheets was investigated experimentally by determining peeling strength and shear strength. Then, the theoretical relation was used to determine the fracture toughness in the normal and shear directions. The cohesive zone model was based on the surface and applying traction–separation rule. Finally, the tensile strength and forming limit curve were simulated for the Al/Mg composite sheet via LS-DYNA R6.1 software. The obtained results showed that the cohesive zone model could accurately predict the mechanical characteristics and forming limit diagram of the Al/Mg laminated composite so that the errors in ultimate tensile strength, strain at the delamination, and fracture strain are 2%, 7%, and 6.7%, respectively. The maximum discrepancy in comparison between the experimental and numeral results is 6.67% in all of the limit strains in the Nakazima test.

Prediction of Hot Formability of AA7075 Aluminum Alloy Sheet

A uniaxial high-temperature tensile test of an AA7075 aluminum alloy sheet was conducted using an established induction heating test system. Five different types of specimens were designed to obtain the stress–strain curves at different forming temperatures and strain rates so as to construct and modify the Johnson–Cook constitutive model. The uniaxial tensile test of different stress states was numerically simulated using ABAQUS finite element software, and the stress triaxiality and equivalent fracture strain parameters were extracted. The Johnson–Cook ductile fracture model was constructed, and an error evaluation scheme was designed to determine the best failure parameter combination. Based on the obtained Johnson–Cook ductile fracture model, finite element models of different strain paths were constructed, and theoretical forming limit curves at different temperatures and strain rates were obtained. The results of the Nakazima test and finite element simulation are mostly consistent, which confirms the reliability of the constructed fracture model and theoretical forming limit curves.

Tensile And Formability Studies on AISI310 Austenitic Stainless Steel

Stainless steel is an alloy of iron, chromium, and, occasionally, nickel and other metals that resists corrosion. Metal is made into thin, flat pieces through an industrial process called sheet metal. One of the fundamental shapes used in metalworking, it can be cut and bent into many other shapes. Metal sheet is used to create a vast array of common items. The aim of the current work is to examine the 310 austenitic stainless steel’s formability at room temperature with different strain rates (i.e 0.1&0.01mm/s). The study’s outcomes were achieved through the utilization of the Nakazima test during stretch forming. Before performing formability test, The mechanical properties of a high-strength stainless steel AISI 310 were examined by conducting tensile tests at room temperature with 0.1,0.01mm/s strain rates. The failure modes, stress-strain curves of all the test specimens were obtained and analyzed. In the current experiment, the stretch forming of different shaped metal was tested in servo electric hot forming machine with different strain rates i.e, (0.1,0.01) at room temperature and plotted forming limit diagrams based on the results. Then simulations of the experiments were performed in LS-dyna software and compared with the practical experiment results.

Experimental Formability and Finite Element Studies on AISI310 Austenitic Stainless Steel

Stainless steel, an alloy comprising chromium, iron and occasionally nickel and other metals, demonstrates exceptional corrosion resistance. The transformation of metal into thin, flat components is achieved through the industrial process known as sheet metal fabrication. The utilization of metal sheets is widespread, contributing to the creation of numerous everyday items. This study aims to investigate the formability of 310 austenitic stainless steel under varying temperatures (623K, 723K, and 823K). The evaluation was executed utilizing the Nakazima test method within the context of the stretch forming procedure. Prior to delving into the assessment of formability, an exhaustive examination of the mechanical properties of the high-strength stainless steel AISI 310 was conducted. This involved subjecting the material to tensile tests at varying temperatures - specifically, 623K, 723K, and 823K - each performed at a consistent strain rate of 0.1/s. The resultant data encompassed an array of failure modes and stress-strain curves for the individual test specimens, all of which were meticulously obtained and subjected to thorough analysis.Forming limit diagrams were subsequently constructed based on the gleaned results, affording a visual representation of the material’s formability under the specific conditions studied. Moreover, these experiments were replicated through simulations employing the LS-DYNA software, with a subsequent comparative examination conducted against the tangible outcomes derived from practical experimentation.