Determination Of Forming Limit Curve Research Articles

A Method for Measuring In-Plane Forming Limit Curves Using 2D Digital Image Correlation

<div>With the introduction of advanced lightweight materials with complex microstructures and behaviors, more focus is put on the accurate determination of their forming limits, and that can only be possible through experiments as the conventional theoretical models for the forming limit curve (FLC) prediction fail to perform. Despite that, CAE engineers, designers, and toolmakers still rely heavily on theoretical models due to the steep costs associated with formability testing, including mechanical setup, a large number of tests, and the cost of a stereo digital image correlation (DIC) system. The international standard ISO 12004-2:2021 recommends using a stereo DIC system for formability testing since two-dimensional (2D) DIC systems are considered incapable of producing reliable strains due to errors associated with out-of-plane motion and deformation. This work challenges that notion and proposes a simple strain compensation method for the determination of FLCs using a low-cost single-camera (2D) DIC system. In this study, formability tests are performed on an automotive-grade 6xxx series aluminum alloy using the Marciniak in-plane FLC testing method. The tests are performed on a custom setup that enables simultaneous optical strain measurements using a stereo DIC as well as a 2D DIC system. The results show how 2D DIC FLC points match those obtained by stereo DIC using two popular FLC approaches: ISO 12004-2 section-based spatial method and a time-dependent linear best fit (LBF) method.</div>

Biaxial test method for determination of FLCs and FFLCs for sheet metals: validation against standard Nakajima method

Recently, a biaxial test method comprising a cruciform specimen design and spatio-temporal method to determine the limit strains has been proposed for the determination of forming limit curves (FLCs) and fracture forming limit curves (FFLCs) for sheet metals. However, this test method has not yet been validated against the existing standard methods. In the present work, this biaxial test method has been applied to the aluminium alloy AA5754 for formability evaluation at room temperature and results from the biaxial test method have been compared with those from the standard Nakajima method. Theoretical analysis has been carried out to compare equi-biaxial tension cases for the two methods; a similar variation of thickness strain with radial distance normalised by the radius of the gauge area is found between the two methods. In the biaxial tests, decreasing the radius of the through-thickness dome profile, with which the gauge area is thinned, leads to fracture nearer the specimen centre but produces a less uniform strain distribution. Importantly, the major strains at necking on the FLC, as determined using the biaxial and the standard test methods, are almost the same in the plane-strain state, while in other strain states, the major strains are slightly lower for the biaxial method than that for the Nakajima method. An FFLC for AA5754 has also been determined using the biaxial test method, in which the major strain at fracture decreases with increasing strain ratio β from −0.5 to 0, while it changes only slightly when β > 0.

Comparative Investigation of the Experimental Determination of AA5086 FLCs under Different Necking Criteria.

The construction of a forming limit diagram (FLD) is a conventional approach to obtain limit strains and to evaluate the formability of sheet metal. Appropriate necking criteria should be applied to determine the forming limit curve (FLC) accurately. In recent years, deep research on the determination of the FLC has been carried out; meanwhile, several necking criteria have been proposed. However, the application of inappropriate necking criteria would cause deviations when determining FLCs. In this study, both Marciniak and Nakajima tests were carried out on the AA5086 aluminum sheet to make a comparative investigation of different necking criteria in the determination of FLCs. In the Marciniak test, four existing necking criteria were chosen to construct FLCs, and analyzed in detail. The well-performed time dependent and position dependent methods were selected for the Nakajima test. Meanwhile, the modified Wang method based on the height change of the adjacent points was proposed. The comparative results showed that the time and position dependent methods were relatively conservative in both experiments, while the modified Wang method could identify the onset of localized necking more accurately.

A new Device for Determination of Forming-Limit-Curves under Hot-Forming Conditions

Forming-Limit-Curves (FLCs) are widely used to characterize the forming behaviour of materials. Nevertheless, the determination of FLCs for hot forming processes is a challenging and time-consuming procedure. At the Chair of Automotive Lightweight Design, a new device for the determination of FLCs under hot forming conditions was developed. In a sealed isothermal oven atmosphere, blank holder, die and punch are used for the FLC determination relying on the DIN EN ISO 12004-2. External hydraulic forces actuate the punch and blank holder. To ensure insulation from the thermal load set inside the hot oven atmosphere an innovative cooling system with extensive use of additively manufactured components with integrated cooling channels is used. For the feed of the different deep drawing tests geometries an airlock is installed, which allows keeping the temperatures constant during the testing procedure. Afterward the forming limits for the different geometries are evaluated with optical measurement systems. The developed test rig proved the ability to determine FLCs for isothermal temperatures up to 800° C.

Finite Element Analysis of Size Effect for Forming-Limit Curves

Abstract Nowadays, finite element (FE) methods are widely used for the analysis of Body in White parts production. An FE software applies the forming-limit diagram to predict the failure of the sheet metal. There are many new materials for weight reduction; for these new materials, the determination of forming-limit curves (FLC) is important to studying formability issues. There are some cases where the available material for the measurements is not enough or due to some specific measurement parameter, the standard test specimen cannot be used. In these cases, the geometry of the test pieces and the testing equipment should be reduced. In this paper, the material card for DC05 (1.0312) steel was determined based on a tensile test and the Nakajima test. With the material card, simulations were performed to investigate the size effect of the hemispherical punch used for Nakajima forming method. Based on the simulations, the difference between the FLC-s (determined with different equipment) was found to be negligible.

Determination of the Forming-Limit Diagram from Deformations within Necking Instability: A Digital Image Correlation-Based Approach

It is now possible using digital-image correlation techniques to precisely measure deformation within a developing necking instability, during forming-limit experiments. However, the current standards for measuring limit strains rely only on data outside of the instability. We propose exactly the opposite, to use just those deformations from the material where the instability will develop. Marciniak and Kuczynski experiments were performed on a drawing-quality steel and the entire deformation history recorded with a high-resolution photographic camera. The strain fields from these image were analyzed with the digital-image correlation program NCORR, concentrating on where the necking instability would form. The Merklein et al. (CIRP Ann Manuf Technol 59:295-298, 2010) and Hotz et al. (Key Eng Mater 549:397-404, 2013) temporal analyses were modified through an original smoothing technique to uniquely identify, through a correspondence of results, when the deformation acceleration rate begins to rapidly increase within the developing instability. This defines a limit strain. These results were compared to the standard Bragard-type determination specified in the norm International Standard ISO 12004-2:2008 (Metallic materials—sheet and strip: determination of forming-limit curves. Part 2—determination of forming-limit curves in the laboratory, International Organization for Standardization, Geneva, 2008). We found a close agreement in balanced-biaxial tension between our proposed technique and the standard Bragard-type analysis. However, in plane-strain and uniaxial deformation the standard analysis appeared to be excessively conservative, by as much as 40% for our steel.

Investigation and Compensation of Biaxial Pre-strain During the Standard Nakajima- and Marciniak-test Using Generalized Forming Limit Concept

One of the most important tasks in sheet metal forming is the prediction of formability. The common criterion for ductile fracture in industrial application is the evaluation of the so-called Forming Limit Curve (FLC). The determination of FLCs is standardized in the international standard 12004-2 by two different experimental methods, the Marciniak- and the Nakajima-test. Several effects, for example bending or contact pressure, are leading to biaxial pre-forming and to a slightly non-linear load path. This results in inaccuracies of the FLC. The so-called Generalized Forming Limit Concept (GFLC) is a phenomenological approach, which was introduced to predict the local necking of non-linear load paths. The accuracy and robustness of the GFLC has already been shown in several papers. In this investigation the GFLC was used to compensate the biaxial pre-forming and to calculate a linear FLC. Input parameters are the Marciniak- and Nakajima-FLCs of the material HC340LA.

EXPERIMENTAL FLC DETERMINATION OF HIGH STRENGTH STEEL SHEET METAL

To assess formability in sheet forming, experimentally determined Forming Limit Curves (FLC) are often used. These conventional FLCs represent the forming limits (i.e. onset of necking) of a sheet material subjected to in-plane deformation or almost in-plane deformation. A widely used approach to experimentally determine the onset of necking of sheet material subjected to in-plane and almost in-plane deformation is formulated in ISO 12004. The aim of this work is to investigate limit strains for deep drawing quality sheet metal of HX180BD with nominal thickness 0.6 mm. The FLC curve has been measured by implementation of Nakajima test on universal testing machine Erichsen 145-60. The Nakajima test has been measured according to EN ISO 12004-2. Limit strains have been measured using 3D photogrammetric system ARAMIS by GOM. Forming limit curve was evaluated both the section method and the time dependent technique. The resulting experimental FLC curves were compared. With the time based method for the determination of FLC a greater strain values was achieved.

An experimental and numerical study of forming limits of AA5182-O

Forming limit curve (FLC) has been applied for evaluating the formability of sheet metal in a standardized way. Various experimental procedures and theoretical models were introduced in the past decades. However, bunches of tests required in the experimental determination of FLC make the procedures more burdensome. In the present study, a combination of experiment and simulation study was conducted with AA5182-O in terms of localized necking and fracture. In the proposed methodology, three experimental procedures, uniaxial tensile, deep drawing with round cup, and dome stretching, were performed and analyzed by using the finite element (FE) simulations. The feasibility of FE models were preliminarily examined by the experimental results. The progression-dependent criterion was developed to determine the process of localized necking to fracture. In the criterion, evolutions of principal strains and their derivatives were calculated and calibrated by validated FE models. The limiting strains obtained from the proposed method showed a good agreement with FLCs obtained using other methods.

Strategies and limits in multi-stage single-point incremental forming

Multi-stage single-point incremental forming (SPIF) is a state-of-the-art manufacturing process that allows small-quantity production of complex sheet metal parts with vertical walls. This paper is focused on the application of multi-stage SPIF with the objective of producing cylindrical cups with vertical walls. The strategy consists of forming a conical cup with a taper angle in the first stage, followed by three subsequent stages that progressively move the conical shape towards the desired cylindrical geometry.The investigation includes material characterization, determination of forming-limit curves and fracture forming-limit curves (FFLCs), numerical simulation, and experimentation, namely the evaluation of strain paths and fracture strains in actual multi-stage parts.Assessment of numerical simulation with experimentation shows good agreement between computed and measured strain and strain paths. The results also reveal that the sequence of multi-stage forming has a large effect on the location of strain points in the principal strain space. Strain paths are linear in the first stage and highly non-linear in the subsequent forming stages. The overall results show that the experimentally determined FFLCs can successfully be employed to establish the forming limits of multi-stage SPIF.