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The use of computer simulation to imitate physical processes has proven to be a time-efficient and cost-effective way of performing scenario testing for process optimisation in different applications. The finite element analysis (FEA) is the dominant numerical simulation method for analysing sheet metal forming processes. It uses mathematical tools and computer-aided engineering software programmes to predict forming processes. To improve the quality of output from the simulation, accurate material characterisation data that correctly model the behaviour of the material when it undergoes deformation must be provided. This paper outlines the stages of conducting material characterisation experiments, such as tensile, hardness, and formability tests, using the aluminium alloy AA1050-O. Sample preparation, the machine setup, and testing procedures for the material characterisation tests are given. Subsequent data preparation methods for input into an FEA software programme are also outlined. Implications of the testing results to a deep drawing process are examined while considering the formation of a rectangular monolithic component measuring 2300 mm by 1400 mm with a drawing depth of approximately 150 mm. The results from the characterisation tests indicate that the forming process for the product can be achieved using cold forming at room temperatures as a 25% strain was recorded before necking against an anticipated uniaxial strain of 5.93%. The aluminium alloy AA1050-O demonstrated a negligible strain rate sensitivity in the forming region, thus eliminating tool velocity from the key process parameters that should be considered during FEA simulations. A 50% increase in hardness was recorded after strain hardening.

The Nakajima test is a well-known material test from the steel and metal industry to determine the forming limit of sheet metal. It is demonstrated how FE2TI, our highly parallel scalable implementation of the computational homogenization method FE 2 , can be used for the simulation of the Nakajima test. In this test, a sample sheet geometry is clamped between a blank holder and a die. Then, a hemispherical punch is driven into the specimen until material failure occurs. For the simulation of the Nakajima test, our software package FE2TI has been enhanced with a frictionless contact formulation on the macroscopic level using the penalty method. The appropriate choice of suitable boundary conditions as well as the influence of symmetry assumptions regarding the symmetric test setup are discussed. In order to be able to solve larger macroscopic problems more efficiently, the balancing domain decomposition by constraints (BDDC) approach has been implemented on the macroscopic level as an alternative to a sparse direct solver. To improve the computational efficiency of FE2TI even further, additionally, an adaptive load step approach has been implemented and different extrapolation strategies are compared. Both strategies yield a significant reduction of the overall computing time. Furthermore, a strategy to dynamically increase the penalty parameter is presented which allows to resolve the contact conditions more accurately without increasing the overall computing time too much. Numerically computed forming limit diagrams based on virtual Nakajima tests are presented.

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 forming limit diagram (FLD) is commonly used as a useful means for characterising the formability of sheet metal forming processes. In this study, the Nakajima test was used to construct the forming limit curve at necking (FLCN) and fracture (FLCF). The results of the FLCF are compared with incremental sheet forming (ISF) to evaluate the ability of the Nakajima test to describe the fracture in ISF. Tests were carried out to construct the forming limit diagram at necking and fracture to cover the strain states from uniaxial tension to equi-biaxial tension with different stress triaxialities—from 0.33 for uniaxial tension to 0.67 for equi-biaxial tension. Due to the fact that the Gurson–Tvergaard-Needleman (GTN) model can be used to capture fracture occurrence at high stress triaxiality, and the shear modified GTN model (Nahshon-Hutchinson’s shear mechanism) was developed to predict the fracture at zero stress or even negative stress triaxiality, the original GTN model and shear modified GTN model may be not suitable to predict the fracture in all samples of the Nakajima test as some samples are deformed under moderate stress triaxiality. In this study, the fractures are compared using the original GTN model, shear modified GTN model and the Nielsen-Tvergaard model with regard to stress triaxiality. To validate the ability of these models, and to assess which model is more accurate in predicting the fracture with different stress triaxialities, finite element (FE) simulations of the Nakajima test were compared with an experimental results to evaluate the applicability of the Nakajima test to characterise the fracture from ISF. The experimental and FE results showed that the shear modified GTN model could predict the fracture accurately with samples under uniaxial tension condition due to low stress triaxiality and that the original GTN model is suitable for an equi-biaxial strain state (high stress triaxiality), whereas the stress triaxiality modified GTN model should be considered for samples which have moderate stress triaxiality (from plain strain to biaxial strain). The numerical and experimental FLCF of pure titanium from the Nakajima test showed a good agreement between the experimental and numerical results of ISF.

One of the unique characteristics of sheet metals is their formability, which is determined by the forming limit diagrams (FLDs). These diagrams specify the maximum deformation limit before part failure. For several applications of metal sheets, they have to be in the perforated format. The existence of holes in the perforated sheets may adversely deteriorate the forming limit of metal sheets. In this study, the effect of perforated sheets' hole size and hole layout on their formability are investigated. Several specimens of St12 steel with 0.6 mm thickness, different widths, two various hole sizes of 2 mm and 4 mm, and two layouts of triangular and square arrangements were prepared. The specimens were tested using the Nakajima test (stretch with a hemispherical punch) to generate the FLDs. It was observed that both the diameter and layout of the punched holes have a significant effect on the formability of the perforated sheets. The perforated sheets with a triangular hole layout showed higher forming limits due to their larger ligament ratios.

Hybrid Laminar Flow Control (HLFC) is a promising technology for reducing aircraft drag and, therefore, emissions and fuel consumption. The integration of HLFC systems within the small space of the wing leading edge, together with de-icing and high lift systems, is one of the main challenges of this technology. This challenge can be tackled by using microholes along the outer skin panels to control suction without the need for an internal chamber. However, microperforations modify the mechanical properties of titanium sheets, which bring new challenges in terms of wing manufacturability. These modified properties create uncertainty that must be investigated. The present paper studies the mechanical properties of micro-drilled titanium grade 2 sheets and their modeling using the Finite Element Method (FEM). First, an experimental campaign consisting of tensile and Nakajima tests is conducted. Then, an FEM model is developed to understand the role of the anisotropy in sheet formability. The anisotropy ratios are found by combination of Design of Experiments (DoE) and the Response Surface Method (RSM); these ratios are as follows: 1.050, 1.320, and 0.975 in the directions Y, Z, and XY, respectively. Some mechanical properties are affected by the presence of microholes, especially the elongation and formability that are significantly reduced. The reduction in elongation depends on the orientation: 20% in longitudinal, 17% in diagonal, and 31% in transversal.

This paper delves into the formability of material deposited by wire arc additive manufacturing. It presents a novel dieless Nakajima testing procedure that offers a practical solution for obtaining strain loading paths up to failure directly from the deposited material without the need for extracting sheet blanks. The procedure involved machining a region of the deposited material to the desired shape and thickness and using a press to drive and control the movement of a hemispherical punch. The test was designed using finite element modeling, and its effectiveness in obtaining the required strain loading paths directly from the deposited material was verified through experimentation with digital image correlation. Importantly, this novel test eliminates the need for the special-purpose tool setup required in conventional Nakajima sheet formability tests, thereby simplifying the overall testing process.

Within the framework of the formability limit assessment in sheet metal forming, testing of notched tensile samples coupled with digital image correlation (DIC) has been analysed as an alternative to overcome the implications of Nakajima testing in relation to times of test preparation, cost of the equipment, presence of friction, and amount of material required for the test. Additionally, the complications of the Nakajima testing at elevated temperatures need to also be considered. In this work, specific notched sample geometries have been investigated to accurately identify the forming limits of Aluminium alloy AA6016 in T4 condition. Once the notched geometry had been defined, experimental tensile testing of the samples coupled with DIC technology allowed us to identify the formability limits of interest. Finally, a comparison at room temperature with the conventional Nakajima testing was performed experimentally. Two different methodologies for strain limit evaluation in notched samples have been investigated in the present analysis. The first one is called a position-dependent method and is based on the inverse best-fit parabola of the “bell-shaped curve”, which is used in the conventional Nakajima test. The second approach referred to a time-dependent method and is based on the strain rate evaluation at the necking zone. This strain-rate-dependent method, which works in combination with DIC measurements, was found to be more accurate to determine the necking limits than the previous one; in addition, it also provides more accurate information for the safe zone of forming.

Brass sheets are extensively utilized in the automotive, electrical, and other industries, where an in-depth understanding of their formability is crucial for achieving optimal performance in production applications. This study investigates the influence of uniaxial pre-strains on the Forming Limit Curve (FLC) of CuZn 70-30 brass sheets, which aims to enhance their formability by identifying and optimizing key forming parameters. Adding a new variable, the impact of uniaxial pre-strain upon FLC, was our aim of this study and, consequently, the CuZn 70-30 brass sheet formability using punch-stretching tests with purpose-built tools, we experimentally obtained FLCs for brass sheets under varying levels of pre-strain (0.04, 0.06, and 0.08) applied through uniaxial tension by using Nakajima tests with purpose-built tools. The objective was to understand how specific factors such as punch parameters, punch corner radius, and strain rate impact the FLC and, consequently, the brass sheets formability. Results indicate a distinct trend of increasing pre-strain levels leading to a significant rise in minor strain capacity along the right portionof the FLC, with a comparatively insignificant effect on the left. This consistent elevation across strain paths suggests improved formability due to pre-straining, highlighting the potential for optimized manufacturing processes and enhanced product quality across industrial applications.

The demand for advanced high-strength steel (AHSS) in the automotive industry has increased over the last few years. Nevertheless, it is known that AHSSs are susceptible to hydrogen embrittlement. Therefore, the influence of hydrogen on the localization and damage behavior of a CP1000 steel sheet was investigated in this work. The sheet metal was electrochemically charged to a hydrogen content of about 3 ppm (by weight). Tensile tests were performed at different nominal strain rates between 0.00004 s−1 and 0.01 s−1 to investigate the effects of strain rates on their susceptibility to hydrogen embrittlement. Nakajima tests were utilized to investigate the hydrogen effects on the steel’s formability under different stress states. Three different Nakajima specimen geometries were employed to represent a uniaxial stress state, a nearly plane strain stress state, and an equibiaxial stress state. Further, forming limits were evaluated with the standardized section line method. Hydrogen embrittlement, during tensile testing, occurred independent of the strain rate, unlike the Nakajima test results, which showed hydrogen effects that were strongly dependent on the stress state.