Forming Limit Diagrams of Perforated St12 Steel Sheets

One of the unique characteristics of sheet metals is their formability, which is determined by the forming limit diagrams. These diagrams specify the maximum deformation limit before part’s failure. For several applications of metal sheets, they have to be in the perforated format. 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 and 4 mm, and two layouts of triangular and square were prepared. The specimens were tested using Nakajima test (stretch with a hemispherical punch) to generate the forming limit diagrams. 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 triangular hole layout showed higher forming limits due to their larger ligament ratios.

Forming Limit Diagrams of Perforated St12 Steel Sheets

One of the unique characteristics of sheet metals is their formability, which is determined by the forming limit diagrams. These diagrams specify the maximum deformation limit before part’s failure. For several applications of metal sheets, they have to be in the perforated format. 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 and 4 mm, and two layouts of triangular and square were prepared. The specimens were tested using Nakajima test (stretch with a hemispherical punch) to generate the forming limit diagrams. 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 triangular hole layout showed higher forming limits due to their larger ligament ratios.

Fully-coupled micro–macro finite element simulations of the Nakajima test using parallel computational homogenization

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$$^2$$ 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.

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.

Influence of the contact with friction on the deformation behavior of advanced high strength steels in the Nakajima test

This work presents a new understanding on the deformation mechanics involved in the Nakajima test, which is commonly used to determine the forming limit curve of sheet metals, and is focused on the interaction between the friction conditions and the deformation behaviour of a dual phase steel. The methodology is based on the finite element analysis of the Nakajima test, considering different values of the classic Coulomb friction coefficient, including a pressure-dependent model. The validity of the finite element model is examined through a comparison with experimental data. The results show that friction affects the location and strain path of the necking point by changing the strain rate distribution in the specimen. The strain localization alters the contact status from slip to stick at a portion of the contact area from the pole to the necking zone. This leads to the sharp increase of the strain rate at the necking point, as the punch rises further. The influence of the pressure-dependent friction coefficient on the deformation behaviour is very small, due to the uniform distribution of the contact pressure in the Nakajima test. Moreover, the low contact pressure range attained cannot properly replicate real contact condition in sheet metal forming processes of advanced high strength steels.