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Streszczenie:
This paper presents an investigation on the determination of forming limit curves (FLCs) by finite element simulations. The numerical FLCs are determined applying the criteria of strain localization in simulations of the Nakazima formability tests. Two methods to determine the onset of localized necking have been compared. The first criterion is based on the analysis of the through-thickness thinning (through-thickness strain) and its first time derivative in the most strained zone. The onset of necking is assumed to occur at the point corresponding to a sudden change of the slope of the strain rate vs. time curve. The limit strain in the second method is determined by the maximum of the strain acceleration, which corresponds to the inflection point of the strain velocity vs. time curve. The limit strains have been determined for different specimens undergoing deformation at different strain paths covering the whole range of the strain paths typical for sheet forming processes. This has made it possible to construct numerical forming limit curves (FLCs). The numerical FLCs have been compared with the experimental one, showing quite a good agreement, especially in the case of the first criterion. This shows that finite element simulations can be used as a potential alternative tool to determine formability limits for sheet forming processes.

Słowa kluczowe:
Sheet metal forming, Formability, Forming limit curve, Finite element simulation

Streszczenie:
This paper presents a comparison of two criteria of strain localization in experimental research and numerical simulation of sheet metal forming. The first criterion is based on the analysis of the through-thickness thinning (through thickness strain) and its first time derivative in the most strained zone. The limit strain in the second method is determined by the maximum of the strain acceleration. Experimental and numerical investigation have been carried out for the Nakajima test performed for different specimens of the DC04 grade steel sheet. The strain localization has been identified by analysis of experimental and numerical curves showing the evolution of strains and their derivatives in failure zones. The numerical and experimental limit strains calculated from both criteria have been compared with the experimental FLC evaluated according to the ISO 12004-2 norm. It has been shown that the first method predicts formability limits closer to the experimental FLC. The second criterion predicts values of strains higher than FLC determined according to ISO norm. These values are closer to the strains corresponding to the fracture limit. The results show that analysis of strain evolution allows us to determine strain localization in numerical simulation and experimental studies.

Słowa kluczowe:
Sheet forming, Formability, Forming limit diagram, Strain localization, Numerical simulation

Streszczenie:
This work presents results of investigations on the determination of strain localization in sheet forming. Nakajima formability test has been chosen for the experimental studies and numerical analysis. The onset of localized necking has been determined using the criteria studied in the authors' earlier works, based on the analysis of the principal strains evolution in time. The first criterion is based on the analysis of the through-thickness thinning (through–thickness strain) and its first time derivative in the most strained zone. The limit strain in the second method is determined by the maximum of the strain acceleration. Limit strains obtained from these criteria have been confronted with the experimental forming limit curve (FLC) evaluated according to modified Bragard method used in the ISO standard. The comparison shows that the first criterion predicts formability limits closer to the experimental FLC and second method predicts values of strains higher than FLC. These values are closer to the maximum strains measured before fracture appears in experiment. These investigations show that criteria based on the analysis of strain evolution used in numerical simulation and experimental studies allow us to determine strain localization.

Streszczenie:
This paper presents the investigation on detection of strain localization in experimental research and numerical simulation of sheet metal forming. Experimental tests and numerical simulations of the Nakazima test have been performed for the DC04 grade steel sheet. The onset of localized necking has been determined using the criterion based on analysis of the major principal strain and its first and second time derivatives in the most strained zone. The strain localization has been evaluated by the maximum of strain acceleration which corresponds to the inflection point of the strain velocity vs. time. The limit strains have been calculated numerically and experimentally for specimens undergoing deformation at different strain paths. It has been shown that the numerical model predicts formability limits close to the experimental results. Analyzed criterion can be used as a potential alternative tool to determine formability in standard finite element simulations of sheet forming processes.

Słowa kluczowe:
sheet forming, formability, forming limit curve, numerical simulation

Streszczenie:
This work presents an investigation on the determination of forming limit curves (FLCs) by finite element simulations and experimental approach. Nakajima formability test has been chosen for the experimental studies and numerical analysis. The onset of localized necking has been determined using the criteria studied in the authors’ earlier works, based on the analysis of the principal strains evolution in time. The criterion is based on the analysis of the through-thickness thinning (through-thickness strain) and its first time derivative in the most strained zone. The onset of necking is assumed to occur at the point corresponding to a sudden change of the slope of the strain rate vs. time curve. The limit strains have been determined for different specimens undergoing deformation at different strain paths covering the whole range of the strain paths typical for sheet forming processes. Therefore, determined limit strains allowed us to construct experimental and numerical FLC determined using the presented algorithm. The FLCs have been compared with the conventional FLC determined according to the ISO 12004 standard, showing quite a good agreement. These results indicate that the used methodology of the limit strain determination can be used in finite element simulations as a potential alternative tool to determine formability limits for the sheet forming processes.

Słowa kluczowe:
Steel and aluminum structures