New modelling of localized necking in sheet metal stretching - Bressan J.D.* (2010)
Present work examines a new mathematical model to predict the onset of localized necking in the industrial processes of sheet metal forming such as biaxial stretching. Sheet metal formability is usually assessed experimentally by testing such as the Nakajima test to obtain the Forming Limit Curve, FLC, which is an essential material parameter necessary to numerical simulations by FEM. The Forming Limit Diagram or "Forming Principal Strain Map" shows the experimental FLC which is the plot of principal true strains in the sheet metal surface, ε1 and ε2, occurring at critical points obtained in laboratory formability tests or in the fabrication process. Two types of undesirable rupture mechanisms can occur in sheet metal forming products: localized necking and shear induced fracture. Therefore, two kinds of limit strain curves can be plotted: the local necking limit curve FLC-N and the shear fracture limit curve FLC-S. Localized necking is theoretically anticipated to initiate at a thickness defect fin=hib/hia inside the grooved sheet thickness hia, but only at the instability point of maximum load. The inception of grooving on the sheet surface evolves from instability point to localized necking and final rupture, during further sheet metal straining. Work hardening law is defined for a strain and strain rate material by the effective stress σ̄= σo(1+βε̄)nεM. The average experimental hardening law curve for tensile tests at 0°, 45° and 90°, assuming isotropic plasticity, was used to analyze the plasticity behavior during the biaxial stretching of sheet metals. Theoretical predicted curves of local necking limits are plotted in the positive quadrant of FPSM for different defect values in and plasticity parameters. Limit strains are obtained from a software developed by the author. Some experimental results of forming limit curve obtained from experiments for IF steel sheets are compared with the theoretical predicted curves: the correlation is good. © 2010 American Institute of Physics.