A study of strain localization in the fine-blanking process using the large deformation finite element method

Abstract

Abstract In this paper, an updated Lagrangian large deformation finite-element method was developed for solving metal forming problems with an incrementally objective mid-interval integration algorithm. In order to avoid oscillatory behaviour, the Green–Naghdi stress rate was adopted in the finite-element programme, this stress rate being determined implicitly by means of the rotation tensor. A consistent tangent operator and the Newton–Raphson iterative method were employed to solve the incremental equilibrium equations. The hypoelastic constitutive equations have been integrated numerically by the projection algorithm. The target material is assumed to be a low-carbon steel having a stress–strain relationship which exhibits strain hardening and damage softening. With this model, a numerical computation of strain localization in the fine-blanking process was conducted. The computed deformed mesh agrees with experimental observation. The calculated equivalent plastic strain was high at the clearance zone and the plastic flow was localized in this area. Thus, the localization of plastic flow may cause the initiation of shear bands. Under the high hydrostatic stress of the fine-blanking process, further increase in the strains within the shear band will not contribute significantly to the overall deformation of the material. Hence, shearing fracture will occur at the cutting edges and a good cutting surface can be achieved.