Material Modeling of Perforated Sheet Metals with Different Hole Arrangements by Homogenization Method

Abstract

The homogenization method is effective for analyzing macroscopic mechanical properties from the substructure of a material. In perforated sheet metal, macroscopic mechanical properties depend on the pattern of hole arrangement. In this study, the macro–plastic properties of perforated sheets with 60° standard staggered and 90° square arrangements are modeled. Biaxial stress is applied to the unit cells given the periodic boundary condition, and the contours of equal plastic work are obtained. The yield surfaces of the perforated sheets on the tension–compression combined stress state are strongly affected by the hole arrangement. To model the yield surface, a yield function for the rotational symmetry peculiar to the perforated sheet is proposed. The yield surfaces are modeled using the CPB2006 yield function that takes into consideration tension–compression asymmetry. Also, a surface–interpolated differential hardening model is applied to model the changes of yield surfaces. The analysis results obtained using the modeled yield surfaces are compared with the experimental ones obtained on the uniaxial tensile and deep drawing tests. The results of both tests show good agreement.