Forming-limit strains of perforated steel sheets under biaxial stress state

The forming-limit strains of cold-rolled steel sheets perforated with regularly arranged round-, square-, and cross-shaped holes were experimentally and theoretically estimated. Two types of hole arrangements, i.e. square and triangular patterns, were considered for each hole shape and the experimental forming-limit strains were determined using the hemispherical dome test (also known as Nakazima test). The theoretical forming-limit curves were computed using the finite element method with Hill's quadratic yield function and a plastic instability criterion determined from the external force power. By comparing the experimental results and theoretical calculations under proportional loading, the formability prediction performance of the theoretical approach was evaluated. It was found that although the approach is not applicable for the triangular array of cross-shaped holes, it can achieve partially acceptable prediction for the other cases.