Analysis of forming limits using ductile fracture criteria

Forming limit diagram (FLD) of sheet metal is usually determined based on localized necking. However, neck initiation under various sheet metal forming conditions is a complex process and there is no well-established experimental, analytical or numerical procedure for its determination. In order to overcome this difficulty, various analytical and numerical methods are explored to predict necking and to construct the forming limit diagrams. In this research, empirical types of ductile fracture criteria were studied in detail, and the computed data were compared against results obtained from laboratory experiments.; Finite element models were developed using ABAQUS/Standard to simulate an out-of-plane formability test. Different sample geometries and lubricating conditions were tested to produce different strain paths on the FLD. In this work, both Hill's anisotropic and the Mises isotropic plasticity models were used and discussed. The limit strains were determined by substituting the values of stress and strain histories calculated by the finite element simulations into the ductile fracture criteria. An experimental FLD and an analytical FLD were determined for aluminum killed drawing quality electrogalvanized (AKDQ) steel to validate the numerical findings. The fracture strains at the left side of the FLD were predicted successfully by a number of ductile fracture criteria. However, these criteria could not be used directly to determine the FLD because it is determined based on neck initiation not fracture strain. Due to the limitation of ductile fracture criteria, extensive thickness strain studies were performed to find the relationship between localized necking and the thickness strain. Based on numerical findings, it has been proposed that fracture criteria constants should be calculated at a thickness strain around 20%–25%, and be considered as a critical value of the ductile fracture criteria for strain localization. This new proposed approach was successful for the left side of the FLD. For general acceptance, this new approach should be tested on several materials. Although the predictions of the right side of the FLD with this new approach were not quite successful, some improvements were made for the Mises model.