Compensation for process-dependent effects in the determination of localized necking limits

This work describes a new procedure to remove the differences in measured forming limits obtained from Marciniak and Nakazima tests, which are the two most frequently used testing methods to obtain necking limits for forming limit diagrams (FLD) used in formability analysis of sheet metal stamping processes. The procedure compensates for the combined effects of curvature and nonlinear strain path that occur during these tests, using measurements recorded by digital image correlation (DIC) throughout the deformation history of the point on the test specimen that eventually necks. The severity of forming is then determined by presenting the critical forming conditions in a stress diagram in order to account for the effects of through-thickness pressure that influences the onset of localized necking in the Nakazima test. These stress-based forming limits are then transformed back to the familiar strain limits (or FLD), but now representing the limits under the restriction of in-plane perfectly linear stretching and plane-stress conditions. Accounting for the effects of nonlinear strain path is particularly sensitive to the detection of the actual onset of localized necking, so this work also recommends the use of realistic methods to detect the actual onset of localized necking. The method adopted in this work is based on a new method described by Min et al. 13, 14, in which a change in the surface curvature is used to detect a geometric effect associated with the onset of localized necking. In addition to demonstrating that the standard Marciniak and Nakazima tests (punch diameter of 101.6 mm) produce essentially identical limit curves for a 980 MPa grade multi-phase high strength steel after correction for curvature, nonlinear strain path, and pressure, the method is also applied to the analysis of data from a non-standard Nakazima test with a smaller punch diameter of 50.8 mm, where the severity of these processing conditions are significantly enhanced. This additional test is further proof of the validity and comprehensive coverage of the corrections for the different processing conditions involved in measurement of forming limit curves.