An improved curvature method of detecting the onset of localized necking in Marciniak tests and its extension to Nakazima tests

Abstract

A method using surface curvatures to detect the onset of localized necking in forming limit tests [Min J, Stoughton TB, Carsley JE, Lin J. A Method of Detecting the Onset of Localized Necking Based on Surface Geometry Measurements. Exp Mech 2016; DOI:10.1007/s11340-016–0232-4.] is improved to be more robust and operator-independent. The improved method is referred to as the 3D curvature method, whereby the curvature is fitted on the basis of a small narrow surface encompassing the neck band, and the onset of localized necking is still detected by the sudden increase of the fitted curvature according to the neck expansion theory proposed by Min et al. [Min J, Stoughton TB, Carsley JE, Lin J. A Method of Detecting the Onset of Localized Necking Based on Surface Geometry Measurements. Exp Mech 2016; DOI:10.1007/s11340-016–0232-4.] Appropriate widths and lengths of the small narrow area on the specimen surface are determined by investigation of their effects on the curvature fitting procedure and on the curvature increase that signals the onset of localized necking. In addition, the 3D curvature method is successfully extended to detect the onset of localized necking in Nakazima tests, where the deformation is characterized as out-of-plane, as opposed to the nearly in-plane deformation of Marciniak testing. As a result, forming limit strains associated with the onset of localized necking can be obtained from both commonly used Marciniak and Nakazima tests on an equivalent basis of geometrical change of specimen surface. This is significant for the reconciliation of forming limits from the two tests after compensation for the effects of non-linear strain path, bending and contact pressure described by Min et al. [Min J, Stoughton TB, Carsley JE, Lin J. Compensation for process-dependent effects in the determination of localized necking limits. Int J Mech Sci 2016; 117: 115–134.]