ORIGINAL RESEARCH Investigation on the strain-path dependency of stress-based forming limit curves Morteza Nurcheshmeh & Daniel E. Green Received: 17 March 2010 / Accepted: 3 June 2010 / Published online: 15 June 2010 # Springer-Verlag France 2010 Abstract Path-dependent forming limits have been com- puted for sheet metals undergoing various combinations of plane stress loading conditions. This paper presents a theoretical model for prediction of stress-based forming limit curves (SFLC) based on the Marciniak and Kuczynski (MK) model. Acceptable agreement was observed between calculated forming limit curves (FLC) and experimental data for AISI-1012 steel (Molaei 1999) and AA-2008-T4 alloys (Graf and Hosford Metallurgical Trans 24A:2503– 2512, 1993). In this paper, the path dependency of SFLCs predicted for different non-proportional loading histories has been investigated. For a range of prestrain values in different bilinear loading paths, the SFLC remains practically unchanged. However, some strain path dependency is observed for large values of prestrain ( e  0:35 for AISI- 1012 steel) and for abrupt changes in strain path. Never- theless, the SFLC remains a good failure criterion for virtual forming simulations because the path dependency of SFLCs is much less significant than that of strain-based FLCs. Keywords Stress-based forming limit curve . Strain-path dependency . Loading history . Non-linear loading paths . MK analysis . Strain localization Introduction The formability of sheet metals is commonly evaluated using a forming limit curve (FLC), a curve in principal strain space that defines a boundary between combinations of strain that lead to a part that is free of necks and those that present a risk of necking and splitting. The concept of the FLC was initially developed by Keeler and Backhofen [3] and Goodwin [4] and provides a useful empirical gauge of forming severity in the absence of a visible neck or split. The shape and location of the forming limit curve (FLC) in principal strain space are a characteristic of the metal that is independent of the forming process or work piece geom- etry. Forming limit curves are determined experimentally by conducting hemispherical punch stretching tests up to the onset of necking on gridded blanks. The experimental testing and grid strain measurement procedure is costly, time-consuming and requires both experience and care in order to determine accurate forming limits. Therefore many researchers have sought to predict the forming limits of sheet materials. The most common analytical approach for the prediction of FLCs have generally relied on the continuum theory of plasticity, which includes a yield criterion, a flow or hard- ening rule and an instability criterion [5]. In recent years, however, various aspects of the microstructure have been incorporated into the theoretical methods to improve their predictive capability [6–8]. In a metal sheet, failure by splitting usually occurs when the local thickness strain reaches a critical value, such that the sheet has thinned significantly and can no longer sustain the imposed in-plane tensile stresses. The theoretical estimation of the limit strain, which is the largest strain produced in the neighbor- hood of a neck before failure, is evidently an extremely difficult proposition when all of the relevant parameters in the forming operation are duly taken into consideration. The influence of strain path changes on the FLC limits its applicability to processes in which the loading path is quasi linear; in other words, one in which the ratios of the M. Nurcheshmeh (*) : D. E. Green University of Windsor, Windsor, ON, Canada e-mail: nurches@uwindsor.ca Int J Mater Form (2011) 4:25–37 DOI 10.1007/s12289-010-0989-4