Date of Award


Publication Type

Doctoral Thesis

Degree Name



Mechanical, Automotive, and Materials Engineering

First Advisor

Green, Daniel (Mechanical, Automotive and Materials Engineering)


Mechanical Engineering.




This dissertation proposes a number of significant enhancements to the conventional Marciniak-Kuczynski (MK) approach including a more realistic definition of the imperfection band, consideration of strain rate sensitivity and the effect of material anisotropy. Each enhancement was evaluated by comparing the predictions to experimental FLCs found in the literature.An analytical method of determining the forming limit curve (FLC) of sheet materials was developed by Marciniak & Kuczynski in 1967 and has been used extensively since then. In the current research, a numerical code was developed based on the MK analysis in order to predict the FLCs of sheet metals undergoing plane-stress loading along non-proportional strain paths. The constitutive equations that govern plastic behaviour were developed using Hill's 1948 yield function and the associated flow rule.Stress-based FLCs were also predicted with this MK analysis code and the strain-path dependency of SFLCs was investigated for different non-proportional loading histories. It was found that the SFLC remains essentially unchanged for lower magnitudes of prestrain, but after significant levels of prestrain, it was observed to shift up somewhat toward the vicinity of plane-strain deformation.Two different work hardening models were implemented in the MK model to predict the FLC. Both isotropic hardening and mixed isotropic - nonlinear kinematic hardening models were used in cases that involve unloading and subsequent reloading along a different strain path. The FLC predicted with the mixed hardening model was in better agreement with experimental data when the prestrain was in the domain of the positive minor strains, but the assumption of isotropic hardening led to acceptable agreement with experimental data when the prestrain was in the domain of the negative minor strains.The consideration of a through-thickness stress applied during the forming process was also added to the model and it was shown that the normal stress has a positive effect on formability. Moreover, changes in certain mechanical properties can significantly increase the sensitivity to the normal stress.Finally, a non-quadratic yield criterion was implemented into the predictive model and it was found that, generally, a non-quadratic yield function leads to more accurate predictions of the FLC.