Date of Award


Publication Type

Master Thesis

Degree Name



Mechanical, Automotive, and Materials Engineering

First Advisor

Green, Daniel (Mechanical, Automotive and Materials Engineering)


Engineering, Mechanical.




In sheet metal forming, the discrepancy between the fully loaded shape at the end of forming stage and the unloaded configuration is called springback. Springback is a major factor in preventing accurate dimensions of final products. Therefore, it is very important that springback be quantitatively predicted and compensated in the die design stage. In sheet metal stamping, especially when drawbead is used, the material experiences several cycles of bending-unbending-reverse bending. Therefore, in to order to accurately predict springback, the constitutive model must be able to accurately describe the material behaviour during cyclic loading. Yoshida-Uemori (YU) two-surface model is one of the most sophisticated models which is capable of reproducing the transient Bauschinger effect, permanent softening and workhardening stagnation. In this work, two different yield functions, i.e. Hill’s 1948 and Yld 2000-2d, were used in conjunction with YU two-surface model. Moreover, two different numerical procedures were developed for numerical implementation of these models: a) a semi-implicit approach and b) a fully-implicit approach. The numerical procedures were used to develop user material subroutines for ABAQUS commercial software. Then, the subroutines were used to evaluate the capability of the model in prediction of springback for a channel draw process. In addition, the isotopic hardening (IH) and combined isotropic-nonlinear kinematic hardening (IH+NKH) models were also used to predict the springback of the problem. Finally, the springback profiles obtained by each model were compared with the experimental data. For DP600, the error in springback prediction is around 3% when YU model is used. For HSLA and AA6022, the error associated with YU model is less than 3% and 13% at 25% and 100% drawbead penetrations, respectively. The YU model does not predict the springback accurately for AKDQ and the error is around 30%. The results also show that the IH model overestimates the springback for all materials. For DP600 and AA6022, the results obtained by IH+NKH model are the same as those obtained by YU model. However, the YU model considerably improves the springback prediction compared to IH+NKH model for HSLA; while for AKDQ the IH+NKH model improves the springback prediction compared to YU model.