Implementation of the forming limit stress diagram to obtain suitable load path in tube hydroforming considering M–K model

The purpose of this work is to obtain a theoretical forming limit stress diagram (FLSD) and a suitable load path in tube hydroforming. The methodology for prediction of hydroforming stress limit diagram is based on Marciniak and Kuczynski (M–K) model. The numerical approach is based on the modified Newton–Raphson method. The comparison between the experimental and theoretical results for hydroforming stress limit diagrams as predicted by different methods indicates that the present approach is suitable for prediction of necking in tube hydroforming. Then the forming limit stress diagram determined by the proposed methodology is implemented to obtain the suitable load path in tube hydroforming. As a case study, the finite element (FE) model for bulge forming of straight tube has been constructed and verified with published experimental data. Ultimately, the suitable load path has been obtained by applying Adaptive Simulation Method in ANSYS Parametric Design Language (APDL).