An Analytical Approach in Prediction of Necking and Suitable Load Path in Tube Hydroforming by Using the Strain Gradient

A theoretical forming limit stress diagram (FLSD) for necking prediction which is based on the strain gradient theory of plasticity in conjunction with the M-K approach was represented and used in tube hydroforming. This approach introduces an internal length scale into conventional constitutive equations and takes into account the effects of deformation inhomogeneity and material softening. The nonlinear second order ordinary differential equation of the thickness of tube has been solved by collocation method. It has been shown that this method overcomes the imperfection sensitivity encountered in the conventional M-K method. The predicted FLSD has been compared with published experimental hydroforming stress limit diagram and good agreement was found between them. The purpose of this work is the implementation of the forming limit stress diagram determined by the proposed methodology to obtain suitable load path in tube hydroforming. As a case study, the FE model for bulge forming of straight tube has been constructed and verified with published experimental data. Ultimately suitable load path has been obtained by applying Adaptive Simulation Method in ANSYS Parametric Design Language (APDL).