Simulation of Tube Hydroforming Process using an Internal State Variable Model
Tube hydroforming is a metal forming process in which tubes are formed into complex shapes within a die cavity using internal pressure and axial compressive forces simultaneously.
A synopsis of a hydroforming process is presented in Figure 1. A copper blank with a previous deformation is being formed by a simultaneous application of axial velocity and internal pressure loads whose time variation during the proces has very well defined profiles. Besides these processing variables, a so-called bucking system (bucking plate and hard stop) is also utilized in the forming process. The weight of the bucking plate and the position of the hard stop are additional process parameters that control the formation of the tee branch, and hence, avoid an excessive thinning of the tube wall and the consequent failure by bursting (fracture). As expected, depending on the specific values used for these parameters, the hydroforming process may produce a good or bad tube fitting, as shown in Figure 1. There are three stages in this hydroforming process, denoted as sealing, forming and coining. During sealing, the rams move to position to provide a tight seal for the pressure to build up inside the copper blank. During forming, the rams begin to compress the blank, the internal pressure increases, and the branch starts to form against the bucking system. As the top of the branch approaches the hard stop, the pressure ramps from the forming to the coining pressure, filling up the gaps between the dies and the hydroformed tee, and bringing the process to an end. In general, modeling the hydroforming process should account for the six components of the system: two rams, top and bottom die, copper blank, and the bucking plate. However, due to symmetry, only one quarter model can be used. The three-dimensional finite element mesh of the hydroforming components (die, bucking plate, ram and copper biller) is presented in Figure 2. In this finite element model, all components are represented as rigid bodies except the copper blank, which is deformable. Characterization studies have been performed on the tube’s material (DHP copper) to understand the effect of the deformation history on the material microstructure as well as to obtain experimental data to calibrate the multiscale internal state variable (ISV) model. The ISV material model  based upon a hierarchical multiscale methodology has been calibrated with the experimental data presented above. The plasticity parameters of the model has been determined from the true strain-true stress data using a parameter identification procedure implemented in MATLAB, while the damage parameters have been computed from finite element simulations of the tensile tests using ABAQUS. The corresponding experimental and computed responses as well as the the geometry of the tensile specimen (physical sample and finite element model) are presented in Figure 3.
A validation study was performed with the constructed finite element model of the hydroforming process and the calibrated multiscale ISV material model. The material model was implemented in ABAQUS through a user material routine. Figure 4 depicts the formation of the T-shape fitting during the hydroforming process as predicted by the numerical model. The process curves for the ram velocity and fluid pressure used in the simulation are shown at the top of the figure. These curves have vertical markers indicating the times at which the snapshots of the deforming tube have been extracted from the simulation, so that one can relate the progression of the forming process with the different stages (sealing, forming, coining) defined by the processing variables. A movie of the process is presented in Figuure 5. The validation of the numerical model was accomplished by comparing the material flow patterns and tube geometry between simulated and manufactured T-shape tube fittings. The experimental flow patterns were obtained from a copper blank etched with straigth lines before being hydroformed. The resulting flow patterns are presented in Figure 5 together with the predicted ones from the simulations. Clearly, the flow lines match well. The same figure also presents a comparison of the thickness profiles between the predicted and manufactured T-shape fittings. Again, the results from the finite element model agrees well with the experimental ones.