February 19, 2001
Simulation is used in the hydroforming process to replace the experimental investigation and tests required in a real tryout process.
Simulation is used in the hydroforming process to replace the experimental investigation and tests required in a real tryout process. Simulation of hydroforming becomes especially relevant if the feasibility of the metal forming processes has to be checked before expensive tools are actually manufactured.
This article discusses the aims of simulating metal forming processes, as well as some specific aspects and further necessary developments in hydroforming simulation.
The special features and objectives of a multistage simulation are explained by typical tasks for the development and production of hydroformed parts. The complete sequence of developing a hydroformed part is explained. This sequence includes the idea, the process-specific design of the part, the feasibility study, and the first hydroformed prototype.
Because hydroforming can be considered a method of sheet metal forming, the workpieces usually are discretized using shell elements. The number of shell elements to be used usually varies between a few thousand and about 100,000, depending on the complexity of the part.
A realistic collection of material behavior data during hydroforming requires that possibly all previous stages of production also have to be investigated by simulation. In general, the production stages of tube manufacturing (roll forming, welding, heat treatment) are not taken into consideration. The starting point of simulative calculations is a geometrically perfect, homogeneous tube that is free of residual stresses.
Some hydroforming-specific aspects and the idealization of finite element method (FEM) simulations are explained in this section through the typical sequence of manufacturing a hydroformed part.
Bending a tube or profile changes the wall thickness of the workpiece (thinning of the outside region, thickening of the inside region), the geometrical shape (flattening of the cross section, possible forming of wrinkles on the inside region), and the properties of the material (work hardening). In principle, three methods can be used to model the bending process:
1. CAD modeling of the already-bent tube as an ideal, homogeneous tube. This method of modeling neglects all three of the previously mentioned changes. Therefore, this method should be applied only if the bending angles are very small and the workpiece is heat-treated (soft-annealed) after bending.
2. CAD modeling of the tube, considering the flattening and the wall thickness change, based on empirical values of measured results. This method requires a great deal of manual work (allocation of the shell thickness to the individual finite elements in the bending region). It is useful only if bending is followed by a heat treatment and no formation of wrinkles is expected because of the geometrical conditions during the bending process.
3. FEM simulation of the bending process. This is the only method for studying the basic aspects of the real material behavior.
To avoid having to repeat simulations and to reduce simulation time, springback behavior for the most part is neglected in this method of bending simulation.
Preforming, Inserting the Workpiece, and Closing the Tool. Besides bending, other preforming actions often are necessary to allow the fabricator to insert the workpiece into the hydroforming tool and close it without squeezing off the material.
The optimization of the preforming processes for long parts, which are slightly bent but have a complicated cross section, can be made more efficient using 2-D simulation. Those cross sections that are expected to cause the most problems—such as the largest circumference (highest thinning) and the smallest circumference (wrinkle formation)—are investigated. Such cross sections allow the behavior of various preforms to be studied.
The "intermediate optimization" using 2-D simulation must be followed by a 3-D simulation to check areas of connection to other parts or bending zones, where the danger of wrinkle formation exists, and to make further geometrical changes to the preform if necessary.
Two-dimensional simulation also can be used for the hydroforming process, as well as for investigating the axial feeding by modeling a 1-millimeter-wide tube segment with one row of finite elements. All nodes of one edge are fixed, and all nodes of the other edge are displaced (by 0.1 millimeter, for example). This value must be estimated according to the geometrical conditions. This 2-D simulation also must be followed by a 3-D simulation to gain exact information about the complete extension of the part.
For the simulation of hydroforming processes, the axial pistons, which are used for sealing and axial feeding, can be replaced through displacement and/or force boundary conditions applied to the boundary nodes. This means that sealing has no importance for the simulation. Sealing is assumed as a precondition.
Further Developments: Shell Theory & Failure Criteria
Although the present possibilities allow very good hydroforming simulation results to be achieved in correlation with practical tests, theoretical and software technical deficits still exist. To eliminate these, much effort has been made in many areas.
Shell Theory. Hydroformed parts often are thick-walled tubes. The radii to be formed sometimes are not much bigger than the wall thickness. Under such conditions, the simplifying assumptions of the shell theory are not valid, and the accuracy of the simulation results decreases. The shell theory—looking on the material behavior based on thin shell models—is a state-of-the-art method that is used mostly in simulation programs.
Currently, solid elements cannot be used for many typical hydroforming simulation tasks because they require too much CPU time, and efforts are being focused on improving the shell elements. A partial use of solid elements also is imaginable, especially for the areas of biggest curvature.
The classical shell theory neglects stresses that act vertically to the shell plane. Because of the use of high pressure in hydroforming (typical pressures are up to 55,000 pounds per square inch [PSI]), these stress components can reach very high values. This area requires a further improvement of the current shell element formulation.
Failure Criteria. Typically, the forming diagram is compared with the forming limit curve (FLC) to assess possible cracks. The deformation path is strongly nonlinear and deviates significantly from the conditions when recording the FLC. Therefore, the information gained from such FLCs has to be put in clearer perspective than in other sheet metal forming processes. Investigations of actual parts have shown that, in general, larger deformations can be achieved than those expected with the FLC.
Behavior of Machines and Tools
In FEM process simulation, the elastic deformations of tools or machines are considered in exceptional cases only. The real conditions inside the high-pressure system and the hydraulic systems of the axial feeding cylinders are neglected, too. It is just assumed that the specified internal pressure and axial feeding trajectories can be realized absolutely in practice.
A first step toward approximating the real internal pressure trajectory is the "fluid cell" option that is integrated in various FEM programs. This option allows the user to record pressure variations according to the volume change of the part and the flow rate of the fluid.
Another assumption made in hydroforming simulation is that the sealing surfaces are leakproof. Actually, this requirement is not always met by the machine. Plastic deformation may lead to uneven ends of the part or the profile. Displacement-controlled axial feeding in the simulation (displacement boundary conditions of the boundary nodes) can be used to check the signs of the respective axial forces.
Preforming Operations. For many hydroformed parts, typical bending operations are characterized by a complex tool geometry and arrangement and a complicated application of forces. Some of the restrictions of the shell theory also have consequences here. Some of the effects caused by the bending operation cannot be simulated using shell elements. One example is the thinning of the tube regions—which are thickened during bending—when they are pulled through the gap between the mandrel and the wiper die.
Analysis of Final Part Properties. The static and dynamic properties of the part are influenced by the geometry that is created during the metal forming process, by work hardening, and by the residual stresses of the part. Currently, different software is used for the simulation of metal forming processes and for structure-analytical calculations of single hydroformed parts or complete subassemblies. The necessary data transfer results in loss and/or falsification of information (such as when remeshing is required).
Practice-relevant simulation of hydroforming is used to check and optimize metal forming processes and to determine their feasibility before expensive tools are manufactured. FEM simulation improves the understanding of the process and serves as a tool for process planning.
Besides the fundamental questions within the scope of feasibility studies, other special targets of simulation are the material flow and the use of the deformation capacity of the material used for manufacturing hydroforming parts. The matching of calculated values and those determined in experiments, especially during the intermediate stages of the metal forming process, including preforming, is necessary to understand the hydroforming theoretically.
FEM process simulation of hydroforming requires more development. It is integrated into an overall concept of complex simulations that includes the simulation of the final properties of a part, as well as the simulation of technical aspects of the machines. The complete production process takes place in a virtual world, as a sort of virtual prototyping.