SESSION TITLE WILL BE COMPLETED BY MSC SOFTWARE FORMING SIMULATION USING RIGID-PLASTIC MATERIAL MODEL IN MARC Gary Huang, Simufact-Americas LLC April 8, 2013 SUMMARY When simulating large deformation in forming, elastic effect is often trivial compared to the large plastic deformation. The rigid-plastic material model provided in Marc allows users to utilize this feature and improve the performance of the simulation. The paper specifically focuses on the study of the applications in 3-D forming processes using tetrahedral element type 157. The comparisons of its performance with the elastic-plastic material model are demonstrated. Enhancement in Marc for the rigid-plastic material model is described. It can be concluded in this study that the rigid-plastic material model in Marc speeds up the simulation with less computational power required. Users can use this material model to simulate relatively complex, closed-die and hot forging in shorter time and with more elements in the model. KEYWORDS FEM, Rigid-Plastic, Forming, Marc
1: Introduction Simufact Engineering has been an MSC partner for manufacturing simulation for the last 17 years. We are specialized in metal forming and welding simulations, using Marc and Dytran as our finite element and finite volume solvers. Since the beginning of metal forming simulation using FEM around 1970s, FEM has become an indispensable tool for forming process designers and engineers. More and more trials are done on the computers using the simulations before the dies are cut and real shop flour processes are done. However, as the model size gets larger and larger the demanding of the speed is increasing. In this paper, we would like to explore the possibilities of using the rigid-plastic model supported in Marc to help speed up forming simulations. Figure 1: Metal forming simulation using FEM 2: Rigid-plastic material model Rigid-plastic material model is an idealized material model in that the elastic deformation is ignored. Figure 2 is a comparison of a typical elastic-plastic material and a rigid-plastic material.
TYPE PAPER TITLE HERE USE HEADER STYLE Figure 2: Comparisons of EP and RP material models Because of the simplification, Levy-Mises flow rule can be used as (Equation 1) where is the deviatoric stress and is plastic multiplier. Using the rate form and von-mises yield criterion, we can rewrite the above equation into the following flow formulation (Zienkiewicz): (Equation 2) where is the effective stress equalling to the yield stress and is the equivalent plastic strain rate. A cut-off value is used so that when Marc program sets to avoid numerical difficulties., Once material flow stress function is known, solving above equation is trivial compared to the radial return-mapping scheme used for the elastic-plastic material model where iteration is need to compute the stress state on the yield surface (Figure 3) if the material becomes plastic.
Figure 3: Radial Return Mapping Scheme Because the radial return mapping is performed at the integration point, it is reasonable to believe that the computational effort for the elastic-plastic material model is much more than the rigid-plastic. Also because of the savings for the elastic result, the memory consumption is less for the rigid-plastic material model. Here are two simple examples to show the differences using Marc. Figure 4: Simple comparison between RP and EP The above example shows a speed up of 1.26. If the mesh is refined to have 30592 elements, the wall time changes to 377 sec. with RP and 492 sec with EP. The speed up is increased to 1.78. With the same number of increments and iterations, the following figures show a breakdown, item-to-item comparisons. The obvious saving of memory is in the element storage. The computation time shows big differences in stiffness assembly and stress recovery, each scoring 44% and 200% time savings with RP. All these happen while the FEM results are comparable between EP and RP.
Figure 5: Element Storage savings from 220Mb to 158Mb Figure 6: Main computation saving is in Stiffness Assembly and Stress Recovery Further test with friction, thermal-mechanical coupling and remeshing also shows promising results. Figure 7: Comparison of hot upsetting with friction and remeshing
3: Difficulties using RP in Marc In order to use RP effectively the plastic strain rate cut-off value is important. The rigid-plastic control parameters are input from the numerical preferences in Mentat. Figure 7: Mentat menu to enter the rigid-plastic control parameters When the rigid-plastic strain cut-off rate is too large, we force most of the forming body to be plastic. This is in general not correct at the beginning of the forming process. If the cut-off rate is too small, we force most of the forming body to be rigid. This could cause solution to be divergent. Also we noticed that Marc adds the plastic strain rate cut-off value to the plastic strain. This is incorrect. The following heading process shows the problem. Figure 8: Heading Forming Process
In this heading process, the workpiece is positioned into the die and then moving with the die because of a spring. The plastic deformation is minimum or close to zero, in other words, the material is mostly rigid in the positioning stage. When the spring is fully compressed and the deformation starts, the heading area is deformed with a large plastic strain. Obviously, it is difficult to use the same cut-off plastic strain rate to simulate the whole process. In Simufact, we use the following approach to resolve this problem. Figure 9: Approaches to resolve constant cut-off plastic strain rate problem This approach resolves fictitious plastic strain and provides proper cut-off rate values as the deformation proceeds. The following figure displays different cut-off values at certain steps of the deformation. Figure 9: Evolutions of the cut-off plastic strain rate
It can be shown that the cut-off rate value changes from a very small value to about 0.64e04. This helps convergence and improves the results. 4: More Examples More examples are used to test rigid-plastic material model in Marc. Here are some of them.
Figure 10: Examples using Rigid-plastic material model 5: Conclusions In this paper, we show that rigid-plastic material model in Marc can be used to speed up forming simulation and allow more elements are used in the simulation. The paper also shows enhancement to Marc to avoid convergence problem or incorrect results because of the constant plastic strain rate given in the input. More work is to follow to further improve Marc simulation using the rigid-plastic material model.