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These days, all the engineering designs would be examined using Finite Element Method (FEM) to see any potential weakness. A partial differential equation system that solves real world problems often has no solution, so it is usually solved with method of FEM. FEM is a common solution for the real world problems, and it provides answers to both stress and temperature. If the single answer is to seek, then Finite Differential Method (FDM) is preferred. I hosted an FDM solution in my website (www.metalpass.com) since 2005. FDM requires much less cost than FEM (FEM usually costs days of computing, especially before my Ph.D. work). My FDM program only costs a fraction of a second to compute in a website.

I performed FEM simulation for various Deformation processes during my Ph.D. study in Germany, and during my employment in Morgan Construction Company (Boston, now merged with Siemens) in USA, etc. The simulation was done mainly in HP UNIX workstations and Silicon Graphics, etc., under application of an multi-purpose code MARC and its per- and postprocessor MENTAT. MENTAT helped for mesh generation and result evaluation. This stage is to write code (subroutine) to fit with the FEM software, and to display results with MENTAT. It is exactly the way of today's software coding with a Compiler. Engineering testing was mainly done by the M.S. student and the B.S. students, and the data processing was directed by me. In early 90s, the UNIX workstation, which has equivalently 30 PC's power, has only a Hard Disk of 256MB!!!

Programming techniques applied

During my FEM simulation, following programming have been applied to achieve results of high quality:
  • Three dimensional definition for tools. The tools are a pair of cylinder rolls with grooves milled on each of the rolls. For a roll to press a round bar, for example, the groove cross-section shape is almost semi-round.
  • Contact surface description. While using a shell to represent groove surface, there are two faces for each surface. Various contact situations have to be considered.
  • Input work piece geometry. In most cases, the entry shape of the stock (work piece) is irregular. This is particularly true in the case of multiple pass rolling, in which the rolled shape of the previous pass has to be accurately entered as the initial shape of the current pass.
  • Definition of FEM technical parameters. Since the incremental, updated Lagrangian approach was applied in most of the simulation, time step and (number of) auto load should be determined correctly. For thermo-mechanical solution, the time step should be much smaller than that of the mechanical approach (without temperature calculation). In addition, the time step for shape rolling should be much smaller than for flat rolling.
  • Definition of the movement for stock and tools for each pass. During rolling, the stock is bitten into the roll gap through friction. However, in FEM simulation, a push action has to be applied to the stock until about one third contact length has been filled with the stock. This push speed has to be modeled carefully to establish a steady rolling process.
  • Input of the material data and boundary conditions. Since the code MARC is only a general-purpose program, complicated material data and boundary conditions have to be modeled and programmed (e.g. with Fortran) to feed into the code MARC. Those material data and boundary conditions include flow stress (as function of strain, strain rate, temperature and initial grain size, etc.), heat transfer coefficient between the stock and the tools (depending on cooling speed and surface conditions, etc.), specific heat (depending on temperature and phase for a given metal grade), friction (as function of e.g. materials, relative speed, temperature and pressure), and so on.
  • Extra models such as those on microstructure evolution, to simulate metallurgical process. To predict and plot microstructure parameters, an interface with FEM predicted parameters (e.g. strain, train rate and temperature, etc.) has to be established. Usually, the microstructure evolution process is modeled as function of material, temperature, strain and strain rate for every stage of the rolling and cooling. The microstructure model is then entered into the FEM model as user subroutine.
  • Retrieval and graphical presentation of rolling technical parameters. Since MARC is not specifically designed for rolling process, most rolling technical parameters can be neither directly calculated nor graphically presented. Customized programming has to be done to allow the the program to display metal forming technical parameters, such as local spread, local recrystallized percentage and local grain size. As long as a parameter is defined, the code MARC can display it, either with graphics or the color contour.

Selected simulation operational issues

  • Determination of FEM algorithm. In the simulation, coupled thermal and mechanical model and the incremental, updated Lagrangian algorithm was used.
  • Optimization for grids, process parameters, etc. to achieve high accuracy and low computational cost
  • Describing material behaviors and boundary conditions as accurate as possible. In the simulation, stock was assumed as elastic-plastic, tools were taken as rigid. Both heat transfer behavior and friction coefficient were determined through FEM variation together with measurement.
  • Accurate determination of the temperature during the measurement of flow stress. For this purpose, an FEM simulation of the torsion test was done to determine temperature profile in the torsion samples.
  • Use of temperature profile in the entry stock, instead of an average temperature value. Before the stock enter each roll gap, FEM simulation for cooling process was perform to determine temperature profile in the stock at the moment it enter the roll gap.
  • Validation of established model through comparing simulated results with experiment data.

Example of analyzed processes

  • Forging
  • 2D flat rolling
  • 3D flat rolling, with isothermal model and then coupled thermo-mechanical model
  • 6 passes of angle steel rolling (must be 3D model), with isothermal model and then coupled thermo-mechanical model. Special attention was paid to determine local metal flow during rolling, cross-section after rolling, and load and power requirements, and to validate the calculated results by comparing them with corresponding measurement. The error of FEM prediction are normally < 10% in rolling forces, and constantly < 1% in geometry. Fig. 1 shows predicted temperature profile in the 1st pass, with the upper and lower rolls represented with rigid shell.
  • Rolling with a specially simplified FEM model, which takes only 0.5% of regular computational time and receives sufficiently accurate output. The model attracts great attention from engineers and researchers
  • 4 main rolling passes of H-beam rolling, with coupled thermo-mechanical model Cast-Rolling (combined casting and rolling) with liquid core, with coupled thermo-mechanical model. Fig. 2 is the geometry after fourth pass, with predicted equivalent plastic strain.
  • Steel rod rolling to roll steel from round cross-section to oval cross-section, and from oval cross-section to round. Special attention is paid to predict microstructure formation process.

Fig. 1: FEM simulated temperature distribution for the angle steel rolling, 1st pass (click on the picture to enlarge)


Fig. 2: FEM Simulation for angle steel rolling, 2nd pass (click on the picture to enlarge)


Fig. 3: FEM simulated H-beam after 4th pass, with equiv. Plastic strain (click on the picture to enlarge)


Figure 4: Wire rod rolling pass over-round, distribution of 3rd comp. of stress (click on the picture to enlarge)


Topic Summary on FEM Investigation and Experimental Verification



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Bingji (Benjamin) Li 2009. All rights reserved.