
FEM SIMULATION
Where  When 
Hardware  Software
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 multipurpose 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
crosssection shape is almost semiround.
 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 thermomechanical 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 generalpurpose
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 elasticplastic, 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
thermomechanical model
 6 passes of angle steel rolling (must be 3D
model), with isothermal model
and then coupled thermomechanical model. Special attention was paid to
determine local metal flow during rolling, crosssection 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 1^{st}
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 Hbeam rolling, with coupled
thermomechanical model CastRolling (combined casting and rolling) with
liquid core, with coupled thermomechanical model. Fig. 2 is the geometry
after fourth pass, with predicted equivalent plastic strain.
 Steel rod rolling to roll steel
from round crosssection to oval crosssection, and from oval
crosssection 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 Hbeam after 4th pass, with
equiv. Plastic strain (click on the picture to enlarge)
Figure 4: Wire rod rolling pass overround, distribution of 3rd comp.
of stress (click on the picture to enlarge)
Topic Summary
on FEM Investigation and Experimental Verification
