Numerical implementation of a state variable model for friction Page: 4 of 9
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Numerical implementation of a state variable model for friction
D.A. Korzekwa
Los Alamos National Laboratory, Los Alamos, NM 87545
D.E. Boyce
Cornell University, Ithaca NY
To be presented at Numiform 95, Ithaca, NY, June 1995.
ABSTRACT: A general state variable model for friction has been incorporated into a finite element code
for viscoplasticity. A contact area evolution model is used in a finite element model of a sheet forming
friction test. The results show that a state variable model can be used to capture complex friction behavior
in metal forming simulations. It is proposed that simulations can play an important role in the analysis of
friction experiments and the development of friction models.1 INTRODUCTION
Control of friction and lubrication is important for
the success of many material processing and fabri-
cation operations. Although the tribology of metal
working has been studied extensively[1-4], there is no
concise theory that can be easily implemented into
numerical simulations of metal forming processes. The
primary reason for this is that a wide range of phe-
nomena may be responsible for friction and wear at
the tool-workpiece interface. Consequently, for a given
metal forming operation, a friction model should be
tailored to reflect the appropriate physical mecha-
nisms.
It is desirable to express models for friction and lu-
brication in terms of physically identifiable quantities
that describe the state of the interface[5]. Candidates
for these state variables are numerous, including mea-
sures of surface roughness, lubricant film thickness,
fractional coverage of boundary lubricant, and the
material strength at the surface. In some cases it
is useful to pose a model in terms of the fraction of
the interface area that is in boundary contact, which
combines the effects of other state parameters. It is
very important to recognize that these state variables
can have different values at different points along the
interface and that they evolve with time.
In this article a numerical framework for state
variable friction models is presented with examples
appropriate for metal forming. A general scheme for
such models has been implemented in the viscoplas-
tic finite element code HICKORY[6]. A simple model
that uses the fractional area in boundary contact as
a state variable is compared to Coulomb friction." Bulk element and surface element
nodes
o Bulk element nodes
x Surface quadrature points0
Figure 1: Surface and bulk elements with surface
quadrature points.
2 NUMERICAL IMPLEMENTATION
The implementation of a state variable friction model
in a numerical code requires a data structure appro-
priate for the state variables at the interface. A rou-
tine to compute the friction tractions is executed us-
ing the current values of the state variables and other
external variables from the solution. Routines to up-
date the interface state variables are called at ap-
propriate intervals. The state variables are defined
at surface elements as a single value per element.
For two-dimensional applications the bulk elements
are either nine node quadrilaterals or six node tri-
angles, and the surface elements are defined on the
three nodes of an element boundary that lie on the
surface of the mesh, as illustrated in Figure 1.
A relatively simple state variable model has beenk~. ~
~~I~~1W~~~r~~r1C -~ I~~~ A)W '
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Korzekwa, D. A. & Boyce, D. E. Numerical implementation of a state variable model for friction, article, March 1995; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc683684/m1/4/: accessed April 20, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.