computational modeling of polymer flow in microcavities
DESCRIPTION
Presentation at ASMETRANSCRIPT
Jie Chen and Ranga PitchumaniAdvanced Materials and Technologies Laboratory
Department of Mechanical Engineering
Virginia Tech
Blacksburg, Virginia 24061-0238
[email protected] • http://www.me.vt.edu/amtl • (540) 231-1776
Computational Modeling of Polymer Flow in
Microcavities through a Microscreen
Paper No. IMECE2010-38675 presented at the ASME IMECE 2010 • November 18, 2010 •
Vancouver, BC, Canada
The work is being supported by a grant from the National Science Foundation through
Grant No. CBET-0934008
Advanced Materials and Technologies Laboratory
LIGA Processing Steps
DevelopmentMicromolds
Lithography:
Synchrotron
generated X-rays
X-ray Mask
(Patterned gold on
silicon)
Resist material
Metallized
Substrate
Lithography:
Exposure
Plastic replicate
via injection
molding or hot
embossing
Molding:Electrodeposition:
Microstamp
Mold Filling Planarization/Mold Dissolution
Electrodeposited
Metal
LIGA (an acronym for the German words for Lithography, Electroforming and
Molding) is a microfabrication process that can produce high aspect ratio
microstructures (HARMs) with excellent feature fidelity and sidewall tolerance.
Advanced Materials and Technologies Laboratory
Demolded
Replicate
Replication of Electroforming Molds with
Integral Metallic Screen
Metallic
Screen
LIGA Stamp
CONCEPT
In practice, a porous region and a flow channel are added on top of the
screen for flow distribution and screen support
Advanced Materials and Technologies Laboratory
Problem with Replicating Small Features
During filling of small microcavities adjacent to larger microcavities on a
microtool stamp, fluid preferentially fills larger cavity first; Resulting pressure
imbalance across a feature wall causes feature collapse on the microstamp tool.
Effective process development calls for designing the microfeature layout on the
stamp and the molding process and material parameters so as to elminate such
feature failures.
A fundamental understanding of the microstructural evolution during
electrodeposition onto the metallic microscreens is essential to design and
optimize the overall micropart fabrication process.
Advanced Materials and Technologies Laboratory
Mathematical Model
0u
τuuu
pt
)(
)()( uτ)u( TkpρEt
E
Dτ2
|| 2u
hE
0)( ut
τuuu
pt
)(
)()()(
uτ)u( TkpEρt
E
Dτ2
|| 2up
hE
0Ft
Fu
PMMA
air
Volume of fluid
Solidification/melting
uu mushATkHt
H
)(
)1()()(
)(3
2
Advanced Materials and Technologies Laboratory
Example Case of Mold Filling
PMMA volume fraction Pressure
m80LW K361WT K576inTcc/s30Q
Advanced Materials and Technologies Laboratory
Stress Calculation
H
w
x
pL(y, z)
pR(y, z)
Wall width (normal
to the page): L
L H
RLb
b
dzzppdyM
wLI
I
wMσ
0 0
3
max
12
1
2
2max
6
wL
Mσ b
RIGHT the toDeflection0
LEFT the toDeflection0
max
max
σ
σ
yz
Advanced Materials and Technologies Laboratory
Maximum Stresses on the Walls
Peak Stress, p
Advanced Materials and Technologies Laboratory
Incomplete Fill
m80LW K338WT K536inTcc/s30Q
The stress values are higher than that in the case of higher mold temperature
and inlet temperature.
Due to incomplete fill, the stress is larger than zero at the end of fill.
Advanced Materials and Technologies Laboratory
Three 3-level factors are considered
The experiments are set up based
on the Taguchi L9 orthogonal array
Outputs of interest
Fill ratio, – defined as the volume
ratio of the filled micro cavities
Peak stress, p
Design of Experiments
Levels Q [cc/s] Tw [K] Tin [K]
1 15 338 496
2 30 361 536
3 45 373 576
Fil
l fr
acti
on
Fil
l ti
me
Str
ess
WT inTQ
Advanced Materials and Technologies Laboratory
Correlation and Processing Windows
A Q*aTW* bTin
* c
p A Q*dTW* eTin
* f
m80LW
m200LW
cc/s45Q
cc/s45Q
Advanced Materials and Technologies Laboratory
Design Plots
1
p 2 GPa
1
p 2 GPa
1Tw = 334 K
Tin = 694.5 K
GPa421.1
Advanced Materials and Technologies Laboratory
A computational model is developed for the polymer flow during the
fabrication of electroforming micromolds incorporating the temperature
dependent, non-Newtonian rheology of the polymer melt.
The mold temperature, the inlet temperature, and the inlet flow rate are
investigated as the control parameters. The mold temperature plays the
most important role in the filling process.
In some cases, full blockage is produced in the small cavities because
PMMA solidifies. Therefore, the filling process is incomplete.
In most of the cases, the peak stress appears on the wall next to the
large cavity earlier than on all the other walls.
Design plots for geometric design as well as process design were
developed from the studies.
Summary