Advancements in Composite Materials for Wind Blades
davidldummer_ThesisExam_20070430secure
1. Composite Materials, Manufacture
and Structures Laboratory
3D PERCOLATION MODEL FOR
THE PREDICTION OF
CRITICAL VOLUME FRACTION
IN PARTICULATE COMPOSITES
Dave Dummer P.E.
Masters of Science Final Examination
Colorado State University
Department of Mechanical Engineering
Spring 2007
3. Composite Materials, Manufacture
and Structures Laboratory
INTRODUCTION
What is the motivation for this effort?
A need to increase the applicability of 3D
modeling of Particulate Composite Material
Study and predict the effects of filler and matrix
material variations on the conductivity behavior
Simulation tool to aid in “tailoring” a material
4. Composite Materials, Manufacture
and Structures Laboratory
…..Percolation Theory
Modeling Approach
Applied to Forest Fire
Propagation, Oil Field
Exploration, Adv.
Physics, Diffusion in
Porous Media
Lattice Site or bond
Site occupied or not
Bond active or not
Restrictive geometry of
discrete fixed locations
Discrete connections
Look for cluster to span
across lattice
Predicts percolation
higher than actually
seen
Not So Realistic?!
5. Composite Materials, Manufacture
and Structures Laboratory
…..Conductive Composites
Conductive composites are formed from conductive filler
particles mixed into a dielectric matrix material
Dielectric Matrix
Thermoplastics
Thermosets
Epoxy
Filler particles
Shape – variation such at spheres, fibers, rods, disks,
nodules, etc..
Size - variations in distribution type - they have a mean
particle size and distribution spread of the particles
Conductive Behavior
Within the matrix, a network of conductive filler particles
begins to form.
Bulk conductive behavior seen at and above some critical
volume fraction of filler
Conductivity generates shielding against incident
electromagnetic energy
6. Composite Materials, Manufacture
and Structures Laboratory
…..Experiments
Signal Generator
Specimen Holder
Receiver
Attenuator Attenuator
10 dB
50Ω
10 dB
50Ω
Test Sample Reference Sample
Coaxial
Cable
Coaxial
Cable
Sweep Oscillator Digital Voltmeter
0-50
dB
Attenuator
8-12 GHz
Frequency
@ 0-15 dBm
Power
X-Band
Waveguide
Vernier Scale to Measure
Displacement of the Minimum/Maximum
Value of the Standing Wave
Voltage Probe (mV)
Sample
Test
Short Circuit Varying Loss-Less
Sample Lengths
Lossy Samples -Length Unimportant
(Sample Thicker Than Skin Depth)
0.2" Thick
Aluminum
TEST SAMPLE SETUP IS DEPENDENT ON MATERIAL CONDUCTIVITY
Past Work by Cheng, Olivero, &
Radford
Tests
ASTM D 4935 Transmission
VSWR Reflection
7-350 µm silver coated particle
Results
Frequency Dependant
>100 dB Shielding Max
Transition to conductive
behavior at 30 - 40% for size
Reducing dm reduced Vf
for percolation
Equivalent SE at lower Vf
Taken from D.
Radford, “Volume
Fraction Effects in
Ultra-Lightweight
Composite materials
for EMI Shielding,”
Journal of Advanced
Materials, Vol.26
No.1, 1994, p.45,
RefID 0054.
Taken from Olivero, David, “Percolation in particulate
composites for EMI shielding,” Masters of Science
Thesis, Colorado State University, Fall 1997, RefID 0850.
7. Composite Materials, Manufacture
and Structures Laboratory
…..Size Dependence
0
5
10
15
20
25
30
0% 10% 20% 30% 40% 50% 60% 70%
Vcf of Conductive Microsphere/Epon 828 Composites
SE(dB/mm)at10.0GHz
SG in 828
SF-20 in 828
7 mm (Ag/Ni in 828)7 µm (Ag/Ni)
50 µm (SF-20)
~350 µm (SG)
• Smaller size particles:
Lower Vfc generates for
same SE
• Similar particle
clustering in all sizes
Taken from Olivero, David, “Percolation in particulate composites for EMI shielding,”
Masters of Science Thesis, Colorado State University, Fall 1997, RefID 0850.
8. Composite Materials, Manufacture
and Structures Laboratory
..…Material Dependence
Same particulate
filler material
Differing matrix
materials
Highly variable
shielding
0
20
40
60
80
100
120
140
160
0% 10% 20% 30% 40% 50% 60% 70%
Conductive Microballoon Volume Fraction
SE(dB/mm)at10.0GHz
Coated/Uncoated SF20
SF20 / LaRC-IA(300 psi)
SF20 / epoxy (800 cP)
SF20 / epoxy (13,000 cP)
Taken from Olivero, David, “Percolation in particulate composites for EMI shielding,”
Masters of Science Thesis, Colorado State University, Fall 1997, RefID 0850.
9. Composite Materials, Manufacture
and Structures Laboratory
..…Models
Olivero, Wang & Ogala
Percolation model
Semi-discrete lattice
2-D sphere simulation
Wang & Ogala’s “Soft-
shell” surrounding an
impenetrable particle
Allows soft shell regions
to overlap
Soft Shell Thickness
Increasing Thickness-To-Diameter Ratio
Hard
Particle
No overlap of hard cores
Scaled soft-shell
Goal: explore Vf & soft-shell
thickness varation
Taken from Olivero, David, “Percolation in particulate composites for EMI shielding,”
Masters of Science Thesis, Colorado State University, Fall 1997, RefID 0850.
10. Composite Materials, Manufacture
and Structures Laboratory
..…Observations
Conductive behavior initiates long before
particle-to-particle surface contact should
be generated.
Matrix materials may affect the conductive
behavior
Particle characteristics appears to affect
the conductive behavior
11. Composite Materials, Manufacture
and Structures Laboratory
..…What else?
Can we improve the ability
to predict the
characteristics of these
materials?
Make-Up Performance
12. Composite Materials, Manufacture
and Structures Laboratory
to examine the measured conductive or percolation
behavior in a fabricated composite
to develop a 3D Continuum Percolation Simulation
Tool
to examine the simulated trends & predicted results
for percolation behavior with respect to variations in:
particle distribution characteristics
soft-shell type and thickness
to examine the model’s percolation behavior when
compared to experimental percolation results from
real particulate composites
OBJECTIVES
13. Composite Materials, Manufacture
and Structures Laboratory
EXPERIMENTS
Conduct a series of experiments on
particulate composites to examine
the variation of conductive behavior
based on….
Influence of the mean particle size
Influence of the particle size distribution
14. Composite Materials, Manufacture
and Structures Laboratory
..…Particulate Filler Requirements
Spherical Shape
Conductive - Silver Coated
3 Different Mean Diameter Values
3 Different Distribution Spreads at one of the Mean
Diameter Values
20. Composite Materials, Manufacture
and Structures Laboratory
…..NIST Test Data Manipulation
0.02
0.1388
0.2576
0.3764
0.4952
0.614
0.7328
0.8516
0.9704
1.0892
1.208
1.3268
1.4456
1.5644
1.6832
1.802
1.9208
0
16
25
28
31
34
37
40
49
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
SE (dB)
Frequency, GHz
Volum
e Fraction, %
S3000-S3E Shielding Effectiveness, SE(dB)
(Conductive Paint on Sample OD)
0.02
0.1388
0.2576
0.3764
0.4952
0.614
0.7328
0.8516
0.9704
1.0892
1.208
1.3268
1.4456
1.5644
1.6832
1.802
1.9208
0
16
25
28
31
34
37
40
49
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Conductivity
(S/m)
Frequency, GHz
Volum
e
Fraction, %
S3000-S3E Conductivity
(Conductive Paint on Sample OD)
"2 εεπσ of=
σµπ
δ
of
1
=
)(log
1
20
32
log10 1010 e
f
d
f
SE
o
o
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎝
⎛
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
′′
=
σµπ
επ
σ
⎟
⎠
⎞
⎜
⎝
⎛
+=
2
377
1log10 10
σd
SE
Skin Depth
δ>d
δ<d
Using NIST ε”, f, & value of µo
Unfortunately, the calculated
values appear factor of 10 low
for:
Conductivity
Shielding Effectiveness
Taken from N.F. Colaneri and L.W. Shacklette, “EMI Shielding Measurements of Conductive Polymer Blends”,
IEEE Transactions on Instrumentation and Measurement, Vol. 41, Num. 2, April 1992, p 291, RefID 0058.
Shielding Effectiveness
Conductivity
21. Composite Materials, Manufacture
and Structures Laboratory
3D MODEL
Develop a 3D continuum model of
particulate composites to examine
the variation of conductive behavior
based on….
Influence of the mean particle size
Influence of the particle size distribution
Influence of the particle soft-shell
thickness
22. Composite Materials, Manufacture
and Structures Laboratory
…..Attributes & Tasks
Particle placed in 3D continuum space
Particles from size distribution, not just mono-size capability
Enables particle diameter distribution(s)
Particle volumes closely tracked
“Soft-shell” idea used to represent connections between
particles
Particle surface interference prohibited, but “soft-shell”
interference allowed
Interconnections evaluated & particle clustering tracked
Cluster spanning system in any of X, Y or Z directions
defines percolation event
Primary output is the critical volume fraction threshold at
percolation
Critical volume fraction at percolation is all total of all
particles
Written in the MATLAB programming environment
23. Composite Materials, Manufacture
and Structures Laboratory
…..Particle Volume
)23(
6
1 2
hdhVhemisphere −= π
3
3
4
rVsphere π=
Total
volume is
important
Minimize
any error
Closed
solutions
if possible
24. Composite Materials, Manufacture
and Structures Laboratory
…..“Soft-Shell” Concept
“Soft-shell” idea
from Wang &
Ogale & 3D model
Mono-sized only
Conductive
particle surface
Represents
particle-to-particle
non-contact
conductivity
Suggest electron
hopping over gap
“Soft-shell” Model
25. Composite Materials, Manufacture
and Structures Laboratory
…..“Soft-Shell” Connectivity
Penetrable shell
around particle
Thickness in fixed
value & % of
particle diameter
Over-lap of surface
and shell to
connect
A & B don’t signify
a connection
C is non-existent
condition in fixed
thickness
“Soft-shell” Connectivity
26. Composite Materials, Manufacture
and Structures Laboratory
…..Particle Fillers & Matrix
Diameter distribution type defined as function
3 distributions with differing mean values (µ)
3 distribution standard deviation values (σ) about one of the
mean values
Soft-shell thickness value
Fixed values – 0.125, 0.25, 0.5, 1, 1.5, 2.5, 5. 7.5, & 10
% values – 5%, 6%, 7%, 8%, 9%, 12%, 18%, & 30%
27. Composite Materials, Manufacture
and Structures Laboratory
…..Output
Modeled system in array/matrix form
Particle locations & interconnect
information
Clustering information (three largest)
Percolation volume fraction information
Statistical information
32. Composite Materials, Manufacture
and Structures Laboratory
…..Percolation
Model tracks 3 largest clusters
Largest cluster percolation most of the time.
This cluster DID percolate!
33. Composite Materials, Manufacture
and Structures Laboratory
…..Percolation
Smaller clusters can percolate first!
Hand full of instances among 20k runs
3rd Largest never percolated
This cluster did NOT percolate!
34. Composite Materials, Manufacture
and Structures Laboratory
…..Model Validation
Extreme Value Function
representation of the radii on
a 3D cross-section by From
Input to function are
characteristics of Gaussian
particle distribution
Similar function for
lognormal particle
distribution from same author
P. From, “Stereological Characterization of Microstructure Morphology for Two
Phase Materials”, Ph.D. Dissertation, Institute of Mechanical Engineering Aalborg
University, August 1996, RefID 1045.
35. Composite Materials, Manufacture
and Structures Laboratory
…..Simulation of Conductivity
Possible circuit
representation of
connection between two
particles
Added capacitive
component to model to
represent frequency
dependence
Resistor network within
cluster of particles could
be used to approximate
the material’s bulk
conductivity
Estimate material
Properties
36. Composite Materials, Manufacture
and Structures Laboratory
…..Circuit Matrix
Graph Theory
Network analysis
Simulate the
electrical network
Generates node &
loop equations
38. Composite Materials, Manufacture
and Structures Laboratory
…..Fractal Dimension
Potential means
of study
Real composite
comparisons
Micrographs
Two types
(L)
Occupied Lattice Point
Length
Scale
L
M
Taken from Olivero, David, “Percolation in particulate composites for EMI shielding,”
Masters of Science Thesis, Colorado State University, Fall 1997, RefID 0850.
39. Composite Materials, Manufacture
and Structures Laboratory
RESULTS
Compare the 3D modeling and
experiments of these particulate
composites to examine how
variations in conductive behavior
are influenced by….
Influence of the mean particle size
Influence of the particle size distribution
Influence of the particle soft-shell
thickness
40. Composite Materials, Manufacture
and Structures Laboratory
…..NIST Experiments
Shielding Effectiveness (SE) for All 5 Particle Grades at 1 GHz
S-5000-S3, S-3000-S3NN, S-3000-S3N, S-3000-S3E, & S-2429-S
0
2
4
6
8
10
12
0 5 10 15 20 25 30 35 40 45 50
Volume Fraction (%)
SE(dB)
S-5000-S3
S-3000-S3NN
S-3000-S3N
S-3000-S3E
S-2429-S
S-5000-S3
S-3000-S3N
S-3000-S3E
S-3000-S3NN
S-2429-S
Transition regions
All 5 particle
grades at 1 GHz
Each transitions
to shielding
behavior
Transition range
Bands are
predicted
transitions for
each
Data could be
stronger
41. Composite Materials, Manufacture
and Structures Laboratory
…..% Value “Soft-Shell”
Modeled Output
“Soft-shell”
thickness in
% of diameter
Scales with each
particles diameter
Self-similar
behavior
Not representative
of a real composite
42. Composite Materials, Manufacture
and Structures Laboratory
…..Fixed Value “Soft-Shell”
Modeled Output
“Soft-shell” as a
fixed value
Same thickness on
every particle.
Smaller particles
percolate sooner.
Trends are linear
on log scale
Physically
correlates to
changes in matrix
characteristics.
43. Composite Materials, Manufacture
and Structures Laboratory
…..Fixed Value “Soft-Shell”
3D Peroclation Model Run Data - Fixed Thickness Softshell
Percolation Threshold
Data Converted and Graphed as Percentage Softshell Thickness
0
5
10
15
20
25
30
35
40
45
50
1.0% 10.0% 100.0%
Fixed Softshell Thickness as a % of the Particle Diameter
PercolationThreshold
Modeled Output
“Soft-shell” –
fixed value data
represented as a %
Normalized
representation
Overall trend is
linear on log scale
44. Composite Materials, Manufacture
and Structures Laboratory
Model Percolation Threshold versus Diameter Standard Deviation
with Fixed Softshell Thickness
0
5
10
15
20
25
30
35
40
45
50
0 2 4 6 8 10 12
Standard Deviation of Particle Diameters (µm)
AveragePercolationThreshold
1.5 2.5 5
7.5 10 1
…..Distribution Spread
Modeled Output
Three σ values
about µ ≃ 34
microns
Trend obscured
at center σ value
by variation of
distribution
diameter
45. Composite Materials, Manufacture
and Structures Laboratory
…..Distribution Spread
Modeled
Output
Multiple σ
values at µ ≃
33.82 microns
Clear trend that
narrow
distributions
percolation
sooner
Model Percolation Threshold versus
Diameter Distribution Standard Deviation
at Several Fixed Softshell Thicknesses (33.82 micrometer Diameter)
15
20
25
30
35
40
45
50
0 5 10 15 20 25
Particle Diameter Distribution Standard Deviation (micrometers)
PercolationVolumeFractionThreshold
2
3
4
5
7.5
46. Composite Materials, Manufacture
and Structures Laboratory
…..Model vs. Experiments
All 5
modeled
grades
All 5 particle
grades
Compared
Experiment
data in
banded area
“Soft-Shell”
predicted 1
to 2.5 µm
47. Composite Materials, Manufacture
and Structures Laboratory
CONCLUSIONS
3D continuum model representative
Soft-shell envelope provides a mechanism for
the simulation of non-contact conductivity
Model & experiments show evidence that:
decreasing particle size decreases percolation Vfc
decreasing distribution spread decreases Vfc
Soft-shell of 1 to 2.5 µm is predicted by
comparison of model and experimental data
Percolation seen in experimental data around
30% for size, which is consistent with other
works
