Generation, Modification, and Analysis of Synthetic FRP
Microstructures Based on Experimentally Observed
Microstructures
E. John Barsotti
Seyed Hamid Reza Sanei
Dr. Ray S. Fertig
Undergraduate Research Day
April 30, 2016 • University of Wyoming
Overview
In this speech, I will …
1. Define what FRP microstructures are
2. Explain the motivation for the research
3. Explain the research methodology
4. Draw conclusions from the implementation of the methodology
5. Explain where the research is headed
2
What are FRP microstructures?
Generally speaking,
• On the microscale, all materials consist of microstructures.
• Microstructures are the underlying lattices of materials.
• Microstructure composition changes depending on what material you are looking at
(e.g., crystalline or noncrystalline materials) and what processes they have undergone.
FRPs
• The microstructures discussed here are fiber reinforced polymers (FRPs).
• FRPs have composite microstructures.
• They consist of carbon fiber–reinforced epoxy matrices.
• FRP geometries are largely random.
3
Optical Micrograph of
Carbon Epoxy
4
Research motivation
• The high specific stiffness and strength of FRP
composites have led to their widespread use in the
automobile and aerospace industries.
but
• Predicting composite reliability has been a challenge
given the large variability in their mechanical properties.
• No specific link between this variability and the physics
of the underlying microstructures has yet been
established.
5
Importance of microstructural variability
• Ideal computer-generated models (such as square and
hexpack) can predict the macroscopic elastic response,
but
• Damage evolution is highly influenced by microstructural
variability.
• The onset of damage is a local phenomenon depending
on the local stress state resulting from local
microstructural features and material properties.
• Ideal microstructures do not predict scatter because they
do not permit variability.
• A comprehensive model of microstructures would be able
to (1) accurately predict failure and (2) capture the
variation in the strengths of composites.
6
Scatter in Strength:
Objective Experimental Results
25
Tension
Microstructural compression
Variability 20
15
Synthetic Microstructure
10
5
0
0.8 0.9 1 1.1 1.2 1.3
Strength (psi)
Simulations
Ideal Microstructure models
7
Probability
Image acquisition
Scanning Electron Microscopy
• The wavelength of electrons is between 2
to 15 pm.
• Wave-Particle Duality nature of electrons
make it superior to other high energy
waves.
Optical Microscopy Image
• User friendly
• Cost efficient
• Fast image acquisition
• Defects stand out
8
Irregular fiber packing Hexagonal Packing
Square Packing
9
Presence of alignment fiber and void
Alignment fiber:
Alignment fibers
• Thermoplastic fibers
• Orienting the plies in stacking a laminate
Void and alignment fiber Effect:
• Lower stiffness and strength Voids
• Lower fatigue resistance
• Lower moisture resistance
Characterization:
• Volume fraction
• Shape
• Location
10
Fiber Geometry
• Investigating the possible elliptical nature of fibers.
• 170 fibers were measure to obtain the radii distributions.
0.9 Actual distribution Actual distribution
Normal 1.2 Normal0.8
LogNormal LogNormal
Weibull Weibull0.7
1
0.6
0.8
0.5
0.4 0.6
0.3
0.4
0.2
0.1 0.2
0
5 5.5 6 6.5 7 0
Small Fiber Diameter 6 6.5 7 7.5 8
Large Fiber Diameter
11
Probability Density
Probability Density
Fiber volume fraction
• Even though it is obvious to human eye, it is not
necessarily easy to calculate.
• Segmentation method is used for determining the
fiber volume fraction.
4
x 10
3.5
Segmentation Method
3 Matrix Fiber
• Threshold value
2.5
• Edge detection
• Region growth 2
• Morphological 1.5
1
0.5
0
0 50 100 150 200 250 300
Gray Level
12
Number of pixcels
Synthetic Generation of Microstructure
• In most simulations, ideal circular fibers with a single radius are modeled.
• There have been some efforts in linking the finding of image processing to synthetic
generation of microstructure.
Gusev et al. , Composites Science Pan et. al Composites Science
Vajariet al., Composites Science
and Technology, 2000. and Technology, 2008
and Technology, 2014
• A comprehensive model inclusive of all defects is required for accurate prediction of
variability in mechanical properties.
13
Synthetic Generation of Microstructure
• Characterizing of actual microstructures is a
crucial but insufficient step.
• There are limited realizations of experimental
microstructures.
• An infinite number microstructures must be
synthetically reconstructed.
To investigate the effect of defects on the
macroscopic properties
Capturing scatter observed experimentally
Fiber Generation:
1. Center Coordinate of fiber (X,Y)
2. Small radius of fiber
3. Large radius of fiber
4. Angle
14
0.9 Actual distribution
Normal
Fiber radius distribution 0.8 LogNormal
0.7 Weibull
0.6
0.5
0.4
0.3
0.2
0.1
0
5 5.5 6 6.5 7
Small Fiber Diameter
Actual distribution Actual distribution
6 Beta Distribution 1.2 Normal
LogNormal
Weibull
5 1
4 0.8
3 0.6
2 0.4
1 0.2
0 0
0.7 0.8 0.9 1 6 6.5 7 7.5 8
Large to small fiber radii ratio Large Fiber Diameter
15
Probability Density
Probability Density
Probability Density
Periodicity
• The material periodicity
facilitates the application of
displacement periodic
boundary conditions in
simulation.
16
Synthetic generation of microstructure with defects
Microstructural defects:
• Resin seams
• Alignment fiber
• Void
• Fiber volume fraction variability
Random parameters
• Size
• Location
• Volume fraction
17
Comparison of actual with synthetic microstructures
Actual Microstructure Synthetic Microstructure I Synthetic Microstructure II
18
Hexagonal Packing
Comparison of Microstructures
• Statistical equivalence analyses are implemented.
Nearest fiber distance (nearest neighbor function)
Radial distribution(pair distribution) using K
Ripley’s function
Square Packing Experimental Synthetic
14.38
19
Nearest neighbor distribution
1
Experimental
0.9 Square
0.8 Hexagonal
Synthetic
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 5 10 15 20
Nearest fiber distance (micron)
20
Probability
Radial distribution function 𝑁1 1
𝐺 𝑟 = 𝑛 𝑟
2𝜋𝑟𝜌𝑑𝑟 𝑁 𝑖
𝑖=1
3
Radial distribution analysis for Hex
microstructure comparison Square
2.5
Experimental
Synthetic
r 2
dr
1.5
1
0.5
0
0 2 4 6 8 10
Sampling radius divided by fiber Radius
21
G(R)
Microstructure modification
• Use MATLAB to create a program that moves fibers in microstructures at random.
1. Start by telling program to converge nearest neighbor first.
2. Move fibers at random, maintaining periodicity and fiber overlap
rules.
3. Check nearest neighbor convergence.
4. If converged, move on to radial distribution.
22
Nearest neighbor results
1.4 1.4
Experimental Experimental
1.2 1.2
Synthetic Original Synthetic
Rearranged Synthetic
1 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
6 8 10 12 14 6 8 10 12 14
Nearest Fiber Distance (m) Nearest Fiber Distance (m)
Before modification After modification
23
Probability
Probability
Radial distribution results
1.2 Experimental 1.2 Experimental
Synthetic Rearranged Synthetic
1 1 Original Synthetic
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
2 4 6 8 10 2 4 6 8 10
R/r R/r
Before modification After modification
24
G(r)
G(r)
Conclusions — microstructure generation
• We can model microstructures with a
variety of geometries and fiber
morphologies.
• Although many geometric parameters are
chosen pseudo-randomly, they are all
based on experimental observations.
• Limitations exist (e.g., fiber volume Average Fiber Radius Distribution
fraction is limited to < 0.6). 2.5
Actual
2 extreme value
weibull
generalized
1.5 extreme value
logistic
1
0.5
0
2.8 3 3.2 3.4 3.6 3.8
Average fiber radius (m)
25
Probability Density
Conclusions — microstructure modification
Rearranged
Original
• Modification is time-consuming yet
necessary.
• The random movement method is one of
many.
• It takes a surprisingly few number of
moves to obtain radial distribution 1
convergence. Fiber Movements
0.8
• It takes movement of nearly all fibers for
0.6
nearest neighbor convergence.
0.4
• It works for microstructures with defects
as well as microstructures with no defects. 0.2
0
0 50 100 150 200 250
Square Image Dimensions ( m )
26
Fraction of fibers moved
Now what?
• Generation and modification of the synthetic microstructures is only the initial step.
• By transferring the microstructures to ABAQUS, the elastic properties and fracture
mechanics of the microstructures can be studied.
• The data recorded will be used to extrapolate the strengths of FRPs to the
macroscale.
27
Exx Modulus for Synthetic Microstructures Eyy Modulus for Synthetic Microstructures
110 9
8.5 Elastic Modulusi
100 Elastic Modulus
Linear Trendline
Linear Trendline
8
90
7.5
80 7
6.5
70
6
60
5.5
50
0.25 0.3 0.35 0.4 0.45 0.5 0.55 5 0.25 0.3 0.35 0.4 0.45 0.5 0.55
Fiber Volume Fraction
Ezz Modulus for Synthetic Microstructures Fiber Volume Fraction
9
8.5 Elastic Modulus
Linear Trendline
8
7.5
7
6.5
6
5.5
5
0.25 0.3 0.35 0.4 0.45 0.5 0.55
Fiber Volume Fraction
28
Modulus (GPa)
Modulus (GPa)
Modulus (GPa)
XFEM crack propagation
29
Summary
• Ideal models cannot predict the scatter in strengths observed experimentally.
• Synthetic microstructures can be generated that account for microstructural
variability.
• The correlation between microstructural features observed experimentally and the
mechanical properties of composites needs to be considered when measuring
material strength.
• Progressive failure analysis of synthetic microstructures using ABAQUS XFEM
must be done and compared with experimental results.
30
Questions?