Developing Structure Property Linkages for fiber reinforced polymer composites
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ME 8883/CSE 8803: Materials Informatics
8th December 2014
Developing Structure-Property Linkage for Glass Fibre Reinforced Polymer Composites
Presented by
Alicia White, 2nd Year MSE PhD Student
In Collaboration with
Geet Lahoti, 2nd Year ISyE PhD Student
Guided by
Prof. Surya Kalidindi
Dr. Tony Fast
Background
• Forming processes create varied
and complex microstructures
• Microstructure varies even within a
simple part such as this plate
• Understanding the complexity of
these microstructures is an open
field which can give insight to the
properties of these materials
Figure 4: Variety in microstructure across an injected part
12/10/2014 2
Motivation
• The structure and organization of the
reinforcement greatly affect the final
properties of the part
• Conventional approaches to property
determination do not take into account
the microstructure of the reinforcement
• Voigt model [4]
• Ruess Model [5]
• Those that do are based on a assumed
configurations of the fibres, not the
actual microstructure [6]Figure 5: Complex microstructure of FRPC.
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Project Outline
• Objective: Develop Structure-Property Linkage for GFRPs
Manufacture
GFRP Samples
Is the no.
of
samples
enough?
Segmentation
Spatial
Correlation
Dimensionality
Reduction
Microstructure
Simulation
Perform
Micro-computed
tomography
(micro-CT)
Physical Property
from Finite
Element Analysis
Physical Property
from
Experimental
Testing
Relationship
Modelling
Yes
No
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Project Execution
Step 1: Samples and Micro-CT Data
• Fibre: Glass
• Polymer: Polypropylene
• Processing: hot melt impregnation and extrusion/compression molding
• Micro-CT Images: DICOM Format
• No. of Samples: 2
• Dimensions under consideration: 300 X 300 X 300 voxels
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Project Execution
Step 2: Segmentation
• Need to separate the fiber from the matrix to get an
accurate representation of microstructure
• Apply peak fitting algorithm to histogram of pixel values
• Segmentation based on Gaussian Likelihood Maximization
• Gaussian Function
f(x) = 1
𝑎𝑒
−(𝑥−𝑏)2
2𝑐2
where, a=height, b=center, c=width
• Multi Otsu’s Method
Original Microstructure
Segmented Microstructure
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Project Execution
Step 3: Microstructure Simulation
Fibers Elongated along Y Axis Fibers Elongated along Diagonal Fibers Elongated along X Axis
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Dimensions: 21 X 21 X 21
Project Execution
Step 4: Physical Property Simulation• Finite Element was performed under uniaxial strain conditions
• Property under consideration is going to be C11.
• Stress and strain were calculated and used to find the components of the
stiffness tensor corresponding to Ɛ1
StrainStress
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Project Execution
Step 5: 2-Point Statistics• 2-Point Statistics: Probability density associated with finding local states h and
h’ at the tail and head, respectively, of a prescribed vector r randomly placed
into the microstructure[7]
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Project Execution
Step 6: Dimensionality Reduction• 2-Point Statistics: Extremely large set
• Low dimensional representation
• Principal Components Analysis [7]
• Linear transformation of high-dimensional data to a new orthogonal frame
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Project Execution
Step 6: Dimensionality Reduction• Please add description about 2-Point Stats
PCs for Sample 1: 0.0104 0.0000 0.0000 -0.0003 -0.0001
PCs for Sample 2: 0.0104 0.0000 0.0001 0.0002 0.0002
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Project Execution
Step 7: Structure-Property Linkage• Regression
Property = 𝟑𝟑. 𝟔 +0.88 PC1 + 15.76 PC2 + 3.83 PC3 - 5.83 PC4 + 17.22 PC5
Property Predicted by model
for sample 1 : 33.6129
and
for sample 2: 33.6098
Rsquare: 0.9638
CV Mean Absolute Error: 0.14237
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Conclusion & Future Work
• Investigated digital representations of sample microstructures
• Developed a S-P linkage based on simulated dataset
• Validating linkages with the segmented real microstructures
• Carry out physical experimental testing of samples
• Simulate a rich set of microstructures
• Other Studies using the same protocol: Consider other composites like
Carbon Fibre Reinforced Polymers
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References1. http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1517-70762010000200006
2. http://www.reinforcedplastics.com/view/4437/india-on-the-up/
3. http://essaywritingserviceuk.co.uk/advice-and-guidance/free-essays/the-potential-of-frp-
materials-in-a-passenger-aircraft-structure/
4. W. Voigt, ”On the relation between the elasticity constants of isotropic bodies," Ann
Phys Chem 274 (1889): 573-587.
5. A. Reuss and Z. Angrew, ”A calculation of bulk modulus of polycrystaliine materials."
ZAMM- Journal of Apllied Mathmatics and Mechanics, Vol. 9, No. 1, 1929, pp.49-58
6. http://onlinelibrary.wiley.com/doi/10.1002/pc.20002/pdf
7. Surya R. Kalidindi, “Data Science and Cyberinfrastructure: Critical Enablers for
Accelerated Development of Hierarchical Materials
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Acknowledgements
Geet Lahoti
Ahmed At Hassen – UAB
Dr. Kalidindi and Dr. Fast
Materials Informatics Class
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