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The Pennsylvania State University
The Graduate School
DATA-DRIVEN LEARNING AND MODELING OF
CARBON FIBER REINFORCED POLYMER COMPOSITES
A Dissertation in
Industrial Engineering
by
Shenli Pei
© 2020 Shenli Pei
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
August 2020
ii
The dissertation of Shenli Pei was reviewed and approved by the following:
Hui Yang
Associate Professor of
Industrial and Manufacturing Engineering
Dissertation Co-Adviser, Co-Chair of Committee
Jingjing Li
William and Wendy Korb Early Career Professor (Associate Professor) of
Industrial and Manufacturing Engineering
Dissertation Co-Adviser, Co-Chair of Committee
Soundar Kumara
Allen E. Pearce and Allen M. Pearce Professor of
Industrial and Manufacturing Engineering
Timothy Simpson
Paul Morrow Professor in Engineering Design and Manufacturing
Danielle Zeng
Special Member
Technical Expert, Ford Motor Company
Steven Landry
Department Head of
Industrial and Manufacturing Engineering
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ABSTRACT
Carbon-fiber-reinforced polymer (CFRP) composites are being widely used as lightweight and
high strength material in aerospace and automotive industries, owing to their high specific modulus, high
specific strength, and good corrosion and fatigue resistance. The material performance of CFRP
composites highly depends on the material manufacturing process and the inherent internal
microstructure. Therefore, this dissertation attempts to unveil the underlying process-structure and
structure-property relations by integrating data science and informatics with microstructure
characterization. Specifically, this dissertation focuses on developing analytical approaches for CFRP
composites from X-ray computed tomography (XCT) images, a nondestructive testing, and three key
research topics were identified. These topics include a) developing a 3D microstructure characterization
approach for non-uniformly oriented CFRP composites, b) establishing physics-based features to quantify
the spatiotemporal progression of tensile fractures in CFRP composites, and c) comprehending the
process-structure-property (P-S-P) relations of fused filament fabricated CFRP composite through
developing image-based analytical methods that quantitatively examines the microstructure variations and
its effect on the tensile property.
For the first research topic, a 3D microstructure analysis framework was developed to
quantitatively analyze fiber morphology (e.g. fiber curvature, orientation, and length distribution) for non-
uniformly orientated fiber systems using micro-XCT (µXCT) images. For this purpose, numerical image
processing techniques and iterative local fiber-tracking approaches were developed to extract individual
fibers from congested fiber systems, and statistical distribution of the fiber morphology was formulated
using tensor representation. The derived statistics were integrated with the physics-based Halpin-Tsai
model and laminate analogy to estimate the material modulus. The fidelity of the characterization was
validated through experimental results for injection molded short and long CFRP composites, which
provided a valid alternative for finite element analysis.
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For the second research topic, the spatiotemporal characterization of the fracture behavior of
CFRP composites was established through the implementation of in-situ µXCT. The fracture features
were automatically extracted from the 3D µXCT image using the image processing techniques, and
physics-based features were developed to quantitatively measure the progression of failure behavior. The
proposed characterization approach was implemented on sheet molding compound and injection molded
CFRP composites, where the spatiotemporal characterization of fracture behavior was quantified and
visualized. It provided insights into the microscale failure mechanism, and the validity of the proposed
characterization approach was confirmed by the strain field calculation using a volumetric digital image
correlation.
For the third research topic, a P-S-P approach was proposed to unveil the underlying relation
between the process parameter of fused filament fabrication (FFF) and uncertainties in the microstructure
of the printed CFRP composite. An image-based statistical analysis was developed to formulate a
stochastic model for the microstructure distribution (i.e., fiber and void volume fraction), and analysis of
variance was implemented to establish the correlation between the process parameters and resulting
microstructure. The structure-property relation was investigated by employing the physics-based Halpin-
Tsai model to predict the material modulus. A data-driven optimization scheme was developed for the
Halpin-Tsai model to account for the complex effect from the FFF process and craze nucleation from
voids; therefore, the optimized model provided an accurate estimation of longitudinal modulus of FFF
parts. Further, a Monte-Carlo sampling method was adopted to investigate the propagated uncertainties in
the structure-property relation.
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TABLE OF CONTENTS
LIST OF FIGURES ................................................................................................................. vii
LIST OF TABLES ................................................................................................................... x
ACKNOWLEDGMENT .......................................................................................................... xi
Chapter 1: Introduction ............................................................................................................ 1
1.1 Motivation ................................................................................................................... 1 1.2 Research Background ................................................................................................. 2
1.2.1 Micro X-ray Computed Tomography .............................................................. 4 1.2.2 Image Processing ............................................................................................. 5 1.2.3 Statistical Characterization of the Microstructure of CFRP Composites ........ 7
1.3 Research Objectives ................................................................................................... 8 1.4 Organization of the Dissertation ................................................................................ 9 1.5 References .................................................................................................................. 10
Chapter 2: Mechanical Properties Prediction of Injection Molded Short/Long Carbon Fiber
Reinforced Polymer Composites Using Micro X-Ray Computed Tomography ............. 16
Abstract ............................................................................................................................ 16 2.1 Introduction ................................................................................................................ 16 2.2 Experimental Procedure and Methodology of CFRP Reconstruction ........................ 20
2.2.1 Materials and Experimental Procedure of µXCT ............................................ 20 2.2.2 Fiber Reconstruction using Iterative Template Matching ............................... 20 2.2.3 Description of Microstructure ......................................................................... 28
2.3 Results and Discussion ............................................................................................... 32 2.3.1 Short CFRP (SCFRP) Composite with Curved Fibers .................................... 32 2.3.2 Long CFRP (LCFRP) Composite with Curved Fibers .................................... 36
2.4 Conclusions ................................................................................................................ 41 2.5 References .................................................................................................................. 42
Chapter 3: Spatiotemporal Characterization of 3D Fracture Behavior of Carbon-fiber-reinforced
Polymer Composites ........................................................................................................ 47
Abstract ............................................................................................................................ 47 3.1 Introduction ................................................................................................................ 47 3.2 Materials and Experimental Procedures ..................................................................... 49
3.2.1 Materials .......................................................................................................... 49 3.2.2 Experimental Procedures ................................................................................. 50
3.3 Development of Image Processing Algorithm ........................................................... 50 3.3.1 Image Reconstruction Procedure ..................................................................... 51 3.3.2 Image Segmentation ........................................................................................ 51 3.3.3 Fracture Feature Visualization and Analysis ................................................... 54 3.3.4 Volumetric Digital Image Correlation (V-DIC) .............................................. 55
3.4 Case Study .................................................................................................................. 56 3.4.1 SMC CFRP Composite ................................................................................... 56 3.4.2 BASF CFRP Composite .................................................................................. 61
vi
3.5 Conclusions ................................................................................................................ 64 3.6 References .................................................................................................................. 64
Chapter 4: Process-structure-property Analysis of Short Carbon Fiber Reinforced Polymer
Composite via Fused Filament Fabrication ...................................................................... 69
Abstract ............................................................................................................................ 69 4.1 Introduction ................................................................................................................ 69 4.2 Experimental Procedure ............................................................................................. 72
4.2.1 Filament and Preconditioning ......................................................................... 72 4.2.2 Printing Procedure and Design of Experiment ................................................ 73 4.2.3 IR Camera Temperature Measurement ........................................................... 74 4.2.4 Optical Microscopy for Image-based Characterization ................................... 75 4.2.5 Quasi-static Tensile Testing ............................................................................ 75
4.3 Analysis Methodology ............................................................................................... 75 4.3.1 Image-based Uncertainty Quantification in FFF-AM of CFRP Composites .. 76 4.3.2 Calibration of Halpin-Tsai Model Based on Data-driven Approach ............... 79 4.3.3 Physics-based Stochastic Modeling and Uncertainty Analysis ....................... 81
4.4 Results and Discussion ............................................................................................... 81 4.4.1 Microstructure and Uncertainty Quantification ............................................... 81 4.4.2 Halpin-Tsai Model Optimization and Uncertainty Propagation ..................... 89
4.5 Conclusions ................................................................................................................ 93 4.6 Appendices ................................................................................................................. 94 4.7 References .................................................................................................................. 96
Chapter 5: Conclusions and Future Work ................................................................................ 102
5.1 Conclusions ................................................................................................................ 102 5.2 Theoretical Contributions and Industrial Applications .............................................. 104 5.3 Future Work ............................................................................................................... 106
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LIST OF FIGURES
Figure 1-1: Illustration of the hierarchical material structure in laminated CFRP composite for
aircraft structural materials [23]. ...................................................................................... 3
Figure 1-2: Schematic of XCT imaging process: (a) scanning stage, (b) projected image (i.e., raw
data), and (c) 2D slices of the 3D image after tomographic reconstruction. .................... 4
Figure 2-1: The flow chart of the iterative template matching algorithm: (a) grayscale image
stacks as data input, (b) segmentation of 3D images using Otsu’s multilevel thresholding, (c)
skeletonized volume of further segmentation using local intensity gradient segmentation, and
(d) fiber tracking. ............................................................................................................. 21
Figure 2-2: (a) Original XCT image, (b) grayscale intensity histogram of the original XCT
image, (c) the filtered image after single-level thresholding, (d) the filtered image after two-
level thresholding, and (e) the filtered image after three-level thresholding. .................. 22
Figure 2-3: Probability distributions of absolute intensity gradients in (a) LD, (b) TD, (c) ND
using the extracted volume of 400 × 200 × 200 voxels in SCFRP composite. (d) a
representative µXCT image after intensity gradient segmentation. ................................. 23
Figure 2-4: (a) Initial template of the short straight fiber and (b) cross-section of the template. 25
Figure 2-5: Schematics of local fiber tracking and orientation update where “X”s present location
of fiber centers: (a) linear line propagation of orientation estimated from template matching
in blue dotted line and selected coordinates in red, (b) identification of connected
components shaded in gray and PCA in a red oval, and (c) local orientation update in dotted
blue arrow and new starting point update outlined in the blue box. ................................ 27
Figure 2-6: Configurations of (a) straight cylindrical fiber, (b) Euler ZYX convention, and (c)
fiber with curvature. ......................................................................................................... 29
Figure 2-7: Representative 2D µXCT reconstruction of skin-core-skin structure in the LD/ND
plane; TD is out of the plane. ........................................................................................... 33
Figure 2-8: Representative reconstruction of SCFRP composite for (a) Skin layer 1, (b) Core
layer, and (c) Skin layer 2. ............................................................................................... 33
Figure 2-9: Representative color-coded reconstruction of fiber orientations for (a) Core Layer
and (b) Skin Layer 1. (c) The fiber orientation distribution of the Core Layer and Skin Layer
1. ....................................................................................................................................... 34
Figure 2-10: Representative 2D µXCT reconstruction of skin-core-skin structure in the TD/ND
plane. Out-of-plane direction (i.e., LD) is the same as the direction of tensile loading. .. 37
Figure 2-11: Representative reconstruction of LCFRP composite for (a) a single fiber, curvature
ratio color-coded, (b) Skin layer 1, (c) Core layer, (d) Skin layer 2, and (e) representative
fiber of η = 0, 0.2, and 0.5 from Skin layer 2.................................................................. 38
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Figure 2-12: Representative reconstruction of LCFRP composite in (a) Skin layer 1, (b) Core
layer, and (c) Skin layer 2. ............................................................................................... 40
Figure 2-13: Spatial distribution of calculated ELD for the skin–core interface ..................... 41
Figure 3-1: Experimental setup: (a) the load frame and (b) µXCT platform. ......................... 50
Figure 3-2: Image segmentation procedure. ........................................................................... 51
Figure 3-3: Image segmentation procedure: (a) original image, (b) negative image, (c) pixel
intensity histogram, (d) Otsu’s multilevel thresholding segmentation with six levels, (e)
segmented image, and (f) post-processing image containing only fracture features. ...... 52
Figure 3-4: Illustration of Mode I fracture and the related crack characteristics. ................... 55
Figure 3-5: Representative 2D reconstruction of scanned SMC composites. ......................... 56
Figure 3-6: Representative 3D reconstruction of scanned SMC composite. .......................... 57
Figure 3-7: 2D reconstruction of SMC under different engineering stresses: (a) 0 loading, it
shows a pre-existing crack within the material; (b)-(e) images at the same location at 168
MPa, 176 MPa, 194 MPa, and 201 MPa, respectively. .................................................... 58
Figure 3-8: Representative post-fracture image illustrating the fracture mechanisms, and the
white dotted lines indicate the fracture path. .................................................................... 59
Figure 3-9: Representative cracks in SMC CFRP composites in 3D. ..................................... 59
Figure 3-10: Spatiotemporal crack analysis result of SMC sample: (a) width (x)–thickness (y)
projections indicating the progression of crack front and crack opening, and (b) width (x)–
length (z) projections indicating the progression of crack length, bifurcation, and crack
thickness. .......................................................................................................................... 61
Figure 3-11: Reconstruction of injection-molded BASF sample: (a) 2D scanned image exhibiting
fracture features (fiber pullouts) and (b) 3D reconstructions under different tensile loads
indicating the progression of tip-end crack. ..................................................................... 62
Figure 3-12: Spatiotemporal void analysis result of BASF sample: (a)-(d) width (x)–length (z)
projections indicating the progression of the tip-end crack volumes at 106 MPa, 114 MPa,
124 MPa, and 135 MPa, respectively; (e) corresponding V-DIC strain calculation at 135
MPa. ................................................................................................................................. 63
Figure 4-1: (a) 2D CAD drawing (all dimensions in mm) of printed specimen, (b) schematic of
FFF process, (c) print path (solid color lines) for each layer with green and red arrows
indicating the start and end of the continuous extrusion with an extrusion order of yellow-
white-blue-orange, (d) schematic of the region of length-width cross-sectional area, (e)
approximate locations for the width-thickness cross-sectional area and their labels, and (f)
labels of width and thickness locations for cross-sectional area of ND-TD plane. .......... 74
Figure 4-2: The flowchart P-S-P analysis for the short carbon fiber reinforced polymer in this
study. ................................................................................................................................ 76
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Figure 4-3: The flow chart of the image-based uncertainty quantification and modeling: (a)
stitched grayscale optical image of width-thickness cross-sectional area, (b) dissected optical
images, (c) segmented image representing voids, (d) segmented image representing fiber,
and (e) representative bi-variate probability distribution of fiber volume fraction and void
volume fraction. ............................................................................................................... 77
Figure 4-4: A representative of (a) original histogram of fiber volume fraction and void volume
fraction, (b) transformed histogram using Box-Cox Transform, and (c) cumulative
distribution function of experimental data and simulated data. ....................................... 78
Figure 4-5: Representative width-thickness microstructure of specimens using low moisture
filament, print temperature of 270°C, print speed of 20 mm/s, and layer height of 2 mm. (a)
overall width-thickness microstructure, regional microstructure has (b) lower void volume
fraction, and (c) higher void volume fraction. ................................................................ 82
Figure 4-6: Representative width-thickness microstructure of specimens using low moisture
content filament with a combination of printing parameters of (a) 270°C, 20 mm/s, 0.2 mm,
(b) 270°C, 60 mm/s, 0.2 mm, (c) 270°C, 20 mm/s, 0.3 mm, and (d) 270°C, 60 mm/s, 0.3
mm. Yellow ovals approximately indicate the cross-section of each print path. ............. 83
Figure 4-7: Main effects plot of print parameters on (a) average fiber volume fraction, (b) average
void volume fraction, and (c) standard deviation of void volume fraction distribution. .. 85
Figure 4-8: (a) Representative in-situ IR image of the printed sample. (b-f) Extracted cooling
curve from IR images of Layer 1,2,4,7, and13, respectively. .......................................... 86
Figure 4-9: Representative evaporation duration of (a) midpoint of each path, (b) 4 points along
the length direction for part printed at 270°C with a printing see of 20 mm/s, and layer height
of 0.3 mm using high moisture content filament. ............................................................ 88
Figure 4-10: Representative segments of (a) length-width optical microscopy of the printed
sample, (b) filtered image using thresholding, and (c) probability distribution of fiber
orientation. ....................................................................................................................... 90
Figure 4-11: Comparison of longitudinal modulus of samples printed using (a) high moisture
content filament and (b) low moisture content filament. ................................................. 92
Figure 4-12: Representative of simulated probability distributions of longitudinal modulus of
samples printed using process conditions of (a) dry | 270°C | 20 mm/s | 0.2 mm, (b) moist |
270°C | 20 mm/s | 0.2 mm, (c) dry | 270°C | 60 mm/s | 0.2 mm, and (d) dry | 270°C | 20 mm/s
| 0.3 mm. ........................................................................................................................... 93
x
LIST OF TABLES
Table 2-1: Material Composition and Mechanical Property of CFRP composites ................. 20
Table 4-1: Print parameters of a full-factorial DOE. ............................................................... 73
xi
ACKNOWLEDGMENT
I thank my beloved parents and family members for their endless love and unlimited support in
all aspects of my Ph.D. journey Their words of wisdom and encouragement always help me get through
difficulties and they have always cheered and believed in me at every step of the way.
I extend my deepest and sincere gratitude to my advisors, Dr. Jingjing Li, and Dr. Hui Yang, for
their greatest guidance and support for my Ph.D. research and study. Our countless discussions provided
the needed guidance to discover independently, express clearly, and think critically. I appreciate their
patience and immense knowledge when I faltered. I also thank my dissertation committee members: Dr.
Soundar Kumara, Dr. Timothy Simpson, and Dr. Danielle Zeng, for their valuable comments and
suggestions on my research. I am very grateful to my post-doctoral fellows, Dr. Kaifeng Wang, and Dr.
Nannan Chen, who always provided insightful knowledge and guidance for this research. I thank Dr.
Yang Li for your expertise in material structure and modeling, which was critical for this research.
Next, I thank all my past and present colleagues and friends in the Materials Processing and
Characterization Lab, Complex System Monitoring, Modeling and Analysis Laboratory (Complex), and
Laboratory for Intelligent Systems and Analytics (LISA) for all the support and help during my Ph.D.
study. I thank Haris Khan for providing an inspiring environment for research and guidance for critical
thinking. I thank Cheng-Bang Chen for your thoughtful suggestions and supports for data-driven analysis.
I thank Dr. Qiulian Wang for your encouragement. I thank Dr. Sarah Root for your guidance and your
continuous improvement spirit that will guide me many years to come. Special recognition also goes to
the staff of FAME lab, Travis Richner, Brent Johnston, and Christ Anderson, for their technical supports
during these years. I extend my gratitude to staff members, Dr. Xianghui Xiao and Pavel D. Shevchenko
from Advanced Photon Source in Argonne National Lab for your valuable contribution to this research.
Last but not the least, I gratefully acknowledge the financial support from the ICS seed grant,
Ford Motor Company University Research Program (“Unveiling 3D Deformation and Failure
Mechanisms in Carbon Fiber Reinforced Polymer Composites by In-situ Micro X-ray Computed
xii
Tomography”), and the National Science Foundation (No. CMMI-1651024, CMMI-1617148) for this
dissertation. Any opinions, findings, and conclusions or recommendations expressed in this material are
those of the author and do not necessarily reflect the view of the National Science Foundation.
Chapter 1: Introduction
1.1 Motivation
Carbon-fiber-reinforced polymer (CFRP) composites are a versatile group of engineering
materials and they are increasingly applied in a wide range of industries such as aerospace [1-4],
automotive [5-8], oil and gas [9], and medical [10] owing to their high specific modulus, high specific
strength, good corrosion and fatigue resistance [11-13]. In addition to their favorable qualities, CFRP
composites also exhibit tailored strength characteristics for a given load [14], where thermoplastic or
thermoset polymers reinforced with different types of carbon fibers (i.e., discontinuous, unidirectional, or
woven carbon fibers) to achieve various architectures that ensure desired strength and performance
[15,16]. For example, the fuselage section of the Boeing 787 is made from layers of CFRP composites,
where reinforcing carbon fibers are oriented in a specific direction to achieve maximum strength along
the maximum load paths [16]. The wings of Airbus A350 XWB have a “saber-like” double-curvature
configuration to improve the aerodynamics of the system, thereby enhancing the fuel efficiency and climb
performance, and such configuration cannot be achieved using traditional metallic wings [16]. The
application of CFRP composites as load-carrying structures for large commercial transports demonstrates
the significant advancement in understanding and usage of CFRP composites. However, the safety of
CFRP structural components still relies on extensive certification tests and procedures which are
expensive and costly [16], and the lengthy and costly certification process brings significant challenges in
approving new materials and designs for an increasingly demanding market for CFRP composites [14].
Many research efforts have targeted to develop approaches to accelerate the development of new
or improved materials into certified products. One research stream, material informatics, leverages the
advancement in data science and informatics to focus on efficient material selection algorithms for
desired properties or performance [17-19]. MIT and Lawrence Berkeley National Laboratory jointly
developed the Materials Project, a searchable repository of data opens to the entire materials science
community that uses computational material science to simulate compounds at the atomic level for
2
desired properties [20]. However, mechanical properties are strongly influenced by the hierarchical
material structure. For example, the interfaces of the carbon fibers and polymer matrix (i.e., microscale),
the spatial distribution of carbon fibers and defects (i.e., mesoscale), and interlaminar properties of
laminated CFRP composite (i.e. continuum) are essential for the CFRP composites to achieve superior
performance [19, 21,22]. This collection of these structures is generally referred to as a material
microstructure that has an essential role in determining the structure-property relations. There is a need to
integrate the data science and informatics with microstructure to bridge the gaps between material
processing, microstructural patterns, and material property of interest, thereby establishing the
fundamental understanding of correlations that governs the process-structure and structure-property
relations and accelerating the development of new or improved advanced CFRP composites. Therefore,
this dissertation endeavors to develop innovative methodologies and frameworks to characterize and
quantify the morphology of microstructures of CFRP composites. The underlying process-structure and
structure-property relations are investigated, exploited, and modeled.
1.2 Research Background
Microstructure informatics, a branch of materials data science and informatics, focuses on
identification and quantification of microstructure at dominant scales of the hierarchical material
structure, where microstructure can be characterized, digitally represented, and systematically
investigated to provide a fundamental understanding of the correlations that govern process-structure and
structure-property relations [19]. Figure 1-1 presents an example of the hierarchical material structure of
laminated CFRP composite for damage modeling of aircraft structural materials [23], where a range of
damage mechanisms (e.g., fiber fracture, matrix failure, delamination) [24-27] can occur in the laminated
composite at different length scales. The final failure of the composite may due to multiple damage
mechanisms; therefore, it is critical to fully understand the underlying phenomena of structure
degradation and failure mechanism. By applying data science and informatics to investigating
microstructures, high resolution and rapid characterization methods, computational modeling, and
3
simulation tools are increasingly available to identify and examine the correlations between various
microstructural parameters and material properties and performances [19].
Figure 1-1: Illustration of the hierarchical material structure in laminated CFRP composite for aircraft
structural materials [23].
There are many challenges in quantifying microstructures as summarized in [19]:
- three-dimensional (3D) characterization of the structure,
- spatiotemporal identification across the hierarchical structures,
- statistical distribution of structures and properties,
- evolution of microstructure over temperature and time for long-term durability and
sustainability.
The underlying grant challenge for microstructure informatics is to develop a widely accepted statistical
framework for rigorous quantification of microstructure [28], and much progress has been made in many
areas of microstructure characterization for CFRP composites. Recent advancement in the methodologies
for 3D characterization and statistical characterization are addressed in the subsequent sections
4
1.2.1 Micro X-ray Computed Tomography
Advances in using micro X-ray computed tomography (µXCT) has gained considerable
acceptance for characterizing the material internal structure and unveiling the deformation phenomena of
CFRP composites [29-35]. µXCT is radiographic nondestructive testing (NDT) method, where a
specimen is positioned on a rotary stage between the X-ray source and the detector as illustrated in Figure
1-2a. As the specimen rotates increment by increment, the detector takes projection images at each
angular position (Figure 1-2b). A tomographic reconstruction script computes the collected radiographic
raw data and reconstructs them into 2D slices of the 3D image (Figure 1-2c) as grayscale images. The
grayscale intensity corresponds to the spatial X-ray attenuation which correlates to the density of the
material. Lower density materials (e.g., void, polymer matrix) will have a darker color, while higher
density materials (e.g., carbon fiber) will be represented by lighter colors.
Figure 1-2: Schematic of XCT imaging process: (a) scanning stage, (b) projected image (i.e., raw data),
and (c) 2D slices of the 3D image after tomographic reconstruction.
The capability and limitation of µXCT constrain the detectability of internal details such as crack
initiation and microcracks. Schilling et al. [29] examined the effect of µXCT resolution on the ability to
determine the internal geometry of flaws such as delamination and microcracking in glass fiber reinforced
polymer composite using a laboratory X-ray scanner, where the detection of microcracks (i.e. 0.5 – 1 µm)
is feasible for an imaging resolution of 4 µm/pixel and the sample size is limited to 1.5 mm in width and
thickness. However, the samples must be penetrated with dye as a contrasting agent, which limited the
detectability due to the requirement of connected damage and penetration of the dye. Bull et al. [30]
5
investigated the impact damage of laminated CFRP composite using another laboratory scanner without
any contrast agent; however, the scan time for each sample was approximately 2.5 hours. Similar long
scanning duration is observed in different laboratory XCT scanners [31-34] due to the polychromatic and
divergent (cone) beams resulting in a long scanning duration for a good phase contrast [35]. In contrast,
synchrotron XCT uses a parallel, monochromatic X-ray beam, which is more coherent and brighter, thus
improving image quality and reducing acquisition time. Landis et al. [36] studied the internal crack
growth in small mortar cylinders using synchrotron µXCT beamline, where a series of scans were made at
different compressive loads to observe the crack propagation. The short scanning time of synchrotron
µXCT enables in-situ 3D monitoring of the material deformation, where damage mechanism (e.g.
initiation, propagation, and damage modes) can be monitored as a function of time, stress state and/or
heating cycle. Sket et al. [37] examined the shear behavior of ±45° laminated CFRP composite, where
quantitative damage evolution was measured by monitoring the fiber orientation between consecutive
plies, crack volumes, and the fraction of interply delamination at the different applied strain. Croom et al.
[38] combined µXCT and volumetric digital image correlation (V-DIC) to quantify the in-situ volumetric
strain thereby identifying local mechanical properties. Therefore, utilizing in-situ 3D XCT images to
characterize and model the mechanical behavior of CFRP composites is necessary for unveiling the
underlying structure-property relation, thereby accelerating material design and optimization.
1.2.2 Image Processing
Despite the increasing application of high-resolution, high-speed, synchrotron-based µXCT, one
of the challenges to fully exploit the rich information that captured by this method is the large image data
generated (>100 GB raw data/per sample for in-situ monitoring), which made them difficult to visualize
and analyze [39]. The sheer amount of data derived from the µXCT and the inherently complex
microstructure of CFRP composites have created an urgent need to develop an efficient and automatic
segmentation of the physical features (i.e., fibers, voids, matrix) from 2D images or 3D image stacks,
which will provide the foundation for statistical characterization and modeling of the microstructure
6
morphology (e.g., fiber geometry, the spatial distribution of voids and defects). Kastner et. al.
implemented a global grayscale thresholding method to evaluate the defects and porosity in CFRP
composites and found that the porosity value was depended on the selected threshold value, which
required visual validation to select the best result [40]. The simple grayscale thresholding is a ubiquitous
and intuitive segmentation approach [29, 40-42], which is available in many open-sourced or commercial
software such as ImageJ, Avizo, and Dragonfly. However, global grayscale thresholding relies on clear
contrast between the object of interest and the background, which is not adequate for many CFRP
composite systems that exhibit low contrast among fibers, polymer matrix, and voids/cracks.
Furthermore, the inherent complexity in the structural morphology of CFRP composites, such as densely
packed fibers with blurred boundaries with adjacent fibers, variations in size, orientation, and shape of
fibers, voids, and cracks, present challenges for segmentation of individual fibers, voids, and cracks.
Integrating achievements from data science and informatics, sophisticated image segmentation
methods such as the Bayesian inference theory-based and machine learning-based approaches were
developed [35,43,44]. Sencu et al. [45] proposed a Bayesian inference theory-based approach to segment
fibers and track the fiber centerlines, which was demonstrated on multidirectional laminate CFRP
composites with a stacking sequence of [+45°/90°/-45°/0°] by separating 90° ply from the rest of the
material and treating it as 0° UD carbon fibers through the rotation. This approach required the user’s
visual inspection to empirically determine the size of kernel and convolution factors. Emerson et al. [46]
proposed a dictionary-based probabilistic segmentation technique to indicate the likelihood of a voxel
belonging to a fiber or the matrix, which required the user’s inputs, including dictionary patch size and
representative labeled patches to identify fiber centroid from 2D images. In the revised version of this
approach, Emerson et al. [47] reduced the computation time for training the supervised learning model
and the probabilistic segmentation phase and improved the fiber centerline tracking using a bidirectional
approach. This algorithm was implemented on the unidirectional CFRP composite. To address the
variations in fiber morphology, Hessman et al. [48] proposed an iterative single fiber segmentation and
7
merging approach to obtain fiber microstructural characteristics such as orientation, location, radius, and
length directly from the scanned images. Although the approach was implemented on artificial µCT data,
it achieved a higher quality compared to the commercial software. The fidelity of microstructural
characterization of CFRP composites from high-resolution µXCT is essential for unveiling the process-
structure and structure-property relations; therefore, there is an urgent need to develop physics-based
characterization methods that can be deployed automatically for different CFRP composite systems.
1.2.3 Statistical Characterization of the Microstructure of CFRP Composites
The conventional description of microstructure characteristics (e.g., fiber length, fiber orientation,
and void volume fraction) typically uses the average value to present the property; however, a statistical
distribution of the property is often the interest, for example, estimating materials reliability, determining
the remaining lifetime, and optimization for a robust design [19,49]. Without a proper understanding of
the origin and effect of variations on the microstructure, it is impossible to assess the validity of models
that use these values for computational simulations and predictions [49-51]. Uncertainty quantification
(UQ) technique is a suitable approach to address such variabilities, and uncertainties are generally
classified as aleatory and epistemic [52,53]. Aleatory uncertainty is the inherent randomness in the system
which is irreducible, and it can only be properly quantified in the form of the probability distribution. For
CFRP composites, aleatory uncertainty refers to the variations in manufacturing processes (e.g. process
parameters), and fiber and matrix characteristics (e.g., geometric morphology, material properties).
Epistemic uncertainty refers to uncertainty due to partial knowledge of the problem and its influencing
factors, such as assumptions made during experimental and modeling methods. It is also noted that
instrumental and regression errors can also cause uncertainties, where some scholars considered them as
aleatory uncertainty while others referred them as error uncertainties. Zhu et al. [54] proposed a
stochastic constitutive model for a woven CFRP composite, where a series of stochastic volume elements
were constructed to incorporate the spatial variation observed from µXCT images. The stochastic
constitutive model was validated with experimental results of axial tension, axial compression, and in-
8
plane shear testing. Although numerous studies emphasize on incorporating stochastic microstructure in
the simulation models to provide a stochastic prediction of the material property and performance, limited
research has thoroughly examined the effect of process parameters on microstructural variations and the
corresponding variations on material performance, which hinders the understanding of process-structure-
property (P-S-P) relations. Hence, there is a need to establishing a comprehensive P-S-P relation through
stochastic characterization of the microstructure of CFRP composite thereby accelerating its deployment
in the industrial applications.
1.3 Research Objectives
The overall objective of this dissertation is to quantitatively characterize the microstructural
features of CFRP composites, which addresses a few challenges in microstructure informatics. The
specific tasks of this dissertation include:
1. Developing a 3D microstructure characterization approach to analyze complex-structured data
from advanced imaging of CFRP composites, e.g. µXCT, and then provide a 3D digital
representation of the microstructure morphology using voxels. The statistical microstructure
morphology is quantified, providing needed data for microstructure modeling. Further, the
fidelity of the microstructure representation is validated using experimental results.
2. Developing a spatiotemporal characterization framework to extract and quantify damage features
such as crack initiation and crack propagation from µXCT images of CFRP composites. Through
this task, different failure mechanisms and failure modes are unveiled. Furthermore, this task
aims to provide excellent visualization of spatiotemporal crack propagation and produce a precise
quantitative measurement of crack growth.
3. Tailoring a new P-S-P approach for the analysis of CFRP composites processed via fused
filament fabrication (FFF), as well as the quantification of microstructure variations from optical
microscopy images. Stochastic models are developed to represent microstructure uncertainties
9
and account for process induced variations. The adverse effect of uncertainties at the
microstructure level is further investigated to unveil the structure-property relation.
The dissertation focuses on developing an image-based and data-driven approach by providing 3D
microstructural characterization, spatiotemporal characterization of fracture behavior, and UQ of process-
induced microstructure variations, which are essential for accurate estimation of mechanical properties.
The fulfillment of the objectives provides a comprehensive understanding of the process-structure and
structure-property relations in CFRP composite, which will accelerate the development and
implementation of the advanced composite to certified products.
1.4 Organization of the Dissertation
This dissertation is organized based on multiple manuscripts. Chapters 2, 3, and 4 are written as
individual research papers and they are partially revised for this dissertation. Chapter 5 summarizes the
investigations and proposes future work.
In Chapter 2, an image-based microstructural analysis framework is developed to quantitatively
analyze fiber morphology (e.g. fiber curvature, orientation, and length distribution) for non-uniformly
orientated fiber systems using µXCT images. The framework leverages the numerical image processing
techniques and iterative local fiber-tracking approach to quantify the statistical distribution of the fiber
morphology. The characterized data is then integrated with the Halpin-Tsai model and laminate analogy
for material property prediction, which is evaluated and validated using experimental results for injection-
molded short and long CFRP composites.
In Chapter 3, a spatiotemporal algorithm is proposed to quantitatively represent and characterize
the in-situ 3D fracture behavior of CFRP composites by leveraging advanced image acquisition and
processing techniques using µXCT images. The proposed algorithm analyzes the fracture mechanisms
and fracture propagation of sheet molding compound and injection molded CFRP composites, where
spatiotemporal complexity and dimension of fracture features (e.g. crack opening, crack thickness, and
tip-end crack volume) are quantified and visualized.
10
In Chapter 4, a P-S-P approach is proposed to understand the uncertainties in the FFF printed
CFRP composite from the micro-level to the macro-level. The proposed approach integrates image-based
statistical analysis and physics-based modeling to predict the longitudinal modulus of FFF parts, where a
data-driven optimization scheme is developed to consider the complex effect from the FFF process and
craze nucleation from voids, thereby avoiding overestimation. Further, a Monte-Carlo simulation is
adopted to investigate the propagated uncertainty in the structure-property relation.
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Chapter 2: Mechanical Properties Prediction of Injection Molded Short/Long Carbon Fiber
Reinforced Polymer Composites Using Micro X-Ray Computed Tomography 1
Abstract
This paper addresses the challenge of reconstructing nonuniformly orientated fiber-reinforced
polymer composites (FRPs) with three-dimensional (3D) geometric complexity, especially for fibers with
curvatures, and proposes a framework using micro X-ray computed tomography (μXCT) images to
quantify the fiber characteristics in 3D space for elastic modulus prediction. The FRP microstructure is
first obtained from the μXCT images. Then, the fiber centerlines are efficiently extracted with the
proposed fiber reconstruction algorithm, i.e., iterative template matching and the 3D coordinates of the
fiber centerlines are adopted for quantitative characterization of the fiber morphology. Finally, Young's
modulus is predicted using the Halpin-Tsai model and laminate analogy approach, and the fiber
configuration averaging method with the consideration of the fiber morphology. The new framework is
demonstrated on both injection-molded short and long carbon fiber-reinforced polymer composites,
whose fiber morphology and predicted mechanical properties are validated through previous pyrolysis
and quasi-static tensile tests, respectively.
2.1 Introduction
Micro X-ray computed tomography (µXCT), as a typical nondestructive imaging technique, has
demonstrated its advantages to explore the detailed three-dimensional (3D) internal structure of carbon
fiber-reinforced polymer (CFRP) composites including unidirectional, laminated, injection-molded, and
chopped-fiber composites [1–5]. By leveraging the variation of X-ray attenuations owing to the
differences in density and atomic number, the captured microscale XCT images can unveil the composite
constituents, e.g., fibers, matrix, and defects [3–8], where the high-density material (e.g., fibers) appears
1 The Contents of this chapter has been published as Pei S, Wang K, Li J, Li Y, Zeng D, Su X, Xiao X, Yang H.
Mechanical properties prediction of injection molded short/long carbon fiber reinforced polymer composites using
micro X-ray computed tomography. Composite Part A 130 (2020):105732.
17
brighter than the low-density material (e.g., matrix). At present, µXCT is effectively used to understand
the initiation and evolution of damage and to determine the in-situ fracture mechanics of CFRP
composites [4,6,9–14]. However, only limited quantitative image analyses of µXCT images have been
reported for non-uniformly orientated CFRP composites, especially for those consisting of curved fibers.
This is because the appropriate post-image processing algorithms such as the Bayesian inference theory-
based and machine learning-based approaches depend considerably on the image quality and material
nature [15–17]. Emerson et al. [18] proposed a dictionary-based probabilistic segmentation technique to
indicate the likelihood of a voxel belonging to a fiber or the matrix, which required the user’s inputs,
including dictionary patch size and representative labeled patches to identify fiber centroid from 2D
images. In the revised version of this approach, Emerson et al. [19] reduced the computation time for
training the supervised learning model and the probabilistic segmentation phase and improved the fiber
centerline tracking using a bidirectional approach. This approach was presented on unidirectional carbon
fiber. Czabaj et al. [7] proposed a two-step algorithm based on 2D template matching for fiber
identification followed by a Kalman filtering approach for tracking. Creveling et al. [20] proposed an
extension to this approach, replacing the manually picked templates for synthetically created 2D fiber
templates to identify the fibers and determine the fiber centroids and the fiber diameters. This approach
was demonstrated on laminate CFRP composites with a stacking sequence of [+45°/-60°/+60°]. Sencu et
al. [21] proposed a Bayesian inference theory-based approach to segment fibers and track the fiber
centerlines, in which the size of the kernel and convolution factors are determined semi-empirically by
user’s visual inspection. The use of the local inference model to track fiber centerlines required a series of
tuning for different fiber shifts completed by the user. The proposed approach was demonstrated on
multidirectional laminate CFRP composites with a stacking sequence of [+45°/90°/-45°/0°] by separating
90° ply from the rest of the material and treating it as 0° UD carbon fibers through the rotation.
Discontinuous FRPs exhibit complex microstructures owing to a variety of fiber lengths,
orientations, and curvatures. There is an urgent need to develop new analytical methods for the
18
characterization and analysis of individual fiber segments. Agyei et al. [22] proposed a framework that
consisted of a four-step sequential 2D segmentation approach and a 3D volume rendering algorithm to
generate a 3D morphology that represented the microstructure for short fiber-reinforced composites. In
this four-step sequential 2D segmentation approach, the researchers adopted iterative sharpening, iterative
marker-controlled watershed, case-by-case comparison for highly clustered out-of-plane fibers, and
replacement of segmented regions with fitted ellipses to achieve an optimum segmentation. The 3D
volume rendering approach refined the microstructure by separating connected fibers and stitching over-
segmented fibers. The proposed framework was demonstrated on an injection molded glass fiber
reinforced polymer composite. Hessman et al. [23] proposed an iterative single fiber segmentation and
merging approach to obtain fiber microstructural characteristics such as orientation, location, radius, and
length directly from the scanned images. This approach was implemented on artificial µCT data, which
achieved a higher quality compared to the commercial software, though the approach neglected the
possible curvatures. The challenges of reconstructing non-uniformly orientated CFRP composites with
curved fibers are the inherent variabilities from the material owing to orientation and curvature variants,
the computational complexity of the 3D image data, and tracking of a curved fiber from a congested fiber
system in a 3D space. Therefore, there is a need to develop a suitable segmentation and tracking
algorithm to extract the internal structures of CFRP composites, considering the fiber orientation and fiber
curvature.
Image-based modeling has recently demonstrated the advantages of using XCT images to
generate a realistic finite element mesh for material behavior modeling [24–26]. However, the process of
extracting and replicating complex geometry for a numerical model requires more intensive computation
than models using idealized representative volume elements [17]. Thus, establishing a relationship
between the image-based spatial statistics and material properties at a different length scale with less
computational effort is desired. A number of attempts have been made to predict the mechanical behavior
of fiber-reinforced composites [27–30]. Huang proposed a micromechanical strength theory to calculate
19
the mechanical properties of unidirectional fiber composites [28]; however, complex fiber morphologies
were not considered. Nguyen et al. employed the Eshelby’s equivalent inclusion method to calculate a
material’s overall stiffness using an orientation averaging approach, where the fiber orientation and fiber
length distributions were measured from 2D microscopic images [29]. Kunc et al. proposed a fiber
configuration with curvatures and extended the orientation averaging approach to configuration averaging
to account for the fiber curvature. The statistical distributions of fiber length and fiber curvature were
measured separately, in which the fiber length distribution was achieved by pyrolysis tests, and the fiber
curvature distribution was measured from XCT images. The corresponding fiber morphology distribution
considering both fiber length and fiber curvature was then generated by a random number generator to
pair these two distributions. This approach reported an error of 15% in the experimental results [30]. The
realistic 3D spatial statistics of the material microstructure must be considered when implementing
mechanical property prediction models in order to obtain an accurate estimation of a material’s
mechanical properties,
The present study demonstrates a combined computational and analytical framework for image-
based reconstruction, quantitative morphological characterization, and a mechanical prediction of short
and long fiber reinforced polymer composites with non-uniformly oriented fibers. The framework
consists of a non-destructive imaging technique (µXCT) for capturing the internal microstructures, the
proposed reconstruction algorithm (iterative template matching) for extracting and tracking fiber
centerlines, and spatial statistic characterization of the 3D fiber geometric properties (i.e., fiber volume
fraction, length, orientation, and curvature distributions) for elastic property calculations such as Young’s
modulus prediction. The framework leverages the benefits of µXCT to obtain a realistic internal 3D
microstructure and the advantages of the proposed iterative template matching approach that account for
non-uniform fiber orientation, fiber curvatures, and congested fiber systems to improve the mechanical
property estimation and provide the spatial characterization and mechanical properties of the material.
The proposed framework is applied to short CFRP (SCFRP) composites with straight fibers and long
20
CFRP (LCFRP) composites with curved fibers. The reported computational results are validated through
quasi-static tensile [31] and pyrolysis tests [32].
2.2 Experimental Procedure and Methodology of CFRP Reconstruction
2.2.1 Materials and Experimental Procedure of µXCT
The µXCT was performed on the micro-tomography beamline 2-BM-A at the Argonne National
Laboratory to obtain the internal microstructure of the materials. In this study, two CFRP composites
were scanned separately, and the material composition and mechanical property are listed in Table 2-1.
The µXCT scans were performed over a rotation of 180 using a beam energy of 27 keV with an
exposure time of 0.05 seconds per image. Each scan captured more than 1400 2D grayscale images with a
dimension of 2560 × 2560 pixels at a voxel size of 1.3 µm, so the ratio between the fiber diameter to the
number of pixels is 5-6. The constituents of the CFRP composites (i.e., fiber and matrix) were
differentiated through variations in X-ray absorption. The initial data conversion from the raw data to
grayscale images was performed using TomoPy, a well-established open-source Python package designed
for processing and reconstructing tomographic data [34]. Interested readers can refer to [4] for further
details of the post-experiment image conversion.
Table 2-1: Material Composition and Mechanical Property of CFRP composites
Composite Matrix Fiber weight
fraction (%)
Avg. Fiber
Length (µm)
Avg. Fiber
Diameter (µm)
Avg. Young’s
Modulus (GPa)
Short
CFRP
Polyamide
6/6 40a 104.8 (Core Layer)a
117.9 (Skin Layer)a 7 13.8 (Core Layer)a
21.9 (Skin Layer)a
Long
CFRP PA 66 40b - 7 29.3b
aTaken from ref [8] bTaken from ref [33]
2.2.2 Fiber Reconstruction using Iterative Template Matching
The complete workflow of the proposed iterative template matching reconstruction algorithm is
displayed in Figure 2-1; the algorithm is divided into three sections and implemented in Matlab®. In the
first step (initialization), a global segmentation method, Otsu’s multilevel thresholding [35], is employed
21
to separate the fibers from the matrix as indicated in Figure 2-1b, where the input images are grayscale
image stacks obtained from µXCT as presented in Figure 2-1a. In the second step, the local intensity
gradient segmentation further isolates the fiber voxels based on the 3D grayscale intensity gradient
changes by removing the edge voxels. The remaining voxels are skeletonized to preserve the
morphological shape of the fibrous structure and to represent fiber centerlines, as illustrated in Figure 2-
1c. In the third step, fiber tracking, template matching [7,20,21,36], and a local fiber-tracking scheme are
performed to determine and assign the fiber centerlines for the individual fibers throughout the volume
while removing voxels that belong to fibers that are in contact. One of the outputs of the reconstruction
algorithm is a labeled volume in which voxels with the same label represent the centerline of an
individual fiber. A detailed description of each step is presented in the following subsections.
Figure 2-1: The flow chart of the iterative template matching algorithm: (a) grayscale image stacks as data
input, (b) segmentation of 3D images using Otsu’s multilevel thresholding, (c) skeletonized volume of
further segmentation using local intensity gradient segmentation, and (d) fiber tracking.
2.2.2.1 Initialization
To generate the initial isolation of the fibers, the original grayscale XCT 3D images (Figure 2-2a)
are processed with Otsu’s method [35] which coarsely clustered the constituents in the composite into
different groups by minimizing the voxel intensity variance of each group and maximizing the voxel
intensity variance across groups. A representative of grayscale intensity histogram, presented in Figure 2-
22
2b, has a probability distribution containing three peaks and two valleys, where three peaks are located
approximately at grayscale values of 100, 190, and 250, and two valleys are located approximately at
grayscale values of 175 and 145. Although fibrous composites can be considered as a biphasic material, a
single threshold level separating the voxels into two groups may not be sufficient to remove matrix
voxels, as demonstrated in Figure 2-2c, where a one-level threshold value of 139 is adopted, and the
voxels belonging to the brighter grayscale intensity class are retained with the original grayscale intensity.
Figures 2-2c and 2-2d present the two-level (174) and three-level thresholding (195) of the original
image, respectively, and voxels in the brightest grayscale intensity class are retained with the original
grayscale intensity. Figure 2-2e shows that the three-level thresholding leads to an over truncation,
whereas the one-level thresholding is not quite effective in removing matrix voxels as presented in Figure
2-2c. Two-level thresholding results in the best global segmentation with a value located at one of the
local minima of the grayscale intensity histogram illustrated in Figure 2-2b. It should be noted that a
small number of gray-colored voxels, representing the polymer matrix and fiber edges, are retained
because Otsu’s method is a global thresholding method and cannot differentiate polymer voxels with a
similar grayscale intensity to that of the fiber voxels.
Figure 2-2: (a) Original XCT image, (b) grayscale intensity histogram of the original XCT image, (c) the
filtered image after single-level thresholding, (d) the filtered image after two-level thresholding, and (e) the
filtered image after three-level thresholding.
23
2.2.2.2 Local Intensity Gradient Segmentation
The initial coarsely segmented grayscale volumetric images then undergo a local intensity
gradient segmentation to remove fiber edge voxels through the calculation of the absolute grayscale
intensity gradients in the longitudinal direction (LD), transverse direction (TD), and normal direction
(ND), i.e., 𝐼𝐿𝐷′ , 𝐼𝑇𝐷
′ , and 𝐼𝑁𝐷′ , where 𝐼(𝑥, 𝑦, 𝑧) represents the voxel intensity at the location (𝑥, 𝑦, 𝑧) and the
tilde symbol and subscripts indicate the intensity gradients in the corresponding directions. The grayscale
intensities of fiber voxels change gradually with higher grayscale intensities at the fiber centers and lower
grayscale intensities at fiber edges. Hence, the fiber edge voxels have a more positive or negative
grayscale intensity gradient. As presented in Figure 2-3, the typical probability distributions of the
absolute voxel-intensity gradients of an image volume with dimensions of 400 × 200 × 200 voxels (LD ×
TD × ND) naturally contain a thresholding criterion distinguishing edge voxels from fiber voxels, where
the edge voxels have a considerably larger absolute intensity gradient than fiber voxels. Voxels with near-
zero grayscale intensity gradients in all three directions (i.e., LD, TD, and ND) are retained as presented
in Figure 2-3d, resulting in a separation of a few connected fibers as illustrated by yellow arrows. The
segmented volume is then skeletonized to obtain voxels representing the centerline of each fiber as
displayed in Figure 2-1c.
Figure 2-3: Probability distributions of absolute intensity gradients in (a) LD, (b) TD, (c) ND using the
extracted volume of 400 × 200 × 200 voxels in SCFRP composite. (d) a representative µXCT image after
intensity gradient segmentation.
24
2.2.2.3 Fiber Tracking
The skeletonized volume is converted to a set of sorted 3D voxel locations (denoted as S = {s})
for fiber tracking, and these voxel locations are sorted according to their spatial locations in the directions
of LD and ND. The set, S, designates coordinates of approximate locations for fiber centers. A small
portion of misidentified voxel locations is related to touching fibers in the congested fiber systems, where
the proportion of misidentified voxel locations is determined by comparing the total numbers of voxel
locations of the skeletonized volume and the labeled volume. The average difference measured in this
study is 6.6 ± 1.1%, which is less than 8%. The fiber-tracking algorithm is developed based on 3D
template matching to estimate orientations of fibers, and a local fiber tracking is then implemented to
obtain robust fiber tracks, through which voxels belonging to the same fiber are identified. Although
template matching is a well-established technique in image processing using the morphology of a
template to identify similar parts in a larger target image, the accuracy of the detection depends on the
selection of templates [7]. A brief summary is presented here for clarity; the detailed formation and
description can be found in [36]. Template matching calculates the normal cross-correlation (NCC) score
for each voxel in the skeletonized volume using the following expression:
𝑁𝐶𝐶(𝑢, 𝑣, 𝑤) = ∑ [𝐼(𝑢,𝑣,𝑤)−𝐼]̅[𝑇(𝑢−𝑢′,𝑣−𝑣′,𝑤−𝑤′)−�̅�]𝑢,𝑣,𝑤
√∑ [𝐼(𝑢,𝑣,𝑤)−𝐼]̅2𝑢,𝑣,𝑤 ∑ [𝑇(𝑢−𝑢′,𝑣−𝑣′,𝑤−𝑤′)−�̅�]2𝑢,𝑣,𝑤
, 2.1
where I(u,v,w) is the grayscale intensity of location (u,v,w) with size M N L (i.e., the dimension of the
volume for reconstruction); T(u-u’, v-v’,w-w’) is the grayscale intensity of the template with size m n l
(i.e., the dimension of the template), which is shifted by u’ voxels in the LD, v’ voxels in the TD, and w’
voxels in the ND; 𝐼 ̅is the average grayscale intensity in the m n l region centered at (u,v,w); �̅� is the
average grayscale intensity of the template. All summations in Equation 2.1 are performed over the m n
l and a perfect positive (negative) correlation reveals an NCC value of “1” (“-1”).
Numerous CFRP composites contain fibers in different orientations; therefore, one single
template cannot sufficiently nor accurately estimate fiber orientation, and a set of templates based on a
25
short straight fiber, presented in Figure 2-4a, is preferred. The fiber diameter of the template is set to be
six voxels, which is estimated by visual inspection from the µXCT images. The cross-section of a short
straight fiber template is emulated using a Gaussian filter, as presented in Figure 2-4b, which ensures the
highest grayscale intensity at the fiber centerline and a gradual intensity decrease from the center to the
edge. Templates with different fiber orientations are generated by rotating the initial short fiber template
around the ND-axis from -90° to +90° with a 10° increment, and then the TD-axis from -90° to +90° with
a 10° increment to ensure the templates are robust against all fiber orientations. The NCC score for a
voxel location, s, is calculated according to Equation 2.1, and the estimated orientation is chosen by
selecting the orientation corresponding to the highest NCC score.
Figure 2-4: (a) Initial template of the short straight fiber and (b) cross-section of the template.
To determine the appropriate length of the fiber template, a preliminary study was performed to
examine the orientation estimation accuracy and computational time for the fiber templates with a length
of 8, 16, and 32 voxels. The tested volume was synthesized containing 110 straight fibers with a length of
at least 50 voxels and known orientations ranging from -90 to +90 with a 10 increment in both the ND-
and TD-axes forming a uniform distribution for fiber orientation with a volume size of 200×100×100
voxels. The experiment was performed in Matlab® with an Intel® Core i7-8700 CPU at 3.20 GHz and
64.0 GB memory. The template with a fiber length of 32 voxels achieved the highest accuracy (98.9%)
among all three cases with the longest computational time (approximately 10 min); the computational
time and orientation estimation accuracy for the templates with fiber lengths of 8 and 16 voxels were
approximately 2.5 min, 78.9%, and approximately 5 min, 94.7%, respectively. When considering both
orientation estimation accuracy and computational cost, the template with a fiber length of 16 voxels was
selected. The fiber template was then tested on a synthesized volume containing 121 curved fibers, where
26
109 of the curved fibers were correctly identified and all of the misidentified fibers had a fiber length
shorter than that of the fiber template, indicating that the proposed template can identify both straight and
curved fibers.
For a reasonably sized 3D image, computing the NCC scores for all voxel locations can be
computationally expensive. Therefore, a fiber-tracking algorithm using a linear line propagation-approach
[37] is implemented to identify voxel locations along with the estimated orientation. As described below,
the NCC scores do not have to be computed at these locations, thereby reducing the amount of
computation time. The local orientation is updated using the identified voxel locations for fiber tracking
in the next iteration. Figure 2-5 demonstrates the local fiber tracking and orientation update algorithm in
2D space (e.g., TD-LD plane), where the grid represents each pixel in the 2D image (i.e., search space),
and “X” is the pixel of the fiber centerline, whose pixel location is an element of S. In Figure 2-5a, an “X”
in a blue box represents the current pixel that is being tracked, and the estimated fiber orientation
calculated from the template matching step is presented as a blue dashed line. For a given orientation, a
linear line propagation can be used to detect other locations aligned with the estimated orientation, which
forms a tracking path. The length of the linear line propagation is the same as the length of a fiber
template (i.e., 16 voxels). In the example illustrated in Figure 2-5a, a short linear line propagation length
is implemented for demonstration. Pixels on the linear line propagation (Figure 2-5a) are shaded in grey,
which narrows the search space, and only four “X”s, indicated in red, are selected for local orientation
update. These four locations are then used for image dilation to obtain the connected centerlines displayed
in the gray-shaded boxes in Figure 2-5b. The localized orientation is computed through principal
component analysis (PCA) of the selected coordinates. The eigenvector corresponding to the largest
eigenvalue indicates the direction of the largest spatial variation (i.e., the fiber orientation), which is
presented by a new blue dotted line in Figure 2-5c. The endpoint of the linear line propagation becomes
the new starting point for the tracking presented by the blue box in Figure 2-5c. This tracking procedure
continues until one of the terminating conditions is satisfied. The terminating process is initiated when
27
less than three voxel locations are identified on the tracking path. The algorithm will extend the linear line
propagation for another length of 16 voxels to enlarge the search region. In the first scenario, there are
less than three locations identified, so the tracking procedure is terminated immediately. The rational of
this termination condition is that the minimum required number of locations for PCA in 3D is three. In the
second scenario, more than three locations are identified, and the PCA captures an abrupt change in fiber
orientation. This implies that the tracking algorithm identifies another nearby fiber with different
orientations. After the termination of the tracking procedure, a unique label is then assigned to the
locations representing the fiber centerline, excluding locations identified during the termination process.
The labeled voxel locations are noted as visited locations, and a new search will be initiated at the first
unvisited voxel location of the set S until all voxel locations are visited. For congested fiber systems, the
change of local fiber orientation is monitored. An abrupt change in local fiber orientation is identified as a
possible crossing fiber. The tracking procedure continues by extending the linear line propagation along
the fiber orientation determined from the previous iteration. Voxels identified only in the second linear
line extension are then used for computing local orientation. When a smooth orientation change is
identified, voxels in the region of fiber intersection are then interpolated, and the tracking procedure
continues. In contrast, an abrupt orientation change will trigger the second terminating condition. By
tracking each fiber in segments, the gradual local orientation change for fibers with curvatures is
identified and the global fiber orientation and fiber curvature are then characterized (see Section 2.2.3.1).
Figure 2-5: Schematics of local fiber tracking and orientation update where “X”s present location of fiber
centers: (a) linear line propagation of orientation estimated from template matching in blue dotted line and
selected coordinates in red, (b) identification of connected components shaded in gray and PCA in a red
oval, and (c) local orientation update in dotted blue arrow and new starting point update outlined in the blue
box.
X
X X X
X X X
X X X
X X X
X X
X
X X
X
X X
X
X
X X
X
X X
X
X
(a) (b) (c)
LD
TD
28
2.2.3 Description of Microstructure
To consider the effect of fiber curvatures on the mechanical properties of the composite material,
Kunc et al. introduced a configuration to describe curved fibers [30], where the ensemble of curved fibers
with different morphologies can be characterized via tensor representation by summarizing the probability
density function of each configuration. Using the proposed fiber configuration and configuration
averaging approach, this paper extends the existing stress-strain constitutive equations [27, 30] to
calculate the stiffness tensor with the consideration of the local fiber length and local fiber curvature
distributions simultaneously, thereby providing a prediction of Young’s modulus. The following
subsections present detailed descriptions of fiber configuration, tensor representation, and stiffness tensor.
2.2.3.1 Configuration of a Single Fiber
A brief description of a single fiber configuration with and without curvature is presented in this
subsection. For a straight fiber, it can be assumed that the fibers are rigid cylinders with a uniform
diameter, as presented in Figure 6a, where the centroid of the fiber coincides with the origin of the
coordinate system. The fiber orientation is defined by a unit vector, �⃑⃑� , along the centerline of the fiber,
which can also be represented by the angles (𝜃, 𝜑) defined in Figure 2-6a with the spherical coordinate
system. The components of the vector �⃑⃑� can be written as follows:
�⃑⃑� = (𝑝𝐿𝐷 , 𝑝𝑇𝐷 , 𝑝𝑁𝐷) = (cos𝜃 , sin 𝜃 cos𝜑 , sin𝜃 sin𝜑). 2.2
For a curved fiber, Kunc et al. [30] presented a fiber coordinate system (�⃑⃑� , �⃑⃑� , �⃑� ) through the
transformation of three Euler angles, following the Euler ZYX (i.e., LD-ND-TD) convention, where
rotation is performed about an LD of angle α, then about the new ND (i.e., ND’) of angle β, and lastly
about the new TD (i.e., TD’’) of angle γ, as illustrated in Figure 2-6b. The defined fiber coordinate system
is presented in Figure 2-6c, where the centroid of the fiber coincides with the origin of the fiber
coordinate system (�⃑⃑� , �⃑⃑� , �⃑� ). Hence, �⃑⃑� is tangent to the fiber centerline at the fiber centroid, 𝑞 is in the
direction of the curvature radius, and 𝑠 is normal to both �⃑⃑� and �⃑⃑� . The components of vectors �⃑⃑� and �⃑⃑� can
be written as follows:
29
�⃑⃑� = (𝑝𝐿𝐷 , 𝑝𝑇𝐷 , 𝑝𝑁𝐷) = (− sin𝛽 , cos 𝛼 cos𝛽 , sin 𝛼 cos𝛽), 2.3a
�⃑⃑� = (𝑞𝐿𝐷 , 𝑞𝑇𝐷 , 𝑞𝑁𝐷)
= (cos𝛽 sin 𝛾 , cos 𝛼 sin𝛽 sin 𝛾 − sin𝛼 cos 𝛾 , sin𝛼 sin𝛽 sin 𝛾 − cos𝛼 cos 𝛾). 2.3b
The geometric shape of a single fiber is defined by two dimensionless parameters, namely the aspect
ratio, 𝜉 = 𝐿/𝑑, and the curvature ratio, 𝜂 = 𝐿/𝑅, where L is the length of the fiber, d is the diameter of
the fiber, and R is the radius of the curvature at the centroid of the fiber. The limiting case of a straight
fiber implies 𝜂 = 0.
Figure 2-6: Configurations of (a) straight cylindrical fiber, (b) Euler ZYX convention, and (c) fiber with
curvature.
To estimate fiber morphology from the reconstructed volume, the voxel locations of one fiber are
used, where the mathematical definition of the centroid is applied to determine the location of fiber
centroid. The orientation vector is then calculated by extracting the first principal component of the fiber
centroid voxel location and its neighboring voxel locations that are within a distance of 8 voxels (i.e., half
of the fiber template length) from the centroid. The fiber curvature vector is the unit vector from the fiber
centroid to the center of a fitted a sphere with the least-square approach, which is computed using all
voxel locations belonging to a fiber.
2.2.3.2 Tensor Representation of an Ensemble of Fibers
For a given material containing fibers with different configurations, the morphology of an
ensemble of fibers with their Euler angles (𝛼, 𝛽, 𝛾) and shape parameters (𝜉, 𝜂) can be represented by the
probability density function 𝜓𝐶(𝛼, 𝛽, 𝛾, 𝜉, 𝜂). The probability of finding a fiber with a given
configuration, e.g., (𝛼1, 𝛽1, 𝛾1, 𝜉1, 𝜂1), is defined by [30]:
30
𝑃(𝛼1 ≤ 𝛼 < 𝛼1 + 𝑑𝛼, 𝛽1 ≤ 𝛽 < 𝛽1 + 𝑑𝛽, 𝛾1 ≤ 𝛾 < 𝛾1 + 𝑑𝛾, 𝜉1 ≤ 𝜉 < 𝜉1 + 𝑑𝜉, 𝜂1 ≤ 𝜂
< 𝜂1 + 𝑑𝜂) = 𝜓𝐶(𝛼1, 𝛽1, 𝛾1, 𝜉1, 𝜂1) cos𝛽1 𝑑𝛼𝑑𝛽𝑑𝛾𝑑𝜉𝑑𝜂, 2.4
which is normalized as the following:
∫ ∫ ∫ ∫ ∫ 𝜓𝐶(𝛼, 𝛽, 𝛾, 𝜉, 𝜂)2𝜋
𝛼=0
cos𝛽𝜋/2
𝛽=−𝜋/2
2𝜋
𝛾=0
∞
𝜉=0
∞
𝜂=0
𝑑𝛼𝑑𝛽𝑑𝛾𝑑𝜉𝑑𝜂 = 1. 2.5
Assuming the independence between the Euler angles and shape parameters, 𝜓𝐶 can be separated into
rotation probability density function (𝜓𝑅), and shape probability density function (𝜓𝑆), and can be written
as 𝜓𝐶 = 𝜓𝑅(𝛼, 𝛽, 𝛾)𝜓𝑆(𝜉, 𝜂). Using even-order tensors to describe the rotation component can reduce
the computational costs and present a compact representation of the ensemble [38]. Advani and Tucker
[38] suggested that only second- and fourth-order tensors are required to estimate the material fourth-
order stiffness tensor (i.e., [Cijkl]); the second- and fourth-order orientation tensors (i.e., [aij] and [aijkl]),
curvature tensors (i.e., [bij] and [bijkl]), and mixed tensor (i.e., [cijlk]) are described as follows [30]:
𝒂𝟐 = [𝑎𝑖𝑗] = ∫ ∫ 𝑝𝑖𝑝𝑗𝜓(𝛼, 𝛽) cos 𝛽2𝜋
𝛼=0
𝜋/2
𝛽=−𝜋/2
𝑑𝛼𝑑𝛽, 𝑖, 𝑗 = 𝐿𝐷, 𝑇𝐷,𝑁𝐷, 2.6a
𝒃𝟐 = [𝑏𝑖𝑗] = ∫ ∫ ∫ 𝑞𝑖𝑞𝑗𝜓𝑅(𝛼, 𝛽, 𝛾) cos𝛽2𝜋
𝛼=0
𝜋/2
𝛽=−𝜋/2
2𝜋
𝛾=0
𝑑𝛼𝑑𝛽𝑑𝛾, 𝑖, 𝑗 = 𝐿𝐷, 𝑇𝐷,𝑁𝐷, 2.6b
𝒂𝟒 = [𝑎𝑖𝑗𝑘𝑙] = ∫ ∫ 𝑝𝑖𝑝𝑗𝑝𝑘𝑝𝑙𝜓(𝛼, 𝛽) cos 𝛽2𝜋
𝛼=0
𝜋/2
𝛽=−𝜋/2
𝑑𝛼𝑑𝛽, 𝑖, 𝑗, 𝑘, 𝑙 = 𝐿𝐷, 𝑇𝐷,𝑁𝐷, 2.6c
𝒃𝟒 = [𝑏𝑖𝑗𝑘𝑙] = ∫ ∫ ∫ 𝑞𝑖𝑞𝑗𝑞𝑘𝑞𝑙𝜓𝑅(𝛼, 𝛽, 𝛾) cos 𝛽2𝜋
𝛼=0
𝜋/2
𝛽=−𝜋/2
2𝜋
𝛾=0
𝑑𝛼𝑑𝛽𝑑𝛾, 𝑖, 𝑗, 𝑘, 𝑙 = 𝐿𝐷, 𝑇𝐷,𝑁𝐷, 2.6d
𝒄𝟒 = [𝑐𝑖𝑗𝑘𝑙] = ∫ ∫ ∫ 𝑝𝑖𝑝𝑗𝑞𝑘𝑞𝑙𝜓𝑅(𝛼, 𝛽, 𝛾) cos𝛽2𝜋
𝛼=0
𝜋/2
𝛽=−𝜋/2
2𝜋
𝛾=0
𝑑𝛼𝑑𝛽𝑑𝛾, 𝑖, 𝑗, 𝑘, 𝑙 = 𝐿𝐷, 𝑇𝐷,𝑁𝐷, 2.6e
where the subscripts “2” and “4” present the second- and fourth-order tensors, pi, and qi are components
of the orientation vector �⃑⃑� and the curvature vector �⃑⃑� , and 𝜓(𝛼, 𝛽) = ∫ 𝜓𝑅(𝛼, 𝛽, 𝛾)2𝜋
𝛾=0𝑑𝛾. For an
ensemble of fibers with known fiber orientation and curvature vectors, their Euler angles, (𝛼, 𝛽, 𝛾), can be
calculated through Equation 2.3, and the statistical distribution of the Euler angles is summarized to
31
formulate the probability density function of 𝜓𝑅(𝛼, 𝛽, 𝛾) and 𝜓(𝛼, 𝛽) with Equation 2.4. The tensors in
Equation 2.6 are calculated accordingly where 𝑝𝑖 and 𝑞𝑖 values are determined by the Euler angles
(𝛼, 𝛽, 𝛾). Hence, the tensor representation considers the statistical distribution of the fiber orientation and
fiber curvature, and fourth-order tensors are adequate to capture variations within a distribution [38].
2.2.3.3 Stiffness Tensor for an Ensemble of Fibers using Configuration Averaging
The fourth-order stiffness tensor, Cijkl, of composites containing curved fibers, is extended from
the orientation averaging approach that considers only 𝑎𝑖𝑗 and 𝑎𝑖𝑗𝑘𝑙, and is formulated as [30]:
𝐶𝑖𝑗𝑘𝑙 = 𝜇(𝛿𝑖𝑘𝛿𝑗𝑙 + 𝛿𝑖𝑙𝛿𝑗𝑘) + 𝜆𝛿𝑖𝑗𝛿𝑘𝑙 + 𝑘𝑝2(𝑎𝑖𝑗𝛿𝑘𝑙 + 𝑎𝑘𝑙𝛿𝑖𝑗) + 𝑘𝑞2
(𝑏𝑖𝑗𝛿𝑘𝑙 + 𝑏𝑘𝑙𝛿𝑖𝑗)
+ 2𝜇1(𝑎𝑗𝑙𝛿𝑖𝑘 + 𝑎𝑗𝑘𝛿𝑖𝑙 + 𝑎𝑖𝑘𝛿𝑗𝑙 + 𝑎𝑖𝑙𝛿𝑗𝑘)
+ 2𝜇2(𝑏𝑗𝑙𝛿𝑖𝑘 + 𝑏𝑗𝑘𝛿𝑖𝑙 + 𝑏𝑖𝑘𝛿𝑗𝑙 + 𝑏𝑖𝑙𝛿𝑗𝑘) + 𝑘𝑝4𝑎𝑖𝑗𝑘𝑙 + 𝑘𝑞4𝑏𝑖𝑗𝑘𝑙
+ 𝑘𝑠4(𝑐𝑖𝑗𝑘𝑙 + 𝑐𝑘𝑙𝑖𝑗), 𝑖, 𝑗, 𝑘, 𝑙 = 𝐿𝐷, 𝑇𝐷,𝑁𝐷,
2.7
where 𝛿 is the Kronecker delta and 𝜇, 𝜆, 𝑘𝑝2, 𝑘𝑞2
, 𝜇1, 𝜇2, 𝑘𝑝4, 𝑘𝑞4, and 𝑘𝑠4 are material constants with
the consideration of the shape probability density function, 𝜓𝑆(𝜉, 𝜂) [30] using the configuration
averaging method:
�̅� = ∫ ∫ 𝑛(𝜉, 𝜂)𝜓𝑆(𝜉, 𝜂)𝑑𝜉𝑑𝜂∞
𝜂=0
∞
𝜉=0
, 2.8
where �̅� represents all nine material constants in Equation 2.7, and 𝑛(𝜉, 𝜂) is extended from the material
constants for straight fibers, namely 𝜇𝑠, 𝜇0, 𝜆𝑠, 𝜁2, and 𝜁4, obtained from the Halpin–Kardos [39] and
Halpin–Tsai [40] equations with Young’s modulus (E) and Poisson’s ratio (ν). Interested readers should
refer to [40] and [30] for a detailed calculation of the material constants for materials with straight fibers
and curved fibers, respectively. For the limiting case of 𝜂 = 0 (i.e., 𝑅 = ∞ for a straight fiber), Equation
2.7 is reduced to the stiffness tensor for a transversely isotropic material, which is written as the
following:
32
𝐶𝑖𝑗𝑘𝑙 = 𝜇𝑠(𝛿𝑖𝑘𝛿𝑗𝑙 + 𝛿𝑖𝑙𝛿𝑗𝑘) + 𝜆𝑠𝛿𝑖𝑗𝛿𝑘𝑙
+ 𝜁2(𝑎𝑖𝑗𝛿𝑘𝑙 + 𝑎𝑘𝑙𝛿𝑖𝑗) + (𝜇0 − 𝜇𝑠)(𝑎𝑗𝑙𝛿𝑖𝑘 + 𝑎𝑗𝑘𝛿𝑖𝑙 + 𝑎𝑖𝑘𝛿𝑗𝑙 + 𝑎𝑖𝑙𝛿𝑗𝑘)
+ 𝜁4𝑎𝑖𝑗𝑘𝑙.
2.9
2.3 Results and Discussion
The following demonstrates the application of the proposed framework using the non-destructive
image-based technique to obtain the microstructure and mechanical property prediction of Young’s
modulus for short CFRP (SCFRP) and long CFRP (LCFRP) composites. The reconstruction and
analytical results (e.g., fiber orientation and Young’s modulus) are discussed and compared with the
experimental results.
2.3.1 Short CFRP (SCFRP) Composite with Curved Fibers
This research examined a SCFRP composite manufactured by PolyOne Corp. consisting of 40
weight percent (wt%) carbon fibers and Polyamide 66 as the polymer matrix was examined; this is a
special case of an injection-molded CFRP composite having short and straight carbon fibers. Each
dogbone SCFRP sample was machined from the as-received sheet, where the LD of the sample was
aligned with the mold fill direction (i.e., the LD of the plaque), and the gauge dimension was 10 mm × 1.8
mm × 2.5 mm (LD × TD × ND, i.e., length × width × thickness). The fiber volume fraction and fiber
length distributions were measured in reference [8] from the µXCT images and a pyrolysis experiment,
where the reported values from the second approach were adopted as a validation for this study. The
Young’s modulus of the SCFRP composite, measured through tensile tests reported in [8], was used to
validate the calculated modulus obtained in this study.
The original µXCT image, displayed in Figure 2-7, indicates that this material has a skin-core-
skin structure, where more fibers in both skin layers are aligned in the LD than in the core layer. Detailed
fiber characteristics in each layer were investigated through the proposed iterative template matching
reconstruction algorithm, where three individual cuboids were extracted from the same layer with a size
33
of 400 × 200 × 200 voxels (i.e., 0.520 mm × 0.260 mm × 0.260 mm) in the LD × TD × ND. Using the
same computation configuration mentioned in section 2.2.3, the computation time for each volume was
about 4 hours on average when three cores were used during the tracking phase, and each reconstructed
volume contained an average of 1780 ± 198 fibers.
Figure 2-7: Representative 2D µXCT reconstruction of skin-core-skin structure in the LD/ND plane; TD
is out of the plane.
The reconstructed volumes of each layer are displayed in Figure 2-8, where the fibers in all three
volumes have a non-uniformly oriented distribution, and the fibers in the skin layers have tended to align
in the LD (Figures 2-8a and 2-8c), the whereas fibers in the core layer have tended to align diagonally in
the LD-TD plane (Figure 2-8b). Using the fiber configuration defined in Section 2.2.3.1, the average
curvature ratio of the reconstructed volumes is 0.045 ± 0.009, implying that the radius of the curvature is,
on average, 22.2 times the fiber length. Therefore, the fibers in the SCFRP composites are essentially
straight fibers with an infinite radius of fiber curvature.
Figure 2-8: Representative reconstruction of SCFRP composite for (a) Skin layer 1, (b) Core layer, and (c)
Skin layer 2.
34
Using the straight fiber configuration (Figure 2-6a), [8] detailed the fiber length distribution from
the reconstructed volumes of Skin layer 1, Core layer, and Skin layer 2, where the average fiber length of
Skin layer 1, Core layer, and Skin layer 2 was 117 ± 1 µm, 104 ± 4 µm, and 118 ± 2 µm, respectively.
The fiber length distribution from the reconstructed volumes was validated via a pyrolysis experiment [8,
32]. Spatial representations of the color-coded fiber centerlines, with regard to the fiber angle between the
fiber centerline and the LD direction, θ, are presented in Figure 2-9, where Figures 2-9a and 2-9b are
color-coded fiber centerlines of the Core layer and Skin layer 1 cuboids, respectively. From visual
observation, the fiber orientation distributions for these two layers are significantly different. The
majority of the fibers in the Core layer have an orientation of 25°–30° (Figure 2-9b); whereas the majority
of the fibers in the Skin layer 1 have an orientation of 5°–10° (Figure 2-9d). The fiber orientation
distribution of the Core layer and the Skin layer 1 are presented in Figure 2-9c, where the average values
for the Core layer and the Skin layer 1 are 26°, and 13°, respectively. Through these quantitative
visualizations, the image-based reconstruction allows spatial characterization of the SCFRP composite.
Figure 2-9: Representative color-coded reconstruction of fiber orientations for (a) Core Layer and (b) Skin
Layer 1. (c) The fiber orientation distribution of the Core Layer and Skin Layer 1.
35
To compute the stiffness tensors for composites with straight fibers, only the fiber orientation
tensor is required for the calculation. Using the PCA approach according to the coordinate system defined
in Figure 2-6a, the second-order tensors of fiber orientations for the reconstructed volumes displayed in
Figure 2-8 are:
𝒂𝟐𝑺𝒌𝒊𝒏 𝒍𝒂𝒚𝒆𝒓 𝟏 = [ 0.83 0.01 0.02 0.01 0.07 0.00 0.02 0.00 0.10
], 2.10a
𝒂𝟐𝑪𝒐𝒓𝒆 𝒍𝒂𝒚𝒆𝒓 = [ 0.78 −0.02 −0.16−0.02 0.08 0.01−0.16 0.01 0.14
], 2.10b
𝒂𝟐𝑺𝒌𝒊𝒏 𝒍𝒂𝒚𝒆𝒓 𝟐 = [ 0.85 −0.01 0.06−0.01 0.04 0.00 0.06 0.00 0.11
]. 2.10c
As indicated in the second-order orientation tensors, 𝒂𝟐, the LD-LD component, 𝑎𝐿𝐷 𝐿𝐷 was 0.83,
0.78, and 0.85 for Skin layer 1, Core layer, and Skin layer 2, respectively, which is the largest value in the
second-order tensor. Therefore, the fibers in the SCFRP composites provide the highest reinforcement in
the LD direction. It should be noted that the orientation tensors of both skin layers are similar. The 𝑎𝐿𝐷 𝐿𝐷
from the 𝒂𝟐𝒄𝒐𝒓𝒆 𝒍𝒂𝒚𝒆𝒓 was 0.78, which is less than in the skin layers. This implies that the core layer has a
marginally smaller reinforcing efficiency in the LD than in the skin layers. The stiffness tensor for each
cuboid was calculated by Equation 2.9 for a given set of Young’s modulus (𝐸) and Poisson’s ratios (𝜈), in
which the superscript specifies the type of material (e.g., fiber), and the subscript specifies the directional
property (e.g., LD). Here, 𝐸𝐿𝐷𝑓𝑖𝑏𝑒𝑟
, 𝐸𝐿𝐷𝑚𝑎𝑡𝑟𝑖𝑥, are assumed to be 210 GPa, and 2.75 GPa, respectively, where
the values were stated in [8]. 𝜈𝑓𝑖𝑏𝑒𝑟, and 𝜈𝑚𝑎𝑡𝑟𝑖𝑥 are assumed to be 0.2 and 0.35, respectively, which are
typical values for carbon fiber and PA 66 [33]. Assuming the diameter of the fibers is six voxels (i.e., 7.8
µm), the average fiber volume fractions of skin and core layers were determined as 0.291 ± 0.020 and
0.290 ± 0.019, respectively, which are statistically consistent with the pyrolysis experiment (i.e., 0.286
and 0.284) through the two-sample t-test with a significance level of 0.05, as reported in ref. [8]. The
36
volume fraction calculated from the pyrolysis experiment was measured by weighing the mass of the
sample before and after heating and using the following formulation:
𝑉𝑓 =𝑚𝑓/𝜌𝑓
𝑚𝑓/𝜌𝑓 + (𝑚𝑜 − 𝑚𝑓)/𝜌𝑚, 2.11
where 𝑚𝑜 is the specimen’s original mass, 𝑚𝑓 is the specimen’s final mass after the pyrolysis, 𝜌𝑓 is the
density of the carbon fiber, and 𝜌𝑚 is the density of the matrix, Polyamide 66. To unveil the relationship
between the microscale morphology and associated macroscale mechanical properties, Young’s modulus
for each layer can be computed by:
𝐸𝐿𝐷 = 𝐶𝐿𝐷 𝐿𝐷𝐶𝑇𝐷 𝑇𝐷 − 𝐶𝐿𝐷 𝑇𝐷
2
𝐶𝑇𝐷 𝑇𝐷, 2.12
where 𝐶𝐿𝐷 𝐿𝐷, 𝐶𝑇𝐷 𝑇𝐷, and 𝐶𝐿𝐷 𝑇𝐷 are 𝐶𝐿𝐷 𝐿𝐷 𝐿𝐷 𝐿𝐷, 𝐶𝑇𝐷 𝑇𝐷 𝑇𝐷 𝑇𝐷, and 𝐶𝐿𝐷 𝐿𝐷 𝑇𝐷 𝑇𝐷, respectively from the
stiffness tensor [Cijkl]. This resulted in an average 𝐸𝐿𝐷 of 20.98 GPa, 14.78 GPa, and 21.05 GPa for Skin
layer 1, Core layer, and Skin layer 2, respectively. Additional quasi-static tensile tests according to ASTM
D638-14 [29] were performed in the previous study [8], where Young’s modulus of the Skin Layer was
measured as 21.9 GPa and the value was 13.8 GPa for the Core Layer. The estimation errors of the
proposed approach by comparing the experimental results were 4.20%, 7.10%, and 3.88% for Skin layer
1, Core layer, and Skin layer 2, respectively. Comparing to the estimation results reported in [8], the
proposed framework provided a more accurate prediction than that of using classical laminate theory.
Hence, the proposed framework provides a valid mechanical property estimation of the elastic modulus
for an SCFRP composite with non-uniform fiber orientation using the non-destructive image-based
technique.
2.3.2 Long CFRP (LCFRP) Composite with Curved Fibers
For fiber systems with curved fibers, an LCFRP composite was examined, which was
manufactured by BASF Corp. consisting of 40 wt% carbon fiber and PA66 as the polymer matrix. Each
LCFRP composite sample was machined from an injection molded oil pan part as described in [33] and
37
was cut to a dogbone shape with a gauge dimension of 6 ± 0.2 mm × 2.3 ± 0.1 mm × 2.4 ± 0.1 mm in LD,
TD, and ND, respectively. The previous study concluded Young’s modulus of studied samples was 29.3 ±
1.85 GPa [33]. The preliminary 2D µXCT image of the LCFRP composite, displayed in Figure 2-10,
illustrates that the fiber orientations are distinctively different along with the ND, implying a skin-core-
skin structure. From visual observation, the majority of fibers in the core layer are aligned in the TD,
whereas the specific orientation of the fibers in the skin layers requires in-depth characterization, as the
2D representations of the fibers in the skin layers are presented as ellipses with varied aspect ratios. Three
individual cuboids were extracted with a size of 400 × 250 × 250 voxels (i.e., 0.520 mm × 0.325 mm ×
0.325 mm) in the LD × TD × ND for fiber characterization and mechanical property prediction. Each
cuboid from the same layer was extracted from the same width and thickness location, with different
length locations (i.e., covering a length span of 1.56 mm). The size of the cuboids was limited in the ND
due to the thickness of each layer, and the average thickness of Skin layer 1, Core layer, and Skin layer 2
was 0.878 mm, 0.435 mm, and 1.105 mm, respectively.
Figure 2-10: Representative 2D µXCT reconstruction of skin-core-skin structure in the TD/ND plane. Out-
of-plane direction (i.e., LD) is the same as the direction of tensile loading.
A 3D reconstruction of each cuboid was employed with the proposed iterative template matching
algorithm, where the reconstruction time was approximately 4 hours, and each reconstructed volume
contained an average of 2093 ± 162 fibers. Each fiber was represented by the set of coordinates forming
38
its centerline (e.g., Figure 2-11a). The fiber orientation and curvature vectors, �⃑⃑� and �⃑⃑� , are defined
according to the coordinate system illustrated in Figure 2-6b. For example, Figure 11a is a singular fiber
with a curvature ratio of 0.80 and an orientation and curvature vector of �⃑⃑� = [0.90,0.04,−0.44] and �⃑⃑� =
[−0.36,0.63,0.69], respectively. Figures 2-11b–d show the color-coded fiber centerlines with respect to
fiber curvature ratio for Skin layer 1, Core layer, and the Skin layer 2, respectively. Representations of the
fibers with low (𝜂 = 0), medium (𝜂 = 0.2), and high (𝜂 = 0.5) curvature ratios are presented in Figure
11e; these were extracted from the Skin layer 2. From Figures 2-11b–d, no particular pattern is presented
in the spatial distribution, and the average curvature ratio, �̅�, for Skin layer 1, Core layer, and Skin layer 2
is 0.280, 0.251, and 0.266, respectively. Hence, the presence of fiber curvatures in the LCFRP composite
is confirmed. It is important to note that when two materials have the same orientation tensor, the material
with smaller 𝜂 (i.e., straighter fibers) has a larger stiffness modulus in the LD than the material with larger
𝜂. This implies that the elastic property in LD would be over-estimated if the curvature is not considered.
Figure 2-11: Representative reconstruction of LCFRP composite for (a) a single fiber, curvature ratio color-
coded, (b) Skin layer 1, (c) Core layer, (d) Skin layer 2, and (e) representative fiber of 𝜂 = 0, 0.2, and 0.5
from Skin layer 2.
39
The fiber orientation and curvature tensors were then computed by summarizing all the fibers in a
cuboid using Equations 2.3–2.6. The corresponding second-order orientation and curvature tensors of the
reconstructed volumes displayed in Figure 2-12 are:
𝒂𝟐𝒔𝒌𝒊𝒏 𝒍𝒂𝒚𝒆𝒓 𝟏 = [ 0.69 0.19 −0.06 0.19 0.17 −0.03−0.06 −0.03 0.14
] , 𝒃𝟐𝒔𝒌𝒊𝒏 𝒍𝒂𝒚𝒆𝒓 𝟏 = [ 0.15 −0.12 0.03−0.12 0.48 0.01 0.03 0.01 0.37
] 2.13a
𝒂𝟐𝒄𝒐𝒓𝒆 𝒍𝒂𝒚𝒆𝒓 = [ 0.35 −0.04 0.00−0.04 0.53 0.05 0.00 0.05 0.12
] , 𝒃𝟐𝒄𝒐𝒓𝒆 𝒍𝒂𝒚𝒆𝒓 = [ 0.33 0.02 −0.03 0.02 0.26 −0.05−0.03 −0.05 0.41
] 2.13b
𝒂𝟐𝒔𝒌𝒊𝒏 𝒍𝒂𝒚𝒆𝒓 𝟐 = [ 0.49 0.04 0.01 0.04 0.41 0.01 0.01 0.01 0.10
] , 𝒃𝟐𝒔𝒌𝒊𝒏 𝒍𝒂𝒚𝒆𝒓 𝟐 = [ 0.28 −0.03 −0.01−0.03 0.35 0.01−0.01 −0.04 0.37
]. 2.13c
As indicated in the second-order orientation tensors, 𝒂𝟐, the LD-LD component, 𝑎𝐿𝐷 𝐿𝐷, in Skin layer 1
and 2 is 0.69 and 0.49, respectively, which is the largest value in each tensor, providing the highest
reinforcement in the LD direction; whereas the largest tensor value in the core layer is 𝑎𝑇𝐷 𝑇𝐷 = 0.53,
indicating that the fibers in the core layers align with the TD axis. This trend is also observed in the
reconstructed volumes, illustrated in Figure 2-12. It can be noted that the 𝑎𝐿𝐷 𝐿𝐷 and 𝑎𝑇𝐷 𝑇𝐷 components
of Skin layer 2 are 0.49 and 0.41, respectively, and their difference (0.08) is considerably less than in Skin
layer 1 (0.52) and Core layer (0.18), which indicates that the majority of the fibers in Skin layer 2 are
aligned diagonally in the LD-TD plane (Figure 2-12c). In the curvature tensor, the
(𝑏𝐿𝐷 𝐿𝐷 , 𝑏𝑇𝐷 𝑇𝐷 , 𝑏𝑁𝐷 𝑁𝐷) for Skin layer 1 and 2 is (0.15, 0.48, 0.37) and (0.28, 0.35,0.37), respectively.
𝑏𝑇𝐷 𝑇𝐷 and 𝑏𝑁𝐷 𝑁𝐷 are the two largest values in the tensor, and their small differences indicate that the
fiber curvature vectors in the skin layers align diagonally in the TD-ND plane, thereby providing
reinforcement associated with fiber curvatures in the direction diagonally in the TD-ND plane. The
diagonal values of the core layer curvature tensor are 0.33, 0.26, and 0.41, such that the curvature vectors
in the core layer are aligned diagonally in the LD-ND plane.
40
Figure 2-12: Representative reconstruction of LCFRP composite in (a) Skin layer 1, (b) Core layer, and (c)
Skin layer 2.
To unveil the relationship of the microscale morphology of the LCFRP composites and its
corresponding mechanical properties, Equation 2.7 is used for computing the stiffness tensor of the
extracted cuboids with the values of moduli and Poisson ratios of carbon fiber and polymer matrix, PA 66
reported in [33]. The fiber volume fraction of the LCFRP composite is set to be 30% converted from the
fiber weight fraction of 40% [33]. To calculate the overall stiffness matrix of the material, the laminate
analogy derived in [39] is adopted considering the layer thickness, which was estimated as the following:
𝐴𝑖𝑗 = ∑ 𝐶𝑖𝑗𝑔
𝐺
𝑔=1
𝑎𝑔, 𝑖, 𝑗 = 𝐿𝐷, 𝑇𝐷,𝑁𝐷, 2.14
where 𝑎𝑔 is the thickness proportion of layer g, and G is the total number of layers (i.e., three in this
case). The overall longitudinal modulus is estimated as:
𝐸𝐿𝐷 = 𝐴𝐿𝐷 𝐿𝐷𝐴𝑇𝐷 𝑇𝐷 − 𝐴𝐿𝐷 𝑇𝐷
2
𝐴𝑇𝐷 𝑇𝐷. 2.15
The thickness fraction of Skin layer 1, Core layer, and Skin layer 2 was measured as 36.3%,
18.0%, and 45.7%, respectively, by random sampling at multiple longitudinal locations of µXCT images.
The calculated 𝐸𝐿𝐷 was 30.4 GPa, which is within the error margin of the experimental result from [33].
Without consideration of the curvature, the calculated 𝐸𝐿𝐷 would have been 32.56 GPa, which would lead
to an overestimation. It is important to note that the proposed framework can estimate the longitudinal
modulus for each layer as it is demonstrated for SCFRP composites; however, only the entire sample’s
longitudinal modulus is available for the validation of the LCFRP composites.
41
Furthermore, the localized 𝐸𝐿𝐷 was estimated by calculating the stiffness tensors of a smaller
volume from the cuboid; Figure 2-13 illustrates the spatial distribution of the calculated 𝐸𝐿𝐷 of a cuboid
extracted at the interface of Skin layer 1 and Core layer. Higher local 𝐸𝐿𝐷 values are located on the side of
Skin layer 1, whereas lower local 𝐸𝐿𝐷 values are located on the side of the core layer owing to the
different microscale morphologies in the skin and core layers. The gradual transition in the localized 𝐸𝐿𝐷
from the Skin layer 1 to the Core layer implies a gradual transition of the fiber orientation and curvature
tensors. The image-based reconstruction approach allows spatial characterization of the fiber orientation
and curvatures of an LCFRP composite thereby enabling the spatial characterization of the material
property without the requirement for executing a time-consuming finite element analysis (FEA)
simulation on the 3D model of the reconstructed geometry from the XCT.
Figure 2-13: Spatial distribution of calculated 𝐸𝐿𝐷 for the skin–core interface
2.4 Conclusions
This study proposed a framework using image-based techniques to quantitatively analyze fiber
characteristics for material mechanical property prediction of non-uniformly orientated fiber systems, i.e.,
injection-molded SCFRP and LCFRP composites. The internal microstructure was revealed through
µXCT, implying a skin-core-skin structure for both materials. Quantitative fiber morphologies (i.e., fiber
curvatures, orientation, length distributions) were characterized, and the curvature distributions indicated
that the SCFRP composite contained straight fibers, whereas curved fibers were present in the LCFRP
composite. Furthermore, the statistical and spatial characterizations of the fiber geometric properties
42
provided essential microstructural data for material property calculation (i.e., stiffness tensor and Young’s
modulus). The proposed 3D image-based mechanical property prediction of Young’s modulus yielded
reliable and robust results for both SCFRP and LCFRP composites.
This research demonstrates that microstructural characterizations extracted from µXCT images
can be implemented for spatial characterization and mechanical property predictions. The framework
leverages the numerical image processing techniques and local fiber-tracking approach to account for
non-uniformly orientated fiber systems with the straight or curved fibers. The statistical distributions of
the extracted fiber centerlines are calculated using tensor representations with a configuration averaging
approach, and the corresponding stiffness matrix and Young’s modulus estimation of the material are
evaluated by employing the Halpin–Tsai model and laminate analogy approach. The proposed framework
provides a valid estimation of elastic properties with image-based microstructural analysis, which enables
to replace the traditional FEA method.
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Int. Soc. Opt. Eng. 4387(2001) 95-102.
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47
Chapter 3: Spatiotemporal Characterization of 3D Fracture Behavior of Carbon-fiber-
reinforced Polymer Composites2
Abstract
This study proposed a spatiotemporal algorithm to quantitatively characterize the in-situ 3D
fracture behavior of two carbon-fiber-reinforced polymer (CFRP) composites (i.e., sheet molding
compounds and injection-molded CFRP composites) at the microscale. In-situ micro X-ray computed
tomography (µXCT) integrated with a tensile stage was applied to capture the 3D fracture evolution of
the CFRP composites, where the initiation and propagation of fracture features (e.g., fiber tip-end crack
and fiber/matrix debonding) were identified. In the proposed spatiotemporal algorithm, the 3D material
microstructure was first reconstructed from µXCT data using TomoPy, a Python-based open-source
framework. Fracture features were thereafter extracted by employing multiple image processing
techniques for quantitative analysis. A similar distribution of the fracture features obtained from the
spatiotemporal algorithm and the 3D strain obtained from the volumetric digital image correlation
demonstrated the feasibility of the developed spatiotemporal algorithm. Moreover, this algorithm was
demonstrated to be adequate to provide an in-depth and quantitative analysis of the crack opening, crack
thickness, crack orientation, and the volume of tip-end cracks, which provided insights into the
microscale failure mechanism and thus shed light on the improvement of failure criteria for CFRP
composites with complex microstructures.
3.1 Introduction
To reduce structural weight and improve fuel efficiency, carbon-fiber-reinforced polymer (CFRP)
composites are increasingly applied in various domains, such as aerospace, and automotive, owing to
their high modulus and high strength [1-4]. Recently, extensive studies have been conducted on different
2 The Contents of this chapter has been published as Pei S, Wang K, Li Y, Zeng D, Su X, Li J, Yang H, Xiao X.
Spatiotemporal characterization of 3D fracture behavior of carbon-fiber-reinforced polymer composites. Composite
Structures 203(2018):30-37.
48
aspects of CFRP composites, including material manufacturing [1,5,6], fracture feature characterization
[7-11], and performance and fracture modeling [12-14], wherein the fracture feature characterization has
intrinsic connections to anterior material manufacturing and succedent performance and fracture
modeling. Hence, accurate characterization of fracture feature initiation and propagation is important,
especially for CFRP composites with complex microstructures, e.g., sheet molding compounds (SMCs)
and injection-molded composites. Notably, the fracture feature initiation and propagation are highly
dependent on the microstructure of the local material, and thus the development of failure criteria for such
materials requires adequate information at the microscale in addition to macroscopic mechanical testing.
Two major classes of characterization methods have been proposed to determine the fractography
of CFRP composites, i.e., destructive and non-destructive imaging. For destructive imaging, optical
microscopy [7,8,15] and scanning electron microscopy [9,15-18] are frequently used to estimate the fiber
orientation and volume fractions of fiber and cracks, which are highly correlated to material fracture
behavior [7,19]. However, destructive imaging inherently possesses limitations such as possible
information loss, and damages or twisting of carbon fibers during sample preparation, and it is applicable
for postmortem analysis of the regions at which cracks or damages are visible. In contrast, non-
destructive imaging (e.g., X-ray diffraction [20], acoustic microscopy [21-25], and X-ray computed
tomography (XCT) [16,22,26-30]) avoids possible material damage and loss of information and thus
achieves more accurate and comprehensive fracture characterization compared with destructive imaging.
When combined with the digital image correlation (DIC) analysis method, the internal fracture
mechanisms of CFRP composites are revealed [7,9,16,31,32], and coupling XCT and DIC has attracted
increasing attention owing to the rapid advancements in image acquisition and image processing [33].
Tang et al. examined the tensile mechanical properties of a chopped carbon fiber chip-reinforced SMC
composite by employing two 3D DIC systems that captured the progression of in-situ strain fields of two
opposing surfaces during the tensile test [8]. Landis et al. applied image segmentation techniques to in-
situ scanned XCT images and calculated the progression of the volume fraction of damages (e.g., pores
49
and cracks) [29]. To capture both spatial and temporal progression of the internal deformation, studies
were conducted by integrating XCT and DIC techniques, wherein volumetric digital image correlation
(V-DIC) based on scanned XCT images was used to quantify the in-situ deformation [34]. However, the
accuracy of V-DIC was constrained by the image quality and the choice of subset size [35], and the
characteristics of fracture features, such as crack opening and tip-end crack volume occurring at the
microscale, were not captured. It is essential to develop an alternative approach based on high-quality
XCT images at the microscale (i.e., µXCT) to extract and measure the 3D deformation phenomena.
In the present study, in-situ µXCT tensile testing was performed on two CFRP composites, where
3D microstructures of the composites were reconstructed using a tomographic package developed in
Python [36]. Quantitative analysis of the fracture progression during the tensile tests was facilitated by a
spatiotemporal algorithm developed in this study, which employed multiple image processing techniques.
The remaining paper is organized as follows: Section 3.2 describes the materials and experimental
procedures; Section 3.3 presents the development of the image processing algorithm; Section 3.4 presents
case studies based on two CFRP composites; Section 3.5 concludes the paper.
3.2 Materials and Experimental Procedures
3.2.1 Materials
Two groups of CFRP composites were used in this study. The first group was a chopped carbon
fiber SMC manufactured via compression molding. The SMC material consisted of a thermoset matrix
resin with a glass transition temperature of 140 °C and 50.1 wt% of carbon fiber in the form of 1-inch-
long bundles. The tensile test samples were cut into a straight rectangular bar with a thickness of 2.55
0.05 mm and width of 1.80 0.10 mm. The second group was an injection-molded CFRP composite
manufactured using the BASF Ultramid compound with PA66 as the matrix polymer and 40 wt% of short
carbon fiber (~0.2 mm in length) as the filler. The test sample was cut into a straight rectangular bar with
a thickness of 3.10 0.10 mm and width of 1.50 0.20 mm.
50
3.2.2 Experimental Procedures
3.2.2.1 Tensile testing
The tensile testing was performed using an SML 1000 loading frame, which was a displacement-
controlled loading cell, at a constant rate of 0.01 mm/step. The capacity of the loading cell is 1000 lb
(4448 N). The experimental setup of the load frame and µXCT platform is presented in Figure 3-1a, and
Figure 3-1b, respectively.
Figure 3-1: Experimental setup: (a) the load frame and (b) µXCT platform.
3.2.2.2 Micro X-ray Computed Tomography (µXCT)
Micro-tomography beamline 2-BM-A at the Argonne National Laboratory, with a beam energy of
26 keV, was used in this study. For every increment of 50 N, the loading frame was held constant, and
thereafter, the load frame platform rotated allowing the beamline to scan the object. The time duration of
a µXCT scan was approximately 1 min. During each scan, 2160 slices of 2048 2048 grayscale images
were captured, in which each voxel was equivalent to 1.3 µm. The constituents and microscale features of
the CFRP composites (e.g., fiber, matrix, voids, and fracture features) were differentiated by the variance
in X-ray absorption [37]. TomoPy package [36] was utilized to reconstruct the 3D microstructure from
the µXCT data collected in reciprocal space. The detailed reconstruction procedure will be described in
Section 3.3.1.
3.3 Development of Image Processing Algorithm
The fracture features are characterized using the developed image processing algorithm, in which
µXCT scanned images are first enhanced and reconstructed using a post-processing Python software
package. Subsequently, volumetric image processing techniques including image segmentation and planar
51
projections are applied and the 3D fracture features (i.e., void volumes, fiber/matrix debonding, and fiber
pullout) are demarcated based on the histogram of pixel intensity.
3.3.1 Image Reconstruction Procedure
The scanned images are reconstructed using TomoPy, an open-source Python package that
processes and reconstructs tomographic data [37]. The reconstruction process is a two-step procedure, in
which the center of rotation (CoR) for each scanning is first determined by comparing the resolution of
partially reconstructed images with a pixel shifting, where the position having the least impairing effects
is selected as the CoR. In the second step, the reconstruction of the scanned image is automated in Python
using the predetermined CoR. Notably, each reconstructed 2D image is in 32-bit grayscale, which is
converted to 8-bit grayscale with the pixel intensity ranging from 0 (black) to 255 (white) to reduce disk
and memory usage.
3.3.2 Image Segmentation
Image segmentation isolates the object of interest (e.g., the fracture features) from a background
(e.g., fiber, matrix, and pre-existing defects) based on pixel intensity. The segmentation procedure in the
proposed algorithm involves three sub-steps, namely obtaining the negative, thresholding, and cleaning,
as summarized in Figure 3-2. The detailed explanation of each sub-step is presented in this section.
Figure 3-2: Image segmentation procedure.
In the original reconstructed 2D image (e.g., Figure 3-3a), the fibers are in bright/white colors, the
matrix is in grey colors, and the fracture features are in dark/black colors. To characterize the fracture
52
features and their progression intuitively, necessary negative transformation is performed to isolate the
fracture features, as shown in Figure 3-3b, where the negative of the image is obtained as follows:
𝐼𝑛𝑒𝑔 = 255 − 𝐼𝑜𝑟𝑖𝑔, 3.1
where 𝐼𝑜𝑟𝑖𝑔 and 𝐼𝑛𝑒𝑔 are the pixel intensity and negative of the original image, respectively. After the
negative transformation of the image, the fracture features become bright/white, and other constituent
elements are in darker colors.
Figure 3-3: Image segmentation procedure: (a) original image, (b) negative image, (c) pixel intensity
histogram, (d) Otsu’s multilevel thresholding segmentation with six levels, (e) segmented image, and (f)
post-processing image containing only fracture features.
From previous studies [33,38], it is known that two classes of segmentation algorithms can be
used to separate the object of interest from the background, namely global and local approaches. Global
approaches are performed based on the assumption that there are inherent differences between the object
and the background such as pixel intensity, whereas the local approaches focus on the boundaries of the
object of interest. As the pixel intensity is directly correlated to the density of the scanned object owing to
the nature of XCT, global approaches are selected to differentiate constituents in the composites.
53
In this study, a grey-level histogram was used to determine the thresholding level (a value
between 0 and 255). Figure 3-3c presents the grey-level histogram of the area of interest, and the
discrepancy between the fracture features and the background can be detected when the slope of the
histogram changes from negative to positive. This method analyzes the concavity of the histogram,
through which it identifies the thresholding level at the shoulder of the histogram by calculating the set-
theoretic differences of the histogram [38]. Mathematically, 𝐺 is denoted as the grey-level histogram, 𝑓𝑝
as the frequency of the histogram 𝐺 at each grey level 𝑝 = {0, 1,… , 255}, and �̅� as the smallest convex
hull that contains 𝐺. Let 𝑓�̅� be equal to the frequency of �̅� at each grey level 𝑝. The set-theoretic
difference is defined as 𝑓�̅� − 𝑓𝑝, which contains local maxima (i.e., thresholding values). Intuitively, the
frequency of grey-level values at the right shoulder increases as fracture features are observed; such a
change alters the concavities of the grey-level histogram and the value of 𝑓�̅� for the right shoulder will
increase. The local maxima of the set-theoretic difference occur when the derivative of the slope of the
histogram changes from negative to positive. This critical value is used to determine the thresholding
level and it separates the fracture features from the background. A representative segmented image based
on the pixel intensity histogram plot is presented in Figure 3-3e, where the thresholding level is
determined to be 210.
To validate the reliability of the thresholding level obtained using the pixel intensity histogram,
Otsu’s multilevel thresholding method [39] is conducted, which can be briefly described as follows. For a
given 8-bit grayscale image, after obtaining the negative 𝐼𝑛𝑒𝑔, each pixel, 𝑝, has an integer value between
0 to 255. The image is segmented into 𝑀 classes using 𝑀 − 1 threshold values denoted as 𝑡𝑘, 𝑘 =
1,… ,𝑀 − 1. The threshold values are determined by maximizing the intensity variance for each class as
follows:
{𝑡1∗, 𝑡2
∗, …𝑡𝑀−1∗ } = 𝑎𝑟𝑔𝑚𝑎𝑥
0<𝑡1< …<𝑡𝑀−1<255𝜎𝐵
2(𝑡1, 𝑡2, … , 𝑡𝑀−1), 3.2
where the intensity variance is defined as
54
𝜎𝐵2(𝑡1, 𝑡2, … , 𝑡𝑀−1) = ∑ 𝜔𝑘(𝜇𝑘 − 𝜇)2,
𝑀
𝑘=1
3.3
where 𝜔𝑘 is the portion of pixels belonging to class k, 𝜇𝑘 is the average intensity of the class k, and 𝜇 is
the average intensity of the image 𝐼𝑛𝑒𝑔. As the fracture features are in bright/white color, 𝑡𝑀−1 is the
thresholding level used to separate the fracture features from the background. Figure 3-3d is a
representative multilevel thresholding result, and the thresholding level determined using Otsu’s approach
is 209, which is close to the value obtained using the histogram method (210).
After segmentation, a few pixels that are not part of the fracture features are observed because of
the similar pixel intensity of some matrix and fracture features, as presented in Figure 3-3e. The
segmentation is thereafter improved by manually identifying the crack region image-by-image, and a final
segmented image is illustrated in Figure 3-3f.
3.3.3 Fracture Feature Visualization and Analysis
A novel spatiotemporal quantification based on the numerical computation of the 3D fracture
features is proposed, which not only presents the geometric complexity of the fracture features, but also
provides quantitative measurements of crack thickness, crack opening, and crack length which are
illustrated in Figure 3-4. Notably, the crack opening gradually decreases as it moves from the end of the
crack to the crack front. Inspired by 2D engineering drawings, the planar projections of the fracture
features are used to capture the geometric complexity.
Using the planar projections, the geometric complexity of the fracture features under each load is
captured. Crack parameters such as the crack opening and crack thickness are measured and
superimposed onto the planar projections using a colored contour. By comparing the progression of these
projections under different loads, the in-situ 3D visualization algorithm addresses the shortcomings of
traditional 2D µXCT images by revealing the morphology of the fracture features in both spatial and
temporal domains; more importantly, this algorithm involves detailed and quantitative measurements of
the fracture features in the spatiotemporal domain.
55
Figure 3-4: Illustration of Mode I fracture and the related crack characteristics.
3.3.4 Volumetric Digital Image Correlation (V-DIC)
To validate the developed image analysis algorithm, the characteristic of fracture features
obtained from the image analysis algorithm was compared with the in-situ 3D strain field of the test
samples obtained from the V-DIC algorithm. Note that the V-DIC algorithm, as an extension of 3D DIC,
can be used to quantify the internal deformation of test samples by calculating the correlation between
deformed and undeformed images [40]. The correlation coefficient is minimized when a location in the
undeformed image is successfully identified in a deformed image, and thereafter, the material
deformation can be tracked using an optimization process to determine the smallest correlation
coefficient. Notably, several criteria can be used to calculate the correlation coefficient based on the
image intensity, such as the summation of square deviation (SSD), cross-correlation, and summation of
absolute differences [40]. For each formulation criterion, each image should be divided into L subsets. In
this study, the SSD criteria were used, where the undeformed and deformed image intensities are denoted
as 𝐼𝑟𝑒𝑓 and 𝐼𝑑𝑒𝑓, respectively; each 𝐼𝑟𝑒𝑓 and 𝐼𝑑𝑒𝑓 was divided into 𝐼𝑟𝑒𝑓(𝑙)
and 𝐼𝑑𝑒𝑓(𝑙)
(l = 1, …, L), and the
corresponding correlation coefficient (CSSD) is expressed as follows:
𝐶𝑆𝑆𝐷 = ∑(𝐼𝑟𝑒𝑓(𝑙)
− 𝐼𝑑𝑒𝑓(𝑙)
)2
𝐿
𝑙=1
3.4
and the optimal displacement vector 𝒅𝒐𝒑𝒕 is determined by optimizing:
𝒅𝒐𝒑𝒕 = 𝑎𝑟𝑔𝑚𝑖𝑛 ∑(𝐼𝑟𝑒𝑓(𝑙) (𝒙 + 𝒅) − 𝐼𝑑𝑒𝑓
(𝑙) (𝒙))2
,
𝐿
𝑙=1
3.5
56
where 𝒙 is a 3D vector indicating the location of a pixel in the subset image and 𝒅 is the displacement
vector from 𝒙. Thus, the displacement field was calculated based on the local variation between the
undeformed and deformed images.
3.4 Case Study
Based on the developed image processing algorithm, two case studies are described in this section
to reveal the in-situ fracture behavior of the SMC and BSAF CFRP composites under various tensile
loads.
3.4.1 SMC CFRP Composite
By applying the image reconstruction procedure described in Section 3.3.1, the CoR is first
determined by examining partially reconstructed 2D images via pixel shifting. Subsequently, the
reconstruction of the scanned images is automated using Python TomoPy, and the default reconstruction
is based on the width–thickness plane (e.g., Figure 3-5), which reveals the microstructures of the sample
in the cross-sectional area, consisting of the boundary of fiber tows (bright/white color) and matrix rich
region. A typical 3D reconstruction of the SMC is presented in Figure 3-6, from which the packing of
fiber tows, fiber orientation, length of the fiber, and cracks can be observed.
Figure 3-5: Representative 2D reconstruction of scanned SMC composites.
57
Figure 3-6: Representative 3D reconstruction of scanned SMC composite.
Other 2D planar reconstructions are converted as shown in Figure. 3-7, where Figure 3-7a
indicates the 2D orientation of each fiber tow and a pre-existing crack (dark/black color) as labeled. With
an increase in the quasi-static mechanical load, new cracks are observed by examining the images slice-
by-slice, and typical cracks are identified as indicated in Figure 3-7e. Representative fracture features
(i.e., cracks in this case) under different engineering tensile stresses in the width–length plane of the
sample are presented in Figures 3-7b-d. Notably, the maximum engineering tensile strength (201 MPa) is
different from that in the macroscopic test (~250 MPa) because of the geometric limitation of scanned
specimens, which are smaller than the representative volume of this material. From the 2D reconstruction,
it can be observed that cracks are not apparent under visual examination, and thus, these cracks should be
extracted by applying image segmentation. Although the images in Figure 3-7 are scanned at the same
thickness, the lower half of Figure 3-7a separated by a white dotted line is slightly different from Figures
3-7b-d. By examining several images (four slices in this study) before and after the image shown in
Figure 3-7a, the exact images of the lower half are determined. This indicates that there is a displacement
shifting in the thickness direction (~5.2 µm) under tensile loading, i.e., the deformation through the
thickness is not uniform. After loading, the nonuniform deformation is not significant as indicated by
Figures 3-7b-e. As the loading direction is parallel to the length (z) axis, these cracks are caused by mode
I fracture, in which the crack opening (the distance between fracture surfaces) is parallel to the z-axis.
These 2D images also indicate that the progression of fracture features follows the orientation of the fiber
58
tow, and slight fiber breakage is observed, which indicates a weak adhesion between the fiber and matrix,
and consequently, debonding is the main fracture mechanism.
Figure 3-7: 2D reconstruction of SMC under different engineering stresses: (a) 0 loading, it shows a pre-
existing crack within the material; (b)-(e) images at the same location at 168 MPa, 176 MPa, 194 MPa, and
201 MPa, respectively.
Figure 3-8 presents a post-fracture image in the thickness (y)–length (z) plane. From the
fractographic analysis, it can be deduced that the initial mode I fracture reaches the boundary of a fiber
tow, and thereafter, the crack propagates following the path along with the interface between two fiber
tows (called crack deflection). Notably, the crack deflection is caused by the fiber tow with different fiber
orientations, where the fiber tow acts as an obstacle for crack propagation [6], and the crack travels
between the fiber tows following the path of the smallest energy consumption. Consequently, the crack
becomes a Mode II fracture, which leads to delamination between fiber tows, as illustrated by white
dotted lines. This fracture behavior is consistent with the findings by other researchers of SMC CFRP
composites, where the brittle fractures are initiated at the sample surface and thereafter transformed into
delamination of fiber tows as the fracture path follows the path of the least resistance (i.e., location with
the smallest energy consumption) [7].
59
Figure 3-8: Representative post-fracture image illustrating the fracture mechanisms, and the white dotted
lines indicate the fracture path.
The fracture mechanisms of SMC CFRP composites are studied by comparing 2D scanned
images; however, quantitative measurements of crack propagation based on a visual comparison are not
conclusive. By applying the segmentation method described in Section 3.3.2, the fracture features are
extracted, and a representative 3D view of cracks in the SMC sample is presented in Figure 3-9. It is
observed that the SMC fracture features have multiple bifurcations, the crack front is discontinuous, and
the fracture surface is irregular. Hence, traditional crack characterization parameters such as overall crack
opening, crack front growth rate and crack orientation fail to reflect such detailed and complex
information on the irregular cracks of the SMC samples.
Figure 3-9: Representative cracks in SMC CFRP composites in 3D.
Using the proposed fracture feature analysis method mentioned in Section 3.3.3, the
spatiotemporal analyses of the fracture features from Figure 3-9 are presented in Figures 3-10a-b. Figure
3-10a illustrates the spatiotemporal width–thickness planar analysis, where the projections indicate the
spatial progression of the crack front and the crack opening under increasing static load (i.e., temporal
60
changes), and the quantitative value of crack opening is indicated by the color contour. The discontinuous
crack front indicates that the cracks are initiated at multiple locations. With the increase in tensile load,
these cracks become enlarged and connected, resulting in a complete crack. The crack opening (i.e., the
color contour) is larger at the edge of the sample (i.e., left side) and gradually reduces in the width
direction. However, the crack opening is not uniformly distributed in the thickness direction contrary to a
traditional Mode I fracture owing to the complex fiber orientation in the SMC samples.
The temporal projection of the width (x)–length (z) planar analysis (Figure 3-10b) reveals the
growth of the crack length and the deflection of the fracture features. Upon examining the geometric
relationship of the projection, the fracture features are observed to have two orientations. The one with the
shallower angle from the width (x) axis is considered the main crack as it develops under a lower load
(starting at 168 MPa), and bifurcations occur from this main crack. At 176 MPa, the projection indicates
the beginning of the bifurcation and the development of another crack with a larger angle from the x-axis.
Additionally, it is observed that the bifurcations have the same orientation as the smaller crack located
above the main crack. This coincidence indicates the crack deflection. Notably, the bifurcation occurs at
the position with the thickest crack (i.e., with the red color contour). As cracks travel following the path
of the lowest energy consumption, the main crack first advances in both width and thickness directions
within a fiber tow, and once it reaches the boundary of the fiber tow, small cracks are deflected to a
nearby fiber tow.
61
Figure 3-10: Spatiotemporal crack analysis result of SMC sample: (a) width (x)–thickness (y) projections
indicating the progression of crack front and crack opening, and (b) width (x)–length (z) projections
indicating the progression of crack length, bifurcation, and crack thickness.
3.4.2 BASF CFRP Composite
The second case study is performed using an injection-molded BASF CFRP composite to verify
the applicability of the developed algorithm to different CFRP composites, as the material characteristics
of the BASF CFRP composite (e.g., fiber length, fiber orientation, and manufacturing methods) are
different from those of the SMC CFRP composite used in the first case study. For BASF CFRP composite
samples, a curved edge with a radius of 2.34 0.10 mm is prepared at the tensile sample gage area to
ensure that the fracture occurs in the µXCT scanning window. The same image processing algorithm
(including CoR determination, 2D and 3D reconstruction, and fracture feature extraction and
characterization) is applied to the BASF CFRP composite. The partially reconstructed 2D and 3D images
are shown in Figures 3-11a-b, in which the orientation of the fibers exhibits a random pattern, and the
fracture features (i.e., the tip-end crack in this case) are discontinuous and scattered. This fracture
behavior is caused by fiber pullout, resulting in the tip-end crack at the ends of short fibers. Owing to the
nature of this type of crack, analyzing the crack opening or crack thickness deviates from the true purpose
of characterizing the spatiotemporal behavior of the fracture features of this CFRP composite.
62
Figure 3-11: Reconstruction of injection-molded BASF sample: (a) 2D scanned image exhibiting fracture
features (fiber pullouts) and (b) 3D reconstructions under different tensile loads indicating the progression
of tip-end crack.
An appropriate approach to quantify the fiber pullout is to analyze the tip-end crack volume and
thereafter use the volume changes to evaluate the fracture feature progression as presented in Figures
3.12a-d. From the width and length planar projection, tip-end cracks are initiated along the curvature
owing to stress concentration. These cracks gradually progress toward the straight edge in the width
direction as the tensile load increases, indicating that the tip-end cracks evolved from the side of curvature
to the straight edge. Notably, this type of evolution is only observed in the region with the narrowest
width, and the spatial distribution of the fracture feature is not uniform as shown in Figure 3-12d at 135
MPa. More tip-end cracks are observed in the lower half of the images indicating more fiber pullout in
this region, which is influenced by the distribution of fiber orientation and fiber length within the BASF
samples. This heterogeneity is consistent with the V-DIC strain analysis of the sample at the same loading
condition as indicated by Figure 3-12e, where the subset and step size are set to be 15 and 7, respectively,
and a Gaussian filter with a size of 10 is used to smooth the strain calculation. From Figure 3-12e, the
color contour of the strain distribution resembles the color contour of the tip-end crack volume, which
confirms the validity of the proposed image segmentation and visualization toolbox to characterize the
fracture features of CFRP composites.
63
Figure 3-12: Spatiotemporal void analysis result of BASF sample: (a)-(d) width (x)–length (z) projections
indicating the progression of the tip-end crack volumes at 106 MPa, 114 MPa, 124 MPa, and 135 MPa,
respectively; (e) corresponding V-DIC strain calculation at 135 MPa.
In summary, in-situ µXCT images indicate that the primary fracture features of the SMC sample
are mode I fractures within a fiber tow. With an increase in tensile load, mode I fractures lead to mode II
fractures, resulting in delamination between fiber tows. The primary fracture features of injection-molded
BASF samples are tip-end crack left by fiber pullout. The progression of these different fracture features
is extracted and thereafter quantified using the proposed procedure, which includes image segmentation
and a spatiotemporal 3D visualization tool. This algorithm provides an in-depth and quantitative analysis
of crack opening, crack thickness, crack orientation, and tip-end crack volume. Through quantitative
analysis, the initiation and progression of different types of fracture features are characterized, which
might be directly used to derive a failure criterion. Owing to the limitation of the sample dimensions
allowed in the in-situ µXCT testing (smaller than the representative volume for such materials), the
observed failure mechanisms are inevitably subject to the boundary effect, and thus, quantitative
measurement based on microscale representative volume models is necessary to validate the derived
failure criteria.
64
3.5 Conclusions
This study proposed a novel spatiotemporal algorithm to quantitatively represent and characterize
the in-situ 3D fracture behavior of CFRP composites, which leveraged the advancements in image
acquisition and image processing technologies. The in-situ 3D fracture behavior was accurately captured
using µXCT, and the 3D fracture features were extracted by applying a series of image processing
algorithms including tomography reconstruction, image segmentation, projection method, and
spatiotemporal visualization. This study developed an image-data-driven approach for the representation
and characterization of failure mechanisms of CFRP composites. The proposed spatiotemporal algorithm
accounted for the spatial complexity and dimensions of the fracture features (i.e., crack opening, crack
thickness, and tip-end crack volume) and presented the temporal progression of these fracture features,
which was overlooked by the traditional 2D image analysis.
Fracture mechanisms for both the SMC and BASF samples were examined based on the
developed algorithm. Experimental results revealed that the mode I fracture within a fiber tow was the
primary failure mechanism of the SMC samples. Once the fracture traveled to the boundary of the fiber
tow, it transitioned into a mode II fracture owing to fracture deflection to delaminate the fiber tows. For
the BASF samples, fiber pullout was the primary fracture mechanism and it left numerous tip-end cracks.
In-situ µXCT revealed the fracture mechanisms of both CFRP composites at the microscopic level, which
facilitated the accurate characterization of the failure mechanisms of CFRP composites.
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69
Chapter 4: Process-structure-property Analysis of Short Carbon Fiber Reinforced
Polymer Composite via Fused Filament Fabrication
Abstract
This study investigates the effects of process conditions on the inherent variabilities in fused
filament fabrication (FFF) of short carbon-fiber-reinforced Nylon-6 composites, where the sources of
uncertainty and their adverse effects on microstructures and Young’s modulus are quantified.
Microstructural characteristics such as fiber volume fraction, void volume fraction, and their spatial
distributions are first extracted via image-based data analytics, and then their uncertainties are quantified
by the analysis of variance. A Monte Carlo simulation is introduced to enrich the datasets for analyzing
uncertainty propagation from micro-level (microstructures) to macro-level (mechanical property). A
modified Halpin-Tsai model with the consideration of fiber and void distributions is developed to
quantify the propagated uncertainties on Young’s modulus, which are further validated through quasi-
static tensile tests. This study examined the process-structure-property relationship of FFF samples and
quantified the underlying variations in both micro- and macro-levels.
4.1 Introduction
Fused filament fabrication (FFF), one of the technique of additive manufacturing (AM), has been
widely implemented to fabricate polymer structures owing to its affordability, high process speed,
minimal material waste, and ease of material change [1-2]. The polymer filament is fed through a heated
hot end to reach a semi-liquid state, and it is then deposited on a build surface or previously printed layer
through a nozzle. Coupling with the movement of a build surface and the extruder head, extruded material
can be deposited layer by layer in 3D space as programmed, forming a desired structure [3]. The
simplicity of the FFF process enables freedom of design and mass customization [2], which has attracted
rapid commercial development of a wide range of FFF 3D printing machines that are suitable for large-
scale production, laboratory studies, and personal/office use [4]. Thermoplastic polymers, such as
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acrylonitrile butadiene styrene (ABS) [5-7], polylactic acid (PLA) [5,7,8], polyamide (PA) [9], and
polycarbonate (PC) [10] are commonly used for FFF, and their limited mechanical properties hinder their
potentials for wide applications as load-bearing structural components. Therefore, in recent years, the
development of fiber-reinforced filament for FFF has received increasing attention, where promising
results of strengthening the mechanical properties of FFF samples have been demonstrated [11-16] by
infusing glass fibers [13] and carbon fibers (CFs) [15-19].
The mechanical properties of fiber-reinforced composite (FRC) fabricated via FFF highly depend
on the process-induced microstructure (e.g., the volume fraction of fiber and voids and fiber orientation).
Compared with the counterparts from conventional manufacturing processes such as injection molding
and compression molding, FRC in FFF often exhibits a more complicated process-structure-property (P-
S-P) relation. Tekinalp et al. fabricated ABS-CF filament with 10, 20, 30, and 40 weight percent (wt%) of
CF and demonstrated an approximate increase of 115% in tensile strength with 40 wt% CF and 700%
increase in modulus with 30 wt% CF, compared to neat-ABS FFF parts [15]. Ning et al investigated the
effect of fiber content on the tensile and flexural property of ABS-CF composite with 3, 5, 7.5, 10, and 15
wt% of CF, and concluded that 7.5 wt% CF content resulted in the highest improvement (i.e., 31.6%) in
tensile modulus and 5 wt% CF content yielded the highest tensile strength [16]. This variation can be
attributed to the variations in fiber orientation, the interfacial bonding between fiber and polymer
composite, interfacial bonding between adjacent layers, and the void formation [12,21]. Zhang et al.
examined the interfacial bonding strength between polymer matrix and fiber through in-plane shear and
double notch shear tests of ±45° short CF-ABS FFF parts, and concluded that matrix fracture, fiber pull-
out, and fiber-matrix interfacial debonding were the dominating failure modes [22]. Abbott et al. assessed
the bond strength between layers and within layers of FFF parts using ABS filament, where contact length
between each print path was measured [23]. It was found that greater contact length resulted in higher
tensile strength, and a plateau in tensile strength was achieved when a normalized contact length is greater
than 0.6 [23]. Many studies have observed the porosity of FFF fiber-reinforced composite with a range of
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porosities [15,16,18,22]. Ning et al. examined the effects of process parameters on tensile properties and
concluded that print temperature was the primary factor for pores formation [18]. Zaldivar et al.
investigated the effect of initial moisture content in the ULTEM® 9085 filament on microstructure and
found a 41% decrease in failure strength for 0.16% of moisture in the filament [24]. The moisture content
in the filament vaporized when the filament was extruded resulting in porosity in printed parts [4, 24].
Despite many studies that reported individual aspects of P-S-P relation, few of them focused on
establishing a comprehensive P-S-P relation, which would be capable of predicting the variations of
mechanical properties based on the process condition in FFF. Khanzedeh et al. proposed a self-organizing
map (SOM) approach to quantify the geometric deviation of FFF parts using point cloud data from a
desktop 3D laser scanner, where different SOM clusters were identified for different FFF process
conditions [25]. Quinsat et al. proposed a multi-scale discrimination method to characterize the surface
geometry (internal and external) by calculating the relevant internal area measured from 3D computer
tomography images and concluded that the process parameter is relevant to surface topographies [26]. Lu
et al. proposed a physics-based compressive sensing approach to monitor the 3D temperature field
variations during FFF, and a Gaussian process uncertainty quantification approach was developed to
predict systematic error from the reconstruction of sensing data [27]. Papon et al. investigated the effect
of process parameters (print temperature, bed temperature, and print speed) on dimensional accuracy in
FFF parts using polylactic acid/carbon fiber filaments and identified optimal process conditions for
minimum dimensional misalignment. Then they characterized the randomness of void content for the
optimized process using an uncertainty quantification technique and incorporated the predicted void
content to predict laminate axial load distribution using classic laminate theory [28]. However, the effect
of process parameters on microstructural variations was not examined, which impeded the fundamental
understanding of the FFF-fabricated FRP composites and consequently inhibits their deployment in the
industrial applications.
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In the present study, a P-S-P approach was employed to understand the impact of process
parameters on the FFF printed CFRP composite from the micro level to the macro level by integrating
image-based statistical analysis with physics-based modeling. The microscopic variations of CFRP
composite were examined in terms of fiber volume fraction, void volume fraction, and their spatial
variations for each process condition, and a data-driven Halpin-Tsai model was proposed to accurately
predict the longitudinal modulus of FFF samples; the prediction results were validated through the quasi-
static tensile test. The remainder of this paper is organized as follows: Section 4.2 describes the material
and experimental procedures; Section 4.3 presents the methodology of the proposed P-S-P study;
experimental and analytical results are discussed in Section 4.4; and Section 4.5 concludes this study.
4.2 Experimental Procedure
4.2.1 Filament and Preconditioning
Short carbon fiber reinforced polymer (SCFRP) composite filament was obtained from 3DTECH,
MI. The commercial filament with a diameter of 1.75 mm consists of 20 wt% of short carbon fibers and
polyamide nylon matrix. It is generally accepted that water uptake in FFF polymer filament should be
taken with great care because the moisture content in the filament may affect the quality of FFF samples
owing to the change in flow characteristics and increase in porosity during high-temperature extrusion
[29]. Therefore, the effect of moisture content in the filament was investigated. The baseline material,
low-moisture-content filament, was the as-received filament, and it was stored in a sealed container to
prevent ambient moisture absorption. The high-moisture-content filament specimens were submerged in
distilled water at room temperature for 48 hours. Once the specimens were removed from the distilled
water, their surface water was wiped off before printing. The weight change of high-moisture-content
filament was measured to be 1.92%, which is approximately equivalent to the moisture content change for
the filament being exposed in standing air with 50% relative humidity for a prolonged period (i.e., 2000
hours) [30].
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4.2.2 Printing Procedure and Design of Experiment
FFF-AM specimens were printed according to ASTM D638-14 type V as illustrated in Figure 4-
1a [31]. All specimens were manufactured using a commercial desktop FFF unit (LulzBot Mini from
LulzBot, CO) as illustrated in Figure 4-1b. The raster angle of the specimens was set to be 0. A full-
factorial design of the experimental procedure was used to investigate the various process parameters as a
function of the selected print parameter which is presented in Table 4-1. The printing parameters (i.e.,
extruder temperature, print speed, and layer height) were selected according to the recommendations
provided by the filament supplier. It was found that the print quality of low-moisture-content filament
with an extruder temperature of 240 C was poor, where an insufficient material flow was identified.
Thus, the extruder temperature for the low-moisture-content filament was adjusted to 250 C. Therefore,
the extruder temperature was not an independent factor and it was nested under the filament moisture
content factor. The print bed temperature was set for 105 C as recommended by the supplier of the
filament. Five replicates were printed for each combination, where three samples were used to measure
tensile properties and two samples were used to investigate the microstructure variations.
Table 4-1: Print parameters of a full-factorial DOE.
Factor Low Level High Level
Filament Moisture Content Low (denoted as “Dry”) High (denoted as “Moist”)
Extruder Temperature (C) 240 (high moisture filament)
250 (low moisture filament) 270
Print Speed (mm/s) 20 60
Layer Height (mm) 0.2 0.3
The software accompanying the FFF printer, CURA, was employed to control the slicing and
determine the scan sequence during the printing process. The print path for each layer is illustrated in
Figure 4-1c with solid color lines, where the starting and ending of a continuous extrusion are indicating
by green and red arrows, respectively. The printer first generates an outline of the specimen referred to as
a “wall” (i.e. yellow solid lines in Figure 4-1c) and then fills the inner component referred to as “infill” in
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the order of white, blue, and orange solid lines as illustrated in Figure 4-1c. The print head then returns to
the starting point of the outline and repeats for the next layer.
Figure 4-1: (a) 2D CAD drawing (all dimensions in mm) of printed specimen, (b) schematic of FFF process,
(c) print path (solid color lines) for each layer with green and red arrows indicating the start and end of the
continuous extrusion with an extrusion order of yellow-white-blue-orange, (d) schematic of the region of
length-width cross-sectional area, (e) approximate locations for the width-thickness cross-sectional area
and their labels, and (f) labels of width and thickness locations for cross-sectional area of ND-TD plane.
4.2.3 IR Camera Temperature Measurement
Print path temperature was observed for printed specimens using an IR camera (FLIR A325sc,
FLIR Systems, Inc.) equipped with an uncooled Vanadium Oxide microbolometer detector lens with a
temperature range of 0 C to 350 C. The captured images were approximately 80 60 mm with a
resolution of 320 240 pixels at a frame rate of 60 Hz.
75
4.2.4 Optical Microscopy for Image-based Characterization
The microstructure of the printed specimens was examined using optical microscopy (Nikon
Eclipse MA 100L) with a 10 objective. The captured images have a field of view of 655 µm 490 µm
with a resolution of 0.64 µm/pixel. The samples for microscopic images were cut from the gauge section
of the specimens to visualize one length-width cross-sectional area (as shown in Figure 4-1d) and four
width-thickness cross-sectional areas (as shown in Figure 4-1e). Captured images were stitched using the
ImageJ Stitching plug-in for a complete cross-sectional area of the infill. The minimum dimensions of the
length-width and width-thickness cross-sectional area of the infill are 10240 4096 pixels and 4096
4096 pixels, respectively. An image analysis script was developed in Matlab® to measure fiber volume
fraction, fiber orientation, and void volume fraction. A detailed description of the process is presented in
Section 4.3.1.
4.2.5 Quasi-static Tensile Testing
The quasi-static tensile tests of all specimens were carried out using an Instron Electro E3000
instrument at a constant crosshead speed of 2 mm/min at room temperature. All tensile specimens were
stored in an air-tight container immediately after they were removed from the print bed until the tensile
experiment to prevent any ambient moisture absorption.
4.3 Analysis Methodology
A P-S-P approach was implemented to analyze the uncertainties in the FFF-AM process as
summarized in Figure 4-2. An image-based statistical analysis approach was developed to extract physical
features such as void volume fraction, fiber volume fraction, and fiber orientation from the optical
microscopy. The effects of process parameters on the structure and its variations were investigated using
an uncertainty quantification approach, where a full-factorial analysis of variance (ANOVA) was
implemented. The relationship between the structure and property was then analyzed using the Halpin-
Tsai model with a data-driven parameter calibration procedure to account for the effect of the void
76
volume fraction in the printed specimens, and the predicted longitudinal modulus of the FFF samples was
validated through the experimental result. A detailed description of the images-based statistical analysis
and modified Halpin-Tsai model for the FFF-AM process is presented in the following subsections.
Figure 4-2: The flowchart P-S-P analysis for the short carbon fiber reinforced polymer in this study.
4.3.1 Image-based Uncertainty Quantification in FFF-AM of CFRP Composites
The complete workflow of the image-based uncertainty quantification approach is displayed in
Figure 4-3, where the algorithm consists of three sections and is implemented in Matlab®. In the first step
(i.e., dissect optical images), stitched microstructure images of the width-length cross-sectional area
(Figure 4-3a) are dissected into multiple smaller patches with a dimension of 256 256 pixels as
demonstrated in Figure 4-3b. It is noted that the wall of the width-length cross-sectional area is discarded
automatically by the Matlab® script so that only the infill is considered for microstructure analysis. The
width of the wall is estimated to be 0.5 mm (i.e., the diameter of the extruder head), so that at least 780
pixels were removed from all edges. The location of each patch is recorded to investigate spatial variation
by (w, t, l), which indicates the width, thickness, and length direction, respectively as illustrated in Figure
4-1e and 4-1f. Each direction is evenly divided into 4 groups so that each location group contains at least
16 patches. In the second step, Otsu’s multilevel thresholding [32] and the local intensity gradient
segmentation [33] were implemented to isolate the void pixels and fiber pixels as presented in Figure 4-3c
and Figure 4-3d, respectively. The void volume fraction and fiber volume fraction of each patch were
77
then calculated using the ratio between the number of non-black pixels and the total number of pixels in
each patch. In the third step, the statistical distribution of void volume fraction and fiber volume fraction
for each process condition was modeled. The sensitivity analysis of the patch size was first investigated
during the preliminary study by analyzing eight width-thickness microstructure images randomly selected
from all images. The analysis was performed in Matlab® with an Intel® Core i7-8700 CPU at 3.20 GHz
and 64.0 GB memory. Patch sizes of 64, 128, 256, 512, and 1024 were selected to calculate the fiber
volume fraction and void volume fraction. A patch size of 1024 served as the baseline measurement as it
contained the most information, and statistical distribution results from other patch sizes were compared
to the baseline. Distribution results calculated from patch sizes 128, 256, and 512 were comparable with
the baseline; however, the computation time of patch size 512 was significantly longer than that of patch
sizes 128 and 256. Hence patch size 256 was selected for this study.
Figure 4-3: The flow chart of the image-based uncertainty quantification and modeling: (a) stitched
grayscale optical image of width-thickness cross-sectional area, (b) dissected optical images, (c) segmented
image representing voids, (d) segmented image representing fiber, and (e) representative bi-variate
probability distribution of fiber volume fraction and void volume fraction.
The void volume fraction and fiber volume fraction distributions were modeled as multivariate
Gaussian distribution to consider the correlation between these two datasets. To implement the
multivariate Gaussian distribution, the normality assumption must be evaluated first. The probability
distribution of the void volume fraction presented in Figure 4-4a is not normal. Therefore, a Box-Cox
78
transformation [34], a well-established data transformation approach converting non-normal distribution
to normal distribution, was implemented before modeling as demonstrated in Figure 4-4b. To ensure the
model fitness, data generated from the fitted probability distribution were compared with the transformed
data using the Kolmogorov–Smirnov (K-S) test as presented in Figure 4-4c. The p-values for the K-S test
for all process conditions were greater than a significance level of 0.05, indicating a good fit of the
models.
Figure 4-4: A representative of (a) original histogram of fiber volume fraction and void volume fraction,
(b) transformed histogram using Box-Cox transformation, and (c) cumulative distribution function of
experimental data and simulated data.
The length-width microstructure images were used for analyzing the overall fiber orientation;
therefore, no dissection was needed. The same image process approach mentioned above was
implemented to extract fiber pixels, where Otsu’s multithresholding method was used to separate fiber
pixels from the matrix and void pixels so that each connected component was an individual fiber. Then
the fiber orientation was calculated by measuring the angle between the major axis of the fiber and the
horizontal axis of the image, which was automatically performed in the Matlab® program as well.
79
4.3.2 Calibration of Halpin-Tsai Model Based on Data-driven Approach
Standard models, such as Halpin-Tsai equations, provide accurate predictions of the modulus of
fiber-reinforced polymer (FRP) composite without the presence of voids, and Rodriguez et al. proposed to
modify the Halpin-Tsai equations to consider the presence of void by using the effective cross-sectional
area to account for the loss of load-carrying material [35]. Hence, the elastic constants of the
unidirectional FFF composite with the presence of void can be calculated as [28]:
𝐸11𝑐𝑎𝑙𝑐 = (1 − 𝑉𝑣𝑜𝑖𝑑)𝐸11 4.1a
𝐸22𝑐𝑎𝑙𝑐 = (1 − √𝑉𝑣𝑜𝑖𝑑)𝐸22 4.1b
𝐺12𝑐𝑎𝑙𝑐 =(1 − 𝑉𝑣𝑜𝑖𝑑)(1 − √𝑉𝑣𝑜𝑖𝑑)
(1 − 𝑉𝑣𝑜𝑖𝑑) + (1 − √𝑉𝑣𝑜𝑖𝑑)𝐺12 4.1c
𝑣12𝑐𝑎𝑙𝑐 = (1 − 𝑉𝑣𝑜𝑖𝑑)𝑣 4.1d
𝑣21𝑐𝑎𝑙𝑐 = (1 − √𝑉𝑣𝑜𝑖𝑑)𝑣 4.1e
where 𝐸11, 𝐸22, 𝐺12, and 𝑣 are the material constants of the short unidirectional FRP composite calculated
using Halpin-Tsai equations with the consideration of the fiber aspect ratio; ‘1’ is indicated as the fiber
direction, and ‘2’ is the transverse direction; 𝑉𝑣𝑜𝑖𝑑 is the volume fraction measured from the cross-
sectional area. The stiffness matrix 𝑸 of the unidirectional FFF FRP composite can be calculated using
the Halpin-Tsai equations [36,37]:
𝑸 = [
𝑄11 𝑄12 𝑄16
𝑄12 𝑄22 𝑄26
𝑄16 𝑄26 𝑄66
] =
[
𝐸11𝑐𝑎𝑙𝑐
(1 − 𝑣12𝑐𝑎𝑙𝑐𝑣21𝑐𝑎𝑙𝑐)𝑣21𝑐𝑎𝑙𝑐𝑄11 0
𝑣21𝑐𝑎𝑙𝑐𝑄11
𝐸22𝑐𝑎𝑙𝑐
(1 − 𝑣12𝑐𝑎𝑙𝑐𝑣21𝑐𝑎𝑙𝑐)0
0 0 𝐺12𝑐𝑎𝑙𝑐]
4.2
The stiffness matrix of the actual FFF sample using the global coordinate system (LD, TD, ND) is
transformed as the following:
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�̅� =
[ 𝑄𝐿𝐷𝐿𝐷
𝑄𝑇𝐷𝑇𝐷
𝑄𝐿𝐷𝑇𝐷
𝐺𝑁𝐷𝑁𝐷
𝐺𝐿𝐷𝑁𝐷
𝐺𝑇𝐷𝑁𝐷]
=
[
𝑚4 𝑛4 2𝑚2𝑛2 4𝑚2𝑛2
𝑛4 𝑚4 2𝑚2𝑛2 4𝑚2𝑛2
𝑚2𝑛2
𝑚2𝑛2
𝑚3𝑛𝑚𝑛3
𝑚2𝑛2
𝑚2𝑛2
−𝑚𝑛3
−𝑚3𝑛
𝑚4 + 𝑛4
−2𝑚2𝑛2
𝑚𝑛3 − 𝑚3𝑛𝑚3𝑛 − 𝑚𝑛3
−4𝑚2𝑛2
(𝑚2 − 𝑛2)2
2(𝑚𝑛3 − 𝑚3𝑛)
2(𝑚𝑛3 − 𝑚3𝑛)]
[
𝑄11
𝑄22
𝑄12
𝑄66
] 4.3
where 𝑚 = 𝑐𝑜𝑠𝜃, 𝑛 = 𝑠𝑖𝑛𝜃, and 𝜃 is the fiber orientation. The longitudinal modulus of the FFF sample
can then be computed by:
𝐸𝐿𝐷 = 𝑄𝐿𝐷 𝐿𝐷𝑄𝑇𝐷 𝑇𝐷 − 𝑄𝐿𝐷 𝑇𝐷
2
𝑄𝑇𝐷 𝑇𝐷 4.4
Rodriguez et al. discussed that the conventional approach of using the effective cross-sectional area tends
to overestimate [31]. This may be influenced by a change in “bulk” properties during the process and the
complex geometric and spatial distribution of the voids, resulting in craze nucleation [35]. A data-driven
optimization approach is proposed to address this complex effect, where a new parameter, α, is introduced
to consider the effectiveness of load transferring through data-driven features by adjusting the material
property of the polymer matrix. Hence, the calculated modulus of the matrix material, 𝐸𝑚𝑐𝑎𝑙𝑐, is
modified as:
𝐸𝑚𝑐𝑎𝑙𝑐= 𝛼𝐸𝑚 4.5
where 𝐸𝑚 is the original tensile modulus of the polymer matrix material.
To determine the appropriate value of 𝛼, the principal component analysis (PCA), a well
understood and used unsupervised feature extraction technique, is implemented, where data-driven
features, the PC scores, are extracted from the void and fiber volume fraction data [38]. 𝛼 is proposed to
have the following form:
𝛼 = 𝛽1𝑒𝑇1 + 𝛽2𝑒
𝑇2 4.6
where 𝑇𝑖 are the components of the PC scores and 𝛽𝑖 are the hyperparameters needed to be optimized.
The rationale for selecting an exponential function is that 𝛼 must be a positive value while PC scores have
a range of (−∞,+∞). The exponential function will ensure the positivity of 𝛼 so that no negative stiffness
value is permitted. By implementing the data-driven features, α considers the complex effect of the
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reinforcer (i.e., fiber) and the voids. To determine the value of hyperparameters, 𝛽𝑖, minimum mean
square error estimation method is implemented where the objective function consists of the error from
both targeted mean and targeted variance written as the following:
argmin𝛽1, 𝛽2
1
𝑁∑(𝐸11𝐿𝐷 − 𝐸11𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒
(𝛽1, 𝛽2, 𝑖))2
𝑖
+ (𝜎𝑡𝑎𝑟𝑔𝑒𝑡2 − 𝑉𝐴𝑅[𝐸11𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒
(𝛽1, 𝛽2)])2 4.7
where 𝐸11𝐿𝐷 is the average longitudinal modulus measured from the quasi-static tensile test, 𝐸11𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒 is
estimated longitudinal modulus calculated according to Equations 4.1-4.6, 𝜎𝑡𝑎𝑟𝑔𝑒𝑡2 is the variance of the
longitudinal modulus measured from the quasi-static tensile test, and 𝑉𝐴𝑅[𝐸11𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒(𝛽1, 𝛽2)] is the
variance of the estimated longitudinal modulus. Gradient descent with a learning rate of 0.01 is
implemented to identify the optimal solutions for 𝛽𝑖’s.
4.3.3 Physics-based Stochastic Modeling and Uncertainty Analysis
The effect of uncertainties at the microscale on the macroscale mechanical property is evaluated
through extensive Monte Carlo (MC) simulation [39, 40], where the stochastic variables are void and
fiber volume fraction. Details of modeling of these stochastic variables are described in Section 4.3.1,
where the joint probability distribution function provides a probabilistic characterization of the
microstructure of the specimen for each process condition. The MC simulation samples the stochastic
variables according to their probabilistic distribution models, and the stochastic variables are then
implemented into Equations 4.1-4.4 to calculate the longitudinal modulus of the FFF sample. The
statistical distribution of longitudinal modulus for each process condition is summarized across 1000 MC
simulations, which addresses the random variation of the mechanical property owing to variations at the
microscale.
4.4 Results and Discussion
4.4.1 Microstructure and Uncertainty Quantification
The microstructure of the FFF samples with all combinations of process conditions was examined
using an optical microscope, where the overall width-thickness cross-sectional area was obtained by
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stitching regional images using ImageJ stitching plug-in. A complete overall cross-sectional area of the
FFF sample is illustrated in Figure 4-5a; this part was printed using low moisture filaments, a print
temperature of 270 °C, a print speed of 20 mm/s, and a layer height of 2 mm. Voids in the sample are
presented as dark/black colors, while the fibers are presented as bright/light colors. The gray colors
present the matrix material. Some regions (Figure 4-5c) show a cluster of voids with a much higher void
volume fraction than the other regions (Figure 4-5b). Hence, the spatial variation of voids volume fraction
within one part is present, and the characterization of the microstructure uncertainty must consider the
spatial variation. The inherent spatial variations could be attributed to the variations within the filament
and/or the variations during the FFF process. The possibility of variations within the filament relates to
the homogenization of the filament, which is considered as an inevitable error, and the variations during
the FFF process are examined below using the IR camera to analyze the extrudate temperature profile.
Figure 4-5: Representative width-thickness microstructure of specimens using low-moisture-content
filament, print temperature of 270 °C, print speed of 20 mm/s, and layer height of 2 mm. (a) overall width-
thickness microstructure, regional microstructure has (b) lower void volume fraction, and (c) higher void
volume fraction.
Furthermore, the effect of printing speed and layer height on the microstructure is ubiquitous as
illustrated in Figure 4-6, where the yellow ovals approximately indicate the cross-section of each print
path. Samples printed with a lower printing speed (i.e., 20 mm/s) (Figure 4-6a and c) have fewer voids
than samples processed with a higher printing speed (i.e., 60 mm/s) (Figure 4-6b and d), and the
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boundaries between adjacent printing paths can be distinguished for samples printed with a slower
printing speed as triangular shaped interstitial voids could be easily identified. The samples printed with
smaller layer height (i.e., 0.2 mm) have fewer voids than samples printed with larger layer height (i.e., 0.3
mm), especially the inter-layer voids. The reduced layer height exerted a higher pressure between the
print nozzle and the previously printed layer than a higher layer height, therefore the extrudate from a
lower layer height appeared to form a better adhesion with the adjacent print path and layer, thus forming
smaller and fewer inter-layer voids.
Figure 4-6: Representative width-thickness microstructure of specimens using low-moisture-content
filament with a combination of printing parameters of (a) 270 °C, 20 mm/s, 0.2 mm, (b) 270 °C, 60 mm/s,
0.2 mm, (c) 270 °C, 20 mm/s, 0.3 mm, and (d) 270 °C, 60 mm/s, 0.3 mm. Yellow ovals approximately
indicate the cross-section of each print path.
A full factorial ANOVA is employed to address the quantitative effect of printing parameters
with the consideration of spatial variations in length, width, and thickness directions. Figure 4-7 presents
the main effects of each printing parameter and spatial location on the average value of fiber volume
fraction, average value of void volume fraction, and the standard deviation of void volume fraction
distribution. It is noted that the main effects on the average fiber volume fraction (Figure 4-7a) are
opposite to the main effects on the average void volume fraction (Figure 4-7b). This is explained in that
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there is a negative correlation between fiber volume fraction and void volume fraction as fiber volume
fraction in the original filament can be assumed to be constant with a negligible amount of voids. A
preliminary study examined the microstructure of the filament with a low moisture content, where ten
cross-sectional areas were selected, and each was 140 mm apart to include spatial variation within the
filament. The optical microscopy indicates the average void volume fraction is 0.41 ± 0.34%, which can
be relatively small compared to the average void volume fraction observed in all samples, which is
9.15%. From the main effects plot for void volume fraction (Figure 4-7b), it can be concluded that the
high level of moisture content in the filament, printing speed, and printing layer height results in a higher
void volume fraction, and similar observations are found in [18, 22, 23]. With the presence of moisture,
plasticization occurs within the nylon polymer, where the guest water molecules replace hydrogen bonds
in the amorphous phase of nylon and separate the polymer chains, thereby increasing the mobility of the
polymer chains, reducing the glass transition temperature (𝑇𝑔) and reducing the viscosity of the polymer
[41]. During the heating process of the FFF, solid-state polymerization condenses short polymer chains,
and this chemical reaction results in the diffusion of the water and formation of polymers with longer
chains [42]. At the elevated temperature environment, the moisture remains dissolved in the polymer
matrix. The formation of the voids involves the pressure of the polymer matrix and the pressure within the
pores. At a high level of moisture content, the reduced viscosity decreases the pressure of the polymer
matrix, and the pressure within the evaporated water grows and expands, which forms voids as the
extrudate cools [24]. One approach that could minimize the formation of the voids is by applying external
pressure in the FFF process chamber, which will counter the pressure within the voids and allows void-
free extrudate. At a higher printing speed (i.e., 60 mm/s), the extrudate was unable to cool below the 𝑇𝑔
prior to the arrival of an adjacent path, and the printing of the adjacent path reheated the previous
extrudate through conduction. Hence the duration for solid-state polymerization is prolonged, thereby
forming more voids in the samples printed with higher printing speed. It is noted that printing temperature
is not displayed in the main effect plot as it is nested under moisture content; however, the ANOVA
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results (see Appendix A-1) indicate that temperature is indeed a significant factor, where printing
temperature 270 °C results in higher void volume fraction as a positive coefficient is associated with the
temperature 270 °C. The higher printing temperature increases the initial temperature of the extrudate,
which inherently increases the duration and reaction rate for thermally induced solid-state polymerization;
therefore, a higher amount of voids formed at the higher printing temperature. The discussion of the effect
of processing parameters on the standard deviation of the void volume fraction is presented in a later part
of the result and discussion section.
Figure 4-7: Main effects plot of print parameters on (a) average fiber volume fraction, (b) average void
volume fraction, and (c) standard deviation of void volume fraction distribution.
As discussed above, temperature is critical for solid-state polymerization. When above 𝑇𝑔
shorter polymer chains are consolidated, forming water as a byproduct. Hence, the spatial variation of
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void volume fraction is further investigated by analyzing the in-situ temperature profile of the printed
sample as presented in Figure 4-8a. As moisture content within the filament evaporated during the FFF
process, this generates extensive porosity with volatiles trapped within both the polymer-extrudate
interface and within the bulk resin [4, 24]. The evaporation duration should be carefully monitored, as it
indicates the duration of porosity generation. To determine the evaporation duration, the cooling curve of
each print path at each print layer is extracted using a customized Matlab® code, and the cooling curves
are shown in Figure 4-8b-f. The cooling rate in layer 1 is much slower than that of other layers owing to
the heated print bed, which was set to be 105 °C. The temperature of printed material in layer 1 cooled
below the print bed temperature owing to the cooling fan which provided constant inflow of room
temperature air. The effect of a heated print bed on cooling rate decreases drastically starting at layer 2,
where the duration for the printed material to cool below 100 °C is much shorter at layer 2 than at layer 1.
Figure 4-8: (a) Representative in-situ IR image of the printed sample; (b-f) extracted cooling curve from
IR images of layers 1, 2, 4, 7, and 13, respectively.
87
To extract the evaporation duration, 𝐷𝑒𝑣𝑎𝑝, a threshold of 100 °C is selected because the
evaporation of moisture (i.e., H2O) occurs at a temperature above 100 °C, and the 𝐷𝑒𝑣𝑎𝑝 for each print
path of print layers 2, 4, 7, and 13 are displayed in Figure 4-9a. It is shown that 𝐷𝑒𝑣𝑎𝑝 for each layer has a
similar trend, where path 3 has the highest 𝐷𝑒𝑣𝑎𝑝 compared to all other print paths and there is a slight
upward trend as it prints from path 1 to path 5. In addition, the 𝐷𝑒𝑣𝑎𝑝 gradually decreases in the build
direction. The effects of 𝐷𝑒𝑣𝑎𝑝 are consistent with the results from the main effects plot for void volume
fraction (Figure 4-7b), where width region 3 has the highest void volume fraction, there is an upward
trend of void volume fraction in the width direction (i.e., from path 1 to path 5), and there is a downward
trend in void volume fraction in the thickness direction (i.e., from layer 2 to layer 13). Since the cooling
fan is mounted in the front of the extruder head, print paths that are closer to the front of the extruder head
(i.e., paths 1 and 2) experience a higher cooling rate than paths located near the back of the extruder head.
As the extruder prints more layers, the effect of print bed temperature diminishes so that layers that are
closer to the print bed experience a lower cooling rate than layers that are printed later. The similar trend
of evaporation duration of the different print paths and the void volume fraction in width (i.e., different
print path) and thickness (i.e., different layer) direction indicates that the evaporation duration is
positively correlated with the void volume fraction as longer evaporation duration allows more moisture
content to evaporate creating more voids. A similar comparison of the 𝐷𝑒𝑣𝑎𝑝 in the gauge region was
conducted for each layer, and the result of layer 4 is presented in Figure 4-9b. It indicates that 𝐷𝑒𝑣𝑎𝑝 is
relatively small in the middle of the gauge section while it is higher at the two ends of the gauge section.
This trend is consistent with the length effect on void volume fraction (Figure 4-7b). Hence, the in-situ
temperature profile is an important state variable to monitor the print quality in terms of void volume
fraction, and an appropriate cooling rate is essential for minimizing void volume fraction in FFF samples.
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Figure 4-9: Representative evaporation duration of (a) midpoint of each path, (b) 4 points along the length
direction for part printed at 270°C with a printing see of 20 mm/s, and layer height of 0.3 mm using high
moisture content filament.
Figure 4-7c presents the main effects for the standard deviation of void volume fraction
distribution, where all factors except moisture content present a similar trend as the main effects for
average void volume fraction. Higher moisture content results in a smaller variation of void volume
fraction distribution because the evaporation can occur more often at the path-path interface and within
the bulk resin. The temperature effect on the variation of void volume fraction is significant (see
Appendix A-2), though the impact is dependent on the moisture content of the filament. For low-
moisture-content filament, higher printing temperature results in higher void variation, while it has the
opposite effect when low-moisture-content filament is used.
By examining the ANOVA results, the effect intensity of each factor is evaluated by comparing
the F-statistics, which is a ratio of variation between sample means and variation within the samples.
From Appendix A-1, it is apparent that layer height has the most prominent effect on void volume
fraction, followed by print speed, moisture content, and print temperature. The effect of spatial variation
on void volume fraction is relatively small compared to the processing parameters; however, they are all
significant, as their P-value is much smaller than a 0.05 significance level.
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4.4.2 Halpin-Tsai Model Optimization and Uncertainty Propagation
To predict the overall structural property (i.e., longitudinal modulus), a stochastic Halpin-Tsai
model is implemented, where fiber and void volume fraction are modeled according to Section 4.3.1.
Here, the values of moduli and Poisson ratios of carbon fiber and nylon polymer are assumed to be 210
GPa, 0.2, 2.6 GPa, and 0.35, respectively, which are typical values for carbon fiber and nylon-6
[33,43,44]. The fiber aspect ratio is measured to be approximately 24, where an average fiber length and
fiber diameter were quantified to be 182 µm and 7.6 µm, respectively by summarizing fibers from all of
the length-width cross-sectional images. The fiber orientation, 𝜃, is calculated from the optical
microscopy of the length-width (LD-ND) plane as shown in Figure 4-10 following the Bay and Tucker
method [45], where the cross-sectional area of the entire gauge section was considered. Figure 4-10b
illustrated the output of filtered image from the original image Figure 4-10a, where only fiber pixels were
preserved using Otsu’s multilevel thresholding. The fiber orientation, 𝜃, for each fiber is then calculated
by measuring the angle between the major axis of the fiber and the horizontal axis as shown in Figure 4-
10c. The fiber orientation distribution for each process condition is then summarized. It was shown that
fiber orientation for samples printed using high-moisture-content filaments has a larger 𝜃 value than that
for samples printed using low-moisture-content filaments, as illustrated in Figure 4-10d. The moisture
content in the filament decreases the viscosity and the 𝑇𝑔 of the extrudate, therefore high-moisture-
content extrudate remains liquid for a longer period than extrudate from low-moisture-content filaments.
During the consolidation, the characteristics of the flow within the extrudate change as the liquid material
flows toward the unbounded region, creating a slump in shape [24]. The reinforcing fibers follow the flow
direction, which deviates from the raster direction (i.e., length/longitudinal direction); hence, a larger
average 𝜃 value was observed for samples printed using high-moisture-content filaments than for low-
moisture-content filaments. When calculating the transformed stiffness matrix, �̅�, in Equation 4.3, 𝜃 is
chosen according to the moisture content of the filament.
90
Figure 4-10: Representative segments of (a) length-width optical microscopy of the printed sample, (b)
filtered image using thresholding, and (c) probability distribution of fiber orientation.
Monte Carlo simulation is employed to determine the stochastic distribution of the predicted
longitudinal modulus, and 1000 simulations were generated for each process condition as described in
Section 4.3.3. The mean value of the predicted longitudinal modulus without and with the proposed data-
driven optimization (discussed in Section 4.3.2) is presented in Figure 4-11. It is shown that the prediction
without optimization has an error between -16.5% and 57.2% and most of the predictions are
overestimated; a similar overestimation of the modulus of FFF processed samples was observed by
Rodriguez et al. [35]. The proposed data-driven optimization employed a combination of the PC scores
calculated from the distribution of fiber and void volume fractions to adjust the material property of the
polymer matrix, and it reduced the estimation error to a range of -0.6 % to 2.5%, improving the accuracy
of the modified Halpin-Tsai model. It is noted that the average value of 𝛼 (Equations 4.5 and 4.6) for
high- and low-moisture-content filament is 0.92 and 0.75, respectively, which indicates that more
compensation of the polymer matrix modulus is needed for low-moisture-content filament than that of
high-moisture-content filament. This phenomenon involves the bonding strength of polymer during the
FFF process. Although the presence of moisture content plasticizes the polymer chains, it lowers the 𝑇𝑔 of
the filament, which induces a longer diffusion duration (i.e. the duration when the temperature of the
extrudate is above the 𝑇𝑔) than dry filaments. As Li et al. [46] concluded in their study of the bond
91
formation behavior of ABS filament after FFF deposition, longer diffusion duration enhances the
formation of randomized polymeric bonding between two adjacent print paths. Therefore, the reduction of
the “bulk” material property is lower for high-moisture-content filaments than for low-moisture-content
filaments, as a better bonding strength was achieved through a longer diffusion duration. Comparing the
results in Figure 4-11a and Figure 4-11b, it is clear that the samples printed using high-moisture-content
filaments have lower longitudinal modulus than those printed using low-moisture-content filaments,
which is caused by the added porosity introduced by moisture evaporation and reduced the tensile
modulus significantly. For low-moisture-content filaments, samples printed with lower printing
temperature (i.e., 240 °C) and slower printing speed (i.e., 20 mm/s) achieved a higher longitudinal
modulus, which is attributable to a higher molecular orientation. Fritch [47] investigated the molecular
orientation of injection molded polymer and concluded that lower extrusion temperatures and slower
extrusion rates tend to increase the degree of molecular orientation. With a higher degree of molecular
orientation, the primary bonds between atoms in the polymer chain are the dominant load-carrier, which
are much stiffer and stronger than the secondary bonds between the polymer chains. Therefore, samples
printed with a lower temperature and a lower printing speed achieved a higher tensile modulus.
The stochastic distribution of the longitudinal modulus is illustrated in Figure 4-12 to present the
propagated variation from micro-level (i.e., fiber and void volume fraction) to the macro-level. Figure 4-
12a and Figure 4-12b illustrate that samples printed with high moisture contents have a lower average in
longitudinal modulus with a smaller variation compared to the samples with low moisture contents. As
discussed in Section 4.4.1, high-moisture-content filaments produce samples with a higher average void
volume fraction which reduces the effective load-bearing material resulting in a lower longitudinal
modulus. High-moisture-content filament also lowers the standard deviation of the void volume fraction
distribution, which results in a smaller variation in longitudinal modulus distribution. Similar
observations of the process-structure-property relationship can be inferred, such as higher printing speed
(layer height) leads to higher void volume fraction and larger void volume fraction variation, the
92
longitudinal distribution of Figure 4-12c (Figure 4-12d) has a lower average and a wider variance than
that of Figure 4-12a.
Figure 4-11: Comparison of longitudinal modulus of samples printed using (a) high-moisture-content
filaments and (b) low-moisture-content filaments.
93
Figure 4-12: Representative of simulated probability distributions of longitudinal modulus of samples
printed using process conditions of (a) dry | 270°C | 20 mm/s | 0.2 mm, (b) moist | 270°C | 20 mm/s | 0.2
mm, (c) dry | 270°C | 60 mm/s | 0.2 mm, and (d) dry | 270°C | 20 mm/s | 0.3 mm.
4.5 Conclusions
The uncertainties of CFRP composite manufactured by FFF were investigated through a P-S-P
approach, where stochastic models were developed to characterize the uncertainties and the propagated
effect from the micro-level to the macro-level. An image-based statistical analysis was developed to
quantify the microstructure uncertainties by extracting physics-based features such as fiber volume
fraction, void volume fraction, and fiber orientation from the optical microscopy images of the CFRP
composite. The adverse effect of process parameters (i.e., moisture content in the initial filament, printing
temperature, printing speed, and layer height) on the physics-based features was then evaluated with DoE
methodology. It was found that processing parameters are the primary contributors to void generation and
variation in the distribution of void volume fraction, though spatial factors were also found to be
94
statistically significant. The spatial variation of void volume fraction was attributed to the cooling rate of
the printed material, which was monitored by the IR camera. The image-based statistical analysis
provides a fundamental understanding of the process-structure relationship of FFF.
The structure-property relationship of FFF samples was then examined through the modified
Halpin-Tsai equations, where a data-driven optimization scheme was proposed to consider the complex
effect from the FFF process and craze nucleation from voids. The predicted longitudinal modulus was
validated with the experimental result. The stochastic model of the predicted longitudinal modulus of FFF
samples was developed using a Monte-Carlo based uncertainty analysis that integrates statistical
distributions of fiber volume fraction and void volume fraction. It was found that the propagated
uncertainty of the longitudinal modulus has a similar trend as the uncertainty observed in the distribution
of void volume fraction, explaining the structure-property relationship.
This study demonstrates that the proposed P-S-P approach using image-based statistical analysis
and data-driven optimization can be implemented for uncertainty quantification and propagation analysis
of CFRP composite. The proposed framework integrates physics-based approach with numerical methods
to provide stochastic characterization and modeling of voids volume fraction, fiber volume fraction, and
material properties of FFF samples. Therefore, the proposed framework is a viable tool to analyze the
structural behavior and uncertainties of CFRP composite manufactured through the FFF process before
building a large-scale structure.
4.6 Appendices
A-1: ANOVA on Average Void Volume Fraction
Source DF Adj SS Adj MS F-Value P-Value
Moisture Content 1 0.10467 0.104671 135.85 0.000
Speed 1 0.29875 0.298751 387.75 0.000
Layer Height 1 0.81741 0.817413 1060.92 0.000
95
Width 3 0.04339 0.014465 18.77 0.000
Thickness 3 0.02854 0.009512 12.35 0.000
Length 3 0.04498 0.014995 19.46 0.000
Temperature(Moisture Content) 2 0.17414 0.087068 113.01 0.000
Moisture Content*Speed 1 0.15579 0.155790 202.20 0.000
Moisture Content*Layer Height 1 0.05909 0.059087 76.69 0.000
Speed*Layer Height 1 0.00083 0.000827 1.07 0.301
Width*Thickness 9 0.00206 0.000229 0.30 0.976
Width*Length 9 0.04372 0.004857 6.30 0.000
Thickness*Length 9 0.00499 0.000554 0.72 0.692
Temperature(Moisture Content)*Speed 2 0.14075 0.070374 91.34 0.000
Temperature(Moisture Content)*Layer Height 2 0.11053 0.055266 71.73 0.000
Error 975 0.75122 0.000770
Total 1023 2.78084
S R-sq R-sq(adj) R-sq(pred)
0.0277575 72.99% 71.66% 70.20%
A-2: ANOVA on Standard Deviation of Void Volume Fraction Distribution
Source DF Adj SS Adj MS F-Value P-Value
Moisture Content 1 0.002222 0.002222 6.25 0.013
Speed 1 0.040548 0.040548 114.07 0.000
Layer Height 1 0.273905 0.273905 770.55 0.000
Width 3 0.007371 0.002457 6.91 0.000
Thickness 3 0.002659 0.000886 2.49 0.059
96
Length 3 0.011660 0.003887 10.93 0.000
Temperature(Moisture Content) 2 0.016938 0.008469 23.83 0.000
Moisture Content*Speed 1 0.035754 0.035754 100.58 0.000
Moisture Content*Layer Height 1 0.000139 0.000139 0.39 0.531
Speed*Layer Height 1 0.003226 0.003226 9.08 0.003
Width*Thickness 9 0.003093 0.000344 0.97 0.466
Width*Length 9 0.010691 0.001188 3.34 0.000
Thickness*Length 9 0.002100 0.000233 0.66 0.749
Temperature(Moisture Content)*Speed 2 0.011236 0.005618 15.80 0.000
Temperature(Moisture Content)*Layer Height 2 0.014257 0.007129 20.05 0.000
Error 975 0.346581 0.000355
Total 1023 0.782381
S R-sq R-sq(adj) R-sq(pred)
0.0188539 55.70% 53.52% 51.14%
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Chapter 5: Conclusions and Future Work
5.1 Conclusions
Carbon-fiber-reinforced polymer (CFRP) composites have been increasingly applied in a wide
range of industries including aerospace, automotive, sports goods, oil and gas, and healthcare owing to
their favorable mechanical properties and tailor-made strength characteristics for a given load. Although
extensive experimental and simulation studies have advanced the understanding and usage of CFRP
composites, the lengthy and costly certification process hinders the approval of new material and designs
for industrial applications. Therefore, integrating data science and microstructure characterization to
accelerate the material development process is indispensable to enhance the understanding of the
underlying physics and chemistry that governs the process-structure and structure-property relations. This
dissertation aimed to address some challenges in microstructure informatics, specifically a) developing an
automatic 3D characterization framework that extracts and calculates the individual fiber morphology, b)
spatiotemporal fracture behavior analysis of CFRP composites, and c) establishing process-structure-
property (P-S-P) relation of CFRP composite manufactured using fused filament fabrication (FFF). The
major findings of this dissertation include the following:
1. 3D microstructure characterization of short and long CFRP composite. An image-based 3D
characterization framework that quantitatively analyzes the fiber characteristics using µXCT images was
proposed. Quantitative fiber morphologies (i.e., fiber curvature, orientation, and length distributions) were
analyzed through numerical image processing techniques and local fiber-tracking approach which was
capable of tracking both straight and curve fibers for non-uniformly oriented fiber systems. The statistical
representation of fiber morphology was developed and integrated into the Halpin-Tsai model to predict
the material’s longitudinal property using a configuration averaging approach. The proposed framework
was employed on injection molded short and long CFRP composites, where the estimated material
modulus was validated experimentally. The proposed framework provided a valid alternative for the
traditional finite element analysis method.
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2. Spatiotemporal characterization of crack propagation in CFRP composites. A spatiotemporal
characterization algorithm was proposed to quantitatively analyze the in-situ 3D fracture behavior of
CFRP composite using in-situ µXCT images. The 3D fracture features were extracted through series of
image processing algorithms and visualized through the proposed algorithm, where spatiotemporal
propagation (i.e., cracking opening, cracking growth, and tip-end crack volume growth under varied
tensile load) were presented. The spatiotemporal characterization was validated using the volumetric
digital image correlation (V-DIC) method, where the characterized crack propagation was in good
agreement with the strain field calculation from V-DIC. The fracture mechanism of both sheet molding
compound (SMC) and injection molded CFRP composite was unveiled from the in-situ 3D images. Mode
I fracture within a fiber tow was the initial failure mechanism for SMC samples, and it transitioned into
mode II fracture resulting in delamination between fiber tows. Fiber pullout was the dominant failure
mechanism for the injection molded sample. The developed characterization algorithm facilitated the
accurate characterization of fracture propagation and failure mechanisms of CFRP composites.
3. P-S-P analysis CFRP composite processed via FFF. The uncertainty of CFRP composite
manufactured by FFF in terms of fiber and void volume fraction and their spatial variations were
investigated through a P-S-P approach. Stochastic models of fiber and void volume fraction were
modeled from optical images using the proposed image-based statistical analysis approach. The adverse
effect of process parameters and moisture content in the filament on microstructure uncertainty was
evaluated, providing a fundamental understanding of the process-structure relation of FFF. The structure-
property relation was studied through modified Halpin-Tsai equations, where a data-driven optimization
scheme was implemented by adjusting the material property of the polymer matrix. The stochastic
models of fiber and void volume fraction distributions were incorporated into the Halpin-Tsai equations
to examine the propagated uncertainty. The proposed analysis investigated the microstructure
uncertainties in the process-structure and structure-property relations of CFRP composite processed via
FFF.
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5.2 Contributions, Applications, and Limitations
In Chapter 2, the 3D characterization algorithm for reconstruction of individual fibers was
achieved by extending the 2D template matching approach from the computer vision to the 3D template
matching, which enabled the reconstruction and characterization of fibers with non-uniformed
orientations. In addition, the local fiber orientation tracking enabled the fiber reconstruction of the curved
fibers, which is especially useful for long-fiber characterizations, thereby enhancing the fidelity of
material property estimation. The theoretical concept of using 3D template matching and local orientation
tracking for fiber reconstruction can be implemented for XCT images of other fiber reinforced polymer
composites, such as glass fiber systems and natural fiber systems. However, the results (i.e., reconstructed
fiber volume, fiber morphology characteristics, and estimated longitudinal modulus of the fiber volumes)
from the 3D characterization of the short and long CFRP composites, described in Chapter 2, are only
applicable for those two specific materials, as the material microstructure is highly depended on its
manufacturing process and there may exist other microstructural features needed to consider. Thus, the
direct use of these results from the microstructure reconstruction should be taken with great care. In
Chapter 2, the Otsu’s multilevel thresholding was implemented to remove most of the unwanted voxels
from the µXCT images, where two-level thresholding approved the most effective in this case. This
method does require additional evaluation to determine the suitable level providing the best segmentation;
however, the thresholding value can also be validated by examining the grayscale intensity of the image.
As demonstrated in Chapter 2, the thresholding value from the two-level thresholding method matched
with the local minimum value from the intensity histogram of the image. Therefore, the thresholding level
should be evaluated by comparing the results from the Otsu’s multilevel thresholding and the grayscale
intensity histogram to ensure the quality of the segmentation.
Chapter 3 demonstrated that the in-situ XCT enabled the observation of the crack initiation, crack
propagation, and failure mechanisms in both SMC and injection molded short CFRP composites, which
are not available from traditional postmortem or destructive testing method. In addition, the quantitative
105
spatiotemporal measurement of the fracture behavior improved the conventional fracture analysis from a
qualitative to a quantitative approach. Similar to the framework proposed in Chapter 2, the proposed
approach for quantitatively analyzing the crack propagation can be implemented for other fiber reinforced
polymer composites. However, it is important to be aware of what is measured from the 3D cracks. As
demonstrated in Chapter 3, crack opening and crack thickness were measured for the fracture behavior in
SMC material, and the tip-end void volume was measured for the short injection molded CFRP
composites. It was because the fracture mechanisms were different for these two materials, and different
measurements should be used to effectively extract the fracture characteristics. Thus, when applying the
spatiotemporal characterization framework, it should be aware of the specific fracture behavior to avoid
wrong feature extractions.
In Chapter 4, the process-structure-property analysis of the FFF process was developed to
understand the statistical effect of process parameters on the microstructural variations, specifically, the
fiber and void volume fractions, and consequent effects on the material property variations. In this
framework, an optimization scheme was integrated to estimate the polymer matrix material property. This
innovative approach improved the model estimation accuracy of the longitudinal modulus. In this
framework, a similar image segmentation scheme used in Chapter 2 was implemented for the optical
microscopic images, which implied that the segmentation methods (Otsu’s multilevel thresholding and
the intensity gradient segmentation) can be applied for grayscale images obtained from different image
acquisition techniques to measure the statistical distribution of material microstructures. In Chapter 4, the
fiber and void volume fractions were measured. The reason for measuring these two properties is that the
physical-based equation, such as the Halpin-Tsai model, requires these two volume fractions to compute
the mechanical properties of the composite. However, more complicated morphologies, such as the
geometric effect of the voids and the spatial distribution of the voids were not taken into consideration.
Thus, it may hinder the evaluation of the impacts of processing parameters on the microstructure, and the
effect of microstructural variations on the variations in the material property.
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5.3 Future Work
The results and experience gained from the presented research provided a solid foundation for
continued research and investigation in the microstructure informatics of CFRP composites. The potential
future work can adhere to the following directions.
1. 3D characterization of fatigue behavior of CFRP composites. The current research focuses on
the relationship between microstructure and tensile behavior of CFRP composites. However, the fatigue
behavior of CFRP composite is much more complicated and less understood than the tensile behavior. It
depends not only on its constituent fiber and matrix but also the interaction between fiber tows or
laminate sequence, which may vary from part to part. Therefore, utilizing the µXCT to unveil the fatigue
failure mode and the propagation of fatigue fracture will provide fundamental understanding for structural
materials especially for the applications in aerospace and automotive.
2. Impacts of spatial and geometric variations of defects and voids. Previous studies indicated
that a CFRP composite consists of geometric and spatial variations of its constituents (e.g., fiber, defects,
void), where the effect of fiber characteristics has been investigated extensively. However, the adverse
effects of defects and voids, especially its geometric shape and spatial distribution, have not been
understood thoroughly. A data-mining and/or machine learning approach can be implemented using in-
situ XCT images to develop a correlation between void/defect morphology and material property, which
will accelerate the understanding of its effects on material performance.
3. Online monitoring and closed-loop feedback control for the FFF process. Commercial FFF
machines do not have an online monitoring system to ensure the print quality, therefore the print quality
can only be assessed post-printing. Based on previous studies, the cooling rate of extruded material is
correlated with the generation of voids; therefore, in-situ temperature monitoring can be developed as a
means for online monitoring. A Markov process can be used to model the transition probability of print
quality based on the cooling rate; therefore, a feedback control loop can be developed based on the
modeling result. It is critical to developing efficient monitoring schemes so that it can provide real-time
107
feedback to the printer to adjust the printing parameter. An online-monitoring and closed-loop feedback
control system that can assess the in-print quality will eliminate the presence of an undesirable effect, and
thus will improve the print quality and accelerate the industrial application of FFF parts.
Shenli Pei
Industrial and Manufacturing Engineering
The Pennsylvania State University
University Park, PA 16802
E-mail: [email protected]
EDUCATION
Pennsylvania State University, State College, PA
Ph.D. in Industrial and Manufacturing Engineering
2015 - 2020
Michigan State University, East Lansing, MI
B.S. Mechanical Engineering with Manufacturing Concentration
Minor in Mathematics
2010 - 2014
INTERNSHIP EXPERIENCE
Ford Motor Company, Dearborn, Michigan Jun. 2018 – Aug. 2018
Product Development Intern
• Integrate multiple software packages to characterize and analyze the uncertain propagation of
Woven CFRP composites under different length scales.
• Analyze the uncertain propagation of Woven CFRP composites of uncertainties from
manufacturing variations.
Stryker (Suzhou) Medical Technology Co. Ltd., Suzhou, China
Jun. 2013 – Nov. 2013
Engineering Department Intern
• Collaborate with the quotation team and technicians to quote 500+ potential in-house
manufacturing parts, which would be the breakeven project for the plant net income.
• Implement Project Management Office and provide a weekly summary of 10+ multi-department
projects for the management team to oversee and mitigate potential delays and risks.
SELECTED PUBLICATION
[1] S. Pei, K. Wang, C-B. Chen, J. Li, Y. Li, D. Zeng, X. Su, H. Yang, Process-structure-property
analysis of short carbon fiber reinforced polymer composite via fused filament fabrication,
Compos. Struct. submitted.
[2] S. Pei, K. Wang, J. Li, Y. Li, D. Zeng, X. Su, X. Xiao H. Yang, Mechanical properties prediction
of injection molded short/long carbon fiber reinforced polymer composites using micro X-ray
computed tomography, Compos. Part A, 130 (2020) 105732.
[3] K. Wang, S. Pei, Y. Li, J. Li, D. Zeng, X. Su, X. Xiao, N. Chen, In-situ 3D Fracture Propagation of
Short Carbon Fiber Reinforced Polymer Composites, Compos. Sci. Technol, 128 (2019) 107788.
[4] S. Pei, K. Wang, Y. Li, D. Zeng, X. Su, J. Li, H. Yang, X. Xiao, Spatiotemporal characterization of
3D fracture behavior of carbon-fiber-reinforced polymer composites, Compos. Struct. 203 (2018)
30-37.
