Developing Structure-Property Linkage for Glass Fibre Reinforced Polymer Composites

Background and Motivation

This project was motivated by the need to have an accurate way of predicting the properties of a long fiber reinforced thermoplastic composite part. A complication to being able to predict the properties of composites is the rich variety of microstructures. Even within a simple part, there is variation of the microstructure caused by the forming methods. Our samples were taken from a simple sheet but have a variety of microstructures due to the flow of the material as the part is formed. For an explanation of the how the part is formed see this post. The configuration of the fibers within the part is important knowledge to have for property prediction.

During the course of the project we researched how this type of problem has been approached in the past. The simplest models predict properties based solely on the properties of the individual components and their volume fractions. For example, the Voigt and Ruess models are used to determine bounds on what the mechanical properties can be. However, to get more accurate predictions, more knowledge of the actual structure is necessary. Other researchers have attempted to look at similar systems by using a variety of different assumptions. One common assumption is that the fibers are rigid. This assumption allows the reconstruction of the microstructure from images of slices of the material. While this assumption can produce reasonable results for short fiber composites, it is not a valid method for long fiber composites.

Project Outline

Considering GFRP composites’ tremendous applications and inability of theoretical models to accurately predict the properties, we propose to establish a structure-property linkage. In oder to achieve this objective, we followed the steps as shown in following figure.

GFRP Sample Collection

Two samples were cut from a molded plate created by the process explained in this post.
Our samples were labeled S and N. Sample S was cut from near the injection location. Sample N was cut from an area away from the injection location in the direction of flow.

Micro-CT and DICOM Data

After the samples are manufactured, Micro-CT is performed to get the layered cross-sections of the samples. Micro-CT was chosen for the ability to create accurate 3D images and to differentiate between materials of differing densities. A few of the example cross-sections can be seen here. Micro-CT produces data in a DICOM format. Matlab’s dicomread was used to extract the data from these files.

Data Visualization and Analytics

Visualization and analytics are the integral part of data analysis. Details of data visualization and analytics can be found in the following posts: Post 1, Post 2, Post 3. The challenge in visualization was finding a method that showed the rich variety of our microstructures. We used a combination of 2D slides and 3D imaging to get an accurate view of our samples. The analytics guided us in beginning the segmentation and the visualization was also very helpful in visually confirming the segmentation.

Image Segmentation

For digital representation of the material structure, it is required to segment the two phases in our samples. In collaboration with Dr. Tony Fast, we developed a image segmentation algorithm known as “Multimodal Data Segmentation using Peak Fitting Algorithm and Gaussian Likelihood Maximization” to segment the highly complex and uncertain fibrous microstructures. We also collaborated with classmates Nils Persson and Dalar Nazarian for brainstorming segementation ideas.
Some work was done on using the segmented images to determine fiber metrics but that work is not complete.

Microstructure and Physical Property Simulation

To establish a structure-property linkage, we require a rich dataset consisting of varied microstructures and their corresponding properties. Due to lack of enough number of real samples, we go for simulating a variety of microstructures as shown in following figure. These microstructures were chosen to simulate the extremes of possible fiber orientations. We simulated over 300 structures for each extreem. The elongated samples represent strain being applied parallel and perpendicular to the fiber direction respectively. The diagonal fibers were to simulate the case that the fibers were at an angle to applied strain. Our real samples include fibers with all of these extremes. We also varied volume fraction to get a more rich field of microstructures. Because our fibers are of constant diameter, we chose not to vary the diameter of the fibers in our simulations.
To do this task, we extensively collaborated with our Materials Informatics class mate Dipen Patel.

Abaqus input files were created from the simulated microstructures. Finite element method is used to calculate the first component of the stiffness tensor. A code was developed to read the Abaqus files and extract the sigma and epsilon values. Then the values were used to calculate the stiffness tensor. This was done on both the physical and the simulated microstructures for comparison.

Spatial Statistics

In order to quantify spatial correlations in the microstructures, we employ 2-point statistics that informs “probability density associated with finding local states h and h’ at the tail and head of a prescribed vector r randomly placed into the microstructure” (Kalidindi, 2014). Details about the 2-point statistics on real samples can be found in the following posts: Post 1, Post 2, Post 3.

Dimensionality Reduction

2-point statistics of each of the microstructures are a high-dimensional data. We use classic statistical technique known as principal components analysis to obtain a low-dimension representation of this spatial correlations.

Structure Property Linkage

Regression model is developed to establish the linkage. Reduced order representation of spatial correlations (2-Point Statistics) and property obtained from FEM for the microstructures are the inputs and ouput respectively for the regression model.

Challenges Encountered

1) Simple segmentation is insufficient to resolve the image into 2 phases

2) Fiber metrics are difficult to extract in the 3D space particularly because of overlapping fibers at our resolution

3) Insufficient variety of data to create linkages

4) FEM data from simulated samples is inconsistent with that performed on the real samples

Successes and Closure

1) Carried out analysis of real microstructures: Visualization, Analytics, Segmentation, 2-Point Statistics

2) Simulated microstructures and property data to build a dataset required for linkage development

3) Calculated 2-Point Statistics for simulated microstructures and then performed Principal Components Analysis

4) Developed Regression Model for structure-property linkage

Collaboration

1) Dr. Tony Fast: Data Visualization and Analytics, Segmentation and 2-Point Statistics

2) Nils Persson and Dalar Nazarian: Brainstorming on segmentation

3) Dipen Patel: Microstructure Simulation and Finite Element Analysis

Scope for Future Work

1) Need to obtain some more real microstructures.

2) Carry out physical experimental testing on those real samples to get real property data

3) Measure fibre metrics like length, width, curvature etc.

4) Incorporate aforementioned fibre metrics while simulating some more variety of microstructures

5) Use established process to improve linkage using new microstructures

Matlab Tools

1) Image Reconstruction: http://stackoverflow.com/questions/12800333/matlab-3d-ct-image-reconstruction-by-2d-slices

2) Sliceomatic: http://www.mathworks.com/matlabcentral/fileexchange/764-sliceomatic

3) Peak Fitter: http://www.mathworks.com/matlabcentral/fileexchange/23611-peak-fitter

4) 2-Point Statistics: https://github.com/tonyfast/SpatialStatisticsFFT

5) Fiber Extraction: http://loci.wisc.edu/software/ctfire

6) Multivariate Polynomial Regression: http://www.mathworks.com/matlabcentral/fileexchange/34918-multivariate-polynomial-regression

Project Timeline

Primary Responsibilities

Work primarily done by Alicia

• Coordinate collection of CT data

• 2D Visualization

• Collection of 2 Point Statistics

• Initial Thresholding

• Work on determining fiber metrics

• Literature Search

• Analysis of FEM Results

• Website management

Work Primarily done by Geet

• 3D Microstructure Visualization

• Looking at Segmentation Algorithms for 3D Microstructures: Otsu’s Method

• Multimodal Histogram Peak Fitting & Gaussian Likelihood Maximization for Segmentation

• Looking at FIRE for Fibre Exraction

• Microstructure Simulation

• FEM Simulation

• Principal Components Analysis

• Linkage Development - Regression