About The Class

"The course objectives are to train students to become familiar with composite materials in terms of design, manufacturing, and testing. Additionally, students will learn about the tradeoffs in using different constituent materials and also design parameters. Special topics such as bioinspired materials and machine learning methods will be introduced as well. Students will be exposed to how composites are used in various applications in aerospace, biomedical, sports, among other fields." (taken from class syllabus)

Project'

My group of 5 engineers, including myself, was allowed to choose the type of final project we wanted to take on: a literature review of a topic, a research project of your choice, or a simulation project. As the name of our project suggests, we decided to pursue a simulation project!

Abstract

Our objective was to validate the Halpin-Tsai equations for calculating the elastic modulus of composite materials through ANSYS simulations. The Halpin-Tsai equations for unidirectional continuous lamina are often used over other methods for calculating transverse modulus, because of its accuracy.

The validation required repeated simulations on a Carbon Fiber-Reinforced Resin Epoxy Composite at various Vf values ranging from 0.1 to 0.5. We compared the simulated results or the transverse modulus to the results from Halpin-Tsai using the conventional zeta value of 2. We applied the same concept to calculate and compare the transverse modulus values for the E-glass Fiber Reinforced Resin Epoxy Composite. The statistical analysis is then used to determine if there’s a significant difference between the simulated and theoretical values.

Our findings showed validation for the Halpin-Tsai equations for both composites with an error of up to 7%.

Background and Previous Work

Halpin and Tsai proposed that there was a correlation between ζ and the geometry of the fiber reinforcement. In order to calculate E11, ζ should vary as a function of the fiber aspect ratio l/d from approximately zero to infinity. By comparing model predictions with available 2-D finite element results, they found that ζ=2(l/d) gave good predictions for E11 of short-fiber systems. For calculating the the transverse modulus, ζ = 2 is usually used (specifically for continuous fibers).

On the other hand, other engineering constants of short-fiber composites are only weakly dependent on the fiber aspect ratio, and can instead be approximated using the formulas for continuous fibers.

https://www.sciencedirect.com/topics/engineering/halpin-tsai-model

Objectives

Our objective was to validate the Halpin-Tsai equations for calculating the elastic modulus of composite materials through ANSYS simulations!

Goal: Evaluate the accuracy of Halpin-Tsai equations by comparing the predicted elastic modulus with experimental data.

Big Vision: Different models are used to predict mechanical properties and it’s important to understand the structural integrity and performance of components.

Hypothesis: We expect that there will be 2-3% error between the Halpin-Tsai theoretical values vs ANSYS simulations.

Methods

SolidWorks: Create the SolidWorks models for each lamina
Ansys: Run the simulations to solve for E2 of each lamina
Matlab: Calculate Halpin Tsai E2 and ANSYS simulation E2

SolidWorks Models

A team member and I created models consisting of Vf ranges from 0.1 to 0.5, which we were able to display by increasing the number of fibers. The following are dimensions that remained consistent in each lamina.

Lamina dimension: 125 mm x 1 mm x 15 mm

Fiber radius: 0.4 mm

ANSYS Static Structural Simulations

How it was done:

Assigned material properties to fibers and matrix
Created mesh
Inserted fixed support on 125mm x 1mm face
Created a 1 mm displacement on the face across to simulate a transverse pull
Collected force reaction for each simulation

https://drive.google.com/file/d/19CDJbi6Q78IeIHNjSrSDt1fSR6-4x-ew/view?usp=sharing

Mesh Quality

Matlab Data Processing - Useful Equations

Results & Analysis

For the E-glass composite, our theoretical E2 values at first undershot the simulated values. At Vf = 0.4 there was a switch and the theoretical E2 values overshot the simulated values. There was a range of error for the simulated versus theoretical values of 0.01% to 6.42%

For the Carbon-Fiber Composite, our simulated values tended higher than the E2 values calculated from Halpin-Tsai for volume fractions of 0.2-0.4. In addition, the range of error for the simulated versus theoretical values were 0.4% to 4.85% error.

Possible errors: The mesh has a large impact on the simulation results. A different mesh was created for each composite geometry, this could’ve impacted our results if the mesh was of different qualities.

In addition, the size of the the composite volume and number of fibers largely inhibited the quantity and quality of the nodes we could produce for simulations. Ansys limits the number of nodes and elements to 32000. This meant that resizing the composite part would drastically reduce error.

Conclusion

Our findings showed validation for the Halpin-Tsai equations for the Carbon Fiber-Reinforced Resin Epoxy and E-glass Reinforced Resin Epoxy. The Halpin-Tsai equations resulted in ≤7% error from the simulated values.

Our mesh quality and metrics illustrate that for more fibers, it became more difficult to maintain the quality of the mesh. We can make changes to future analysis by reducing the size of the composite and refining the mesh.

References

Halpin-Tsai Validation Through Ansys Simulation