Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Zhong Hu


carbon, fiber, laminate, misalignment, modulus, unidirectional


Nondestructive Evaluation (NDE) is an effective way for determining material properties. More specifically, ultrasonic waves along with visual measurements from a microscope can be used to systematically determine the elastic modulus of single ply composites that are subject to an altered manufacturing process. In this approach, the magnitude of specific ultrasonic wave velocities is applied through Chirstoffel's equations to determine the necessary five elastic constants that describe the elastic modulus of transversely isotropic composites. On the other hand, fiber misalignment measurements are taken through via digital microscopy to satisfy a statistical approach for the determination of the same elastic modulus. The Paper Physics Approach (PPA) and Laminate Analogy Approach (LAA) are utilized to predict the elastic modulus of unidirectional carbon fiber samples. A two parameter Weibull distribution is expected to satisfy the probability density of the fiber length and fiber orientation variation which will then be implemented into the Halpin-Tsai equations that will determine the elastic modulus. In terms of results, the mean fiber length from the visual approach is approximately 250 μm and the mean fiber misalignment is just over 3°. The elastic constants range from 7 GPa to 9 GPa depending on the approach. Destructive mechanical testing led to an average elastic modulus value of 8.49 GPa.

Library of Congress Subject Headings

Carbon fibers

Composite materials -- Testing

Strength of materials

Nondestructive testing

Ultrasonic testing


Includes bibliographical references (page 72-73)



Number of Pages



South Dakota State University


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