Exploring Nondestructive Evaluation Methods
Figure 1. The ultimate destructive test—a nuclear weapon test.Copyright 1946 U.S. Department of Defense, Wikimedia Commons (public domain) https://commons.wikimedia.org/wiki/File:Operation_Crossroads_Baker_Edit.jpg
Through this lesson and its series of hands-on mini-activities, students answer the question: How can we investigate and measure the inside of an object or its structure if we cannot take it apart? Unlike the destructive nuclear weapon test (!), nondestructive evaluation (NDE) methods are able to accomplish this. After an introductory slide presentation, small groups rotate through five mini-activity stations: 1) applying Maxwell’s equations, 2) generating currents, 3) creating magnetic fields, 4) solving a system of equations, and 5) understanding why the finite element method (FEM) is important. Through the short experiments, students become familiar with the science and physics being used and make the mathematical connections. They explore components of NDE and see how engineers find unseen flaws and cracks in materials that make aircraft. A pre/post quiz, slide presentation and worksheet are included.
While the fields of mechanical and electrical engineering, physics and mathematics might seem quite different from each other to the average person, they not only depend on each other, but overlap in a way that enables the average engineer and physicist to be more successful in their own practices. Thus, mirroring the real world, this lesson requires basic knowledge of each of these fields.
In this lesson, students explore components of nondestructive evaluation—the term for a wide group of analysis techniques designed to inspect the properties of materials, components and systems without causing damage to them. Nondestructive testing methods introduce energy into materials as a way to locate flaws that cannot been seen that could lead to failures and potential catastrophe. Some common techniques are eddy current, magnetic particle, liquid penetrant, radiographic and ultrasonic. NDE is valuable for product evaluation, troubleshooting and research because the objects being examined—everything from concrete structures to planes, vehicles, machine parts and the human body—are not permanently damaged, and “invisible” defects can be found and measured.
Students also learn about finite element analysis as a numerical way to solve real-world engineering and mathematical problems by subdividing a large problem into smaller, simpler parts that are assembled to model the entire problem and approximate a solution. The approach enables detailed visualization of structures, where they bend or twist, indicating areas of stress and defect.
After this lesson, students should be able to:
- Connect systems of equations to real-world applications.
- Model an experiment using a smaller-scale problem and solve systems by hand, by using the TI-Nspire and comparing results.
- Compare and contrast a model to a proposed experiment.
- Apply physics, mechanical engineering and electrical engineering concepts by running a non-routine experiment.
- Determine an optimal solution by running a computer program and interpreting the graphical results.
- Express their knowledge by answering the following question in a short paragraph: How does this real-world experience and its connection with mathematics and engineering impact you?