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Project Grant Team
John S. Pazdar Peter A. Wursthorn Project Director Principal Investigator Capital Comm-Tech College Capital Comm-Tech College Hartford, Connecticut Hartford, Connecticut
This project was supported, in part, by the Patricia L. Hirschy National Science Foundation Principal Investigator Opinions expressed are those of the authors Asnuntuck Comm-Tech College and not necessarily those of the Foundation Enfield, Connecticut
NASA - AMATYC - NSF
SPINOFFS
Spinoffs are relatively short learning modules inspired by the LTAs. They can be easily implemented to support student learning in courses ranging from prealgebra through calculus. The Spinoffs typically give students an opportunity to use mathematics in a real world context.
LTA - SPINOFF 4A Measuring Cracks in the Space Shuttle
LTA - SPINOFF 4B Calculating Cracks in the Space Shuttle
Karen Gaines - AMATYC Writing Team Member St Louis Community College - Meramec, Kirkwood, Missouri
Kathy Mowers - AMATYC Writing Team Member Owensboro Community College, Owensboro, Kentucky
Eric Thaxton - NASA Scientist/Engineer Kennedy Space Center, Florida
NASA - AMATYC - NSF
SPINOFF 4A
Measuring Cracks in the Space Shuttle
The Background
Eric Thaxton, one of the Mechanical Engineers at NASA’s Kennedy Space Center, often is asked to analyze cracks that occur in various structures. These cracks can be found in metallic structures such as tubes, pipes, liquid storage tanks, the Space Shuttle, or components for the space station.
If a crack reaches its critical stage, the crack will then expand at the speed of sound and the structure will most likely burst, causing possibly catastrophic consequences. Years ago, when engineers realized that a critical crack was often the cause for ships to break in half, the need for experts in cracks emerged. The intensive study of cracks, called Fracture Mechanics, is a relatively new field in Mechanical Engineering. As a result of this intensive study, great strides have been made in detecting and analyzing cracks, especially cracks that were previously undetected. The use of ultrasound and/or x-rays enables the engineer to detect microscopic surface cracks as well as cracks embedded in the metal.
Environmental concerns necessitate that we reuse or extend the current use of metal structures that too often would previously have been abandoned. Since pressure vessels (liquid storage tanks with the liquid under pressure) may cost hundreds of thousands of dollars, budgetary concerns demand that they be used as long as possible. Obviously, safety must be an overriding concern of the engineers charged with the decision on continued use.
The Problem
Your task will be to measure a set of cracks and to determine which ones are critical.
You will need to measure the crack using the metric system of measurement since the stress value that you will be given is in the metric system. So a brief introduction to the metric system might be appropriate. You can see below a metric measurer.
NASA - AMATYC - NSF
To develop a working understanding of the formulas, complete the following exercises. The length of the crack has been measured for you.
Exercises
Calculate K if σ = 110 MPa and the length of the crack is 22 mm.
Determine the Stress Intensity Factor when σ = 125 MPa and the length of the crack is 3.2 cm.
Find K when σ = 150 MPa and a = 1.1 mm.
Once you calculate the Stress Intensity Factor ( K ), you can compare its value to the allowable Stress Intensity Factor ( Ka ). The allowable Stress Intensity Factor is governed by the type of
metal involved as well as a safety factor which varies according to the use of the metal as well as any weight considerations.
If your calculated value of K is greater than the given value of Ka , you would take corrective
action — usually this would require cutting out a plug around the crack and welding in a new piece of metal.
To help your team remember this process, complete the following flowchart:
Measure the length of the crack
Take action – repair or replace
Take no action
NASA - AMATYC - NSF
Exercises
For each of the following cracks, assume that Ka = 500 MPa- (^) mm and
A) Measure and record the length of the crack; B) Find ½ of the length of the crack and record this value as a = ; C) Calculate K ; D) Report your recommendation for each crack - No-Action or Action (repair/replace tank).
σ = 80 Mpa 9) σ = 100 Mpa 10) σ = 120 MPa
σ = 120 Mpa 12) σ = 150 MPa 13) σ = 285 MPa
σ = 80 MPa 15) σ = 70 MPa
Compare and contrast your results from the cracks and pressures of Exercises 10 and 11.
Compare and contrast your results from the cracks and pressures of Exercises 13 and 15.
Explain why you think a long crack is sometimes safe while a comparatively small crack is sometimes critical.
