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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 4B
Calculating 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 the cause for ships to break in half was often a result of a critical crack, the need for experts in cracks emerged. The intensive study of cracks is a relatively new field in Mechanical Engineering called Fracture Mechanics. As a result of this intensive study, great strides have been made in detecting and analyzing cracks, especially in cracks that were previously undetected. The use of ultrasound and/or x-rays enables the engineer to detect microscopic cracks as well as cracks embedded in the metal that are not visible to the naked eye.
Environmental concerns necessitate that we reuse or extend the current use of metal structures that too often would previously have been abandoned. With pressure vessels (liquid storage tanks with the liquid under pressure) priced in the hundreds of thousands of dollars, budgetary concerns also demand 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
Because many of these cracks are microscopic, sometimes it is necessary to calculate their lengths since measuring them would be impossible. To do so a grid printed on a transparent film is placed over the crack. A picture is taken, which is then ‘blown-up’to a size more easily seen by the human eye. Your task will be to calculate the lengths of cracks to determine if the crack is critical or not.
NASA - AMATYC - NSF
- Assume that Ka = 250 MPa- mm and that the grids are 1mm x 1mm. For cracks 1- 4, do
the following. a) Estimate the length of the crack. b) Calculate the length of the crack c) Find ½ of the length of the crack and record this value as a = ____. d) Calculate K. e) Determine whether the Shuttle is still safe or if corrective action is necessary.
Crack 1 σ = 120 MPa
Crack 2 σ = 120 MPa
Crack 4 σ = 100 MPa
Crack 3 σ = 50 MPa
NASA - AMATYC - NSF
- Assume that Ka = 70 psi- (^) in and that the grids are
F in in
H
G
I
K
J×
F
H
G
I
K
J. For cracks 5-8, do the
following. a) Estimate the length of the crack. b) Calculate the length of the crack c) Find ½ of the length of the crack and record this value as a = ____. d) Calculate K. e) Determine whether the Shuttle is still safe or if corrective action is necessary.
Address the following statements using your results from the preceding eight cracks:
Compare and contrast your observations of cracks 1 and 2.
Compare and contrast your observations of cracks 3 and 4.
Compare and contrast your results from crack 6 with other members of your class.
Compare and contrast your observations of cracks 7 and 8.
Explain why you think a long crack is sometimes safe while a comparatively small crack is sometimes critical.
Crack 5 σ = 100 psi
Crack 6 σ = 100 psi
Crack 7 σ = 110 psi
Crack 8 σ = 20 psi
