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Lecture Problem 136

Lecture Problem 136. E106 Section 2 Corina Tom 3-7-07. Problem Statement. Calculate the maximum radius and wall thickness of a spherical pressure vessel made of Ti-6A1-4V Titanium Alloy periodically pressurized to 500 kPa, so that it will leak before breaking.

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Lecture Problem 136

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  1. Lecture Problem 136 E106 Section 2 Corina Tom 3-7-07

  2. Problem Statement • Calculate the maximum radius and wall thickness of a spherical pressure vessel made of Ti-6A1-4V Titanium Alloy periodically pressurized to 500 kPa, so that it will leak before breaking. • Use data on Table 9.1 on pg. 298 of Callister.

  3. Pressure Vessels! • Designed to contain a significant pressure • Force is distributed evenly over the entire surface • Usually spherical or cylindrical (curvy!) • Sharp angles = stress concentrations • Pressure results in membrane stresses

  4. σxx = σyy P It’s a stressful state • Stress does not depend on direction • Thin-wall t ≤ 0.1ri • ri = ro = r • Balance forces:

  5. 2a t Leak-Before-Break • Want crack through entire thickness before rapid crack propagation

  6. Leak-Before-Break • Vessel must contain pressure without yielding

  7. Assumptions • Thin-walled pressure vessel • Plane Strain • Y = 1 • One half internal crack length equal to thickness will ensure leakage

  8. Max t • Kic = 55 MPa m1/2 • σy= 910 MPa • Y = 1 t = 1.16 mm

  9. Max r • σy= 910 MPa • P = 500 kPa = .5 MPa • T = 0.00116 m r = 4.23 m

  10. Design Review • Leak-before-break • No plastic deformation • Want critical crack length = thickness • Yielding before failure • Plastic deformation of walls • Want large critical crack lengths

  11. Great Molasses Flood • North End - Boston • Jan. 15, 1919 • Purity Distilling Company • Neglected safety precautions • 21 people and many horses killed • Over 150 injured Aftermath - wikipedia.org

  12. Applications • Poor pressure vessel design may lead to catastrophic failure • Methods to catch safety hazards • Leaking • Vessel Distortion

  13. References • Callister, W. Fundamentals of Materials Science and Engineering. 2nd Edition. John Wiley & Sons, Inc., 2005. • “Great Molasses Flood.” Massachusetts Foundation for the Humanities. <massmoments.org> • Rossman and Dym. Continuum Mechanics: Mechanics of Solids and Fluids. Harvey Mudd College, 2006.

  14. Questions???

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