Lecture Problem 136
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Transcript of Lecture Problem 136
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Lecture Problem 136
E106 Section 2Corina Tom
3-7-07
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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.
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Pressure Vessels!
Designed to contain a significant pressure
Force is distributed evenly over the entire surface
Usually spherical or cylindrical (curvy!)Sharp angles = stress concentrationsPressure results in membrane stresses
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It’s a stressful state
Stress does not depend on direction
Thin-wall t ≤ 0.1ri
ri = ro = r
Balance forces:
P σxx = σyy
€
σ xx =rP
2t
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Leak-Before-Break
Want crack through entire thickness before rapid crack propagation
€
K Ic =Yσ πa
€
ac = t → leakage
€
ac = a 2a
t
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Leak-Before-Break
Vessel must contain pressure without yielding
€
K Ic =Yσ y πt
€
σ =σ y
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Assumptions
Thin-walled pressure vesselPlane StrainY = 1One half internal crack length
equal to thickness will ensure leakage
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Max t
Kic = 55 MPa m1/2
σy = 910 MPa Y = 1
€
t =K Ic
2
πY 2σ y2
= 0.001163€
K Ic =Yσ y πt
t = 1.16 mm
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Max r
σy = 910 MPaP = 500 kPa = .5
MPaT = 0.00116 m
€
r =2tσ yP
= 4.2325
r = 4.23 m
€
σ y =rP
2t
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Design Review
Leak-before-breakNo plastic deformationWant critical crack length = thickness
Yielding before failurePlastic deformation of wallsWant large critical crack lengths
€
K Ic =Yσ y πt
€
σ y =rP
2t
€
K Ic =Yσ yN
⎛
⎝ ⎜
⎞
⎠ ⎟ πac
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Great Molasses FloodNorth End - BostonJan. 15, 1919Purity Distilling
CompanyNeglected safety
precautions21 people and
many horses killedOver 150 injured Aftermath - wikipedia.org
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Applications
Poor pressure vessel design may lead to catastrophic failure
Methods to catch safety hazardsLeakingVessel Distortion
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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.
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Questions???