Lecture Problem 136

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Lecture Problem 136

• Jowene Wong
• March 7, 2007

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Problem Statement

• 136) Calculate the maximum radius and wall
  thickness of a spherical pressure vessel made of
  Ti-6Al-4V Titanium alloy periodically pressurized
  to 500 kPa, so that it will leak before breaking.
  Use data on Table 9.1 on p. 298 of Callister.

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Background

• Fracture mechanics relationship between
  material properties, stress level, presence of
  crack-producing flaws, and crack propagation
  mechanisms
• Fracture occurs when applied stress exceeds sc
• Design structures to avoid failure or detect
  failure early on to avoid catastrophic results
• Kc fracture toughness, materials resistance
  to brittle fracture when crack present
• KIc plane strain fracture toughness
• Kic lt Kc

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Background

• Yield-before-break
• Wall material plastically deforms due to
  formation of critical size crack and its rapid
  propagation
• Materials with large critical crack lengths
  desired
• Leak-before-break
• Crack grows through walls thickness prior to
  rapid propagation such that crack penetrates wall
  completely, allowing contents to leak
• Preferable because easier to detect by monitoring
  pressure

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What Do We Know?

• Given values
• Crack propagation equations

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What Do We Know?
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What Do We Know?
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What Do We Know?

• Material properties of Ti-6Al-4V from Table 9.1

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Assumptions

• Thin-walled pressure vessel.
• Y 1.
• Leak-before-break occurs when ac t, not 2ac t
  (at wall surfaces, NOT internally).
• Plane strain.

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Solution Procedure

• Let ac t, sc s sy.

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Solution Procedure

• Substitute t into KIc to solve for r

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Solution Procedure

• Use hoop stress to solve for t
• t ltlt r affirms our thin wall assumption

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Applications

• Pressure vessels are everywhere
• Fire extinguishers
• Propane tanks
• Paintball cylinders
• Chemical plants
• Spider-Mans web shooters
• Want to design them such that you can detect
  failure before they explode