E106 Lecture Problem 136

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E106 Lecture Problem 136

• David Schimon
• March 7, 2006

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Problem Statement

• Caluate the maximum radius and wall thickness of
  a spherical pressure vessel made of Ti-6Al-4V
  Titanium alloy periodically pressurized to 500
  kPa, s.t. it will leak before breaking.

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Given Information

• For Titanium Alloy Ti-6Al-4V,
• syield 910 MPa
• KIc 55 MPa sqrt(m)
• Relevant forumlae
• Plane strain toughness definition
• Circumferential wall stress
• Design Objective leak-before-break

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Formulae

• Plane Strain Toughness Definition
• Y 1.0 for sphere, a crack length
• Circumferential wall stress
• p pressure, t thickness, r radius

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Exploration Leak-before-break

• In pressure vessels, useful to allow a crack to
  propagate fully through the wall so that gas will
  detectably leak before catastrophically failing.
• To allow for this, let the thickness of the wall
  be half the critical crack length, or
• ac t rather than ac t/2
• This allows gas to leak through before fracture.

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Revised Formulae

• Include yield stress and leak criterion

• Solve for t and combine

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Plugging and Chugging
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Conclusions

• Extremely useful for defining upper bounds
• Important in determining safety measures
• A useful method to identify the ability of
  materials to leak before breaking
• The constant term is a good measure of
  this effectiveness titanium alloy has a value
  of 3.3, while mild steel is 11.2
• Requires a balance of ductility and yield
  strength

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The End

• ?