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Static Failure Lecture 18 ME EN 372 Andrew Ning aning@byu.edu - - PDF document
Static Failure Lecture 18 ME EN 372 Andrew Ning aning@byu.edu - - PDF document
Static Failure Lecture 18 ME EN 372 Andrew Ning aning@byu.edu Outline Static Failure Maximum Shear Stress Theory (or Tresca Theory) Distortion Energy Theory (or von Mises Theory) Static Failure Ductile vs. Brittle Maximum Shear Stress
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Maximum Shear Stress Theory (or Tresca Theory)
F A σx = F A
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Distortion Energy Theory (or von Mises Theory)
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triaxial hydrostatic distortional
Distortional strain energy: ud = u − uh = 1 + ν 3E (σ1 − σ2)2 + (σ2 − σ3)2 + (σ3 − σ1)2 2
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σ′ ≤ σy where σ′ = (σ1 − σ2)2 + (σ2 − σ3)2 + (σ3 − σ1)2 2 1/2
von Mises Max Shear
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In terms of xyz components (rather than principal stresses):
σ′ = 1 √ 2[(σx−σy)2+(σy−σz)2+(σz−σx)2+6(τ 2
xy+τ 2 yz+τ 2 xz)]1/2
If in plane stress: σ′ = (σ2
x − σxσy + σ2 y + 3τ 2 xy)1/2