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 Theory (or Tresca Theory) F σ x = F A A

Distortion Energy Theory (or von Mises Theory)

triaxial hydrostatic distortional Distortional strain energy: u d = u − u h � ( σ 1 − σ 2 ) 2 + ( σ 2 − σ 3 ) 2 + ( σ 3 − σ 1 ) 2 = 1 + ν � 3 E 2

σ ′ ≤ σ y where � ( σ 1 − σ 2 ) 2 + ( σ 2 − σ 3 ) 2 + ( σ 3 − σ 1 ) 2 � 1 / 2 σ ′ = 2 von Mises Max Shear

In terms of xyz components (rather than principal stresses): σ ′ = 1 xz )] 1 / 2 2[( σ x − σ y ) 2 +( σ y − σ z ) 2 +( σ z − σ x ) 2 +6( τ 2 xy + τ 2 yz + τ 2 √ If in plane stress: σ ′ = ( σ 2 xy ) 1 / 2 x − σ x σ y + σ 2 y + 3 τ 2