ME_423_lecture_7 - ME 423 09/16/2010 Lecture 7 Failure...

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Unformatted text preview: ME 423 09/16/2010 Lecture 7 Failure theories 2.2.3 Ductile failure (yield criteria) Tresca’s maximum shear stress criterion σ1 − σ 2 σ 2 − σ 3 σ 3 − σ1 , , 2 2 2 S τ y - shear stress at yield, τ y = Y 2 S y - uniaxial yield stress τ max = max =τy σ E = max(σ 1 − σ 2 , σ 2 − σ 3 , σ 3 − σ 1 ) = S y Von Mises’ deviatoric strain energy criterion ) Strain energy density U 0 = U 0 + U 0 U 0 - dilatational strain energy density ) U 0 - deviatoric strain energy density [ ) (σ 1 − σ 2 ) 2 + (σ 2 − σ 3 ) 2 + (σ 3 − σ 1 ) 2 (1 + ν ) ) U0 ≡ = UY 6E σE ≡ (σ 1 − σ 2 ) 2 + (σ 2 − σ 3 ) 2 + (σ 3 − σ 1 ) 2 = σY 2 or 2 2 2 2 2 2 σ E = σ xx + σ yy + σ zz − σ xxσ yy − σ yyσ zz − σ zz σ xx + 3σ xy + 3σ yz + 3σ xz = σ y SF = SY σE Octahedral shear stress 1 1 τ oct = 2( I 12 − 3I 2 ) (σ 1 − σ 2 ) 2 + (σ 2 − σ 3 ) 2 + (σ 3 − σ 1 ) 2 = 3 3 ...
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ME_423_lecture_7 - ME 423 09/16/2010 Lecture 7 Failure...

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