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Lecture10

# Lecture10 - ME 382 Lecture 10 YIELD CRITERIA Yield is a...

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ME 382 Lecture 10 29/ix/10 1 Y IELD C RITERIA Yield is a shear driven process Tresca yield criterion Yield occurs when shear stress on any plane equals k (shear yield strength) Loading parameter: τ max(1-2) or τ max(2-3) or τ max(1-3) Material parameter: k Tresca yield criterion: τ max(1 2) or τ max( 2 3 ) or τ max(1 3) k Example: Uniaxial test ( σ xx = σ ο ) From Mohr’s circle: τ max = σ o /2 yield when σ o /2 k Uniaxial yield stress: σ Y = 2 k (by Tresca) Tresca yield criterion can also be stated by defining an effective normal stress : σ S = max σ 1 σ 2 , σ 2 σ 3 , σ 1 σ 3 ( ) Loading parameter: σ S Material property: σ Y Tresca yield criterion: σ S σ Y For uniaxial loading this reduces to the special case of σ o σ Y Example Torsion of a cylinder (assume material property for yield is σ Y ): Maximum shear stress on surface of cylinder τ θ z = τ o = TR / J

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ME 382 Lecture 10 29/ix/10 2 τ r θ = τ rz = σ θθ = σ rr = σ zz = 0 σ 11 = τ ο , σ 22 = - τ ο , σ 33 = 0 Loading parameter: σ s = 2 τ o Yield if τ ο σ Y /2 (or if τ ο k ) Example: σ 1 = 150 MPa, σ 2 = 50 MPa, σ 3 = 0 MPa. Does yield occur if σ Y = 200 MPa?
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