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

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ME 382 Lecture 10 26/ix/07 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: ! max(1 " 2) or max(2 " 3) or max(1 " # 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 : S = max 1 " 2 , 2 " 3 , 1 " 3 ( ) Loading parameter: S Material property: σ Y Tresca yield criterion: " S # 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 z = o = TR / J

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ME 382 Lecture 10 26/ix/07 2 τ r θ = rz = σ θθ = rr = zz = 0 11 = ο , 22 = - , 33 = 0 Loading parameter: ! s = 2 " o Yield if 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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This note was uploaded on 10/12/2008 for the course MECHENG 382 taught by Professor Thouless during the Spring '08 term at University of Michigan.

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

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