# Lecture10 - VK250 Lecture 10 YIELD CRITERIA • Yield is a...

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VK250 Lecture 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: ! 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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VK250 Lecture 10 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? Loading parameter for yield max(1 " 3) = 75 MPa , Material parameter for yield k = 200/2 = 100 MPa no yield Alternatively: Loading parameter: S = 1 " 3 = 150MPa Material parameter for yield Y = 200 MPa no yield Note: If 3 = 100 MPa, then S = 1 " 3 = 250MPa 250 MPa > Y yield Example: Cylindrical pressure vessel made of ASTM A517-F pressure vessel steel ( σ Y = 760 MPa) R = 5m, t = 10 mm, P = 1 MPa r = 0 MPa, σ l = PR/2t = 5 (1x 10 6 )/(2x 10 -2 ) = 250 MPa, h = PR/t = 500 MPa 1 =500 MPa, 2 = 250 MPa, 3 = 0 MPa, Loading parameter for yield : S = σ 1 σ 2 = 500 MPa
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Lecture10 - VK250 Lecture 10 YIELD CRITERIA • Yield is a...

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