Min max y 2 y material yield stress use max out of

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Unformatted text preview: 10 5 7.7 Yield Criteria for Ductile Materials Under Plane Stress Maximum shearing stress (Tresca) criterion Structural component is safe as long as max τ is < max τ in a tensile test specimen at yield. σ min σ τ max < Y 2 σY = material yield stress Use τmax out of plane if it exists! σ max 11 σ max σ min Maximum distortion energy (Von Mises) criterion Structural component is safe as long as distortion energy per unit volume is < that occurring in a tensile test specimen at yield. For 3 D : (σ 1 − σ 2 ) 2 + (σ 2 − σ 3 ) 2 + (σ 3 − σ 1 ) 2 < 2σ 2 y For 2 D : σ 12 − σ 1σ 2 + σ 2 2 < σ 2 y σy is yield stress σ1 > σ2 > σ3 12 6 7.8 Fracture Criteria for Brittle Materials Under Plane Stress σ max Brittle materials fail suddenly through rupture or fracture. Failure condition is characterized by ultimate strength σ U σ min Maximum normal stress (Coulomb’s) criterion Structural component is safe as long as the absolute max normal stress is < σ U of a tensile test specimen. σ max < σ U σ min < σ U 13 7.9 Stresses in Thin-Walled Pressure Vessels • Cylindrical vessel with principal σ1 stresses σ 1 = hoop stress σ 2 = lon...
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