notes_21_yield_criter

notes_21_yield_criter - Yield Criteria Ref Shames section...

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σ Y Yield Criteria Ref: Shames section 7.5 and 9.2 or Crandall and Dahl section 5.11 page 312 ff general state of stress => expressing maximum shear stress on octahedral plane closing in on a point = τ oct τ oct := 1 σ 1 σ 2 ( 2 σ 1 σ 3 ( 2 + 2 σ 3 ( 2 + ) ) σ ) where σ 1 , σ 2 , and σ 3 are principal stresses 3 ( τ 12 = τ 13 = τ 23 = 0) onset of yielding occurs when τ oct reaches a point depending only on the material. It can be evaluated from a tensile test where: σ 1 = σ y ; σ 2 = 0 ; σ 3 = 0 ; τ = 0 τ oct_Y := 1 σ y 0 ( 2 σ y 0 ( 2 + 00 ( 2 + ) ) ) τ oct_Y := 2 Y or . ...... 3 3 σ 1 σ 2 ( 2 σ 1 σ 3 ( 2 + 2 σ 3 ( 2 + ) ) σ ) = 2 σ Y => onset of yielding in 2D we have Mohr's circle (Shames 7.5): 3 σ a := σ x + σ y + σ x σ y 2 2 τ xy 2 + () 2 4 σ b := σ x + σ y σ x σ y 2 2 τ xy 2 + 2 ( σ x- σ y ) 2 /2 + τ xy 2 ( σ x - σ y )/2 τ xy τ xy σ x σ y Mohr’s circle σ τ τ extreme := σ x σ y 2 2 τ xy 2 + where +/- applies 1 if x and y are principal axes +> τ extreme := σ x σ y ( 2 ) and as above 2 1

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σ 3 τ oct_extreme := 1 1 − σ 2 ) 2 + 1 ) 2 + 2 − σ 3 ) 2 where σ 1 , σ 2 , and σ 3 are principal stresses 3 ( τ 12 = τ 13 = τ 23 = 0)
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notes_21_yield_criter - Yield Criteria Ref Shames section...

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