lecture11B - Distortion Energy Theory (Huber-von...

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1 Distortion Energy Theory (Huber-von Mises-Hencky) The plastic yielding is predicted to occur if the equivalent (von Mises) stress is equal or exceeds the uni-axial yield limit σ 0 or ys . 0 eq Where: - for general 3-D stress state: () ()() 22 2 2 1 6 2 eq xx yy yy zz zz xx xy yz zx σσ =− + + + + + - for 3-D stress state in principal stresses: ( ) 2 12 23 31 222 123 1 2 2 3 3 1 1 2 eq + + =+ +
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2 Plastic yielding conditions under uni-axial stress state ( typical at the notch tip for a notched body in plane stress) Plastic yielding will occur if : () 22 2 222 2 1 6 2 1 0 0 0 0 6 000 2 eq xx yy yy zz zz xx xy yz zx yy yy eq yy σ σσ σσσ =− + + + + + + + + + + = 0 0 yy xx zz xy yz zx σσσσσ ===== 0 0 1 yy eq yy or when = ≥≥ σ yy = σ 0
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3 Plastic yielding conditions under uni-axial loading in plane strain (typical at the notch tip for a notched body in plane strain) Plastic yielding will occur if : () ( ) ( ) 22 2 222 2 2 1 6 2 1 00 6 0 0 0 2 1 eq xx yy yy zz zz xx xy yz zx yy yy yy yy eq yy σ σσ σσσ νσ ν =− + + + + + + + + + + + 0 0 0 yy
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lecture11B - Distortion Energy Theory (Huber-von...

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