lec17 - 2.001 - MECHANICS AND MATERIALS I Lecture #18...

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±± 2.001 - MECHANICS AND MATERIALS I Lecture 11/13/2006 Prof. Carol Livermore Failure of Materials 3-D: x-y-z frame: ± σ σσ ± xx xy xz [ σ ]= σ xy σ yy σ yz . ± σ xz σ σ zz ± Express in principal frame x’-y’-z’ ± σ 1 00 ± [ σ ± 0 σ 2 0 ± . ± σ 3 ± x’-y’-z’: Principal Directions σ 1 2 3 : Principal Stresses Ductile Can be drawn out to a wire (Al, Cu) Fail in shear yielding Brittle Will fracture Fail in tension/compression Recall description of interatomic bonds 1 #18
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What about loading in shear? (For ductile materials) Bonds broke and were re-formed This is called a ”slip-and”, it leads to yielding (bonds are reformed and do not want to go back). This yielding is 45 to the uniaxial tension test due to the direction of maximum shear. τ y = Shear yield stress Note: τ y = σ 2 y . How do you get a measure of yield under more arbitrary loading? Tresca Yield Criterion 2
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± τ y > σ 1 σ 3 for no failure 2 vonM isesY ie ldCr iter ion :usesameasureo fstra inenergy 1 [( σ 1 σ 3 ) 2 +( σ 1
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This note was uploaded on 05/05/2010 for the course MSE 2.001 taught by Professor Carollivermore during the Fall '06 term at MIT.

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lec17 - 2.001 - MECHANICS AND MATERIALS I Lecture #18...

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