lecture16 - 1 LECTURE DATE:07/12/2009 PREPARED BY:EBRU SEMA...

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Unformatted text preview: 1 LECTURE DATE:07/12/2009 PREPARED BY:EBRU SEMA KOŞAROĞLU & FARAJ KHALIKOV STATIC FAILURE THEORIES DUCTILE BRITTLE UNIAXIAL TEST MAXIMUM NORMAL STRESS THEORY For maximum normal stress theory, the failure occurs when one of the principal stresses ( ° 1 , ° 2 ±?? ° 3 ) equals to the yield strength. TRESCA CRITERIAN VON-MISES THEORY MOHR-COLOUMB THEORY MAXIMUM NORMAL STRESS THEORY(MNST) MSST :MAXIMUM SHEAR STRESS MDET :MAXIMUM DISTORTION ENERGY THEORY ? ² ? ² BRITTLE DUCTILE 2 ° 1 > ° 2 > ° 3 Failure occurs when either ° 1 = ? ? or ° 3 = −? ± ,where ? ? is strength in tension and ? ± is strenght in compression. MOHR-COULOMB THEORY The Coulomb-Mohr theory or internal friction theory assumes that the critical shearing stress is related to internal friction. MAXIMUM DISTORTION ENERGY THEORY(VON-MISES THEORY) The maximum distortion energy theory ,also known as the Von Mises theory, was proposed by M.T.Huber in 1904 and further developed by R.von Mises(1913).In this theory failure by yielding occurs when at any point in the body ,the distortion energy per unit volume in a state of combined stress becomes equal to that associated with yielding in a simple tension test. STRAIN ENERGY Generally strain energy U is obtained by this equation. U = 1 2 σ ij ε ij ² 1 = 1 ³ ( ° 1 − ´° 2 − ´° 3 ) ² 2 = 1 ³ ( −´° 1 + ° 2 − ´° 3 ) ² 3 = 1 ³ ( −´° 1 − ´° 2 + ° 3 ) Then, substituting these three equations in to general strain energy equation: U= 1 2 °...
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lecture16 - 1 LECTURE DATE:07/12/2009 PREPARED BY:EBRU SEMA...

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