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Lecture29-Notes

# Lecture29-Notes - ME 382 Lecture 29 CREEP Instantaneous...

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ME 382 Lecture 29 1 C REEP Instantaneous response to a load is elastic or plastic deformation ε = f σ ( ) In general, all materials exhibit additional deformation with time ε = f σ , t ( ) This is known as creep Importance of instantaneous response vs. creep response depends on i) Time scale Ice is elastic, but glaciers creep over a period of years ii) Temperature Al 2 O 3 is elastic at room temperature, but creeps at 1300 ° C Creep deformation occurs in response to shear (constant volume) - like yield Therefore, loading parameter for creep is von Mises effective normal stress ˜ σ H = 1 2 σ 1 σ 2 ( ) 2 + σ 1 σ 3 ( ) 2 + σ 2 σ 3 ( ) 2 [ ] Constitutive equations for creep are of the form: d ˜ ε H dt = f ˜ σ H ( ) where, the effective strain is given by ˜ ε H = 2 9 ε 1 ε 2 ( ) 2 + ε 1 ε 3 ( ) 2 + ε 2 ε 3 ( ) 2 [ ] Remember, that the von Mises effective stress was used so that the multiaxial yield criterion was the same as the criterion for uniaxial tension. The same reasoning applies to this definition of effective strain: (i) Creep is deformation by shear (ii) Therefore, volume is conserved (iii) In uniaxial creep: σ 1 = σ o ; σ 2 = 0; σ 3 = 0 If ε 1 = ε o

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