Lecture 7 Dislocations

Lecture 7 Dislocations - Elasticity dislocations Energy...

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Elasticity –dislocations Energy Thinks first: 1) Dislocation stresses go as 1/r (with additional complications for edge dislocation, but let’s ignore. 2) Work done is going to scale as = b R r rdr C d W 0 0 / ε Move faces (that will later be glued) by “ ε ” and integrate from 0->b; take the forces from some core cut “r 0 ” out to the size of the crystal R. Scaling is therefore (per unit length) W Scales as b 2 Scales as ln(R/r 0 ) The core radius “c” could be taken as where the elastic solution becomes nonsense, but there is a better way. There is going to be an energy per unit length for the local “bond breaking” at the core of the dislocation. We take c such that it represents this energy contribution. For a screw dislocation result is W = μ b 2 /2 π ln(R/r 0 ) Edge is almost the same W = μ b 2 /2 π(1-ν29 ln(R/r 0 ) Poisson’s ratio is ~ 1/3, so the energy of an edge dislocation is about 1.5 times the energy of a screw dislocation. Some conceptual points:
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This note was uploaded on 04/13/2010 for the course MAT SCI 404 taught by Professor Matsci during the Winter '10 term at Northwestern.

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Lecture 7 Dislocations - Elasticity dislocations Energy...

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