Lecture 6 Elasticity Cases

# Lecture 6 Elasticity Cases - Fix C so that at some...

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Elasticity –specifics Case 1: Point Defect Think about it first. At large distances displacements must go to zero, so must go as 1/r n or exp(-ar) At large distances form should not depend upon exact “shape” of point defect, although we are approximating perhaps for small distances. Spherically symmetric, so only radial term – in spherical polars u r = C/r 2 ; C needs to be determined some other fashion. u θ = u φ = 0 e rr = du r /dr = -2C/r 3 e θθ = e φφ = u r /r = C/r 3 = 0 σ rr = -2 μ C/r 3 = -2 σ θθ = -2 σ φφ d σ rr /dr = -3 σ rr /r 2 σ rr - σ θθ - σ φφ = 3σ rr Hence, 1st equation of the 3 is satisfied – can show others are How to determine C? Remove an atom, atoms nearby move closer – unbalanced forces.

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Unformatted text preview: Fix C so that at some appropriate distance displacements match We cannot simply get C from elasticity. Case 2: Spherical Precipitate Two parts to this problem: a sphere under pressure (material 1) and a long-range component (in material 2) For the sphere, e rr = constant, problem we did before-P = rr Match the stress at the boundary of the particle (R) rr = -2 2 C/R 3 = -P Dislocations Taken from Hull and Bacon xx yy xy The total energy can. Dislocation Interactions. Consider two dislocations...
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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 6 Elasticity Cases - Fix C so that at some...

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