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Lecture note 21 (11-15-2011)

Lecture note 21 (11-15-2011) - MAE 581 Advanced Materials...

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1 MAE 581 Advanced Materials Science Lecture note 21 Line defects Stress fields of screw and edge dislocations The distortion around a dislocation line is evident (shown below). At the center of the dislocation the strains are too large to be treated by elasticity theory, but beyond a distance r 0 , equal to a few atom spacings, Hooke’s law can be applied. It is therefore necessary to define a core to the dislocation at a cut-off radius r 0 ( b ) inside which elasticity theory is no longer applicable. A screw dislocation can then be considered as a cylindrical shell of length l and radius r contained in an elastically isotropic medium (Figure 3.21). Fig. At the center of the dislocation (red circle area) the strains are too large to be treated by elasticity theory. Under what assumption can we use Hooke’s law? Hooke’s law is only valid when the deformation relationship (between strain and stress) is linear.
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2 A discontinuity in displacement exists only in the z -direction, i.e. parallel to the dislocation, such that u = v = 0, w = b . The elastic strain thus has to accommodate a displacement w = b around a length 2 π r . In an elastically isotropic crystal the accommodation must occur equally all round the
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