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| Plastic Deformation | |||||||||||||||
| ·
The
deformation associated with this element is in the linear
elastic range, with an elastic energy per unit volume of the element
given by: Energy/Volume = (½Gγθz2)
= (½G ){b/2πr}2
· The total elastic energy stored in the element per unit length of dislocation line is: dES = (G/2){b/2πr}2[2πr dr] = (Gb2/4π){dr/r} · Integrating this quantity over the volume of the crystal between r0 and r1 gives the total elastic energy per unit length of the straight screw dislocation, ES . · For a typical dislocation density in a material (r1/r0) ~106 and (1/4π)Ln(106) = 1. Using this value, the elastic energy per unit length of a straight screw dislocation has the approximate value: ES ~ Gb2 |
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