Dynamic dislocation pile-ups
- 1 May 1983
- journal article
- research article
- Published by Taylor & Francis in Philosophical Magazine Part B
- Vol. 47 (5) , 707-719
- https://doi.org/10.1080/13642818308246470
Abstract
The motion of a continuous distribution of dislocations moving under a constant imposed stress towards a small locked dislocation is considered. This problem can be modelled as a non-linear partial differential equation for a complex stress function if a linear stress–velocity law is assumed. If the initial density of the distribution is sufficiently small. the dynamic pile-up that occurs can be described using matched asymptotic expansions. In particular, the force on the locked dislocation is derived as a function of time, It is further shown that the solution remains valid when the velocity in proportional to any positive power of the stress.Keywords
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