Critical Behavior of a Depinning Dislocation
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Critical Beha vior of a Depinning Dislocation Stefano Zapperi and Mic hael Zaiser 1
INFM, Univ ersita "La Sapienza", P.le A. Moro 2, 00185 Roma, Italy MPI fur Metallforsc hung, Heisenbergstr.1, D-70569 Stuttgart, German y
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ABSTRACT The dynamics of dislocations at yield can be understood within the framew ork of the depinning transition of elastic manifolds in random media. Close to the threshold stress for their long-range motion, the geometry and dynamics of dislocations are c haracterized by a set of critical exponents. W e consider a single exible dislocation gliding through a random stress eld, taking in to account long-range self stresses, and estimate the critical stress where depinning takes place. Sim ulations of a discretized lattice model con rm the analytical estimate and yield n umerical values of the critical exponents which are in agreemen t with theoretical predictions for an elastic string mo ving on a plane.
INTR ODUCTION
The motion of a dislocation across a random arra y of obstacles on its glide plane is a 'classical' topic of dislocation theory (for an overview, see e.g. the review by Kocks, Argon and Ashby [1]). From a statistical ph ysics viewpoint, this is a special case of a general problem, namely the dynamics of elastic manifolds in random media, which has attracted considerable attention in the statistical physics literature of the last decade [2,3]. Results from these in vestigations have been applied occasionally to dislocation problems [4,5], mostly considering dislocations in teracting with point obstacles and using a local (line tension) approximation for the dislocation self-in teraction. In the present study we take into account that bending of a dislocation line produces long-range self-stresses [6,7] and the relevant obstacles to dislocation motion are often forest dislocations whic h should not be envisaged as point obstacles: They give rise to long-range stresses, and also their 'short-range' interactions with a mo ving dislocation (formation of junctions) ha ve a range of the order of the junction length, which is comparable to the forest dislocation spacing. In the absence of applied stress, a dislocation in an obstacle eld assumes an equilibrium con guration where the self stresses balance the dislocation-obstacle interactions. With increasing external stress this con guration beomes unstable at some poin t, and segmen ts of the dislocation line jump forw ard to nd a new equilibrium . As is increased further, more jumps tak e place and the average area swept in a jump increases until, at a critical stress , the dislocation starts to mo ve inde nitely. The average velocity of the dislocation vanishes in the long time limit for < , and scales as ( ; ) for > . In metallurgical terms, the depinning transition at corresponds to the transition from the microplastic to the plastic regime. It can be envisaged as a critical non-equilibrium phase transition where an order parameter (the dislocation velocity) increases from zero when a con trol parameter (the
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