The influence of many body interactions in the stress-velocity relation of a single dislocation in a 2D lattice
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The influence of many body interactions in the stress-velocity relation of a single dislocation in a 2D lattice. M. Robles , V. Mustonen, K. Kaski and M. Patriarca Helsinki University of Technology, Laboratory of Computational Engineering P.O.Box 9400, FIN-02015 HUT, FINLAND Centro de Investigac´on en Energ´ıa UNAM, Priv. Xochicalco S/N, Col. Centro, Temixco, Mor.; A.P. 34, C.P. 62580 M´exico ABSTRACT The stress-velocity relation of a single dislocation moving in a 2-D lattice has been studied using interactive molecular dynamic simulations. A hybrid interatomic model potential which couples Lennard-Jones(LJ) potential and the Embedded Atom Model (EAM) potential, is used to include radial and many body interactions. Both parts are assembled by a parameter so that the potential can be changed to describe a pure radial interaction to a strong many body interaction in a continuous way. Setting up a constant-stress scenario, the movement of a single dislocation is tracked from zero velocity state, up to a terminal velocity state. The external stress vs. terminal velocity curves have been obtained in the subsonic regime for different values of the coupling parameter. Non-linear relations are found velocity regime to , where is the transverse speed of sound. Results have been analyzed using an augmented Peierls model to seek the connection between atomic scale, continuum variables and the limiting speed of dislocations INTRODUCTION The external stress-velocity relation, for dislocations moving in crystaline materials, is considered to be a very important dynamical relation in the theory of dislocations. Experimentally these curves have been obtained for numerous materials and exhibit very rich behaviour, for example linear relations have been reported for copper when the velocity of the dislocation is subsonic[1]. In other regimes power laws with very high exponents in the velocity have been reported for ductile metals and with low exponents for some brittle semiconductors[2, 3]. Theoretical models which are able to describe all these observations are not simple due to many factors that affect the dragging force acting on the dislocation core[4]. Most of these factors are atomic-scale related and hence difficult to include to the elasticity theory. One recent attempt to describe some of these effects was done by Rosakis [5] with the augmented Peierls model valid for subsonic, intersonic and supersonic dislocation velocity regimes. One way to clarify the molecular source of the parameters involved in the Peierls like models (or any other continuous model) is to correlate them with some parameters of the interaction potential in numerical simulations. In the early nineties Holian et al. [6–8]
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proposed a potential model composed of two parts: a Lennard-Jones (LJ) 12-6 radial potential and Embedded Atom Model (EAM) potential. Both parts were coupled with a weight parameter to tune the many body interactions. Over the time EAM models have shown to be suitable in reproducing the elastic properties
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