Homogeneous nucleation of dislocations as bifurcations in a periodized discrete elasticity model
Abstract
A novel analysis of homogeneous nucleation of dislocations in sheared twodimensional crystals described by periodized discrete elasticity models is presented. When the crystal is sheared beyond a critical strain $F=F_{c}$, the strained dislocationfree state becomes unstable via a subcritical pitchfork bifurcation. Selecting a fixed final applied strain $F_{f}>F_{c}$, different simultaneously stable stationary configurations containing two or four edge dislocations may be reached by setting $F=F_{f}t/t_{r}$ during different time intervals $t_{r}$. At a characteristic time after $t_{r}$, one or two dipoles are nucleated, split, and the resulting two edge dislocations move in opposite directions to the sample boundary. Numerical continuation shows how configurations with different numbers of edge dislocation pairs emerge as bifurcations from the dislocationfree state.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 February 2008
 DOI:
 10.1209/02955075/81/36001
 arXiv:
 arXiv:0711.3744
 Bibcode:
 2008EL.....8136001P
 Keywords:

 Condensed Matter  Materials Science
 EPrint:
 6 pages, 4 figures, to appear in Europhys. Lett