Homogeneous Nucleation of Dislocations as Bifurcations in a Periodized Discrete Elasticity Model Articles uri icon

published in

  • EPL  Journal

publication date

  • February 2008

start page

  • 36001

issue

  • 3

volume

  • 81

international standard serial number (ISSN)

  • 0295-5075

electronic international standard serial number (EISSN)

  • 1286-4854

abstract

  • A novel analysis of homogeneous nucleation of dislocations in sheared two-dimensional crystals described by periodized-discrete-elasticity models is presented. When the crystal is sheared beyond a critical strain F=Fc, the strained dislocation-free state becomes unstable via a subcritical pitchfork bifurcation. Selecting a fixed final applied strain Ff >Fc, different simultaneously stable stationary configurations containing two or four edge dislocations may be reached by setting F=Fft/tr during different time intervals tr. At a characteristic time after tr, 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 dislocation-free state.