Depinning of a discrete elastic string from a two dimensional random array of weak pinning points
arXiv:0904.3357 · doi:10.1016/j.aop.2009.10.001
Abstract
The present work is essentially concerned with the development of statistical theory for the low temperature dislocation glide in concentrated solid solutions where atom-sized obstacles impede plastic flow. In connection with such a problem, we compute analytically the external force required to drag an elastic string along a discrete two-dimensional square lattice, where some obstacles have been randomly distributed. The corresponding numerical simulations allow us to demonstrate a remarkable agreement between simulations and theory for an obstacle density ranging from 1 to 50 % and for lattices with different aspect ratios. The theory proves efficient on the condition that the obstacle-chain interaction remains sufficiently weak compared to the string stiffness.
21 pages
References in corpus (7)
- Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys
- Pinning and Sliding of Driven Elastic Systems: from Domain Walls to Charge Density Waves
- Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition
- Depinning transition for a screw dislocation in a model solid solution
- Thermally Activated Motion of Dislocations in Fields of Obstacles: Effect of Obstacle Distribution
- Slow Crack Propagation in Heterogeneous Materials
- Correlation Functions for an Elastic String in a Random Potential: Instanton Approach