Back to Search
Start Over
Derivation of Orowan's law from the Peierls-Nabarro model
- Publication Year :
- 2012
-
Abstract
- In this paper we consider the time dependent Peierls-Nabarro model in dimension one. This model is a semi-linear integro-differential equation associated to the half Laplacian. This model describes the evolution of phase transitions associated to dislocations. At large scale with well separated dislocations, we show that the dislocations move at a velocity proportional to the effective stress. This implies Orowan's law which claims that the plastic strain velocity is proportional to the product of the density of dislocations by the effective stress.<br />Comment: 23 pages. arXiv admin note: text overlap with arXiv:1007.2915
- Subjects :
- Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1207.4412
- Document Type :
- Working Paper