Derivation of Orowan's Law from the Peierls-Nabarro Model

作者：Monneau Regis; Patrizi Stefania^*

来源：Communications in Partial Differential Equations, 2012, 37(10): 1887-1911.

DOI：10.1080/03605302.2012.683504

• Dislocation dynamics
• Non-local equations
• Orowan's law
• Peierls-Nabarro model
• Periodic homogenization
• Transition layer

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.

• 出版日期2012