Skip to Main content Skip to Navigation

Crystal plasticity : Transport equation and dislocation density

Abstract : The mechanical behavior of industrial metallic alloys, in particular those used in the aerospace industry, is controlled by the existence of several types of precipitates and by the nucleation and propagation of crystalline defects such as dis- locations. The understanding of this behavior requires continuous models to access the macroscopic scale. However, even today, conventional plasticity theories use mesoscopic variables and evolution equations that are not based on the transport of dislocations. Therefore, these theories are based on phenomenological laws that must be calibrated for each material, or, for each specific applications. It is therefore highly desirable to make link between the micro and macro scales, in order to derive a continuous theory of plasticity from the fundamental equations of the dislocation dynamics. The aim of this thesis is precisely to contribute the elaboration of such a theory. The first step has consisted to rigorously establish a coarse graining procedure in a simplified situation. We have then obtained a set of hyperbolic transport equations on dislocation densities, controlled by a local friction stress and a local back-stress that emerge from the scale change. We have then developed a numerical procedure to compute these local terms and analyze their behavior. Finally, we have developed an efficient numerical scheme to integrate the transport equations as well as a multigrid spectral scheme to solve elastic equilibrium associated to an arbitrary eigenstrain in an elastically heterogeneous and anisotropic medium.
Document type :
Complete list of metadata

Cited literature [102 references]  Display  Hide  Download
Contributor : ABES STAR :  Contact
Submitted on : Thursday, December 15, 2016 - 4:57:08 PM
Last modification on : Wednesday, November 17, 2021 - 12:28:19 PM
Long-term archiving on: : Monday, March 20, 2017 - 6:59:53 PM


Version validated by the jury (STAR)


  • HAL Id : tel-01417559, version 1


Pierre-Louis Valdenaire. Crystal plasticity : Transport equation and dislocation density. Materials. Université Paris sciences et lettres, 2016. English. ⟨NNT : 2016PSLEM002⟩. ⟨tel-01417559⟩



Record views


Files downloads