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February 1, 2016

Thesis defense of Pierre-Louis VALDENAIRE

from centre des matériaux of MINES ParisTech

Thesis defense of Pierre-Louis VALDENAIRE

Pierre-Louis VALDENAIRE will defend his thesis, called

" Crystal plasticity: Transport equation and dislocation density"

on February, 1st 2016 à 2pm

at MINES ParisTech 60, boulevard Saint-Michel 75272 Paris cedex 06

Room V334

Thesis directors : Alphonse FINEL, Samuel FOREST

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.

Thesis Defence of PL VALDENAIRE - MINES ParisTech

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