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Starting from the fundamental relation between the diffusion flux of point defects (vacancies, interstitials) and the gradient of the diffusion potential the diffusion equation is set up and applied to the calculation of the concentrations of both types of point defects. Thereby, all possible sources and sinks and their mutual effects are taken into consideration. These equations are coupled with the equations for the temporal derivatives of dislocation density, porosity, pore size and temperature. For the close-up region of spherical inhomogeneities (pores, hard inclusions) and a grain boundary this system of six partial differential equations is solved numerically. For simplicity a one dimensional model in space is used and uniaxial tension or pure shear load is assumed. Hardening and the simultaneous recovery are characterized by the local and temporal development of the point defect concentrations and especially of the dislocation density, which is proportional to the intrinsic strain energy. The gradients of both strain energy and lattice rotation determine the formation and growth of recrystallization nuclei. It is the aim of this work to present a new mathematical model and also to give a perceptual general view on the concerted action of the fundamental physical processes, which necessarily lead to hardening, recovery (softening) and recrystallization nucleation. Moreover it seems to be a basis of a future general theory of microstructure changes.

international journal of materials research

A continuum based microstructure model of inhomogeneous hardening and recovery as a pre-stage of recrystallization nucleation: Dedicated to Professor Dr. H.-P. Degischer on the occasion of his 65 th  birthday