Analysis of non-steady-state distribution functions for grain growth and coarsening

Franz Dieter Fischer (1) , Jiri Svoboda (2) , Ernst Gamsjäger (3)

1 Institute of Mechanics
2 Institute of Physics of Materials
3 Institute of Mechanics

The description of non-steady-state grain growth or precipitate coarsening by means of object radius distribution functions with multiple time dependent parameters (distribution concept) seems to be promising. The present paper deals with the simplest case of non-steady-state distribution functions with two parameters – the first one scaling the object radius, the second one determining the shape of the distribution function. The main question concerns the physical basis behind the evolution of these two parameters. The principle of maximum dissipation has proven to be a proper tool to derive the evolution equations. Semi-analytical solutions for the evolving parameters of arbitrary two-parameter distribution functions can be developed. As examples Kirkaldy and Weibull-type distribution functions are investigated. It is shown that the parameters of the Kirkaldy distribution function are not independent, and, thus, the general non-steady-state analysis fails. For a Weibull-type distribution function nearly exact and simple analytical expressions for both parameters are presented and discussed for the grain growth and coarsening cases.

Mots clés: Physical Sciences

Franz Dieter Fischer, Jiri Svoboda, Ernst Gamsjäger. Analysis of non-steady-state distribution functions for grain growth and coarsening. Philosophical Magazine, 2009, 89 (17), pp.1425-1438. ⟨10.1080/14786430902988757⟩. ⟨hal-00514026⟩