A new treatment of transient grain growth

0463998 - ÚFM 2017 RIV GB eng J - Článek v odborném periodiku
Svoboda, Jiří - Fratzl, P. - Zickler, G. A. - Fischer, F. D.
A new treatment of transient grain growth.
Acta Materialia. Roč. 115, AUG (2016), s. 442-447. ISSN 1359-6454. E-ISSN 1873-2453
Grant CEP: GA ČR(CZ) GA15-06390S
Institucionální podpora: RVO:68081723
Klíčová slova: Grain size distribution * Grain growth * Growth kinetics * Thermodynamic modelling * Numerical solution of integro-differential equations
Kód oboru RIV: BJ - Termodynamika
Impakt faktor: 5.301, rok: 2016

The grain radius R distribution ftmction f(R, t) with R-c(t) as critical grain radius is formulated, inspired by the Hillert self-similar solution concept, as product of 1/R-c(4) and of a shape function g(rho, t) as function of the dimension-free radius rho = R/R-c and time t, contrarily to the Hillert self-similar solution concept with time-independent g(rho). The evolution equations for R-c(t) as well as for g(rho, t) are derived, guaranteeing that the total volume of grains remains constant. The solution of the resulting integro-differential equations for R-c(t) and g(rho, t) is performed by standard numerical tools. Remarkable advantages of this semi-analytical concept are: (i) the concept is a deterministic one, (ii) its computational treatment is very efficient and (iii) the shape function g(rho, t) remains localized in a fixed interval of rho. The shape function g(rho, t) evolves towards the well-known Hillert self-similar distribution, which is demonstrated for two initial shape functions (one of them is triangular). Also a study on "nearly" self-similar distribution functions proposed as useful approximations of experimental data is presented.
Trvalý link: http://hdl.handle.net/11104/0263104