Modelling of Precipitation Kinetics with Simultanous Stress Relaxation
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0979-HH11-04
Modelling of Precipitation Kinetics with Simultanous Stress Relaxation Franz Dieter Fischer1,2, Jiri Svoboda2,3, Ernst Gamsjäger1,2, Ernst Kozeschnik2,4, and Bernhard Sonderegger2,4 1 Institute of Mechanics, Montanuniversität Leoben, Franz-Josef-Strasse 18, Leoben, A-8700, Austria 2 Materials Center Leoben Forschungsgesellschaft GmbH, Leoben, A-8700, Austria 3 Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Zizkova 22, Brno, CZ-616 62, Czech Republic 4 Institute for Materials Science, Welding and Forming, University of Technology, Kopernikusgase 24, Graz, A-8010, Austria
ABSTRACT Misfit strain connected with the formation of large internal stresses may drastically influence the kinetics of precipitation. A new model for the simultaneous precipitate growth and misfit stress relaxation in binary systems has been developed based on the idea that the internal stresses are relaxed by generation or annihilation of vacancies at the matrix/precipitate interface. The model is applied to the Fe-C system by considering the growth of the cementite precipitate in the ferritic matrix. The influence of the stress relaxation on the precipitate growth kinetics is demonstrated. INTRODUCTION Significant elastic stress fields can be formed due to misfit strains during precipitation, which can prohibit the growth of precipitates. It is generally assumed that the stress fields can be relaxed by the matrix plasticity and so the negative driving force is significantly reduced. This concept, however, fails for nano-sized precipitates, because the matrix plasticity caused by motion of dislocations is not a sufficiently fine tool for the relaxation of the highly localized stress fields. Very recently, experimental and theoretical studies have been published by Dahmen, Johnson and coworkers [1-3], demonstrating that the stress fields formed in and around the precipitates can be effectively relaxed by generation or annihilation of vacancies at the precipitate/matrix interfaces accompanied by the diffusion of vacancies and their annihilation or generation in the matrix. It was clearly shown that no dislocation plasticity contributes to the stress relaxation. Inspired by these experimental findings, Svoboda et al. developed in [4] a nonequilibrium model with one relaxation parameter d - the thickness of a layer of matrix atoms deposited at the interface - and used the Gibbs energy balance equation to find an evolution equation for the parameter d. Very recently, a model for the growth of stoichiometric precipitates in binary systems driven by both chemical and (negative) mechanical thermodynamic forces, during which the stress field is relaxed by the transport of vacancies, was presented in [5]. The model uses two parameters for the description of the state of the precipitate: ρ - the radius of the precipitate and d - the thickness of the deposited layer. The evolution equations for these
parameters are derived by means of the thermodynamic extremal principle, see e.g. Svoboda et al. [6]. The aim of
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