Modeling of the Precipitation Kinetics During Aging a Predeformed Fe-Cu Alloy
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UCTION
AGING of Fe-Cu alloys or steels containing Cu may result in the formation of the dispersion of nanometric precipitates in the matrix. Such steels provide a good combination of strength and toughness and are good candidates for the applications in natural gas pipelines, shipbuilding,[1–5] etc. The Cu precipitation has been investigated with a variety of experimental techniques. It has been revealed that the precipitation begins with the nucleation of the metastable body-centered-cubic (bcc) Cu precipitates. These precipitates grow/coarsen in the matrix. They transform to 9R structure (the facecentered-cubic (fcc) structure with high density of twins) when the precipitates reach a critical size. Finally, the twins disappear and the precipitates attain the equilibrium fcc structure. The microstructure evolution during aging is the result of the concurrent actions of the nucleation, growth, coarsening, and structural transformation of the precipitates. It is very complicated. Deformation before aging treatment may also affect the microstructure development. Several studies were made to investigate the age hardening characteristics of the predeformed Cu bearing steels.[6,7] However, the effect of dislocations on the precipitation process is not unequivocally understood. Some authors reported that dislocations had no catalyzing effect on the nucleation of precipitates,[7] while others found that dislocations promoted the nucleation of precipitates.[6]
J.Z. ZHAO, Professor, Q.L. WANG, Doctoral Candidate, H.L. LI, Postdoctoral Candidate, and J. HE, Associate Professor, are with the Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China. Contact e-mail: [email protected] Manuscript submitted November 9, 2010. Article published online May 20, 2011 3200—VOLUME 42A, OCTOBER 2011
The modeling of the nanoscale precipitation during aging an alloy has attracted considerable attention in recent years.[5–10] Most of the existing models are based on the model presented by Langer and Schwartz[11] and its modified versions.[12,13] They treated simultaneously the nucleation, growth, and coarsening of precipitates by using some unsatisfactory assumptions regarding the precipitates of radius smaller than the critical radius for dissolution.[14] In order to eliminate the shortcomings of these models, Mathon et al.[15] developed a model based on the cluster dynamics approach. They found that although their model did not overcome all the shortcomings of the previous ones, it nearly fit the aging experimental data with Fe-Cu alloy if they assumed a low reaction kinetic parameter at the matrix/precipitate interface and a heterogeneous nucleation. Deschamps and co-workers[14,16] developed a model by simply separating the precipitation process into two stages: the simultaneous nucleation and growth stage and the simultaneous growth and coarsening stage. In order to investigate the kinetic details of the precipitation process during aging a Fe-Cu alloy, we present in this article a model to calcula
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