Particle distance distributions and their effect on precipitation strengthening
Bernhard Sonderegger1,2
, Ivan Holzer1, Ernst Kozeschnik3, Christof Sommitsch1
1Institute for Materials Science and Welding, Christian Doppler Laboratory for Materials Modelling and Simulation, Graz University of Technology, Kopernikusgasse 24, 8010 Graz, Austria.
2Materials Center Leoben Forschung GmbH, Rosseggerstraße 12, 8700 Leoben, Austria.
3Christian Doppler Laboratory for Early Stages of Precipitation, Institute of Materials Science and Technology, Vienna University of Technology, Favoritenstraße 9-11/ E308, 1040 Vienna, Austria.
DOI:
https://doi.org/10.7494/cmms.2011.1.0326
Abstract:
In this work, a general formulation of particle distances in glide planes is derived for arbitrary size distributions. The approach is designed to use the results of Wagner-Kampmann-type models. Size distributions are represented by a set of precipitate classes, where each class contains precipitates of a specific radius and a corresponding number density. The outputs of the calculation are not only particle distances, but particle distance distributions. This representation provides the convenience that any user-defined criterion for the precipitate-dislocation interaction can be applied, e.g. the side condition that at least one third of all spaces between obstacles have to be “open” for dislocation movement in order to allow plastic deformation. As a result, the combination of distribution function and side condition allows a direct calculation of the precipitates strengthening effect. It is shown, that the accordance of simulation and measurements is very promising. The method thus provides the potential to bridge the gap between the simulation of precipitate parameters and the quantitative calculation of precipitate strengthening.
Cite as:
Sonderegger, B., Holzer, I., Kozeschnik, E., & Sommitsch, C. (2011). Particle distance distributions and their effect on precipitation strengthening. Computer Methods in Materials Science, 11(1), 148-153. https://doi.org/10.7494/cmms.2011.1.0326
Article (PDF):
Keywords:
Precipitate distances, Precipitation hardening
References:
Ashby, M., 1968, The theory of critical shear stress and work hardening of dispersion-hardened crystals, Metallurgical Society Conference Vol. 47, eds, Ansell, G. S., Cooper, T. D., Lenel, F. V., Gordon and Breach, New York, 143-205.
Brown. L. M., 1975, Comment on the ‘Friedel relation’ in precipitate hardening, Scripta Metall., 9, 591-593.
Chandrasekhar, S., 1943, Stochastic problems in physics and chemistry, Rev. Mod. Phys., 15, 1-89.
Fullman, R. L., 1953, Measurement of approximately cylindrical particles in opaque samples, Trans. AIME, 197, 1267-1268.
Goodman, S. R., Brenner, S. S., Low Jr., J. R, 1973, FIM-atom probe study of precipitation of Copper from Iron-1.4at% Copper, Metall. Trans., 4, 2363-2369.
Holzer, I., Kozeschnik, E., 2010, Computer simulation of the yield strength evolution in Cu-precipitation strengthened ferritic steel, Mater. Sci. Engng., A 527, 3546-3551.
Kelly, P. M., 1973, The quantitative relationship between micro-structure and properties in two-phase alloys, Int. Met. Rev., 18, 31-36.
Kocks, U. F., 1966a, On the spacing of dispersed obstacles, Acta Metall., 14, 1629-1631.
Kocks, U. F., 1966b, A statistical theory of flow stress and work-hardening, Phil. Mag., 13, 541-550.
Kozeschnik, E., Svoboda, J., Fratzl, P., Fischer, F. D., 2004, Modelling of kinetics in multi-component multi-phase systems with spherical precipitates -II: Numerical solution and application, Mater. Sci. Engng., A 385, 157-165.
Leggoe, J. W., 2005, Nth- nearest neighbor statistics for analysis of particle distribution data derived by micrographs, Scripta Mater., 53, 1263-1268.
Lui, M. W., Le May, I., 1975, On the “Friedel relation” in precipitate hardening, Scripta Metall., 9, 587-589.
Nembach, E., 1982, How the choice of the dislocations’ outer cut-off radius affects the evaluation of precipitate hardening data”, Scripta Metall., 16, 1261-1265.
Russell, K. C, Brown, L. M., 1972, Dispersion strengthening model based on differing elastic-moduli applied to Iron-Copper system, Acta Metall. Mater., 20, 969-974.
Sonderegger, B., Kozeschnik, E., 2009a, Generalized nearest-neighbor broken-bond analysis of randomly oriented interfaces in multicomponent fcc and bcc structures, Metall. Mater. Trans., 40 A, 499-510.
Sonderegger, B., Kozeschnik, E., 2009b, Size dependence of the interfacial energy in the generalized nearest-neighbor broken-bond approach, Scripta Mater., 60, 635-638.
Sonderegger, B., Kozeschnik, E., 2010, Interfacial energy of diffuse phase boundaries in the generalized broken-bond approach, Metall. Mater. Trans. 41 A, 3262-3269.
Svoboda, J., Fischer, F. D., Fratzl, P., Kozeschnik, E., 2004, Modelling of kinetics in multi-component multi-phase systems with spherical precipitates -I: Theory, Mater. Sci. Engng., A 385, 166-174.