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B. Sonderegger, I. Holzer, E. Kozeschnik, C. Sommitsch:
"Particle distance distributions and their effect on precipitation strengthening";
Computer Methods in Materials Science, 11 (2011), 1; 148 - 153.

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 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 precipitation 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.