In this article, a new relationship for the calculation of the Zener drag pressure is described in which the effect of the size distribution of nanoscale dispersed particles is taken into account, in addition to particle radius and volume fraction, which have been incorporated in the existing relationships. Microstructural observations indicated a clear correlation between the size distribution of dispersed particles and recrystallized grain sizes in the AA7020 aluminum alloy. However, the existing relationship to calculate the Zener drag pressure yielded a negligible difference of 0.016 pct between the two structures homogenized at different conditions resulting in totally different size distributions of nanoscale dispersed particles and, consequently, recrystallized grain sizes. The difference in the Zener drag pressure calculated by the application of the new relationship was 5.1 pct, being in line with the experimental observations of the recrystallized grain sizes. Mathematical investigations showed that the ratio of the Zener drag pressure from the new equation to that from the existing equation is maximized when the number densities of all the particles with different sizes are equal. This finding indicates that in the two structures with identical parameters except the size distribution of nanoscale dispersed particles, the one that possesses a broader size distribution of particles, i.e., the number densities of particles with different sizes being equal, gives rise to a larger Zener drag pressure than that having a narrow size distribution of nanoscale dispersed particles, i.e., most of the particles being in the same size range.
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