Abstract
Recently, the author has provided a mathematical validation for the Taylor relationship in strain hardening by noticing that the process of dislocation storage in the slip plane can be described by the formalism of a Delaunnay triangulation on a plane Poisson process. This also allows determining the percolation limit for dislocation storage in the case of non-penetrable obstacles. For this case, the free path of the dislocations, and therefore the slope of the strain hardening curve in stage II can be calculated analytically. New results for the probability distribution of the Delaunay triangles are presented in the process. It will be indicated how precipitates can be incorporated an how to account for the existence of penetrable obstacles in this formalism.
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Schouwenaars, R. (2013). The Statistical Analysis of Dislocation Percolation: A Mathematical Contribution to Strain Hardening Theory. In: Marquis, F. (eds) Proceedings of the 8th Pacific Rim International Congress on Advanced Materials and Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-48764-9_345
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DOI: https://doi.org/10.1007/978-3-319-48764-9_345
Publisher Name: Springer, Cham
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