Use of the Generalized Lambda Distribution in Materials Science, with Examples in Fatigue Lifetime, Fracture Mechanics, Polycrystalline Calculations, and Pitting Corrosion

Authored by: B. Fournier , N. Rupin , M. Bigerelle , D. Najjar , A. Iost , Till Vallée

Handbook of Fitting Statistical Distributions with R

Print publication date:  October  2010
Online publication date:  April  2016

Print ISBN: 9781584887119
eBook ISBN: 9781584887126
Adobe ISBN:

10.1201/b10159-37

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Abstract

As in many scientific fields, statistical analyses are becoming more and more used in mechanics and materials sciences. Most materials are intrinsically heterogeneous. This heterogeneity can lie at very different scales. At the atomic scale, for crystalline materials (e.g., metals), additional elements (impurities or voluntary added elements, like carbon in iron to obtain steel) perturb the atomic arrangement either by substitution or insertion (François, Pineau, and Zaoui (1998)). Locally, vacancies (one atom missing) are also point defects modifying the perfect crystalline arrangement. Linear defects, named dislocations (see Friedel (1956) and Nabarro (1952)), are another type of heterogeneity, responsible for plastic (irreversible) deformation. These dislocations are an essential feature, e.g., for forming materials, but their arrangement does not obey a definite order and can change during the “life” of a material (Polak, Petrenec, and Man (2005)). Most metallic materials are polycrystalline materials, which means that the crystallographic arrangement is different depending on the grain orientation (Sutton and Balluffi (1995)). These grains are separated by grain boundaries which are surfaces where the atomic arrangement is not respected. At that scale, both the shape, the size, and the orientation of grains can only be described by statistical distributions (Kocks, Tomé and Wenk (1998)).

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