is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. a b s t r a c tThis paper proposes a new method of roughness peaks curvature radii calculation and its application to tribological contact analysis as characteristic signature of tribological contact. This method is introduced via the classical approach of the calculation of radius of asperity. In fact, the proposed approach provides a generalization to fractal profiles of the Nowicki's method [Nowicki. Wear Vol. 102, p. 161-176, 1985] by introducing a fractal concept of curvature radii of surfaces, depending on the observation scale and also numerically depending on horizontal lines intercepted by the studied profile. It is then established the increasing of the dispersion of the measures of that lines with that of the corresponding radii and the dependence of calculated radii on the fractal dimension of the studied curve. Consequently, the notion of peak is mathematically reformulated. The efficiency of the proposed method was tested via simulations of fractal curves such as those described by Brownian motions. A new fractal function allowing the modelling of a large number of physical phenomena was also introduced, and one of the great applications developed in this paper consists in detecting the scale on which the measurement system introduces a smoothing artifact on the data measurement. New methodology is applied to analysis of tribological contact in metal forming process.
is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This paper outlines a new methodology to predict accurately the maximum pit depth related to a localized corrosion process. It combines two statistical methods: the Generalized Lambda Distribution (GLD), to determine a model of distribution fitting with the experimental frequency distribution of depths, and the Computer Based Bootstrap Method (CBBM), to generate simulated distributions equivalent to the experimental one. In comparison with conventionally established statistical methods that are restricted to the use of inferred distributions constrained by specific mathematical assumptions, the major advantage of the methodology presented in this paper is that both the GLD and the CBBM enable a statistical treatment of the experimental data without making any preconceived choice neither on the unknown theoretical parent underlying distribution of pit depth which characterizes the global corrosion phenomenon nor on the unknown associated theoretical extreme value distribution which characterizes the deepest pits.Considering an experimental distribution of depths of pits produced on an aluminium sample, estimations of maximum pit depth using a GLD model are compared to similar estimations based on usual Gumbel and Generalized Extreme Value (GEV) methods proposed in the corrosion engineering literature. The GLD approach is shown having smaller bias and dispersion in the estimation of the maximum pit depth than the Gumbel approach both for its realization and mean. This leads to comparing the GLD approach to the GEV one. The former is shown to be relevant and its advantages are discussed compared to previous methods.
A particular thanks to Professor Maxence Bigerelle (UTC, Compiègne, France) and to research and development engineer Dr. Benjamin Fournier (CEA, Saclay, France) for their interesting discussions and useful advices about the scientific problem of pitting corrosion.A statistical methodology for detecting pits interactions based on a two-dimensional spectral analysis is presented. This method can be used as a tool for the exploratory analysis of spatial point patterns and can be advanced as an alternative of classical methods based on distance. One of the major advantages of the spectral analysis approach over the use of classical methods is its ability to reveal more details about the spatial structure like the scale for which pits corrosion can be considered as independent. Furthermore, directional components of pattern can be investigated. The method is validated in a first time using numerical simulations on random, regular and aggregated structures. The density of pits, used in the numerical simulations, corresponds to that assessed from a corroded aluminium sheet. In a second time, this method is applied to verify the independence of the corrosion pits observed on the aforementioned aluminium sheet before applying the Gumbel theory to determine the maximum pit depth. Indeed, the property of independence is a prerequisite of the Gumbel theory which is one of the most frequently used in the field of safety and reliability.International audienceA statistical methodology for detecting pits interactions based on a two-dimensional spectral analysis is presented. This method can be used as a tool for the exploratory analysis of spatial point patterns and can be advanced as an alternative of classical methods based on distance. One of the major advantages of the spectral analysis approach over the use of classical methods is its ability to reveal more details about the spatial structure like the scale for which pits corrosion can be considered as independent. Furthermore, directional components of pattern can be investigated. The method is validated in a first time using numerical simulations on random, regular and aggregated structures. The density of pits, used in the numerical simulations, corresponds to that assessed from a corroded aluminium sheet. In a second time, this method is applied to verify the independence of the corrosion pits observed on the aforementioned aluminium sheet before applying the Gumbel theory to determine the maximum pit depth. Indeed, the property of independence is a prerequisite of the Gumbel theory which is one of the most frequently used in the field of safety and reliability
Fatigue design is of vital importance to avoid fatigue small crack growth in engineering structures. This study shows that the critical fatigue design stress can be defined below the usual endurance limit, considered in rules and codes. The material constitutive behaviour is using linear isotropic elasticity. Lassere and Pallin-Luc [1-2] use the elastic energy and over-energy under uniaxial load (tension and rotating bending). The authors deduce the influencing critical stress value corresponding to σ*. It's a linear approach. We propose an over-energy under dissymmetrical rotating bending and expressed in the ellipse axes. An asymptotic approach is transformed the over-energy in polynomial function of critical stress. Unknown depend on experimental service conditions, endurance limit of tension and rotating bending of specimen. The fatigue database of 30NCD16 steel studied by Froustey and Dubar [3-13] is used. Critical stresses are evaluated (Fig. 2). The research done by Manning and all [4] has shown the small crack effect to be as large as 0.3 mm. Small crack and critical stress are illustrated here in as resulting from pure bending approach expressed by Bazant law [7]. It's reproduces well the Kitagawa diagram [6] (Fig. 3). When the short cracks are hidden in the material, we shows that the number
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