Multiscale functional analysis of wear: A fractal model of the grinding process

International audienceIn this paper, we propose to create a fractal function defined by an infinite series to model worn surfaces obtained by a grinding process. In this series, each elementary term characterizes a wear process at a given scale. This series is only defined by two parameters: an amplitude parameter and the fractal dimension. This model is tested on worn profiles obtained by using different grinding paper grades and roughness is assessed by tactile profilometry. Then an inverse method is developed to obtain simulated profiles that present the same morphology as the experimental ones. The results from this study prove that our method allows simulation of profiles with elementary functions that characterize the wear process

Contribution of statistical methods to the study of worn paint coatings surface topography

A surface morphology can be described by numerous roughness parameters. Making the most of the power of modern computers, the relative relevance of a hundred surface roughness parameters is assessed in this investigation with regard to the relationships between the morphological texture, the low wear damage and the gloss of polymer coatings. The relevance of each roughness parameter is quantitatively determined by statistical indexes of performance defined and calculated by combining the two-way ANalysis Of VAriance (ANOVA) and the Computer Based Bootstrap Method (CBBM). The fractal dimension is shown to be the most relevant parameter for characterising the different morphological textures of studied coatings and the average curvature radius of peaks for characterising the effect of wear. A linear relationship is found between the reduction of gloss and the reduction of the average curvature radius of peaks due to wear. Besides, it is also shown that angles of 85° and 20° are the most relevant for characterising, respectively, the effects of the morphological texture of polymer coatings and wear on the gloss measurements

About the relevance of roughness parameters used for characterizing worn femoral heads

This study aims to contribute to the definition of a methodology, which can help to select a relevant roughness parameter with a view to describing the topography of orthopaedic bearing surfaces. In this investigation, the surface topography of a retrieved titanium alloy (TA6V) femoral head was characterized using visual inspection, optical microscopy and three-dimensional contacting profilometry. A numerical analysis of roughness measurements was then undertaken to assess in a first step the values of different roughness parameters of interest found in papers dealing with the topography of orthopaedic bearing surfaces. In a second step, the Analysis of Variance (ANOVA) and the Computer-Based Bootstrap Method were combined to determine statistically, and without preconceived opinion, which of those parameters is the most relevant to describe the different investigated worn regions of the studied femoral head

Assessment of the constitutive law by inverse methodology: Small punch test and hardness

The relevance of small-punch tests and indentation (hardness) tests are compared with regard to the determination of a constitutive law in the case of non active ferrite–bainite steel taken from a French power plant. Firstly, small-punch tests were performed on material samples and the load deflection curves were compared with finite element calculations using the FORGE2 Standard code. As a result the strength coefficient and the strain hardening exponent of Hollomon’s constitutive law were determined by an inverse method (Simplex method). Besides, it was shown that a three-parameter constitutive law such as Ludwik Hollomon’s leads to an indetermination since its parameters are correlated with each other. Secondly indentation tests were performed with a ball indenter and the parameters of the constitutive law were determined from the analysis of the load–indentation depth curves. Both methods give results in good agreement with the true stress–true strain curve obtained by classical tensile testing, thus proving their applicability to nuclear materials

Corrosion pit depth extreme value prediction from limited inspection data

Passive alloys like stainless steels are prone to localized corrosion in chlorides containing environments. The greater the depth of the localized corrosion phenomenon, the more dramatic the related damage that can lead to a structure weakening by fast perforation. In practical situations, because measurements are time consuming and expensive, the challenge is usually to predict the maximum pit depth that could be found in a large scale installation from the processing of a limited inspection data. As far as the parent distribution of pit depths is assumed to be of exponential type, the most successful method was found in the application of the statistical extreme-value analysis developed by Gumbel. This study aims to present a new and alternative methodology to the Gumbel approach with a view towards accurately estimating the maximum pit depth observed on a ferritic stainless steel AISI 409 subjected to an accelerated corrosion test (ECC1) used in automotive industry. This methodology consists in characterising and modelling both the morphology of pits and the statistical distribution of their depths from a limited inspection dataset. The heart of the data processing is based on the combination of two recent statistical methods that avoid making any choice about the type of the theoretical underlying parent distribution of pit depths: the Generalized Lambda Distribution (GLD) is used to model the distribution of pit depths and the Bootstrap technique to determine a confidence interval on the maximum pit depth

On the detection of corrosion pit interactions using two-dimensional spectral analysis

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

A multi-scale approach of roughness measurements: Evaluation of the relevant scale

This paper proposes a new multi-scale measurement approach performed to compare the surface roughness and the visual aspect of polished surfaces. In this investigation, five specimens of glass moulds presenting different visual aspects are considered. All roughness profiles assessed by tactile profilometry were rectified by a first degree polynomial fitting, and current roughness parameters were calculated with respect to the evaluation length among which they are estimated. A variance analysis was then performed to discriminate each roughness parameter and each evaluation length with regard to a correlation with the visual aspect. Although the average roughness amplitude is about 100 nm, the results show that the optimal correlation with the visual aspect is obtained for a 400 μm evaluation length. Moreover, the multi-scale method allows to confirm results already found in the bibliography about the high wavelengths origin of “orange peel” aspect. This application allowed us to conclude on the advantages and the limits of the implemented method

Estimating the parameters of a generalized lambda distribution

International audienceThe method of moments is a popular technique for estimating the parameters of a generalized lambda distribution (GLD), but published results suggest that the percentile method gives superior results. However, the percentile method cannot be implemented in an automatic fashion, and automatic methods, like the starship method, can lead to prohibitive execution time with large sample sizes. A new estimation method is proposed that is automatic (it does not require the use of special tables or graphs), and it reduces the computational time. Based partly on the usual percentile method, this new method also requires choosing which quantile u to use when fitting a GLD to data. The choice for u is studied and it is found that the best choice depends on the final goal of the modeling process. The sampling distribution of the new estimator is studied and compared to the sampling distribution of estimators that have been proposed. Naturally, all estimators are biased and here it is found that the bias becomes negligible with sample sizes n⩾2×103. The .025 and .975 quantiles of the sampling distribution are investigated, and the difference between these quantiles is found to decrease proportionally to View the MathML source. The same results hold for the moment and percentile estimates. Finally, the influence of the sample size is studied when a normal distribution is modeled by a GLD. Both bounded and unbounded GLDs are used and the bounded GLD turns out to be the most accurate. Indeed it is shown that, up to n=106, bounded GLD modeling cannot be rejected by usual goodness-of-fit tests

An expert system to characterise the surfaces morphological properties according to their tribological functionalities: The relevance of a pair of roughness parameters

Knowing that a surface or profile can be characterized by numerous roughness parameters, the objective of this investigation was to present a methodology which aims to determine quantitatively and without preconceived opinion the most relevant pair of roughness parameters that describe an abraded surface. The methodology was firstly validated on simulated fractal profiles having different amplitudes and Hölder exponents and it was secondly applied to characterise different worn regions of a retrieved metallic femoral head articulated against an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup containing an embedded metallic fibber into its surface. The methodology consists in combining the recent Bootstrap method with the usual discriminant analysis. It was validated on simulated fractal profiles showing that, among more than 3000 pairs tested, the total amplitude Rt and the fractal dimension Δ is the most relevant pair of roughness parameters; parameters corresponding to the variables modulated in the analytical expression of the fractal function. The application of this methodology on a retrieved metallic femoral head shows that the most relevant pair of parameters for discriminating the different investigated worn regions is the arithmetic roughness parameter Ra paired with the mean peak height Rpm. This methodology finally helps in a better understanding of the scratch mechanism of this orthopedic bearing component

MESURE DE LA TENACITE DE L’HYDROXYAPATITE PAR INDENTATION

L’objectif de cette étude est de caractériser le comportement fragile de l’hydroxyapatite (HAP) par évaluation de sa ténacité. Cette ténacité a été estimée pour des d’échantillons sous forme massive et pour des revêtements par indentation Vickers. Pour les échantillons d’HAP sous forme massive, des fissures de type Médian sont visibles à chaque coin des empreintes pour des charges ≥ 200g. Un phénomène de fissuration latérale pouvant conduire à un écaillage est observé pour les charges testées les plus élevées. La mesure de la longueur des fissures, couplée à l’utilisation de la formule analytique d’Evans et Charles, permet de calculer une valeur de ténacité qui est inférieure au MPa.m1/2. Pour les revêtements d’HAP, l’indentation latérale produit des empreintes qui sont accompagnées d’un phénomène de multi-fissuration. En intégrant ce phénomène de multi-fissuration, la valeur de la ténacité estimée pour les revêtements d’HAP est du même ordre de grandeur que celle des échantillons sous forme massive