Issue 21

A. De Iorio et alii, Frattura ed Integrità Strutturale, 21 (2012) 21-29; DOI: 10.3221/IGF-ESIS.21.03 21 A three-parameter model for fatigue crack growth data analysis A. De Iorio, M. Grasso, F. Penta, G.P. Pucillo Università di Napoli Federico II, Dipartimento di Meccanica ed Energetica,Via Claudio 21 – 80125 Napoli antdeior@unina.it A BSTRACT . A three-parameters model for the interpolation of fatigue crack propagation data is proposed. It has been validated by a Literature data set obtained by testing 180 M(T) specimens under three different loading levels. In details, it is highlighted that the results of the analysis carried out by means of the proposed model are more smooth and clear than those obtainable using other methods or models. Also, the parameters of the model have been computed and some peculiarities have been picked out. K EYWORDS . Fatigue crack growth; Data analysis; Non-linear regression. I NTRODUCTION he assessment of the fatigue damage by means of phenomenological models notoriously is closely linked to the analysis of experimental results obtained from standard specimens of a given material tested with suitably chosen loading programs. However, it is well known that crack growth data have stochastic nature, as the phenomenon which generates them, due to, essentially, the random evolution of the local combinations, at each point of the crack front, of the induced stress state and material properties. For this reason, in order to identify a deterministic law describing the phenomenon, that is able to represent the common data trend independently of the global scatter or the position of the single data point, data have to be elaborated by means of a best-fit method after having selected an analytical model. Since the availability of a reliable crack propagation model has a tremendous impact on the fatigue design practice, for over half a century this problem has been faced by many researchers [1]. For the same reason, the attention of the researchers has been focused also on the accuracy by which the experimental data are produced and analysed, with the aim of defining a standard procedure for material testing and related results analysis (ASTM) and to formulate interpretative models of the experimental data. The most used methods for crack growth testing and data analysis are those suggested by ASTM Standard [2], which, concerning the data analysis, proposes two different approaches: the Secant Method and the Incremental Polynomial Method. Since both methods are based on local interpolation of experimental data, irregularities and/or anomalies in the data distribution, for the first method, and the number of data points chosen for the best-fit parabola, for the second one, affect significantly the results. On the other hand, the foremost polynomial or exponential analytical formulas found in Literature [3-6] do not seem to have solved completely the problem. Hence our interest in facing this problem, in order to contribute, if possible, to improve on the quality of raw crack propagation data analysis by formulating an interpretative model for the whole lives field of the acquired data. F ORMULATION OF THE MODEL mong the various analysis methods developed till now, besides those proposed by the ASTM Standards, we mention for their popularity: - Mukherjee Method [3], which is based on the linear interpolation of the finite differences computed between T A