Digital Repository, CONVEGNO IGF XXII ROMA 2013

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Interpolation model of fatigue crack propagation data
M. Grasso, F. Penta, P. Pinto, G.P. Pucillo

Last modified: 2013-06-27


It is well known that the assessment of fatigue damage by means of phenomenological models is
closely linked to the procedure and accuracy with which experimental raw crack growth data are analysed. Very
often they are discontinuous and naturally irregular and their analysis has to be made on different levels to reach
the model formulation or, at least, a the canonical graphical correlation between the crack growth rates and the
stress intensity factor range, which is the parameter controlling the phenomenon.
Actually, when experimental results are analysed, in addition to normal scatter due to both the phenomenon
random character and measurement uncertainty, some further anomalies are often usually observed in the
homogeneous sequences of data points of the crack growth curves: significant deviations, apparently
inconsistent and absolutely uncontrollable, of some data from the trend followed by all the remaining
experimental points of the same curve. They are probably due to the random evolution of the local
combinations, in the infinite points of the crack front, of the stress states and the material strengths. Thus,
pursuing an improvement in the analysis of crack growth data would mean to formulate a correlation model
able to reproduce more accurately the aforementioned trend and not only simply and solely improve the data
points interpolation by new averaging techniques and alternative fitting methods.
Although Standard procedures to carry out both fatigue crack propagation tests and experimental data analysis
are currently in use, these do not guarantee that the anomalies in acquired data are absent and do not provide a
mean nor a criterion to filter them. The different analysis methods developed to interpolate crack propagation
data, besides those proposed by the ASTM Standard [1], are essentially based on the preliminary choice of a
technique or a method to interpret the experimental raw data, i.e. crack length values as function of time or load
cycles, without establishing a correlation between the observed variables. Generally, they essentially are local
interpolation methods of the data, which are not able to filter the irregularities or anomalies characterizing this
type of measurements. Since the evolution of the propagation phenomenon is fast (o rapid) when the crack is
approaching the critical condition, the validity range of propagation models built on results obtained from a
limited number of tests is closely linked to the particular experimentation carried out. Moreover, they are not
able to fit all crack growth data with the same accuracy for the whole field of cycles number of each test [].
The main analytical models found in Literature [2÷8], based on polynomial or exponential interpolation
formula, do not seem having solved completely the problem. Consequently, to improve the quality of raw crack
propagation data analysis we propose an interpretative model whose validity has been analysed with a very wide
set of crack growth data. A similar attempt, reported in [9] and concerning a three parameters model, has been
successfully tested using only experimental data produced by Ghonem and Dore [10]. However, this model
revealed some limitations when used to interpolate both data produced by Virkler and co-workers [11] and
those recently produced by Wu and Ni [12]. For this reason the model has been modified introducing two more

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