Issue 21

A. De Iorio et alii, Frattura ed Integrità Strutturale, 21 (2012) 21-29; DOI: 10.3221/IGF-ESIS.21.03 22 two consecutive points, in order to estimate the rate of growth at the central point; - polynomial expressions of Smith [4], Davies and Feddersen [5], that interpolate locally or globally the experimental data; - Polak and Knesl Method [6], which uses splines to fit and reduce the scatter in the data. Most of the methods until now proposed are local interpolations of experimental points, as already stated in the introduction, and are strongly affected by the real distribution of the analysed data, being unable to filter both the irregularities and anomalies that are always present in the sample. Therefore, most analytical models derived in such a way are very often closely linked to the particular experimental practice adopted to produce the data and, above all, do not fit all data with the needed and controlled accuracy in the whole cycles number range of each test. In a previous paper [7], some of the Authors already discussed the possibility to use splines of an arbitrary order to globally interpolate the raw data and reduce the scatter of the crack growth material constants when gapped or noisily data are used. In order to formulate a new model able to (at least) partially fill the aforementioned lacks, the results of 180 crack growth tests carried out by Ghonem and Dore [8] have been analysed. To find the curve that better interpolates all the examined data, different analytical formulations have been tested. By means of successive refinements, the following three parameters model has been defined:   0 β f a γ a α N 1 N          where: a 0 = initial crack length; N f = number of cycles to failure;  , β, γ = model parameters identified by a non-linear least squares method; N = number of cycles corresponding to a given crack length. The crack growth rate can be directly evaluated in the range [N 0 -N f ] by means of the previous expression without amplify the irregularities and/or anomalies of the raw data and without losing information in the initial and final part of the aforementioned range, as it occurs with other procedures as those suggested by ASTM Standards. V ERIFICATION OF THE MODEL he data of the 180 tests of Ghonem and Dore, which are fully described in term of both specimens and testing conditions in the paper [8], are summarized in Fig. 1-3. Each figure reports the results of a series of 60 tests carried out under the same loading conditions. Once the model has been defined, the goodness-of-fit has been evaluated computing the residuals and the values attained by the coefficient of determination R 2 , which is reported in the graphs of Fig. 4-6, for each data set. For a quick (non-objective) evaluation of the goodness of the interpolation, the results of some tests together with the related best-fitting curves obtained by the proposed model are also reported in Fig. 7. Figure 1 : Fatigue crack growth curves set I (R = 0.6). Figure 2 : Fatigue crack growth curves set II (R = 0.5). T