Issue 47

A. Spagnoli et alii, Frattura ed Integrità Strutturale, 47 (2019) 394-400; DOI: 10.3221/IGF-ESIS.47.29 397 reported in Fig. 3, where the load range level is expressed as the range of the applied SIF (calculated for a crack length equal to a 0 ), normalized by the estimated SIF threshold  0.5 , = 0.74 MPam I th K (see the last paragraph of the present Section). Run-out specimens (see open circle in Fig. 3) correspond to unbroken specimens after a number of loading cycles larger than N 0 = 100,000. A log-log linear fitting of the experimental points with 0 < f N N is attempted (negative inverse slope of 50), bearing in mind that the paucity of experimental data, along with the inherent scatter of the material properties, do not allow us to draw any conclusion on the behavioural trend observed. For illustrative purposes, Fig. 4a shows the experimental curve of the CMOD at maximum load in the loading cycle against the number of cycles to failure for a notched specimen loaded with a ratio   , = 1.16 I I th K K . By means of classical LEFM formulas, by knowledge of the applied load and the Young modulus of the marble under investigation, the effective crack length can be calculated from the measured CMOD. Consequently, crack length against number of cycles to failure curves can be obtained (see red curve in Fig. 4a). 10 2 10 3 10 4 10 5 10 6 10 7 Numer of cycles to failure, N f 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Relative SIF range,  K I /  K I,th Figure 3 : SN plot of fatigue results on notched specimens (open circles indicate run-out data). The experimental fatigue crack growth results, now expressed in terms of crack length a versus number of loading cycles, are analysed. In particular, the material parameters C and m of the Paris law (   / m I da dN C K ) are estimated. Such a law has been proved to describe well the experimental trend of the fatigue growth of the so-called long cracks for a variety of engineering materials with particular regards to metals. For this purpose, the crack growth rate da/dN versus number of cycles is determined according to ASTM E647 standard. The experimental d a /d N - N data are analyzed by an incremental polynomial method. This method for computing da/dN involves fitting a second-order polynomial (parabola) to sets of (2n+1) successive data points a-N, where n is usually 1, 2, 3, or 4 ( n = 4 is assumed here). The rate of crack growth at each central point a i , in the range a i-n – a i+n , is obtained from the derivative of the above parabola. The SIF range  K I is determined according to classical LEFM expression for the current crack length a . As an example, in Fig. 4b the d a /d N-  K I plot is reported for the same specimen of Fig. 4a. The mean values based on five experimental tests of the estimated parameters of the Paris law are C =0.0002 and m =3.3 expressing d a /d N as m/cycle and  K I as MPam 0.5 , although a large scatter in the results is recorded (coefficient of variation of C and m is equal to 0.34 and 0.80, respectively), and a degree of arbitrariness is introduced in the selection of the range of Paris law validity for best-fitting of experimental data point. The obtained values are in line with those reported in Ref. [4] ( C = 0.00029 and m = 3.9). Finally, by considering the run-out fatigue tests on notched specimens (considering a conventional number of cycles for the fatigue limit N 0 = 100,000), an estimation of a fatigue limit for the marble under investigation is attempted. In particular, a threshold condition in terms of SIF range (related to the initial notch length a 0 ) is obtained. The resulting mean value of  K th is 0.74 MPam 0.5 for loading ratio R = 0.1 (     max, , / (1 ) I th I th K K R 0.83 MPam 0.5 ). It is instructive to note that the ratio max, / I th sIC K K is equal to 0.44, which indicates a behavior slightly in the range of fatigue insensitive materials with flaws according to the seminal work of Fleck et al [11].