Issue 49

G. Meneghetti et alii, Frattura ed Integrità Strutturale, 49 (2019) 82-96; DOI: 10.3221/IGF-ESIS.49.09 92 of Figs. 10, 11, it is in particular found  K I =36.51 MPa·m 0.5 . This value is about 3.2% higher than the value calculated by means of linear-elastic FE analysis. In [29], it was pointed out that, considering the analysed test conditions, values of  K I have been found to differ from numerical values obtained from linear elastic FE analyses by generally less than 10 %. This level of approximation is comparable to that generally reported in the literature [40]. Having K I (K I =  K I /2), the elastic J- integral can be evaluated according to Eqn.(6a), finding J max,e =1712 J/m 2 . Figure 12 : Plot of y versus (1/  T max ) 2 for specimen with crack length 11.66 mm, and  K I,FE =35.4 MPa·m 0.5 . Evaluating the plastic component of J-integral by the heat energy loss During the crack propagation fatigue tests, the crack length and the temperature field were measured at several times t = t s , regularly distributed during each fatigue test after thermal equilibrium was achieved. As stated above, 1000 infrared images were acquired at each time t s , then they were processed with the MotionByInterpolation algorithm and finally Eqn. (4) was applied. As an example, the temperature fields related to the sample shown in Fig. 8 for  =0° and 135° (see Fig. 2) are shown in Fig. 13a and 13b, respectively. Red circles are the data considered for the evaluation of spatial temperature gradient at r=R c and the specific heat flux h calculated along the boundary of V c is shown in Fig. 14. Then, * Q was evaluated according to Eqn.(2), finding * 3 Q =0.67 MJ/(m cycle)  and the plastic component of J-integral was finally calculated according to Eqn.(17), as J max,p =443 J/m 2 , giving J= J max,e + J max,p =1712+443=2155 J/m 2 . Figure 13 : Experimental radial temperature profiles measured for  =0° (a) and  =135° (b) and evaluation of temperature gradient for r=R c =0.52 mm. 0.5 1 1.5 2 1/( T max ) 2 [1/°C 2 ] 0 1 2 3 4 5 y [mm] non-linear fracture process zone SIF dominated zone non-linear far field zone 308.8 308.9 309 309.1 309.2 309.3 309.4 309.5 309.6 309.7 309.8 T m [K] r [m]  g =81 MPa  =0 ° R c =5.2  10 -4 m a=11.66 mm  K FE = 35.4 MPa·m 0.5 f L =35 Hz r=R c 0 10 -3 2·10 -3 3·10 -3 c m r R T 77 K/m r      (a) 308.8 308.9 309 309.1 309.2 309.3 309.4 309.5 309.6 309.7 309.8 T m [K] r [m]  g = 81 MPa  = 135 ° R c =5.2  10 -4 m a=11.66 mm  K FE = 35.4 MPa·m 0.5 f L =35 Hz  = 16 W/(m  K) r=R c 0 10 -3 2·10 -3 3·10 -3 c m r R T 600 K/m r      (b)