Issue 49

G. Meneghetti et alii, Frattura ed Integrità Strutturale, 49 (2019) 82-96; DOI: 10.3221/IGF-ESIS.49.09

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 .

5

non-linear fracture process zone

SIF dominated zone

non-linear far field zone

4

3

2 y [mm]

1

0

0.5

1

1.5

2

) 2 [1/°C 2 ]

1/( T max

) 2 for specimen with crack length 11.66 mm, and  K I,FE

=35.4 MPa·m 0.5 .

Figure 12 : Plot of y versus (1/  T max

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 .

(a)

308.8 308.9 309 309.1 309.2 309.3 309.4 309.5 309.6 309.7 309.8

308.8 308.9 309 309.1 309.2 309.3 309.4 309.5 309.6 309.7 309.8

(b)

T



77 K/m

 

m

r



r R 

c

T



600 K/m

 

m

r



T m [K]

T m [K]

= 81 MPa

r R 

 g

c

 g

=81 MPa

 = 135 ° R c =5.2  10 -4 m a=11.66 mm  K FE =35 Hz  = 16 W/(m  K) f L

 =0 ° R c

=5.2  10 -4 m a=11.66 mm  K FE

= 35.4 MPa·m 0.5

r=R c

r=R c

= 35.4 MPa·m 0.5

f L

=35 Hz

0

10 -3

2·10 -3

3·10 -3

0

10 -3

2·10 -3

3·10 -3

r [m]

r [m]

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.

92