Issue 35

G. Meneghetti et alii, Frattura ed Integrità Strutturale, 35 (2016) 172-181; DOI: 10.3221/IGF-ESIS.35.20

significantly higher in Fig. 4b than in Fig. 4a. To evaluate the first derivative at r=R (Eq. (6)), the temperature-distance data along the seven considered paths were fitted using a proper polynomial function, shown with a continuous line in Fig. 4.

293 293.2 293.4 293.6 293.8 294 294.2 294.4

(a)

315 316 317 318 319 320 321 322

(b)

 =0° R=3·10 -4 m f L =35 Hz  K=60 MPa ·m 0.5

 = 0° R=3·10 -4 m f L =37 Hz  K=26 MPa·m 0.5



r T



r T





Rr





Rr

T m [K]

T m [K]

r=R

r=R

0

5.0·10 -4

1·10 -3

1.5·10 -3

2.0·10 -3

2.5·10 -3

0

5.0·10 -4

1·10 -3

1.5·10 -3

2.0·10 -3

2.5·10 -3

r [m]

r [m]

Figure 4 : Typical radial temperature profiles measured during the tension-compression fatigue tests in the case of (a)  K=26 MPa·m 0.5 and (b)  K =60 MPa·m 0.5 .

E NERGY PER CYCLE AVERAGED IN A VOLUME AT THE CRACK TIP

F

ig. 5a, 5b and 5c show the specific thermal flux h at the different points along the boundary of V (Fig. 1) for specimen V_3, V_4 and V_5, respectively, using  =16 W/(m·K) [8]. Finally, Fig. 5d shows, as an example, the specific energy flux per cycle q , obtained simply dividing h by the load test frequency. In the authors’ opinion, for the material and the experimental conditions analysed in the present paper, a reasonably accurate evaluation of the heat power can be achieved by considering  K values higher than 25 MPa·m 0.5 (K max >12.5 MPa·m 0.5 ). Having in hand the specific thermal flux h evaluated at different angles  of the boundary of V, numerical integration was performed according to Eq. (6). To evaluate the errors due to the discretisation, Eq. (6) was solved by dividing the 360° angle starting from a minimum of 4 intervals (  =90°) to a maximum of 24 (  =15°). A 0.51% variation on results was found by using 8 as compared to 24 intervals. Therefore, 8 intervals (  =45°) were adopted in numerical calculations. Finally, the energy per cycle averaged in the volume V, Q*, was evaluated by means of Eq. (7b). Results are listed in Tab. 1 and it can be seen that Q* increases as  K increases. It should be noted that  K are elastically calculated, independently on plastic zone size evaluations.

V_3 specimen  K [MPa·m 0.5 ] Q* [MJ/m 3 cycle] 26.3 0.813 26.8 0.504 28.4 0.655 31.2 0.727 35.6 0.829 45.2 1.02 49.6 1.32 55.3 1.33 64.1 3.28

V_4 specimen  K [MPa·m 0.5 ] Q* [MJ/m 3 cycle] 31.5 1.21 36.7 1.47 42.0 1.55 78.7 4.64 98.0 5.19

V_5 specimen  K [MPa·m 0.5 ] Q* [MJ/m 3 cycle] 28.5 0.581 30.3 1.80 32.9 1.91 36.9 2.18 40.6 1.93 45.7 2.60 53.2 2.99 60.1 4.00 66.9 5.96

Table 1 : Q* values calculated for different specimens at different  K values.

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