Issue 35

S. Blasón et alii, Frattura ed Integrità Strutturale, 35 (2016) 187-195; DOI: 10.3221/IGF-ESIS.35.22

b- Minimization of function Q Thereafter, the parameters fitting the crack growth rate curve are determined from the experimental data (see Tab. 4).

α

γ

log(ΔK th * ) log(ΔK up * )

-3.7462 0.5721 Table 4: Parameter values found by fitting the crack growth rate curve as a cumulative distribution function. Fig. 6 exhibits the normalized values for log(ΔK*) vs. log(da*/dN*) along with the curve fitting obtained after minimization. 1.9224 -1.7159

g

2

0

-2

-4

-6

-8

-10 log(da*/dN*)

-12

-14

-16

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

log(  K*)

Figure 6: Representation of the normalized experimental data and fitting obtained.

c- Obtaining crack growth curves Figs. 7 and 8 represent the result of the integration of Expr. (4), firstly for different initial crack sizes a 0 * when maintaining a fixed value for the non-dimensional stress range, Δσ*.

=141[MPa]

a

=3.4 [mm]



0

0

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

a a a a

=3.4 mm =3.6 mm =4.0 mm =4.5 mm

 =136 MPa  =146 MPa  =171 MPa  =196 MPa

0

0.3

0.3

0

normalized crack length, a*

normalized crack length, a*

0

0.2

0.2

0

0.1

0 50 100 150 200 250 300 350 400 0.1

0

100

200

300

400

500

600

normalized number of cycles, N*

normalized number of cycles, N*

Figure 7: Curves a*-N* for different initial crack sizes a 0

*, while

Figure 8: a*-N* curves for different stress ranges, Δσ*, while maintaining the initial crack size, a 0 * constant

maintaining constant Δσ*.

The integration follows after fitting the geometric factor to the first Expression in (6). Fig. 9 illustrates the fit obtained for the geometrical crack factor in the specimen

193