Crack Paths 2006

the considered angles D we can observe a higher crack growth rate for mode III. The

experimental results shown in Figs. 6 to 8 for II and III range of crack growth rate were

described with the following model [6]

§'

n

¸ ¸ ¹ ·

J B

¨

da

J

©

0

(1)

,

J R - 1

dN

I c 2 '

J

where JIc – critical value of the J-integral, 'J = Jmax - Jmin, J0 = 1 MPa˜m - unit value

of the J-integral, B and n – coefficients determined experimentally.

The 'J integral range for modeI and modeIII is calculated from

' Q

n / a M E / K c H ' V ' S ,

(2)

'

1 J I

2 I 2

p 2 1 k

n / a M E / K p 2 3 k 2III c J ' W ' S ,

' Q

(3)

'

1 J III

where a – crack length, E – Young’s modulus, Q - Poisson’s ratio, n’ - cyclic strain

hardening exponent, 'KI, 'KIII - stress intensity factors ranges for mode I and modeIII,

Mk1, Mk3 - correction coefficients for modeI and modeIII [6], 'V, 'W - ranges of stress

under bending and torsion in the notch root, respectively, 'Hp, 'Jp – ranges of plastic

strains under bending and torsion in the notch root, respectively.

The empirical coefficients B and n occurring in Eq. (1) were calculated with the least

square method and they were shown in Table 2.

Table 2. Coefficients B, n Eq. (1) and correlation coefficient r for the curves in Figs. 6 - 8

cyBcle

GFrigasp.,hs

mcyMcBleP a 2 ˜

n

r

GFrigasp.,hs

n

r

m M P a 2 ˜

Fig. 6a-3 0.31˜10-7

0.35

0.99 Fig. 6b-3 0.80˜10-7

0.49

0.99

Fig. 6a-2 0.70˜10-7

0.40

0.99 Fig. 6b-2 1.31˜10-7

0.43

0.99

Fig. 6a-1 0.91˜10-7

0.77

0.99 Fig. 6b-1 2.30˜10-7

0.81

0.99

Fig. 7a-3 0.57˜10-7

0.28

0.98 Fig. 7b-3 0.50˜10-7

0.21

0.97

Fig. 7a-2 1.42˜10-7

0.38

0.99 Fig. 7b-2 1.22˜10-7

0.28

0.99

Fig. 7a-1 3.23˜10-7

0.85

0.99 Fig. 7b-1 1.35˜10-6

1.17

0.99

Fig. 8a-3 0.51˜10-7

0.24

0.98 Fig. 8b-3 1.08˜10-6

0.71

0.99

Fig. 8a-2 1.88˜10-7

0.31

0.99 Fig. 8b-2 6.22˜10-7

0.46

0.99

Fig. 8a-1 1.61˜10-6

0.97

0.99 Fig. 8b-1 2.16˜10-6

1.16

0.99