Issue34
F. Berto, Frattura ed Integrità Strutturale, 34 (2015) 169-179; DOI: 10.3221/IGF-ESIS.34.18
1
1
1
1 ( ) r
r
( , 0) (1 ) r
2
K
(3)
1
1
1 2 1
1 2 2
2
r
r
1 g g
g
g
2
3
4
When the notch radius tends to zero, K 1 tends to the mode 1 notch stress intensity factor K 1
defined according to
Gross and Mendelson [31]:
1 r 1
2 lim r
K
(4)
1
0
Considering the V-notch with root hole under mode 2 loading, the stress components for the antisymmetric mode result also from Ref. [21]:
2
2 2 1
2
K
2
1
r
r
r
2
21 ( )
22 22 ( ) ( )
2 sin(1 ) (
1)
2
2
2
(1 )
( )
2
(5.1)
2
2
2
2(
1)
r
r
2
2 2 ( )sin(1 ) 1 (1 ) 2
2
2
2 2 1
2
K
2
1
r
r
r
2
21 ( )
22 22 ( ) ( )
2 sin(1 ) (3 ) 2
rr
2
2
(1 )
( )
2
(5.2)
2
2
2
2(
1)
r
r
2
2 2 ( )sin(1 ) 1 (3 ) 2
2
2
2 2 1
2
K
2
1
r
r
r
2
21 ( )
22 21 ( ) ( )
2 cos(1 ) (1 ) 2
r
2
2 ( )
(1 )
2
(5.3)
2
2
2
2(
1)
r
r
2
2 ( )cos(1 ) 1 (1 ) 2 2
2
The parameter 2
is Williams’ [30] mode 2 eigenvalue, which is dependent on the notch opening angle
The generalised mode 2 notch stress intensity factor K 2 can be expressed as follows:
2
1
r
r
( , 0) r
2
K
(6)
2
2
2 2 1
2 2 2
2
r
r
r
h
h
h
1
1
2
3
When the notch root radius tends to zero, K 2 tends to the mode 2 notch stress intensity factor K 2
defined according to
the following expression:
2 r 1
2 lim r
r
K
(7)
2
0
It is important to underline that the property of K to converge to the stress intensity factor of the pointed V-notch, K 2 , when the notch root radius tends to zero, is a characteristic of the set of equations provided in Ref. [21] for V-notches with root hole. Other sets of equations [32, 33] applicable to rounded V-notches of different shape do not have this property as discussed in Ref. [34]. In that paper it was also documented the stable trend of the generalized notch stress
172
Made with FlippingBook Ebook Creator