Issue 37
M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16
P ROCESSING OF DISPLACEMENT INFORMATION
D
isplacement data ahead of the crack was measured by using DIC. The obtained displacement data was then fitted into Williams' series [29, 30]:
2 n
n n 2 2
r
2 n
( 4) n
n
u
a
( 1) cos
cos
I
n
2
2
n
1
ModeI
(1)
2 n
( 4 ) n
n n 2 2
r
2 n
n
v
a
( 1) sin
sin
I
n
2
2
n
1
and,
v u
2 n
n n n )4 ( sin
2 n
n
sin )1(
n b r
II
2
2 2
2
1
n
ModeII
(2)
2 n
n n n )4 ( cos
2 n
n
cos )1(
n b r
II
2
2 2
2
1
n
where u I
and v I
are horizontal and vertical displacements in mode I respectively, u II
and v II
are horizontal and vertical
displacements in mode II respectively, is the shear modulus, (3 ) / (1 ) for plane stress and for plane strain condition, is the Poisson’s ratio, r and θ are polar coordinates with the crack-tip being the origin of coordinates, and a and b are constants. Eqs. 1 and 2 can be written in terms of the SIFs and T-stress as follows:
K
r
K
r
T
2
2
I
II
u
r
(3)
cos (
1 2sin )
sin (
1 2cos )
(
1)cos
2 2
2 2 2 2
2
2 8
K
r
K
r
T
2
2
I
II
v
r
(4)
sin (
1 2cos )
cos (
1 2cos )
(
3)sin
2 2 2
2 2 2
2
2 8
by using
4 T a
1
1 II K b
I K a
,
,
(5)
2
2
2
where K I are mode I and II of SIF respectively and T represents T-stress. Having employed a post processing routine, the crack opening displacement, COD, has been determined at various distances behind crack-tip. COD was determined as follows: and K II
2 2 2 2 ( ) bot bot top top u v
COD x u v
(6)
Where u and v are the horizontal and vertical displacement respectively, and x is the distance of the extensometer behind the crack-tip. The subscripts “top” and “bot” refer to the position of the virtual extensometer points relative to the crack line.
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