Issue 37

M. Mokhtarishirazbad et alii, Frattura ed Integrità Strutturale, 37 (2016) 114-123; DOI: 10.3221/IGF-ESIS37.16 118 P ROCESSING OF DISPLACEMENT INFORMATION isplacement data ahead of the crack was measured by using DIC. The obtained displacement data was then fitted into Williams' series [29, 30]:                                                                     2 1 2 1 ( 4) ( 1) cos cos 2 2 2 2 2 ( 4 ) ( 1) sin sin 2 2 2 2 2 n n I n n n n I n n n r n n n u a ModeI n r n n n v a (1) and,                                                     1 2 1 2 2 )4 ( cos 2 2 cos )1( 2 2 2 )4 ( sin 2 2 sin )1( 2 2 n n n n II n n n n II n n n n b r v n n n n b r u ModeII         (2) 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:                      2 2 cos ( 1 2sin ) sin ( 1 2cos ) ( 1)cos 2 2 2 2 2 2 2 2 8 I II K K r r T u r (3)                      2 2 sin ( 1 2cos ) cos ( 1 2cos ) ( 3)sin 2 2 2 2 2 2 2 2 8 I II K K r r T v r (4) by using   1 2 I K a ,    1 2 II K b ,  2 4 T a (5) where K I and K II 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:     2 2 2 2 ( ) bot bot top top COD x u v 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. D