Issue 41

S. Seitl et alii, Frattura ed Integrità Strutturale, 41 (2017) 323-331; DOI: 10.3221/IGF-ESIS.41.43 325 Method of measurement: Digital Image Correlation (DIC) DIC was used to investigate the crack tip behaviour of the CT specimen for two different crack lengths and three load levels (see Tab. 2). DIC provides full-field displacement information by comparing images taken before and after straining the body. Each image is divided into smaller regions or interrogation windows. The cross-correlation product [7] is used to measure the similarity between interrogation windows before and after straining the body in study:       2 2 2 2 , , , , N N x y A B N N x y c u v I x y I x u y v          (1) where c is the cross-correlation product which is a function of u and v , the displacement vectors joining the centres of the two regions of interest along directions x and y respectively, I A and I B are the intensity distribution of the two digital images before and after straining the sample, respectively, and N is the number of interrogation windows into which the digital images were divided. The maximum value of the cross-correlation product (Eq. 1) is the probable displacement vector for the centre of the each interrogation window in I A . The camera was placed horizontally so that the positive x coordinate matched the crack growing direction and the y coordinate matched the crack opening direction [8]. This improves and makes the post-processing of the results easier under conditions leading to non-horizontal cracks [9]. DIC requires the surface to have a random pattern so that each interrogation window is unique in each image and can be located easily in the same image after it has undergone some deformation or rigid body movement. In this work, this pattern with random grey intensity distribution was obtained by scratching the sample surface with abrasive SiC sand papers grades 240, 380 and 800 [10], [11] for better imaging of the crack tip [12]. An 8-bit 2452x2052 pixels CCD camera with the maximum frame rate of 12 was used for taking images and recommendations from previous analyses were followed [13]. The experimental setup was similar to the one used previously [14]. DIC generated a pair of matrices, u and v , with displacement values that were combined with an analytical model to infer fracture mechanics parameters (see next section). M ULTI - PARAMETER FRACTURE MECHANICS Crack tip fields for mode I fracture problem illiams [15] derived that the crack tip stress and displacement distribution can be expressed by means of a power series. Assuming a plane crack with traction-free faces in a homogeneous linear-elastic isotropic material subjected to arbitrary remote mode I loading, the stress/displacement field around the crack tip obtained by the Williams eigenfunction expansion can be expressed as:       1 2 2 1 cos 1 1 cos 3 2 2 2 2 2 1 cos 1 1 cos 3 2 2 2 2 2 1 sin 1 1 sin 3 2 2 2 2 n n x n y n xy n n n n n n n n n n r A n n n n                                                                                                                                 1 n            (2) Similarly, the displacement vector can be written as:                                                                      /2 1 1 cos cos 2 2 2 2 2 2 1 sin sin 2 2 2 2 2 n n n n n n n n n u r A v n n n n (3) In Eq. 2 and 3, r and θ are polar coordinates centred at the crack tip (considering the crack faces coincident with the negative x -axis),  is shear modulus defined as  = E /2(1+  ), where E and  are Young’s modulus and Poisson’s ratio; n represents the index of the term of the power expansion and  is Kolosov’s constant depending on plane stress or plane strain