Issue 31

R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 5 As a result, the procedure of an experiment is to measure the history of P , a ,  n and  o . The cohesive law in tension can then be estimated by plotting G n in Eq. (1) as a function of  n , polynomial fitting of the obtained curve and differentiation [21]. Optical method for the parameter measurement For calculating  n and  o for a given image, the optical method requires the identification of eight points (Fig. 3): two points ( p 1 , p 2 ) for measuring the current t A value at the crack tip ( t A CT ) during loading in image units (pixels), two points ( p 3 , p 4 ) identifying a line segment in the image for which the length ( d ) is known in real world units (mm), two points ( p 5 , p 6 ) on the top specimen and two points ( p 7 , p 8 ) on the bottom specimen. Figure 3 : Points taken by the optical method for measuring  o and G n c . Points Identification All eight points are manually identified in the first picture of a trial using an in-house software tool. The identification of the points is aided by the ruler attached to the specimens. Using the location of the points in the first picture, the points of the following pictures are automatically identified using a computer algorithm implemented in Matlab ® . Basically, for each point p i , a rectangular region centred in p i is extracted from the first image forming a template ( t ). This template describes the image pattern that surrounds the point and is used for locating the point in the next image. This is done by finding the position ( u,v ) in the next image ( I ) that has the highest normalized cross-correlation with the template. The normalized cross-correlation is a measure of similarity between two grayscale images that is invariant to linear changes in illumination and that quantifies the correlation between the grayscale levels of two images/regions. The normalized cross-correlation (  ) of template t with image I at the position ( u,v ) of image I is defined as:           , , 0.5 2 2 , , , , . , , , . ,                                    x y u v x y x y u v f x y f t x u y v t u v f x y f t x u y v t (4)