PSI- Issue 9

Liviu Marsavina et al. / Procedia Structural Integrity 9 (2018) 47–54 Author name / Structural Integrity Procedia 00 (2018) 000–000

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can be calculated form the displacement fields measured by optical metrologies. As stated before, for this application, Digital Image Correlation has been chosen. Then the Crack Relative Displacement Factor is calculated from the experimental displacement field via an adjustment procedure based on an iterative Newton-Raphson algorithm. This consists in a fitting of analytical solutions of Kolossov–Muskhelishvili’s series on the displacement fields measured by Digital Image Correlation. Then an “equivalent” displacement field can be created without the experiment noises, the knowledge of the material properties or the nonlinear phenomena presence. Based on the results obtained by the adjustment procedure the CRDF can be calculated by using Dubois et al (2002, 2005) developments and weighting coefficients of the analytical solutions of Kolossov–Muskhelishvili’s series. Using the weighting coefficients, the CRDF can be expressed as follows Pop et al. (2011), Meite et al. (2013), Muskhelishvili (1933), Williams (1957): where 1 2 , i i A A are the weighting coefficients associated with opening and shear modes; k is a weighting coefficient. 2.3. Optical metrology In the present study, Digital Image Correlation was implemented to measure the displacement field evolution. The DIC principle is based on comparison of two images acquired before and after deformation, Sutton et al. (1986), Hild and Roux (2006) (see Fig.1). The displacement vector coincides with the displacement of the subset center. It should be noted that in DIC the analysis of displacement field is performed inside of a Region Of Interest (ROI) divided into discrete subsets Sutton et al. (1986), Hild and Roux (2006), Pop et al. (2011), Meite et al. (2013). Supposing that the light intensity distribution during the test does not change, the displacement field is estimated by searching the subset distortions in terms of translations, rotations and rigid body motions. Furthermore, the displacement is supposed homogeneous and bilinear inside the subset. A very thin black and white speckle pattern was sprayed on the specimen surface, in accordance with the principle of method (see Fig. 1).    i K A k   1 8         (2)

a. SENB

b. CS Fig. 1. Samples with black and white speckle pattern