Issue 47

L. Marsavina et al., Frattura ed Integrità Strutturale, 47 (2019) 266-276; DOI: 10.3221/IGF-ESIS.47.20 272 Figure 6 : Principle of DIC Evaluation of crack relative displacement factor As detailed in works of [19, 20, 25, 52], the CRDF is calculated from the experimental displacement field via an adjustment procedure based on an iterative Newton-Raphson algorithm (see Fig. 7). Figure 7 : Methodology of CRDF calculation. This consists in a fitting of analytical solutions of Kolossov–Muskhelishvili’s series [53, 54] on the displacement fields measured by DIC. Dubois et al. [16, 17], Pop et al. [19] and Meite et al. [20] show that by using this approach, an “equivalent” displacement field can be created without experiment noises, the knowledge of the material properties or the nonlinear phenomena presence [17-20]. Then, the CRDF can be expressed as a function to the weighting coefficients of the analytical solutions of Kolossov–Muskhelishvili’s series. x 1 x 2 ZOI x 1 x 2 ZOI h subset v subset D h D v 1 m m* Undeformed image Deformed image subset x 1 x 2 Subset m (4x4pixels) Subset center pixel x 2 pixel x 2 subset x 1 pixel x 1 subset Sample with Black and white speckle pattern ZOI Subsets Optimization                     N /2 /2 1 1 2 1 N /2 /2 2 1 2 1 u A r f , A r g , u A r l , A r z ,                                      By an adjustment procedure Optimization of displacement field Experimental  displacement field Equivalent  displacement field Experimental boundary conditions  experimental noises Adjustment procedure ( Newton-Raphson) Identification of the weighting coefficients 1 1 N N 0 0 1 2 1 2 1 2 1 2 0 A A A A T T R x x        Rigid body motions Crack geometry Optimized fields   ( ) 1 1 1 K 2 2 A 1            ( ) 1 2 2 K 2 2 A 1           Analytical solutions of Kolossov–Muskhelishvili’s series Crack Relative Displacement Factor