PSI - Issue 28

Mohamed Ali Bouaziz et al. / Procedia Structural Integrity 28 (2020) 1039–1046 M.A. BOUAZIZ et al / Structural Integrity Procedia 00 (2019) 000–000

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4. DIC results analysis 4.1. Characteristic size estimation

The autocorrelation function can be used as the basis of a texture measure ( Rosenfeld and Troy 1970). Peaks in the autocorrelation function of a regular-texture image characterize characteristic sizes. The locations of peaks in the autocorrelation function involve the shape and arrangement of texture primitives in the image (Lin et al. 1997). The full width at half maximum of the auto-correlation is often used to estimate the radii of speckle patterns (Besnard et al. 2006; Bornert et al. 2009). Here the auto-correlation is applied to strain fields (Doumalin et al. 2003) to estimate the radius, in transverse and longitudinal directions, of the concentrations zones. Figure 4(a-b) shows the normalized autocorrelation of the strain field measured for the last loading step of both samples (Figure 3(b,d)). For both materials, the strain field patterns are elongated in the transverse direction. Details of the autocorrelation functions about their maximum (centred at 0) are shown in Figure 4(c-d). From this information, the full widths at half maximum were determined along the longitudinal and transverse directions. In the sequel, these quantities are referred to pattern radii.

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Fig. 4. Normalized auto-correlation of strain fields shown in Figure 3 for (a) the 50 µm sample, and (b) the 125 µm specimen. Corresponding profiles of the autocorrelation about its maximum along both directions and for both samples ((c) 50 µm and (d) 125 µm). Evaluation of the pattern radii as full widths at half maximum (horizontal dotted lines).

4.2. Characteristic size history Figure 5 shows the pattern radii histories for both tested samples. It is observed that the pattern size is almost constant for all test steps and both tested materials. The patterns are elongated in the transverse direction since r x is greater than r y . For the material made of 50 µm layers, the average pattern radius in the transverse direction r x is equal