PSI - Issue 39

Riccardo Cappello et al. / Procedia Structural Integrity 39 (2022) 179–193 Author name / Structural Integrity Procedia 00 (2019) 000–000

189 11

growth. Moreover, the numerical approach can be totally automated, thus resulting in a faster and more straightforward tool for the determination of the crack tip. The knowledge of the crack tip location, combined with the SIF extracted from the ODLSF of the Williams’ series enables the determination of a Paris’ law curve, that correlates the crack growth and the SIF: = Δ [28]. If the Paris law is rewritten in logarithmic coordinates, a simple linear regression allows the evaluation of the coefficients C and m.

Figure 12 – Crack length vs the number of cycles. The crack length is retrieved numerically (left) and optically (right)

Figure 13, left, shows the Paris law obtained via the numerical crack tip, while Figure 13, right, shows the regression using the optical measurements. Even though the curve obtained using the numerical crack length appears to be less noisy (this is further confirmed by the higher determination factor), the coefficients of C and m determined using both approaches are quite similar. Table 1 summarizes the values of those coefficients.

Figure 13 – Paris’ law linear fitting in logarithmic coordinates. The linear regression equation and determination factor are written on the graphs. The numerical (left) and optical (right) crack lengths are employed.

Table 1 – Paris’ law coefficients determined using the SIF obtained via the Williams’ over deterministic solution and the crack lengths evaluated using the numerical and optical measurements. Crack length measurement C m Numerical 10 -11 2.827 Optical 10 -11.1 2.881