Issue 31

J. Xavier et alii, Frattura ed Integrità Strutturale, 31 (2015) 13-22; DOI: 10.3221/IGF-ESIS.31.02 19 These results point out that an underestimation of I G can be obtained if the actual crack length is used (Eq. 1) because a fraction of fracture energy dissipation at the FPZ is not properly taken into account. It should be noted that the density values among specimens have a coefficient of variation (C.V.) lower than 4%. Consequently, it is not surprising that scatter of Ii G and Ic G was not statistically correlated with density. Indeed, as already pointed out, this scatter is likely due to natural variability of wood cellular structure at the crack tip among specimens. As can be concluded, the evaluation of the strain energy release rate in mode I by the Irwin-Kies equation is slightly lower than the one from CBMM. This difference is of 11.8% and 12.9% for Ii G and Ic G respectively, which is lower than the coefficients of variation among the tested specimens. The higher scatter observed in the R -curves resulting from CBBM relative to Irwin-Kies is explained by the scatter on elastic properties. In fact, since CBBM is based on specimen compliance it becomes more susceptible to material variability. From the DIC measurements both normal and transverse CTOD, with regard to the crack plane, were determined during the DCB test. As expected, CTOD in mode II ( II w ) was negligible. Characteristic R –curves in mode I I I ( ) G w  were then obtained as shown in Fig. 4a and Fig. 5a for the CBBM and Irwin-Kies equations, respectively. The numerical characteristic R –curve obtained by FEA of the DCB test was generically in relative good agreement with the experimental ones. For determining the cohesive law (Eq. 5), a logistic function (Eq. 6) was firstly fitted to the experimental data as shown in Figs. 4b (CBBM) and 5b (Irwin-Kies). For this analysis, only the data points just before initial crack propagation, where the FPZ is assumed to be completely developed were considered. As it can be seen, a relatively good approximation was obtained in both cases. This procedure allows filtering experimental data and provides a basis for analytical differentiation, which is less prone to noise amplification. The cohesive laws in mode I obtained from the DCB test are shown in Figs. 4c (CBBM) and 5c (Irwin-Kies), together with the numerical curve. Figure 4 : DCB test processed by CBBM: (a) characteristic R–curves; (b) least-square regression with the logistic function; (c) cohesive laws in mode I; (d) comparison between logistic and exponential mean cohesive laws. The parameters ( 1 A , 2 A , p and I,0 w ) of the logistic function (Eq. 6) obtained from this study are reported in Tab. 3 (CBBM) and 4 (Irwin-Kies), together with the characteristic values of maximum stress ( Iu  ) and relative displacements ( I u w , I c w in Fig. 2) in mode I. The mean value of 2 A (Tab. 3 and 4) represents an estimation of Ic G . In this case, a systematic lower evaluation was obtained from this fitting with regard to the independent measurements based on the R –