Issue 31

J. Xavier et alii, Frattura ed Integrità Strutturale, 31 (2015) 13-22; DOI: 10.3221/IGF-ESIS.31.02 18 R ESULTS AND DISCUSSION he crack length propagation during the fracture test was determined based on DIC measurements: DIC 0 ( ) ( ) a a a      . The algorithm proposed for this evaluation together with a further comparison between eq a and DIC a as a function of the applied displacement in the DCB test is described in detailed in Ref. [10]. Hereafter, a systematic evaluation of mode I fracture properties ( R – curve and cohesive law) obtained from both CBBM and Irwin- Kies equations is addressed. To start with, the R –curves determined from both Irwin–Kies equation and CBBM (Eq. 3) were analysed. The compliance versus crack length ( DIC a ) function was fitted in the least-square sense by a cubic function of the form: 3 C ma n   . The analytical differentiation of this function was then used in order to compute I G . Fig. 3a shows the P   curves obtained experimentally together with the numerical one resulting from FEA using the trilinear cohesive law (Fig. 2). This law was defined using the average values of Ic G and Iu  in order to outline the area circumscribed by the law and the peak stress value, respectively. The coordinates of the inflection point ( Ib w = 0.04 mm, Ib  = 2.0 MPa) were taken from the experimental cohesive laws, considering the issuing average values. The scatter on the initial compliance among the curves ( 0 0.072 0.0076 C   mm/N) is expected due to the inherent variability of the material. Moreover, qualitatively, the numerical prediction of the P   curve was in good agreement with the experimental ones. In Fig. 3a it is also shown a macroscopic visualisation of crack propagation. As it can be seen, micro- cracking and fibre bridging can be identified. This confirms the difficulties in measuring accurately the crack length using conventional monitoring techniques. Some authors (e.g., [21]) report that the main mechanism of mode I fracture is fibre bridging. However, these observations suggest that both micro-cracking and fibre bridging contribute significantly for the energy dissipation in the FPZ. The R –curves in mode I obtained from the DCB test by both CBBM and Irwin-Kies equations are shown in Fig. 3b and 3c, respectively, together with the numerical resistance curve. The wide dispersion of the experimental curves is most likely a reflection of the local variability of wood microstructure at the initial crack tip (e.g., earlywood and latewood constituents). Specimens CBBM IK  f E Ii G Ic G Ii G Ic G (g/cm 3 ) (N/mm 2 ) (N/mm) (N/mm) (N/mm) (N/mm) 1 0.539 9888 0.22 0.41 0.18 0.34 2 0.566 7279 0.14 0.28 0.10 0.21 3 0.529 8890 0.10 0.18 0.15 0.25 4 0.545 7423 0.14 0.41 0.14 0.40 5 0.548 8585 0.20 0.30 0.18 0.27 6 0.550 9833 0.17 0.29 0.15 0.27 7 0.535 7585 0.13 0.21 0.12 0.19 8 0.496 8473 0.20 0.37 0.16 0.30 9 0.566 8043 0.25 0.34 0.20 0.27 10 0.553 10105 0.17 0.27 0.15 0.25 Mean 0.543 8610 0.17 0.31 0.15 0.27 C.V.(%) 3.8 12.2 26.3 25.4 18.6 22.1 Table 2 : Density (  ), flexural modulus ( f E ), initial ( Ii G ) and critical ( Ic G ) strain energy release rates in mode I obtained from the DCB tests by CBBM and Irwin-Kies (IK) equation. From the R –curves, the evaluation of the strain energy release rate in mode I was carried out at two distinct stages. The first corresponds to the starting point of the non-linearity in the P   curve and therefore the initialisation of the FPZ ( Ii G ), whilst the second is defined at the maximum loading ( Im G ). Due to the fact that some of the R– curves do not reveal a clear plateau identifying the critical strain energy release rate, it was assumed that: Im Ic G G  . This value is then related to the complete development of the FPZ and initial steady-state crack propagation [7,10]. The Ii G and Ic G values for both CBBM and Irwin-Kies equations are reported in Tab. 2, together with density and flexural modulus (Eq. 2). T