Issue 31

J. Xavier et alii, Frattura ed Integrità Strutturale, 31 (2015) 13-22; DOI: 10.3221/IGF-ESIS.31.02 16 In the literature, several analytical expressions for the cohesive law in mode I have been proposed. Among them, there is the Xu and Needleman exponential law [11] Ic I I I Iu Iu Iu exp G w w w w w               (7) in which Iu w is the crack tip opening displacement at maximum stress ( Iu  ) (see cohesive law in Fig. 2). The logistic (Eq. 6) and exponential (Eq. 7) cohesive laws are then compared and discussed during the analysis. D IGITAL IMAGE CORRELATION ull-field optical techniques have become very important tools in experimental solid mechanics. Among them, DIC has become widely used, following the development of digital cameras and automatic digital image processing techniques [12]. This computer vision technique has the advantages of a simple principle and experimental set-up, which can switch from large down to small scales of observation. In DIC-2D, a planar object is imaged by a single camera-lens optical system connected to a computer for real-time visualisation. It is assumed that the surface of interest has a local random textured pattern uniquely characterising the material surface. A matching process is then carried out between images taken before and after deformation. Typically, the reference (undeformed) image is divided into subsets, whose number of pixels defines the displacement spatial resolution (i.e., the smaller distance separating two independent displacement measurements). The selection of these measuring parameters, together with the quality of the speckle pattern, are key issues for determining the spatial resolution and accuracy associated to DIC measurements. Therefore, they should be carefully chosen in a compromise between correlation (small subsets) and interpolation (large subsets) errors. Crack tip opening displacement The CTOD in mode I I ( ) w was determined by processing the displacements provided by DIC. For a complex material such as wood, this technique can be advantageous with regard to standard monitoring methods. As a procedure, the initial crack length is firstly identified in the reference (undeformed) image. A suitable pair of subsets near the crack tip is then selected. During the test, the relative displacement of these points is evaluated. The I w can then be determined by [13, 14] I I I w w w     (8) where I w  and I w  are the components of the displacement in the direction perpendicular to the crack propagation associated, respectively, to the upper and the lower cracked surface and . represent the Euclidean norm. Mechanical Properties Fracture properties (Mode I, trilinear cohesive law) L E (GPa) R E (GPa) LR  (-) LR G (GPa) Ic G (N/mm) Iu  (MPa) Ib  (MPa) Ib w (mm) 7.7 1.91 0.47 1.12 0.26 5.34 0.49 0.076 Table 1 : Mechanical and fracture properties of P. pinaster used in the finite element analyses of the DCB test. F INITE ELEMENT SIMULATION wo-dimensional finite element analyses (FEA) of the DCB test under plane strain state, including cohesive zone modelling, were performed in order to validate the proposed procedure using CBBM. Nominal dimensions of the DCB specimen were (Fig. 1): 2 h = 20 mm, 1 L = 300 mm, L = 280 mm, B = 20 mm and 0 a = 100 mm. F T