PSI - Issue 13

Odounga Bernard et al. / Procedia Structural Integrity 13 (2018) 347–352 Odounga Bernard / Structural Integrity Procedia 00 (2018) 000–000

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to deduce from the displacement maps obtained with this technique the opening and the crack propagation in order to be able to apply Equation (1) given below.

2.4. Compliance method

The imposed displacement compliance method was used to calculate the energy release rate, by using Equation 1.

F 2 c 2 · b ·

∆ C ∆ a d

(1)

G =

where: F c is the critical force at the origin of a crack propagation of length ∆ a , b is the thickness of the specimen. Compliance is defined by ∆ C = U / F c , where U is the crack opening induced by each critical force F c . Index d means that we are in imposed displacement.

3. Results

The results are presented in terms of displacement and strain maps, and force versus crack opening. The di ff erent energy release rates are calculated after decoupling modes 1 and 2. The results of G are given as a function of the crack length (Figures 5 and 6). The curves concerning the mode 1 ( G I ) and mode 2 ( G II ) are given. The minimum average values G ic calculated at the beginning of the crack propagation are given for the three species and the two modes.

3.1. Displacement and strain maps

Figure 3 presents some displacement and strain maps for the three species. The opening and the length of the crack were deduced from these maps. The method used to obtain these parameter is described in Odounga et al. (2018). We can see that for iroko and padouk, the propagation of the crack is rectilinear and horizontal whereas for padouk, it is inclined. This seems to indicate the specificity of these tropical species which have the particularity of having a continuous growth and often present a change in the orientation of the grain thread, contrary to temperate woods, for which annual rings make it possible to distinguish the initial wood from the final wood.

Fig. 3. Typical maps of displacements for mid-course MMCG specimens for the thickness b = 20 mm , α = 15 0 .