Issue 16

G. Pesquet et alii, Frattura ed Integrità Strutturale, 16 (2011) 18-27; DOI: 10.3221/IGF-ESIS.16.02 26 rate of the material in mode I (GIc). VCCT does not need special elements or remeshing but needs two surfaces that are initially partially bonded. The experimental results showed that the maximum deflection is low compared to the size of the specimen, therefore geometric linearity can be assumed. The maximum deflection (obtained with 2015 20wt%) of the SENB specimens was always under 3 mm. However, geometric nonlinearity option was used to help the convergence of the VCCT analysis. Plane strain condition was assumed. Because first-order elements generally work best for crack propagation analysis [15], plain-strain, four-node, linear CPE4 [15] element were selected. 100 elements were used along the height and 100 elements were used along the length of each part with a geometric decrease in size next to the bonded surface. 20 000 elements were used in total. The width of elements next to the bonding area was 2.4×10  mm. VCCT does not exhibit a strong mesh dependency. Two computations were done with the same geometry and material properties but with 360 and 20,000 elements, respectively. The coarse mesh is slightly stiffer but the displacement needed to disbond the first nodes was rather accurately found with the coarse mesh. Results of the numerical simulation Three cases are presented here for illustration purposes: Araldite 2015 0wt%, Araldite AW106 25wt%, Araldite AV138M 20wt%. Similar conclusions were obtained for the other cases. The three experimental load-displacement curves come from SENB specimens with a crack opened under fatigue. For each case, both experimental and numerical curves are plotted for comparison purposes. The first case presented is for the ductile 2015 adhesive in Fig. 12(a). As VCCT use LEFM approximation, there is no plasticity. That explains that the peak of the experimental curve is smoother than the numerical one. However, the prediction is overall correct. The same conclusion can be drawn from the case of adhesive AW106 with 25wt% of TEMs (Fig. 12(b)). The third case is for adhesive AV138M with 20wt% TEMs in Fig. 12(c). In this case, the experimental failure of the specimen was instantaneous. The starting of disbonding was accurately determined by VCCT. However, there is a softening of the specimen in the numerical simulation that was not captured experimentally. The numerical results show that modified adhesives can be properly simulated with a homogenous model knowing the critical strain energy release rate. The macroscopic deformation of the experimental specimens was ruled by linear elasticity and the assumption of LEFM was correct for simulating these SENB specimens. (a) (b) (c) Figure 12 : Numerical and experimental load-displacement curves for (a) adhesive 2015 non modified; (b) adhesive AW106 with 25wt% TEMs; (c) adhesive AV138 with 20wt% TEMs.