Issue 31

J. Lopes et alii, Frattura ed Integrità Strutturale, 31 (2015) 67-79; DOI: 10.3221/IGF-ESIS.31.06 76 Fig. 8 and Fig. 9 show the plots of several numerical simulations for several values of G IIC for the reference beam and the hybrid beam respectively. Fig. 8 shows an initial linear trend followed by a slight decrease in slope. This decrease is the beginning of the yielding of the cohesive elements. The load increases at an apparently linear rate until it reaches its peak. After the peak there is a sudden drop in the apparent shear stress load indicating the unstable crack propagation. After the shear stress increases again. This increase is the result of the reaction of two half beams fully delaminated one above the other and it is no longer meaningful. In the case of the reference beam the solver is able to converge to a solution in every step. In the case of the hybrid beam after the peak shear stress the ABAQUS solver is unable to converge to a solution of its current step. This is due to the fact that in the case of an unstable crack propagation the kinetic energy associated with it is relevant and it’s not considered in an ABAQUS implicit analysis. However the maximum load is correctly calculated by the solver. One common feature of either the reference or hybrid beams is that the stiffness of the numerical simulation is higher than the stiffness of the experimental results. This discrepancy is analysed in the next section. D ISCUSSION he numerical models predict a maximum ILSS shear strength close to the experimental maximum ILSS provided that the proper G IIC is set. The results predicted by the numerical models have a higher stiffness than the stiffness of the experimental tests. There are several factors that contribute for this discrepancy: i. In the experimental tests the displacement is measured by an LVDT above the specimen in the movable part of the testing machine while in the numerical simulation the displacement is measured directly in the loading member. The effect of the compliance of the testing machine is therefore expected; ii. There is an unavoidable initial slack in the experimental test that does not occur in the numerical simulation; iii. The testing machine has some elasticity that, however small, cannot be ignored. The first factor is considered as the most relevant. In these tests the measured displacement until failure is extremely low (≈ 0.45mm). It is possible that the LVDT may be unable to measure accurately the displacement in such a small range. There is also a small contribution of the initial slack of the testing fixtures. It is observed some irregular data in the beginning of the experimental tests plots. The third factor is the less significant. The maximum measured loads [3.4 kN – 3.5 kN] are far lower than the maximum capacity of the testing machine (100 kN). These accumulated factors, although in different weights, are responsible for the discrepancy in slope between the numerical and experimental curves. The experimental results show that the maximum ILSS of the hybrid beams is very close to the ILSS of the reference beam. Vacuum blasting surface treatment is clearly the best in terms of hybrid ILSS performance. The one day storage between surface treatment and composite manufacturing does not affect ILSS performance. The remainder surface treatments are clearly less competitive. The numerical results show that with a proper adjustment of the critical energy release rate G IIC it is possible to predict accurately the maximum load (therefore the ILSS) of both the reference and hybrid beams. The standard deviation of the ILSS of the hybrid beams is considerably higher that the reference beam. It is also noted that the standard deviation of the treatment with one day storage is higher than the same treatment with no storage. However, it is unlikely that it will have an impact in actual aircraft design due to the conservative factor of safety of composite aircraft structures. The short beam test method was chosen due to the previous experiences in assessing ILSS in hybrid composites [2],[6]. The small size of the specimens does not affect a purely experimental research where different specimens are compared and any eventual effect of the compliance of the testing machine has an identical impact in all results. However, it poses a greater difficulty when trying to replicate the test in a FEM simulation because the eventual effect of the compliance of the testing machine is increased with specimens that have such a small displacement. It is suggested therefore that in a future research of inter-laminar shear stress by three-point bending the size of the specimens should be bigger than the size prescribed by EN14130 in order to reduce the effect of the factors that induce uncertainty in this test.