PSI - Issue 28

Mamadou Abdoul Mbacké et al. / Procedia Structural Integrity 28 (2020) 1431–1437 Mamadou Abdoul MBACKE/ Structural Integrity Procedia 00 (2019) 000–000

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strength and b is assumed to be equal to the characteristic length of the element (Turon et al. 2007). C, m, G th (fatigue threshold value of the energy release rate) and G c (fracture toughness) are crack growth rate parameters for Paris Law. In the framework of the present study, the damaged elements are post-treated and the damaged area num CZ A is subsequently calculated using computations data. ∆G=G max -G min =G max (1-R 2 ) is the variation of the energy release rate ( R is load ratio and G min is the minimum energy release rate). A strategy known as “cycle jump" is adopted in order to reduce calculation cost that could be highly expensive from CPU time required (Turon et al. 2007). This technique decreases the difficulty of realisation of high-cycle fatigue finite element analysis. The cycle jump jump N  is determined for a given maximum damage max D  and a corresponding quantity D N   according to:

D



max

jump   N

(10)

D N        

max

Fig. 2. Flowchart of the numerical integration of the model

The fatigue parameters are computed at each integration point through the USDFLD subroutine while the role of the UEXTERNALDB subroutine consists on the access to the different quantities relative to the integration points in order to find maximum and minimum values of different outputs recorded in arrays. 4. Model validation In order to be ensure of the consistency of the model, validation tests are performed taking as reference the experimental work of Al-Khudairi et al. (Al-Khudairi et al. 2015). In that work, delamination tests on a unidirectional composite were performed in both quasi-static and fatigue conditions. In the present work, the issue is adapted to the adhesive bonding case. First, the quasi static model is calibrated in order to fix the interface mechanical properties, note that the composite material parameters (E 11 =38.9GPa, E 22 =13.0GPa, G 12 =5.0GPa, υ 12 =0.24) are given by Al-Khudairi et al. (Al-Khudairi et al. 2015). The quasi-static test is simulated using the cohesive zone model available in Abaqus. The model is governed by a bi-linear traction-separation law. Figure 3 shows that the calibration of the finite element model (identification of the parameters n K and 0  for CZM in quasi static) from the experimental test is successfully achieved. The quasi-static model is considered as valid and the parameters obtained from calibration are used for the needs of fatigue analysis, in addition to other parameters necessary to run the cyclic analysis. These parameters ( G IC =0.764mJ/mm 2 , m I =5.27, C I =4.47 10 -2 and G Ith =15%G IC ) are also available from Al-Khudairi et al. (Al-Khudairi et al. 2015). Once all the parameters are available, fatigue simulation is executed using the suitable loading conditions in a sake of representativeness. The figure 4 represents the crack-growth rate versus the normalized energy release rate for experimental test and numerical simulations with the implemented fatigue model. The results obtained from fatigue simulations show a good agreement comparatively to the experimental test results (DCB fatigue test). This shows that the model implemented is strong enough to predict the high-cycle fatigue crack-growth in adhesive joints. The main purpose of the model is to predict the fatigue life of composite assemblies and the fatigue damage accumulation. Thus, Figure 5 shows the damage evolution within the specimen subjected to cyclic loading. As for figure 6, it highlights lifetime prediction (number of cycles required to failure) within the specimen.