PSI - Issue 5

Ahmed Bahloul et al. / Procedia Structural Integrity 5 (2017) 430–437 Ahmed Bahloul et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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3

Finally, the total FCG life at the end of each iteration is evaluated as follows: = −1 + ∆

(5)

2.2. FE modeling

2D FE analysis using ABAQUS commercial software was implemented. The attachment lug was considered to estimate the residual fatigue life under different load ratios (R=0.1 and R=0.5). The geometry of the lug is shown in Fig.1, having L=200 mm, D=38.1 mm, t=12.7 mm and w=3D. A crack was positioned near the hole edge with an initial size equals to 0.635 mm. In order to compute the high stress distribution in the vicinity of the crack, a very fine structured mesh has been modeled around the crack region with 0.05 mm element size. The finite element mesh of the cracked lug is illustrated in Fig.1. The non-linear isotropic/kinematic hardening model is considered to describe the material behavior. This plasticity model is capable to characterize the material behavior during cyclic loading considering the Baushinger effect, mean stress relaxation, ratcheting and cyclic hardening. During FE analysis, a growing crack is considered. When the applied load reaches its maximum value, a constant crack growth increment length is released during a loading cycle. The residual stress distributions near crack tip are evaluated at each crack growth increment at the end of the unloading step, from which the residual stress intensity factor can be evaluated using the weight function. 2.3. Computation of FCG Reliability In this section, a probabilistic approach for predicting FCG life of cracked attachment lug, under cyclic loading is implemented. The main procedure for developing the probabilistic model using FE-analysis, RC-SIF and Monte Carlo simulation method is summarized as follows: (i) In the first stage, a FE model is developed upon ABAQUS commercial code. An elastic-plastic analysis using the non-linear isotropic/kinematic hardening model is used to extract the residual stress distribution surrounding the crack tip. Crack growth path is simulated using XFEM .In this context, a numerical fatigue crack growth code was developed by an iterative procedure within the framework of Python script. (ii) The residual corrected stress intensity factor RC-SIF parameter is used to predict the FCG life of the cracked attachment lug. (iii) Due to the significant fatigue data scatter of the attachment lug, the proposed approach was carried out by taking into account the effect of residual stress distribution near crack tip and material dispersions which are assumed to be normally distributed. The reliability is computed using the Monte Carlo simulation method. (iv) The iso-probabilistic a-N curves of the cracked attachment lug are determined at 5% ,50% and 95% of reliability.

3. Results and discussion (i)

FCG simulations are determined using the XFEM. In this context, a numerical code was developed within the framework of Python script. In the first step, model geometry, mesh generation, loading conditions and material parameters are implemented in Abaqus. Then, the Python code was called to extract SIF for each increment in which the first five contour integrals are chosen for evaluating the average of SIFs. Fig.2 shows the crack growth path of different structure configurations, under cyclic loading.