PSI - Issue 37

960 Reza Soleimanpour et al. / Procedia Structural Integrity 37 (2022) 956–963 Reza Soleimanpour, Sayed Mohamad Soleimani and Naser Khaled Mohammad/ Structural Integrity Procedia 00 (2019) 000 – 000 5 3.2 Modeling methodology The setup was modeled using the 3D explicit FE method. ABAQUS was used to model the specimen. In the FE model, only the plates and bolts holes of the specimen were modeled and the effect of the bolt tightening was modeled by applying pressure on washer area using the following equation recommended by Caccese et al.( 2004). = (2) where P is the applied pressure due to bolt tightening, T is the torque applied on the bolt, k is the torque coefficient (k = 0.2), d is the nominal diameter of the bolt and A is the area of the washer. In this study, for the sake of simplicity, the washer area was considered as square area with length of twice the bolt diameter and width equal to the plate width. The specimens were modeled using eight-node linear brick elements full integration (C3D8). The hourglass energy was limited to less than 2% of the total energy to ensure the stability of the simulations. The mesh size used was 0.2mm × 0.2mm × 0.2mm. This ensures that there are at least 20 elements in the wavelength and also 12 elements per thickness of steel plates to accurately model the A0 guided wave mode shape. The excitation signal is a 5 cycle tone burst sinusoidal wave with central frequency of 140 kHz modulated by Hann window. The asymmetric guided wave was generated by applying out of plane nodal displacement at the top surface of the plate with same size as piezoelectric transducers. The loosen bolt was modeled by separating the nodes at loosened bolt joint. This was done by assigning a “Seam crack” at the area of loosened bolt and then assigning two native mesh surfaces for the top and bottom separated surfaces to ensure the functionality of contact pairs. The interaction between the surfaces of loosen bolted joints were modeled by the surface to surface contact interaction in ABAQUS which was successfully used in previous studies (Soleimanpour et al 2017). Damping effect of the materials was considered in the simulation. It was simulated using the Rayleigh mass proportional and stiffness proportional damping and was implemented in FE models. The noise effect was considered in the numerical data, which was simulated by adding white noise to the time-domain guided wave response. The noise level considered in this study was approximately 1.2% of the maximum amplitude of each signal. 3.3 Results and discussion Fig. shows a snapshot of the finite element simulation results when the A0 guided wave interacting with the loosened bolt for the bolt size of 10mm. For this model, the receiver is located at 85mm away from the centre of the loosened bolt respectively. As shown in Fig. , the contact interaction applied to the subsurface of the joint at the loosened bolt, which prevents the interpenetration between the subsurface and causes clapping simulates the CAN in joint area. The data captured was the time-domain out-of-plane displacement responses at the location of the both transducers.

Fig. 3 Snapshot of 3D FE model for bolt size of 10mm at 115 μsec