PSI - Issue 60

A.M. Sreenath et al. / Procedia Structural Integrity 60 (2024) 256–263 A. M. Sreenath and R. V. Prakash / Structural Integrity Procedia 00 (2024) 000–000

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The interface behavior is generally modelled using a cohesive element [Cheng et al. (2018)]. The element acts as a linear elastic member till the damage evolves. After the damages evolve, the member will act as a linear elastic solid with reduced stiffness. The reduction in stiffness is calculated using the damage parameter, which depends on the failure properties. A quadratic traction separation law is used as the criteria for the damage initiation. Benzeggagh and Kenane (B-K) criteria are used as the rule for the propagation of the damage. The material properties used for the analysis are given in Table 3. Table 3. Material Properties of the Interface, Epoxy and Chopped Fiber Composites [Williamson and Daadbin(1993), Wan and Takahashi (2016), and Cheng et al. (2018)] Property Value Property Value Property Value Property Value Interface (σ u ) normal 66 MPa (σ u ) shear 40 MPa (G c ) normal 1.2 kJ/m 2 (G c ) shear 2.5 kJ/m 2 Epoxy E Epoxy 5.2 GPa ν Epoxy 0.379 (G c ) Epoxy 2.5 kJ/m 2 (σ u ) Epoxy 17.6 MPa Chopped Fiber Composite E Chopped 30 GPa ν Chopped 0.3 (G c ) Chopped 2.7 kJ/m 2 (σ u ) Epoxy 300 MPa Epoxy, a potential filler material in the damaged area, is a homogeneous and isotropic material. The chopped fiber composite is an inhomogeneous but isotropic material, considering the random directions and the small size of the chopped fiber composites. Ductile damage models were used to simulate the mechanical behavior of the filler materials. 2.3 Numerical Implementation The simulation of low-velocity impact was carried out using finite element analysis using commercial FEA software ABAQUS®/ Explicit. Shell elements are used to model the composite material and the patch. Cohesive elements are used to model the interface interaction. A uniform mesh size of 1 mm is used throughout the simulation. The impactor is assumed to be rigid, and discrete rigid elements are used to model the rigid impactor. Accuracy and the correctness of the simulation methodology are ensured by simulating a low velocity impact problem and by comparing it with the results available in scientific literature. Sreenath and Prakash (2021) already discussed the results in their paper. Damage obtained using the impact simulation is used as the initial state of the repaired specimen. The peak load of the load-displacement curve is considered as the failure load of the specimen. The analysis took roughly 3 hours in a computer with an Intel i5 processor and 8 GB of RAM. The procedure was repeated for all the repair configurations. The tabulated results are discussed in the next section. 3. Results & Discussions Low-velocity impact on the composite specimen was modelled to simulate the impact damage. A rigid impactor having 10 J input energy is assumed to impact an hourglass specimen made of cross-play quasi-isotropic laminate. The setup and the boundary conditions are mentioned in Figure 2. The damage produced due to the impact is comparable to standard damage patterns. The bottom side of the specimen had tensile damage, and the top part had compressive damage. If the impact is approximated as a static problem, the damage pattern would also be similar pattern. The simulated impact damage is used as the initial condition of the load test. The patches were attached to the damaged specimen using the cohesive elements, as discussed in Figure 1. The refilling was simulated by adding suitable material properties at the selected region. Reaction force and displacement at the ends of the specimen are logged at regular intervals, and the load-displacement curve is plotted. As a baseline study, repair on the specimens was simulated without any treatment on the impacted area. Three different patch configurations were used, i.e. patch on the top, bottom or both sides. The top or bottom sides do not affect the specimen with the circular hole damage. However, this is also represented as top and bottom for easier comparison. The results obtained by the load test are shown in Figure 3. Patching on the bottom side gives better repair efficiency compared with the top. The fiber breakage on an impact may happen at the bottom side (i.e. the opposite side of the impact) [Doung and Hui Wang(2007), Jefferson et.al. (2018)]. So, patching at the damaged side may improve the symmetry of the specimen by adding an external patch to compensate for the damage in the specimen, which may improve the repair efficiency. In the case of the impacted specimens, the patch at the bottom or the top does make a difference because impact damage is not symmetric about the mid-plane of the laminate.