PSI - Issue 52

126 Quaiyum M. Ansari et al. / Procedia Structural Integrity 52 (2024) 122–132 Quaiyum M. Ansari/ Fernando Sánchez/Luis Doménech-Ballester/ Trevor M. Young / Structural Integrity Procedia 00 (2019) 000 – 000 5 =0.56 0.95 2.98 (4) where, and are the peak force and impulse respectively and is the density of water. 3. Numerical Modelling In this study, the axisymmetric model is used as a baseline study to simulate the single rain droplet impact before complex 3D FE modeling is set up to evaluate the damage evolution on LEP, primer, filler and substrate models. 3.1. Axisymmetric modelling The geometry and mesh of the axisymmetric FE model are shown in Fig. (4). During the mesh sensitivity study, it was discovered that mesh sizes ranging from 15 µm to 25 µm provide good convergence which is aligned with Mitchell et al. [28] mesh sensitivity study. To avoid mesh distortion during impact, the ball's area has been divided as shown to generate high-quality mesh. In Abaqus, the ball has meshed with the linear quadrilateral element CAX4R, and the plate has meshed with the linear line element RAX2. The ball and plate have 9428 and 675 elements, respectively. Furthermore, the plate's rigid node is fixed to obtain the nodal forces after droplet impact. In addition, contact between the ball and the rigid plate has been defined in Abaqus using surface to surface explicit interactions. The droplet material water properties have been considered as follows: density = 1000 kg/m 3 , speed of sound = 1450 m/sec and equation of state variables = 0 and = 0 considered for this analysis. Normal contact property is defined as hard, and separations are allowed after contact, whereas tangential contact property considers frictionless behaviour.

Fig. 4. FE model of rain droplet impact. Moreover, adaptive mesh, also known as Arbitrary Lagrangian-Eulerian (ALE) mesh, is used to avoid excessive mesh distortion during the impact. The ALE method prevents the node from punching toward the centre of the element to avoid excessive distortion in explicit analysis. It also increases the aspect ratio of the elements, keeps the mesh smooth, and speeds up the simulation. For droplets, ALE control is used with a default frequency of 10 and 5 remeshing sweeps per increment. The rain droplet is then subjected to vertically downward velocity. The simulation is performed with a low velocity impact of 1.33 m/sec and 3.27 m/sec respectively to validate the FE model with experiments. The comparison of experimental results and FE simulations are shown in Fig. (5), and they are found to be in good agreement. The plots also show that for lower velocity, the droplet impact time is around 2000 µs, whereas for higher velocity, the impact time is 1000 µs. In addition, the maximum force for 1.33 m/sec is approximately 12 mN, whereas the maximum force for 3.27 m/sec is approximately 67 mN. The theoretical peak force calculated from equation (3) for 1.33 m/sec and 3.27 m/sec droplet impact is 12.5 mN and 75 mN for a 2.9 mm droplet, respectively. The theoretical peak force was also found to be well correlated with the peak force obtained through FE modelling.