*3.1. Material Properties*

The ISF process is more widely adopted in the automobile and aerospace industries where lightweight materials are preferred. Aluminum and its alloys have gained tremendous popularity in recent decades in aerospace and automobile applications. Keeping these factors in mind, a commercial aluminum alloy AA1050 was used for the current research purpose. A sheet of 1 mm thickness was used during the experimentation. The tensile test was performed on the mechanical testing equipment GLEEBLE 350 (GLEEBLE—A VPG Brand, Poestenkill, NY, United States) to obtain the mechanical properties and elastoplastic response of AA1050 at room temperature. Table 1 depicts the material properties of aluminum alloy AA1050 at room temperature, which is responsible for the material behaviour. Figure 7 shows the flow stress-strain curves for different strain rates at room temperature obtained through mechanical testing.

**Table 1.** Material properties of aluminum alloy AA1050.


**Figure 7.** Flow stress-strain curves at different strain rates of aluminum alloy AA1050.

### *3.2. Numerical Simulation*

The numerical simulations of both the processes were carried out in the ABAQUS/CAE (SIMULIA ™ by Dassault Systèmes ®, Vélizy-Villacoublay, France) version 2017 platform with a built-in explicit solver. The explicit approach was selected because it is computationally more efficient. Figure 8 shows the meshed model used during the numerical simulation. The workpiece material, i.e., sheet blank with a thickness of 1 mm, was modelled. The ratio of the material thickness (*h*) to the length of the workpiece (*L*) was less than 0.3 which allows usage of shell elements instead of solid elements [20]. Therefore, the sheet was meshed using the four-node square shell element S4R, having a mesh size of 1 mm. Chung et al. [21] had reported that the shell elements are not able to properly predict the plastic deformation in the thickness direction. Li et al. [22] had suggested that the use of shell elements lead to an inaccurate evaluation of transverse shear strain when the bending effect is important. In the present work, the numerical simulation results are used only to access qualitative differences between the two processes, thus, the numerical simulation was carried out with explicit solver and shell elements due to their computational efficiency. To satisfy the experimental conditions, the sheet was fixed at its outer boundary with the help of upper and lower clamps. The upper and lower clamps were meshed as discrete rigid elements as these fixtures were assumed to be non-deformable. The hemispherical tool of diameter 10 mm was modelled and meshed with the help of discrete rigid shell elements, which moves according to the toolpath strategies developed for both processes. The size of the sheet blank was 110 mm × 110 mm. The simulation of the incremental forming process has various nonlinearities due to the nature of the process. Furthermore, the incremental forming process is 3D in nature without any symmetry plane. Typically, a significant number of elements must be employed, and the tool must follow a longer trajectory, which makes the finite element analysis difficult and time-consuming. A high-velocity artificial tool was found to be suitable for the simulation of the incremental forming process [23]. Thus, the artificially increased feed rate was taken as 2000 mm/s to reduce the computational time maintaining quasi-static conditions. The computation time depends on many factors like element size, analysis procedure, i.e., explicit or implicit and the machine specifications. The total step time for forming a CWATC was 4.0041 s with the ISF process, while it took 4.7169 s in the case of the ISH process. The hammering operation was incorporated in the toolpath strategy of the ISH process; thus, the computation time and production time was higher in the case of the ISH process than the ISF process. Further, the time for forming a component in the ISH process depends on the overlapping region and the amount of predefined amplitude. In the present work, the overlapping region in the case of the ISH process was 25%, i.e., 1/4th of the trailing deformed area overlapped with the leading area. The increasing amplitude of hammering results in the poor surface quality of the component and it eventually leads to early rupture of the component [15]. Therefore, the amplitude of hammering was considered as 0.05 mm. The contact condition and the type of interaction of the deforming tool with the sheet during processing has a grea<sup>t</sup> influence on the redistribution of the material of the surface layer [24,25]. The interaction between tool and sheet was described using master and slave algorithm with the coefficient of friction taken as 0.05 [26]. The results obtained through the numerical simulation are further compared with experimental results and are discussed later in the results section.

**Figure 8.** Numerical model used during simulation of ISF and ISH processes.
