## 4 Methodology  
### Turning Simulation--2024-T351  
The 2D numerical model developed for the cutting simulations is shown in Figure 2. The work piece was developed into three sections: the chipped off material, the damage zone at tool-chip interface, and the uncut material. The configuration of the work piece into three different sections was essential to define different material properties, constitutive relationships, contact conditions, and the material damage laws. For example, JC material damage model and the damage evolution law were applied in the damage zone with a specific fracture energy; JC material damage model with a different fracture energy and the contact conditions were defined in the chipped off material; and the uncut material section was defined without JC damage parameters. The assembly of three parts was done by applying the standard join constraint (tie constraint) available in Abaqus. A tie constraint fuses the model surfaces with different mesh sizes and element types. Due to tie condition, each node at the slave surface attains the same displacement, stress, temperature, pressure, etc. corresponding to its closest node at the master surface. Tie condition makes the model computationally expensive and requires a compatible mesh between the part instances. Generally, Abaqus picks the slave surface with a finer mesh. For fidelity of the results of a multi-parts model assembled with the standard tie constraint, interested readers may refer to the online Abaqus documentation (tie constraints, Section 34.3.1, Abaqus Analysis User's Manual) [49]. The model comprises 4134 four nodes quadrilateral continuum elements with plane strain (CPE4 RT) and coupled temperature-displacement conditions. Cutting tool geometry consists of a nose radius (\(R_{n}\)) of 0.02 mm and a clearance angle \(7^{\circ}\). A parametric sensitivity analysis was performed with different rake angles, cutting speeds, chip thickness, and the contact conditions to study the effect of tool rake angle on the chip temperature, the effect of contact friction on the cutting reaction force, the effect of cutting speeds on the equivalent plastic strain, the effect of feed upon the chip temperature, and the effect of friction coefficients on chip temperature. The cutting tool was constrained in \(y\)-direction and a self-contact was defined over the chip surface to avoid the penetration of deformed chip elements into the uncut chip and cutting tool. Contact conditions were established between the contact interfaces of the cutting tool, chip, damage zone, and the uncut material [50]. Selection of the proper friction coefficient and governing law is a critical and sensitive task in numerical cutting simulations. The friction characteristic at the tool-chip interface is difficult to determine since it is influenced by many factors; such as, the local cutting speed, contact pressure, temperature, cutting tool, work piece material, etc. [51]. An improper selection of the friction coefficient affects the results and findings. Extensive studies have been reported on the interaction of the tool-chip interface during the dry turning process. Several models have also been proposed to determine the contact friction. The most widely used method to determine the contact friction is [PERSON]'s stick-slip friction model [52] which is also known as an extended Columb's law. In the present numerical simulations, the interaction between AA2024 material and the tungsten carbide tool insert, two different values of the friction coefficients (0.1 and 0.15) are used considering the similar experimental conditions [42] and also investigated by [PERSON]'s friction model. Different properties and parameters used in the model are given in Table 1[42]. The outcomes of turning simulations were compared with the available experimental results, given in Table 2[42].