## 1 Introduction  
The metalworking industry has always aimed to enhance the mechanical properties of metals, focusing on hardness, strength, and ductility, which are crucial properties for engineering applications. Severe Plastic Deformation (SPD) has become a key technique for achieving this goal. SPD processes apply high levels of strain to the metals without changing their volume significantly. This process initiates grain refinement, which reduces the average size of the grains in the metal and results in an Ultra-Fine Grain (UFG) structure. As a result, the mechanical properties of the materials enhances [1, 2]. The Hall-Petch relation, a basic concept in metallurgy, supports this improvement by indicating that the strength of a material is inversely proportional to its grain size. In other words, smaller grains lead to stronger materials [3, 4]. This principle demonstrates the potential of SPD applications in material science, driving continued research and interest in these field. Over the past three decades, a variety of SPD methods have been developed and implemented. Each has been designed to optimize grain refinement, improve mechanical properties, and reduce processing times. Well-established methods include Equal-Channel Angular Pressing (ECAP), where a metal billet is pressed through a sharply angled die channel, refining the grain structure and increasing the strength of the materials [5; 6; 7; 8]. One other SPD method is Twist Extrusion (TE), involving the twisting of a metal billet through a die channel to produce high strain without significant dimensional changes [9; 10]. Another well-known SPD method is High-Pressure Torsion (HPT), which uses high pressure to twist a metal workpiece, creating highly uniform, refined grains for better mechanical properties [11; 12]. Accumulative Roll-Bonding (ARB) is one of the famous SPD methods, which is a simpler method that is easier to scale and stacks, rolls, and sections thin metal sheets repeatedly, progressively refining their grain structure [13; 14]. Despite the examples of SPD methods mentioned above, researchers continue to develop new techniques to achieve further grain refinement, to create more uniform microstructures, and to reduce the processing time for greater efficiency. When the literature is examined in more detail based on the efficiency of the SPD techniques, ECAP remains one of the most commonly used techniques due to its simplicity and efficient process, which significantly enhances the mechanical properties of materials by obtaining UFG structures. However, achieving the desired mechanical properties and homogeneity often requires multiple processing iterations, called passes, extending process durations. To address these challenges, researchers have developed several modifications based on the ECAP method by integrating new die designs. Some of these modifications include C-ECAP (Conform ECAP) [15; 16; 17], ECAP-BP (ECAP with Back Pressure) [18; 19], RD-ECAP (Rotary-die ECAP) [20], I-ECAP (Incremental ECAP) [21], and Exp.-ECAP (Expansion Equal-Channel Angular Pressing) [22]. Apart from classical SPD techniques, in recent years, researchers have developed new extrusion-based techniques to produce UFG structures and enhance the mechanical properties of materials. Some of these techniques include Twist Extrusion (TE) [9; 10], Vortex Extrusion [23; 24; 25; 26], Simple Shear Extrusion (SSE) [27; 28], Equal-Channel Forward Extrusion (ECFE) [29; 30], Repetitive Upsetting Extrusion (RUE) [31; 32], Gradation Extrusion (GE) [33; 34], and Thin-Walled Open-Channel Angular Pressing (TWO-CAP) [35; 36; 37]. Among these methods, one of the most interesting methods is Vortex Extrusion (VE), which was introduced by [PERSON] et al. in 2011 as a new extrusion-based SPD technique. In this method, the material passes through a specially designed 'vortex zone' that induces rotational motion [24]. A subsequent study explored the material flow and mathematical modeling of the vortex zone [23].