## 1 Introduction  
The global demand for end-uses of aluminum products has been rising [1]. One of the potential areas where one can add value for aluminum is in micro-products development [2]. An example of a micro aluminum product is a micro-gear [3]. Not only are aluminum micro-parts suitable for lightweight miniaturized applications in the automotive and electronic industries, but they can also be produced for biomedical applications (rod, wire, ribbon, screw, and tube drawing shapes) [4]. Many of the processing techniques can be applied to produce aluminum micro-parts [5]. Machine developments and manufacturing systems were also developed in this area [6]. Recent trends in micro-forming processes that are particularly suitable for lightweight materials (aluminum, titanium, and magnesium alloys) have been reviewed [7]. Most of the macro-forming processes could be downsized to micro-formingprocesses, with some challenges due to the reduced scale [8]. The concept of traditional extrusion to produce sub-millimeter parts by using the micro-extrusion process was developed [9]. An example of aluminum micro-extruded components was also investigated [10]. In macro-extrusion, one of the relevant issues related to the grain size is surface grain coarsening [11]. The effects of the grain size can also be commonly observed and becomes quite problematic in micro-extrusion. The main challenge in micro-forming processes is the size effects that show a reduced geometrical accuracy, flow stress, and an increase in the scattering of the flow stress and part geometry when the grain size is comparable to the specimen size [12]. An inverse relationship between the yield stress of aluminum and its grain size has been observed [13]. This relationship follows the Hall-Petch effect [14]. A scaling model taking into account the specimen/feature size in micro-forming was proposed [15]. The influence of single-grain orientations affected deformation [16]. The micro-extruded pins were curved when the grain size was enlarged so as to be close to the specimen size [17]. Tribology plays an essential role in size effects in micro-forming processes [18]. The tribological characteristics in this scale could be described by using the open and closed lubricant pockets model. The friction condition depended on the specimen size in the micro-extrusion process [19]. The tool-billet interface of the micro-extrusion process under both static and dynamic conditions was observed [20]. The tribological phenomena in various micro-forming processes were significantly influenced by the size effects [21]. The interfacial friction and grain size effects were dependent [22]. The conventional material model could not be applied in micro-extrusion. The experimental and numerical studies showed that the interactions of the friction interfaces, material properties, and size effects contributed to the forming loads and parts geometry [23]. An approach to determine the stress-strain curve in micro-extrusion by taking into account the friction factor was proposed [24]. A forming load prediction taking into account the surface area was also developed [25]. The microstructural evolution in the open-die forging/extrusion process was investigated, and the results showed that the grain size and specimen size influenced the microstructures [26]. An upper bound approach to predict the forming behavior in the open-die forging/extrusion process was also proposed [27]. The role of subgrains larger than the specimen diameter contributed to a reduced flow stress in the micro-compression tests [28]. In the micro-extrusion of both copper and aluminum alloys, the flow stress decreased along with the surface grain [29]. If the cavity width in micro-coining consisted of only one grain, the grain would be fragmented into smaller sizes along the extrusion direction [30]. The area of interest in this research was the effects of the grain size on the curving behavior of micro-extruded pins. Generally, extrusion profiles are curved due to the unbalanced flows/velocities in macro-extrusion [31].