## 1 Introduction  
Environmental pollution and global warming forced many countries in the world to set regulations to improve the life of human beings. Specifically, exhaust fumes by an automobile were cited as one of the reasons for environmental pollution and global warming. The demand to increase fuel efficiency becomes an issue because of the problem of finite resources. To increase fuel efficiency, it is better to reduce the vehicles deadweight. When the weight of an automobile decreases by 10%, its fuel efficiency could increase by about 5 to 10%. There have been many attempts to replace the heavy steel parts of vehicles with new materials that are light weight and have high strength, such as Magnesium alloys [1; 2; 3; 4; 5]. Magnesium alloy has a 1.74 g/cm\({}^{3}\) density which is two-thirds of aluminum alloy, one-third of titanium, and one-fourth of steel. Moreover, magnesium alloys have good machinability, superior dent resistance, and excellent vibration damping properties. Thus, magnesium alloy has been studied as a new light material for automobile parts. Nevertheless, its extended applications are limited by its low formability at room temperature [6; 7]. Its low formability is due to its hexagonal close packed crystal structure, which has less slip systems to yield applied external deformation. Traditionally, Mg alloy products have been made mostly by casting or semi-solid die casting. However, casting and semi-solid die casting inherently have a weak point of air pollution, defects of casting, and poor surface quality. Poor formability and easy oxidation of Mg alloys create requirements for delicate process conditions for successful forming. Although many researches were carried out to improve forming technology of Mg alloys [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18], further research is still needed to understand forming characteristics of Mg alloys during bulk forming process such as extrusion or rolling. For instance, hydrostatic extrusion was utilized to increase the formability of AZ 31 Mg alloys by reducing damage evolution under high pressure [8; 9]. Many previous works focused on the examination of microstructural developments and corresponding mechanical property changes during the bulk forming of AZ31 Mg alloys [10; 11; 12; 13; 14; 15; 16; 17; 18]. Among them, [PERSON] et al. [10; 11; 12; 13] reported that the forming temperature for bulk forming processes such as forging and extrusion, is very influential. It was also shown that the backward extrusion of Mg alloys at warm temperatures was very successful when forming a cup-shaped product. They also reported the localized deformation behaviors observed near the punch corner and the inside of the lower die with micro structure investigation [13]. More recently, some research has presented improvements to the mechanical properties and formability of Mg alloys by examining extrusion conditions [14] or by adding other elements [15; 16; 17]. Some cup-rod shaped automobile parts, having the cup-shaped side with the other rod-shaped side, could be formed using the Combined Forward-Backward Extrusion (CFBE) process with AZ Mg alloys [12] and with aluminum alloys [18]. Figure 1 is a schematic drawing of a typical CFBE process, which shows some material flows. As the punch advances, the main material flows are in two opposite directions with a divergence point. Such complicated metal flows in the CFBE process require delicate process conditions for a successful CFBE. The current authors examined microstructural changes in a CFBE process of AZ31B Mg alloys at warm temperatures [13], and found that further studies would be needed to figure out the process conditions for a successful process. This study was a continuation of our previous work, wherein, in this study, both experimental studies and finite element studies were carried out. In addition, the forming temperature, forward extrusion ratio (FER), backward extrusion ratio (BER), and punch speed were chosen as important process parameters based on previous work.