Nickel-based super-alloys have been widely used in the aircraft and nuclear industry due to their exceptional thermal resistance and their ability to retain mechanical properties at elevated temperatures [1, 2], strong corrosion resistance and excellent thermal fatigue properties as well as thermal stability [3, 4]. Consequently, these alloys are classified to be difficult-to-machine materials [1-3]. The tool wear during machining of the Inconel 718 depends on the combined effect of several factors which is the result of complicated physical, chemical and thermo- mechanical phenomena forming through the different mechanisms such as adhesion, abrasion, diffusion and oxidation [1, 5]. Because of low thermal conductivity, machining of the nickel-based super- alloys in general and the Inconel 718 materials in particular, leads to a significant increase in the cutting temperature and high tresses; the adhesive wear through welding is thus developed rapidly and forming built-up-edge (BUE), it occurs even at a low cutting speed of 20m/min .Several research efforts have been conducted in order to improve the machined surface accuracy, reduce the tool wear and subsequently extend the tool life; which directly affects to the cost of machining and productivity. Some of the solutions have recommended concerning with the cutting tool selection: using PVD coated (TiAlN) cutting tool  or multilayer coating of TiAl/TiAlN [7, 8] can be improved the cutting speed up to 100m/min compared to uncoated cutting tool (less than 30m/min). By considering the different coating materials, I. Ucun et al. have reported that the performance of cutting tools coated with AlTiN, TiAlN+AlCrN, and AlCrN are improved, while the coated with TiAlN+WC/C and DLC are more significant against BUE formation. So far, it is also believed that polycrystalline cubic boron nitride (PCBN) tooling [9-11], and ceramic cutting tools [12,13] allows machining at higher cutting speed in comparison with the coated carbides due to their superior hot hardness and notch wear resistant. Although machining of the Inconel 718 has been carried out in several various studied; however, most of main characteristics and the results of cutting surface quality, and performance could only be determined experimentally . The experimental studies should therefore be investigated with any further improvement of the cutting tool, machine design, the workpiece materials or methodology approaches. In the case of cutting process, Response Surface Methodology (RSM); which is a set of sequential experimental design  has been already proved in regard to efficient analyzing the effect of cutting conditions on the response factors such of the tool wear , surface roughness and cutting force [17, 18]. The relationship between the cutting parameters and the respond factors has mainly analyzed of variables (ANOVA) by using a quadratic regression through transformation of square root.In this sense, it is thus worthy to use such the response surface methodology within the present framework. Furthermore, with the aim of getting more precise information about the tool wear mechanism and the surface roughness during machining process; the quadratic regression through transformation of natural logarithm will be applied for the first time according to our best knowledge in the field. First of all, the flank wear mechanism during machining of the Inconel 718 steel (hardened ∼ 44HRC) using PVD coated cutting tool will be investigated; part of the work is then analyzing effect of the cutting parameters on the flank wear and surface roughness. The machining experiments are performed with assistance of the response surface methodology in accordance to central composite design (CCD). The experimental design was considered three level of each factor for the cutting speed in range of Vc=10-110m/min, feed rate f=0.02-0.12mm/min and depth of cut ap=0.05-0.55mm. 2. EXPERIMENTAL PROCEDURE 2.1. Experimental design The matrix of the experiment should be well planned to optimize the number of the machining test and evaluate the effects of certain factors on some specific results; as well as quantify the effects of one or more input variables on the response factors. Based on the CCD method, the matrix design for k factor experiment is defined through the level of independent variables and the number of the experiment as given by :
where are experiments in factorial design are experiments in star design and is the number of central point. In current experimentation, three experimental factors and six central points have led to twenty of the total runs are considered. The level of independent parameters is then modeled as summarized in the table 1; therein, the lowest and highest values are calculated through the scaled parameter (α). It depends on the number of the factor experiment considered through the relation of formula α = (2k )1/ 4 ; with the three mentioned factors, one obtains α=1.682.
Table 1 level of independent variables for CCD