Inuence of Dry Friction on the Wear Behavior of X52 Steel -Experimental Study and Simulation Using Response Surfaces Method

The objective of this work is to identify the most inuential parameters on the friction coecient and wear rate, using the response surface method. The friction tests were carried out by adopting the methodology of complete planes 2 3 at three factors ("D", "V" et "Py"), at two level for each factor. The results show a decrease in the wear rate when the three factors are at their highest level and a decrease in the friction coecient when using minimum loads and speeds on important distances. In addition, the developed mathematical models make it possible to reveal a correlation between the test parameters and the responses studied in their studied domain. An evaluation of the volume parameters "Vmc" and "Vvv" was carried out. The morphology of the worn surface shows that the friction under a load of 1 N leads to the predominance of an abrasive wear mechanism, while a load of 10 N favors an adhesive wear mechanism, increasing the parameters "Vmc" and "Vvv" to the maximum.


Introduction
The surface is the most important part of any engineering component [1]. In service, the surfaces of mechanical systems are subjected to severe conditions, they are the most exposed to external attacks such as wear, corrosion and fatigue, which reduces their service life [2] and compromises the operation.Therefore, interface phenomena play a crucial role in engineering, and their evaluation and their control contribute to the development of many advanced domain such as electronics, information technologies, energy, optics and tribology [3,4]. To improve the performance and the surfaces lifetime of mechanical parts, several techniques, among which, heat treatments which are applied to mechanical parts to strengthen their wear resistance, corrosion and fatigue.These treatments enhance the mechanical properties of steels, such as the elasticity limit, tensile strength and hardness as well as tribological characteristics [5,6]. Friction is a very important parameter, which provides information on the materials behavior in contact. In addition, it governs many variables such as the contact stresses and its conditions as well as the formation of transfer lm/debris. Friction coe cient (COF) and the formation of transfer lm/debris are subject to several factors during sliding contact, among which, the surface topography is one of the most in uential factors [7]. Surface topography re ects the characterization of surface wear, fatigue and corrosion behavior of materials [8][9][10]. Surface roughness constitutes one of topography elements, which allow to characterize the materials degradation subjected to different tribological conditions (friction, lubrication and wear) [11][12][13][14].The evaluation methods based on response surface models (RSM) as well as numerical simulations used to predict the surfaces behavior of materials during mechanical contact. This work aims to study the evolution of the volumetric parameters (Vmc and Vvv) after friction test as well as the prediction of friction coe cient and the wear rate by mathematical models established by the complete factorial designs 2 3 according to parameters, in this case the normal load "Py", the linear speed "V" and the traveled distance "D". The experiment is carried out on a materialsteel X52, treated by quenching and tempering.Surface examinations by scanning electronic microscope (SEM) and a 3D pro lometerwere carried out in order to assess the frictional behaviour and the wear resistance of steel.

Material
The used material in this study is steel X52 in the treated state (quenched at 920 ° C and tempered at 740 ° C) obtained from a pipeline used in the petroleum industry. The chemical composition was made by spectrophotometric analysis on a "SPECTRO Rp 212" machine at URASM, El-Hadjar complex in Annaba, the result of this analysis is shown in Table 1.

Experimental methodology
It is proposed to perform friction tests on a HLE-X52 steel throughplans for experiments planning"complete factorial designs 2 3 " according to the principle indicated in the diagram of Figure 1.

Friction test
The friction tests were carried out at ambient temperature accordance with ASTM G99-95 norm, using a Ball-Pin/Disc tribometer from CSM-Instrument. The principle test consists of the application of a perpendicular load through a steel ball 100C6 of diameter ϕ 6mm as presented in Figure 2. Accordance with factorial plans 2 3 , eight (08) samples were cut and their surfaces polished with SiC abrasivepaper of different grain sizes ranging from 400 to 1200. The tests are carried out according to the experiment matrix indicated in Table 3. The friction coe cient was recorded in real time by data acquisition using Tribox 4.49 software. The wear volume was estimated by measuring the surface pro le of the wear track. The wear rate was calculated according to the wear law proposed by Archard according to equation (1) [19]. Where: The volume parameters (Vmc, Vvv) were measured using a 3D pro lometer with a laser source type: Cyber Technology CT100, according to DIN ISO 25178 norm. The measurement results of the wear rate and the measured roughness parameters are shown in Table 4. The morphology of the worn surfaces and the wear mechanisms were established by Quanta 250/FEI scanning electron microscopy.

Evolution of the friction coe cient
Generally, friction depends on the structural properties and mechanical characteristics of material. The analysis of the curves presented in Figs. 3a, b, indicate the evolution of the friction coe cient for the tribological couple X52/100C6 according to the traveled distance. According to these curves, there are three phases (I, II and III) of friction and wear [23]. Friction begins with a lapping period during which the friction coe cient increases rapidly to reach a maximum value. This period is characterized by signi cant wear and plastic deformation of the surface roughness.The second phase is transition, whichis characterized by a slight decrease in the friction coe cient; this is due to the formation of the third body, which under the effect of friction wear on the track plays a similar role to that of a solid lubricant. In the third phase, we observes the stabilization of the friction coe cient where the value is maintain constant whatever the traveled distance. The results of the friction coe cient recorded a minimum value of 0.293 and a maximum value of 0.71 for test N°2 and test N°4 respectively (see Table 3).

Regression analysis
The digital processing according to the complete factorial plans (2 3 ) allowed the elaboration of mathematical models for each of the responses ("f", "Ws") according to three considered parameters (Py, V, D). These mathematical models offer the ability to predict the studied responses in the study domain. The friction coe cient "f" and the wear rate "Ws" are respectively expressed by equations (2) and (3).
Statistical analysis shows that the residuals of the friction coe cient "f" and the wear rate "Ws" follow a straight line ( Figure.4a-4b) where there is no evidence of non-normality or d 'asymmetry. The residual distribution curve ( Figure.4c-4d) shows that these residuals are distributed randomly around zero and without any particular trend; hence the established model explains perfectly the obtained results.
The difference between the measured and predicted responses for the friction coe cient "f" and the wear rate "W" isshown in Figures 5 (a-b). These indicate that the mathematical models obtained for the two studied responses can represent the experimental study domain. The comparison demonstrates that the predicted values of different studied responses are closer to those observed experimentally.

Surfaces of 3D response and contours
The interaction between the parameters (D, V and Py) is highlighted by the 3D plots ( gures.6-7), of responses "f" and "Ws", measured and predicted by the model (equations 2 and 3). Figures 6 (a, b and c), show that the effect of traveled distance on the friction coe cient is less signi cant compared to the effect of speed and load.The increase in speed leads to an increase in the coe cient "f", on the other hand, the increase in the load leads to its decrease; this is due to the iron oxide layer, which serves as protection by preventing the direct contact of two rubbing systems [22]. It can be concluded that the speed is the most in uential parameter on the friction coe cient. Indeed, its increase generates a signi cant amount of wear debris (third body), which causes the formation of a transfer layer in the contact area. The periodic and localized rupture of this transfer layer, thus causing the increase of COF [20, 21]. The contour graphs are shown in Figures 8 and 9; they describe the response surfaces and allow establishing the response values ("f" and "Ws") and the corresponding parameters (D, V and Py).
The average effects ( gure.10a), showing the impact of each of parameters (D, V and Py) on the friction coe cient, show a load predominance "Py" tending to reduce the friction coe cient which converges towards a value less than 0.42 for Py = 10N.These graphs reveal that there seems to be a big difference in the effects magnitude where the applied load is the most signi cant versus the speed and traveled distance. However, the average effects of each of these parameters on the wear rate ( gure.10b) indicate that the traveled distance "D" followed by the applied load "Py" being the most signi cant versus the speed.
Concerning the interaction between the different parameters (D, V and Py) and their in uences on the friction coe cient "f" (Figure.11a), the curves particularly show two interactions (traveled distance/speed) and (speed/load. Moreover, Figure 11b shows that only the speed interaction and the traveled distance on the wear rate "Ws" is the most signi cant.

Evolution of volume parameters after friction test
• Volume of core material "Vmc" Currently, the volume core material"Vmc"is an important functional parameter in tribology, it allows to determine the quantity of lost material through wear during a work cycle [24].Thus, more this parameter increases, more the surface better resists in fatigue, thus increasing its lifespan. The histogram in gure 12 shows the evolution of the volume of core material "Vmc" during the friction tests. The results reveal that the "Vmc" parameter reaches a maximum value of 1.45 (μm 3 /μm 2 ) for an applied load Py = 10N combined at a speed V = 2cm/s and a distance D = 10m(test E5).The minimum value of "Vmc" which is equivalent to 0.22 (μm 3 /μm 2 ) was recorded during test E1 using a load Py = 1N, at a speed V = 2cm/s over a distance D = 10m.So, we can see the signi cant effect of the load whatever the speed and the traveled distance; indeed the "Vmc" parameter tends to increase considerably for a maximum load of 10N.
This can be explained by the fact that a high load favors a larger contact surface and a more regular ow of material, hence a lesser removal of debris, which is in agreement with Bourebia et al [25]. This debris is crushed under the load effect and adheres to the contact surface that allowing the reinforcement of "Vmc".
• Volume of the valleys void "Vvv" The volume of thevalleys void "Vvv" is an essential element in lubrication, it plays an important role in lubricant retention, and it reduces friction and preserves the state of the contact surfaces [16].The results illustrated in gure 13, show that the applied load is the most dominant factor which affects the parameter "Vvv" where a strong load Py = 10N generates an increase in "Vvv" reaching a maximum of 0.23 (μm 3 /μm 2 ) for a speed V = 5cm/s.This is explained by the fact that animportant load ensures a better penetration of the rubbing body in the contact zone, which has the effect of generating pockets serving as lubricant retention, which is shown by F. Blateyron [24].However, the applications of a low loadPy = 1N generates wear debris thatis pushed back into the valleys and encrusted in the contact zone causing a decrease in the voids volume.

Morphology of wear tracks
The SEM micrographs taken from the worn surfaces for test E1 and test E8 show the highest and lowest wear rates, respectively (see gure 14).
The micrograph of the test "E1" reveals theparallel grooves to the sliding direction, con rming the predominance of abrasive wear favoring the delamination of the rubbed surface. This degradation of the surface is produced by the detachment of asperities generated by plastic deformation and hardening [26].In addition, the micrograph of the test "E8", shows the existence of detached akes from the contact surface, it is a sign of the appearance of adhesive wear. This explains that during sliding, the contact asperity undergoes plastic deformation which accumulates during repeated contact [27].Hence the predominant wear mechanism is adhesive wear, which is more intense for the 10N load [28]. This can be linked to the structural state and to the adhesion of iron oxide to the contact surface forming the third body. In addition, the good ductility of these iron oxides makes non-abrasive particles favorite the wear by adhesion [26].

Conclusion
From theobtained experimental results in this work, the ball friction tests on the surfaces of steel X52 under loads, at different speeds and traveled distances, allowed to determine the most signi cant parameters on the friction coe cient and the wear rate. The methodology of complete factorial plans (2 3 ) has allowed us to quantify the friction coe cient "f" and the wear rate "Ws" according to parameters (D, V and Py). The following conclusions can be drawn.
1. The mathematical models developed allowed to predict the friction coe cient "f" and the wear rate "Ws" according to the test parameters (D, V and Py) in the study eld.
2. The main effects and interactions curves as well as the 3D contour curves obtained by numerical simulation, permitted to elucidate the in uence of parameters (D, V and Py) on the studied responses "f" and "Ws".
5. The application of a maximum load at a minimum distance increases the parameters"Vmc" and "Vvv" which respectively reach their maximum 1.45 (μm 3 / μm 2 ) and 0.23 (μm 3 /μm 2 ) for minimum and maximum speeds.
6. The adhesive wear mechanism was observed when using a load 10 N; conversely, the use of a low load of 1N generates an abrasive wear mechanism.  Residual plots for "f "and "Ws" Predicted and measured values of responses: a-the COF "f"; b-the wear rate "Ws" Figure 6 Iso response curve of friction coe cient versus the load, speed and traveled distance Iso response curve of wear rate versus the load, speed and traveled distance.

Figure 8
Contour graphs for friction coe cient depending on Py, V, D.

Figure 9
Contour graphs for wear rate depending on Py, V, D. Evolution of the volume of the core material "Vmc", after friction test Figure 13 Evolution of volume of the valleys void "Vvv" after the friction test