Characterization of friction properties at the work material/cutting tool interface during the machining of randomly structured carbon fibers reinforced polymer with Poly Crystalline Diamond tool under dry conditions

Carbon fiber reinforced polymers (CFRP) are increasingly employed within the aerospace industry. Therefore, a lot of Finite Element models have been developed in order to understand their material removal mechanisms. Among the scientific issues faced by these works, the identification of friction coefficients remains a strategic field of research. This paper aims at characterizing the friction properties between composite and cutting tool materials. The specific tribological conditions during machining of such heterogeneous materials are discussed in the paper, especially the configuration of the tribosystem. This paper presents the development of an original tribometer designed to simulate conditions corresponding to machining of randomly structured CFRP materials. It provides quantitative values of friction coefficient and heat partition coefficient depending on sliding velocities.


Characterization of friction properties at the work material/cutting tool interface during the machining of randomly structured carbon fibers reinforced polymer with Poly Crystalline Diamond tool under dry conditions
Grégory Chardon, Olga Klinkova, Joel Rech, Sylvain Drapier, Jean-Michel Bergheau

Introduction
Composite materials such as carbon fiber reinforced polymer (CFRP) are increasingly used in industrial fields, such as aerospace, aircraft, automotive and sports, owing to their advantages in mechanical properties (higher specific strength and stiffness) compared with their low density.Most of composite products are made to near-net-shape.However, machining processes such as milling or drilling are frequently used to achieve dimensional tolerance and assembly requirements.Previous works have shown that machining composite materials differs significantly from machining conventional metals (matrix cracking, fiber fracture, interlaminar delamination, etc.) due to the material properties of the fibers and to their heterogeneous structure [1][2][3].The important material abrasiveness leads manufacturers to make use of hard substrates to limit rapid tool wear.
Productivity improvement of machining operations requires the optimization of tool geometry and cutting conditions.In parallel, a lot of attention has to be paid on the surface integrity of machined parts, since cutting may induce functional problems [1].Numerical modeling of cutting is a way to enable this optimization and to ensure the quality of machined surfaces.Among the key input data necessary to perform numerical models, a friction model between composite material and cutting tool material is required.However, obtaining realistic friction data in CFRP cutting remains an issue for several reasons.On one hand, due to the kinematic of a cutting operation, the workmaterial is separated in two parts (Fig. 1): the chip and the machined surface.From the chip point of view, the shearing zone is called the secondary shear zone.From the machined surface point of view, the shearing zone is called the rubbing zone or the third shear zone.In both cases, the surface of the workmaterial will be in contact with the cutting tool material during a very short period (typically some milliseconds) under very high pressure and velocity.Moreover, this surface will no longer be in contact with the cutting tool material.From the cutting tool point of view, there is a continuous flow of new workmaterial in these zones.This tribological situation corresponds to a so-called : 'opened tribosystem', which will be described later in the paper.The wide majority of tribometers are 'closed tribosystem', such as pin on disc systems, where a pin always rubs on the same part of a material.This situation is not suitable to provide relevant data for cutting applications.Indeed, there are very few tribometers able to simulate such 'opened tribosystem' [4].On other hand, a CFRP is a heterogeneous material made of several orientated layers in the case laminated structure, or of several short fiber bundles in the case of randomly structured structure.For each layer or short fiber bundles, fibers are oriented in a defined direction.Therefore, a cutting edge has to cut fibers having various orientations.It is shown by [5] that the layer orientation may influence friction at the tool/CFRP interface.

Fig. 1 Basic modeling of metal cutting
In the scientific literature, a lot of efforts has been made recently to initiate the Finite Element Modeling of composite materials in order to understand the local material removal mechanisms.The wide majority of these works considers the Coulomb model with a constant coefficient [6][7][8][9][10] or does not consider any friction at all [11][12][13][14].The values of the friction coefficient reported vary between 0.1 [5], 0.15 [8,15], 0.3 [6,10,16] and 0.5 [8,17] depending on the couple of materials involved (tool material/nature of composite material).Other authors consider a coefficient of friction with respect to fibers orientation [10,18] from 0.09 to 0.9.Finally [5] has shown that the presence of a cutting fluid can reduce the friction coefficient from 0.1 to 0.06 during machining of laminated CFRP with diamond cutting tools.
The identification conditions of friction coefficients are rarely explained in details, this makes it difficult to apply for other investigations.In the field of tribology, several works consider the friction of composites against metals or sapphire, which are not relevant substrates for cutting tools [19,20].Consequently, such values are not usable to model cutting processes with PCD tools as considered in the present work.
Some works such as [9,10] have performed pin on disc tests with High Speed Steel pins (HSS) and a Glass FRP disc, which is not a relevant tribological test as mentioned previously.Additionally, the testing conditions (sliding velocity ≈0.008 m/s) do not make sense for CFRP machining.For example, [21] reports that cutting speeds usually applied during machining of CFRP with HSS tools are in the range from 10 to 40 m/min (0.16 to 0.66 m/s).Other works such as [5] have characterized the friction coefficients between a laminated CFRP and a diamond tool under sliding velocities up to 20 m/min (0.33 m/s).
Unfortunately most of the papers use friction coefficients which have not been identified by any friction test [6,7,8,16,17].Only few papers have applied relevant friction conditions (i.e.measured with an opened tribosystem).It is only possible to mention the work done by Mondelin et al. [5] who have developed an opened Accepted Manuscript 3 tribometer specifically designed for laminated CFRP.However this system is limited to perform tests under sliding velocities up to 20 m/min (0.33 m/s), which is quite low compared with industrially expected cutting speeds up to 800 m/min (13.33 m/s) for PCD tools in a milling process.
As a summary, it can be stated, that there is no data already published in a scientific journal presenting friction coefficients for a randomly structured CFRP and a PCD tool, that have been performed on an opened tribometer under high sliding velocities up to 800 m/min (13.33 m/s).Such tribometers have already been developed to characterize friction coefficients in metal cutting [4,22,23].Indeed, standard substrates such as high speed steel or carbide are more and more replaced by PCD because of its high hardness and resistance to wear [1][2][3].In fact, carbide allows to make inexpensive tools but his low resistance to wear is not suitable for long machining or mass production [24][25].PCD seems to be the best industrial solution in machining CFRP.We can notice that single crystalline diamond is not suitable for cutting tools with large depth of cut because insert sizes are very limited.
In fact, a previous work by the same authors [15] enables characterizing friction coefficients between randomly structured CFRP and carbide tools with sliding velocities up to 120m/min (2 m/s).This paper follows and is a complement of this previous work [15].Consequently, the objective of this work is to adapt the principle of this tribometer to characterize friction coefficients between randomly structured CFRP and PCD tools for a large range of sliding velocities (up to 800m/min (13.33 m/s)).

Description of CFRP structure
The HexTOOL TM material is a new composite solution for manufacturing molds to produce aerospace components.HexTOOL TM uses Hexcel's established HexMC® technology.This product consists of high strength carbon fiber, with a nominal fiber volume of 60%, and HexPly M61 BMI (bismaleimide) resin, at 40% resin volume content, cured at 190°C in autoclave under 7 bar pressure.This is an alternative to conventional tooling materials, including metal.Specifically developed for tooling, the M61 resin is toughened and modified to reduce resin flow so that the pre-impregnated sections stay in place during tool cure to maintain their quasiisotropic fiber distribution.Compared with epoxy resins, this provides superior machinability without distortion, permitting the manufacture of mould with complex shapes and tight tolerances.The HexTOOL TM structure is presented in Fig. 2, where one can see the unidirectional carbon fiber pre-impregnated bundles of 50 mm length and 8mm width presented in a quasi-isotropic orientation.The manufacturing process of composite components generally involves the lay-up of pre-impregnated bundles onto a tool surface, vacuum bagging followed by autoclave cure.The lay-up process aims at obtaining the desired composite mold thickness; it is done by stacking several plies.The autoclave curing induces resin reticulation by applying the temperature cycle.Once the composite mold is cured, the HexTOOL TM mold has a rough surface.A machining operation is necessary so as to obtain a smooth and accurate surface.Fig. 3 shows an image of a section at a mesoscopic scale (view B) and at a microscopic scale (view C).The wavy structure is induced by the stacking of the randomly distributed fiber bundles during the lay-up process.After a machining operation, the structure appears as marbled without any specific orientation of fibers (view A).Hence machined surfaces can be considered as randomly Fig. 3 Partially machined HexTOOL TM part (A) view of its structure at a mesoscopic scale; (B) at a microscopic scale; (C) external view of a machined surface at a macroscopic scale.

Experimental set-up
The principle of the open tribometer (Fig. 4) has already been applied and validated in several previous works [4,22,23].The workmaterial is simulated through a cylindrical bar made of HexTOOL TM (its manufacturing will be described later).A turning operation followed by a belt finishing operation is performed on the HexTOOL TM cylindrical bar in order to obtain a low surface roughness and a constant surface before each test.Cutting tools are simulated through pins made of PCD with a grade similar to the one used for cutting tools dedicated to composite material machining.The pin is maintained by an instrumented pin-holder which is able to provide data about the instantaneous heat flow (Φ) entering into the pin.The detailed information about heat flow measuring system can be found in [23].The pin-holder is fixed onto a dynamometer in order to measure the normal force F n and the tangential force F t (macroscopic forces).The apparent friction coefficient µ app is provided by the ratio between the tangential and the normal forces (Fig. 6), taken as an average value in the stable zone.
The term 'apparent friction coefficient' is used since it differs significantly from the 'interfacial friction coefficient' induced by adhesion at the pin/workmaterial interface.Indeed the macroscopic forces measured by the tribometer include friction phenomena (adhesion -> µ adh ), elastic deformation and plastic deformation of the workmaterial, which cannot be neglected under such severe contact conditions (F n ≈600 N).The identification of the evolution of µ adh with the present data will be presented later in the paper.Manufacturing a tube made of HexTOOL TM (Fig. 5) involves the same autoclave process as shown previously (Fig. 2).A tube having a rough shape is obtained.Then extremities are machined in order to facilitate clamping on the tribometer.As mentioned previously, the cylindrical surface is turned before performing any friction tests.
The same marbled surface as the one observed on tools is obtained (Fig. 3).Therefore during friction tests, it can be considered that pins rub against a randomly structured composite material.Each velocity has been replicated at least three times so as to evaluate the deviations.

Estimation of interfacial friction coefficient
The apparent friction coefficient previously introduced in Eq. ( 1) can be decomposed into two components [27] where µ adh is the adhesive contribution and µ def is the deformation contribution made up of elastic and plastic partitions.To extract the part of adhesion and deformation from the apparent friction coefficient, it is possible to rely on an analytical solution developed by Lafaye et al. [28,29] (Fig. 6).This model depends on real contact material properties taking into account the elastic recovery.In this approach, the pin is considered as infinitely rigid and the workmaterial is supposed to be elasto-plastic.For each point of the contact surface, an elementary mechanical action is considered, which can be decomposed into two parts, an elementary contact pressure: where n and t are, respectively, the normal and the tangential unit vector of the considered elementary surface, Sc is the effective contact surface area, which can be St or Sn standing for the contact surface projection respectively in planes xy and yz.The interfacial friction coefficient (adhesive friction coefficient) µ adh is defined by . .( . .).

P dS PdS n P dS PdS
Accepted Manuscript 6 These forces can be also written as measure of the projection of the contact surface Sc along X X , ( . ) ( . ) measure of the projection of the contact surface Sc along Z Z .
The contact area Sc is the sum of the front area (half of the disc with radius R) and the rear area (part of the rear half disc).These projected areas (Fig. 6c and d) are calculated using the analytical solution presented in [28] for spherical tip with elastic recovery.
Where ω is the rear contact angle, a is the contact radius  Therefore, the apparent friction coefficient may be written as a function of the adhesive friction coefficient: Finally, the adhesive friction coefficient can be calculated, based on the effective contact area estimated from experimental measurements, as follws:

Results and discussion
7 Table 1 summarizes the experimental data obtained in the present work.Fig. 7 outlines the image obtained by binocular microscope observation of a pin surface, presenting an example of the real contact area for velocity of 30 m/min (0.5 m/s), where it can be clearly noticed the shape of the normally projected contact area with the elastic recovery.Table 2. Experimental data obtained by binocular microscope for four different sliding velocities.

Identification of a friction model
Fig. 8 depicts the evolution of the friction coefficients versus sliding velocity for PCD pins.First, it is remarkable to see that apparent friction coefficients µ app are rather low (0.06 -> 0.08) compared with friction coefficients during metal cutting whatever the workmaterial/cutting tool material are.For instance [4,23] report values in the range 0.5 for the AISI4140 steel and 0.8 for the AISI316L stainless steel machined with a TiN coated carbide tool under similar sliding velocities.Additionally, [30] has also shown that PCD leads to the smallest cutting forces during the machining of GFRP compared with carbide.The very low coefficient of friction is assumed to be responsible for this experimental statement.Similar observations have been made by [31] in drilling of CFRP with diamond coated carbide drills compared with uncoated carbide drills.Therefore, the lower macroscopic friction coefficient observed for diamond pins compared with carbide pins is coherent with previous observations obtained in cutting.
Furthermore, it can be noticed that the values obtained in this paper are smaller than friction coefficient reported by the same authors [15] (0.1 -> 0.25) in exactly the same conditions but with carbide tools.These results are also in agreement with values obtained by [5] for CFRP against diamond (≈0.1) for sliding velocities around 10-20 m/min (0.16-0.33 m/s).Slightly lower values obtained here could be explained by the differences induced by the workmaterial (This shows that carbide leads to more adhesion than PCD against CFRP).

Fig. 8. Evolution of apparent friction coefficient versus sliding velocity for various substrates
As mentioned previously, µ app may be decomposed into a elasto-plastic deformation coefficient µ def and an interfacial friction coefficient µ adh (also called adhesive friction coefficient).In order to extract the friction coefficient µ adh , it is possible to use the analytical model presented previously.Based on our experimental results, it is possible to estimate an average value of µ def and µ adh for each testing situation (Fig. 9.).

Fig. 9. Evolution of apparent and adhesive friction coefficients versus sliding velocity
Therefore, different conclusions can be extracted from this analytical approach.The model shows that the major part of the apparent friction coefficient is due to adhesive friction.It represents about 65% of the apparent friction coefficient.This observation is totally different from friction phenomena between HexTOOL TM and carbides [15], in this case the ratio of µ adh and µ def was inverted.Indeed, during sliding, chemical links between PCD and HexTOOL TM are very limited, which is confirmed by the absence of stuck composite material on pins.
These observations are in accordance with results reported by [1], who indicates that adhesion is never observed on cutting tools after machining when the matrix is not carbonized or molten.
In Fig. 9, the value of adhesive and apparent friction coefficients decrease slightly as the velocity increases whereas the value of deformation friction coefficient µ def seems to be constant.It is remarkable to see that friction coefficients are closed to be constant with PCD pins compared their change following the sliding velocities in the case of carbide pins [15].The dispersion on the experimental values is limited (average 0.01), however, a larger dispersion is observed to 800m/min (13.33 m/s), this can be explained by the vibrations that occur for high velocities.
Thus, the combination of experimental results with the analytical model enables to provide data for future numerical modeling of machining operations in dry regime between CFRP and PCD tools: where F t is the tangential force (N) and V is the macroscopic sliding velocity (m/s).By assuming that all frictional energy is transformed into heat, a heat partition coefficient α at the interface can be estimated by : pin tot D (20) It means that α % of energy is transmitted to pins, whereas the workmaterial supports (1-α)% of this energy.

~0.96
Unfortunately, for dynamic sliding interfaces, the standard thermal model is no more valid.Therefore, Fig. 11 reports the experimental values of the heat partition coefficient α as a function of sliding velocity.One can notice that decreases with sliding velocity which is a similar trend as the one observed for metal [4].
Furthermore, the experimental values of the heat partition coefficient α are very close to those obtained with carbide pins [15].Actually, values of α are slightly larger for PCD pins, this could be explained by the greater effusivity of the PCD (50000 against 11350 for carbide in (N.m -1 .°C - .s -1/2 ) at 20°C).

Conclusions
The input data required to the numerical simulation models of the cutting process are the true contact area,  -We provide values of friction coefficient depending on sliding velocities.
-We provide quantitative values of heat partition coefficient.
-We found that PCD tools conducted to lower friction coefficients.

Fig. 2
Fig. 2 Manufacture of a part made of the HexTOOL TM composite material [26]

Fig. 5
Fig. 5 Preparation of cylindrical parts of HexTOOL TM2.3 Design of experimentsIn this work, two range of sliding velocities have been investigated:-A range of 10 to 200 m/min (0.16 to 3.33 m/s).For this range, each friction test has 20 s duration approximately.This duration is necessary to stabilize the heat flow measurement.-Arange of 200 to 800 m/min (3.33 to 13.33 m/s) in accordance with industrial cutting speed.For this range, the experimental set-up does not provide a sufficient duration of friction to measure the heat flow.Indeed, from 200 m/min (3.33 m/s), duration of friction is below 10 s, so for this range, only the friction coefficient is normal and tangential forces, which are measured during friction tests, are the sum of elementary mechanical actions: Z is the radius of projected area, R the radius of the spherical tip.

3 . 2
Fig. 10 reports the evolution of heat flux transmitted to pins ϕ pin during friction tests.It is observed that heat flux increases with sliding velocity as expected.It should be underlined that only a percentage of the total energy ϕ tot , dissipated during tests is transmitted to pins.An amount of heat remains in the workmaterial ϕ workmaterial .It is possible to estimate the total energy ϕ tot by : tot t FV
the heat partition and the friction coefficients.An original set-up presenting the rotary open tribometer has been used in the paper.This tribometer enables to conduct friction tests up to 800 m/min (13.33 m/s) under high contact pressure with continuously regenerated contact surface.The intensive contact between PCD pins and HexTOOL TM CFRP parts leads to a strong elasto-plastic deformation in parallel to the friction at the interface.An analytical model has been proposed in order to extract the interfacial friction coefficient from macroscopic measurements.This model considers the real contact depending on material properties taking into account the elastic recovery of this composite material.The binocular microscope observation of pin's surface have been conducted in order to determine the real contact area.Based on this new experimental set-up combined with this analytical model, the true local friction coefficient at the interface between a PCD tip and HexTOOL TM material is deduced.It has been shown that friction coefficient is lower than those for carbide pins.Futhermore, sliding velocity seems to have a low influence on friction coefficient especially for high velocities.Moreover, a model of friction has been identified in order to be implemented in any cutting model.The heat partition coefficient at the interface has also been investigated.It has been shown that it decreases as sliding velocity increases and is lower than those for carbide pins.Finally, a model has been identified, which can easily be fitted into cutting FE simulations.

Table 1 .
Table 2 reports the experimental measurements of the contact radius and the rear distance (Wr) Experimental data