Séverine Levasseur

Hélène Welemane

Djimédo Kondo

Microcracks-induced damage modelling for transversely isotropic rock

, a closed-form expression of the overall free energy of the microcracked medium is presented. This expression is implemented in an appropriate thermodynamics framework which allows formulating a complete constitutive damage model. The salient features of the model such as the coupling between anisotropies and its effect on the damage yield function and on the tangent operator of the model are illustrated and validated on the identification of a transversely isotropic argillite. It is shown that under direct tensile loadings (including off-axis tests), the theoretical mechanical responses predicted by the proposed model well capture experimental data. Owing to the above results, the response of the material is studied along a tension loading followed by an unloading and a reloading in compression in order to illustrate the so-called unilateral damage effects due to microcracks closure.

INTRODUCTION

The inelasticity of rock behaviour under mechanical loading results generally form damage phenomena due to evolving microcracks. To model it, both phenomenological and micromechanical approaches have been developed in the last decades in the framework of Continuum Damage Mechanics (CDM) (see for instance [START_REF] Krajcinovic | Damage mechanics[END_REF][START_REF] Lemaitre | Mechanics of Solid Materials[END_REF][START_REF] Costanzo | Micromechanics and homogenization of inelastic composite materials with growing cracks[END_REF][START_REF] Ju | Micromechanical damage model for brittle solids. Part 1: Tensile loading. Part 2: Compressive loading[END_REF][START_REF] Kachanov | A microcrack model of rock inelasticity. Part 1: Frictional sliding on microcracks. Part 2: Propagation of microcracks[END_REF][START_REF] Levasseur | A two scale anisotropic damage model accounting for initial stresses in microcracked materials[END_REF][START_REF] Pensée | Micromechanical analysis of anisotropic damage in brittle materials[END_REF][START_REF] Zhu | Micromechanical coupling of anisotropic damage in brittle rocks and application[END_REF]). However despite their interest, the above cited models concern mainly materials which are isotropic in their undamaged state. The modelling of coupling between initial and damage-induced anisotropies can only be found on studies devoted to brittle matrix composites, like [START_REF] Cazacu | On modeling the interaction between initial and damage-induced anisotropy in transversely isotropic solids[END_REF] and [START_REF] Halm | A model of anisotropic damage by mesocrack growth: unilateral effect[END_REF] for purely macroscopic models or [START_REF] Baste | Inelastic behaviour of ceramic-matrix composites[END_REF] and more recently [START_REF] Monchiet | A micromechanical approach of crack-induced damage in orthotropic media: application to a brittle matrix composite[END_REF] in the context of micro-macro models. But, this class of models still need to be completed in order to properly account for unilateral effects due to microcracks closure, which are of paramount importance and necessary for the modelling of quasi brittle geomaterials generally subjected to tensile loadings as well as to compression. In this way, [START_REF] Goidescu | Microcracks closure effects in initially orthotropic materials[END_REF] recently established closed-form expressions of the overall free energy of orthotropic materials weakened by microcracks, either open or closed. The present study takes advantage of these recent results to formulate a complete model with coupling between initial anisotropy and evolving unilateral damage due to 2D systems of open or closed microcracks under frictionless conditions.

For this purpose, the closed-form expression of the macroscopic free energy is recalled in this paper to constitute the thermodynamics potential of damaged geomaterials. Based on a discrete damage representation defined by microcrack densities, the state laws are deduced providing the macroscopic stress as well as the damage energy release rate in function of the macroscopic strain and the damage characteristics. It follows a damage yield function associated to each microcracks family and the damage evolution law by assuming normality rule as in CDM framework. This allows to establish the complete rate formulation of the anisotropic constitutive damage law with microcracks closure effects. After a simple calibration step, the ability of the model to account for the coupling between the initial anisotropy and microcracks-induced one is assessed first by comparing its prediction to available data on the behaviour of an argillite subjected to a tensile loading [START_REF] Liao | Direct tensile behavior of a transversely isotropic rock[END_REF], second by analysing the response of the material along a tension loading followed by an unloading and a reloading in compression illustrating the so-called unilateral damage effects due to microcracks closure.

Notations: Standard tensorial notations is used throughout the paper. Lower bold script letter describes vector, bold script capital letters is associated to second-order tensors and mathematical double-struck capital letter denotes fourth-order tensors. The following vector and tensor products are exemplified:

(A.b) i = A ij b j , (A.B) ij = A ik B kj , (A : B) ij = A ijkl B kl , (A : B) ijkl = A ijpq B pqkl .
Einstein summation convention, applied for the repeated indices and Cartesian coordinates are used. As usually, small respectively large characters refer to microscopic (resp. macroscopic) quantities. I and I are, respectively, the second and fourth order identity tensors, the components of the former is represented by the Kronecker symbol (δ ij ) while for the latter one has I ijkl = (1/2)(δ ik δ jl + δ il δ jk ).

MICROCRACKS-INDUCED DAMAGE MODEL

2.1 Representative volume element (r.v.e.)

Micromechanical formulation of damage model requires the homogenization of the microcracked material by defining a representative volume element r.v.e. of the material (noted Ω) constituted of an elastic orthotropic solid matrix s (occupying a domain Ω s ) and an arbitrary system of microcracks families (denoted r and occupying a domain Ω r ). This r.v.e. is subjected to uniform strain boundary conditions (the so-called Hashin boundary conditions):

ξ = E • z : ∀z ∈ ∂Ω (1)
z denoting the vector position, ξ the displacement vector, and E the macroscopic strain tensor.

The local constitutive equation in the heterogeneous medium follows elastic relation:

(z ∈ Ω) σ(z) = C(z) : ε(z) (2)
with σ(z) the local stress tensor and C(z) the heterogeneous stiffness tensor such as:

C(z) = C s in matrix (Ω s ) C r in microcracks domain (Ω r ) (3)
In the two dimensional approach considered in this paper, the solid matrix stiffness has an orthotropic structure with symmetry axes corresponding to the orthonormal basis (e 1 ,e 2 ) defined in Figure 1 and is described by means of the structural fabric tensor A = e 1 ⊗ e 1 , such as:

C s = a 1 I ⊗ I + a 2 I⊗I + a 3 A ⊗ A + a 4 (A ⊗ I + I ⊗ A) (4)
where

a 1 = C s 2222 -2C s 1212 a 2 = 2C s 1212 a 3 = C s 1111 + C s 2222 -2C s 1122 -4C s 1212 a 4 = C s 1122 -C s 2222 + 2C s 1212 (5)
and

C s 1111 = E 1 1 -υ 12 υ 21 , C s 2222 = E 2 1 -υ 12 υ 21 , C s 1212 = G 12 , C s 1122 = C s 2211 = υ 21 E 1 1 -υ 12 υ 21 with υ 12 E 1 = υ 21 E 2 (6)
in which E 1 and E 2 are the Young modulus in anisotropic directions related respectively to e 1 and e 2 , G 12 is the shear modulus and υ 12 and υ 21 are Poisson's ratios related to (e 1 ,e 2 ).

Ψ (E, d) = 1 2 E : C s : E - No r=1 d r {H r nn (N r : E) 2 + 2H r nt (N r : E)(T r : E) + H r tt (T r : E) 2 } + Nc r=1 d r H r nn H r tt -H r 2 nt {H r nn H r 2 nt (N r : E) 2 + 2H r 3 nt (N r : E)(T r : E) +H r tt (2H r 2 nt -H r nn H r tt )(T r : E) 2 } (7) in which N r = C s : (n r ⊗ n r ), T r = 1 2 C s : (n r ⊗ t r + t r ⊗ n r ) (8)
are two second order symetric tensors, and H r nn , H r nt and H r tt are material parameters that depend on the virgin matrix properties and on the crack orientation φ r = (e 1 , n r ) as:

H r nn = C(1 -D cos 2φ r ), H r nt = CD sin 2φ r , H r tt = C(1 + D cos 2φ r ) (9)
with scalars C and D related to the initial stiffness components:

C = π 4 C s 1111 + C s 2222 C s 1111 C s 2222 -(C s 1122 ) 2 1 C s 1212 + 2 C s 1111 C s 2222 -C s 1122 C s 1111 C s 2222 -(C s 1122 ) 2 (10) D = C s 1111 -C s 2222 C s 1111 + C s 2222 (11)
The transition between open and closed cracks is described by g(E, n r ) function:

g(E, n r ) = H r nn N r : E + H r nt T r : E (12)
If g(E, n r ) > 0 microcracks are open, while they are closed if not.

The following unified formulation of equation ( 7) can also be adopted in case of open or closed cracks:

Ψ (E, d) = 1 2 E : C hom : E (13)
with

C hom = C s - N r=1 2d r {C r 1 N r ⊗ N r + C r 2 [N r ⊗ T r + N r ⊗ T r ] + C r 3 T r ⊗ T r } (14)
in which constants C r 1 , C r 2 and C r 3 are defined in case of open cracks (index o) as:

C r 1o = H r nn , C r 2o = H r nt , C r 3o = H r ttn ( 15
)
while for closed cracks (index c) one has:

C r 1c = - H r nn H r 2 nt H r nn H r tt -H r 2 nt , C r 2c = - H r 3 nt H r nn H r tt -H r 2 nt , C r 3c = - H r tt (2H r 2 nt -H r nn H r tt ) H r nn H r tt -H r 2 nt (16)
Then from equation ( 13), the first state law which gives the macroscopic stress tensor Σ can be obtained by derivation:

Σ = ∂Ψ ∂E = C hom : E (17)
as well as the second state law which provides the expression of the damage energy release rate

F d r : F d r = - ∂Ψ ∂d r = E : (C r 1 N r ⊗ N r + C r 2 [N r ⊗ T r + T r ⊗ N r ] + C r 3 T r ⊗ T r ) : E (18)
Both the homogenized stiffness tensor C hom and the damage energy release rate F d r are then affected by the anisotropic properties of the solid matrix and depends on the orientation of the considered microcracks family. This is at the origin of the complex coupling between initial anisotropy and damage-induced one, as already discussed in [START_REF] Goidescu | Microcracks closure effects in initially orthotropic materials[END_REF].

Damage yield function

Based on classical thermodynamics arguments in CDM, the following general form is adopted for the damage criterion corresponding to each family of microcracks:

f (F d r , d r ) = F d r -R(d r ) = 0 (19)
The function R(d r ) represents the resistance to the damage evolution by microcracks growth.

It can be a priori determined from experimental investigations. For the sake of simplicity and following [START_REF] Marigo | Modeling of brittle and fatigue damage for elastic material by growth of microvoids[END_REF] in the context of isotropic matrix, we consider an affine function in d r :

R(d r ) = c 0 + c 1 d r (20)
where c 0 (ψ) and c 1 are two model parameters which determine the initial damage threshold and damage evolution respectively and that can be identified from experimental data.

Owing to the definition of F d r in equation ( 18), the damage yield surface corresponding to f (F d r , d r ) = 0 is a conic and mainly depends on anisotropic properties of solid matrix through N r and T r tensors. For illustration purpose, let's consider an orthotropic medium defined by the following material parameters (which correspond to the material studied by [START_REF] Liao | Direct tensile behavior of a transversely isotropic rock[END_REF] and analysed in section 3): E 1 = 60 GPa, E 2 = 27 GPa, G 12 = 13 GPa, ν 12 = 0.22, ν 21 = 0.10, and the damage yield surface parameters: c 0 =12 kJ/m 2 and c 1 =10 kJ/m 2 without any isotropic damage value (d r =0). E 1 denotes the elastic modulus in a direction parallel to orthotropy axis, while E 2 denotes the elastic modulus in the direction perpendicular to this axis. For instance, figure 2 presents the damage yield surface in the (E 11 , E 22 ), (E 11 , E 12 ) and (E 22 , E 12 ) strain spaces for one microcrack family orientation φ r =20 o (see [START_REF] Levasseur | A microcrackes-induced damage model accounting for unilateral effects: application to transversely isotropic rock[END_REF] for other microcrack family orientations). By definition, once the yield surface is reached, damage appears and can evolve. However, from figure 2, one can see that damage criterion is reached earlier for open cracks than for closed cracks characterizing more damaging capabilities in case of open cracks than in case of closed cracks. Furthermore, due to the conic definition of f (F d r , d r ), it appears that the branch of the damage yield surface associated to open cracks presents a closed-shape, whereas the branch associated to closed cracks always presents an open-shape. This will have a strong incidence in material response that can significantly differ under tensile or compression loadings.

Damage evolution law and rate form of the constitutive model

For a given family of microcracks, the consistency condition, ḟ r = 0, provides the damage evolution in the following form:

ḋr = 1 c 1 Ḟ d r = 2 c 1 E : B r : Ė (21) with B r = C r 1 N r ⊗ N r + C r 2 [N r ⊗ T r + T r ⊗ N r ] + C r 3 T r ⊗ T r (22)
And, by differentiating the macroscopic stress-strain relation given by ( 17), the macroscopic stress increment is expressed as:

Σ = C hom t : Ė = C hom - 1 c 1 E : N r=1 B r ⊗ B r : E : Ė (

APPLICATIONS

Simulation of uniaxial tensile test on argillite

To validate the damage model proposed in this paper, we consider uniaxial tensile tests carried out on a transversely isotropic argillite of Taiwan by [START_REF] Liao | Direct tensile behavior of a transversely isotropic rock[END_REF] for several anisotropy orientations from ψ = 0 o to ψ = 90 o . Modelling is based on 2D plane strain approach schematized in figure 3. Owing to symmetry considerations, only one quarter of the sample is considered. Vertical displacements are locked on the bottom and horizontal displacements are locked on the left side. The tensile loading is applied on the top of the sample. The intact argillite behaviour is modelled as a linear transversely isotropic elastic material in the material axis (m 1 ,m 2 ) defined by means of ψ angle. The corresponding generalized Hooke's law takes the form:

E = S s : Σ (24)
in which the matrix of components of S s = C s -1 in Voigt notation is:

S s =        1 E 1 - υ 21 E 2 0 - υ 12 E 1 1 E 2 0 0 0 1 G 12        (25)
and E 1 and E 2 still denote the Young modulus in the two materials directions, G 12 is the shear modulus and υ 12 and υ 21 are Poisson ratios verifying the symmetry:

υ 12 /E 1 = υ 21 /E 2 .
For the considered argillite, these parameters are estimated to: E 1 =60 GPa, E 2 =27 GPa, ν 12 =0.22, ν 21 =0.10, G 12 =13 GPa, assuming an initial isotropic damage value d r =0.01. Damage parameter c 1 of equation ( 20) has been calibrated to 10 kJ/m 2 whereas c 0 estimation seems to vary with anisotropy angle ψ as given in table 1. This evolution of c 0 with anisotropy angle ψ follows tensile strength variations (observed by Liao et al., see Levasseur et al. (2013)). The results of this model calibration are shown in figure 4 for ψ=0 o , 45 o , 60 o and 90 o (see [START_REF] Levasseur | A microcrackes-induced damage model accounting for unilateral effects: application to transversely isotropic rock[END_REF] for other anisotropy orientations). The stress-strain curves (Σ 22 , E 22 ) are then well captured by the model and the evolutions of damage seems realistic. As observed in the laboratory tests on specimen with low inclination ψ, the predicted stress-strain curves exhibit apparent non linearity before failure; for specimen with high inclination ψ, the stress-strain curves are quasi-linear. These findings indicate that even in the theoretical approach, the influence of microcracks on the tensile behaviour decreases when the anisotropy angle ψ increases. For specimen with low inclination, damage appears gradually causing a more pronounced non linear behaviour of argillite. For specimen with high inclination, damage occurs more suddenly. Numerically, this corresponds to non convergence of the model because of the too strong and sudden damage levels which are reached. Similarly to stress paths in elasto-plasticity theory, a "damage path" can be drawn in strain spaces: see for instance in Figure 5 "damage paths" in (E 11 , E 22 ) space for one microcrack orientation φ=20 o and two anisotropy orientations ψ=0 o (corresponding to a loading case along anisotropy axis) and ψ=60 o (corresponding to a loading out of anisotropy axis). Figure 5 put in evidence that once strain state reaches damage criterion, the criterion evolves linearly with damage both in open and closed crack domains due to equation ( 20) and similarly in all directions. Then, final damage surface is homothetic to the initial one. The consequence of damage coupling with matrix anisotropy induces variations of homogenized tensor components with strain and anisotropy orientations. When damage occurs, moduli are degraded. However, because of a strong coupling between matrix anisotropy and damage induced anisotropy, these degradations differ from one direction to the others. In case of ψ = 0 o , loading direction corresponds to an anisotropy axis and then the weakest direction (along loading axis in this case) is more degraded than the hardest one (perpendicular to loading axis in this case). In case of ψ = 60 o , loading direction does not correspond to the anisotropy axis and the main degradation of Young modulus does not correspond to the initial weakest direction. Uniaxial tensile test still generates microcracks in horizontal directions even if anisotropy axis are oriented at 60 o and then major modulus degradations result from a combined effect of matrix anisotropy and damage induced anisotropy.

Microcracks closure effect: tension-compression loading

The modelling of tensile loading followed by an unloading and reloading in compression allows to study unilateral effect by evaluating how progressive closure of open microcracks generated during the tension loading step affects the macroscopic material response during the compression phase. Figure 6 presents the stress-strain curve corresponding to the described loading path for anisotropy ψ=0 o . In the same figure, the evolution of overall damage variable with strain is given. The obtained stress-strain curve shows continuous response at the tension-compression transition when axial stress is equal to zero (corresponding to the opening/closure transition) despite the discontinuity of the macroscopic elastic properties. In fact, during tension-compression loading damage yield surface evolves as follows (see figure 7):

• As long as loading does not reach damage criteria, damage is constant and stress-strain relation is linear; • When damage criterion is attained for a given family of microcracks, damage evolves providing on one hand the non linearity of stress-strain curve due to the degradation of stiffness tensor and on the other hand the growth of damage surface; • During unloading phases, we leave the damage criteria and no more damage evolves since the damage criteria is reached once again during reloading phase.

The same kind of results is obtained whatever is the anisotropy orientation ψ. Fig. 6. Simulation of tensile loading followed by unloading and reloading in compression in the case of anisotropy orientation equals to 0 (full line: stress-strain curve; dashed line: damage evolution with strain)

CONCLUSION

Taking advantage of the recent study by [START_REF] Goidescu | Microcracks closure effects in initially orthotropic materials[END_REF], this paper presents a full 2D anisotropic micromechanical damage model accounting for couplings between the damageinduced anisotropy and the solid matrix orthotropy and characterizing unilateral effect of evolving microcracks in transversely isotropic rocks. Applied to argillite, it is shown that the initial anisotropy of the rock strongly affects the damage criterion and evolving and subsequently the ) strain space for anisotropy orientation ψ=0 and for one crack orientation φ r =45 due to traction-compression loading represents by diamond symbols macroscopic response of the material through the stiffness degradation. Furthermore, depending of the inclination of transversely isotropic properties of rocks, damage can occur gradually generating non linear behaviour of argillite, or more suddenly, causing quasi-linear behaviour as observed in the laboratory. Moreover, by a systematic analysis of damage criteria in strain spaces, an appropriate description of damage evolution process and of the opening/closure properties of microcracks is provided.

Fig. 1 .

 1 Fig. 1. (a) Representative volume element in two-dimensional case; (b) crack coordinate system

Fig. 3 .

 3 Fig. 3. Geometry of uniaxial tensile test in relation with anisotropy orientation ψ

Fig. 4 .

 4 Fig. 4. Prediction of the stress-Strain curves and damage evolution as function of strain for 4 orthotropic axis orientations: 0 o , 45 o , 60 o and 90 o (symbols: lab measurements; full lines: numerical results)

Fig. 5 .

 5 Fig. 5. Initial (full lines) and final (dash lines) damage yield surfaces f (F d r , d r )=0 in (E11, E22) space for anisotropy orientations ψ=0 o (top) and ψ=60 o (bottom) for one crack orientation φ r =20 o due to tensile loading represents by diamond symbols

Fig. 7 .

 7 Fig. 7. Evolution of damage criteria f (F d r , d r )=0 in (E11, E22) strain space for anisotropy orientation ψ=0 and for one crack orientation φ r =45 due to traction-compression loading represents by diamond symbols

Table 1 .

 1 Estimation of c0 with anisotropy angle ψ

	ψ ( o )	0	30	45	60	75	90
	c0 (kJ/m 2 )	0.2	0.2	0.3	0.6	6	10

ACKNOWLEDGEMENTS

The authors would like to thank the F.R.S.-FNRS, the national funds of scientific research in Belgium, for their financial support in FRFC project.


Andrei Popa

Maher Baili

Gilles Dessein

Vincent Dutilh

Identification of tool failure modes in drilling Udimet ® 720 superalloy

The ACCENT Project (FP7-AAT-2007-RTD-1) will allow the European Aero Engine manufacturers to improve their competitiveness by applying adaptive control techniques to the manufacturing of their components. For the critical rotating parts of aircraft engines, the surface integrity generated after machining is a key factor on the life cycle. In this context, one particular attention has to be carried on tool condition. The aim of this paper is to identify the main failure modes characterizing this particular Nickel base drilling. By experimental techniques, cartography of failure modes was realized. The results show that flank wear and notching are the main failure modes limiting the tool life. For some cutting conditions, the tool failure arrives after the first hole due to the important cutting forces. Some interesting associations are made between the spindle current/accelerometers/ thrust force and flank wear, tool breakage and notching.

Introduction

The super alloys can be classified in three categories: Nickel base, Iron base and Cobalt base. In the aircraft industry, the Nickel base super alloys are often employed in the applications at high temperature, such as turbine discs. The Udimet ® 720 has replaced the Inconel 718 due to its higher mechanical properties at elevated temperatures and other advantages in terms of corrosion resistance. However, their properties, the tool life and anomalies which may occur during the machining, make the Nickel base super alloys "difficultto-cut" [START_REF] Ezugwu | Key improvements in the machining of difficult-to-cut aerospace superalloys[END_REF]. The choice of cutting parameters (cutting speed, feedrate, percentage of emulsion in cutting fluid, etc), the low thermal conductivity which characterize these materials, the chemical affinity for tool materials, the tool geometry and the coating type are essential factors on the tool life. A tool geometry variation (i.e. built-up edge, chipping, excessive wear or tool failure) during drilling can lead to surface integrity problems (roughness profile deviation, thermo-mechanically affected layer, etc.). For the critical parts, it is crucial to prevent these anomalies. All these appreciations make the tool wear a key factor for the quality of produced parts. Sharman et al. [START_REF] Sharman | Tool life and surface integrity aspects when drilling and hole making in Inconel 718[END_REF] show the influence of the geometry and type of coating on the tool life in drilling of Inconel 718. In this study, the drills having a curved edge and radius on the periphery had a higher performance comparing to drills with either a straight or concave cutting edge or sharp periphery. In the same direction, for turning of Inconel 718 without lubricant, Devillez et al. [START_REF] Devillez | Cutting forces and wear in dry machining of Inconel 718 with coated carbide tools[END_REF] present the influence of coating type. Several coatings were evaluated on different cutting speed, chosen between 20 and 200 m/min and feederate 0.1 and 0.2mm/rev. The best coated type was used for a bar turning operation. During these tests, the principal wear modes were welding, adhesion of workpiece material onto the tool and abrasion flank wear. Chen [START_REF] Chen | Study on wear mechanisms in drilling of Inconel 718 superalloy[END_REF] studied the wear mechanisms in drilling Inconel 718 with multi-layer TiAlN PVD coated tungsten carbide twist drills. Selected cutting speed was 13.2 m/min and feedrate was 0.1 mm/rev. The authors explained the wear evolution by dividing into four steps. At first phase, due to the friction force, the coated layer is removed. The next period is represented by the apparition of flank wear and chipping. For the third stage, micro cracks appear in the chipping region. Finally, corroborating with crater wear causes the drill failure. More and more researches are focused on process monitoring, and more precisely by using physical measures as non-destructive control. Generally, two types of methods (direct and indirect) can be applied. Most of direct methods (e.g. cameras for visual inspection or laser beams) can be employed only as laboratories technics (even they have a high accuracy), due to some limitations in industry, such as use of cutting fluid, low light, etc. Indirect methods are based on physical quantities, such as cutting forces, power, temperature being more suitable for industrial applications. A large number of papers deal with Tool Condition Monitoring (TCM). Jantunen [START_REF] Jantunen | A summary of methods applied to tool condition monitoring in drilling[END_REF] presents principals monitoring technics and signal analyses available in the literature. Statistical parameters (mean value, maximum value, kurtosis, skewness, etc.), frequency analyses on signals are used in order to monitor the tool condition. The power signal recorded during the machining is compared by Axinte [START_REF] Axinte | Assessment of the effectiveness of a spindle power signal for tool condition monitoring in machining processes[END_REF] with force and torque signals in order to verify the sensitivity of this physical quantity in tool condition monitoring. In continuous machining processes, i.e. turning and drilling, the power can be considered appropriate to detect both chipping and gradual tool wear. On other hand, for the intermittent processes (milling) the power is not sensitive enough to identify a chipped cutter. This can be attributed to the fact that this signal lost the intermittent "sow teeth" patterns, that's allowed to detect eventual events. The vibration signal is often used as source of information about the process. In drilling of high speed steel C 1040, Abu-Mahfouz [START_REF] Abu-Mahfouz | Drilling wear detection and classification using vibration signals and artificial neural network[END_REF] uses features extracted by vibration signal as input parameters in neural network for prediction and classification of wear (chisel wear, crater wear, flank wear, edge fracture). Another interesting approach is proposed by Kalvoda [START_REF] Kalvoda | A cutter tool monitoring in machining process using Hilbert-Huang transform[END_REF]. The author uses a new method of time-frequency analysis, Hilbert Huang Transform (HHT), to extract features of sensor signals. It consists of two steps: the Empirical Mode Decomposition (EMD) to decompose a signal into a set of monocomponent signals, called Intrinsic Mode Functions (IMFs), and the application of the HHT to the IMFs. Then Hilbert Spectral Analysis (HSA) it is used to examine the IMFs instantaneous frequency and to generate effective time-frequency distributions called Hilbert spectra.

Experiments

Drilling tests were carried on ∅80 mm forged bars, usually used as raw material in turbine discs manufacturing. These bars have the same heat treatments as the discs (solution Heat Treatment and aged) in order to obtain the nearest routine mechanical properties to the original discs (same microstructure, same grain size 8 (ASTM) and same Hardness HV 410 HV30). 1. Combining the cutting conditions according to classic criteria established by the French specification AFNOR E66-520 (Couple-Tool-Material) to find the optimal cutting speed and feedrate. 2. New operating points (Figure 2) were tested and analyzed using surface integrity criteria in order to define an Acceptable Surface Integrity Domain (A.S.I.D -a window that insures the piece integrity). 3. Machining disturbances (corresponding to tool position defect, cutting fluid emulsion variation or changes of the material hardness) were tested to understand their impact on surface integrity and signals. 4. The purpose of the last campaign was to understand the wear behavior for this combination processmaterial. Based on "Cartography" tests results (Figure 2), several cutting conditions were chosen to drill more than just one hole with the same tool. This stage will help to identify the wear mechanisms.

All the tested points will be described in chapter 3.

Results

Results of drilling tests performed in Udimet 720 ® are presented in terms of failure modes and evolution of physical measurements. After each test, images of the tool were taken with a binocular. To avoid possible damages due to the handling, the tool was left attached on the tool holder. For the flank wear, the mean value was measured. For the notch, only the surface was considered in this study.

Evolution of failure modes

Tool flank wear

The first wear type identified was the flank wear. The coated layer is abraded-off, due to the friction force. In the Figure 3

Notching

Due to the specifity of the process (drilling in a pre-hole) another failure mode observed is the notch wear. The notch apparition is explained by the difference of pressure at the limit of cutting zone. Figure 5b presents the second zone proposed in this study, characterized by flank wear and notching.

a). Notching domain; b). Example of measures ; c). Evolution after the first machining

The flank wear evolution follows the same pattern as before. A slow increasing could be observed for tests having a low feedrate. For cutting speed V c 19 m/min and feedrate 0.2 mm/rev the increasing is more emphasized (more than 50% between 2 holes). At 25 m/min, the results are more interesting. After the first hole, the wear level is about 0.05 mm and is increasing until 0.18 mm for the second test. Further, the tool breakage occurs. For one cutting condition, V c 22 m/min and f 0.15 mm/rev were performed 10 tests with the same tool. It seems that the tool honing is done after the first hole and further the wear is slowly increasing (between 0.1 and 0.15 mm).

Figure 6. Flank wear and notching evolution

The notching evolution after the first hole is presented in the Figure 5c. It is obvious that with higher feedrates, the notch dimensions are increasing.

Tool breakage

When cutting forces become too high, the tool breakage occurs at the limit of the cutting zone (Figure 7b).

Evolution of signals

The first part of this work highlights the tool behavior over a wide range of cutting conditions. In this section, the signals will be analyzed in order to verify which one is more suitable for tool condition monitoring. The signals considered are:

-The signals obtained from the Kistler dynamometer (Mz, Fz, Fx and Fy) are filtered with a low pass (25 Hz). -The accelerometers are another interesting source of information. It must to be mentioned the fact that all the three accelerometers offers the same signal. The only difference is the signal amplitude, caused by distinct length to the cutting zone. A hammer test was performed in order to identify the natural frequencies corresponding to spindle, tool holder, etc. -The last signal considered is the spindle current extracted from NC machine-tool. Figure 8(a) shows the evolution of the current spindle for the 5 holes drilled at V c 10 m/min and f 0.25 mm/rev. The gradual flank wear observed during these tests could be related with the increased amplitude of spindle current. The same results were obtained using thrust force. In terms of vibrations, the tool wear generates an expansion of contact area, having as consequence lower amplitudes (Figure 8b). An example is given for the notching wear in the Figure 8(c). The torque M z , filtered with a low pass and the spindle current have the same topography. This pattern is representative for all the tests presenting a notch. Usually, is characterized by a stable machining (this length is function of cutting conditions) followed by suddenly increased amplitude of signals. The contact area between the tool and the piece increases when a notch occurs, making the cutting forces to evolve as presented. The vibration signal obtained from the accelerometer placed along Y axis show a similar pattern with the spindle current. Has to be mentioned that signal is unfiltered. In the Figure 8(e) and (f) two examples of tool breakage detection are presented. The cutting forces are increasing (two or three times) followed by a stable machining. But, in this situation, the cutting action is replaced by extrusion. The chips thickness is about two times lower. It is interesting to remark that the cutting forces are increasing with higher feedrates. Also, at 40 m/min the average spindle current is similar with tests at 10 m/min. This observation could be explained by the thermal softening. The temperature during machining is increasing due to the severe cutting conditions, making the cutting forces to decrease (Figure 9). This paper presents the results in term of failure modes for the drilling of Udimet 720 ® , obtained from an experimental campaign. All the trials were monitored with a four components dynamometer, three accelerometers and the signals extract from the machine-tool NC.

The results show that flank wear and notching are the main failure modes. The flank wear is slowly increasing. The notch surface increase with higher feedrate and when the cutting forces become too important the tool breakage occurs. Cartography of failure modes was realized from these results. But, it might change due to the variability on the quality of manufactured tools (Figure 10). In terms of tool condition monitoring, promising results could be obtained by associating the flank wear/notch with the spindle current, accelerometers or thrust force. Nevertheless, the spindle current signal issue from machine NC has the advantage to be already filtered and easy to implement in a process monitoring technique for industrial partners, together with the accelerometers. Even some observations are made for the accelerations signals, the next steps of this work should be focus on this direction.

Figure 1 .

 1 Figure 1. Experimental set-up and PM signals

Figure 2 .

 2 Figure 2. Cartography tests and ASID

  (a) two zones are delimited. The first one corresponds to cutting speeds lower than 20 m/min and feedrates 0.1 mm/rev and 0.25 mm/rev. The black circles represent the cutting conditions chosen to drill several holes with the same tool (in production the tool life is limited at 2 holes). Finally were performed 5 holes for V c 10 m/min and 3 holes for the other two points. The results of these tests (Figure4) show a slow increase in terms of flank wear, between 0.05 mm and 0.13 mm (the uncertainty is 0.01 mm). Contrary to this zone, at high cutting speeds the tool behavior is totally different. In the second zone, 2 holes were performed for each point. Initially, the first machining is stable and the results in terms of flank wear are quite similar with tests at low cutting speed. The difference is made by the second hole, having as direct consequence the tool breakage. The recorded signals indicate that the tool failure arrives immediately after the tool entrance in the material (Figure8b-grey curve).

Figure 3 .Figure 4 .

 34 Figure 3. Flank wear

Figure 5 .

 5 Figure 5. a). Notching domain; b). Example of measures ; c). Evolution after the first machining

Figure 7

 7 Figure 7. a.Tool breakage domain ; b. Example Figure 7b illustrates an image with tool breakage. It's the consequence of the most severe cutting conditions, V c 40 m/min and f 0.25 mm/rev. The same results were obtained for the others points tested.

Figure 8 .

 8 Figure 8. Failure modes detection using physical measurements

  Figure 9. Spindle current evolution

Figure 10 .

 10 Figure 10. Cartography of failure modes

Acknowledgments

The research leading to these results has received funding from the European Community's Seventh framework Programme (FP7/2007-2011) under grant agreement number 213855.


Maher Baili

Vincent Wagner

Gilles Dessein

Julien Sallaberry

Daniel Lallement

Influence de la température sur l'usinabilité du Ti-5-5-5-3

The realization of aeronautic parts with strong mechanical properties requires the use of high performance materials. That's why, some new materials are used for landing gears as refractory titanium (as Ti-5-5-5-3). The machining of this material leads to high cutting forces and temperatures. So, it is necessary to use low cutting conditions on the industrial machining process .

In order to increase the productivity, it is possible to increase the initial temperature of the workpiece. Hot machining is a new research track. The principle consists in heating material before machining it, in order to take advantage of its mechanical properties reduction.

First, studying the state of the art permit us to determine all heating instruments used and the thermal alleviation that exists on conventional materials.

A heating by induction was chosen and a system capable to maintain a constant temperature into the workpiece during machining (turning) was conceived.

The measure of the temperature is achieved in the setup of the workpiece by thermocouples and by thermography camera.

Trails permit to identify the variation of cutting forces according to the initial temperature of the workpiece, with fixed cutting conditions according to the TMP (Tool-Material-Pair) methodology at ambient temperature. Tool life and deterioration type are identified notably.

The results analysis shows a low reduction of specific cutting forces for a temperature area compatible with industrial process. The reduction is more important at elevated temperature. However, it has bad consequences on quality of the workpiece surface (oxidation, problem on surface integrity and mechanical properties degradation).

In perspective, different ways of heating are studied to permit a localized and more effective heath compatible with the industrial application.

Introduction

En aéronautique, dans l'objectif de réduire la masse embarquée, réduire les couts de maintenance et améliorer le tenue en fatigue des pièces de structure, les industriels favorisent l'utilisation de matériaux de nouvelles génération. Dans ce cadre, Messier-Dowty Bidos utilise le nouvel alliage de titane Ti-5-5-5-3 (Ti-5Al-5Mo-5V-3Cr) pour la fabrication de certaines pièces de ses trains d'atterrissage. Ce matériau réfractaire présente de très bonnes propriétés mécaniques en termes de résistance à la corrosion, résistance mécanique et tenue à la fatigue. Toutefois, ce matériau présente une très faible usinabilité comparé aux aciers ou encore à l'alliage de titane souvent pris comme référence le Ti-6-4 (Ti-6Al-4V). Sur cet alliage, l'usinabilité est complexe, d'où une productivité limitée : la vitesse de coupe est faible et la durée de vie des outils est réduite, la conséquence est une augmentation importante des temps de cycle ce qui n'est pas sans poser des problèmes de charge capacité. Le coût de fabrication devient une problématique majeure. Le choix des pistes d'amélioration n'est possible que par la compréhension des phénomènes de coupe et d'usure du Ti-5-5-5-3. Le premier objectif sera la recherche de l'amélioration de son usinabilité. L'objectif de cet article est d'étudier l'impact de la température initiale du matériau usiné sur l'évolution des efforts de coupe et sur les modes de dégradation de l'arête de coupe, partant du postulat qu'un gain potentiel en effort de coupe se répercutera sur l'usinabilité. La méthodologie du travail se base sur la démarche Couple-Outil-Matière (COM), le critère représentatif de l'optimisation étant l'énergie spécifique de coupe Kc. En effet, la chauffe du matériau à usiner réduit la contrainte d'écoulement plastique du matériau provoquant ainsi le phénomène d'adoucissement thermique (bien connu en usinage à grande vitesse) qui conduit à la réduction du Kc. Néanmoins, cette température affectera la durée de vie de l'outil (augmentation des contraintes thermiques, usure en dépouille, abrasion du revêtement…). Elle engendrera une transformation microstructurale du matériau et génèrera un abattement des caractéristiques mécaniques de la surface de la pièce. Cet article est organisé comme suit : la section 2 détaille l'état de l'art sur l'usinabilité des matériaux à chaud, les différents moyens de chauffe possibles ainsi que l'impact de la température non seulement sur la durée de vie des outils mais aussi sur les propriétés mécaniques et l'intégrité de surface. La section 3 détaille le dispositif expérimental choisi permettant d'usiner le Ti-5-5-5-3 à chaud. La section suivante exposera les résultats expérimentaux obtenus et sera consacrée à l'analyse et à la discussion de ces résultats. La dernière section a pour objectif de conclure sur cette étude afin de comparer les apports de la méthode par rapport à ses limitations.

État de l'art sur l'usinage à chaud

La faible usinabilité des alliages de titane est essentiellement due à ses propriétés intrinsèques. En effet sa faible conductivité thermique empêche l'évacuation de la chaleur générée par l'usinage. Ceci engendre une température élevée au contact outil-matière. En plus, à haute température, les alliages de titane réagissent chimiquement avec de nombreux matériaux constitutifs des outils de coupe. Avec l'augmentation de la température, tous les matériaux subissent une diminution de leurs propriétés mécaniques (Figure 1). Le chauffage abaisse la contrainte d'écoulement plastique des métaux.

Figure 1 : Évolution de la résistance à la traction en fonction de la température pour différents matériaux [START_REF] Germain | Contribution à l'optimisation du procédé d'usinage assisté laser[END_REF] Pour résoudre les problèmes d'usinabilité de certains matériaux, l'augmentation de la température des pièces est aujourd'hui une piste explorée par de nombreux chercheurs. Le principe de l'usinage à chaud est de profiter de la diminution des propriétés mécaniques du matériau pour l'usiner. Depuis les années 70, de nombreuses études ont été réalisées sur ce sujet. Moore [START_REF] Moore | Hot machining in industry[END_REF] a mené des études sur différents matériaux métalliques et céramiques. Il a constaté l'amélioration de l'usinabilité de matériaux aéronautiques tels que les alliages de titane et de nickel. Les gains généralement observés sont la diminution des efforts de coupe, des vibrations et de l'usure de l'outil, ainsi que l'amélioration de l'état de surface. Des études ont été menées par Ozler [START_REF] Ozler | Theoretical and experimental determination of tool life in hot machining of austenitic manganese steel[END_REF] sur la durée de vie de l'outil lors de l'usinage à chaud d'acier austénitique au manganèse. Il a été conclu que la durée de vie de l'outil est proportionnelle à la température de la pièce jusqu'à 600°C. Toutefois, elle est inversement proportionnelle à la vitesse de coupe. Ces résultats démontrent que l'usinage à chaud permet l'utilisation de vitesses de coupe plus élevées pour une même durée de vie d'outil.

Les travaux de Melhaoui [START_REF] Melhaoui | Contribution à l'étude de l'usure d'outil de coupe en usinage assisté par laser et à l'usinabilité d'une céramique à base d'oxyde de zinc[END_REF] confirment également l'intérêt du chauffage de la pièce pour augmenter la durée de vie de l'outil. Il a étudié l'usinage assisté laser de l'acier 16MnCr5 recuit. Grâce à l'assistance thermique, 80% de l'usure en dépouille et de 60% de l'usure en cratère ont été réduit. Il explique cette baisse importante de l'usure par la baisse de l'effort de coupe dû à l'assistance thermique.

Les travaux de Sun [START_REF] Sun | Laser-assisted machining of titanium alloys[END_REF] sur l'usinage à chaud du Ti-6-4 ont permis d'observer que l'assistance plasma dégrade la durée de vie de l'outil, malgré la diminution des efforts de coupe. Ils confirment cependant que l'assistance laser permet d'augmenter la durée de vie de l'outil. Cela renforce l'intérêt de l'assistance laser en usinage à chaud.

List [START_REF] List | Étude des mécanismes d'endommagement des outils carbure WC-CO par la caractérisation de l'interface outil-copeau. Application à l'usinage à sec de l'alliage d'aluminium aéronautique AA2024 T[END_REF] explique que l'assistance thermique ne diminue pas nécessairement l'usure de l'outil. Les différents mécanismes de l'usure d'outil y sont expliqués, ainsi que l'effet de la température :

• déformation plastique : Les déformations plastiques apparaissent sous l'effet de fortes sollicitations thermiques et mécaniques. Lors de l'usinage, les grandes vitesses de coupe et d'avance et la dureté des matériaux usinés génèrent des pressions et températures élevées, notamment en pointe d'outil. Les fluctuations de température et de chargement conduisent à la fissuration et à la destruction des arêtes de coupe, • usure par abrasion : elle apparait sur la face de coupe et sur la face de dépouille des outils. Au contact outil-pièce, par frottement, les particules dures de la pièce (inclusions) arrachent des éléments de l'outil. Cela génère des stries sur l'outil, • usure par adhésion : sous l'effet de la pression et de la température, des soudures se créent entre l'outil et le copeau. Ce phénomène apparait surtout si les atomes qui constituent les deux surfaces en contact peuvent réagir chimiquement. Les éléments du copeau se collent et s'accumulent sur l'arête de coupe pour former un dépôt macroscopique (appelé arête rapportée). Lorsque ce dépôt se brise, une partie de l'outil est arrachée. L'usure par adhésion apparait surtout à faible vitesse de coupe, • usure par diffusion : la pression et la température élevées sont aussi responsables de phénomènes de diffusion d'atomes de l'outil vers le copeau ou vice-versa. Sur l'outil, il se forme une couche intermétallique moins résistante que le métal d'origine. Des fissures se créent, des grains se détachent de l'outil et créent un cratère sur la face de coupe. List [START_REF] List | Étude des mécanismes d'endommagement des outils carbure WC-CO par la caractérisation de l'interface outil-copeau. Application à l'usinage à sec de l'alliage d'aluminium aéronautique AA2024 T[END_REF] détaille l'influence de la température sur l'apparition de ces mécanismes d'usure (Figure 2). On remarque qu'à basse température, l'adhésion et l'abrasion sont prépondérantes. Toutefois, à haute température, des phénomènes de diffusion, de corrosion et de déformation plastique apparaissent. Selon les matériaux usinés et les paramètres de coupe, l'assistance thermique a des effets contrastés sur l'usure des outils de coupe. En fonction de la température, l'usure peut avoir des origines mécaniques (abrasion) ou chimiques (diffusion). Les propriétés physico-chimiques des matériaux mises en jeu jouent également un rôle important. La haute température abaisse la contrainte des matériaux, mais elle active les réactions chimiques entre outil et matière.

Figure 2 : usure de l'outil en fonction de la température [START_REF] List | Étude des mécanismes d'endommagement des outils carbure WC-CO par la caractérisation de l'interface outil-copeau. Application à l'usinage à sec de l'alliage d'aluminium aéronautique AA2024 T[END_REF] Pour augmenter la température du matériau usiné, plusieurs méthodes ont été adoptées. En effet, lors des premiers travaux, la pièce a été chauffée dans son intégralité avant d'être usinée. Ensuite, des techniques de chauffage localisé ont vu le jour. Le chauffage plasma permet de chauffer localement la zone en amont de la trajectoire de l'outil grâce à une torche plasma. La densité de puissance générée est importante. Ce procédé a été utilisé dans [START_REF] Leshock | Plasma enhanced machining of Inconel 718: Modeling of workpiece temperature with plasma heating and experimental results[END_REF] pour chauffer de l'inconel 718. Un autre procédé pouvant être utilisé est le chauffage par laser. Le principe de ce procédé est similaire à celui du chauffage par plasma. Toutefois, la densité de puissance obtenue est beaucoup plus importante. Trois sources laser peuvent être utilisées. La source CO2 est la plus puissante (10 à 100 KW/mm 2 ). Le transport du faisceau se fait par un jeu de miroirs et nécessite une robotisation lourde ce qui limite son utilisation dans le cas de l'usinage lors du déplacement des axes de la machine. Le laser à semi-conducteurs utilise une deuxième source d'énergie basée sur des diodes laser. Le faisceau laser peut être transporté par fibre optique d'où la possibilité de l'intégrer sur une machine-outil. Néanmoins, la puissance (quelques KW/mm 2 ) reste insuffisante pour monter la pièce en température rapidement pendant l'usinage. Le dernier procédé de chauffage laser est le plus prometteur en usinage à chaud des métaux : il s'agit du laser Nd-YAG (Néodyme -Yttrium Aluminium Garnet). Il permet d'obtenir un faisceau de puissance moyenne (jusqu'à 5 kW/mm 2 ) transportable par fibre optique donc compatible avec l'usinage. Sa longueur d'onde facilite son absorption dans les matériaux métalliques. Le dernier procédé utilisé pour chauffer le matériau usiné est le chauffage par induction. En effet, la pièce à usiner baigne dans un champ magnétique. Le chauffage se fait sans contact et peut très facilement être compatible avec l'usinage. En plus, ce procédé permet de régler la température de chauffe à 10°C près, elle permet de monter la température sur un alliage de titane à 1000°C en 2 min et ne présente pas de danger dans la mesure où c'est uniquement la pièce qui est chauffée et que le rayonnement thermique est très faible. C'est ce dernier procédé qui a attiré notre attention dans nos travaux. Si augmenter la température du matériau usiné permet de baisser sa résistance et d'améliorer son usinabilité, la contrepartie est l'impact sur l'intégrité de surface du matériau : modifications microstructurales et des contraintes résiduelles. En effet, Germain [START_REF] Germain | Contribution à l'optimisation du procédé d'usinage assisté laser[END_REF] a observé des modifications microstructurale dues au traitement thermique engendré par le chauffage superficiel. Les phases et du matériau changent de structure. Ainsi, des fissures apparaissent à cause des contraintes engendrées par le refroidissement rapide de la surface. Leur présence affecte la tenue en fatigue de la pièce au cours de son utilisation. Plus récemment, Jones [START_REF] Jones | Thermomechanical processing of Ti-5Al-5Mo-5V-3Cr[END_REF] a étudié l'impact de la température sur la structure du Ti-5-5-5-3. À température ambiante, cet alliage de titane présente une structure métastable. Cette structure évolue vers une structure + dès le franchissement du -transus au alentour de 845°C. Les sollicitations mécaniques et thermiques dues à l'usinage provoquent une dilatation uniquement de couche superficielle du matériau usiné. La différence de dilation entre les couches du matériau crée des contraintes résiduelles. Une existence maitrisée de ces dernières (des contraintes résiduelles trop importantes engendrent une surface fissurée) améliore les propriétés mécaniques du matériau. En chauffant le Ti-6-4, Germain [START_REF] Germain | Contribution à l'optimisation du procédé d'usinage assisté laser[END_REF] a constaté une évolution des contraintes résiduelles en surface en fonction de la température atteinte. En effet, les contraintes résiduelles dues à la traction augmentent au dépend de celles dues à la compression. Toutefois, les contraintes résiduelles globales en valeur absolue diminuent ce qui dégrade la tenue en fatigue du matériau. Les travaux réalisés jusqu'à aujourd'hui par les chercheurs se limitent à étudier l'influence de l'augmentation de la température sur les efforts de coupe, la durée de vie des outils, la ductilité, l'intégrité de surface du matériau indépendamment. Cependant, elles ne permettent pas de dégager un constat global et industriel en comparant les apports de cette technologie sur l'usinabilité par rapport à ses inconvénients. L'objectif de nos travaux est de compléter la littérature pour affirmer si le chauffage du Ti-5-5-5-3 représente une voie d'amélioration et d'optimisation de l'usinabilité et si elle est industrielle.

Dispositif expérimental

Le dispositif expérimental permettra de réaliser des essais de coupe en tournage du Ti-5-5-5-3 tout en pilotant une température stabilisée de la pièce à usiner. Les entrées du système étudié seront la température et la matière (les paramètres de coupe, l'outil et les conditions d'enlèvement de matière seront des constantes), la variable de sortie sera l'effort sur l'outil. Le mode opératoire consistera à amener la pièce à une température maitrisée, à réaliser l'usinage et récupérer l'effort de coupe. Ce mode opératoire sera conduit pour différente température. La zone usinée sera un embout de matière saine changée à chaque essai d'usinage. Le choix des outils de coupe ainsi que des conditions de coupe est déterminé selon une étude antérieure détaillée dans [START_REF] Wagner | Experimental study of coated carbide tools behavior[END_REF] donnant un résultat optimal à température ambiante, cependant ces conditions ne sont pas déterminantes puisque l'objectif est d'observer un différentiel d'effort et non de rechercher un optimum. En observant le cycle de traitement thermique du Ti-5-5-5-3, trois zones de comportement du matériau sont clairement identifiées en fonction de la température (Figure 3) : la première zone correspond aux températures inférieures à 300°C, l'usinage à chaud ne devrait rien apporter car le Ti-5-5-5-3 est dans sa zone stable d'utilisation. Entre 300 et 640°C, la zone de relâchement des contraintes semble particulièrement intéressante. En effet, c'est dans cette zone où des perspectives de réduction des efforts de coupe et d'usure d'outil sont attendues. La dernière zone correspond aux températures au-delà de 640°C, on assiste à des modifications microstructurales irréversibles qui affecteront les caractéristiques mécaniques du matériau. Par conséquent, tout le matériau chauffé au dessus de 580°C doit être enlevé par l'opération de coupe. Les essais à réaliser sont des essais de tournage sous des températures très élevées, cette température doit être maintenue durant l'usinage. Pour répondre à cette contrainte, le dispositif expérimental est composé d'un inducteur de forme semi-circulaire « pancake » enveloppant partiellement la pièce pendant le tournage, conçu spécifiquement. La géométrie de la pièce tournante a été construite pour intégrer des thermocouples à l'intérieur au plus près de la zone de coupe. La récupération des signaux des thermocouples pendant le tournage passe par un collecteur tournant traversant la broche du tour. Une caméra thermique complémentaire a été utilisée pour confronter ses mesures de température aux mesures données par les thermocouples. L'outil de coupe est monté sur un dynamomètre Kistler pour mesurer les efforts de coupe pendant l'usinage. La Figure 4 illustre le dispositif utilisé pour les essais. Pour les essais, un protocole de montée et de maintien en température de la pièce en rotation dans l'inducteur, avec mesure de la température avec les thermocouples et la caméra thermique à permis de figer la procédure de chauffage (comment garantir la stabilisation de la pièce à la température souhaitée). La phase d'essais de coupe consistait à appliquer le protocole de chauffe et de maintien à température établi et d'effecteur les essais de coupe orthogonal tout en de collectant les mesures d'efforts. Le risque important d'inflammation du titane et la manipulation d'élément chaud ont été entourés de précautions importantes, avec des consignes de sécurités drastiques (vidage du bac à copeaux, carter de sécurité, présence d'un extincteur, périmètre de sécurité…)

Présentation des résultats expérimentaux et discussion

À partir des conditions de coupe et d'outil de coupe dans [START_REF] Wagner | Experimental study of coated carbide tools behavior[END_REF], les paramètres de sortie mesurés sont les efforts de coupe, l'usure de l'outil, la dureté de la surface après usinage ainsi que la rugosité de la surface obtenue.

Efforts de coupe

Le Tableau 1 représente l'évolution des efforts et du coefficient spécifique de coupe en fonction de la température.

Tableau 1 : mesure des efforts en fonction de la température En observant la Figure 5, on remarque que l'évolution des efforts de coupe et du coefficient spécifique de coupe présente 3 phases : pour des températures inférieures à 100°C, l'effort reste constant. Entre 100°C et 500°C, la diminution de l'effort est faible. Elle devient conséquente dès que l'on dépasse les 500°C. En ne considérant que le paramètre coefficient spécifique de coupe, c'est cette zone, qui présenterait un intérêt à l'optimisation de l'usinabilité. La diminution des efforts de coupe grâce à l'augmentation de la température initiale du matériau s'explique par l'adoucissement thermique du matériau. La loi de comportement du matériau (loi de Johnson-Cook) dans la zone de coupe confirme cette tendance présentée par l'équation (1).

()

0 00 .1 l n .1 m n f TT AB C TT ε σε ε - =+ + - - (1)
avec, σ : contrainte, ε : déformation,

Usure d'outil

Pour les trois phases de températures identifiées, des essais d'usures, en coupe quasi orthogonale, ont été effectués. À température ambiante (pièce à 25°C), on constate un léger écaillage sur la face de coupe à la limite de la profondeur de passe. Cette dégradation est liée à une dureté du matériau (écrouissage de la matière dans la passe). Cet écrouissage ne peut avoir lieu qu'à basse température. Lorsque la température augmente, un second mode de dégradation est observé : une arête rapporté se développe d'autant plus importante que la température initiale est haute (Figure 6). Ce mode s'explique par la ductilité du matériau à un niveau de température élevé, le copeau se colle à la face de coupe et refroidit rapidement pour se souder à la plaquette. Sur la face de dépouille, l'usure n'est remarquable que pour l'essai à une température de 750°C. La micro-dureté est représentative de l'intégrité de surface (état de santé) du matériau. Lors de l'usinage, le matériau est écroui en surface et les sollicitations de l'outil génèrent des contraintes résiduelles. Si cet écrouissage est important, le matériau est fragilisé. Des fissures peuvent alors apparaître et diminuer la résistance en fatigue de la pièce. L'influence de l'assistance thermique lors de l'usinage est faible. La micro dureté a tendance à augmenter avec la température de chauffage, mais très faiblement (40 Vickers). Au-delà de 500°C, la structure est modifiée, entraînant de fortes variations de la micro-dureté sur la surface. Cette augmentation de la dureté s'explique par la modification de la structure à haute température.

Rugosité

La Figure 8 montre l'évolution de la rugosité en fonction de la température. La rugosité passe de Ra 1 ,6 à Ra 0,8 pour des usinages réalisés à des températures supérieures à 200°C. Cette diminution peut s'expliquer par la ductilité plus importante du matériau lors de l'usinage à haute température.

Figure 8 : influence de la température sur la rugosité Ra de la surface usinée

Conclusion et perspectives

L'objectif de cet article est d'étudier l'influence de la température sur l'usinabilité du Ti5-5-5-3. Lors de ces travaux, un système d'assistance thermique par induction a été conçu. En se basant sur des conditions de coupes définies dans une étude antérieure, l'impact de la température sur le coefficient spécifique de coupe, la durée de vie des outils et l'intégrité de surface a été étudié. Une réduction de 13% du coefficient spécifique de coupe pour une température de 500°C par rapport à la température ambiante a été chiffrée. Pour une température de 750°C, le gain atteint 34%, toutefois, la structure du matériau est irréversiblement modifiée et la durée de vie des outils est réduite. Afin de palier à cette limitation, un système de chauffage plus localisé (de type laser) pourrait être utilisé. Par conséquent, la zone juste en amont de l'outil serait chauffée à des températures supérieures à 750°C et ensuite intégralement usinée, l'outil pourrait être refroidi à l'intérieur par cryogénie. Une autre voie d'optimisation est possible : varier la vitesse de coupe qui a été figée lors de cette étude (égale à V c,min déterminée à la température ambiante). En effet, V c,min varie en fonction de la température. Enfin, comme nos travaux se sont limités à la mesure de la micro-dureté de la surface, une étude plus approfondie de l'intégrité de surface sera réalisée.

Figure 3 :

 3 Figure 3 : gamme de traitement thermique du Ti-5-5-5-3

Figure 4 :

 4 Figure 4 : Dispositif expérimental

0

  εε : vitesse de déformation plastique sans dimension, 0 T : température ambiante et f T : température de fusion et A, B, C, n et m : constantes. Dans la loi, m > 1. Par suite, si la température T du matériau augmente, la contrainte et donc l'effort de coupe diminuent, et inversement.

Figure 5 :

 5 Figure 5 : Évolution des efforts de coupe et de Kc en fonction de la température

Figure 6 :

 6 Figure 6 : Observation du phénomène d'usure sur la face de coupe

Figure 7 :

 7 Figure 7 : influence de la température sur la dureté Vickers de la surface usinée


Andrei Popa

Vincent Dutilh

Maher Baili

Gilles Dessein

Géraldine Perrin

IDENTIFICATION OF INFLUENT FACTORS ON SURFACE INTEGRITY IN NICKEL-BASE SUPERALLOY DRILLING

Keywords: Machining of Nickel base Alloy, Process Monitoring, Pearson, statistical methods, drilling

For the critical rotating components in aeronautical industry, the metallurgical quality achieved after machining conditions could determine their mechanical behaviour in fatigue. To guarantee this quality, the tools, materials and cutting conditions are frozen during the validation process by a cutup part following by an acceptable surface integrity. Even with the fixed parameters, perturbations can occur during the process and may have a direct impact over the metallurgical quality through the apparition of anomalies, which could reduce the calculated fatigue life. The aim of this study is to define a Process Monitoring technique able to detect the thickness affected by the machining taking into account the flank wear effect.

INTRODUCTION

The increase of turbine aero engines performances requires materials with remarkable mechanical strength at high temperature, such as UDIMET ® 720 or INCONEL718. UDIMET ® 720 shows important advantages, in terms of corrosion resistance (Cr), mechanical properties and oxidation behaviour (Ti, Al and Co to stabilize phase). The material properties and the machining characteristics lead Ezugwu [START_REF] Ezugwu | Key improvements in the machining of difficult-to-cut aerospace superalloys[END_REF] to classify this material as "difficult-to-machine". The low thermal conductivity of this material leads to high cutting temperatures at the rake face which accelerates tool flank wear. The tendency of the γ matrix to work hardening and the rapid flank wear leads to a built-up edge formation. Built-up edge has consequences on surface roughness [START_REF] Kwong | The sensitivity of Ni-based superalloy to hole making operations: Influence of process parameters on subsurface damage and residual stress[END_REF].

Respecting the surface integrity is one of the most important requirements in aerospace industry. The anomalies generated by machining could have an influence on the part fatigue behaviour. Some papers deal with the influence of the "white layers" or residual stresses on fatigue life [START_REF] Perrin | Etude metallurgique, mecanique et thermique de l'integrité de surface des pieces percees au foret helicoidal dans l'Inconel 718TR-Detection et quantification des anomalies par Process Monitoring[END_REF][START_REF] Sharman | Tool life and surface integrity aspects when drilling and hole making in Inconel 718[END_REF]. It was demonstrated that anomalies such as smearing, shear band or heavy distortion can reduce the fatigue life from 1E+01 to 1E+02 cycles [START_REF]Integrating Process Controls with Manufacturing to Produce High Integrity Rotating Parts for Modern Gas Turbines[END_REF] (Inconel 718 and TA6V samples where used). 1, Université de Toulouse, INPT-ENIT, Laboratoire Génie de Production -47 avenue d'Azereix -65016 , Tel 0033562442725, e-mail : andrei.popa@enit.fr 2, Turbomeca Tarnos, avenue de 1 er mai 40220 TARNOS, e-mail : Vincent.dutilh@turbomeca .fr 3, Université de Toulouse, INPT-ENIT, Laboratoire Génie de Production -47 avenue d'Azereix -65016 , Tel 0033562442725, e-mail : maher.baili@enit.fr 4, Université de Toulouse, INPT-ENIT, Laboratoire Génie de Production -47 avenue d'Azereix -65016 , Tel 0033562442725, e-mail : gilles.dessein@enit.fr 5, Turbomeca Tarnos, avenue de 1 er mai 40220 TARNOS, e-mail : geraldine.perrin@turbomeca .fr

The detection of machining process anomalies using output signals from different systems shows, in the last years, one important area for the scientists and end users. The physical dimensions are mostly used in order to control the machining process. Spindle power changes, vibrations signature and forces can detect tool flank wear [START_REF] Kaye | Predicting tool flank wear using spindle speed change[END_REF][START_REF] Choudhury | Tool wear measurement in turning using force ratio[END_REF], the burr [START_REF] Peña | Monitoring of drilling for burr detection using spindle torque[END_REF] or problems of the machine-tool (spindle bearings). Some correlations between the spindle power and surface roughness or metallurgical changes are treated by Dutilh [START_REF] Dutilh | Links between machining parameters and surface integrity in drilling Ni-superalloy[END_REF].

The different statistical methods (Design of Experiments for example) permit to quantify the influence of the cutting parameters on surface or subsurface [START_REF] Gaitonde | Taguchi optimization in drilling of AISI 316L stainless steel to minimize burr size using multiperformance objective based on membership function[END_REF][START_REF] Gravier | The use of linear regression methods and Pearson's correlation matrix to identify mechanicalphysical-chemical parameters controlling the microelectrochemical behaviour of machined copper[END_REF]. Once the most important parameters identified, the linear relations between the terms could be determined with Pearson correlations and further, the linear regression can establish the relations between variables [START_REF] Gravier | The use of linear regression methods and Pearson's correlation matrix to identify mechanicalphysical-chemical parameters controlling the microelectrochemical behaviour of machined copper[END_REF]. Regarding the important number of physical dimensions, criteria and surface integrity anomalies, the choice for using statistical methods is justified considering the large number of variables to correlate. (Table 1). Automating the analyses, this model will help us to see which factors have an important contribution to generate an unacceptable surface integrity and make further Process Monitoring proposals. In the same direction, European Project ACCENT (Adaptive Control of Manufacturing Processes for a New Generation of Jet Engine Components) tries to develop new Process Monitoring systems to control the fabrication process and also to reduce the validation costs.

Through an experimental approach, the impact of machining disturbances on the surface integrity and monitoring signals is studied. Using a statistical method, a model is proposed for monitoring in "real time" of the thickness affected by the machining, taking into account the flank wear behaviour.

EXPERIMENTAL WORK

Work material and equipment

The parts on which we carried out trials were ∅80 mm forged bars, usually used as raw materials before forging turbine discs. These bars have the same heat treatments as the discs (solution Heat Treatment and aged) to obtain the nearest routine mechanical properties to the original discs (same microstructure, same grain size 8 ASTM, and same hardness 410 HV30).

The tool is a ∅15.5 mm drill Iscar Chamdrill with an interchangeable TiAlN coated carbide head. This drill has the particularity of having a very short margin (4 mm), which avoids anomalies generated by frictions all along the hole.

The operation is a drilling in a pre-hole of ∅13 mm with the hole length of 37 mm.

Experimental setup and measuring instruments

All the trials were made on a HURON KX10 3-axis vertical milling center using an 18kW spindle motor and a Siemens 840D numerical controller.

The machine-tool was instrumented by a 4 component Kistler dynamometer (Fx, Fy, Fz and Mz), and three accelerometers placed following the directions X, Y and Z (Fig. 1). The spindle power, the position of Z axis, the spindle current intensity and the three axes current intensity are recorded through the Siemens Profibus.

Fig.1. Experimental set up

Metallographic examinations were carried out on all the experiments with an optical microscope (Olympus GX51), a scanning electron microscope (SEM-FEG JEOL 7000F) and a micro-hardness tester (SHIMADZU HMV).

Experimental procedure

The present paper is part of an important study on drilling Nickel-base superalloys which takes place in the European Project ACCENT. It presents several steps, as it follows:

-In a first time [START_REF] Dutilh | Links between machining parameters and surface integrity in drilling Ni-superalloy[END_REF], combining the cutting conditions according to the classic criteria established by the French specification AFNOR E66-520 (Couple-Tool-Material) and the criteria of surface integrity, an Acceptable Surface Integrity Domain is defined (ASID-Fig. 2). This "window" was established exploring different values of the cutting speed and feed rate and regarding to the specific cutting forces Kc, the tool wear, roughness, hole geometry, without ' dissolute layer and to minimize the distorted layer.

-A second experimental campaign [START_REF] Dutilh | Impact of disturbed drilling conditions on the surface integrity of a Nickel-base superalloy[END_REF] treats the impact of a cutting fluid interruption on the surface integrity and on the Process Monitoring signals.

-In this paper, a new experimental campaign is considered. Based on the results of the first tests, new trials were performed in order to understand the influence of machining disturbances (hardening changes of the material, tool position defect or cutting fluid emulsion variation) on the surface integrity and signals.

Fig. 2. Acceptable Surface Integrity Domain and operating points

In order to study the influence of the cutting parameters and interactions between them on the ASID, the trials were performed according to a Fractional Experimental Design with 2 levels (-1 or 1) for each one of the fives factors (cutting speed, feed rate, material hardness, position defect and cutting fluid emulsion). We chose to alias a factor with the interaction of order 4 to reduce the number of trials to 16 experiences and get a 2 (5-1) The hardness H1 is 6% under the hardness H2. This variation was generated by changing the aging treatment but the microstructure is similar (grain size and γ' phase proportion).

The tool position defect was generated with an x axis displacement compared to the pre-hole. The value was fixed at 0.05 mm which corresponds to twice the value of the production limit. The emulsion variation was established as the limit acceptable in production. The maximum percentage was fixed according to the example of the industrial situation. The cutting conditions parameters used in the industrial applications cannot be disclosed, so the confidential values are changed by indicative variables.

FRACTIONAL EXPERIMENTAL DESIGN RESULTS

The surface integrity of each hole was characterized by the thickness of the ' dissolute layer (Figure 3), the distorted layer, the presence of plucking and smearing, the burr and the micro-hardness value observed at 40 µm from the surface.

The analysis of the experience plan shows that the influencing parameters on the two types of layers and plucking are the emulsion, the hardness and cutting conditions.

The main influential factors on flank wear are the cutting speed and the interaction between the hardness and position defect (Figure ). The evolution of the tool flank wear is significant (even three times between tests). The position defect does not lead to global anomalies on the entire length of the hole or premature degradation of the tool, but local defects can be observed (Figure 5). This type of anomaly is not always visible.

The analysis of the experimental plan shows that the run out has an influence on the smearing and microhardness but given the random distribution of the chips and the large dispersion of micro-hardness measurements, will not be considered in this study. The apparition of the ' dissolute layer is connected with the evolution of the emulsion and the material hardness.

The thickness of the ' dissolute layer varies with the cutting conditions and hence the cutting forces (this observation was also made during the study of the establishment of the ASID). Contrary to the ' dissolute layer, the distorted layer (corresponding to a layer where the ' phase are elongated) is correlated with a more important hardness. On the other hand they evolve in the same sense for the feed and emulsion. Those results have to be balanced with the experimental examination methodology. In the case of the distorted layer, the examination is difficult and it is submitted to the appreciation of the examiner which classify holes by grades (5, 10, 15, 20 µm distorted). Maybe this type of examination has to be completed by a more objective analysis as microhardness measurement. The results obtained are very instructing and at the same time surprising (the emulsion which is the most influent factor on the thermo-mechanically affected layer) but could be due to the scattering regarding the measures or maybe to the experimental design type. Indeed the factor effects are not pure and even if the interactions orders 4 are neglected, the interactions order 3 (summed with interactions order 2) must be included in the study. Hereafter is difficult to determine which is the most influent between the interaction order 3 and order 2. Further analyses will be done in order to verify and understand better these relations.

Furthermore, the sum of two types of layers (sum of the distorted layer and the ' dissolute layer) will be considered in this study (Figure 7) in order to facilitate future analysis and to define a Process Monitoring technique able to estimate in real time the thickness affected by the drilling operation.

Figure 6. Thickness of affected layer by drilling

The first analyses of the experimental plan were made in order to understand the influence of the cutting parameters on the surface integrity. Now, the impact of the parameters on the process monitoring signals will be study.

Among all the signals and the cutting conditions parameters, the bests correlations could be made between the Position and the Mean values for Fy and Fx (visible by analyzing the experimental plan and at the same time with Pearson Correlations -table 3). The defect has been introduced artificially on the x axis and it is easy to understand the contribution of the position following Fx. Detecting the defect on Fy suggests that another defect of position or run-out at least as important as the one introduced. For the same reason, the defect of position couldn't be put in evidence by frequency analysis (observation of the frequency rotation and harmonics). This shows that the position defect was not important enough in order to generate a meaningful variation of the surface integrity and on the Process Monitoring signals.

These experimental trials show that the ASID (Acceptable Surface Integrity Domain) defined for one context (one emulsion percentage, hardness), may not be exactly the same for another context. If we consider only the tests for a 7.5% emulsion and that one compares with results achieved for the second hardness could be observed a relation between the M z couple and the thickness of the thermo-mechanically affected layer (same relation already observed by Dutilh [START_REF] Kwong | The sensitivity of Ni-based superalloy to hole making operations: Influence of process parameters on subsurface damage and residual stress[END_REF] and Perrin [START_REF] Kaye | Predicting tool flank wear using spindle speed change[END_REF] -Fig. 7). Nevertheless, this relation proves to be confirmed only for parts presenting hardness H1. The cutting conditions explored do not permit to verify if the efforts observed have the same evolution of the thickness for hardness H2. This model does not take into account the defect of position because we observed previously that this one does not have an influence on the thermo mechanically affected layer.

PEARSON'S CORRELATIONS

Alongside the experimental plan analyses, another statistical method was introduced in this study, because our purpose was to modeling a surface integrity anomaly as a function of Process Monitoring signals and not using controllable parameters.

The Pearson's correlation matrix describes the correlations among the variables (cutting parameters, surface integrity criterion and the physical measures). It is a square symmetrical P x P matrix with the diagonal elements equal to unity (correlations of variables with themselves). The correlation coefficient (r p ) represents the linear relationship between two variables and the values are between -1 and 1 (0-no correlation; ±1 high correlation). A database was defined using three types of parameters: -Which can be measured during machining (physical dimensions and all the statistical values extracted for each signal); -Which can be measured after the machining (surface integrity criteria); -The wear can be an input parameter (the surface generated with a worn tool is different than machining with a new tool) or an output parameter (the influence of the wear on the recorded signals). It is difficult to treat and for this reason will be an observation.

For each case of the database we will search the influential factors using Pearson's Correlation.

This method comes to confirm the results obtained by analyzing the experimental plan. For example, the fact that the position defect doesn't have an influence on the apparition of the affected layer is shown by correlation coefficient rp=0.09. In the case of this study, when the Pearson's Correlation is used, the intensity between two variables is not so important due exactly to the fact that this statistical method does not take into account the interactions between variables.

MODEL

The linear matrix gives information about the factors which have to be considered in the different models. Some high correlation coefficients can be observed in the Table 3 corresponding to affected layer column. To define a model able to estimate the thickness affected by the drilling operation, it is necessarily to consider only the terms having a high correlation coefficient (Mz, SD Fz , SD Fy , SD Fx, and Flank Wear-Table 3). Also, for this model, the most important interaction between cutting parameters (Figure 5) will be taken into account. The emulsion and the feed rate are important factors in Figure 5 and Table 3. The Mean Power has an important coefficient (Table 3) but will not be considered in the study (it is already tested and is not improving the model).

So

⋅ ⋅ β + ⋅ β + ⋅ β + ⋅ β + ⋅ β + ⋅ β + ⋅ β + ⋅ β + ⋅ β + β =
Regarding these terms, the emulsion, hardness and tool position can be measured before the machining, the torque, the forces along the three directions can be monitored with a dynamometer. The spindle current can be monitored using the NC of the machine tool, but the flank wear could be measured only at the end of the process. To reach the goal of this model, in a first time the tool wear flank should be expressed as a function of process monitoring signals. Coming back to the matrix correlations, we search the most influent factors on the flank wear. For this model, three factors will be taken into account considering the highest values (the standard deviation for the axial force Fz and the mean value for the power and torque), having the expression:

) 2 ( Mean SD Mean Wear Flank Power 4 Fz 3 Mz 2 1 ⋅ α + ⋅ α + ⋅ α + α =
But, the power was obtained using the expression:

) 3 ( V F 2 M Power f z z ⋅ + π ⋅ ω ⋅ =
The coefficients 1 , 2 , 3 and 4 are identified using a multiple regression. Replacing the coefficients with their values and the power expression, the model will be: Some remarks can be made regarding the Figure 8: 1. The mean error between the model and the measured values is 2.7% and a standard deviation of 20%.

2. Some trials have a high error and this could be explained by the fact that the terms of the model were chosen regarding the highest linear correlation coefficients and the interactions between different cutting parameters are neglected by the statistical method. As observation, an important error is registered for the tests having H1 hardness and no position defect (exactly the interaction presented in Figure ).

Once the wear behaviour is known, the next step is to insert (3) in the expression of anomaly (1). The coefficients 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , and 10 were founded using the multiple regressions. The black line represent the values measured for the affected layer thickness. This one is compared with the model obtained-red line. The mean error is 0.24% and the standard deviation 8.3%.

⋅ ⋅ - ⋅ + ⋅ - ⋅ + ⋅ - ⋅ + ⋅ + ⋅ - ⋅ - - =
The measure error for the affected layer is around 2 µm.

This model could be a first step in order to develop some Process Monitoring tehcnics capable to detect anomalies in "real time".

However, it is important to notice that this model could be used only for the cutting parameters tested in these tests. Even if the results obtained are good, maybe the linear model is not the best the choice. Also, a simplification for the model could be one of the next steps (a Student Test was applied to verify if the terms are influential). But, a simplified model, leads to an important error. For this reason, we have to find a way to improve the model.

For instance, only global analsys were performed. Futures researches will be focused on local analysis and also the accelerometers signals will be considered.

The implementation of this process monitoring strategy in the industrial area it is difficult. The fitting of machine tools with dynamometers will generate high costs and therefore futures researches will try to define new simples systems. As an example, the dynamometer's outputs (F x , F y , F z and M z ) could be replaced with the signals from NC of the machine tool (the current for the three axes and the spindle power signal).

CONCLUSIONS

This paper presents the results obtained from an experimental campaign where some machining disturbances were tested (hardening changes of the material, tool position defect or cutting fluid emulsion variation). The trials were monitored with a four components dynamometer, a Siemens signals recorder and three accelerometers. Metallurgical analyses were performed on the holes produced in order to identify and quantify surface integrity anomalies.

Using a statistical approach, a model able to detect the affected layer thickness by the drilling was defined. For the monitoring systems outputs and surface integrity anomalies were defined different criteria. With the Pearson's correlation, the most important factors on the affected layer were defined. One of the highest correlations corresponds to the flank wear. The tool flank wear was expressed as a function of PM signals and then introduced in the affected layer equation. In the end, the thickness of layer affected is a function depending only on physical measurements and cutting parameters.

Moreover, the evolution of the affected layer with the torque M z could be a way to monitor the machining. But, it has to be taken into account the influence of the material hardness regarding the effects on the apparition of anomalies.

  resolution 5 plan. If the five parameters are noted A, B, C, D, E, the alias structure is: A+BCDE; B+ACDE; C+ABDE; D+ABCE; E+ABCD; AB+CDE; AC+BDE; AD+BCE; AE+BCD; BC+ADE; BD+ACE; BE+ACD; CD+ABE; CE+ABD; DE+ABC.

Figure 3 .

 3 Figure 3. Pareto Chart for the main effects on tool flank wear

Figure 4 .

 4 Figure 4. Example of surface integrity anomalies due to the position defect

Figure 5 .

 5 Figure 5. Pareto chart of the effects on affected layer

Figure 7 .

 7 Figure 7. Thickness evolution of ' dissolute layer vs torque Mz

  The results of the flank wear model are compared with the measured values in the figure below.

Figure 8 .

 8 Figure 8. Comparison between measured values for the flank wear and the model

)

Figure 9 .

 9 Figure 9. Comparison of the measured values and the model for the affected layer thickness

Table 1 . Variables to correlate Physical dimensions

 1

		Criteria	Surface
		extracted for	integrity
		each physical	anomalies
		dimension	(examples)
			Thickness of the
	Spindle Power (P), Torque (Mz), Forces (Fx, Fy, Fz), Accelerelations (Ax, Ay, Az), Spindle Current	Mean Value, Standard Deviation [SD], RMS, Skewness, Kurtosis	Thermo-mechanically affected layer, smearing, , burr length ,micro-hardness
			deviation, etc

Table 2 . Experimental Design

 2

	level	Cutting speed	Feed rate	Material hardness	Position over the hole before	Cutting fluid emulsion
					[mm]
	-1	Vc1	f1	H1	0	7,5
	1	Vc2	f2	H2	0,05	12,5

Table 3 . Examples for the linear matrix

 3

	Variables	Affected layer	Flank Wear	Margin Wear
	Cutting speed	-0.01	0.53	0.4
	Feedrate	0.47	0.29	0.28
	Position	-0.09	0.31	0.39
	% Emulsion	-0.51	-0.16	0.28
	Material Hardness	0.16	-0.07	0.43
	Mean Mz	0.55	0.66	0.49
	SD Fz	0.56	0.85	0.43
	SD Fy	0.57	0.38	0.23
	SD Fx	0.54	0.3	0.26
	Flank Wear	0.62	1	0.33
	Margin Wear	0.025	0.33	1
	Mean Ispindle	0.54	0.6	0.5
	Mean Power	0.38	0.76	0.58

ACKNOWLEDGMENTS

The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2011) under grant agreement number 213855.