Wear resistance and induced cutting damage of aeronautical FRP components obtained by machining

Wear 271 (2011) 2542–2548

Contents lists available at ScienceDirect

Wear journal homepage: www.elsevier.com/locate/wear

Wear resistance and induced cutting damage of aeronautical FRP components obtained by machining L. Lasri a , M. Nouari b,∗ , M. El Mansori c a Laboratoire de Mécanique Energétique et Procédés (L.M.E.P.), Université Moulay Ismail, Ecole Nationale Supérieure des Arts et Métiers (ENSAM), Marjane 2, BP 4024 Beni Mhamed, 50000 Meknès, Maroc b Laboratoire dˇıEnergétique et de Mécanique Théorique et Appliquée, LEMTA CNRS-UMR 7563, Ecole Nationale Supérieure des Mines de Nancy (ENSMN), GIP-InSIC, 27 rue d’Hellieule, 88100 Saint Dié des Vosges, France c Laboratoire de Mécanique et Procédés de Fabrication, LMPF EA-4106, Arts et Métiers ParisTech, Rue Saint Dominique BP 508, 51006 Châlons-En-Champagne, France

a r t i c l e

i n f o

Article history: Received 31 August 2010 Received in revised form 23 November 2010 Accepted 23 November 2010

Keywords: FRP composites Wear resistance Dual fracture Induced-cutting damage FE progressive damage analysis

a b s t r a c t A cutting induced-damage process involving matrix cracking, fiber fracture and interlaminar delamination often occurs when machining composite materials. Compared to metals, relatively little research has been carried out in this topic. Generally, damage mechanisms in machining composites include four types of wear modes: transverse matrix cracking, fiber–matrix interface debonding, fiber rupture and inter-ply delamination. The surface quality plays an important role in the improvement of fatigue life and wear resistance of composite components. In the case of high speed machining composite materials, the surface quality of the finished product may be improved by modifying the machining parameters. Due to the complex nature of this process, we focus here on the effect of cutting parameters on surface damage of the machined component and thus wear resistance. The later has been predicted using dynamic explicit finite element method. In this investigation a progressive failure analysis has been adopted for analysing damage process within the fiber reinforced polymer (FRP) workpiece. After damage is detected, selective stiffness degradation is applied to the workpiece material. It has been shown in this study that matrix cracking and interface shearing occur first, followed by wear of fibers. The damage progression in the matrix and interface occurs in parallel directions to the fiber axis. A random growth of fiber fracture has been observed and mainly localized in a plane with a specific direction. The effect of fiber orientation on wear resistance of the composite structure and cutting induced damage process has been investigated. Damage progression was found to be strongly influenced by the fiber orientation of the FRP composite. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Machining processes such as trimming, milling or drilling are frequently used to achieve dimensional tolerance and assembly requirements. Previous works have shown that machining fiberreinforced polymer composites (FRP) materials differs significantly in many aspects from machining conventional metals and their alloys [1–7]. This is due to the heterogeneity and anisotropy of FRP materials. A cutting induced-damage process involving matrix cracking, fiber fracture and interlaminar delamination often occurs when machining this kind of materials. Compared to metals, relatively little research has been carried out in this topic. From an experimental point of view, several studies have been highlighted that machining composites exhibits interactions between different physical parameters. Koplev [3,6] was the first author to conduct a series of experiments under orthogonal cutting of carbon

∗ Corresponding author. Tel.: +33 329422226; fax: +33 329421825. E-mail address: [email protected] (M. Nouari). 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2010.11.056

reinforced polymer composites. It has been found that the chip formation occurs trough a series of successive ruptures and strongly controlled by the fiber orientation. Other authors such as Wang et al. [4] and Arola et al. [5] have been analysed the influence of the tool geometry, the damage process and the fiber orientation on the cutting forces and surface roughness. It was found from their experimental results that the mechanisms of chip formation primarily depend on the fiber orientation with only secondary effect for tool geometry and cutting conditions. An important result also shows that the chip is formed by brittle fracture inside the composite structure. Primary fracture occurred through fiber failure, not interlaminar shear failure, followed by secondary fracture which occurred in the fiber/matrix interface. A discontinuous shape of chips has been noted with different tool-material combinations. Although useful, the experimental approach is not cost effective and provides limited information on the mechanics governing material removal. Therefore, numerical modelling has recently been adopted to better understand the machining of FRP composite materials. Some of them are macromechanical type, based on the “Homogeneous Equivalent Material” (HEM) assumption and

L. Lasri et al. / Wear 271 (2011) 2542–2548

use a dual fracture criterion. These approaches predict the chip formation and sub-surface damage in the workpiece for different cutting conditions. However, these models impose the fracture path in composite structure before starting the machining process [8–10]. Generally, damage mechanisms in machining composite materials include four types of failure modes: transverse matrix cracking, fiber–matrix interface debonding, fiber rupture and interply delamination. The progression of these damage modes during the chip formation process have been analysed by numerical means in several previous studies [8,11]. It has been found from these studies that transverse matrix cracking and interface debonding are the first damage modes developed in the composite structure during chip formation. The damage progresses then until the free surface of the workpiece. The chip formation process is completed when the fiber is broken. The objective of this study is to develop a finite element modelling to analyse the physical mechanisms responsible of the chip formation process during machining the unidirectional FRP composites. As showing in the literature on this topic, ABAQUS/Standard FE code has been the most code used in previous works [8,11]. However, simulations with this implicit procedure often show a large CPU time consuming and many problems of convergence. Using explicit FE procedure can then help to overcome these difficulties [12]. In this work, numerical computations are conducted using the concept of stiffness degradation. The comparison between the results obtained with different failure criteria has been shown that the Hashin criterion is the criterion which reproduces the best results. Thus, to analyse the effect of fiber orientation on the workpiece behaviour, this criterion has been adopted in this work. Damaged-mechanical behaviour has been implemented in 2D numerical model using the “User Material VUMAT subroutine”. The material properties are degraded depending on which set of failure criteria is used: matrix cracking, fiber–matrix debonding due to in-plane-shear or fiber breaking. Further, the damage initiation state and its progression inside the workpiece material during machining process have been simulated. Cutting induced damage has been computed and compared with experimental data. 2. Progressive damage behaviour of FRP composites The experimental observations conducted by several authors like Koplev [3,6] and Wang et al. [4] showed that composite chips are formed through a series of brittle fractures under high mechanical loading. Consequently, we consider in this work that during machining process, a brittle behaviour dominates during the chip formation process. To analyse the later, it is necessary to consider some physical phenomena produced during the machining process of composite materials. To produce the various induced damages responsible for chip formation, the Hashin criterion has been adopted. When a failure occurs, the material properties are degraded as shown in Table 1 [11]. Note that the stresses involved in equations given by Table 1 are written in the principal material coordinate system. In the present analysis, the material properties depend on three solution defined variables, noted SDV [12]: • the first solution defined variable noted SDV1 represents the matrix failure index (tensile and/or compressive), • the second SDV2 represents the fiber–matrix shear failure index, • and the third SDV3 represents the fiber failure index (tensile and/or compressive). As depicted in Fig. 1, at the beginning of the analysis, the solution defined variables are set equal to zero in all integration points and the material properties are equal to their initial values. Then, the

2543

tool advancement generates an increased mechanical loading. For each displacement increment, several iterations are needed before the simulation converges to an equilibrium state. At the end of each increment, stresses and failure indices of equations shown in Table 1 are computed at the integration points of each element. If the failure index exceeds 1, the associated user-defined field variable SDV is set equal to 1 and remains at this value until the end of the process, the material properties are automatically reduced to zero according to the implemented stiffness degradation scheme, see Table 1. The procedure is repeated until the complete chip formation. Indeed, in each case of fiber orientation, tool geometry and cutting condition, tool displacement was extended until the verification of the fiber–matrix shear failure criterion on the free surface of the workpiece and the verification of fiber failure criterion (tensile or compression failure) at anywhere in the workpiece. The applied degradation rules correspond to a brittle failure with no energy absorption. As said before, the assumption of brittle failure has been previously confirmed through experimental observations conducted by Wang et al. [4] and Arola et al. [5,8]. The SDV variables are not independent. The failure criteria used here and the progressive damage model were implemented using VUMAT subroutine. The later allows to the material properties to be a function of the SDV variables, which themselves can be a function of any material point (Gauss point) quantity such as stress, strain, etc. The progressive damage algorithm (Fig. 1) illustrates that the stresses from the previous increment are called into the subroutine at the beginning of the current increment and used to evaluate failure criteria (Table 1). Once the failure criteria are verified, the field variables are updated and used to reduce the material properties to 5% of their original value according to the scheme shown in Table 1. The redefinition of SDV variables is local to the current increment so any history dependence must be introduced with user-defined state-variables that can also be updated in VUMAT subroutine. History dependence is very important for progressive damage modelling because once a material point has been detected to fail, it must remain in that condition and not ‘heal’ after the stresses re-distribute. When material properties are degraded at a point, the load re-distributes to other points, which could then fail themselves. It is therefore necessary to iterate at the same load level when material properties change to determine if other material points undergo failure. This is achieved by rebalancing the equilibrium equations for the updated mechanical properties using a Newton–Raphson iteration scheme.

3. Finite element modelling 2D-model for machining composites has been constructed with orthogonal cutting configuration (Fig. 2). In the numerical model, only a portion of the trimmed specimen adjacent to the cutting tool is modelled (1000 ␮m × 1000 ␮m). The cutting tool is assumed to be in contact with the portion of a workpiece inclined according to the fiber orientation  after the first chip has been removed prior to machining simulation. The workpiece regions are modelled with combination of both four-node quadrilateral and three-node triangular elements. The three-node triangular elements are used for the mesh transition from coarse to fine mesh. Mesh convergence studies were performed and finally, fine mesh is used in the vicinity of the contact zone between the tool and workpiece while coarse mesh’s are used elsewhere. The size of element in fine mesh domain is approximately 0.2 ␮m × 0.2 ␮m and 50 ␮m × 50 ␮m in the extreme sides and bottom of the workpiece. The cutting tool was defined as a rigid body with geometry defined by the rake and clearance angles (˛ and ) and tool nose radius r␧ . The displacements of the bottom of the workpiece in both cutting and perpendicular direction are restrained (ux = uy = 0) in the FE model.

2544

L. Lasri et al. / Wear 271 (2011) 2542–2548

Table 1 Hashin criteria with five modes and associated degradation rules. Failure criteria

Failure index

Matrix tensile failure ( 22 ≥ 0)

2 em

=

Matrix compressive failure ( 22 < 0)

2 em

=

Fiber–matrix shear failure ( 11 ≥ 0)

2 efs =

Fiber tensile failure ( 11 ≥ 0)

ef2 =

Fiber compressive failure ( 11 < 0)

ef2 =

Associated solution defined variable

Reduced material properties

+

12 Sc

SDV1

E22 , 12 , 21 → 0

+

12 Sc

SDV1

E22 , 12 , 21 → 0

+

12 Sc

SDV2

G12 , 12 , 21 → 0

SDV3

E11 , E22 , G12 , 12 , 21 → 0

SDV3

E11 , E22 , G12 , 12 , 21 → 0

  2   2 22 Yt

22 Yc

11 Xc

  2   2   2   2   2 11



Xt

 − X11 c

2

Start

FE model setup Stress analysis Material property degradation Failure analysis

No

Load ement Tool Displac increment increment

Check for completion of chip formation Check for failure

No

Yes Stop

Yes

Fig. 1. Progressive damage algorithm.

The displacements of extreme left side are also restrained (ux = 0) in the cutting direction. The cutting tool is considered as a rigid body (as the elastic modulus of solid carbide cutting tool material is six times the elastic modulus of glass fiber) and a reference point controls the movement of the cutting tool. Prior experiments showed that the cutting velocity marginally affects the cutting of UD-GFRP composite [2]. The material properties of the composite are given in Table 2.

2

Free surface

θ

α

3

Cutting direction 1

ap

Cutting tool rε

γ

Ft Thrust force

To analyse the chip formation, the progressive damage behaviour developed in Section 2 has been implemented in ABAQUS® through the user-subroutine VUMAT [12]. During the chip formation, two contacts occur between the cutting tool and the workpiece, see Fig. 2. The first contact occurs between the tool rake face and the produced chip, and the second contact between the tool flank face and the new generated surface (machined surface). In this approach, a constant friction coefficient of 0.5 has been used to specify friction for both contacts [8,9]. The other assumptions used in the finite element model are as follow: (i) the material is locally homogeneous and orthotropic, (ii) the heat generation between the cutting tool and the work material is considered negligible, Table 2 Mechanical properties of the GFRP composite (glass/epoxy) used in the model [11]. Elastic properties of UD-GFRP composite

Workpiece FC Cutting force y x Fig. 2. Schematic view of the orthogonal cutting model showing the tool geometry and composite workpiece.  is the fiber orientation, ˛ the tool rake angle,  the flank angle and r␧ the tool nose radius. (1 2 3) is the principal material system, ap is the depth of cut.

Longitudinal modulus: E1 (GPa) Transversal modulus: E2 (GPa) In-plan shear modulus: G12 (GPa) Poisson’s ratio: 12

48 12 6 0.19

Ultimate strength (MPa) Longitudinal tensile strength: Xt Longitudinal compressive strength: Xc Transverse tensile strength: Yt Transverse compressive strength: Yc In-plan shear strength: Sc

1200 800 59 128 25

L. Lasri et al. / Wear 271 (2011) 2542–2548

2545

Fig. 3. Damage modes responsible of the chip formation process when the fiber orientation is kept equal to 45◦ . (a) Initiation state. (b) Propagation stage. (c) Chip formation completed. The cutting conditions are: ˛ = 5◦ ,  = 6◦ , r␧ = 20 ␮m, and ap = 200 ␮m. SDV1, SDV2 and SDV3 indicate matrix cracking mode, fiber–matrix shearing or interface debonding mode, and fiber fracture mode, respectively. dm and dint represent the depth of the damaged zone in the matrix and at the interface, respectively.

(iii) a plane stress analysis has been adopted according to the work of Arola et al. [8,9], (iv) the chip formation has been considered completed when both fiber/matrix shearing reaches the free workpiece surface, and the fracture of the fiber is verified. 4. Results and discussion 4.1. Chip formation analysis As mentioned before, the damage variables SDV1, SDV2 and SDV3 indicate the matrix cracking mode, the fiber/matrix shearing

mode (interface debonding) and the fiber fracture mode, respectively. The results in terms of internal damage and corresponding failure modes predicted by the model for the fiber orientation of 45◦ , rake angle of 6◦ , clearance angle of 5◦ , depth of cut of 200 ␮m and tool noise radius of 20 ␮m are shown at different tool advancement stages in Fig. 3. It can be seen from Fig. 3 that the damage starts from a location near the cutting edge of the tool. The matrix cracking and fiber–matrix shearing take place first and followed by fiber fracture (represented by SDV3 variable in Fig. 3(b) and (c)). Damage of different components: fiber, matrix, and interface simultaneously propagate until the complete chip formation. The progression of

2546

L. Lasri et al. / Wear 271 (2011) 2542–2548

Fig. 4. Chip formation process for the 45◦ fiber orientation, (a) model, (b) high speed video image recorded by Iliescu et al. [13] during machining unidirectional fiber reinforced polymer. The cutting conditions are: ˛ = 5◦ ,  = 6◦ , ap = 200 ␮m, and r␧ = 20 ␮m.

damage at the matrix and the interface occurs in the parallel direction to the fiber axis. A random growth of fiber fracture can also be observed and is mainly localized in a plane with a specific direction. The predicted damages are very similar to the primary and secondary fractures previously reported by Wang et al. [4] and Arola et al. [8,9]. The result of the model presented in Fig. 4(a) clearly specify ruptures of fibers and interface debonding with black and gray colours, respectively. These ruptures that were represented in the model by variables SDV3 and SDV2 were found to be consistent with the primary and secondary fracture planes, respectively. The dual fractures can be observed only under macroscopic scale. The primary fracture is defined by the concentration of the fiber fractures located at the lower level close to the cutting edge. While the secondary fracture can be defined by the interface debonding from the free edge of the workpiece to the termination of the primary fracture plane following the fiber orientation. The comparison with the experimental work of Iliescu [13] in Fig. 4(b) shows a good agreement. Moreover, other authors [4,5,8,10] reported that the chip formation occur trough these dual fractures. Using classical and quick stop machining tests, they showed that the secondary fracture occurs along the matrix–fiber interface and follows the fiber orientation. In this case, the fracture is represented by the dominate failure field variable SDV 2 which represents the interface dedonding damage mode. In the case of the primary fracture, only the variable SDV 3 is considered. Indeed, it has been found in a large amount of experimental data from literature that the primary fracture is directly linked to the fiber fracture mode represented by the field variable SVD3, see the experimental work of Wang et al. [4,8], Arola et al. [5] and Zitoune et al. [10]. Other simulations have been performed to show the effect of the fiber orientation on the chip formation process and the induced cutting damage. Fig. 5 shows the damage modes responsible for the chip formation for orientations:  = 15, 30◦ , 45◦ , 60◦ and 75◦ . In the zone of formation of the chip, damages of the matrix and those of the interface predicted by the model are approximately localized in the same zone of the machined part, for all tested orientations of fibers (the damage of the matrix is not represented on Fig. 5). As shown in the same figure, for all orientations, the damage occurs firstly in the vicinity of the cutting edge at the interface and the matrix, followed by rupture of fibers. After its initiation, the damage simultaneously progresses in the three components until the complete formation of the first chip, Fig. 5(c) and (d). The matrix crack-

ing and interface debonding progress toward free surface, while fiber breaking randomly spreads for all tested fiber orientations. It should be noted that the height density of fiber ruptures (represented by the state field variable SDV3) predicted by the model can explain the dusty shape of chips generated during the machining of this kind of materials [2,3,5]. This density of fiber breaking can also induce fiber pullout as well as fiber fragmentation on the machined surface more or less important according to the fiber orientation. The result of Fig. 5 shows that this density decreases with the fiber orientation and the localization zone of these ruptures moves upwards until exceeding even the height of ray of the acuity of the cutting edge. This confirms previous observations reported by Wang et al. [4] on the difference that exists between the nominal depth of cut and the real depth of cut. This difference increases with the fiber orientation. One can also note that regardless of the fiber orientation, the chip is generated by a combination of several modes of ruptures:

• interface debonding, • breaking fibers, • matrix cracking.

The direction and the height of the plan of the primary rupture predicted by the present approach strongly depend on the fiber orientation. It is very close to the horizontal plane in the case of the lower angles of fiber orientations (15◦ and 30◦ ), (see Fig. 5(a) and (b)) and approaches the plan transverse or perpendicular to fiber axis, see Fig. 5 (c) and (d) (45◦ and 60◦ ). In all cases of machining higher fiber orientations such as 75◦ and 90◦ (Fig. 5(e)), the cutting plan becomes again horizontal. This can be explained by the change of the mechanisms controlling the cutting process with respect to the fiber orientation. In the case of the lower angles of orientation, the rupture of fibers can be caused by a combination of compression and tensile loading thus generating a plane of rupture according to the cutting direction. In the case of higher angles of fiber orientation, bending is a predominant mechanism induced by fiber fracture. It can also be noted that the rupture of fibers that occurs on both sides of primary failure plane may explain the pull out of fibers at the subsurface, and the generation of bare fibers on the machined surface.

L. Lasri et al. / Wear 271 (2011) 2542–2548

2547

Fig. 5. Chip formation process and damage mechanisms predicted by the explicit macro-mechanical model with respect to the fiber orientation. The cutting conditions are: ˛ = 10◦ ,  = 6◦ , ap = 200 ␮m, and r␧ = 20 ␮m.

4.2. Cutting induced damage analysis A subsurface damage induced by machining provides a source of crack propagation or further damage development under fatigue loading. This will affect the wear resistance of the composite components. In the present work, the subsurface damage such as matrix cracking (SDV1), fiber–matrix debonding (SDV2) can be predicted by the proposed model. The failure index contours defined by SDV’s contours display the damaged zones. The location at which the failure envelope extended below the surface was used as a measure of sub-surface damage resulting from machining composite workpiece. Fig. 3(c) illustrates an example of the predicted subsurface damage obtained, in the case of 45◦ fiber orientation, in the matrix and at the interface. dm and dint represent the depth of

subsurface damage in the matrix and at the interface, respectively. From all numerical simulations it has been observed that both damage modes initiate from the tool tip and then progress inside the workpiece. Different fiber orientations have been tested: 15◦ , 30◦ and 45◦ . The following cutting conditions were chosen in accordance with the experimental work of Nayak et al. [14]: rake angle ˛ = 5◦ , flank angle  = 6◦ , depth of cut ap = 200 ␮m and tool nose radius r␧ = 50 ␮m. As shown in the results of Fig. 6(a) and (b), a same tendency can be noted between the extension of the subsurface damage predicted by the model and those obtained by experiments of Nayak et al. [14]. However, the model gives the sub-surface damage values lower than the experimental results. This difference can be explained by the fact that the model generates only single chip and thus did not takes into account damages accumulation during

2548

L. Lasri et al. / Wear 271 (2011) 2542–2548

Sub-surface damage in matrix (μm)

(a)

Progressive damage model

1400

Exprements of Nayak et al [14]

1200 1000 800 600 400 200 0 0

10

20

30

40

50

40

50

Fiber oreintation θ (deg)

sub-surface damage in fiber/matrix interface (μm)

(b)

Progressive damage model

1400

Experiments of Nayak et al [14 ]

1200 1000 800 600 400 200 0 0

10

20

30

Fiber orentation θ (deg) Fig. 6. Variation of sub-surface damage with fiber orientation. (a) Damage in matrix. (b) Fiber–matrix debonding: comparison between values calculated with the model and experiments obtained by Nayak et al. [14]. The cutting conditions are: ˛ = 5◦ ,  = 6◦ , ap = 200 ␮m, and r␧ = 50 ␮m.

the machining process. Hence, a more realistic approach requires that the model permits a producing of several macro-chips with tool progression.

5. Conclusion A 2D-finite-element progressive failure analysis has been developed to investigate the chip formation process and induced damage when machining unidirectional fiber reinforced polymer composites (UD-FRP). The numerical analysis provides a physical understanding of composite damage process. The progressive failure analysis includes matrix cracking, fiber–matrix debonding and fiber breaking. It can be concluded that during the chip formation, matrix cracking and fiber–matrix debonding take place first followed by fiber fracture. The damage of different components: fiber, matrix, and fiber–matrix interface, then simultaneously progresses until the complete chip formation process. The present model is a new approach which predicts the macrochip formation process without imposing any trajectory of fracture and/or the order of the various fractures. The model shows that the primary fracture occurred by fibers rupture ahead of the tool nose on a plane which is not often consistent with the flank plane. Direction and level of the primary fracture plane was mainly fiber orientation dependent. The secondary fracture plane occurred at the fiber/matrix interface was found to be always consistent with the reinforcement orientation. The cutting induced damage versus the fiber orientation has also been predicted. A same tendency has been noted between experimental data and the results of the proposed model.

References [1] L. Lasri, M. Nouari, M. El Mansori, Working parameters effects on machining induced damage of fibre-reinforced composites: numerical simulation analysis, International Journal of Materials and Product and Technology 32 (2/3) (2008) 136–151. [2] G. Venu Gopala Rao, P. Mahajan, N. Bhatnagar, Micro-mechanical modelling of machining of FRP composites—cutting force analysis, Composites Science and Technology 67 (3–4) (2007) 579–593. [3] A. Koplev, Cutting of CFRP with single edge tool, in: Proc. 3rd Int. Conf. of Composite Materials, Paris, 1980. [4] D.H. Wang, M. Ramulu, D. Arola, Orthogonal cutting mechanisms of graphite/epoxy composite. Part I: unidirectional laminate, International Journal of Machine Tools and Manufacture 35 (12) (1995) 1623–1638. [5] D. Arola, M. Ramulu, D.H. Wang, Chip formation in orthogonal trimming of graphite/epoxy, Composites: Part A 27 (1996) 121–133. [6] A. Koplev, A. Lystrup, T. Vorm, Cutting process, chips, and cutting forces in machining CFRP, Composites 14 (4) (1983) 371–376. [7] H.Y. Pwu, H. Hocheng, Chip formation model of cutting fibre-reinforced plastics perpendicular to fibre axis, Transactions of ASME 120 (1998) 104–114. [8] D. Arola, M. Ramulu, Orthogonal cutting of fibre-reinforced composites: a finite element analysis, International Journal of Machine Tools and Manufacture 39 (5) (1997) 597–613. [9] D. Arola, M.B. Sultan, M. Ramulu, Finite element modelling of edge trimming fibre-reinforced plastics, Transaction of ASME, Journal of Engineering Materials and Technology 124 (2002) 373–377. [10] R. Zitoune, F. Collombet, F. Lachaud, R. Piquet, P. Pasquet, Experimentalcalculation of the cutting conditions representative of the long fiber composite drilling phase, Composites Science and Technology 65 (2005) 455–466. [11] L. Lasri, M. Nouari, M. El Mansori, Modelling of chip separation in machining unidirectional FRP composites by stiffness degradation concept, Composites Science and Technology 69 (5) (2009) 684–692. [12] KAS. Hibbit, ABAQUS/Standard version 6.6, Theory, example problem and user’s manuals, ABAQUS Inc., Rhode Island, USA, 2006. [13] D. Iliescu, D. Gehin, I. Iordanoff, F. Girot, A discrete element method for the simulation of CFRP cutting, Composites Science and Technology 70 (1) (2010) 73–80. [14] D. Nayak, N. Bathnagar, P. Mahajan, Machining studies of uni-directional glass fiber reinforced plastic (UD-GFRP) composites. Part 1: effect of geometrical and process parameters, Machining Science and Technology 9 (4) (2005) 481–501.