Prediction of critical thrust force for exit-ply delamination during drilling composite laminates: thermo-mechanical analysis

Int. J. Machining and Machinability of Materials, Vol. 18, Nos. 1/, 016 77 Prediction of critical thrust force for exit-ply delamination during drilling composite laminates: thermo-mechanical analysis Jamel Saoudi Université de Toulouse, INSA, UPS, Mines d Albi, ISAE, ICA (Institut Clément Ader), IUTA GMP Toulouse, 133 c Avenue de Rangueil, 31077 Toulouse, France and Laboratoire Génie Mécanique, École Nationale d Ingénieurs de Monastir, Université de Monastir, 5000, Tunisia Email: saoudi_jamel@yahoo.fr Redouane Zitoune Université de Toulouse, INSA, UPS, Mines d Albi, ISAE, ICA (Institut Clément Ader), IUTA GMP Toulouse, 133 c Avenue de Rangueil, 31077 Toulouse, France Email: redouane.zitoune@iut-tlse3.fr Corresponding author Suhasini Gururaja Aerospace Engineering, Indian Institute of Science (IISc), Bangalore 1, Karnataka, India Email: suhasini@aero.iisc.ernet.in Salah Mezlini Laboratoire Génie Mécanique, École Nationale d Ingénieurs de Monastir, Université de Monastir, 5000, Tunisia Email: salah.mezlini@gmail.com Akshay Amaranath Hajjaji Aerospace Engineering, Indian Institute of Science (IISc), Bangalore 1, Karnataka, India Email: akshayhejjaji@gmail.com Copyright 016 Inderscience Enterprises Ltd.

78 J. Saoudi et al. Abstract: Drilling damage, such as delamination at the hole exit, is known to adversely affect the load carrying capability of a structure resulting in reduced endurance limits and overall reduction in structural integrity. In this context, the present work studies the influence of temperature of machining on the critical thrust force responsible for delamiantion at the hole exit. An analytical model considering thermo-elastic field equations has been established with the aim of predicting the critical thrust force. The validation of this model has been conducted at room temperature via punching tests carried out on carbon fibre epoxy multi-directional composite laminates. Some difference in predictions exists which are mainly attributed to the variability in ply thicknesses due to the manufacturing process. Such an analysis underscores the need to explicitly account for machining temperature effects on machining damage characterisation. Keywords: drilling; delamiantion; thermo-mechanical properties. Reference to this paper should be made as follows: Saoudi, J., Zitoune, R., Gururaja, S., Mezlini, S. and Hajjaji, A.A. (016) Prediction of critical thrust force for exit-ply delamination during drilling composite laminates: thermo-mechanical analysis, Int. J. Machining and Machinability of Materials, Vol. 18, Nos. 1/, pp.77 98. Biographical notes: Saoudi Jamel is a second year PhD student in University Paul Sabatier of Toulouse and Ecole Nationale d Ingénieurs de Monastir in Tunisia. His PhD research concerns the development of analytical and numerical models for the prediction of the delamination during drilling of composite structures. Redouane Zitoune is an Associate Professor in Mechanical Engineering at Paul Sabatier University (University of Toulouse, France), since 005. He is focused on the manufacturing and machining (drilling and milling) of composite materials. His current research interests include damage analysis during drilling and milling of composite materials (with conventional machining and abrasive water jet machining) and finites elements simulation of machining. He is also interested in the thermal analysis of composite structures by using an optical fibres and finite element analysis. He has published more than 80 technical papers in national and international journals/conferences. In the area of machining of composite materials, he has organised the first national meeting in May 01. This scientific event has been organised with the collaboration of the French Aerospace Lab (ONERA) and with the consent of the national Association for Composites MAterials (AMAC). Suhasini Gururaja has been serving as an Assistant Professor at the Department of Aerospace Engineering, Indian Institute of Science (IISc) Bangalore since November 010. Prior to joining IISc, she has been with the Boeing Company, USA and GE Global Research, Bangalore as a Structural Analyst and Research Engineer, respectively. At IISc, her group is interested in composite mechanics problems in the nexus of processing, secondary manufacturing and long term sustainability of aerostructures. Salah Mezlini is an Assistant Professor in Mechanical Engineering at Ecole Nationale d Ingénieurs de Monastir (University of Monastir, Tunisia), since 003. His PhD work is focused on the tribological behaviours of aluminum alloys. His current research focuses on the tribological behaviour of both homogeneous and heterogeneous materials, particularly composite material. He is also attracted in the thermo-mechanical analysis of rough contacts using numerical and experimental approaches. Such research works are in close collaboration with the industry and other national as well as international research laboratories.

Prediction of critical thrust force for exit-ply delamination 79 Akshay Amaranath Hajjaji is currently a doctoral student at the Institute Clement Ader of Toulouse University, and his doctoral studies focuses on the impact of the water jet machining process on the mechanical behaviour of composite structure made of carbon fibres. His primary research interests include machining of composites, damage characterisation of composites and non-destructive testing of composites. He received his Master degree from Vellore Institute of Technology, India and has two years research experience at the Indian Institute of Science, Bangalore where he was involved in research related to orthogonal cutting of epoxy and conventional machining of CFRPs. He has two international journal publications in the field of composite machining. 1 Introduction Carbon fibre reinforced plastic (CFRP) composites have received considerable attention from number of industries (Mouritz et al., 001; Renton et al., 004). The aerospace companies Boeing and Airbus have well identified benefits of using CFRPs as primary structures in their aircrafts. The exhibited low density, high strength and high stiffness to weight ratio make CFRPs suitable candidates for many aerospace applications. Components made of CFRP are manufactured near the final shape, after the phase of demoulding to reduce the number of machining operations, which weaken the material. Main machining operations realised on composite materials are trimming, surfacing and drilling (Sheikh-Ahmad, 009). Amongst these operations, drilling is often a final operation during assembly. However, due to the pronounced anisotropy and abrasiveness of carbon fibres, the machinability of composite structures remains a very challenging task. In particular, drilling of composite structures is accompanied by various defects leading to rejection of the machined structures incurring significant cost during production (Stone and Krishnamurthy, 1996). In literature, several studies have focused on experimental characterisation of drilling of carbon/epoxy composites (Abrao et al., 008; Stone and Krishnamurthy, 1996). In fact, different damage modes have been identified when drilling carbon/epoxy composites. Based on the location of damage, three main types of damage have been categorised, viz., at hole entry, along the hole wall and at the hole exit. The following sections describe each of these damage mechanisms in some detail: Entry delamination: Defect at hole entry represents delamination of the first ply and is sometimes referred to as entry-delamination. This damage is mainly dependent on the geometry of the tool (helix angle), the machined materials and the cutting parameters (Campos Rubio et al., 008; Stone and Krishnamurthy, 1996). Given that in aerospace sector drilling operation is often accompanied by countersink operation, entry-delamination is less onerous. Damage along the wall of the hole: Damages observed along hole wall are dependent on the relative angle (θ) between fibres direction and cutting direction, the machined materials and the edge radius of the cutting tool. Different mechanisms of chip removal have been identified depending on this relative angle and generate different quality of machined surface (Davim et al., 007; Langella et al., 005). If we refer to the work of Zitoune and Collombet (007), and Mohan et al. (005), damage along

80 J. Saoudi et al. hole wall occurs mainly for high feed rates and when the relative angle (θ) is close to 45 and 90. According to Cadorin et al. (014), and Cadorin and Zitoune (015), the machining quality of the wall of the hole can be improved with internal lubrication or by using core drill made of diamond grains. Likewise, Zitoune et al. (01) have mentioned that the roughness of the wall of the hole can be improved when the carbon/epoxy structure contains thermoplastic nodules in the interface of the plies. Exit-ply delamination: Defect located at the exit of the hole takes the form of delamination between the plies and has an important influence on endurance limit of the damaged structures when subjected to fatigue loading (Haddad et al., 014, 015; Persson et al., 1997; Saleem et al., 013; Zitoune et al., 011). This defect, also referred to as exit-ply delamination, appears when the thrust force is too high generating a crack propagating at the interface between the two plies. This damage is linked to the interaction between the cutting tool (conventional machining) and the composite material. A number of studies show that this damage is influenced by the choice of machining parameters, geometry of the cutting tool tip (Campos Rubio et al., 008; Dharan and Won, 000), composite material properties as well as the process of manufacturing of the composites parts (Langella et al., 005; Zitoune and Collombet, 009). Kilickap (010) concluded that higher feed rates and cutting speeds resulted in higher damage. Manna et al. (008) found that the spindle speed has the highest effect on surface roughness height (Ra) followed by the feed rate. Gaitonde et al. (008) observed that the feed rate is linearly related to the damage. Zitoune and Collombet (007) demonstrated the suitability of numerical analysis for drilling induced damage quantification considering mixed mode delamination (mode I and mode II). Yashiro et al. (013) showed that drilling conducted with worn tool resulted in thermal damage (matrix degradation) favouring the increasing of delamination size at the hole exit. Overall, there exists a consensus regarding the main cause for exit-ply delamination, namely, the thrust force induced by the interaction between the tool and the composite part. Thrust force is mainly dependent on the feed rate while cutting speed is found to have a lesser effect (Abrao et al., 008; Mohan et al., 005; Rawat and Attia, 009; Shyha et al., 010; Tsao and Hocheng, 005). In order to predict when the exit-ply delamination will be occur, various authors have looked at analytical and numerical prediction of the critical thrust force responsible for the delamination induced at the exit hole as a function of the mechanical properties of the composite material (Jain and Yang, 1993; Rawat and Attia, 009). The different analytical models have been correlated to the punching tests conducted on specimens characterised by blind holes with different plies under the tool. These punching tests have been conducted in a quasi-static frame and at room temperature. Although the predicted critical thrust forces responsible for delamination are in good agreement with the forces obtained from punching tests, these analytical models and their validation are not representative of the physics of delamination that can develop during the drilling process. In fact, during drilling, the temperature of machining is much higher than room temperature and can easily reach around 180 C (Haddad et al., 014). In this case, the delamination phenomenon needs to be analysed using a thermo-mechanical framework. The present work provides such a framework and investigates exit-ply delamination during drilling CFRPs by explicitly considering temperature dependence on material

Prediction of critical thrust force for exit-ply delamination 81 properties of the workpiece. An analytical model considering thermo-elastic field equations has been established with the aim of predicting the critical thrust force responsible for drilling induced exit-ply delamination. Exit-ply delamination: analytical approach Before presenting the thermo-mechanical coupled exit-ply delamination model, a few related critical thrust force prediction models have been presented here. The key theoretical tenets of these models have been highlighted since the proposed framework also follows a similar approach..1 Hocheng-Dharan model Hocheng and Dharan (1990) proposed the first analytical model for critical thrust force prediction for drilling in composite materials. In this model, an energy approach based on the application of the theorem of virtual work for equilibrium of the future delaminated zone of the laminate located under the tool was used. The composite part located under the tool was considered as circular in presence of a circular crack in the vicinity of the nominal diameter of the tool (Figure 1). In addition, the workpiece material was assumed to be isotropic. The boundary conditions/loading for the circular isotropic plate problem were based on the following considerations: clamped along the circumference of the plate contact tool/part was simulated by a single concentrated load. Figure 1 Modelling of the exit-ply delamination according to Hocheng and Dharan (1990) In this situation, the critical thrust force was determined based on the linear elastic fracture mechanics (LEFM) considering mode I energy balance and Kirchoff-Love plate theory as follows (Koenig et al., 1985): dw = GIcdA + du (1)

8 J. Saoudi et al. where dw is the work done by the external forces G Ic is the critical strain energy release rate in mode I da is the infinitesimal increase in area of crack du is the infinitesimal strain energy. The final form of the critical thrust force F c for the Hocheng model is given by the following equation: F ( Hocheng) = π c 3 8GIcEh ( 31 v ) () where E is the Young s modulus. h is the uncut laminate (workpiece) thickness. ν is the Poisson s ratio.. Zhang model Zhang et al. (001) proposed a modified critical thrust force model considering composite laminate anisotropy. This model is more representative of the physics in terms of taking into account the coupling between bending and extension components observed in multidirectional (MD) laminates with an un-symmetrical stacking sequence. In this model, the classical lamination plate theory (CLPT) was used to develop the displacement equations that were in turn used to estimate the critical thrust force using energy balance equation (1). Since the current proposed model uses a similar approach, the methodology used by Zhang et al. (001) is presented here in detail. The authors consider the delamination zone as an elliptical plate with a and being the major and minor axes of the ellipse along fibre and transverse directions, respectively, as shown in Figure. The ellipticity ratio was estimated using an optimisation scheme. Figure Schematic of delamination during drilling of MD-FRPS (see online version for colours)

Prediction of critical thrust force for exit-ply delamination 83 0 0 0 Using small displacement assumption, the in-plane strains ( εx, εy, γ xy) and curvatures (κ x, κ y, κ xy ) used to estimate the stress fields are given by: 0 u 0 v 0 u v εx =, εy =, γxy = + x y y x (3) w w w κx =, κ, y = κ xy = x y x y Here, u, v and w represent the displacement fields in the elliptical plate domain in x-, y- and z-directions, respectively. The following relation gives the constitutive relation for the laminate based on CLPT (Timoshenko and Woinowsky-Krieger, 1959): N A B ε 0 M = B D κ (4) [A] is 3 3 matrix of the extensional stiffness, [B] is 3 3 matrix of the coupling between extension and bending and [D] is 3 3 matrix of bending stiffness. And, ( x, y, xy) T 0 0 0 0 ε = ε ε γ (5) ( x, y, xy) T κ = κ κ κ (6) The in-plane strains ε 0 and κ curvatures have been used to estimate the stress fields. In this case, the small displacement assumption is proposed as follow: 0 u 0 v 0 u v εx =, εy =, γxy = + x y y x w w w κx =, κ, y = κ xy = x y x y where ( x, y, xy) ε = ε ε γ 0 0 0 0 ( x, y, xy) κ = κ κ κ ( ij ij ij ) ij ( ) T T h A, B, D = Q 1, z, z dzi, j = 1to3 (7) h where Q ij is the reduced stiffness matrix for plane stress case and h is the total thickness of the uncut laminate under the drill bit. In addition, the normal/shear forces [N] vector and the moments [M] are related via equilibrium equations: N N + N = 0 xx, xyy, + N = 0 xy, x y, y M + M + M q = 0 xxx, xyxy, yyy, (8)

84 J. Saoudi et al. where Fc Fcξ q = πab = πa (9) q represents the assumed uniformly distributed load acting on the elliptical plate. ξ is the ratio of half the delamination sizes in the L and T directions (see Figure ), i.e., ξ = a/b. Using the approach outlined in Bert (1983), the following displacement fields are assumed a priori: x y x y u = u1 + u 1 a b a b x y x y v = v1 + v 1 a b a b x y w= w0 1 a b Solving the system of equations (4) and (8) using the assumed displacement fields (10), the displacement constants u 1, u, w 0, v 1, v are estimated as: u = FC a, v = FC a, w = FC a, u = FC a, v = FC a (11) 1 c 1 1 c 0 c 3 c 4 c 5 It should be noted that all the C s in the above expression are known in terms of the uncut laminate properties (constituent material properties and lay-up) and ellipticity ratio ξ. Based on the displacement fields in equation (11), the strain energy of the uncut laminate has been estimated: U = KF a (1) c With K given by: (10) A11 A16 ( 3C1 + C4 ) + A1( CC 1 + C4C5) + ( ξcc 1 4 + 3CC 1 5 + CC 4) ξ ξ + A6 ( 3ξCC4 + CC 5 + ξcc 1 5 ) 16D11 ( 4 + C 3 3 D 11 + ξ D 1 + 3 ξ D + 4 ξ D 66 ) ξ π K = A66 ( ) + ξ C1+ C + 3ξ C4 + 3C5 + ξc4c 5 ξ 4B11 + CC 1 3 + 8 B 1 C 3( ξc 1+ C ) ξ C5 + 4B16C3 C4 + + 4Bξ CC ξ 3 + 4B6C3( C5 + ξc4) Using the energy balance equation (1), the critical thrust force has been estimated as (13)

Prediction of critical thrust force for exit-ply delamination 85 F ( Zhang) = c πgic ξ ( C K) 3 (14).3 Gururaja model The Gururaja model (Gururaja and Ramulu, 009) modified the Zhang model (Zhang et al., 001) to account for a more realistic representation of the contact forces experienced by the uncut composite laminate during drilling. By considering uniformly distributed load acting on the elliptical anisotropic plate allowing for bending-extension coupling, a good agreement was observed between predicted thrust force and the experimental data. In this case, the expression for the critical thrust force obtained was: F ( Gururaja) = c πgic ξ (( C3 /3) K) (15) 3 Exit-ply delamination: thermo-mechanical analysis In the present analysis, Gururaja model has been modified to include temperature effects on critical thrust force predictions. The model development has been described in the following sections. 3.1 Influence of the temperature on the strain To begin with, it is assumed that the laminate is subjected to a constant temperature gradient (ΔT) as follows: Δ T = T T 0 (16) where T is the maximum temperature generated during the drilling process T 0 is the reference temperature (room temperature). In this case, the strains and curvatures can be expressed in terms of displacements as follows: m t m t m t εx = εx εx, εy = εy εy, γxy = γxy γxy w w w (17) κx =, κ, y = κ xy = x y xy where ε m = ( ε m, ε m, γ m ) T : Pure mechanical mid-plane strains (without thermal effect). x y xy

86 J. Saoudi et al. t t t t ε ( εx εy γxy) T T u v u v =,, =,, + : x y y x Total mid-plane strains in which (u, v, w) T is defined in equation (10). We are making the assumption that the shape of the delamination does not change due to inclusion of temperature components ε εx εy γxy With T = (,, ) : Thermal mid-plane strains given by: ε = α Δ T, ε = α Δ T, γ = α ΔT (18) x x y y xy xy ( ) T x y xy = T ( 11 ) α, α, α [ ] α, α,0 T (19) c s sc sc sc c s [ T] = s c sc,( c = cos θ, s = sin θ) (0) α 11 and α are respectively the coefficient of thermal expansions in the longitudinal and transversal direction of the k th ply. α 11 and α are expressed as a function of temperature (Gibson, 1994) as: Ef1Vfα f1 + FmEmVmFhα m α 11 = (1) E V + F E V where f1 f m m m ( 1 1 ) ( ) VV v FE v E α = E α V + V Fα + α Fα () f m f m m m f f1 f f m h m f1 h m Ef1Vf + FmEmVm 1 Tg T 1 Fm =, Fh Tg T = (3) 0 Fm Here, f and m denote the fibre and matrix, respectively with 1 and denoting the material longitudinal and transverse direction of the ply (Figure ) V: volume fraction F m : matrix mechanical property retention ratio T: temperature T g : glass transition temperature of the matrix T 0 : reference temperature F h : matrix thermal property retention ratio.

Prediction of critical thrust force for exit-ply delamination 87 3. Influence of the temperature on the constitutive relations Similarly, a constitutive relation for FRPs equation (4) takes the following modified form representative of thermo-mechanical behaviour of the laminate: and N A B ε t = M C D κ t t (4) t m N N N t = m+ (5) M M M where { N t } = { Nx t, Ny t, Nxy t } T and { M t } = { Mx t, M y t, Mxy t } T are the total resultant and total moment, respectively. { N m } = { Nx m, Ny m, Nxy m } T and { M m } = { Mx m, M y m, Mxy m } T are the mechanical resultant and mechanical moment, respectively. N Nx Ny Nxy { } = {,, } T and { M } = { Mx, M y, Mxy} T are the thermal resultant and thermal moment, respectively. The [A], [B] and [D] matrices of the laminate are derived from equation (7). Mechanical properties of the laminate E 11, E, G 1 and v 1 can be written as a function of temperature (Gibson, 1994): E11 = Ef1Vf + FmVmEm FE m m Vf E = ( 1.0 Vf ) FmEm + FE m m 1.0 V f 1.0 E f (6) FG m m Vf G1 = ( 1.0 Vf ) FmGm + FG m m 1.0 V f 1.0 G f1 v = v V + v V 1 f1 f m m According to plate theory (Timoshenko and Woinowsky-Krieger, 1959), the equilibrium equations for flat structural elements are: N + N = 0 N + N = 0 m m m m xx, xyy, xyx, yy, M + M + M q = 0 m m m xxx, xyxy, yyy, (7) where Fc Fξ, a q = = ξ = (8) πab πa b

88 J. Saoudi et al. Introducing equation (5) into equation (7) gives the same equations as equation (8): (Because the thermal deformation strains ε is assumed independent of the spatial coordinates x and y, thus for thermal moment {N }). However, we obtain: N + N = 0, N + N = 0 t t t t xx, xyy, xyx, yy, M + M + M q = 0 t t t xxx, xyxy, yyy, (9) Thus, we obtain the same displacements fields as equation (11): u = FC a, v = FC a, w = FC a, u = FC a, v = FC a (30) 1 c 1 1 c 0 c 3 c 4 c 5 3.3 Infinitesimal strain energy U 3.3.1 Strain energy derivation 1 m 1 ({ t} { U = σ: ε dv = σ: ε ε }) dv V V (31) 1 U = σ ε ε + σ ε ε + σ ε ε + σ ε ε ( ) ( ) ( ) xx xx xx yy yy yy zz zz zz yz ( yz yz ) V (3) ( ) σxz εxz εxz σxy ( εxy εxy ) dv + + Classical assumption of the laminate theory: ε = ε = ε = ε = 0, σ = 0 (33) yz xz yz xz zz ( ) u v u v U = U ε = 0 x y xy N + N + N ds S x y + y x e w e + Mxx M yy M xy + + ds S x y x y (34) h k + h f ( εi ) dzds where S is the limit of integration, i.e. x y S : + 1 0 (35) a b ( i ) ( ) ( ) ( ) k k k k k k k k k k = 11 x + y + 4 66 xy + 4 1 xy y f ε Q ε Q ε Q ε Q ε ε + 4Q ε ε + 4Q ε ε k k k k k k 16 x xy 6 y xy (36)

Prediction of critical thrust force for exit-ply delamination 89 By introducing the displacement fields equation (33), we obtain: u0 v0 u0 v0 Nx + Ny + Nxy + dxdy = 0 x y y x w w w Mxx + M 0 yy + M xy dxdy = x y x y h k πa h ( εi ) dzdzdy = K ξ where K = ( Δ T) [ I11 + I + 4( I1 + I16 + I6 + I66 )] (38) (37) And I 1 n k k k 3 3 ij = ij i j ( 1 );, 1,,6 3 Q αα z k 1 k z k i j = (39) = ( ) U ε = = KF a (40) 0 c Finally, πa U = KFc a + K (41) ξ U e πa du = δa = KFc a+ K δa a ξ (4) 3.4 External work W The determination of external work done due to the distributed load acting on the elliptical plate is: Finally, x ( a ) x ( ) x ( a ) x ( ) a b 1 a b 1 Fc x y W = c 3 qwdydz = F C a 1 dydx a b 1 a b 1 a a πab a b FC c 3 W = 3 a W Fc C3 dw = δa = aδa a 3 (43) (44)

90 J. Saoudi et al. 3.5 Critical thrust force Relation (1) is expressed as a function of (4) and (44): Finally, FC c 3 πa c F c 3 = aδa = KF a+ K δa + πbgicδa ξ ξ ( + G ) π K C (( ) K ) 3 3 Ic (45) (46) 4 Experimental approach In order to establish the relative performance of the analytical model presented in equation (46), a comparison of the predicted thrust forces with the experimental data has been conducted. To this end, quasi-static punching tests for different number of plies under the tool have been conducted. 4.1 Specimen preparation Quasi-isotropic (QI) CFRP laminates of [0/-45/90/45]s layup, 4. mm thickness were used for conducting the punching tests. The CFRP composite is made of unidirectional prepregs supplied by Hexcel Composite Company and referenced under HEXPLY UD T700 68 M1 34% (T700-M1). The laminate was prepared in a controlled atmosphere (white room) and compaction was carried out using vacuum pump. A mould for the laminate was prepared and placed in a vacuum bag and evacuated to 0.7 bars. Curing was then conducted at 180 C for 10 min during which the pressure was maintained at 7 bars in an autoclave (as recommended by Hexcel Composite Company). With this process of manufacturing, the nominal fibre volume fraction is 59% and the glass temperature transition around 180 C. The mechanical properties of the carbon fibre and epoxy matrix given by the manufacturer as well as the composite ply identified in the lab are summarised in Table 1. Table 1 Mechanical properties of carbon (T700) and epoxy (M1) and T700/M1 Carbon fibre (T700) Epoxy matrix (M1) Composite (T700/M1) E f1 (GPa) 30 E m (GPa) 4.5 E 11 (GPa) 137.5 E f (GPa) 13.79 G m (GPa) 1.6e9 E (GPa) 8. E f1 (GPa) 8.97 v m 0.4 G 1 (GPa) 3.7 vf 1 0. α m (1/ C) 7e-6 v 1 0.9 α f1 (1/ C) 0.99e-6 V m 0.41 α 11 (1/ C) 1.09e-8 α f (1/ C) 10.08e-6 α 1 (1/ C) 4.7e-5 V f 0.59

Prediction of critical thrust force for exit-ply delamination 91 4. Drilling setup The blind holes have been machined using CNC machine [Figure 3(a)] and twist drill made of tungsten carbide (K0) with 6 mm diameter. This diameter is chosen based on the requirements of the aircraft industry. For the validation of the analytical model, three configurations of specimens have been tested which are characterised respectively by 1 ply, plies and 3 plies under the tool. These specimens are cut from the same mother plate in order to reduce the variability due the manufacturing process (Collombet et al., 006). After the cutting thanks to the abrasive water jet process, specimens have dimension of 100 70 mm [Figure 3(b)]. In order to remove delamination damage due to the machining process, the feed rate and the spindle speed selected are respectively 0.0 mm/rev and,000 rpm (Table ). Figure 3 Specimens preparation for the punching tests; with (a) drilling process of the blind holes, (b) elementary parts (see online version for colours) (a) (b) Table Summary of experimental conditions for the drilling of the blind holes Drilling of CFRP laminates Machine tool CNC machine Workpiece material CFRP (59% V f, 4. mm thick) Tool Inserts carbide (K0) with drill diameter of 6 mm Point angle 118 Rake angle 7 Clearance angle 6 Drilling condition Spindle speed (rpm) 000 Feed rate (mm/rev) 0.0

9 J. Saoudi et al. Figure 4 Drilling fixture of punching tests on QI specimens conducted on UTM machine (see online version for colours) 4.3 Punching tests For the punching test, the same procedure proposed by Zitoune and Collombet (007) has been adopted in this study. The workpiece is positioned on two supports and clamped. The punching load is applied at rate of 1 mm/min with the same drill as used for machining the blind holes (Figure 4). For each configuration, the punching test is repeated two times. 5 Results and discussion Figure 5 represents a comparison between the critical thrust force measured experimentally and those predicted by the model [equation (46)] at room temperature for different number of plies under the tool. From this figure, it can be confirmed that with increasing the number of plies under the tool (from one ply till three plies), the critical thrust force increases by 103% for the experimental values and 130% for the predicted value. Although the experimental forces are in good agreement with those predicted by the model, it can be inferred that the analytical model underestimates the critical thrust force. In addition, the maximum relative deviation between the predicted force and the measured force is around 44% for the specimens with 1 ply under the tool. This deviation in forces can be explained mainly by the random variation of the ply thickness of the laminates. A similar observation has been made by Collombet et al. (006) for a [0/90/0/90]s T700/M1 laminate where in the ply thicknesses that constitute the laminate vary from 10% to 30% compared to the nominal thickness (cf. Figure 6).

Prediction of critical thrust force for exit-ply delamination 93 Figure 5 Critical thrust force at room temperature (T = 3 C) (see online version for colours) This observation is in good agreement with the SEM images of the CFRP specimens obtained after the punching tests (Figure 7). From these SEM observations, it is clear that the thickness of the uncut part located under the chisel edge of the twist drill (which is equal to 0.68 mm) is higher to the desired value (which is equal to 0.5 mm). In addition, a crack located in the vicinity of the chisel edge is observed [Figure 7(a)]. However, the model considers the presence of crack near the nominal diameter of the hole, which can be responsible for deviation in the forces. Figure 6 SEM observation in the thickness of the T700/M1 laminate with [0/90/0/90]s of stacking sequence (see online version for colours) Source: Collombet et al. (006)

94 J. Saoudi et al. Figure 7 SEM in cross section of the wall of the holes after punching tests, (a) specimen with two plies under the tool (b) zoom of the highlighted zone in red color of Figure 7(a) after polishing (see online version for colours) (a) (b) If we take into account the variation of ply thickness in the analytical model, the relative deviation between the measured force and the predicted force can be reduced till 7% for any number of plies under the tool (Figure 8). In fact, when the ply thickness is increased, the bending stiffness is also increased, and in this case, the critical thrust force increases for any number of plies under the tool (Figure 8). Figure 8 Influence of the variability on the ply thickness of the laminate on the predicted thrust force; with (a) for one ply under the tool and (b) for two plies under the tool (see online version for colours) (a)

Prediction of critical thrust force for exit-ply delamination 95 Figure 8 Influence of the variability on the ply thickness of the laminate on the predicted thrust force; with (a) for one ply under the tool and (b) for two plies under the tool (continued) (see online version for colours) (b) Figure 9 Evolution of the critical thrust force at different level of the temperatures and for different plies under the tool (see online version for colours) Figure 9 depicts the evolution of critical thrust force predicted by the model for different levels of temperature. It is observed that when the temperature increases from 3 C till 150 C the critical thrust force decreases by 10%. This reduction can be attributed to the reduction in transverse Young s modulus and thermal coefficient. If we refer to equation (6), with increase in temperature (below T g ) results in decrease in the transverse modulus E and shear modulus G 1. However, the longitudinal modulus of elasticity E 11 remains practically stable since the carbon fibres are insensitive to variation in temperature. K in equation (38) is proportional to the E, G 1 and thermal coefficient by

96 J. Saoudi et al. equation (39). Therefore, any increase in temperature decreases I ij resulting in lower prediction for the critical thrust force, F c. 6 Conclusions A novel thermo-mechanical exit-ply drill delamination model for critical thrust force predictions has been presented in this work. The following conclusions can be drawn: 1 The thrust force predictions at hole exit at room temperature in good agreement with those identified during quasi-static punching tests. The variation between predictions and experimental values can attributed to the variation in ply thicknesses due to the process of manufacturing of the composite laminate. SEM observations reveal the difficulty in controlling the position of the chisel compared to the uncut plies of the laminates. In addition, SEM images indicate the initiation of the delamination (crack onset) is located in the vicinity of the chisel edge of the tool and not near the nominal diameter of tool as proposed in model. When the thickness variability of the plies (located under the tool) is taken into account in the analytical model, the difference between the critical thrust forces measured and those predicted is reduced to 7%. 3 When the temperature is taken into account in the analytical model, it is clear that a non-negligible reduction of the thrust force is observed. Given that the drilling process induces a marked increase in machining temperature, the current proposed model is more representative of the physics as compared to existing analytical models. Acknowledgements The authors wish to thank Philippe Seitier, engineer at INSA of Toulouse, for his technical support for the preparation of the drilled specimens. References Abrao, A.M., Rubio, J.C.C. and Faria, P.E. (008) The effect of cutting tool geometry on thrust force and delamination when drilling glass fibre reinforced plastic composite, Materials Design, Vol. 9, No., pp.508 513. Bert, C.W. (1983) Closed form solution of an arbitrarily laminated, anisotropic, elliptic plate under uniform pressure, Journal of Elasticity, Vol. 11, No. 3, pp.337 340. Cadorin, N. and Zitoune, R. (015) Wear Signature on Hole Defects as a Function of Cutting Tool Material for Drilling 3D Interlock Composite, Vols. 33 333, pp.74 751, Published online, DOI: 10.1016/j. wear.015.01.019. Cadorin, N., Zitoune, R., Seitier, P. and Collombet, F. (014) Analysis of damage mechanism and tool wear while drilling of 3D woven composite materials using internal and external cutting fluid, Journal of Composite Materials, 7 September, pp.1 17, Published online, DOI: 10.1177/001998314553045.

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