Acta Polytechnica CTU Proceedings doi:10.14311/APP.2016.3.0019 Acta Polytechnica CTU Proceedings 3:19–24, 2016 © Czech Technical University in Prague, 2016 available online at http://ojs.cvut.cz/ojs/index.php/app THE EFFECT OF SUPPORT PLATE ON DRILLING-INDUCED DELAMINATION Navid Zarif Karimia, ∗, Hossein Heidaryb, Parnian Kianfarc, Mahmud Hasanic, Giangiacomo Minaka a University of Bologna, Via Fontanelle 40, Forli, Italy b University of Tafresh, Tehran Road 1, Tafresh, Iran c Amirkabir University of Technology, Hafez 424, Tehran, Iran ∗ corresponding author: navid.zarif@unibo.it Abstract. Delamination is considered as a major problem in drilling of composite materials, which degrades the mechanical properties of these materials. The thrust force exerted by the drill is considered as the major cause of delamination; and one practical approach to reduce delamination is to use a back-up plate under the specimen. In this paper, the effect of exit support plate on delamination in twist drilling of glass fiber reinforced composites is studied. Firstly, two analytical models based on linear fracture mechanics and elastic bending theory of plates are described to find critical thrust forces at the beginning of crack growth for drilling with and without back-up plate. Secondly, two series of experiments are carried out on glass fiber reinforced composites to determine quantitatively the effect of drilling parameters on the amount of delamination. Experimental findings verify a large reduction in the amount of delaminated area when a back-up plate is placed under the specimen. Keywords: drilling, composite materials, delamination, support plate. 1. Introduction Glass fiber reinforced plastics (GFRPs) have been extensively employed in many engineering applications because of their outstanding advantages over other materials. The machining and specially drilling of GPRPs have become very important due to the need for assembling of subcomponents made from these materials. But, composite materials are difficult to machine due to some particular characteristics of them like non-homogeneous, anisotropic and abrasive fibers. This causes significant damages in drilling process such as matrix cracking, fiber breakage, fuzzing and thermal degradation. Among the damages caused by drilling, delamination is considered as one the most crucial, which results in lowering of strength against fatigue and subsequently reducing the long- term performance of composite structures [1, 2]. Several techniques have been suggested to reduce delamination in drilling process that each has its own advantages and limitations. One of the frequently used methods is to place a support plate under the specimen. During supported drilling, in contrast to un- supported drilling, the specimen is not free to bend due to constraints imposed by back-up plate. In drilling with back-up plate, the thrust force increases suddenly and severely as the chisel edge begins to penetrate into the specimen and it continues until the full pene- tration of cutting lips. At this point actual material removal takes place and the force reaches its steady state value, until delamination occurs. In this stage, delamination causes the force to decrease stepwise, each step associates to a crack opening. Unlike sup- ported drilling, during drilling without back-up plate, the force increases gradually at the beginning of pro- cess. This is mainly because the real feed rate is much lower than the adjusted feed due to relative movement of drill bit and workpiece. As the drill bit approaches the last uncut plies, the stress due to the thrust force exceeds its critical value and all the uncut material is burst open [3]. Until now, many researchers have attempted to re- duce drilling induced delamination. Hocheng and Dha- ran used linear elastic fracture mechanics to determine the critical thrust force for twist drilling as push-out delamination begins to propagate [4]. Hocheng and Tsao proposed some analytical models for different drill bits including candle stick drill, saw drill, core drill and step drill to determine the thrust force at the beginning of delamination growth [5, 6]. Based on these models, they realized the delamination can be reduced by lowering the thrust force or distributing the force outward from the center [7]. In a similar work, they studied the effect of exit back-up plate on drilling-induced delamination when using a slot drill bit and a core drill bit [8]. They showed that the critical thrust force is increased when using a back-up plate, hence delamination is less likely to happen. Many efforts have been made to reduce the thrust force exerted by drill bit on the specimen, while few re- searchers studied the effect of support plate on thrust force and associated delamination. This paper inves- tigates the effect of back-up plate on drilling-induced delamination both analytically and experimentally. 19 http://dx.doi.org/10.14311/APP.2016.3.0019 http://ojs.cvut.cz/ojs/index.php/app N. Zarif Karimi, H. Heidary, P. Kianfar et al. Acta Polytechnica CTU Proceedings 2. Experimental Procedure 2.1. Delamination Measurement Chen presented an index to evaluate the amount of delamination called conventional delamination factor [9]. However, this factor is not proper because the crack size does not represent the damage magnitude appropriately and also this procedure does not in- dicate the damage area. Davim et al. suggested a superior approach to determine the delamination fac- tor called the adjusted delamination factor Fda which is expressed as Eq. (1) [10]. The first part of Eq. (1) shows the size of the crack contribution and the second part shows the damage area contribution. Fda = α Dmax D0 + β Amax A0 (1) where the coefficients α and β can be calculated as below: β = Ad A0 − Amax α = 1 − β (2) where D0 is the nominal diameter of the hole, Dmax is the maximum diameter of the damage hole, A0 is the area related to the nominal hole, Amax is the area related to the maximum diameter of the delamination zone and Ad is the delaminated area. 2.2. Materials and Tools The composite plates were produced by hand lay-up method with araldite LY556 epoxy resin reinforced with 60 % E-glass unidirectional fiber. The density of epoxy resin and glass fibers were 1.12 g/cm3 and 292 g/m2, respectively. Tensile strength and tensile modules of resin were 80 MPa and 2.7 GPa, respec- tively, and for glass fibers were 2150 MPa and 74 GPa, respectively. The composite laminates had 16 plies and a thickness of 5 mm. The holes were drilled at the center of plates by standard HSS twist drills 10 mm. During unsupported drilling, a back-up plate of 5 mm thick was positioned under the specimens. An appro- priate clamping system was used to fix the specimens and back-up plate in the drilling machine, shown in Figure 1. The specimens and back-up plate were fixed in position by tightening four screws at the corners. 2.3. Plan of Experiments In the present study, Taguchi method was used to design drilling experiments. Three parameters, feed rate, cutting speed and drill point angle were selected and three levels for each parameter were suggested based on our preliminary researches [11–14]. After determination of parameters and correspond levels, a proper orthogonal array need to be selected. The orthogonal array chosen was the L9. After conducting experiments, the signal to noise ratio (SN) needs to be calculated for each experiment to determine the effect of each parameter. According Figure 1. Experimental setup. to this method, the optimization is done by using three signal to noise ratios; smaller is better, larger is better and nominal is better. Notice that, regardless of what approach is taken, always higher value of the signal to noise ratio is better. In this investigation, the delamination factor needs to be minimized; hence, smaller is better definition of the signal to noise ratio was used. SNi = −10 log( Ni∑ i=1 y2i Ni ) (3) where i is the experiment number and Ni is the num- ber of trials for experiment i [15]. 3. Results and Discussion 3.1. Theoretical Analysis of Critical Thrust Force The energy balance equation at the onset of delami- nation propagation is: dUd = dW − dU (4) in which dU is the infinitesimal strain energy, dW is the infinitesimal work done by the thrust force Fth and drill displacement of dX and dUd is the infinitesimal strain energy absorbed by crack growth which are as following: dW = Fth · dX dUd = GIC · dA (5) where dA is the change in the delamination area and GIC is the critical strain energy release rate in mode I, which is assumed to be constant according to Saghizadeh and Dharan [16]. 3.1.1. Critical Thrust Force in Drilling Without Support Plate Figure 2 depicts the schematic of delamination in unsupported drilling. In Figure 2, Fth is the thrust force exerted by a twist drill at the center of plate, X is the displacement of drill, H is the thickness of 20 vol. 3/2016 The Effect of Support Plate on Drilling-Induced Delamination Figure 2. The schematic of delamination for unsup- ported drilling. specimen, h is the uncut depth under tool, and a is the radius of crack (delamination). In this model, two assumption are considered; the isotropic behavior and pure bending of the laminate. According to the classical plate theory, for a circular plate with clamped edges and concentrated force the amount of deflection can be expressed as [17]: w(r) = Fth 16πM [2r2 ln r a + (a2 − r2)] (6) which is written in polar coordinate system (r is ra- dius). M = Eh3/(12(1 − ϑ2)) is flexural rigidity of the plate, E is modulus of Young, and ϑ is ratio of Poisson. The stored strain energy, the work done and the strain energy absorbed by crack growth are expressed as below equations, respectively. U = F 2tha 2 32πM dU = F 2tha 16πM da (7) W = Fthw(0) = F 2tha 2 16πM dW = F 2tha 8πM da (8) Ud = GIC · A = GICπa2 dUd = GIC 2πada (9) Now it is possible to calculate the critical thrust force at the onset of crack propagation by replacing Eqs. (7), (8) and (9) in the energy balance Eq. (4) as shown below: Fth = π √ 32GICM (10) In order to prevent delamination, the thrust force ex- erted by the drill bit on the specimen which is related to the material properties and the uncut thickness should not go over this value. 3.1.2. Critical Thrust Force in Drilling with Support Plate Figure 3 depicts the schematic of delamination in drilling with back-up plate. In Figure 3, FB is the thrust force with back-up, R is the upward reaction force from the back-up plate, b is the radius of the applied ring force of back-up and c is the drill radius, X is the displacement. For an edge clamped circular plate under the action of a concentrated force in center and upward circular force, the amount of deflection can be expressed as: w1(r) = FB 16πM [2r2 ln r a + (a2 − r2)]− − R 8πM [(r2 + b2) ln b a + 1 2 (1 − b2 a2 )(a2 + r2)] 0 6 r 6 b (11) w2(r) = FB 16πM [2r2 ln r a + (a2 − r2)]− − R 8πM [(r2 + b2) ln r a + 1 2 (1 + b2 a2 )(a2 − r2)] b 6 r 6 a (12) using boundary conditions, w(b) = 0, we get: R = FB [b2 ln b a + ( b 2−a2 2 )] [2b2 ln b a + ( a4−b42a2 )] (13) by replacing R into the plate deflection equations, Eq. (11) and Eq. (12), the total stored strain energy and work done by external forces can be derived as follow: U = π[ ∫ b 0 [M( ∂2w1 ∂r2 + 1 r ∂w1 ∂r )2]rdr+ + ∫ a b [M( ∂2w2 ∂r2 + 1 r ∂w2 ∂r )2]rdr] dU = ∂U ∂a da (14) W = FBw(0) = FB [ FBa 2 16πM − R 8πM (b2 ln b a + + ( a2 − b2 2 ))] dW = ( F 2Ba 8πM − RFB 8πM a2 − b2 a )da (15) finally, by calculating dUd from Eq. (14) and replacing dUd and dW in the energy balance equation, Eq. (4), we get: FB = π √ 32GICM B A (16) where A and B are defined as follow: 21 N. Zarif Karimi, H. Heidary, P. Kianfar et al. Acta Polytechnica CTU Proceedings Figure 3. The schematic of delamination for sup- ported drilling. B = [a4 − b4 − 8a2b2 ln b a ]× × [64b4a4 ln(a2b2) − 128a4b4 ln b ln a + 16a6b2 ln b a + + 16a2b6 ln a b + a8 + b8 − 2a4b4] (17) A = 3(a12 − b12) + 72a10b2 ln b a + 192a4b8 ln a ln b+ + 3072a6b6 ln a2 + b b2 + a + 768a4b8 ln a2 + b b2 + a − − 288a8b4 ln a ln b − 704a6b6 ln b + 192a2b10 ln a ln b+ + 73a4b4(a4 − b4) + 32a2b2(a8 − b8) + 64b4a8 ln b a + + 144a6b6 ln b a + 56a2b10 ln b a + 352a6b6 ln a2b2− − 96a2b10 ln a2b2 + 144a8b4 ln a2b2 + 1024a6b6 ln b3 a3 + + 256a4b8 ln b3 a3 + 768a4b8 ln a ln b − 16b12 ln a2b2+ + 32b12 ln a ln b − 384a4b8 ln a2b2 (18) 3.2. Experimental Results The graphs of thrust force and the scanned images of delamination in drilling with and without support plate at a feed rate of 0.025 mm/rev, spindle speed of 1600 rpm and drill point angle of 130 ◦ are shown in Figure 4. It is believed that the thrust force applied by the drill on the specimen causes delamination and it occurs when the thrust force goes beyond its critical value. However, the graphs of the force in Figure 4 clearly indicate this is only true for drilling with a support plate. During unsupported drilling the force is lower than in supported drilling, whereas the delamination is more extensive, which suggests that in unsupported drilling a different mechanism is in play, and other factors must be considered. These factors can be the dynamics of the workpiece, and the way in which the force is applied. The measured adjusted delamination factor (Fda) and the corresponding signal to noise ratio (SN) de- termined using Taguchi method smaller is better for Figure 4. The graphs of thrust force and the scanned images of delamination in drilling with and without support plate. Figure 5. Comparison of Fda in drilling with and without back-up. the two cases of drilling, supported and unsupported, are reported in Table 1.Symbols I and II in Table 1 represent two measured values for Fda. The t-test on the mean values of adjusted delami- nation factor demonstrates significant differences be- tween the means in these two cases (t0 = 8.00 > t0.005,34 = 2.73). To assist in the practical interpre- tation of this experiment, it is helpful to construct a graph of average responses at each experiment con- dition described in Table 1. This graph is shown in Figure 5. From Figure 5, a significant difference in adjusted delamination factor for supported drilling and unsupported drilling can be observed so that in all drilling tests, the average value of delamination is reduced when applying a back-up plate. This re- duction is in the range of 8-27 % for different drilling conditions. This reduction is mainly due to the re- duction in matrix crack growth as a result of upward reaction of back-up plate. The values of SN data for the adjusted delamina- tion factor for unsupported and supported drilling are given in Table 1 and shown in Figure 6. For unsupported drilling, the most important parame- 22 vol. 3/2016 The Effect of Support Plate on Drilling-Induced Delamination Test no. Parameters Unsupported Supported Feed rate(mm/rev) Speed (rpm) Angle (◦) Fda(1) Fda(2) S/N Fda(1) Fda(2) S/N 1 0.025 800 90 1.41 1.37 -2.86 1.04 1.05 -0.34 2 0.025 1250 118 1.25 1.28 -2.04 1.07 1.06 -0.55 3 0.025 1600 130 1.30 1.26 -2.14 1.11 1.07 -0.75 4 0.05 800 118 1.49 1.52 -3.55 1.09 1.09 -0.87 5 0.05 1250 130 1.20 1.21 -1.62 1.10 1.11 -1.25 6 0.05 1600 90 1.33 1.28 -2.31 1.16 1.15 -0.75 7 0.1 800 130 1.49 1.58 -3.73 1.15 1.14 -1.40 8 0.1 1250 90 1.32 1.30 -2.35 1.18 1.17 -1.17 9 0.1 1600 118 1.36 1.33 -2.57 1.22 1.25 -1.83 Table 1. L9 orthogonal array of Taguchi and experimental results. Figure 6. Effect of process parameters for (a) un- supported drilling, (b) supported drilling. ters affecting the delamination factor are the spindle speed followed by feed rate. The optimum process parameters on the delamination are obtained as feed rate at level 1 (0.025 mm/rev), spindle speed at level 2 (1250 rpm) and drill point angle at level 3 (130 ◦) when drilling without back-up plate. However, when the back-up plate is applied, the effect of feed rate on delamination increases so that it becomes the most im- portant parameter followed by spindle speed, Figure 6 (b). The cause of this phenomenon can be attributed to the cutting mechanism and the relative movement of the tool and specimen. It is observed that the optimal value of the feed rate should be kept at low level in order to minimize the delamination factor. The optimum process parameters on the delamination are obtained as feed rate at level 1 (0.025 mm/rev), spindle speed at level 1 (800 rpm) and drill point angle at level 3 (130 ◦) for supported drilling. 4. Conclusions In this paper, the effect of exit support plate on delam- ination in drilling of glass fiber reinforced composites is studied. A comprehensive analysis of the critical thrust force in drilling with and without back-up plate is presented based on three theories i.e. energy con- servation theory, elastic bending theory and linear elastic fracture mechanics. The experimental results confirm the effects of delamination reduction when using a back-up plate under the specimen. This re- duction is in the range of 8-27 % for different drilling conditions. This reduction is attributed to the crack growth suppression by upward reaction of back-up plate. References [1] R. M. Jones. Mechanics of composite materials. CRC Press, 1998. [2] D. Liu, Y. Tang, W. L. Cong. A review of mechanical drilling for composite laminatesc. Composite Structures 94(4):1265–1279, 2012. [3] E. Capello. Workpiece damping and its effect on delamination damage in drilling thin composite laminates. Journal of Materials Processing Technology 148(1):186–95, 2004. [4] H. Ho-Cheng, C. K. H. Dharan. Delamination during drilling in composite laminates. 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CRC press, 2004. 24 http://dx.doi.org/10.1016/j.compstruct.2012.10.044 http://dx.doi.org/10.1177/0021998314521258 http://dx.doi.org/10.1016/j.compstruct.2015.04.025 Acta Polytechnica CTU Proceedings 3:19–24, 2016 1 Introduction 2 Experimental Procedure 2.1 Delamination Measurement 2.2 Materials and Tools 2.3 Plan of Experiments 3 Results and Discussion 3.1 Theoretical Analysis of Critical Thrust Force 3.1.1 Critical Thrust Force in Drilling Without Support Plate 3.1.2 Critical Thrust Force in Drilling with Support Plate 3.2 Experimental Results 4 Conclusions References