Drilling analysis of chopped composites

Drilling analysis of chopped composites

Composites: Part A 38 (2007) 61–70 www.elsevier.com/locate/compositesa Drilling analysis of chopped composites U.A. Khashaba a a,* , M.A. Seif b, M...

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Composites: Part A 38 (2007) 61–70 www.elsevier.com/locate/compositesa

Drilling analysis of chopped composites U.A. Khashaba a

a,*

, M.A. Seif b, M.A. Elhamid

a

Mechanical Design and Production Engineering Department, Faculty of Engineering, Zagazig University, P.O. Box 44519 Zagazig, Egypt b Mechanical Engineering Department, Alabama A&M University, Normal, AL 35762, USA Received 5 October 2005; received in revised form 12 January 2006; accepted 15 January 2006

Abstract This work investigates the effects of the drilling parameters, speed, and feed, on the required cutting forces and torques in drilling chopped composites with different fiber volume fractions. Three speeds, five feeds, and five fiber volume fractures are used in this study. The results show that feeds and fiber volumes have direct effects on thrust forces and torques. On the other hand, increasing the cutting speed reduces the associated thrust force and torque, especially at high feed values. Using multivariable linear regression analysis, empirical formulas that correlate favorably with the obtained results have been developed. These formulas would be useful in drilling chopped composites. The influence of cutting parameters on peel-up and push-out delaminations that occurs at drill entrance and drill exit respectively the specimen surfaces have been investigated. No clear effect of the cutting speed on the delamination size is observed, while the delamination size decreases with decreasing the feed. Delamination-free in drilling chopped composites with high fiber volume fraction remains as a problem to be further investigated.  2006 Published by Elsevier Ltd. Keywords: A. Laminates; B. Fracture; B. Mechanical properties; E. Machining

1. Introduction The variation of the geometrical parameters along the cutting edge of the twist drill makes drilling a complex machining process. The chisel edge of the drill and the edge of the margins have unfavorable geometrical parameters [1,2]. The rake angles on the chisel edge have large negative values. This makes cutting process difficult and sharply increases the feeding force required for drilling holes. The relief angles at the edge of the margins are equal to zero. This leads to intensive friction and wear. The variation of the rake angle along the whole length of the lip is an essential shortcoming of twist drills, since it leads to complex conditions of chip formation. The actual value of the relief angle during the drill operation differs from that obtained in sharpening and measured in the static state. This is explained by the fact that the drill not only rotates, but also travels axially during operation. The path of the motion of *

Corresponding author. Tel.: +20 10 336 4264; fax: +20 55 230 4987. E-mail address: [email protected] (U.A. Khashaba).

1359-835X/$ - see front matter  2006 Published by Elsevier Ltd. doi:10.1016/j.compositesa.2006.01.020

a point on the lip will not be a circle (as assumed in measuring the relief angle), but a helix of a lead equal to the feed of the drill in millimeters per revolution. Thus, the surface of the cut formed by the whole cutting edge will be a helical surface. The maximum cutting speed is, of course, on the periphery of the drill at the outer corner of the cutting lip. This is one of the principal reasons for intensive wear of this zone, and this limits drill life. The use of fiber-reinforced composite materials in automobile and aerospace industries has grown considerably in recent years because of their unique properties such as high specific stiffness and strength, high damping, good corrosive resistance, and low thermal expansion. Drilling is usually the final operation during the assembly of the structures in these applications. Any defects that lead to the rejection of the parts represent an expensive loss. For example, in the aircraft industry, drilling-associated delamination accounts for 60% of all part rejections during final assembly of an aircraft [3]. The economic impact of this is significant considering the value associated with the part when it reaches the assembly stage. The quality of the

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drilled holes such as waviness/roughness of its wall surface, axial straightness, and roundness of the hole cross-section can cause high stresses on the rivet, which will lead to its failure. Stress concentration, delamination, and microcracking associated with machined holes significantly reduce the composites performance [4–6]. Several hole production processes, including conventional drilling, ultrasonic drilling, laser-beam drilling, water jet drilling, etc., have been proposed for a variety of economic and quality reasons. Conventional drilling is still the most widely used technique in industry today [7]. A major concern that has received considerable attention in drilling holes in FRCM is the delamination, especially at the bottom surface of the workpiece (drill exit). The thrust force developed during the drilling process affects the width of the delamination zone. It is believed that there is a ‘‘critical thrust force’’ below which no damage occurs [3,6,8–11]. Tsao and Hocheng [12] have established a correlation that relates feed rate, spindle speed, and drill diameter to the induced delamination in a CFRP laminate. The correlation is obtained by using a multivariable linear regression analysis. Davim and Reis [13,14] used the same technique to construct the correlations between cutting parameters (cutting velocity, feed rate) and cutting power, specific cutting pressure and delamination factor in CFRP composite laminate. The obtained models demonstrate a feasible and an effective way for the evaluation of the drilling-induced delamination factor. Dharan and Won [15] investigated the effect of feeds in high-rate drilling of woven carbon fiber/epoxy laminates on thrust force and torque using carbide-tipped twist drills. The experimental data was welldescribed empirically by power law expressions relating the thrust force and torque to the feed and tool diameter. The main objective of the present study is to investigate the effects of the cutting variables, speed and feed, on the thrust force, torque, and delamination in drilling chopped composites with different fiber volume fractions. Based on the results from this investigation, empirical formulas are developed. Such formulas would be very useful in selecting the drilling conditions in chopped composites.

in fiber volume fractions was achieved through the variation in the number of fiber layers. Therefore the thickness of the laminates with different fiber volume fraction was in the range 4.14 ± 0.3 mm. Whereas the variation in the laminate thickness, with certain fiber volume fraction, was in the range ±0.05 mm. This variation approximately has insignificant effect on fiber volume fractions. Details about the manufacturing technique are illustrated elsewhere [16]. The chopped composites are investigated to characterize their mechanical properties as affected by the fiber volume fraction [16–18]. Such investigations include uniaxial tension and bending properties [16], notched and pin bearing behavior [17], and environmental effects on compressive strength of notched and unnotched specimens [18]. The constituent materials of the composite laminate are illustrated in Table 1. 2.2. Drilling operations Drilling processes are conducted on chopped glass fiber reinforced epoxy GFRP composites using a radial drilling machine with standard HSS twist drills. To ignore the effect of drill wear each hole was implemented using new drill. The influence of the cutting variables (speed and feed) on the thrust force, torque, and delamination has been investigated experimentally. The drilling variables are  feed, f, with the values of 0.03, 0.08, 0.15, 0.23, and 0.3 mm/rev,  cutting speed, N, with the values 455, 875 and 1850 rpm. Many investigators [13,19,20] show that the hole surface quality (surface roughness and dimensional precision) is strongly dependent on cutting parameters, tool geometry, and cutting forces (thrust and torque). In the present work, the drilling process is carried out using commercial HSS twist drills with constant geometry, Table 2. 2.3. Measurements of the thrust force and torque In the present work, two-component drill dynamometer, Fig. 1, has been used to measure the thrust force (Ft) and

2. Experimental work 2.1. Specimen preparation

Table 1 Composition of GFRP composite laminates

‘‘The drilling processes are carried out on chopped glass fiber-reinforced polyester (GFRP) composites with various values of fiber volume fractions (Vf = 10.2%, 16%, 23.2%, and 27.7%) and compared with pure matrix. The variation

Material

Type

Matrix Hardener Reinforcement

Orthophthalic polyester (RESIPOL 9024 ST) Methylethyl ketone peroxide (0.8% of matrix volume) E-glass, chopped strand mat (450 g/m2)

Table 2 Specifications of HSS twist drill Drill diameter (mm)

Point angle (degree)

Helix angle (degree)

Rake angle (degree)

Clearance angle (degree)

Cutting edge length (mm)

Chisel edge length (mm)

Chisel edge angle (degree)

Land of margin (mm)

8

118

30

30a

12a

3.75

2.2

51

0.8

a

Measured at the outer diameter.

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torque (T) during the drilling processes. Fig. 2 shows the acting forces on the drill [21]. The details about the design and manufacturing of this dynamometer are illustrated elsewhere [1,22]. The measurements of the thrust forces and torques are taken every 0.05 s. The variations of the thrust forces and torques with machining time are plotted as waveforms. The average value of the maximum five peaks in each wave diagram is used to investigate the influence of the cutting variables on the cutting forces. At least two tests are implemented for each cutting condition. The back plate under the test specimen has 14 mm central hole diameter. The center of backing plate hole is coinciding with drill center.

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2.4. Delamination size measurements Two mechanisms of delamination associated with drilling FRP composites are investigated in the present study. They are known as peel-up at the entrance and push-out at the exit [1,3,23]. Peel-up occurs as the drill enters the laminate and is shown schematically in Fig. 3a. After the cutting edge of the drill makes contact with the laminate, the cutting force acting in the peripheral direction is the driving force for delamination. It generates a peeling force in the axial direction through the slope of the drill flute that results in separating the laminas from each other forming a delamination zone at the top surface of the laminate. Push-out is the delamination mechanism occurring as the drill reaches the exit side of the material and is shown schematically in Fig. 3b. As the drill approaches the end, the uncut chip thickness gets smaller and the resistance to deformation decrease. At some point, the thrust force exceeds the interlaminar bond strength and delamination occurs. This happens before the laminate is completely penetrated by the drill as shown in Fig. 3b. An accurate, inexpensive image technique for measuring the delamination size within 103 mm resolution has been used in this study. The technique has been applied to several kinds of quasi-transparent composites [1]. The technique requires a color flatbed scanner and commercial image analysis software. The delamination size is defined as the difference between the maximum damage radius and the drilled hole radius (4 mm), Fig. 4. Details of the measurement technique are illustrated in Khashaba work [1]. This technique is not applicable to carbon fiber-based composites, because their color makes visual inspection difficult. Another techniques can be applied to these materials such as ultrasonic

Fig. 1. Drilling set-up.

Fig. 2. The acting forces on the drill.

Fig. 3. Mechanisms of delamination: (a) peel-up at entrance and (b) pushout at exit [23].

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of the drill point with the specimen. The sharp increase in the thrust force at the start of the drilling process is attributed to the following:

Fig. 4. Photograph illustrating the delamination size (Rmax  R).

C-scan, X-ray computerized tomography [11], and shadow Moire´ laser based imaging technique [24]. 3. Results and discussion Delamination associated with drilling fiber-reinforced composite materials has the tendency of reducing the structural strength. Also, it results in poor assembly tolerance and, hence, it has the potential for long-term performance deterioration. The main key for solving this problem lies in reducing the thrust force associated with drilling. The thrust force, Ft, must overcome the sum of the forces of the resistance acting along the drill axis. Fig. 5 shows the variation of the thrust force and torque during the drilling process in GFRP composites. This figure indicates that the thrust force increases sharply at the start of the drilling process. Then, it increases slowly after the full engagement

1. The chiseling edge produces a high thrust force. The chiseling edge thrust force in drilling metals is 57% [25]. In drilling carbon fiber-reinforced epoxy composites, the average chiseling edge thrust force is 53% of the total thrust force [7]. The high values of the chiseling edge thrust force are due to the negative rake angles at the chisel edge. This makes cutting difficult and sharply increases the feeding force required. The tool does not actually cut, but, instead, it extrudes the material [25]. The region near the drill center is called the extrusion or the indentation zone. 2. The variation of the normal rake angle, cN, along the cutting lips is another contributing factor for increasing the thrust force, Fig. 6. The normal rake angle is negative near the center of the drill and has large positive values near the outer diameter of the drill [2]. The tangential cutting velocity is a linear function of the radial distance with its maximum at the outer radius. The changes in both the normal rake angle and the cutting velocity cause the specific cutting pressures (normal and tangential), and, hence, the forces, to vary along the cutting lips of the drill. The cutting action is much more efficient at the outer region of the cutting lips than toward the drill center. Therefore, the specific cutting pressure has its maximum value at the center of the drill and decreases to reach its minimum at the outer diameter of the drill [7]. 3. The uncut chip area increases with the increase of the cutting depth until the full engagement of the cutting edges occurs. Fig. 5 also shows that the moment of the forces, (Tch), due to scraping and friction on the chisel edge, is approximately insignificant because of the lower value of the moment arm of the chisel edge, (moment arm = half the chisel edge length = 1.1 mm), Table 2. The friction moment of the margins (Tf) is attributed to the chips formation, which are in the form of fine particles. These chips work

Work thickness + High of drill point

80

Mechanical units

Thrust (N)

60

40 Torque (N.Cm)

20

Tch =0 Tf

0 Cutting time

-20

0

5

10

15

20

25

Machining time, (sec.) Fig. 5. Thrust force and torque measurement over a drilling cycle.

Fig. 6. Variation of normal rake angle (cN) and clearance angle (a) along the cutting edge of a twist drill [2].

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as abrasive materials between the margins and the drilled hole, resulting in increasing the friction moment (moment arm = D/2 = 4 mm).

Vf, f

3.1. Thrust force data analysis

At each cutting speed, the values of a0, a1, and a2 are determined from the experimental data of Table 3. The multivariable linear regression models that relate the thrust force with the fiber volume fraction and the feed at each cutting speed, N, are

The effects of feed, speed, and fiber volume fraction on the thrust force in drilling GFRP composites are shown in Table 3. The results in this table can be summarized in the following points:

fiber volume fraction and feed, respectively–independent variables, a0, a1, and a2 multiple regression parameters.

(a) N = 455 rpm 1. The thrust force increases with the increase of the fiber volume fraction. 2. Although it is known that the thrust force increases with the increase of the feed, this work provides quantitative measurements of such relationships for the present composite materials. 3. In general, increasing the cutting speed will decrease the thrust force [1,22]. This work shows that the cutting speed has an insignificant effect on the thrust force when drilling at low feed values (f = 0.03, 0.08, and 0.15 mm/ rev). At high feed values (f = 0.23, and 0.3 mm/rev), the thrust force decreases with an increased cutting speed. 3.2. Thrust force correlation analysis The correlation between thrust force (Ft) and both fiber volume fraction (Vf) and feed (f) at different speeds in drilling GFRP is obtained using the multivariable linear regression analysis [26]. The equations can be expressed as follows: F t ¼ a0 þ a1  V f þ a2  f ; where Ft

F t ¼ 36:603 þ 1:895V f þ 405:753f (b) N = 785 rpm F t ¼ 42:1114 þ 1:746V f þ 356:883f

ð3Þ

(c) N = 1850 rpm F t ¼ 46:361 þ 1:577V f þ 318:626f .

ð4Þ

These equations are very important to the designer who works with such composites. The suitable cutting conditions can be selected so that the thrust force cannot exceed the critical thrust force that is calculated using linear elastic fracture mechanics and classic plate bending theory [3,7,8,10]. Table 3 shows the comparison between the experimental results and the calculated thrust force using the empirical formulas. When more than one independent variable is present in the experiment, the measure of the best-fitting equation is referred to as the multiple correlation coefficients. This can be derived from [26]

ð1Þ rF t V f f

thrust force–dependent variable, which varies due to variation of the independent variables,

ð2Þ

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u S 2F .V f ¼ t1  t 2 f ; SF t

ð5Þ

where

Table 3 Thrust force at different speed, feed, and fiber volume fraction Speed N (rpm)

Fiber volume Vf (%)

Feed, f (mm/rev) 0.03

455

785

1850

00.0 10.2 16.0 23.2 27.6 00.0 10.2 16.0 23.2 27.6 00.0 10.2 16.0 23.2 27.6

0.08

0.15

0.23

0.3

Exp.

Model

Exp.

Model

Exp.

Model

Exp.

Model

Exp.

Model

50.01 66.66 75.07 80.09 83.34 62.68 59.43 69.62 78.62 82.01 59.07 62.24 78.32 75.08 80.01

48.77 68.10 79.09 92.74 101.07 52.82 70.63 80.75 93.33 101.01 55.92 72.00 81.14 92.50 99.43

70.04 86.14 99.57 110.64 122.30 82.01 76.55 90.42 118.75 124.05 75.02 82.60 100.01 110.19 115.00

69.06 88.389 99.38 113.02 121.36 70.66 88.47 98.60 111.17 118.85 71.85 87.93 97.08 108.43 115.36

87.11 143.54 151.51 157.56 158.30 98.24 120.23 152.10 156.68 160.04 102.52 108.72 139.71 154.76 159.63

97.46 116.79 127.78 141.43 149.76 95.64 113.45 123.58 136.15 143.83 94.15 110.23 119.37 130.73 137.66

122.59 160.22 167.30 171.88 176.30 120.01 140.74 163.02 168.78 169.08 122.74 136.44 145.02 161.25 169.51

129.92 149.25 160.24 173.89 182.22 124.19 142.00 152.13 164.70 172.38 119.64 135.73 144.87 156.22 163.16

143.69 175.27 189.14 195.49 203.60 135.03 156.68 181.61 183.83 184.86 139.41 142.95 155.04 170.40 179.11

158.33 177.65 188.65 202.29 210.63 149.18 166.99 177.11 189.68 197.37 141.95 158.03 167.17 178.52 185.46

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rF t .V f f S F t .V f f SF t

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multiple correlation coefficient of Ft on Vf and f, standard error of estimate of Ft on Vf and f, sample standard deviation of Ft.

mechanisms of the polymeric composite materials that have anisotropic and inhomogeneous properties. 3.3. Torque data analysis

The standard error of estimate S F t .V f f can be calculated from the following equation:

S F t .V f f where z z3

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 P P P F t  a0 F t  a1 V f .f  a2 F t .f ; ¼ z3

ð6Þ

number of data points, number of degrees of freedom.

The number of degrees of freedom in Eq. 1 is expressed as z  3, since the number of parameters to be estimated are three a0, a1, and a2. The calculated values of the multiple correlation coefficients for each cutting speed (z = 25 data points; five Vf and five feed values) are r = 0.97, 0.95, and 0.95 for n = 455, 785, and 1850 rpm, respectively. The percent of the total variation in the thrust force (r2 · 100) varies from 90% to 94%. This indicates good correlation, and the equations closely resemble the experimental data, Fig. 7a–c. The variation in Ft can be attributed to the complex cutting

(a)

Table 4 shows the effect of feed, speed, and fiber volume fraction on the resulting torque in drilling GFRP composites. The results indicate that the torque increases as the feed increases. This increase is due to the increasing of the crosssectional area of the undeformed chip (A = Df/4). The results also indicate that the torque increases with the increase of the fiber volume fraction. Increasing fiber volume fraction increases the static strength [16], and, hence, the resistance of the composite to mechanical drilling increases [16]. This leads to the increase in the required thrust force and torque. The table also indicates that the torque decreases when increasing the cutting speed. This phenomena has been observed and discussed by Khashaba et al. [1,22]. 3.4. Torque correlation analysis Similarly, the values of the multiple regression parameters, a0, a1, and a2, are determined from the experimental data in Table 4. The linear regression models can be written as

(b)

(c) Fig. 7. Effect of feed and fiber volume on thrust force at different speeds.

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Table 4 Torque at different speed, feed, and fiber volume fraction Speed N (rpm)

Fiber volume Vf (%)

Feed, f (mm/rev) 0.03

455

785

1850

00.0 10.2 16.0 23.2 27.6 00.0 10.2 16.0 23.2 27.6 00.0 10.2 16.0 23.2 27.6

0.08

0.15

0.23

0.3

Exp.

Model

Exp.

Model

Exp.

Model

Exp.

Model

Exp.

Model

4.69 16.02 18.05 21.03 23.75 5.01 15.04 16.02 20.01 21.37 5.37 11.16 12.03 15.50 15.02

7.30 13.92 17.68 22.35 25.21 8.20 13.69 16.81 20.68 23.05 5.89 11.10 14.06 17.74 19.99

11.16 20.04 22.10 25.02 28.01 10.01 17.97 20.04 23.06 25.02 10.02 15.01 16.26 22.03 23.05

10.51 17.13 20.90 25.57 28.43 10.51 15.99 19.12 22.99 25.36 8.67 13.89 16.85 20.53 22.78

16.26 24.77 26.81 28.18 31.58 16.60 21.37 24.77 26.13 28.18 14.56 19.67 24.77 28.18 26.01

15.01 21.63 25.40 30.07 32.93 13.74 19.23 22.35 26.22 28.59 12.58 17.79 20.75 24.43 26.68

21.37 26.50 28.18 33.03 36.68 16.94 24.09 25.11 29.20 31.58 15.92 23.07 28.18 30.01 30.03

20.16 26.78 30.54 35.21 38.07 17.43 22.92 26.04 29.92 32.28 17.04 22.25 25.21 28.89 31.14

22.05 29.20 31.92 43.49 48.60 18.10 26.01 28.16 33.03 37.36 15.92 23.07 30.01 32.50 35.02

24.66 31.28 35.04 39.72 42.57 20.67 26.15 29.27 33.15 35.52 20.94 26.15 29.12 32.80 35.04

(c) N = 1850 rpm

(a) N = 455 rpm T ¼ 5:369 þ 0:649V f þ 64:299f

ð7Þ

T ¼ 4:213 þ 0:511V f þ 55:758f .

ð8Þ

Table 4 shows the comparison between the experimental results and the calculated values of the torque using the multivariable linear regression models.

(b) N = 785 rpm T ¼ 6:814 þ 0:538V f þ 46:176f

(a)

(b)

(c) Fig. 8. Effect of feed and Vf on torque in drilling of GFRP composites at different speeds.

ð9Þ

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The calculated values of the multiple correlation coefficients, r, at each cutting speed are 0.97, 0.98, and 0.95 for N = 455, 785, and 1850 rpm, respectively. The percent of the total variation in the thrust force (r2 · 100) varies from 90% to 95%. This indicates that there is a good correlation between the experimental values and the proposed models, Fig. 8a–c. 3.5. Delamination data analysis Two delamination mechanisms associated with drilling GFRP composites are observed in the present study peel-

up at the entrance and push-out at the exit. Fig. 9 shows photographs of the peel-up and push-out delamination for the GFRP specimens with a fiber volume fraction, Vf, of 23.2%, and at a cutting speed of 445 rpm at different feeds. At high feed values, the photographs illustrate a massive delamination associated with chipped fibers, especially at the exit side of the drilled holes. Figs. 10a–d and 11a–d show the effect of feed and cutting speed on the peel-up and push-out delamination, respectively, at different fiber volume fractions. The results in these figures indicate that the delaminations associated with push-out are more severe than those associated with

Fig. 9. Delamination in drilling GFRP specimens at different feeds: (a) peel-up delamination and (b) push-out delamination.

(a)

(b)

(c)

(d) Fig. 10. Effect of feed and speed on peel-up delamination at different fiber volume fractions.

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(a)

(b)

(c)

(d)

69

Fig. 11. Effect of feed and speed on peel-up delamination in drilling of GFRP composites with different Vf.

peel-up. Delamination-free in drilling chopped composites with Vf = 10.2% is achieved at feed = 0.03 mm/rev. Although push-out delaminations of specimens with Vf = 16% equal zero at feed = 0.03 mm/rev., peel-up delaminations are observed at this feed value. This may be due to the difference in the peel-up and push-out delamination mechanisms. The cutting force acting in the peripheral direction is the main cause of the peel-up delamination, while the thrust force is the main source of the push-out delamination. These forces are affected by the tool geometry, the friction between the tool and specimen, the applied pressure, and the cutting conditions [3]. In general, delamination increases with the increase of the feed, Figs. 10 and 11. No clear results about the effect of the cutting speed on the delamination size are concluded. Delamination-free in drilling chopped composites with high fiber volume fraction remains a problem that needs to be thoroughly investigated. 4. Conclusions Although it is known that the thrust force and torque increases with the increase of the feed, this work provides quantitative measurements of such relationships for the present composite materials. Fiber volume fraction is directly proportional with thrust force and torque in dril-

ling GFRP composites. On the other hand, increasing the cutting speed reduces the thrust force and the torque. Empirical formulas that determine the cutting forces based on fiber volume fractions, feeds, and speeds are obtained using multivariable linear regression analysis. The percent of the total variation varies from 90% to 95%. This indicates that the correlation is good and the equations could be used to determine the cutting forces and torques. Delamination also increases as the feed increases. In general, push-out delamination is more severe than peel-up delamination for the same-drilled hole. The cutting speed has no clear effect on the delamination size. Delamination-free in drilling chopped composites with high fiber volume fraction remains a problem that needs to be thoroughly investigated. Acknowledgements The work reported herein is sponsored by the US— Egypt Joint Science and Technology Program and National Science Foundation—INT. Profs. Khashaba and Seif would like to acknowledge the support of Dr. F. ElRefaie, President of Academy of Scientific Research and Technology, Egypt, and Dr. O.A. Shinaishin, Senior Program Manager, Office of International Science and Engineering at the National Science Foundation.

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