drilling of composite publié par younes persian

7/30/2019 drilling of composite publi par younes persian

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Drilling of composite structures

Frederic Lachaud, Robert Piquet, Francis Collombet *, Laurent Surcin

Departement de Genie Mecanique et Productique, Institut Universitaire de Technologie Paul Sabatier, Laboratoire de Genie Mecanique de Toulouse,

133 avenue de Rangueil, 31077 Toulouse cedex 4, France

Abstract

Structural parts made of composites have frequently to be drilled in the aircraft industry. However, little is know about the

interacting conditions between the drilling tool and the material, which may be multi-type and multi-size. This study proposes a

model which links the axial penetration of the drill bit to the conditions of delamination (crack opening mode I) of the last few plies.

Several types of tool/material contact conditions were analyzed and were compared with experimental measurements, and with amodel taken from the literature. Our study shows a close correlation between experiment and calculation when the thrust force of

the drill is modeled by taking into account the geometrical nature of the contact between the tool and a laminate composite ma-

terial. 2001 Published by Elsevier Science Ltd.

Keywords: Drilling; Composite laminated; Delamination

1. Introduction

In the aircraft industry, the double uted twist drill is

classically used for the in order to realized repairs or

joining of thin carbon/epoxy structures.

Drilling thin carbon bers/epoxy matrix laminates is

frequently carried out in the aircraft industry when

manufacturing riveted assemblies or for structural re-

pairs.

This study is not a contribution to the design of

drilling tools adapted for composite structures but to

supply to the operator a simple protocol to minimize the

damage events which can occur during drilling. Indeed

the double-uted twist drill used for the machining of

metals is not well adapted for composite materials (Fig.

1) [1]. This drill causes damage, the extent of which in-

creases in the absence of a backing plate. This situation

is often met during structural repairs of airplane com-posite structures.

For a multi-scale heterogeneous material, the damage

depends on:

the nature and mechanical characteristics of the long

bers used in the ply,

the stacking sequence and the mechanical characteris-

tics in dierently oriented ply interfaces (matrix)

throughout the plate thickness.

From the works of various authors [26], a brief sum-

mary of drilling defects is presented here (the hole entry

defect, the circular defect and damage from a heat

source in the wall of the hole, the delamination at the

exit hole). This paper deals with the initiation conditions

of delamination.

An analytical model used the classical plate theory

allows us to model the thrust force applied by the drill

versus the critical energy release rate in mode I for a

given depth of the bit of the drill. The axial load value

for the drill associated with the rst signs of delamina-

tion is calculated by means of an energy criterion. This

procedure leads to a problem simplication process by

ignoring the drill friction eect on the dierent contact

surfaces during drilling.Two representational hypotheses of part/tool contact

have been analyzed:

where thrust force is uniformly distributed on the chi-

sel edge and on the two main cutting edges of the

drill,

where contact geometry has not been specied, and

thrust force is represented by a localized force along

the drill axis.

The analytical values obtained from these hypotheses

are subsequently compared with experimental results,

and a model from the work of [5].

Composite Structures 52 (2001) 511516

www.elsevier.com/locate/compstruct

* Corresponding author.

E-mail addresses: [email protected] (R. Piquet), fran-

[email protected] (F. Collombet).

0263-8223/01/$ - see front matter 2001 Published by Elsevier Science Ltd.

PII: S 0 2 6 3 - 8 2 2 3 ( 0 1 ) 0 0 0 4 0 - X


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This paper shows that the results of our model are the

most close to the experimental results.

2. Review of drilling-induced damages studies

Using a twist drill causes several types of defect in the

laminate, [2,48] which can be divided into four main

types.

Hole entry defect does not appear on every occasion.

It is related to the brous character of material (due to

unidirectional plies) and to the drill geometry. It leads to

the tearing of the rst ply of the rst layer in contact

with the drill (Fig. 2).

Circular defect is linked to the presence of an angle

created by the direction of the bers of the ply con-

cerned, and by the direction of the cutting edge. De-

pending on the angular position of the cutting edges,

Fig. 2. Dierent defects in a composite plate.

Fig. 1. Exemples of drilling thin carbon/epoxy plates without backing plate.

512 F. Lachaud et al. / Composite Structures 52 (2001) 511516


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and just before being cut, the bers are subject to an

alternating action of bending/compression stress. The

unilateral behavior of carbon bers thus leads to an el-

liptical hole shape. The minor axis of the ellipse in

smaller than the drill diameter and coincides with the

direction of the bers of the ply under consideration

(Fig. 2).

Damage from a heat source is due to friction between

the bers and the two minor cutting edges of the drill. It

can cause damage to the matrix at the hole edge, thus

increasing the likelihood of torn bers due to the me-

chanical action of the minor cutting edges. Removal of

bers leads to a roughness defect on the side wall of the

hole.

Delamination at the exit hole is provoked by the cut-

ting conditions imposed by the fact that the chisel edge of

the twist drill cannot cut through the material. The thrust

force of the drill (feed-rate) may cause normal stress

which is likely to open the ply interface (crack opening

mode I). Delamination between plies spreads beyond thehole diameter, and can occur at varying depths as the drill

progresses (Fig. 2). For the purposes of our research, we

have concentrated on the situation where a single del-

amination occurs due to ply bending in the zone beneath

the drill (i.e. with no backing plate) [912].

As can be seen on Fig. 1 delamination occurs mainly

because of localized bending in the zone situated at the

point of attack of the drill.

3. Analytical model (theory)

The multi-directional stacking sequence studied leads

to damage spreading in a circular fashion. As a rst

approach, the crack opening mode is considered to be

due to normal stress perpendicular to the ply surface,

designated as rZZ [511].

The circular defect is considered to be initiated by the

drill in contact with the material during the drilling

process (Fig. 3). The corresponding surface denes the

underlying part of the plate liable to bend as the drill

penetrates the material. We propose a study of the

conditions of extension of this initial defect by means of

an energy analysis in the case of failure mechanics. To

obtain this, the part of the plate located beneath the drillhas been modeled in terms of a thin circular orthotropic

plate. This plate has the same dimension as the drill, and

is clamped on the laminate surface (Fig. 3). This repre-

sentation does not take into account the global deec-

tion of the plate. It is only valid for a weak number of

plies located under the drill.

3.1. First hypothesis (distributed load model)

The contact between drill and plate was initially

modeled by a uniformly distributed load, with resultant

FZ (Fig. 3). By applying the plate theory [13], the equi-

librium equation of a plate element is written thus:

o2Mxx

ox2o

2Myy

oy2

2o2Mxy

oxoy q 1

with Mxx;Myy;Mxy bending moments.The part of the plate in contact with the drill is a

symmetric laminate j Bij 0 j for which the stress/strain law is written:

Mxx

MyyMxy

VbbbbX WbbabbY D11 D12 D16

D12 D22 D26D16 D26 D66

o2wox2

o

2w

oy2

2 o2w

oxoy

VbbbbbbbbX

WbbbbabbbbY: 2

The Dij coecient (bending stiness) has been calculated

by using the relation (3) obtained by means of the theory

of laminates:

j Dij jnk1

Qij

k

Z3k Z3k1

3

: 3

The n plies have a position throughout the thickness in

relation to the mean plane of the plate called Zkwith

Qij T1

Q T; 4

T cos2 a sin2 a 2sin a cos asin2 a cos2 a 2sin a cos a

sin a cos a sin a cos a cos2 a sin2 a

PR

QS;

5

where a denes the angle orientation of the ply. And

Q Q11 Q12 0

Q12 Q22 0

0 0 Q66

PR

QS 6

with

Fig. 3. Dierent cases of drill/plate contact for the analytical model.

F. Lachaud et al. / Composite Structures 52 (2001) 511516 513


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Q11 El

1 mlt mtl; Q22

Et

1 mlt:mtl

Q12 mtlEl

1 vlt vtl

vltEt

1 vlt vtl7

Q66 Glt:

The termsD16 and D26 of the behavior laws are null(orthotropic plate and axisymetrical deection), and the

equilibrium Eq. (1) becomes:

D11o4w

ox4 2 D12 2D66

o4w

ox2oy2 D22

o4w

oy4 q: 8

The transversal displacement w of the clamped circular

plate, radius a, under uniform loading which is a so-lution of Eq. (8) is given by Eq. (9) [13].

wr qa2 r2

2

64 D; 9

where

q FZ

pa210

and

D 1

83D11 2D12 4D66 3D22: 11

An energetic approach based on the application of the

theorem of virtual work to the equilibrium of the part of

the plate aected by the drill, enables the critical drilling

load to be determined.

The parameter which varies virtually is radius a:

dW dU dUd; 12

dW is the work of external forces; dU is the potential

energy variation; and dUd is the energy absorbed by the

spread of cracking.

The strain energy of the circular plate is given by the

relation (13)

2U

s

Mxxo2w

ox2

Myy

o2w

oy2 2Mxy

o2w

oxoy

!ds: 13

The virtual variation of the energy is expressed by:

dU

oU

oa da

FZ

16D 2

a

p

D11 D222

D12 D663

!da: 14

The virtual work of external loads corresponding to the

work of the distributed load q:

W

2p0

a0

q wrr drdh F2Za

2

192pD; 15

oWoW

oada

F2Za

96pDda: 16

Delamination energy Ud is derived by multiplying the

critical energy release rate in mode I GIC by the sup-posedly circular fracture surface:

Ud GIC S GIcpa2: 17

The virtual variation of thus energy is written as

dUd oUdoa

da 2GICpada: 18

Relation (12) is expressed as a function of (14), (16),

(18):

F2Zp2

1

96D

24

DH

16D2

3 2GIC

5 apda 0 Vda; 19

where

DH D11 D12

2D12 D66

3: 20

Eq. (19) must hold for all variations of the virtual crack

extension and therefore the bracketed quantity shouldbe equal to zero. Therefore, the critical value of the

thrust is [4]:

FZ 8pGICD

1=3 DH=8D

1=2; 21

where D and DH are respectively, dened Eqs. (11) and

(20).

3.2. Second hypothesis (point load model)

In a second model, contact between the drill and the

plate is represented by a load at a particular point (Fig.3). In this case, transversal displacement in given by the

Eq. (22).

wr F

16pD2r2 ln

r

a

h a2 r2

i: 22

By carrying out the same procedure as described in the

previous section, the critical drilling stress expression FZ(23) can be obtained.

FZ 8p2GIcD

1 DH=8D

!1=2; 23

where D and DH

are respectively, dened Eqs. (11) and(20).

The expression proposed by the model taken from the

literature is [5] (24)

FZ p8GICE

3 1 m2 h

3

!1=2; 24

where h is the plate thickness beneath the drill, E is the

global tensile modulus and m is homogenized Poisson's

ratio of the plate under consideration. This model does

not taken into account the role played by anisotropy in

localized bending.



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4. Comparison between experiment and results obtained

from the literature

Test plates of carbon/epoxy resin have been manu-

factured from a one-directional sheet of Fibredux 914/

T300 (Hexcel) using the autoclave technique.

The lay-up of the 24 plies is quasi-isotropic. The

characteristics of each ply are as follows: El 144000 MPa; mlt 0:3; Et 8700 MPa, h 0; 125 mmand Glt 4140 MPa. In this experiment, all the modesof rupture are mainly damages by delamination.

Values for the critical energy release rate in mode I

(GIc have been measured by the compliance method[10,14,15] for a given orientation angle between the plies

(Table 1).

These rates have been interpolated by a 2 polyno-

mial from three experimental data (0, 45 and 90) and

reactivated in analytical model (Eqs. (21), (23) and (24))

in relation to the relative orientation of the plies en-

countered during drilling. The quasi-static calculationthus takes into account the relative angular position

between the main cutting edges and the anisotropy di-

rections.

The double uted twist drills used for all the test are

made of K20 rated ``micrograin'' tungsten carbide with

a cruciform grinding (DIN1412). The carbon/epoxy

plates are pre-drilled using a 4.8 mm diameter drill.

Dierent drilling depths enable us to study the bending

of thin plates made of 12, 11, 10 down to 1 ply. The test-

pieces are then placed on a tension/compression testing

machine (Fig. 4).

A perpendicular load FZ is applied to the non-drilled

part of the plate. According to [4] the maximum re-

corded FZ value is the one which causes delamination.

The experimental set-up is presented in Fig. 4. The 4.8

mm diameter drill is used as a punch, without rotation

and its feed-rate is 1mm/mn. GIC is given Fig. 5, the-

oretical and experimental delamination stresses are

given in Fig. 6. When the stress representation takes

into account the geometrical conguration of the tool/

part contact, the results of the analytical model (with a

uniformly distributed load) are close to experimental

measurements. This is veried for a number of plies

situated beneath the drill which is compatible with thin

plate hypotheses. In fact, when the number of plies isgreater than 7 (# 1 mm), this model no longer corre-

lates with experimental results. The representation of

the drill thrust force at a particular point considerably

reduces the analytical values compared with those of

the experiments. This analysis also applies to the

Table 1

Values for critical energy release rate in mode I (GIC)

Angle dierence 0 45 90

GIC J m2 mini 110 150 240

maxi 120 160 260

Fig. 4. Test piece and experimental set up.

Fig. 5. GIC values for carbon/epoxy plate versus relatif angle between

two plies.

Fig. 6. Analytical and experimental results.

F. Lachaud et al. / Composite Structures 52 (2001) 511516 515


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comparison between experimental values and those

derived from an analogous model taken from the lit-

erature [5]. Moreover, the machining study reveals that

the feed-rate per revolution and per cutting edge (f),

associated with the thrust force needed to produce

delamination, are close to the ``minimum turning''

(below this feed-rate value, the drill punches the

material without cutting it). From a practical point of

view, the operator must choose the cutting conditions

that are close to, but less than, the values proposed by

the distributed load model.

5. Conclusion

Among the dierent types of damage caused by

drilling thin carbon/epoxy plates without a backing

plate, we have chosen to model only the relation be-

tween drill thrust force, and localized bending of the last

few plies. It is the relation which is responsible for crackopening mode I of delamination. The analytical model

proposed oers close correlation between experimental

measurements of static punching, as soon as the geo-

metrical distribution of tool/part contact conditions is

respected.This study shows that:

the values of the rst hypothesis which corresponds

to a contact tool/plate uniformly distributed load is

the most close to the experimental results,

the values of the second hypothesis (localized force at

the tip of the drill) and the values proposed by the

model taken from the literature are remote from ex-

perimental results.

Works are in progress to dene with more accuracy

the exact distribution of the thrust force (FZ) on the

chisel edge and two major cutting edges of the drill.

The dynamic and thermomechanical cutting condi-

tions have to be studied experimentally and modeled.

Acknowledgements

We wish to thank R. Toppan, head of the SIDMI

(Societe Industrielle Aeronautique du Midi Corne-

barrieu France) for his nancial assistance, and also P.

Dubourg (IUT Paul Sabatier 31 Toulouse France)

for his invaluable contribution to our study.

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drilling of composite publié par younes persian