mechanical properties of woven laminates and felt composites using carbon fibers. part 1: in-plane...

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Mechanical properties of woven laminates and felt composites using carbon fibers. Part 1: in-plane properties Jaehyun Kim a , Masatoshi Shioya a, * , Haruki Kobayashi a , Junichi Kaneko b , Masahiko Kido b a Department of Organic and Polymeric Materials, Tokyo Institute of Technology, South Bldg. 8, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan b Nippon Felt Co. Ltd, 88, Haramamuro, Konosu-shi, Saitama 365-0043, Japan Received 10 December 2002; received in revised form 23 March 2004; accepted 29 March 2004 Available online 10 May 2004 Abstract In-plane tensile and compressive properties of epoxy resin matrix composites reinforced with carbon fiber woven fabrics and carbon fiber felts have been compared and the influences of weave pattern and needle-punching density have been investigated. The tensile and compressive strengths of the woven laminates were derived as increasing functions of the radius of curvature of yarns, and the resulting equations well represented the measured values. The strengths of the felt/resin composites were influenced by needle-punching density as well as the weave pattern of base fabrics. Although the felt/resin composites showed lower strengths than the woven laminates, the felt reinforcement had the advantage of improving interlaminar properties as will be shown in a succeeding paper [Compos. Sci. Technol., submitted]. The compressive strength of the felt reinforced composites utilizing more brittle carbon matrix has also been investigated. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: A. Carbon fibers; A. Fabrics/textiles; B. Fracture; B. Modeling; B. Strength 1. Introduction Carbon fiber reinforced composites show very high specific strength and modulus, while their weakness is their sensitivity to mechanical damage. When laminate composites are subjected to impact, bending or in-plane compression, interlayer delamination tends to take place. With further application of external load, the delamination propagates through the interlayer leading to catastrophic failure of the composites. Damage tol- erance of composites can be enhanced by improving interlaminar properties through toughening the matrix [2], insertion of an interleaf layer [3], reinforcing with three-dimensional braided and woven fabrics [4], stitching of reinforcements [5] and reinforcing with felts [6,7]. It has been demonstrated that damage tolerance of the composites can be improved by reinforcing with needle-punched, non-woven, glass fiber fabrics [6] and that the crash response of composites can be improved by reinforcing with a needle-punched felt and conven- tional fabric [7]. The present authors have shown that the composites reinforced with carbon fiber felts produced by needle- punching the stack of loose fiber webs and woven fabrics possess good damage tolerance [8]. In this study, me- chanical properties of the epoxy resin matrix composites reinforced with carbon fiber woven fabrics and carbon fiber felts are compared and the influences of weave pattern and needle-punching densities are investigated. The present paper addresses in-plane tensile and com- pressive strengths. The strengths of the woven laminates are theoretically analyzed, and based on the results the strengths of the felt/resin composites are discussed. The strength of the felt reinforced composites using a more brittle matrix is also investigated. Interlaminar and damage tolerant properties of these composites will be addressed in a succeeding paper [1]. The composites * Corresponding author. Tel./fax: +81-3-5734-2434. E-mail address: [email protected] (M. Shioya). 0266-3538/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2004.03.012 Composites Science and Technology 64 (2004) 2221–2229 www.elsevier.com/locate/compscitech COMPOSITES SCIENCE AND TECHNOLOGY

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Page 1: Mechanical properties of woven laminates and felt composites using carbon fibers. Part 1: in-plane properties

COMPOSITESSCIENCE AND

Composites Science and Technology 64 (2004) 2221–2229

www.elsevier.com/locate/compscitech

TECHNOLOGY

Mechanical properties of woven laminates and felt compositesusing carbon fibers. Part 1: in-plane properties

Jaehyun Kim a, Masatoshi Shioya a,*, Haruki Kobayashi a, Junichi Kaneko b,Masahiko Kido b

a Department of Organic and Polymeric Materials, Tokyo Institute of Technology, South Bldg. 8, 2-12-1 O-okayama, Meguro-ku,

Tokyo 152-8552, Japanb Nippon Felt Co. Ltd, 88, Haramamuro, Konosu-shi, Saitama 365-0043, Japan

Received 10 December 2002; received in revised form 23 March 2004; accepted 29 March 2004

Available online 10 May 2004

Abstract

In-plane tensile and compressive properties of epoxy resin matrix composites reinforced with carbon fiber woven fabrics and

carbon fiber felts have been compared and the influences of weave pattern and needle-punching density have been investigated. The

tensile and compressive strengths of the woven laminates were derived as increasing functions of the radius of curvature of yarns,

and the resulting equations well represented the measured values. The strengths of the felt/resin composites were influenced by

needle-punching density as well as the weave pattern of base fabrics. Although the felt/resin composites showed lower strengths than

the woven laminates, the felt reinforcement had the advantage of improving interlaminar properties as will be shown in a succeeding

paper [Compos. Sci. Technol., submitted]. The compressive strength of the felt reinforced composites utilizing more brittle carbon

matrix has also been investigated.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: A. Carbon fibers; A. Fabrics/textiles; B. Fracture; B. Modeling; B. Strength

1. Introduction

Carbon fiber reinforced composites show very high

specific strength and modulus, while their weakness is

their sensitivity to mechanical damage. When laminatecomposites are subjected to impact, bending or in-plane

compression, interlayer delamination tends to take

place. With further application of external load, the

delamination propagates through the interlayer leading

to catastrophic failure of the composites. Damage tol-

erance of composites can be enhanced by improving

interlaminar properties through toughening the matrix

[2], insertion of an interleaf layer [3], reinforcing withthree-dimensional braided and woven fabrics [4],

stitching of reinforcements [5] and reinforcing with felts

[6,7]. It has been demonstrated that damage tolerance of

the composites can be improved by reinforcing with

* Corresponding author. Tel./fax: +81-3-5734-2434.

E-mail address: [email protected] (M. Shioya).

0266-3538/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compscitech.2004.03.012

needle-punched, non-woven, glass fiber fabrics [6] and

that the crash response of composites can be improved

by reinforcing with a needle-punched felt and conven-

tional fabric [7].

The present authors have shown that the compositesreinforced with carbon fiber felts produced by needle-

punching the stack of loose fiber webs and woven fabrics

possess good damage tolerance [8]. In this study, me-

chanical properties of the epoxy resin matrix composites

reinforced with carbon fiber woven fabrics and carbon

fiber felts are compared and the influences of weave

pattern and needle-punching densities are investigated.

The present paper addresses in-plane tensile and com-pressive strengths. The strengths of the woven laminates

are theoretically analyzed, and based on the results the

strengths of the felt/resin composites are discussed. The

strength of the felt reinforced composites using a more

brittle matrix is also investigated. Interlaminar and

damage tolerant properties of these composites will be

addressed in a succeeding paper [1]. The composites

Page 2: Mechanical properties of woven laminates and felt composites using carbon fibers. Part 1: in-plane properties

2222 J. Kim et al. / Composites Science and Technology 64 (2004) 2221–2229

used in this study are carbon fiber woven fabric/epoxy

resin laminate composites, needle-punched carbon fiber

felt/epoxy resin composites, needle-punched carbon fi-

ber felt/carbon composites and unidirectional carbon

fiber bundle/epoxy resin composites. These compositeswill be simply called woven laminates, felt/resin com-

posites, felt/carbon composites and unidirectional com-

posite strands, respectively.

Fig. 1. Schematic diagram of plain weave, 2/2 twill weave and 8-har-

ness satin weave.

2. Experimental

2.1. Materials

Polyacrylonitrile (PAN)-based carbon fibers with a

filament diameter of 7 lm and a density of 1.79 g cm�3

were used for the reinforcing fibers.

The epoxy resin used for the resin matrix composites

was a mixture of a diglycidyl ether of bisphenol A-type

epoxy resin (Epikote 828, Japan Epoxy Resins Co.,

Ltd), methylnadic acid anhydride, and benzyldimethyl-amine with a mass ratio of 100:90:2.5. The curing con-

ditions of the epoxy resin were 110 �C for 2 h and

additionally at 150 �C for 1 h. The tensile strength of the

cured epoxy resin was 75 MPa [9]. The precursor resin

for the carbon matrix composites was a furfuryl alcohol

condensate (Hitafuran 303, Hitachi Chemical Industry)

mixed with alkylbenzene sulfonic acid (curing agent, A3,

Hitachi Chemical Industry) with a mass ratio of 100:0.6.The curing conditions of the furan resin were 70 �C for

2 h and additionally at 150 �C for 1 h.

2.2. Fabrication of woven fabrics and felts

Carbon fibers were woven into fabrics with three

different weave patterns, a plain weave, a 2/2 twill weave

and an 8-harness satin weave (Fig. 1). Both the warpsand the wefts consisted of 3000 filaments. The numbers

of yarns in the fabrics were 5 yarns cm�1 for plain and

twill weaves and 10 yarns cm�1 for the satin weave. The

areal densities of fabrics were 200 g m�2 for plain and

twill weaves and 400 g m�2 for the satin weave.

Carbon fiber felts were produced by stacking webs of

loose carbon fibers (batt) and carbon fiber woven fabrics

(base) and needle-punching the stack [8]. The batt con-tained oxidized PAN fibers (precursor of carbon fibers)

at �17 wt% for facilitating fiber entanglement during

needle-punching. In the stack either single or double

base layers were inserted between every batt layer. In a

needle-punching machine, penetration and retraction of

needles was repeated while the stack advanced through

the machine according to the peripheral speed of deliv-

ery rollers, which were adjusted so that a requirednumber of needle-punches was applied. During needle-

punching, grooves in the needles (barbs) caught the fi-

bers of the batt and drew them through the stack in the

thickness direction. After the needles were retracted

form the stack, through-thickness fibers bridging thelayers were left. Felts were produced as follows. First,

half of the layers were stacked and needle-punched.

Secondly, this felt stack was turned over, remaining

layers were placed atop it and the whole stack was

needle-punched. Thirdly, the resulting stack was turned

over and needle-punched again. At any of the three

steps, the same number of needle-punches was applied.

The needle-punching density (ND) is defined as the totalnumber of needle-punches per unit area of the felt.

2.3. Fabrication of resin matrix composites

The woven laminates and felt/resin composites were

fabricated by employing a vacuum infusion process as

follows: liquid epoxy resin was poured into a mold he-

ated at 80 �C and the stack of woven fabrics or the feltwas placed in the mold. The resin-impregnated fibers

were place in vacuum for 20 and 5 min before and after

the mold was closed, respectively. The resin was cured

with a hydraulic hot press under a pressure of 0.5 MPa.

Unidirectional composite strands were fabricated

from a carbon fiber bundle obtained by aligning four

Page 3: Mechanical properties of woven laminates and felt composites using carbon fibers. Part 1: in-plane properties

J. Kim et al. / Composites Science and Technology 64 (2004) 2221–2229 2223

carbon fiber tows with 3000 filaments each. The bundle

was soaked in a liquid resin, passed through a die with

an inner diameter of 1.3 mm, wound on a steel frame

and cured in an electric furnace. The tensile strength and

modulus of the unidirectional composite strands were1.31 and 102 GPa, respectively.

The constituents of the composites are shown in

Table 1. In this table, the fiber volume fraction was

calculated from the densities of fiber and matrix, the

mass of the composite and that of the fibers left after the

matrix of the composite was burned off [10]. The fiber

fraction of the woven laminates and that of the felt/resin

composites could not be equalized since the specimenthickness was adjusted to a constant value of 2.5 mm.

The woven laminates had slightly higher fiber fraction

than the felt/resin composites. In this paper, waviness of

yarns in the woven laminates was characterized by a

radius of curvature of yarns at antinode ðqmÞ. For a

yarn whose center line follows a sinusoid in x–y coor-

dinate (Fig. 2) as

y ¼ A sinpxL

� �; ð1Þ

qm is given by

qm ¼ L2

p2A: ð2Þ

The wavelength (2L), amplitude (A) and radius (a) ofthe yarns were measured on the edge micrographs of the

woven laminates and qm was calculated using Eq. (2).

For the satin woven fabric, waviness of yarns in bare

fabric has two wavelengths, while waviness in the com-

posite could be represented by a single wavelength. For

Table 1

Constituents of woven laminates and felt/resin composites

Sample Weave pattern Number of layers

Base

Composite strands

S Straight fiber

Woven laminate composites

LP Plain 8

LT Twill 8

LS Satin 4

Felt/resin composites

FP0 Plain 6

FP50 Plain 6

FP150 Plain 6

FP250 Plain 6

FT0 Twill 6

FT50 Twill 6

FT150 Twill 6

FT250 Twill 6

FS0 Satin 3

FS50 Satin 3

FS150 Satin 3

FS250 Satin 3

the plain, twill and satin woven laminates, the measured

values of qm were 4.0, 5.6 and 7.9 mm and those of awere 0.12, 0.16 and 0.21 mm, respectively.

2.4. Fabrication of carbon matrix composites

For fabricating felt/carbon composites, felt/furan re-

sin composites were first fabricated similarly to the

fabrication of felt/epoxy resin composites. Polytetraflu-

oroethylene release film was placed in the mold. The

pressure of the hydraulic hot press during resin cure was

0.44 MPa. The felt/furan resin composites had similar

constituents to the felt/epoxy resin composites, while theaverage fiber volume fraction was 0.43 and the thickness

was 2.4 mm. Felt/carbon composites were produced by

heating the felt/furan resin composites at a rate of 2 �Cmin�1 up to 1300 �C and holding this temperature for

30 min under N2 gas flow.

2.5. In-plane tensile tests

Tensile tests were carried out by bonding aluminum

end tabs to the specimen using an epoxy resin adhesive

to preventing local fracture at loading points. A high

magnification CCD camera and an extensometer were

used for the determination of tensile strain. Specimens

dimensions were 205 mm long� 5 mm wide with a gage

length of 60 mm for the woven laminates, 205 mm

long� 5 mm wide with a gage length of 85 mm for thefelt/resin composites and 205 mm long with a gage

length of 60 mm for the unidirectional composite

strands. The crosshead speed was 0.5 mm min�1.

ND (cm�2) Fiber volume fraction

Batt

0 0.45

0 0 0.46

0 0 0.46

0 0 0.46

4 0 –

4 50 0.40

4 150 0.42

4 250 0.43

4 0 –

4 50 0.40

4 150 –

4 250 0.43

4 0 –

4 50 0.42

4 150 0.43

4 250 0.42

Page 4: Mechanical properties of woven laminates and felt composites using carbon fibers. Part 1: in-plane properties

Fig. 2. Representative unit of longitudinal yarn in woven laminate.

2224 J. Kim et al. / Composites Science and Technology 64 (2004) 2221–2229

2.6. In-plane compression tests

The compressive strength of the woven laminates andfelt/resin composites was measured in accordance with

JIS K7076. Aluminum end tabs were bonded to the

specimen to prevent local fracture at loading points and

a loading jig [8] was used to prevent flexure of the

specimen. A high magnification CCD camera was used

for the detection of compressive strain. Specimens were

of dimensions 78 mm long� 12 mm wide with a gage

length of 8 mm. The crosshead speed was 0.5 mm min�1.Compressive strength of the felt/carbon composites

was measured by bonding polyimide films to the ends of

the specimen using an epoxy resin adhesive to prevent

local fracture at loading points. Specimens were of di-

mensions 30 mm long� 10 mm wide. The crosshead

speed was 0.5 mm min�1.

3. Model analyses

3.1. Fracture mode

Figs. 3 and 4 show the edge photographs of the

woven laminates and felt/resin composites after com-

Fig. 3. Edge photographs of plain woven laminate after compression

test taken with lower (a) and higher magnification (b).

pression tests. It has been reported that the dominant

compressive fracture mode of the laminate and woven

composites is fiber microbuckling of the main load-

bearing plies [11]. For the woven laminates used in the

present study, however, clear fiber microbuckling wasnot observed but a detaching of the longitudinal and

transverse yarns was observed as shown in Fig. 3. For

the felt/resin composites, detaching of yarns was sup-

pressed with increased ND and the failure mode grad-

ually changed into a shear mode as shown in Fig. 4. The

compressive strength ruled by fiber microbuckling has

been represented using Argon’s expression as the matrix

shear yield strength divided by the initial average fibermisalignment angle [12]. It can be considered that for

the woven laminates used in the present study, the

critical stress to cause detaching of yarns is lower than

the critical stress to cause fiber microbuckling. For the

felt/resin composites, the critical stress to cause detach-

ment of yarns is increased with increasing ND and in

turn the shear fracture mode, having a lower critical

stress than that of fiber microbuckling, prevails.In this paper, therefore, the compressive strength of

woven laminates ruled by detaching of yarns will be

analyzed based on the following fracture process: A

compressive force is applied to woven laminates along

either the wefts or the warps. The yarns parallel and

perpendicular to the loading direction will be called

longitudinal and transverse yarns, respectively. With the

compressive force, the longitudinal yarns are compelledto increase the amplitude of waviness. Simultaneously, a

stress resisting the increase of amplitude is imposed on

the side of the longitudinal yarns from the transverse

yarns. The resisting stress increases with increasing

compressive force and reaches a detaching strength. At

the instant when the detachment of yarns occurs, the

bending moment of the longitudinal yarns is suddenly

increased and causes flexural fracture of the longitudinalyarns leading to the fracture of the woven laminate.

In the case of tensile loading of the woven laminates,

the longitudinal yarns are compelled to decrease the

amplitude of waviness and the resisting stress works in

the opposite direction as compared with the compressive

loading. The detachment of yarns, even if happens, is

not the critical event leading to tensile fracture. Tensile

fracture takes place when the multi-axial stress producedby the tensile and resisting stresses satisfies a fracture

criterion instead. In this paper, the tensile strength of

woven laminates loaded in the direction of longitudinal

yarns will be analyzed by applying the Tsai Hill fracture

criterion.

3.2. Compressive strength of woven laminate

A representative unit of a longitudinal yarn and the

x–y coordinate system are shown in Fig. 2. The center

line of the yarn is represented by Eq. (1). The angle

Page 5: Mechanical properties of woven laminates and felt composites using carbon fibers. Part 1: in-plane properties

Fig. 4. Edge photographs of woven laminate (a), felt/resin composite with ND of 50 cm�2 (b) and felt/resin composite with ND of 250 cm�2 (c) after

compression tests. Plain woven fabrics were used for these composites.

J. Kim et al. / Composites Science and Technology 64 (2004) 2221–2229 2225

between the center line and the x-axis is denoted as /. Itis assumed that qm is sufficiently larger than A and the

size of the cross-section which is defined perpendicularly

to the center line. The cross-section is an ellipsoid with

axial radii a in the x–y plane and b perpendicular to it.

The cross-section area (C) is given by pab and the in-

ertial moment of the cross-section around an axis per-

pendicular to the x–y plane and passing through the

center of gravity of the cross-section (I) is given bypa3b=4. In the following, the stresses, the forces, and the

moments in a cross-section at an arbitrary position x willrefer to those arising in the cross-section facing the po-

sitive-x-side except for those in the cross-section at

x ¼ 0. The loading points of the forces and the moments

are the center of gravity of the cross-section. The stres-

ses, the forces, and the moments are working within the

x–y plane.The following stresses and forces are applied ex-

ternally to the unit: At the ends of the unit, a com-

pressive force parallel to the x-axis (P ) is applied. On

the side of the unit, resisting stresses parallel to the

x-axis ðrxðxÞ) and parallel to the y-axis ðryðxÞ) are

imposed by the transverse yarn. These stresses are

defined per unit area perpendicular to the x and yaxes, respectively. From the symmetry of the unitaround x ¼ L=2,

rx Lð � xÞ ¼ �rx xð Þ: ð3Þ

At the ends of the unit transverse forces parallel to

the y-axis (Q) are imposed by the neighboring unit.

From the equilibrium of the forces,

Q ¼ 1

2

Z L

0

2bry xð Þdx: ð4Þ

No moment is applied at the ends of the unit becauseof the symmetry of the yarn around the end points of the

unit.

Due to the external forces and stresses shown above,

the following internal stresses and moments arise in an

arbitrary cross-section: The normal force

NP xð Þ ¼ �P cos/ ð5Þand the moment

MP xð Þ ¼ Py ð6Þare produced by P . The moment

Mr xð Þ ¼ � QxþZ x

0

2b x½ � x1�ry x1ð Þdx1

þZ x

0

2b y½ � y1�rx x1ð Þdy1 ð06 x6L=2Þ ð7Þ

is produced by the resisting stresses and Q where (x1; y1Þis a point on the center line of the unit.

The displacement of the unit in the y-axis direction

produced by these internal moments is represented as

DyT xð Þ ¼ DyP xð Þ þ Dyr xð Þ; ð8Þ

where DyP ðxÞ and DyrðxÞ are the displacements produced

byMP ðxÞ andMrðxÞ, respectively. From the curved beam

theory, the displacement of a sinusoidal unit in the y-axis direction produced by a moment (MðxÞ) in the

cross-section is given by

Dy xð Þ �Z x

0

x1 � x½ �M x1ð ÞEI

dx1 �DyLxL

; ð9Þ

Page 6: Mechanical properties of woven laminates and felt composites using carbon fibers. Part 1: in-plane properties

2226 J. Kim et al. / Composites Science and Technology 64 (2004) 2221–2229

where E is the longitudinal Young modulus of the uni-

directional composite and DyL is a constant determined

so that Dy (0) and DyðLÞ become zero. From Eqs. (6)

and (9),

DyP xð Þ ¼ PL2Ap2EI

sinpxL

� �: ð10Þ

The relative transverse displacement of the longitu-

dinal yarn representing a transverse strain is denoted as

eT

DyT xð Þ ¼ eTy xð Þ: ð11ÞFrom Eqs. (1), (8), (10) and (11),

Dyr xð Þ ¼ eT

�� PL2

p2EI

�A sin

pxL

� �: ð12Þ

By differentiating Eq. (9), a general relationship be-

tween the moment and the displacement of the sinu-

soidal unit can be obtained as

d2M xð Þdx2

� �EId4Dy xð Þdx4

: ð13Þ

By combining Eqs. (7), (12) and (13),

ry xð Þ þ d2ydx2

Z x

0

rx x1ð Þ dy1dx1

dx1 þdydx

� �2

rx xð Þ

¼ P�

� p2eTEIL2

�p2A2bL2

sinpxL

� �ð06 x6L=2Þ: ð14Þ

For determining rxðxÞ and ryðxÞ in an explicit form from

Eq. (14), the relation between these stresses is required.The value of ryðL=2Þ, however, can be determined in-

dividually by considering that d2y=dx2 ¼ �1=qm and

dy=dx ¼ 0 at x ¼ L=2 and assuming that qm is suffi-

ciently large. The resulting equation is

PC¼ 2qm

pary

L2

� �þ eTEa2

4qmA: ð15Þ

If the mechanical response of the transverse yarn will

be analyzed, eT can be represented as a function of P . Inthis paper, however, a postulated value will be used foreT.

The stress ryðL=2Þ increases with increasing com-

pressive force applied to the woven laminate and even-

tually the longitudinal and transverse yarns detach when

ryðL=2Þ reaches a detaching strength ðrdÞ. After the

yarns detach, the resisting stresses do not work. The

stress distribution in the cross-section of the longitudinal

yarn after the yarns detach can be known by applyingthe curved beam theory. That is, the normal stress

(positive in tension) in the cross-section at the concave

side margin is given by

r xð Þ ¼ N xð ÞC

� 4M xð ÞaC

; ð16Þ

where NðxÞ and MðxÞ are a normal force and a moment

in the cross-section, respectively. By combining Eqs. (5),

(6) and (16), the normal stress at the concave side

margin is obtained as

rL2

� �¼ � P

C� 4PA

aC: ð17Þ

This local compressive stress is very large as compared

with the average compressive stress, �P=C and can

cause fracture of the longitudinal yarn leading to com-

pressive fracture of the woven laminate. The compres-

sive strength of the woven laminate ðrcÞ is therefore

obtained by replacing ryðL=2Þ in Eq. (15) with rd as

rc ¼ k2qm

pard

�þ eTEa2

4qmA

�; ð18Þ

where k is the areal fraction of the longitudinal yarns in

the cross-section of the woven laminate perpendicular to

the loading direction. The detaching strength of the

yarns can be approximated by the transverse tensile

strength of the unidirectional composite and the latter

value is about a half of the tensile strength of the matrix

ðrmÞ provided that fiber/matrix interfacial bonding iscomplete and the fiber volume fraction is about 0.5 [13].

Therefore, if the transverse yarns are rigid enough to

constrain the displacement of the longitudinal yarns

ðeT ¼ 0), the compressive strength of woven laminate is

given by

rc ¼ kqm

parm: ð19Þ

The fiber fraction is not incorporated in thisequation in an explicit form but has influences on k,qm, a and the relationship between rd and rm. It

should be also noted that there may be a lower lim-

iting fiber fraction for detaching induced compressive

fracture to take place.

3.3. Tensile strength of woven laminate

The resisting stress in the woven laminate loaded in

tension in the direction of longitudinal yarns is repre-

sented by the same expression as that for compressive

loading with the sign of P being negative. A multi-axial

stress state is produced by the tensile stress, �P=C and

the resisting stress, ry at antinodes of the longitudinal

yarns. By applying Tsai Hill fracture criterion, the

conditions for the longitudinal yarn to fracture underthis stress state are represented as

Prt0C

� �2þ ry

ry0

� �2¼ 1; ð20Þ

where rt0 and ry0 are the strengths of the unidirectional

composite under pure longitudinal tensile and transverse

compressive loadings, respectively. The tensile fracture

of the longitudinal yarn leads to the tensile fracture of

the woven laminate since the longitudinal yarns are the

main load-bearing elements. From Eqs. (15) and (20)

Page 7: Mechanical properties of woven laminates and felt composites using carbon fibers. Part 1: in-plane properties

J. Kim et al. / Composites Science and Technology 64 (2004) 2221–2229 2227

and assuming a rigid transverse yarn, the tensile strength

of the woven laminate ðrtÞ is

rt � krt0 1

"� 1

8

prt0ary0qm

� �2#: ð21Þ

Fig. 6. Compressive strength of felt/carbon composites versus ND.

Weave patterns are indicated by the same symbols as in Fig. 5.

4. Results and discussion

Tensile and compressive properties of the composites

are shown in Figs. 5 and 6 as a function of qm for the

woven laminates and as a function of ND for the felt/resin and felt/carbon composites.

The tensile stress–strain response of the woven lami-

nates was almost linear to fracture regardless of the

weave pattern. The knee phenomenon [14], which is a

non-linear response due to initial failure of woven fab-

rics and often observed for glass fiber woven laminates,

was not observed. The twill woven laminate shows a

higher tensile modulus than the plain woven laminate as

Fig. 5. Tensile modulus, tensile strength and compressive strength of

woven laminates versus qm and those of felt/resin composites versus

ND. Weave patterns of fabrics used for these composites were plain

weave (circles), 2/2 twill weave (triangles) and 8-harness satin weave

(squares).

expected from a larger qm. The satin woven laminatehaving the largest qm, however, shows a lower tensile

modulus. The tensile strength of the woven laminates

increases with increasing qm. Eq. (21) predicts that the

tensile strength of the woven laminates linearly increases

as (a=qmÞ2 decreases. This can be verified in Fig. 7 where

the tensile strength of the unidirectional composite

strand multiplied by 0.5 is also shown as a measure of

the tensile strength of the woven laminate with an infi-nitely large qm. The solid line in Fig. 7 was calculated

using Eq. (21) with the values of rt0 ¼ 1:31 GPa and

ry0 ¼ 0:104 Gpa, which allow Eq. (21) the best fit to the

measured values.

Fig. 7. Tensile strength of woven laminates versus ða=qmÞ2. Weave

patterns are indicated by the same symbols as in Fig. 5. The point at

ða=qmÞ2 ¼ 0 shows tensile strength of unidirectional composite strand

multiplied by 0.5. Solid line shows tensile strength calculated with Eq.

(21).

Page 8: Mechanical properties of woven laminates and felt composites using carbon fibers. Part 1: in-plane properties

Fig. 8. Compressive strength of woven laminates versus qm=a. Weave

patterns are indicated by the same symbols as in Fig. 5. Solid line

shows compressive strength predicted with Eq. (19).

2228 J. Kim et al. / Composites Science and Technology 64 (2004) 2221–2229

The compressive strength of the woven laminates

increases with increasing qm. Eq. (19) predicts that the

compressive strength of the woven laminates increases

linearly as qm=a increases. This can be verified in Fig. 8.The compressive strength of the woven laminates was

predicted using Eq. (19) where k was assumed to be 0.5

since the same amount of fibers were used for the warps

and the wefts in the woven fabrics. The results of the

prediction, as shown by the solid line in Fig. 8, well

represents the measured values.

The tensile modulus of the felt/resin composite with a

low ND is on the same level as that of the woven lam-inates. The tensile and compressive strengths of the felt/

resin composites, however, are lower than those of the

woven laminates. It is considered that qm influences the

mechanical properties of the felt/resin composites simi-

larly to the woven laminates since the woven fabrics are

the main load-bearing elements in the felt/resin com-

posites. Through-thickness fibers introduced by needle-

punching tightly bind the component layers in the felt/resin composites and increase the detaching strength. It

is expected, therefore, that the compressive strength of

the felt/resin composites increases with increasing ND.

There are, however, several factors which deteriorate

mechanical properties of the felt/resin composites. The

felt/resin composites incorporate batt layers having al-

most random fiber orientation and containing oxidized

PAN fibers. If stiff fibers are distributed randomly in alayer as in the batt layer and a parallel mechanical

model can be applied, the stiffness of the layer is reduced

to 3/8 of the stiffness of the layer having unidirectional

fiber orientation. If stiff fibers are distributed ortho-

tropically as in the woven fabric, the stiffness of the layer

is reduced to 1/2 of the stiffness of the unidirectional

layer. The volume fraction of the batt layers in the total

layers of the felt/resin composites was about 1/3.

Therefore, a roughly estimated reduction of the modulus

of the felt/resin composites as compared to that of the

woven laminates is ((1/2)–(3/8))� (1/3)¼ 4%, which is

rather small. It is considered that the existence of thebatt layer causes much larger influence on the strength

than on the modulus since the modulus reflects average

structure of composites while the strength is determined

by the weakest link. In addition, needle-punching can

damage the base fabrics and cause disturbance of fiber

alignment and as a result affect the strength. The me-

chanical properties of the felt/resin composites are also

affected by a slightly lower fiber fraction than that of thewoven laminates in this study. As a consequence of the

counterworking factors shown above, the compressive

strength of the felt/resin composites increases with in-

creasing ND for the plain woven base fabrics but de-

creases for the satin woven base fabrics.

The compressive strength of the felt/carbon compos-

ites increases with increasing ND as shown in Fig. 6.

The difference in the compressive strength of the felt/carbon composites between the plain and the twill wo-

ven base fabrics is small. It is considered that the critical

event leading to compressive fracture differs between the

felt/resin and the felt/carbon composites due to the dif-

ference in the brittleness of matrix. The compressive

fracture of the felt/carbon composites is triggered by

crack propagation from the brittle matrix. The increase

in the compressive strength of the felt/carbon compos-ites with increasing ND can be ascribed to the ability of

through-thickness fibers to arrest crack propagation.

5. Conclusions

The tensile and compressive strengths of the woven

laminates were derived as increasing functions of qm,and the resulting equations well represented the mea-

sured values. The strengths of the felt/resin composites

were influenced by ND as well as the weave pattern of

the base fabrics. The increase in the detaching strength,

brought about by through-thickness fibers in the felt/

resin composites, worked in favor of increasing com-

pressive strength. On the other hand, detrimental factors

decreasing the strengths of the felt/resin composites weredamage to the base fabrics and disturbance of fiber

alignment brought about by needle-punching and ran-

dom fiber orientation in the batt layer. From the results

of the present study and those to be reported in the

succeeding paper [1], it is concluded that the use of the

felt with plain woven fabrics in combination with a high

ND is effective for improved damage tolerance of resin

matrix composites without significant reduction of in-plane compressive strength. The critical event leading to

compressive fracture differs between the felt/resin and

felt/carbon composites due to differences in the brittle-

Page 9: Mechanical properties of woven laminates and felt composites using carbon fibers. Part 1: in-plane properties

J. Kim et al. / Composites Science and Technology 64 (2004) 2221–2229 2229

ness of the matrix. The compressive strength of the felt/

carbon composites increased with increasing ND irre-

spective of the weave pattern of the base fabrics.

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