fom

, M

rsity o

to th

were

inatio

rom

t. C

. Th

such as the tube axial length, aspect ratio and wall thickness on the compressive response and collapse modes of the tested tubes is

thoroughly analysed. In addition, the eect of the laminate material properties such as the bre volume content and stacking se-

particular, researchers attention has been directed to-

reduce signicantly the forces, experienced by the pas-

sengers and the transported cargo in the event of a

sudden collision. On the contrary to conventional ma-

terials such as metals and polymers, most thin-walled

terials and structures, such as FRP tubes and sandwich

The present work contributes to the data bank related

to CFRP collapsible energy absorbers, by presenting

and analysing the results of experimental works per-

taining to the investigation of collapse modes and en-

ergy absorption characteristics of square CFRP tubes

made of carbon woven fabric in epoxy resin, that were

63 (20*wards the improvement of structural vehicle crashwor-

thiness by using FRP composites in specic vehicle parts

as collapsible absorbers of crash energyi.e. as struc-

tural members that are able to absorb large amounts of

impact energy, while collapsing progressively in a con-

trolled manner. Progressive deformation and stable

collapse are desired features of vehicle structures as they

panels have been tried in the eort to achieve improved

level of crashworthiness [615]. Among these materials

carbon bre reinforced plastics (CFRP) in various

shapes, such as thin-wall circular and square tubes and

frustum, have proven to be very ecient crash energy

absorbing components featured by excellent stiness

to weight ratio [3,4].quence on the energy absorbing capability of the thin-wall tubes is also examined. Particular attention is paid on the analysis of the

mechanics of the tube axial collapse modes from macroscopic and microscopic point of view, emphasizing on the mechanisms

related to the crash energy absorption during the compression of the composite tubes.

2003 Elsevier Ltd. All rights reserved.

Keywords: Crashworthiness; Composite tubes; Square cross-section; CFRP; Carbon fabric; Axial compression

1. Introduction

Extensive research works in the recent decades have

shown that the use of bre-reinforced plastic composite

materials in automotive and aerospace applications may

result in signicant functional and economic benets,

ranging from increased strength and durability features

to weight reduction and lower fuel consumption [1,2]. In

FRP composite structures are not deformed plastically

when subjected to compressive load, but they collapse at

various modes featured by extensive micro-cracking

development as the predominant failure mechanism [3

6,10,11]. These failure modes depend on the geometric

and material characteristics of the structures and the

testing parameters such as the strain rate and the envi-

ronmental conditions. Various types of composite ma-Crashworthy characteristics othin-walled square CFRP c

A.G. Mamalis *, D.E. Manolakos

Manufacturing Technology Division, National Technical Unive

Abstract

In this paper the results of experimental works pertaining

acteristics of carbon bre reinforced plastic (CFRP) tubes that

detail. The tested specimens were featured by a material comb

thermosetting epoxy resin, and they were cut at various lengths f

thickness, laminate stacking sequence and bre volume conten

loading capacity at very low-strain rate typical for static testing

Composite StructuresCorresponding author. Tel.: +30-1-772-3688; fax: +30-1-772-3689.

E-mail address: mamalis@central.ntua.gr (A.G. Mamalis).

0263-8223/$ - see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0263-8223(03)00183-1axially statically compressedposite tubes: experimental

.B. Ioannidis, D.P. Papapostolou

f Athens, 9 Iroon Polytechniou Avenue, 15780 Athens, Greece

e crash behaviour, collapse modes and crashworthiness char-

subjected to static axial compressive loading are presented in

n of carbon bres in the form of reinforcing woven fabric in

three CFRP tubes of the same square cross-section but dierent

FRP tubes were compressed in a hydraulic press of 1000 kN

e inuence of the most important specimen geometric features

04) 347360

www.elsevier.com/locate/compstructsubjected to static axial compressive loading. The tested

specimens were tubes of the same cross-section and

in detail. In addition, experimental works focusedby

site Smeans of macroscopic observations and microscopic

examination of selected specimenson the analysis of

the collapse mechanisms appearing during the tube

compression and related to the crash energy absorption.

In particular, the examination concentrated on the types

of micro-failure acting on the corners of the square

tubes in the case of progressive collapse mode, since

these are importance for the spreading of collapsemechanisms in the whole section of the tube, as depicted

in the detailed map of failure mechanisms distribution

prepared for the specimen featured by the maximum

crash energy absorption.

2. Experimental

2.1. Equipment and procedure

The axial compressive testing of the square CFRP

tubes was performed on a fully equipped and automated

SMG hydraulic press of 1000 kN loading capacity. Nomaterials but dierent length, thickness, number of re-

inforcing plies and bre volume content. The inuence

of the most signicant specimen geometric features,

such as tube wall thickness and geometric aspect ratio,

and laminate material properties as the bre content and

stacking sequence, on the compressive response and

collapse modes of the tested square tubes was examined

Nomenclature

Eabs absorbed crash energyEs specic crash energy absorptionL length of the tubeLc length of the central crackLU load uniformity index

m specimen massmc crushed tube massn number of reinforcing plies

348 A.G. Mamalis et al. / Compospecial xturessuch as end clamping deviceswere

used for the tests apart from the standard at crossheads

of the press. All tests were performed at quasi-staticconditions i.e. at constant throughout the test crosshead

speed equal to 7 mm/min, which corresponds to an

overall compression strain rate of 2.6 103 s1.From the load, P /displacement, s curves that were

recorded directly during the testing works the following

compressive characteristics of the test specimens were

calculated and recorded:

peak load, Pmax; absorbed crash energy Eabs, i.e. the area under the P=s

curve; specic energy Es (Es Eabs=mc is the absorbed crashenergy per unit of the crushed specimen mass);

average crushing load, P , dened as the ratio of ab-sorbed energy, Eabs to the total displacement, smax;

load uniformity index LU, dened as the ratio of thepeak load, Pmax to the average crushing load, P .

The testing works were performed without any spe-cial conditioning of the test specimens, since the ambient

conditions in the laboratory room at the time of testing

were within the range of the recommended control

conditions for testing of composites, i.e. temperature

equal to 23 3 C and relative humidity 5060%.

2.2. Test materials

All test specimens were CFRP tubes of square cross-

section with internal tube dimensions equal to 100 100mm and radius of curvature 8 mm at the tube corners.

An overall picture of the shape and the dimensions ofthe test specimens is given in Fig. 1. Regarding the

specimen length, three types of specimens were tested:

short (A), medium (B) and long (C) tubes with length, Lapproximately equal to 50, 100 and 125 mm respec-

tively. The thickness, t of the tested tubes was alsovariable, taking three distinct average values that were

equal to 2.64, 3.51 and 4.39 mm. The exact dimensions

of all tested tubes are detailed in Table 1 listed togetherwith data related to the geometric aspect ratio, L=w and

P compressive loadP average crushing loadPmax peak compressive loads displacement of the press crossheadsmax total displacementt tube wall thicknessVf bre volume contentw side width of the square tube

tructures 63 (2004) 347360mass, m of each specimen. It must be noted that thechoice of specimen dimensions was made based on

preliminary calculations which were performed for de-

termining the tube geometry that would ensure avoid-

ance of overall buckling failure mode.

The test specimens were cut to the required dimen-

sions by means of high-pressure water jet from threesquare tubes designated as CT1, CT2 and CT3 that were

featured by the same material combination but dierent

laminate stacking sequence and thickness. Attention was

paid during the specimen preparation, to ensure at

smooth end surfaces, free of burrs, parallel to each other

and at right angles to the length of the specimen in order

to prevent localised end failures. No trigger mechanisms

Peakload,

P max(K

N)

Average

crushing

load,P

(KN)

Loaduni-

form

ity,

LU

()

Collapse

mode()

Deform

a-

tionen-

ergy,Eabs

(J)

Specimen

mass,mc

(g)

Specic

energy,Es

(kJ/kg)

182.16

68.20

2.67

II1879

166

11.3

136.18

62.40

2.18

I,III

3298

139

23.7

124.20

20.40

6.09

II1255

166

7.6

219.00

70.60

3.10

III

1950

237

8.2

244.00

34.50

7.07

III

1820

199

9.1

219.00

96.20

2.28

I5910

237

24.9

254.53

98.30

2.59

III

2713

117

23.2

254.60

167.50

1.52

I8846

232

38.1

254.60

67.30

3.78

I,III

4134

296

14.0

site Structures 63 (2004) 347360 349Fig. 1. General layout and dimensions of the tested tube specimens.A.G. Mamalis et al. / Composuch as bevelled ends or tulip shaping of the tube ends

were used in the compression tests. The material com-

bination of the laminate walls of the tested tubes in-

cluded carbon bres in the form of reinforcement fabric

impregnated in epoxy resin. More specically the fabric

was Hexcel carbon fabric G939D with surface density

equal to 220 gr/m2 and the epoxy resin was RutapoxLB20 resin with Rutadur SL Hardener. The bre vol-

ume content, Vf and laminate stacking sequence of re-inforcing plies in carbon tubes CT1, CT2 and CT3 was

46.3%, 48.7%, 50.1% and [0]10: [0]14, [0]18 respec-

tively. The 0 directionwhich in this notation is co-incident with the carbon fabric warp direction, was

parallel to the longitudinal axis of all three CFRP tubes.

2.3. Results

The loaddisplacement curves obtained by the axialcompression of the carbon tube specimens are depicted

in the three diagrams of Fig. 2 grouped per tube of ori-

gin, i.e. curves of specimens of dierent length but same

material characteristics are included in a single diagram.

Representative photographs at various stages of the

axial compression were taken during the testing of the

tubes, see Figs. 3(a), 4(a) and 5(a) for test specimens that

collapsed in modes I, II and III respectively. The de-structive testing of the carbon tubes was interrupted T

able

1

Exact

dimensions,materialdata

andcrashworthycharacteristics

ofthetested

specimens

Testspecimen

ID

Numberof

plies,n()

Fibre

vol-

umecon-

tent,V f

(%)

Length,L

(mm)

Aspectratio,

(L=w)()

Thickness,

t(m

m)

Maximum

deform

a-

tion,s m

ax

(mm)

AC-CT1-A

-01

10

46.3

46.0

0.43

2.63

27.60

AC-CT1-B-01

10

46.3

100.1

0.94

2.68

52.88

AC-CT1-C-01

10

46.3

119.2

1.12

2.60

61.40

AC-CT2-A

-01

14

48.7

50.7

0.46

3.73

27.60

AC-CT2-B-01

14

48.7

101.6

0.94

3.40

52.80

AC-CT2-C-01

14

48.7

121.2

1.12

3.40

61.40

AC-CT3-A

-01

18

50.1

50.3

0.46

4.43

27.60

AC-CT3-B-01

18

50.1

99.7

0.90

4.30

52.82

AC-CT3-C-01

18

50.1

127.2

1.15

4.43

61.40

site S350 A.G. Mamalis et al. / Compowhen the total deformation, smax of the tube exceededhalf of the original specimen length, L.

Fig. 2. Loaddisplacement curves of the tested CFRP specimens: (a) carbon t

CT3 specimens.tructures 63 (2004) 347360Subsequent to testing works completion, photographs

of characteristic terminal views of the deformed specimens

ube CT1 specimens, (b) carbon tube CT2 specimens and (c) carbon tube

site SA.G. Mamalis et al. / Compowere taken, clearly showing the macroscopic features of

the collapse modes that were observed during the axial

Fig. 3. Axial compression of CFRP tubes/collapse mode I: (a) views of th

placement curve (The points of the load/displacement curve corresponding to

photograph.) and (c) characteristic terminal side and plan view of the defortructures 63 (2004) 347360 351compression of the tubes (see Figs. 3(c), 4(c) and 5(c)). In

addition, numerous micrographs of characteristic sections

e progressive collapse of test specimen AC-CT3-B-01, (b) loaddis-

the photos of Fig. 3(a) are marked by the sequential number of each

med specimen.

site S352 A.G. Mamalis et al. / Compoof tested tubes were obtained by means a UNIMET op-

tical microscope, in order to enable analysis of the tube

Fig. 4. Axial compression of CFRP tubes/collapse mode II: (a) views of t

placement curve (The points of the load/displacement curve corresponding to

photograph.) and (c) Characteristic terminal side and plan view of the defortructures 63 (2004) 347360walls deformation and failure. To facilitate the micro-

graphic visual examination, certain pieces of the deformed

he progressive collapse of test specimen AC-CT1-C-01, (b) loaddis-

the photos of Fig. 4(a) are marked by the sequential number of each

med specimen.

site SA.G. Mamalis et al. / Compospecimens were removed and encapsulated in acrylic resin

in conventional plastic moulds and the surface to be

Fig. 5. Axial compression of CFRP tubes/collapse mode III: (a) views of t

placement curve (The points of the load/displacement curve corresponding to

photograph.) and (c) characteristic terminal side and plan view of the defortructures 63 (2004) 347360 353examined with the microscope was prepared successively

on 200, 400, 600 and 1200 grit abrasive wheels.

he progressive collapse of test specimen AC-CT2-B-01, (b) loaddis-

the photos of Fig. 5(a) are marked by the sequential number of each

med specimen.

A characteristic set of micrographs representative of

the ndings of all microscopic examination works is

depicted in Fig. 6, which corresponds to the failure map

of the test specimen AC-CT3-B-01 that was featured by

phs o

, 3. m

reinfo

354 A.G. Mamalis et al. / Composite Structures 63 (2004) 347360Fig. 6. Failure map of test specimen AC-CT3-B-01 including microgra

rimeter: (a) micrograph of section (a) (1. external frond, 2. internal frond

wall, 6. debris wedge, 7. reinforcing carbon fabric layer, 8. fracture ofposition is marked on the plan view of the tube cross-section.f characteristic sections of the fractured tube wall along the tube pe-

ain intra-wall crack, 4. longitudinal cracks, 5. delamination of the tube

rcing carbon bre layers) and (b)(k) sections of the tube wall whose

sied as Modes I, II and III respectively, were observed

respectively. It is worthy noticing that on the contrary to

what could be expected from previously reported ex-

site Sperimental works [3,4], progressive collapse was ob-served in approximately 45% of the total number of

compression tests performedeither in all or a part of

the four sides of the tested square CFRP tubeseven

though no trigger mechanisms were used.

Progressive collapse of the CFRP tube is initiated at

the end of the elastic loading phase, when the appliedduring the axial compression tests of the square tubes.

In two test cases, a combination of collapse modes I and

III was observed on dierent sides of the square tube.

Details on the collapse mode corresponding to eachparticular specimen are listed in Table 1.

3.1.1. Mode I

Mode I is characterised by the progressive end-crush-ing of the tube, starting at one end of the tested speci-

menwhich could be either the one in contact with the

upper moving press crosshead or the lower stationary

one, the formation of two continuous fronds per tube

side which spread outwards and inwards and high ab-

sorption of crash energy [6,7,1214]. See Fig. 3(a) and

(c) for representative pictures of the progressive tube

collapse and characteristic terminal views of a deformedtest specimen that collapsed in mode I. This progressive

collapse mode corresponds to the splaying or lamina

bending type of stable brittle fracturein contrast to

transverse shear crushingin accordance with the clas-

sication made by Hull [3] and Farley and Jones [4]the maximum crash energy absorption. The mapping of

the failure mechanisms was performed by including

micrographs of several representative sections along the

tube perimeter, in the same gure with the drawing ofthe tube square cross-section on which the exact loca-

tion of each of the sections is marked.

3. Discussion

3.1. Collapse modes and failure mechanisms

The visual observations made during the testing of

the CFRP tubes, showed that the brittle nature of the

constituent materials i.e. reinforcing carbon bres and

epoxy thermoset resin, generated brittle modes of failure

under compressive load. The other two general ways in

which, according to Hull classication [3], an FRP tube

may fail i.e. Euler overall column buckling (which is

usually observed when compressing long thin tubes) orprogressive folding with hinge formation similar to the

behaviour of ductile metal and plastic tubes, were not

observed. Three distinct modes of brittle collapse, clas-

A.G. Mamalis et al. / Compoload attains a peak compressive value, Pmax. This peakload depends on the geometric and material character-

istics of the tested specimen [3,4,14]. As clearly indicated

in the comparative combination diagrams, the tube wall

thickness, t and the number of plies in the laminatestacking sequence of the tested specimens inuence sig-

nicantly the size of the peak load value. At the peak

load, cracks are formed at the corners of the square tube

specimen due to local stress concentration and begin

to propagate along the tube parallel to the tube axis.

Simultaneously with the crack formation a the tube

corners, the compressive load required for the test

continuation is signicantly reduced.Following this initial fracture phase, two continuous

fronds consisting of lamina bundles are formed and start

to spread outwards and inwards at each of the four sides

of the square tube, as depicted for example in the case of

specimen AC-CT3-B-01 in the terminal views of Fig.

3(c) and in the relative micrographs of sections (a)(e)

and (k) of the same test specimen in Fig. 6. The for-

mation of the two fronds is combined with a maincentral intra-wall crack at the end of the tube adjacent

to the area in contact with the press heads. As recorded

by the microscopic examination of the sections made

along the sides of the square tubes the length, Lc of theintra-wall crack variestaking its maximum value at the

middle of the tube side (section (a) in Fig. 6) and van-

ishing close to the corners of the square tube (sections

(c) and (k) in Fig. 6). Even at its maximum value, thelength Lc of the main crack, which is in the range of oneto ten times the thickness, t of the tube wall remains verysmall compared to the axial length, L of the testedcomposite tubes. The non-uniform crack propagation

through the square tube walls is attributed to the ma-

terial properties [3] and the changes of stresses along the

tube perimeter.

An interesting nding of the microscopic visual ex-amination regarding the main intra-wall crack, is that

the crack does not necessarily lie on the mid-surface of

the tube wall. In fact, its distance from the mid-surface

of the tube sidewall changes along the perimeter of the

tube. This is obvious when comparing for example the

sections (a) and (c) in Fig. 6. In order to visualise this

observation as good as possible in the case of the failure

map of Fig. 6, a dashed curved line representing theexact location of the main crack was drawn, clearly in-

dicating that it is only partially coincident with the mid-

surface of the tube wall in the two sides of the tube that

collapsed in progressive wall splaying mode. The rea-

sons justifying this through-thickness displacement of

the main crack are signicant changes of the stress eld

close to the corners of the tube and lack of uniformity in

the material properties. The immediate result of thisthrough thickness change of main crack position is un-

symmetrical splaying of the tube walls and variable

thickness of the resulting lamina bundles that form the

tructures 63 (2004) 347360 355external and internal fronds.

site SAs deformation proceeds further, the external fronds

are bent and fractured due to the force applied at the

contact with the press crosshead and curl downwards,

while the axial splits at the comers of the tube continueto propagate splitting the tube in four parts. Small ra-

dius bending of the external and internal fronds causes

extensive delamination of the plies of the lamina bun-

dles, as clearly depicted in the microscope images (a)(d)

of Fig. 6. Normal and shear stresses develop at the in-

terface between the steel press platen and the deforming

shell as the fronds slide along this interface. The load

combination on the delaminated fronds results in ex-tensive multiple transverse cracking through the indi-

vidual plies of the bent lamina bundles which facilitates

the transverse attening of the fronds. On the contrary

to what was expected from similar experimental works

[3,14] longitudinal cracking through the delaminated

carbon fabric reinforcing layers was very limited, fact

that is attributed to the structure of the reinforcing -

bres, i.e. the use of carbon fabric instead of unidirec-tional plies.

Fronds bending and exural damage of the lamina

bundles, as well as sliding against high-frictional resis-

tance are among the most signicant sources of crash

energy absorption in the case of collapse of collapse

mode I.

The post-crushing regime of Mode I, apart from the

two exural damaged lamina bundles is also character-ised by the formation of a triangular debris wedge of

pulverised material just above the main intra-wall crack

(see Fig. 6(a)(c)). Its formation is attributed to the local

bre and matrix crushing caused by sliding of the bent

lamina bundles under bending and high-frictional re-

sistance against the press crosshead. The debris wedge

remains unchanged during the compression process and

penetrates the composite material. As loading proceedsfurther, resulting in crushing with the subsequent for-

mation of the internal and external fronds, normal

stresses develop on the sides of the debris wedge, com-

bined with shear stresses along the same sides due to the

friction at the interface between the wedge and the two

fronds. Similar to sliding of the fronds on the steel press

crosshead, a large amount of energy is dissipated due to

friction at the sliding interface between the annularwedge and the deformed lamina bundles.

Concluding from the above analysis of collapse mode

I and considering observations reported by researchers

that have performed similar experimental works on

composite tubes [38,14], the following factors that

contribute to energy dissipation may be listed for mode I

of progressive CFRP tube collapse:

intra-wall crack propagation and axial splitting of thetube walls;

penetration of the debris wedge through the split tube

356 A.G. Mamalis et al. / Compowall with high-frictional resistance; fronds bending and exural damage of individualplies at the lamina bundles at the small radius deec-

tion area next to the debris wedge;

extensive delamination of the bent fronds in the formof multiple transverse cracking through the individ-

ual plies;

sliding between adjacent plies with high-frictional re-sistance;

external and internal fronds sliding against the steelpress crosshead with high-frictional resistance;

longitudinal cracking through the individual plies ofthe fronds.

The friction within the crush zone of the CFRP ma-

terial and between the crushed composite and the press

heads are of particular importance with respect to en-

ergy dissipation, since as it was found by analysis of the

progressive crushing mode and investigation of the

frictional processes associated with the tube compressive

collapse, frictional eects account for more than 50% ofthe total energy absorbed by progressive crushing, even

when very smooth platens are employed [5,11,13,14].

A nal note concerning the visual observations re-

lated to mode I, is that the laminate splaying and pro-

gressive crushing mechanism that was described above

may occur simultaneously with other failure mecha-

nisms on dierent sides of the compressed square tubes.

This is evident for example in the case of failure map inFig. 6, in which transverse shear crushing of the tube

walls (Fig. 6(g) and (h)) or lamina single side bending

and fracture (Fig. 6(f), (i), (j)) are observed together with

laminate splaying and bending (Fig. 6(a)(e), (k)) which

is the dominating collapse mechanism. This fact is at-

tributed to possible lack of uniformity in the structure of

the laminate material along the four sides of the square

tubes and especially at the corners.

3.1.2. Mode II

Mode II is a mode of collapse characterised by un-

stable local tube wall buckling on all four tube sides at

one end of the tested square tube, and shell brittle failureassociated with the formation of a circumferential crack.

See Fig. 4(a) and (c) for pictures of the progressive tube

collapse and characteristic terminal views of one of the

deformed tests specimens.

Local buckling is initiated at the end of the elastic

loading phase which corresponds to the linear part of

the loaddisplacement curve right after a critical peak

value, Pmax of the applied compressive load. It is im-mediately followed by a signicant reduction of the load

required to continue the tube axial compression. As

indicated in Table 1 and the corresponding diagrams,

the size of the critical buckling load, Pmax is inuencedsignicantly by the tube geometric characteristics of the

tested specimen. More specically, its magnitude de-

tructures 63 (2004) 347360creases as the aspect ratio L=w of the compressed tube

site Sspecimen becomes higher. Local buckling is not featured

by hinge formation and folding of the tube walls similar

to the compressive response exhibited by ductile metals

and ductile bre-reinforced materials (such as Kevlar).This is attributed to the combination of brittle rein-

forcing bres (carbon bres) and brittle matrix material

(epoxy resin) with low-failure strain and no plastic de-

formation characteristics.

As deformation proceeds further, local buckling is

followed by fracture of the matrix and the bre rein-

forcement layers of the tube wall. A crack is formed

along the circumference of the tube shell, resulting inunstable extensive splitting of the tube walls almost

perpendicular to the direction of the applied load and

division of the tube in two separate parts. Both parts are

fractured at the tube corners subjected to axial com-

pressive load and subsequently they are bent and de-

formed in contact with the press heads. The fracture

propagation becomes unstable as displacement increases

and local tube wall buckling continues, with new cracksdeveloping also parallel to the tube axis and circumfer-

entially, splitting the tube walls in large parts that do not

contribute to resistance to compressive loading.

As a result, the average compressive load for the tube

crushing in the post-buckling region is much lower than

the test peak load Pmax as clearly indicated by the largevalue of the load uniformity index (LU Pmax=P ) cha-racterising the specimens that collapsed according tomode II (see Table 1). Due to unstable collapse, the

specic energy absorption related to mode II is also very

low (see Fig. 8).

The principal factors contributing to energy dissipa-

tion in the case of collapse mode II are the following:

buckling of the carbon tube walls; fracture, crack propagation and splitting of the tube

walls;

partial bending and exural damage of the fracturedtube walls;

sliding of the fractured tube walls against the steelpress heads with high-frictional resistance.

A note of particular importance with respect to col-

lapse mode II is that it was observed only in the case ofcarbon tube CT1 specimens that were featured by the

smaller thickness (approximately equal to 2.64 mm) and

the minimum number of reinforcing bre layers (10

plies).

3.1.3. Mode IIImid-length collapse

Mode III is featured by brittle fracture and unstable

collapse of the compressed tube, which commences with

a circumferential fracture of the composite laminate at a

local non-uniformity of the material or the geometry at

a distance from the loaded end of the tube approxi-

A.G. Mamalis et al. / Compomately equal to its half the tube length. (Photographs ofthe gradual tube collapse and characteristic terminal

views corresponding to Mode III are depicted in Fig.

5(a) and (c)). Another signicant feature of the mid-

length collapse mode III, is that the absorbed crashenergy is very small compared to the stable progressive

end crushing mode I.

Same as in the case of the other two modes, mid-

length collapse is initiated at a critical peak value Pmax ofthe applied load, which depends on the tube geometric

and material characteristics. Circumferential cracking is

immediately followed by a signicant reduction of the

compressive load, P for the compression continuation.The cracking of the tube around its circumference

results in transverse shear crushing of the walls and

splitting of the tube in two halves. As deformation

proceeds further, the fractured parts of the tube start to

penetrate the rest of the composite tube causing further

unstable collapse of the tube and splitting of the tube

shell at the corners of the square tube while the rest of

the fractured tube walls remain almost un-deformed.Crack propagation at the tube corners takes place at

very low resistance of the compressed tube, fact that is

reected in the almost at part of the load displacement

curve.

However, when the displacement, s of the movingpress crosshead becomes approximately equal to 40

45% of the initial length, L of the tube, both halves ofthe fractured tube shell start to contribute to resistanceto compression. This results in an immediate signicant

increase of the compressive load and consequently af-

fects the average post-crushing load and the absorbed

deformation energy. An interesting visual observation to

note is that at this stage of compression, the transversely

shear-crushed ends of the tube halves act like a trigger

mechanism to the further collapse of the tube walls,

similar to the bevelled ends trigger.The principal sources of energy dissipation for col-

lapse mode III are the following:

fracture, crack propagation and splitting of the tubewalls;

bending and exural damage of the fractured tubewalls;

sliding of the fractured tube walls against the steelpress heads with high-frictional resistance.

3.2. Energy absorption characteristics

The complete set of the crash energy absorptioncharacteristics of the tested CFRP tubesthat includes

the absorbed crash energy Eabs, the specic energy Es,the peak compressive load Pmax, the average compressiveload P , and the load uniformity index LUis given intabulated form in Table 1. For reliable comparison be-

tween the compressive test results all energy data refer-

tructures 63 (2004) 347360 357ring to tubes of the same length were calculated for the

same amount of specimen deformation i.e. same maxi-

mum crosshead displacement smax.In order to have a general graphical representation of

these energy characteristics and examine their depen-dence on the geometric and other material characteris-

tics of the tested composite tubes a set of two

combination diagrams was created. The rst of them

(Fig. 7) depicts the absorbed crash energy Eabs and peakload Pmax per specimen, having the test results groupedper tube of origin of the specimens, which corresponds

to specimens of the same number of reinforcing plies,

stacking sequence and bre volume content. The seconddiagram (Fig. 8) includes the specic absorbed energy Esand the peak load Pmax per specimen but in this diagramthe grouping is made with respect to the tube collapse

mode.

In the following sub-paragraphs the inuence of the

most important geometric and material features and the

collapse mode of the tested CFRP tubes on the crash

energy absorption characteristics is thoroughly exam-ined.

3.2.1. Amount of dissipated crash energy per collapse

contribute to the energy absorption during the tube

progressive collapse, the most important of which being

the tube walls stable progressive collapse, gradual ex-

ural deformation and damage of the bent shell laminatesand relative sliding of the fractured parts under high-

frictional resistance. [3,4,13,14]. Closely related to the

high-energy absorption, is the high-average crushing

load which also characterises the progressive end col-

lapse mode I.

Comparison between modes II and III for the same

amount of deformation shows that mid-length collapse

mode III is featured by slightly higher energy absorp-tion, mainly because of the high resistance to compres-

sion eected when the displacement, s becomes equal to

half the initial tube length, L and both halves of thefractured tube shell resist to further tube collapse.

On the contrary to energy absorption and average

crushing load, the compressive load peak values are not

signicantly dependent on the collapse mode, as they are

primarily determined by the laminate material proper-ties and the geometric characteristics of the tubes. An-

other important crushing characteristic related to the

collapse mode is the load uniformity index LU of the

358 A.G. Mamalis et al. / Composite Structures 63 (2004) 347360mode

The energy absorption data in Table 1 and the spe-

cic energy per collapse mode diagram (Fig. 8) show

that carbon tubes, which collapse according to pro-

gressive end crushing Mode I, absorb considerably

higher amount of crash energy compared to the other

two unstable collapse modes. This feature is attributedto the set of deformation and friction mechanisms thatFig. 7. Energy absorption charaload displacement curves. As indicated by the test results

in Table 1, progressive end collapse mode I is also fea-

tured by the lower values of the load uniformity index

LU, which shows a relatively uniform load throughout

the compressive test. This is a desired feature of com-posite materials in crashworthiness applications, which

unfortunately is not observed in the case of the unstable

collapse modes.cteristics per carbon tube.

harac

site S3.2.2. The eect of laminate construction and tube

geometry

Since all of the tested specimens were featured by thesame constituent materials (carbon bres in the form of

reinforcing fabric impregnated in epoxy resin) the inu-

Fig. 8. Energy absorption c

A.G. Mamalis et al. / Compoence of only two material properties on the tube com-

pressive properties can be examined: the number of

reinforcing layers and the bre volume content Vf whichincrease proportionally to each other. Taking into con-

sideration the geometric and material data of the test

specimens in Table 1, we notice that the inuence of thesetwo material features on the compressive and energy

absorption characteristics of the CFRP tubes is the same

as the inuence of the tube wall thickness, as the thick-

ness also increases in proportion to the number of plies.

A clear nding of the test results depicted in the combi-

nation diagrams, is that the peak load for specimens of

the same length and aspect ratio increases signicantly as

the number of reinforcing layers, n the bre volumecontent, Vf and the tube wall thickness, t increase as well.This is probably the most apparent dependence of the

peak load on material and geometric parameters. In

contrast, the same dependence is not so obvious for the

absorbed crash energy and specic energy.

Regarding the other geometric features of the tested

square tubes apart from the tube wall thickness, the ones

that are of particular importance with respect to thespecimen compressive properties are the tube length and

the aspect ratio of length (L) to side width (w). Bothincrease proportionally to each other since all specimens

had the same cross-section. Considering the tabulatedtest results and the crash energy diagram (Fig. 7), it is

realised that the peak load is signicantly dependent on

the tube length and the aspect ratio only in the case ofthe thinner tube specimens. More specically, the peak

load decreases as the tube length and aspect ratio of the

teristics per collapse mode.tructures 63 (2004) 347360 359thin CFRP tubes get higher. On the contrary, the de-

pendence of peak load and specic crash energy ab-

sorption Es on the tube length and aspect ratio is notsimilarly clear for tubes of greater thickness.

It is worth noticing at this point the inuence of the

tube geometric characteristics on the type of collapsemodeat least for the range of length, L aspect ratio,L=w and thickness, t that featured the tested CFRPtubes. Small thickness is determinative for the occur-

rence of local buckling collapse mode II, since only the

thinner square tubes collapsed according to this mode.

Progressive end-collapse mode I, was observed in all

cases of wall thickness, either separately or concur-

rentlybut at dierent sides of the square tubewiththe mid-length collapse mode III, especially in the case

thicker tubes that were featured by higher values of as-

pect ratio (L=w). In contrast, unstable collapse modeIIIwhich was also observed in all cases of tube wall

thicknessoccurred during the compression of shorter

tubes with lower values of aspect ratio.

4. Conclusions

Summarising the features pertaining to the crash-

worthy characteristics of the static axially compressed

square CFRP tubes the following conclusions may be

drawn:

(a) Under compressive load the tested CFRP tubes col-lapsed not by progressive folding with buckle forma-

tion, but in a brittle manner, mainly because of the

brittle characteristics of the carbon reinforcing bres

and the thermosetting epoxy resin, which were the

laminate constituent materials. As the tested tubes

were relatively short and featured by low length to

side width aspect ratio, Euler buckling failure was

not observed during the testing works.(b) Three modes of brittle collapse were observed dur-

ing the testing works: the rst one (progressive

References

[1] Mamalis A, Robinson M, Manolakos D, Demosthenous G,

Ioannidis M, Carruthers J. Review: Crashworthy capability of

composite material structures. Compos Struct 1997;37:10934.

[2] Thorton P, Jeryan R. Crash energy management in composite

automotive structures. Int J Impact Engng 1988;7:16780.

[3] Hull D. A unied approach to progressive crushing of bre-

reinforced tubes. Compos Sci Technol 1991;40:377421.

[4] Farley G, Jones R. Crushing characteristics of continuous bre-

reinforced composite tubes. J Compos Mater 1992;26:3750.

[5] Fairfull A, Hull D. In: Wierzbicki T, Jones N, editors. Energy

Absorption of Polymer Matrix Composite Structures: Frictional

Eects in Structural Failure. New York: John Wiley & Sons; 1988.

p. 25579.

[6] Mamalis A, Manolakos D, Viegelahn G. Crashworthy behaviour

of thin-walled tubes of breglass composite material subjected to

axial loading. J Compos Mater 1990;24:72.

360 A.G. Mamalis et al. / Composite Structures 63 (2004) 347360end-crushing Mode I) being stable, while the other

two modes (local shell buckling Mode II and mid-

length collapse Mode III) being unstable failure

modes. The recorded progressive crushing mode I

corresponded to tube wall splaying and lamina

bending failure mode rather than transverse shear-ing crushing of the tube walls.

(c) Among the three collapse modes, only the progressive

stable crushing modewhich is featured by a rela-

tively low-load uniformity index and high-average

crushing load, is associated with high absorption of

crash energy. The main failure mechanisms associated

with energy absorption are the frictional eects in the

crush zone of the FRP materials and in the contactarea between the crushed composite material and the

press heads, the exural damage of the lamina bundles

and the inter-laminar and longitudinal crack growth.

(d) Thinner CFRP tubes are likely to collapse by local

tube wall buckling mode II, while thicker tubes in

the range of length and aspect ratio that featured the

tested CFRP tubes, tend to fail either by mid-length

collapse mode III or progressive end-crushing mode I.(e) Independently of the collapse mode, the peak com-

pressive load increases signicantly as the number

of bre reinforcing layers, bre volume content and

thickness of the axially compressed tubes increases.[7] Mamalis A, Manolakos D, Viegelahn G. Deformation character-

istics of crashworthy components. Fortschritt-Berichte der VDI-2,

Reihe 18, Nr. 62, Dusseldorf, Germany, 1989. p. 337.

[8] Mamalis A, Manolakos D, Viegelahn G, Demosthenous G, Yap

S. On the axial crumpling of bre-reinforced composite thin-

walled conical shells. Int J Vehicle Des 1991;12:450.

[9] Mamalis A, Manolakos D, Viegelahn G, Yap S, Demosthenous

G. Microscopic failure of thin-walled bre-reinforced composite

frusta under static axial collapse. Int J Vehicle Des 1991;12:557.

[10] Mamalis A, Yuan Y, Viegelahn G. Collapse of thin-wall

composite sections subjected to high speed axial loading. Int J

Vehicle Des 1992;13:564.

[11] Mamalis A, Manolakos D, Demosthenous GA, Ioannidis M.

Analysis of failure mechanisms observed in axial collapse of thin-

walled circular breglass composite tubes. Thin Wall Struct

1996;24:33552.

[12] Mamalis A, Manolakos D, Demosthenous G, Ioannidis M. Axial

collapse of thin-walled breglass composite tubular components

at elevated strain rates. Compos Engng 1994:3.

[13] Mamalis A, Manolakos D, Demosthenous G, Ioannidis M. The

static and dynamic axial crumbling of thin-walled breglass

composite square tubes. Compos Part B 1997;28B:43951.

[14] Mamalis A, Manolakos D, Demosthenous G, Ioannidis M.

Crashworthiness of composite thin-walled structural components.

Lancaster: Technomic Publishing Company; 1998.

[15] Mamalis A, Manolakos D, Ioannidis M, Papapostolou D,

Kostazos P, Konstantinidis D. On the compression of hybrid

sandwich composite panels reinforced with internal tube inserts:

experimental. Compos Struct 2002;56(2):1919.

Crashworthy characteristics of axially statically compressed thin-walled square CFRP composite tubes: experimentalIntroductionExperimentalEquipment and procedureTest materialsResults

DiscussionCollapse modes and failure mechanismsMode IMode IIMode III--mid-length collapse

Energy absorption characteristicsAmount of dissipated crash energy per collapse modeThe effect of laminate construction and tube geometry

ConclusionsReferences