Dynamic damage initiation of composite beams subjectedto axial impact

Zheng Zhang, Farid Taheri*

Department of Civil Engineering, Dalhousie University, 1360 Barrington Street, Halifax, NS, Canada B3J 1X1

Received 30 January 2003; received in revised form 18 June 2003; accepted 24 July 2003

Abstract

The dynamic damage behavior of carbon-epoxy laminated beams, having initial geometric imperfections, subject to an axial

impulse was investigated numerically and experimentally. The study focused on investigating the damage initiation and damagemechanism in the beams impacted axially by a moving mass. The dynamic equilibrium equations were developed based on theTimoshenko beam assumption with the consideration of beam’s transverse inertia, transverse shear deformation and the crosssection’s rotational inertia effects. The Higher-Order Shear Deformation Theory was adopted to model the nonlinear distributed

shear strain across the beam thickness. The von-Karman Strain–Displacement nonlinear relationship was used to model thedeformation of the beam. Hashin’s failure criteria was used to predict the damage of beams. The experiments were conducted usinga horizontal linear bearing impact setup. Scanning Electron Microscopy results showed that delamination and matrix crack were

the primary damage mechanisms in the beams. Effect of fiber angle, lay-up sequence and initial geometric imperfection on criticalenergy of damage initiation was also investigated.# 2003 Elsevier Ltd. All rights reserved.

Keywords: B. Impact behaviour; C. Damage mechanics; C. Delamination; B. Modeling; D. Fractography

1. Introduction

Due to their high specific stiffness and strength, fiber-reinforced plastic (FRP) laminated composites have beenwidely used in industrial applications such as aerospace,automobile, shipbuilding, marine and civil infra-structures. However, their susceptibility to damageresulted from mechanical, physical and chemical factors,greatly degrades their stiffness, strength and durability.Impact in particular is one of the most significant sourcesof damage that can cause matrix crack, delamination andfiber breakage. Often damages generated in FRP areundetectable to the naked eyes, therefore, it is particu-larly important to understand the damage mechanism(including initiation and progression) in FRP.

Although a great number of investigations have con-sidered FRP impact characterization, most of suchworks [1–10] have considered on the damage due totransverse impact. Choi et al. [1] conducted analytical

and experimental investigations of damage initiation ofgraphite/epoxy composite plates subjected to transverseline-loading impact, in which the effects of laminate lay-upsequence and impactor’s mass were the focus. Pavier andClarke [3] proposed an experimental technique whichcould be used to replicate the damage of composite lami-nates, which was transversely impacted by a drop-weight.Zhou [4] conducted tests on thick glass-fiber-reinforcedlaminates under transverse impact by a flat-ended impac-tor. Post-impact damage mechanism was investigated byvisual inspection and ultrasonic C-scanning techniques.Sohn et al. [5] performed drop-weight impact damage testof carbon-fiber/epoxy composite and used several char-acterization techniques, such as cross-section fracto-graphy, scanning acoustic microscopy, scanning electronmicroscopy (SEM), to observe and assess the damage dueto impact. Park and Zhou [6] investigated the transverseimpact response and damage in composite laminates byobtaining time history results of contact force, displace-ment and energy absorption on a three-point bend fixturein a split Hopkinson pressure bar. With the photo elasticstress coating technique, Franz [7] established an experi-mental method for investigating the dynamic response

0266-3538/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compscitech.2003.07.002

Composites Science and Technology 64 (2004) 719–728

www.elsevier.com/locate/compscitech

* Corresponding author. Tel.: +1-902-494-3935; fax: +1-902-484-

6635.

E-mail address: farid.taheri@dal.ca (F. Taheri).

and damage behavior of composite plates due to impactload. Necib and Mili [8] experimentally investigated thedynamic behavior of various E-glass/epoxy laminatessubjected to a drop weight impact on the transverse sideof the specimens. Luo et al. [9] proposed an approach toevaluate the impact damage initiation and propagationin composite plates, both experimentally and numeri-cally. The plates were impacted by a controlled dropweight transversely and the damage and propagationwere inspected with an optical microscope and X-raychamber. Olsson [10] suggested an analytical model forprediction of impact damage initiation and growth incomposite laminates. Critical loads and energies fordamage initiation and growth were discussed.

Most of the experimental and analytical works havebeen based on transverse impact of composite laminatesdue to a drop weight. Only a few investigations havebeen reported on the response of composite laminatessubject to axial or in-plane impact.

Axially load bearing, slender structural components arecommonly found in various structures. These componentsmay easily buckle when subjected to static or dynamicloads [11]. Due to manufacturing induced factors, manycomposite laminates bear initial imperfections and/orvoids. When such a laminate is subjected to an axial or in-plane static or dynamic load, regardless of whether thecomponent undergoes buckling or not, it may experiencedamage in the form of delamination, fiber breakage andmatrix crack if certain stress or strain components exceedthe limiting criterion during the loading period.

Using a falling weight impact system, Hsiao andDaniel[12] investigated the strain rate effect on the compressiveand shear behavior of carbon/epoxy composite lami-nates. Bogdanovich and Friedrich [13] predicted theinitial failure and ply-by-ply failure processes of compo-site laminates under dynamic loading. Abrate [14] intro-duced an energy-balance model, spring-mass model and afull model to simulate the impact in composite structures.

It can be seen that damage characterization in axialcomposite members, subjected to impulse loading, has notbeen thoroughly investigated. The scarcity of such experi-mental data thus motivated the present investigation.

The purpose of this paper is to therefore experimen-tally investigate the damage initiation mechanism andtype of damage in fiber-reinforced composite laminatedbeams subjected to axial impulse. The objective is alsoto predict and simulate such damage mechanism bycomputational simulations.

2. Analytical considerations and damage models

2.1. Differential equations of motion

To investigate the dynamic behavior of compositelaminated beams subject to axial impulse, we upgraded

the analytical model developed by the authors [16] byincluding the damping effects in the dynamic equili-brium equations. We considered a n-layer FRP compo-site laminated beam with one end impacted by a pulseload as shown in Fig. 1. The cross section of the beamwas rectangular with width b and thickness h. Thelength of the beam is L. The initial geometric imperfec-tion is w0 xð Þ, which is defined as the initial displacementof the beam in Z-direction as a function of location x.

With the Timoshenko beam assumption, the equili-brium equations were constructed for the FRP laminatedbeam. The formulation includes the axial, lateral androtational inertias of the beam, the shear deformationthrough thickness of the beam, and the damping effects inaxial, lateral and rotaional directions as follows:

I1@2u

@t2¼

@Nx

@x� CL

@u

@tð1aÞ

I1@2w

@t2¼

@V

@x�

@ Nx � �@w0

@x

� �� �

@x� CT

@w

@tð1bÞ

I2@2�

@t2¼

@Mx

@x� V� CR

@�

@tð1cÞ

where u x; tð Þ, an unknown, is the axial displacement ofthe beam in x-direction; w x; tð Þ, an unknown, is the lat-eral displacement of the beam in z-direction; � x; tð Þ, alsoan unknown, is the rotation of the cross section of thebeam about the y-axis;

Nx ¼

ðh=2�h=2

�xdz ð2aÞ

are the axial force per unit beam width, �x is the axialstress of each lamina;

Mx ¼

ðh=2�h=2

�xzdz ð2bÞ

are the bending moment per unit beam width;

Fig. 1. Schematics of a FRP beam being impacted by a moving mass.

720 Z. Zhang, F. Taheri / Composites Science and Technology 64 (2004) 719–728

V ¼

ðh=2�h=2

�xzdz ð3Þ

is the shear force per unit beam width across the cross-section of beam, and �x is the shear stress of eachlamina;

I1 ¼

ðh=2�h=2

�dz ð4aÞ

are the translational inertia per unit beam width, and �is the mass density of the lamina.

I2 ¼

ðh=2�h=2

�z2dz ð4bÞ

are rotaional inertia per unit beam width;CL,CT,CR are damping factors in axial, lateral directionand rotation of cross section of beam, respectively.

2.2. Boundary and initial conditions

The boundary conditions for Eqs. (1a)–(1c) can bepinned-end or clamped-end supports or any reasonablecombinations with the provision that the impacted endis allowed to move freely along the axial direction of thebeam. The impact can be due to a known impulse forcetime history F(t), to a known mass M with initial velo-city V0 of the impact body, or other types of impactcontact model. For our current problems, we will onlyconsider the fixed end support conditions [i.e., both theleft end (x=0) and right end (x=L) of the beam arefixed, but the beam can roll in x direction at the rightend]. Thus, the following boundary conditions areestablished,

w ¼@w

@x¼ � ¼ 0 at x ¼ 0; x ¼ L ð5aÞ

u ¼ 0 at x ¼ 0 ð5bÞ

During the impact period, i.e., when Nx x ¼ Lð Þ < 0

u tð Þ ¼ U tð Þ at x ¼ Lð Þ ð5cÞ

During the post-impact period, the right end of thebeam is free to move in the axial direction (i.e.,Nx x ¼ Lð Þ ¼ 0), while the right end’s displacement ofbeam can be obtained through zero neutral axis strain.

In Eq. (5c), U tð Þ is defined as the displacement of themoving mass [15],

U tð Þ ¼

ðt0

V tð Þdt; ð6Þ

in which,V tð Þ is the velocity of the moving mass duringthe impact period and can be represented by:

V tð Þ ¼ V0 þb

MA 1; 1ð Þ

ðt0

"xjx¼Ldt ð7Þ

The beam is assumed to be at rest initially. Therefore,the initial conditions of the current problem are

w xð Þjt¼0¼ w0 xð Þ ð8aÞ

� xð Þjt¼0¼ �@w0

@xð8bÞ

@w

@tjt¼0¼ 0 ð8cÞ

@�

@tjt¼0¼ 0 ð8dÞ

ujt¼0¼ 0 x < Lð Þ ð8eÞ

@u

@tjt¼0¼ 0 x < Lð Þ ð8fÞ

2.3. Constitutive relationship

The strain and stress relationship for the kth layer ofthe laminated beam is,

�x�y�xy

8<:

9=; ¼

Q� 11 Q� 12 Q� 16

Q� 21 Q� 22 Q� 26

Q� 61 Q� 62 Q� 66

24

35 "x

"yxy

8<:

9=; ð9aÞ

�yz�xz

� �¼

Q� 44 Q� 45

Q� 54 Q� 55

� �yzxz

� �ð9bÞ

where Q� ij are the transformed stiffness terms.For the slender laminated beam, we can assume

"y ¼ 0, xy ¼ 0, and yz ¼ 0, then Eq. (9a) and (9b)simplify to:

�x ¼ Q� 11"x ð10aÞ

and

�xz ¼ Q� 55xz ð10bÞ

2.4. Second order shear deformation theory applied tothe current problem

As demonstrated by the authors in their earlier work[16], higher order shear deformation theory (HSDT)

Z. Zhang, F. Taheri / Composites Science and Technology 64 (2004) 719–728 721

provides more accurate solution for the case under theinvestigation than that of the first order shear deforma-tion theory when evaluating the accurate distribution ofshear strain across the thickness. To predict the damageinitiation of composite laminated beams, one also needsto obtain accurate strain and stress distributions acrossthe beam thickness when subject to axial impact. UsingReddy’s higher order shear deformation theory [17],and considering the initial geometric imperfection w0 xð Þ

of the beam, the displacement field of the compositebeam can be defined as follows [16],

ux x; z; tð Þ ¼ u x; tð Þ þ z � �@w

@xþ@w0

@x

� ��

4z3

3h2� ð11aÞ

uz x; z; tð Þ ¼ w x; tð Þ � w0 xð Þ ð11bÞ

From the above equations, one can see that thetransverse shear strain distribution through the thick-ness of the beam is parabolic. Not only the transverseshear strain distribution is nonlinear, but HSDTassumes that the relationship between the axial strainand displacement, and the deflection of the beam is alsononlinear.

The von Karman strain–displacement relationshipwas then used to model the nonlinear relationship,

"x ¼@ux@x

þ1

2

@w

@x

� �2

�1

2

@w0

@x

� �2

ð12aÞ

xz ¼@ux@z

þ@uz@x

ð12bÞ

With the help of Eqs. (2)–(4) and (10)–(12), Eq. (1)could be rewritten in the non-dimensional form andsolved using finite difference method (FDM). Onecould then evaluate the dynamic behavior, (i.e., timehistory results of axial displacement, transversedeflection and rotation of cross section) of the FRPlaminated beam. Moreover, with help of the vonKarman strain–displacement relationship and theconstitutive relationship, the strain and stress timehistory results of each layer of the beam can beevaluated. Refs. [11] and [16] provide detaileddescription and verification of the analytical modeland the FDM solution, and their integrity in pre-dicting post impulse response of such beams.

2.5. Damage criterion

Three failure modes in the forms of fiber failure,matrix failure and delamination can be expected tooccur in the composite laminated components subjectto the dynamic load. For the one-dimensional lami-nated beams subject to axial impulse, we will not

consider the matrix failure along the width of the beamand, therefore, only fiber failure and through the thick-ness delamination of the beam will be considered in thesimulation of laminated beams subject to axial impulsein this investigation.

2.6. Fiber failure

2.6.1. Tension modeAs Hashin [18] stated, both tensile stress, �þ

11 andshear stress, �13 of the fibers affect the failure offibers. The fiber failure occurs if the tension stress �þ

11

and shear stress �13 of fibers satisfy the followingequations,

FTf ¼

�þ11

SþL

� �2

þ�13SLT

� �2

5 1:0 ð13Þ

in which, FTf is the failure index of fiber in tension

mode, the SþL is the tension strength of lamina and SLT

is the shear strength of the lamina in the 1–3 plane.

2.6.2. Compressive modeUnder compressive status, fiber is assumed to fail in

microbuckling and kinking of fibers with the matrix.Rosen [19] stated that fibers under axial compressionbuckle in a shear mode provided that volume fraction offibers is higher than a certain limit (i.e., �60% for car-bon/epoxy). The shear and compressive stresses bothcontribute to the compressive failure of fibers. Thedeviatoric strain energy theory, also known as the Tsai–Hill criterion [20], is similar to Hashin’s failure criteriafor fibers in tension, that is:

FCf ¼

��11

S�L

� �2

þ�13SLT

� �2

5 1:0 ð14Þ

in which, ��11 is the compressive stress, FC

f is the failureindex of fiber in compressive status, the S�

L is the com-pressive strength of fiber.

2.7. Delamination

Delamination occurs in laminates due to the normaland inter-laminar shear stresses. For the current one-dimensional laminated beam subject to axial impulse, asdescribed by the differential equations, the normal andthrough-the-thickness stresses are ignored. The failurecriteria can then be described by [18],

Fd ¼�31STL

� �2

5 1:0 ð15Þ

in which, Fd is the failure index of delamination and STL

is the through-the-thickness shear strength of thelamina.

722 Z. Zhang, F. Taheri / Composites Science and Technology 64 (2004) 719–728

3. Experimental setup

3.1. Experimental setup

Drop weight setup is a common mean for applyingimpact load for dynamic testing, as reported in severalexperimental works [1–10]. The disadvantage is that it isdifficult to eliminate the rebound impact. To overcomethis problem, a new impact setup was designed to per-form the axial impulse, as shown in Fig. 2. The majorcomponents of the system include a pendulum, a guid-ing tube with linear bearings along its full length, speci-men support fixtures and an impactor. The linearbearings were horizontally fixed on a strand. The linearbearing, fixture and specimen were calibrated horizon-tally so that the impact contact would be collinear.When the pendulum hits the impactor, it forces theimpactor to travel through the tube on the bearings. Bythis system the impactor does not rebound and impactthe specimen more than once. Two non-contact opticalsensors were used to monitor the velocity of the impac-tor. The first optical sensor also acted as a trigger forthe data acquisition setup to collect the data. The extantof damage in the specimens was inspected by visualmethod and scanning electron microscopy (SEM).

3.2. Specimen preparation

The material used in this study was TENAX/R6376carbon fiber/epoxy pre-preg by HEXCEL. R6376 is ahigh performance tough matrix formulated for the fab-rication of primary aircraft structures. It offers highimpact resistance and damage tolerance. The laminatewas cured 2 h at temperature 175 �C and 700 kN/m2

pressure with heating rate of 2 �C to 5 �C per min in anoven, as recommended by the manufacturer. The lami-nate was then cut into beams. The mechanical proper-ties of the laminate and geometric properties of beamsare listed in Table 1.

4. Results and discussion

To investigate the damage initiation behavior of car-bon/epoxy composite laminated beams with initial geo-metric imperfections subject to axial impulse of amoving mass, several groups of beams with differentlay-up configurations were fabricated and tested, andalso analyzed numerically. The lay-up configurations inthis study were 012½ , �22:5ð Þ3

� �s, �45ð Þ3� �

s, �67:5ð Þ3� �

s,

0=90ð Þ3� �

sand 0=90ð Þ2=02

� �s. The support condition of

the beam is shown in Fig. 1. The initial geometricshapes of the beams were either in sinusoidal or randomforms [21,22]. Fig. 3 shows the typical initial geometricimperfection forms. The imperfection values wereobtained using a measuring gauge after the beams weremounted on the test fixture (jig), before the impact testswere conducted. The damping coefficient of the beam isapproximately 0.04, as measured by a GrindoSonicMK5 ‘‘Industrial’’ instrument [23].

4.1. Strain records

Fig. 4 shows typical strain values recorded by twostrain gages mounted on beam’s top and bottom sur-faces, at the mid-span of the beam. When a geome-trically imperfect beam is impacted axially, it wouldvibrate in both axial and transverse directions. FromFig. 4, we can see that both top and bottom surfacesexperience compressive strain at the beginning of theevent, because the beam is deformed axially due to theimpact compressive load. As the stress wave propagatesalong the beam, the beam experiences a combinedbending and axial compressive loading, in which the topsurface of the beam is in compressive state, while thebottom is in tension. Due to the damping effect, thevibration diminishes gradually. From this figure, we cansee the maximum strain or stress that occurred duringthe first transverse vibration cycle. Considering the

Fig. 2. Experimental setup.

Table 1

Physical and mechanical properties of carbon-fiber/epoxy laminated

beams

Specimen length (mm)

300

Specimen width (mm)

20

Specimen thickness (mm)

1.6

Imperfection magnitude W0 (mm)

Factor � thickness

Longitudinal modulus E11 (GPa)

1.18E+02

Transverse modulus E22 (GPa)

5.54E+00

In-plane shear modulus G12 (GPa)

4.77E+00

Major Poisson’s ratio (v12)

0.27

Density (Kg/m3)

1512

Longitudinal tensile strength SL+ (MPa)

1094.8

Longitudinal compressive strength SL� (MPa)

712.9

Transverse tensile strength ST+ (MPa)

26.44

Transverse compressive strength ST� (MPa)

84.33

In-plane shear strength SLT (MPa)

84.42

Through-the-thickness shear strength STL (MPa)

65.36

Z. Zhang, F. Taheri / Composites Science and Technology 64 (2004) 719–728 723

dynamic pulse-buckling phenomenon [11], the damagemay occur during pre- and/or post-buckling phases.

4.2. Damage investigation

The damage mechanism of axially impacted FRPbeams differs from the damage of FRP due to trans-verse impact in which the damages, including delami-nation, fiber breakage and matrix crack mainly occursaround the contact area of the impacted region [3–5].Under axial impact, the damage occurs at a locationalong the beam or along the whole length of the beam.Damage location through the beam thickness variesdepending on lay-up configurations. When impactedaxially, the beams with initial geometric imperfectionsdeform transversely and axially. The maximum tensionand/or compression strains occur at the outer plies.According to the higher order shear deformation the-ory, the shear strain through beam thickness varies inparabolic distribution and the maximum occurs on thebeam’s mid-plane. This phenomenon was demonstratedin Fig. 5. Fig. 5 represents a typical demalination andmatrix damage. Initial voids due to manufacturing arenot negligible, and delmination and matrix crack occursusually on the weak regions. For all the tested speci-mens, except those with �67:5ð Þ3

� �sand 0ð Þ12

� �lay-ups,

delamination and matrix cracking dominated thedamage mechanism. For most of the beams with�67:5ð Þ3

� �slay-up, no delamination and matrix crack

were observed after impact, but the deformed shape wasmaintained due to the plastic deformation of matrix, asshown in Fig. 6(a) and (b). The details of such mechan-ism and prediction method will be presented elsewhere.

For those beams with 0ð Þ12� �

lay-up, matrix crackingoccurred normal to the fiber direction, and the beamwas split into two or more parts.

4.2.1. Damage analysis of beams with �22:5ð Þ3� �

slay-up

Three groups of beams, having lay up sequence of�22:5ð Þ3

� �shad three different lengths of 105, 128 and

148 mm. Each group had 4 specimens and each speci-men was impacted with different impact energy.Damage, mostly in the form of delamination, wasobserved between plies 6 and 7. Some of the delamina-tions extended along the whole length of the beams butwas limited between the two restrained ends. Fig. 7(a)and (b) show the time history results of axial displace-ment and lateral deflection at station 0.7 of the beam(0.7 indicates 7/10L distance from the cantilever supportend of the beam), obtained though our numerical ana-lyses for one of the specimens. Fig. 7(c) shows the lat-eral deformed shape at time 0.4ms compared with theinitial shape of the beam. Fig. 8(a) and (b) show thefailure indices of fiber breakage for each layer, anddelamination failure for each inter-laminar interface atstation 0.7 of the beam, obtained though Eqs. (13)–(15).From the figures, we can see that all fiber failure indicesare less than 1.0, which indicates that the fibers do notbreak; some of the delamination failure indices arehowever grater than 1.0, indicating that delaminationwould have occurred. Further analysis of Fig. 8(b)indicated that even though failure indices of interface 5–

Fig. 3. Initial out of plane geometric imperfection shapes of tested

specimens.

Fig. 4. Typical strain records.

Fig. 5. Typical delamination and matrix crack damage.

Fig. 6. Initial and deformed beam shape of one of the beams with

�67:5ð Þ3� �

slay-up.

724 Z. Zhang, F. Taheri / Composites Science and Technology 64 (2004) 719–728

6, and 7–8 were greater than 1.0, but visual observationdid not confirm such a mechanism. This was because theinterface 6–7, which was at the beam’s mid-plane, metthe delamination criterion before the other interfaces. Inthis case the other interfaces did not have the opportu-nity to delaminate, even though the failure factors weregreater than 1.0.

4.2.2. Damage analysis of beams with �45ð Þ3� �

slay-up

Unlike in beams with �22:5ð Þ3� �

slay-up in which the

delamination extended along the whole length of beamand dominated the damage mechanism, the delamina-tion in these beams occurred at several discrete stationsalong the beam length and was predominantly accom-panied by matrix cracking. Fig. 9 is a typical illustrationof delamination and matrix crack in those beams.Fig. 10 is another example of this beam group, showinga major delamination between the ply 6 and 7, whichwas also connected to another delamination (betweenply 3 and 4) by a matrix crack, which was facilitatedthough an initial void. Fig. 11 illustrates a typicalmatrix cracking of this group.

In summary, most of the delaminations in �22:5ð Þ3� �

sand �45ð Þ3

� �sbeams occurred at the beams mid-span,

extending through the beams’ thickness. The specimenshaving 0=90ð Þ3

� �slay-up, however, exhibited different

failure patterns, as follows.

Fig. 8. Numerical results of the failure Indies. (a) Failure index for

fiber breakage. (b) Failure index for delamination.

Fig. 7. Numerical results of time displacements. (a) Time history of

axial displacement at station 0.7 of the beam. (b) Time history of

deflection at station 0.7 of the beam. (c) Deformed shape and initial

shape of beam.

Fig. 9. SEM fractograph showing typical delamination and matrix

crack of a �45ð Þ3� �

sspecimen.

Z. Zhang, F. Taheri / Composites Science and Technology 64 (2004) 719–728 725

4.2.3. Damage analysis of beams with 0=90ð Þ3� �

slay-up

In this group of beams, the two 90� plies placed atthe beam’s mid-plane did not contribute much incarrying the axial force. During the transverse defor-mation stage, outer plies endured most of the tensileand compressive loads. The 3rd, 5th, 8th and 10th 0�

plies would have endured the maximum shear strain.Therefore, it is reasonable to see that delaminationswould occur between plies 1–2, 11–12, 5–6 and 7–8,as was the case. Moreover, the 5–6 interface delami-nation was connected to the 7–8 by a matrix crackrunning through plies 6 and 7. Fig. 12(a) is an exam-ple of delamination between plies 1 and 2. Fig. 12(b)

shows the connection of the two delaminations, asdescribed above.

4.2.4. Damage analysis of beams with 0=90ð Þ2=02

� �s

lay-upFour specimens were tested within this group. Most

delaminations occurred at the mid-plane and delamina-tion dominated the damage mechanism. Similarly,delamination modes were very similar to those discussedearlier.

4.3. Location of damage initiation

When a damage criterion is satisfied, the damage (fiberbreakage, delamination and or matrix crack) would initi-ate due to excessive stresses. According to the visualinspection and the associated numerical analyses of thetest specimens, delamination and matrix cracks are themost dominating damage mechanisms observed in theimperfect beams that were subject of our investigation.

Fig. 10. SEM fractograph showing typical interfacing of two

delaminations.

Fig. 11. SEM fractograph of a typical matrix crack.

Fig. 12. SEM fractographs. (a) delamination between ply 1 and 2. (b)

delamination between plies 5 and 6 connected to delamination

between plies 7 and 8 by a matrix crack.

726 Z. Zhang, F. Taheri / Composites Science and Technology 64 (2004) 719–728

Once the delamination and or matrix crack occurred,the energy absorbed by the beam was partly released bygeneration of damage, and then, whether the delamina-tion would propagate, it would depend on the amountof energy absorbed by the beam. This phenomenon willbe discussed later, in another document. In here, wediscuss the initiation location of delamination, that is,location along the beam and through inter-laminarinterfaces. Visual and microscope inspection of the tes-ted specimens suggested that most delamination occur-red between the supports. Numerical analysis results forall the tested specimens indicated that initial geometricimperfection has a significant effect on the delaminationinitiation position along the beam. Fig. 13(a) and (b) arehistograms showing the density of delamination basedon their relative distance along the beam, and theirinterface location. From Fig. 13, one can see that besidethe initiation positions at station 0.0 (fixed end) and 1.0(impacted end) along the beam, most damage tookplace around stations 0.3 to 0.4 (near to the fixed end)and 0.7 (near to the impacted end). The delaminationpositions through the thickness were at inter-laminar 4,5 and 6. The distribution of shear strain through thebeam thickness was maximum at the beam mid-span,and minimum at the top and bottom surfaces of thebeams. Due to the difference of ply orientation, how-ever, the center plies did not necessarily experience amaximum stress; therefore, a certain amount of delami-nations occurred at the 4-5 interface.

Observation of the experimental results also indicatedthat beam having relatively large imperfection (i.e.,W0=h > 0:2), failed mostly at their ends; otherwise, fail-ure occurred along the length of the beams.

4.4. Critical energy for damage initiation

When addressing the damage initiation of FRP lami-nated beams subject to axial impulse load, one shouldconsider the critical energy used for damage initiation,an unavoidable phenomenon. The angle ply laminateswith relatively large axial and bending stiffness willendure greater axial and transverse deformation resis-tance when subject to impact, and thus would endurelarger stresses; the reverse is true for laminates whichhave smaller axial and bending stiffness. Moreover, thelarger the slenderness ratios, the larger the energyrequired to initiate the damage. This can be seen fromFig. 14, which was constructed based on the inspectionof the experimental results. The axial stiffness on thex-axis is normalized relative to that of the zero degree(uniaxial) layers.

5. Conclusion

Dynamic damage behavior of FRP laminated slenderbeams, having various lay-ups, subjected to axial impulsewas investigated experimentally and numerically. Severalfactors (such as the beam’s axial transverse inertia, crosssection’s rotational inertia, the non-uniform distributionof shear stress across the beam cross-section, dampingeffect, the nonlinear strain-displacement relationshipbetween axial strain and transverse displacement) wereaccounted by our numerical solution.

Our experimental investigation subjected carbon/epoxy laminated beams with different lay-up and slen-derness ratio to axial impact load. The following con-clusions could be drawn from the results obtainedthrough our numerical and experimental analyses:

1. Delamination and matrix cracking were the

dominating damage mechanisms in the carbon/

Fig. 13. Histograms from all specimens of failure occurrence in the

FRP beams. (a) Delamination initiation location. (b) Lamina interface

number.

Fig. 14. Variation of the critical energy for damage initiation as a

function of the axial stiffness and slenderness ratio.

Z. Zhang, F. Taheri / Composites Science and Technology 64 (2004) 719–728 727

epoxy laminated beams subjected to axialimpulse.

2. The density and length of delamination(s)

depend on the lay-up sequences.

3. The delaminations were mainly concentrated at

stations 0.4–0.7 (along the beam length), and atinterface of layers 4 and 5. The damagemechanism was also strongly dependent on nat-ure of the initial geometric imperfections.

4. The critical energy for damage initiation varied

with the lay-up and slenderness ratio.

Acknowledgements

The financial support of NSERC in the form of anoperating grant to the second author in support of thiswork is gratefully acknowledged.

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