Dynamic mixed-mode I/II delamination fracture and energy...

$: Dynamic mixed-mode I/II delamination fracture and energy ...site.icce-nano.org/Clients/iccenanoorg/hui pub/2005... · notched-edge and simply supported with limited movement along$
Engineering Fracture Mechanics 72 (2005) 1531–1558

www.elsevier.com/locate/engfracmech

Dynamic mixed-mode I/II delamination fracture andenergy release rate of unidirectional graphite/epoxy composites

Sylvanus N. Wosu a,*, David Hui b, Piyush K. Dutta c

a Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261, United Statesb Department of Mechanical Engineering, University of New Orleans, New Orleans, LA 70148, United States

c US Army Cold Region Research and Engineering Laboratory, Hanover, NH 03755, United States

Received 31 December 2003; received in revised form 20 August 2004; accepted 24 August 2004

Abstract

Mixed-mode open-notch flexure (MONF), anti-symmetric loaded end-notched flexure (MENF) and center-notched

flexure (MCNF) specimens were used to investigate dynamic mixed I/II mode delamination fracture using a fracturing

split Hopkinson pressure bar (F-SHPB). An expression for dynamic energy release rate Gd is formulated and evaluated.

The experimental results show that dynamic delamination increases linearly with mode mixing. At low input energy

Ei 6 4.0 J, the dynamic (Gd) and total (GT) energy rates are independent of mixed-mode ratio. At higher impact energy

of 4.0 6 Ei 6 9.3 J, Gd decreases slowly with mixed I/II mode ratio while GT is observed to increase more rapidly. In

general, Gd increases more rapidly with increasing delamination than with increasing energy absorbed. The results show

that for the impact energy of 9.3 J before fragmentation of the plate, the effect of kinetic energy is not significant and

should be neglected. For the same energy-absorption level, the delamination is greatest at low mixed-mode ratios cor-

responding to highest Mode II contribution. The results of energy release rates from MONF were compared with

mixed-mode bending (MMB) formulation and show some agreement in Mode II but differences in prediction for Mode

I. Hackle (Mode II) features on SEM photographs decrease as the impact energy is increased but increase as the Mode

I/II ratio decreases. For the same loading conditions, more pure Mode II features are generated on the MCNF

specimen fractured surfaces than the MENF and MONF specimens.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Mixed mode; Delamination; Dynamic interlaminar fracture; Split Hopkinson pressure bar; Energy release rate

0013-7944/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.engfracmech.2004.08.008

* Corresponding author. Fax: +1 412 624 1108.

E-mail address: [email protected] (S.N. Wosu).

mailto:[email protected]

1532 S.N. Wosu et al. / Engineering Fracture Mechanics 72 (2005) 1531–1558

1. Introduction

Dynamic delamination as an interlaminar fracture has been identified as the dominant failure mode in

laminated carbon/epoxy composites [1–3]. The increasing use of composite materials in aerospace and mil-

itary applications necessitates a better understanding of the dynamic modes of failure. Some progress hasbeen made in the determination of both the statical and quasi-statical interlaminar fracture toughness [4–

17]. However, progress in developing dynamic fracture tests has been slow, and data very limited because of

the difficulties in obtaining accurate loading-point displacement of the specimen, speed of the crack tip at

high strain rate, development of accurate closed form model of analysis, and reliable specimen configura-

tions that could be adopted to the existing dynamic testing systems such as the split Hopkinson pressure bar

(SHPB) and Charpy impact test systems. The use of these methods also generates delaminated fracture

damage modes that are usually convoluted with mixed and multiple fractures and delamination. The use

of impact tests for fracture toughness measurements, for example, assumes that the impact test on a station-ary crack will yield the same result as an unstable propagating crack. The analysis is further complicated by

the difficulties of separating the individual modes from the mixed modes or evaluating their contributions

to the composite failure. Todo et al. [17] reported the development of a displacement measuring apparatus

to measure the dynamic fracture toughness. However, the experiment was done at such a low speed and

strain rate that static fracture toughness formulation was again used to estimate the dynamic fracture as

in the cases of other researchers [6–8,16,18–23]. Such approximations have been successfully applied by oth-

ers [22,23], assuming the strain rate is low and the sample attains a quasi-static state of the stress in the

vicinity of the crack tip. However, it still leaves us with the challenge of determining fracture toughnessat high strain rates based on a stress-field that drives the extension of the crack tip. Zhang et al. [24] mea-

sured the fracture toughness of marble and other samples over a wide range of strain rates and showed that

while the fracture toughness increased with loading rate for the marble sample, at high stain rate, the frac-

ture toughness was definitely different from that of the static value. Using modified ENF loaded with MTS,

Tsai and Sun [25] observed that the dynamic fracture toughness was the same as the static fracture tough-

ness up to the crack speed of 1100 m/s. Some investigators [19] reported an increase with crack speed while

others [26] reported a decrease at certain speeds. These apparent inconsistencies are due to the lack of actual

knowledge of the true stress field at the crack tip and show the complexity of dynamic measurements. How-ever, in the absence of a closed form model for dynamic fracture studies, these approximations of dynamic

behavior continue to be useful in providing fracture toughness data that are applicable to structures in

general.

Sohn and Hu [27] studied dynamic delamination at high strain rates using Charpy and Izod impact tests

and specimen configurations for Modes I, II and mixed-mode tests. The major difficulties with the test

methods are the specimen configuration which required two laminate specimens to accomplish the Mode

II test and for which constrained movement only along the specimen length. Glue used to bond the

specimen to steel bars could have compromised the integrity of the plate and the shearing movement inthe Mode II test. The analysis also ignored the effects of kinetic energy in the dynamic process.

The purpose of the studies presented in this paper was to formulate an approximate closed form exten-

sion of Sohn and Hu [27] and Reeder [8] MMB equations to characterize the dynamic mixed-mode delam-

ination fracture of composite materials using a mixed-mode open-notched flexure (MONF) that allows

mode mixing by simply varying the loading position. These difficulties are accounted for in the present

study. In contrast with Sohn and Hu [27], the pre-crack is placed at the mid-plane of the specimen

notched-edge and simply supported with limited movement along the specimen length. Flexing in the spec-

imen thickness direction is allowed. This permits shearing at the notched-edge since bending is an importantfeature of Mode II fracture. The cases of pure mode II have been reported earlier using end-notched (ENF)

and center-notched (CNF) flexure specimens simply supported at the ends and loaded at the center. The use

of a fracturing split Hopkinson pressure bar (F-SHPB) rather than Chary or Izod has the added advantage

S.N. Wosu et al. / Engineering Fracture Mechanics 72 (2005) 1531–1558 1533

of allowing the measurement of the stress field for the determination of energy absorption or fracture

energy at actual dynamic conditions. The F-SHPB apparatus used in this study differs from impact tests

in the sense that the specimen is loaded in sudden compression at a high strain rate. The only impact is

between the striker bar and the input bar. Fracture damage on the specimen is mainly caused by the inter-

action of the resulting incident compressive wave and the specimen. Thus, the flexure vibration generateddue to the sudden compressive loading of the specimen results in stress distribution in the vicinity of the

crack tip that will account for the dynamic crack propagation. In the presence of the stress, the crack will

propagate at a certain speed, making the determination of stress intensity factors or energy release rates

based on static or quasi-static formulation less appropriate. For complete dynamic test analysis, we

acknowledge that the exact crack speed and rate effects are necessary considerations for the total energy

release rate. As a first approximation, however, we assume that (1) the specimen is in a state of uniform

stress and strain for the duration of the measurement, (2) the crack propagates at a constant velocity along

the delamination path, and (3) the average dynamic behavior of an initially stationary crack is the same as acrack propagating at a uniform rate for the same conditions of loading. Assumption 3 is a consequence of

assumptions 1 and 2. Assumptions 1 and 2 are valid, and the method of analysis valid, since the particle

velocity and strain rate are both constant for the time duration of the measurements [28].

2. Mixed-mode model description and analysis

2.1. Quasi-static mixed-mode bending specimen

Generally, the interlaminar fracture toughness or energy release rate, G, is a measure of the specimen

crack growth resistance. Reeder [8] in his studies on failure criteria for mixed-mode delamination, intro-

duced a closed form modified beam analysis of the delaminated surface and included the effects of trans-

verse shear deformation, rotation of the specimen at the delamination tip, and non-linear effects through

the specimen. The energy release rate from that study can be expressed as:

GmI ¼ GkI a2 þ 2a

kþ 1

k2þ h2E11

10G13

� �P 2c ð1Þ

GmII ¼ GkII a2 þ h2E11

5G13

� �P 2c ð2Þ

where Pc is critical load where load–displacement curve deviates from a linear response [8]. The delamina-

tion length, a, is determined by measuring the length of lamination or mid-thickness crack length, D is the

perpendicular distance from the geometric center to the the line of action of the loading force, 2L is the

specimen span length, and the constants k, GkI and GkII are defined as:

GkI ¼3ð3D� LÞ2

4L2B2h3L2E11

GkII ¼9ðDþ LÞ2

16L2B2h3L2E11

k ¼ 1

h6E22

E11

� �14

ð3Þ

Reeder et al. [9,10] had earlier noted the importance of including mixed-mode toughness testing when char-

acterizing failure modes of a composite material. This is because laminated composite materials are often

subjected to mixed-mode loading that cannot be determined from a pure mode toughness test when


following the standard procedure for interlaminar fracture toughness tests [11,12]. Thus, even in cases

where pure Mode II is certain to be the dominating mechanism, we maintain that a small fraction of Mode

I could be expected and should be evaluated. From Eqs. (2) and (3), the GI/GII ratio can be written as:

c ¼ GmI

GmII

¼ 4

3

3D� LDþ L

� �2

F c; D PL3

ð4Þ

where Fc is a correction factor that accounts for deformation caused by shearing and the specimen rotation

at the crack and given as:

F c ¼ðaþ ð1=kÞÞ2 þ ðh2E11=10G13Þ

a2 þ ðh2E11=5G13Þ

" #ð5Þ

Setting Fc = 1, Eq. (4) predicts a mixed-mode ratio of 4/3 when D = 0 and D = L, a situation that is

impossible.

2.2. Dynamic mixed-mode opening notch flexure (MONF) test from modified quasi-static equations

The configuration for the MONF specimen is shown in Fig. 1 in which the span of the upper half plane is

slightly (3 mm) longer than the lower plane and loaded by the reaction (P1) at the support. The specimen

was fabricated with a 0.13 lm Teflon pre-crack placed in the mid-thickness from the opening edge. A line

edge loading applied from the center simultaneously bends the specimen similar to the ENF, and causes a

reaction in the opposite direction at the opening section. Combination of the loading and the reaction

pushes the specimen upper section open in tension, creating an anti-symmetric Mode I similar to the

ELS specimen while the flexure at the center and reaction (P2) contribute to shearing at the edges.Mixed-mode ratio effect is introduced by varying the loading position, D, from the center and away from

the pre-cracked side. Using beam theory analysis, general expressions for a symmetric a plate can be ex-

pressed as [6]:

GELSI ¼ 1

4

P 2ðaþ vhÞ2

BE11Ið6Þ

GENFII ¼ 3

16

P 2ðaþ vhÞ2

BE11Ið7Þ

where I = Bh3/12 is the plate at the moment of inertia and v is a correction for some deflection, curvature

effect, and rotation at the crack tip, and given as:

v ¼ E11

11G133� 2

C1þ C

� �2 !" #1=2

C ¼ 1:18ffiffiffiffiffiffiffiffiffiffiffiffiffiE11E22

p

G13

ð8Þ

where D is loading position with respect to the plate center as shown in Fig. 1 with the anti-symmetric load-

ing force on the specimen expressed as:

P 1 ¼PmðL� DÞ

2L

P 2 ¼PmðLþ DÞ

2L

ð9Þ

(a)

(b)

(c)

Fig. 1. Anti-symmetric loading for mixed-mode I/II (a) end-notched flexure testing (MENF), (b) center-notched flexure (MCNF), and

(c) open-notch flexure test (MONF specimens).


Following Zhang et al. [24], we define the critical loading force Pm as the peak value of the load–displacement curve at time tm as Pm(t) = E0Aet(tm). Thus, replacing P in Eqs. (6) and (7), the mode contri-

butions can be expressed as:

GmI ¼ 3

4

ðE0AetðtÞÞ2ðaþ vhÞ2ðL� DÞ2

E11B2h3L2

GmII ¼

9

16

ðE0AetðtÞÞ2ðaþ vhÞ2ðLþ DÞ2

E11B2h3L2

ð10Þ

where the upper and lower sections of the plate are of equal thickness h with the Teflon pre-crack between

them and B is the l thickness of the composite plate. The delamination length, a, is determined by measur-

ing the length of lamination or mid-thickness crack length. It is clear from Eq. (10) that Mode I is at themaximum when the loading is at the center (D = 0) and decreases as the loading position increases toward

the edge due to increased movement in the upper section of the plate. Moderate incident energy is needed to

initiate the crack in the MONF specimen. Note that GmII in Eq. (10) reduces to pure ENF Mode II at D = 0

and zero when D = L and predicts a mixed ratio expressed as:

c ¼ GmI

GmII

¼ 4

3

L� DDþ L

� �2

; D 6 L ð11Þ


One major difference and advantage of the present mixed-mode formulation can easily be seen: The MMB

specimen is valid for Mode I fracture when D is greater than L/3 compared to the proposed MONF spec-

imen that is valid for any value of D < L, where D = L corresponds to no opening and crack propagation

and GI = 0; D = 0 corresponds to greater crack opening in which Mode I is the dominating fracture mode.

Other specimen configurations such as mixed-mode end-loaded specimen (MELS), mixed-mode flexure(MMF), and cracked lab shear (CLS), and others [13–18] have been used to investigate mixed-mode frac-

ture in composite materials.

The present study postulates that total energy release rate is equal to the sum of the individual contri-

butions, mainly from opening and sliding shear fractures in this case, and expressed as:

GT ¼ GmI þ Gm

II ð12Þ
Delamination crack extension is initiated at a given mixed-mode ratio when GT reaches the material�s frac-ture toughness (GTc). Experimental observations show that the energy release rate is not a linear function of
fracture energy absorbed, impact energy or delamination [28]. A fracture behavior is modeled as a power

law function of the fracture controlling variable X expressed as:

GmI ¼ GIcX a

GmII ¼ GIIcX a ð13Þ

where the variable X is taken as the relative fracture energy absorbed by the specimen or delamination crack

extension. The parameters GIc and GIIc are mode-dependent critical values for each mode and can be deter-

mined from the curve fitting, and the exponent a is a measure of the dependence of the energy release rate on

the variable X. Substituting Eq. (13) into (12), the total critical energy release rate is given as:

GT ¼ ðGIc þ GIIcÞX a ¼ GTcX a ð14Þ
where GTc = GIc + GIIc, and GTc must exceed a critical value for the crack to grow.
2.3. Dynamic energy release rate from energy balance

In general, the total energy of an elastic body whose ends are free to move under dynamic crack growth

can be partitioned into three energies: the potential (elastic) energy contained in the body which is propor-

tional to square of the stress field and increases as the crack grows; the fracture energy, UF which is pro-

portional to the crack length and drives the breaking of bonds and creation of new surfaces and heat; andthe kinetic energy Uk due to the crack motion [29]. These energies are accounted for by the total energy

balance of the body, E, for dynamic crack growth given as:

E ¼ ðUF � F Þ þ Uk þ W ð15Þ
where F is the work done by the external forces, UF is the total fracture energy including elastic strain
energy of the plate, W is the energy required for the crack extension, and Uk is the kinetic energy to drive

the rapid extension of the crack to length da on the crack path. At high strain rate, the crack propagates ata high speed and fracture instability occurs when the energy release rate, G, is greater than the crack resis-

tance (energy consumption rate), R. The force to drive this per unit thickness is obtained after differentiat-

ing Eq. (15) with respect to the crack length as:

0 ¼ dðUF � F Þda

þ dUk

daþ dW

dað16Þ

subject to conservation of total energy of the body and its surrounding, i.e.:

dEda

¼ 0 ð17Þ


A sufficient condition given in Eq. (16) for crack extension is that the energy release rate must exceed the

rate at which the energy is consumed (Gd > R) such that:

Gd ¼dðF � UFÞ

da� dUk

da

� �>

dWda

¼ R ð18Þ

Defining UA = (F � UF) as the fracture energy absorbed for crack extension, the dynamic strain energy

release rate for a plate of B thickness is written in differential form as:

Gd ¼1

BDa½DUA � DUk�max >

dWda

¼ R� �

ð19Þ

where B is the specimen thickness and Da is the crack extension from the critical crack length, and the termsare evaluated at the peak or average values.

For a limiting case given by assumption (1), it is assumed that specimen has reached a state of uniform

stress at a constant energy consumption rate, and an approximate expression for the kinetic energy can be

written as [30]:

DUk ¼pr2

a

E0

ða� acÞ2 ð20Þ

where ra is equal to average stress on the specimen, a is the total delamination crack length, and ac is the

critical crack extension length above which the extension will be unstable. For the first estimation, ac is

taken as the initial pre-crack length equal to 6 mm.The term DUA in Eq. (19) is determined from classical wave mechanics [28] and summarized as follows:

After the impact of a striker bar with the incident (input) bar, a fraction of the compressive wave generated

is reflected at the surface of the plate and others are transmitted through the plate. An elastic wave traveling

through the specimen for time t pumps this energy into the crack tip in the direction of crack propagation.

Delamination damage to the laminate occurs by the transfer of sufficient energy to the delamination sur-

face. Thus, neglecting energy losses within the fixture, the total energy dissipation history for the damage

process can be partitioned as follows:

DU e ¼ DUi ¼AC0

E0

Z t

0

r2i ðtÞdt

DU ss ¼ DUr ¼AC0

E0

Z t

0

r2r ðtÞdt

DU is ¼ DUt ¼AC0

E0

Z t

0

r2t ðtÞdt

ð21Þ

where DUe is the incident energy due to the incident compressive wave, DUss is the surface strain due to the

reflected wave resulting from surface impedance mismatch, and DUis is the internal strain energy in the

specimen. Thus, the energy dissipated in fracture can be expressed as:

DUA ¼ DU e � DU ss � DU is ð22Þ
Substituting Eq. (21) into (22), gives the total energy dissipated in the fracture process as:
DUA ¼ AC0

E0

Z t

0

ðr2i � r2

r � r2t Þdt

DUminA ¼ DU a

DUmaxA ¼ DU a þ DU s

ð23Þ


where Eq. (23) shows the partitioning of the energy absorption into the residual energy absorbed by the

system, DUa, and the total stored elastic strain energy, DUs of the composite plate.

The numerical integration of Eq. (23) is carried out with all time shifted to zero and all three waves

beginning at the same time and for the same time duration, t. Assuming that the energy released by the

Hopkinson input bar is absorbed in fracture (DUR), the total energy dissipated in the fracture process willbe the same as energy released by the input bar (neglecting other losses) and can be expressed from elemen-

tary classical wave formulation as [28]:

DUR ¼Z

P inðtÞdunðtÞ ¼ DUA ð24Þ

where Pin(t) = A(ri(t) + rr(t)) is the external loading force at the input side of the plate and dun =

(C0/E)(ri(t) + rr(t))dt is the net specimen displacement in the direction of the net force.

Thus, the total fracture energy absorbed is obtained from the energy-absorption curve (Eq. (23)) as the dif-

ference between the peak energy dissipated ðDUmaxA Þ and residual energy absorbed by the system,DU a � DUmin

A .Substituting Eqs. (20) and (23) into (19) gives the dynamic (high strain rate) energy release rate as:

Gd ¼1

Bða� acÞDUmax

A � pr2t

E0

ða� acÞ2� �

ð25Þ

As stated earlier by Eq. (12), Eq. (25) represents a total energy release rate equal to the sum of the individ-

ual mode contributions, mainly from opening (Mode I-d) and sliding shear (Mode II-d) fractures in thiscase, and expressed as:

GT ¼ Gd ¼ GI-d þ GII-d ð26Þ
The dynamic energy release rate, Gd is dominated by Mode I-d energy release rate when D = 0 and by Mode
II-d energy release rate whenD = Lwhich is in agreement with earlier observation and that of Sohn et al. [27].

3. Experimental configuration

The experimental set-up shown in Fig. 2 consists of (1) a stress-generating system which is comprised of a

split Hopkinson pressure bar and the striker, (2) a special specimen fixture consisting of a specimen holder

and line edged impactor, (3) a stress measuring system made up of sensors (typically resistance strain

gages), and (4) a data acquisition and analysis system. Each component of the system is described by

Nwosu [28]. Dynamic loading of the composite plates is provided by a split Hopkinson pressure bar

modified for fracture tests using the appropriate specimen fixture.The compressive wave is generated on the Hopkinson input bar by the longitudinal impact between the

input bar and the striker bar at a given impact energy determined by the compressor air pressure. Upon the

arrival of the incident wave at the incident bar/specimen interface, the wave is partially reflected (because of

the impedance mismatch) and partially transmitted through the specimen. The loading is accomplished by a

line edge loading fixture (attached to the input bar) that suddenly compresses the specimen by the forward

motion of the input bar due to the energy of the striker bar. Thus, the initial energy of the striker bar trans-

ferred to the input bar as impact energy determines the incident energy to the bar–specimen interface. Since

the fracture energy released by the input bar is a direct function of the striker impact energy, it is conceiv-able that the effect of increasing the striker impact energy will be the same as increasing fracture energy.

The specimens are fabricated from AS4/3501-6 toughened epoxy unidirectional [0]n composites also used

by Reeder [8]. The experimental parameters are 131 GPa, 9.7 GPa, and 5.9 GPa for the longitudinal mod-

ulus (E11), transverse modulus (E22), and shear modulus (G13), respectively. The dimensions of the graphite/

epoxy specimens used in this present study are 52 mm in total span (2L), 25.4 mm in width (b), and

0.27 mm/ply in thickness (2h). Dimensions were chosen to be of the same (2L/b) scale with Reeder [8].

Fig. 2. Experimental set up for MONF mixed mode test showing (a) sample holder fixture and (b) fracturing split Hopkinson pressure

bar and associated instrumentation.


The stress wave loading force is determined as the average peak loading force in the force–displacement

curve between the input and output bar interfaces, and is related to the stress field transmitted to the crack

tip. This force is stress wave dependent, and is the driving force for the crack propagation. The delamina-

tion length, a, is determined by measuring the length of the mid-thickness crack along the specimen�s edge.A microscope is used for clearer viewing of the extent of the delamination. When the specimen was pulled

apart through the middle, it was observed that the length of the delamination zone measured from the edge

to the crack tip was a little longer than the edge crack length due to the effects of deflection and curvature.

In cases where the specimen is completely split through in mid-thickness by the loading force, the delam-ination length is taken as the total specimen span (2L). The strain measurements (in Volts) are converted to

stress using appropriate system calibrations and known value of the Young�s modulus of the maraging steel

of which the bar is made. With the dynamic process confined within the mid-plane containing the initial

Teflon pre-crack in the test specimen, the experiment was considered successful.

4. Experimental results and discussion

4.1. Dynamic responses

4.1.1. Effect of mode mixing on the stress wave form

Fig. 3(a) and (b) shows the stress field for varying mode mixing for 1.0 J and 4.0 J threshold impact ener-

gies for the crack opening in 16-ply (4.32 mm) and 24-ply (6.48 mm) composite specimen, respectively. No

significant difference in the shape of the wave form is observed at these low impact energies. However, as the

crack propagates at a higher impact energy (9.3 J) for the 16-ply specimen, the amplitude of the reflected

wave increases with decrease in mode mixing as shown in Fig. 3(c). This is a mode dependent effect sincethe amplitude of the incident wave remains independent of the mode mixing as expected. When the I/II mode

0 500 1000 1500 2000 2500

Time (microsec.)

-300

-200

-100

0

100

200

300In

cide

nt a

nd R

efle

cted

Str

ess

(MPa

)

I/II=4/3I/II=20/50I/II=4/50I/II=1/50

16-Ply at Ei = 1.0 JIncident Wave

Reflected Wave

0 500 1000 1500 2000 2500

Time (microsec.)

-40

-30

-20

-10

0

10

20

30

40

Inci

dent

and

Ref

lect

ed S

tres

s (M

Pa)

I/II=4/3I/II=20/50I/II=4/50

24-Ply at Ei = 4.0 J

0 500 1000 1500 2000 2500

Time (microsec.)

-600

-400

-200

0

200

400

600In

cide

nt a

nd R

efle

cted

Str

ess

(MPa

)I/II=1/50, 16-Ply

1.0 J

4.0 J

9.3 J

500 10000 1500 2000 2500Time (microsec.)

-600

-400

-200

0

200

400

600

Inci

dent

and

Ref

lect

ed S

tres

s (M

Pa) 16-Ply at Ei = 9.3 J

Reflected Wave

Incident Wave

I/II=20/50

I/II=4/3

I/II=4/50

I/II=1/50

(a) (b)

(c) (d)

Fig. 3. Stress wave forms for (a) 16-ply MONF specimen at 1.0 J, (b) 24-ply MONF at 4.0 J, (c) 16-ply MONF at 9.3 J for varying

mixed mode ratios and (d) 4/50 mixed mode ratio at varying impact energies.


ratio is fixed at 4/50 (D = 16 mm) while varying the incident impact energy, a significant dependence of the

amplitude of the waveform on the impact energy is observed in Fig. 3(d).

4.1.2. Effect of mode mixing on the force–time history

Fig. 4 displays the force–time curves at varying mixed-mode ratios for 1.0 J and 9.3 J incident impact

energies and shows that the peak force is slightly dependent on mode mixing (due to the observed

dependency of reflected wave on mode mixing) but strongly dependent on the incident impact energy.

Similarly, the amplitude of the loading force in the force–displacement curves in Fig. 5 depends slightly

on mode mixing but depends strongly on the incident energy. It is also noted that the maximum spec-

imen displacement depends on the incident energy with 0.125 mm and 0.225 mm at 1.0 J and 9.3 J,

respectively.

4.1.3. Effect of mode mixing on energy-absorption time history

Fig. 6 shows fracture energy-absorption time histories for varying mode mixing ratios at three impact

energies for the 16-ply specimen. The results for the same impact energies 1.0 J, 4.0 J or 9.3 J are summa-

rized in Fig. 6(c) and show that mode mixing above I/II = 1 has no significant effect on the peak fracture

00 50 100 150 200 250 300

Time (microsec.)

5

10

15

Load

ing

Forc

e (k

N)

I/II =4/3I/II=20/50I/II=4/50I/II=1/50

Ei=9.3 J

I/II=1/50

I/II=4/50

0 50 100 150 200 250 300

Time (microsec.)

0

2

4

6Lo

adin

g Fo

rce

(kN

)I/II =4/3I/II=20/50I/II=4/50I/II=1/50

Ei=1.0 JI/II=4/3

I/II=1/50

(a) (b)

Fig. 4. Force–time histories at (a) 1.0 J and (b) 9.3 J impact energies for varying mode ratios for 16-ply MONF specimen.

0 0.1 0.2 0.3Displacement (mm)

0

5

10

15

Load

ing

Forc

e (k

N) I/II=4/3

I/II=2/5I/II=2/25I/II=1/50

16-Ply at Ei=9.3 J

I/II=1/50

I/II=4/3

0 0.05 0.1 0.15

Displacement (mm)

0

2

4

6

Load

ing

Forc

e (k

N) I/II=4/3

I/II=20/50I/II=4/50I/II=1/50

16-Ply at Ei=1.0 J

I/II=1/50

I/II=4/3

(a) (b)

Fig. 5. Force–displacement curves for 16-ply MONF specimen at (a) 1.0 J and (b) 9.3 J impact energies for varying mixed mode ratios.


energy absorption. A slight decrease in fracture energy absorption observed with increasing mode mixing

for I/II < 0.5 where Mode I is more dominant mode at the higher impact energy of 9.3 J. This implies that

less energy is absorbed in shearing fracture (Mode II) than in opening mode due to greater strain energy

and breaking of bonds in Mode I than in Mode II. The result also shows that the residual energy retained

by the specimen is also more mode dependent at I/II < 0.5. At a higher impact energy above 4.0 J,

approaching unstable crack propagation state, this region (between 150 and 300 ls) decreases with time.

This is because at this energy, the crack length has more than exceeded the critical crack length at which

point the potential energy exceeds the fracturing energy. Thus, the fracture energy absorbed decreasesbecause more energy is released than consumed by the crack growth which is shown to be rapid at these

conditions, and crack propagation dissipates less energy during the period of rapid propagation and insta-

bility than during initiation. As shown in Fig. 6(c), the energy loss to the specimen decreases with increasing

mode mixing with greater residual energy at higher impact energy above the 4.0 J threshold energy. Com-

paring Fig. 6(a) and (b) at lower energy (1.0 and 4.0 J) with the curve at 9.3 J (Fig. 6(c)), it is clear that the

peak energy absorbed at lower impact energies Ei 6 4.0 J exhibits a plateau indicating the region of con-

stant velocity. This is also observed for each mode ratio tested, implying that the observed behavior is

0 100 200 300 400 500

Time (microsec.)

0

0.1

0.2

0.3

0.4

0.5En

ergy

Abs

orbe

d (J

)

Ei=1.0 JI/II=1/50

I/II=4/50

I/II=20/50I/II=4/3

0 100 200 300 400 500

Time (microsec.)

0

0.2

0.4

0.6

0.8

1

Ener

gy A

bsor

bed

(J)

Ei=4.0 J

I/II=4/3

I/II=20/50

I/II=4/50

I/II=1/50

0 0.5 1 1.50

0.5

1

1.5

2

2.5Pe

ak E

nerg

y A

bsor

bed,

Ea

(J)

0

0.5

1

1.5

2

2.5

Ener

gy L

oss

to S

peci

men

, EL(

J)

Ea @ 9.3 J

Ea @ 4.0 J

Ea @ 1.0 J

EL @ 9.3 J

EL @ 4.0 J

EL @ 1.0 J

0 100 200 300 400 500

Time (microsec.) Mixed Mode Ratio (GI/GII)

0

0.5

1

1.5

2

2.5

Ener

gy A

bsor

bed

(J)

Ei=9.3 J

I/II=1/50

I/II=4/50I/II=20/50

I/II=4/3

(a) (b)

(c) (d)

Fig. 6. Fracture energy absorption–time histories for (a) 1.0 J, (b) 4.0 J, (c) 9.3 J impact energies for varying mixed mode ratios, and

(d) peak energy and residual energy loss to specimen as functions of mode mixing.


an energy-dependent factor rather than a mode-dependent factor. At a higher impact energy or as more

energy is transferred to the crack tip, the energy absorbed in the initial plateau region decreases as in

Fig. 6(c). This shows a decease in energy required to sustain the crack extension once the crack is initiated.Fig. 7 shows the energy-absorption time histories for varying impact energies. Points A and B on the

curve represent the peak fracture energy absorbed and residual energy absorbed by the specimen, respec-

tively. The difference between these two points is the elastic strain energy released. For a fixed mode ratio,

the energy absorption depends strongly on the impact energy, with more energy absorbed from 4.0 J to

9.3 J than from 1.0 J to 4.0 J. The summary plot of peak values in Fig. 7(d) clearly shows energy absorbed

is slightly dependent on mode mixing with more energy absorbed as Mode II dominates. In contrast, the

residual energy absorbed is strongly dependent on mode mixing. As in Fig. 6, the summary plot also shows

that the residual energy retained by the specimen is a more mode dependent factor than peak energyabsorbed.

The residual energy absorbed by the system depends on the properties of the specimen, laminate config-

uration, damage energy threshold, and the mode of damage generated. Since the mode mixing effect is a

0 100 200 300 400 500

Time (microsec.)

0

0.5

1

1.5

2

2.5En

ergy

Abs

orbe

d (J

)I/II=4/3 (D=0 mm)

Ea(t) @ 9.3 J

Ea(t) @ 4.0 J J

Ea(t) @ 1.0 J

0 100 200 300 400 500

Time (microsec.)

0

0.5

1

1.5

2

2.5

Ener

gy A

bsor

bed

(J)

I/II=1/50 (D=21 mm)

Ea(t) @ 9.3 J

Ea(t) @ 4.0 J

Ea(t) @ 1.0 J

0 100 200 300 400 500Time (microsec.)

0

0.5

1

1.5

2

2.5

Ener

gy A

bsor

bed

(J)

I/II=20/50 (D=8 mm)

Ea(t) @ 9.3 J

Ea(t) @ 4.0 J

Ea(t) @ 1.0 J

0 10

Impact Energy, Ei(J)

0

0.5

1

1.5

2

2.5

Peak

Ene

rgy

Abs

orbe

d, E

a(J)

0

0.5

1

1.5

2

2.5

Ener

gy L

oss

to S

peci

men

, El(J

)Ea @ I/II=4/3Ea @ I/II=20/50Ea @ I/II=4/50Ea @ I/II=1/50

EL @ I/II=4/3El @ I/II=20/50El @ I/II=4/50El @ I/II=1/50

2 4 6 8

(b)

(c) (d)

(a)

Fig. 7. Fracture energy absorption–time histories for (a) I/II = 4/3, (b) I/II = 4/50, (c) I/II = 1/50 for varying impact energies, and (d)

peak energy absorbed and residual energy loss to specimen as functions of impact energy.


material property, it is conceivable that the residual energy is a more mode-dependent factor than the en-

ergy absorbed.

4.2. Variation of dynamic delamination with impact energy

The expected specimen response to energy absorption is an increase in delamination crack length. Fig. 8

shows variations of dynamic delamination with increasing impact energy and loading positions for MENF

and MONF configurations. It is clearly evident in the figure that delamination, once initiated, increases asimpact energy is increased until the delamination length approaches the specimen span. For the MONF

specimen, 1.0 J and 4.0 J of impact energies were required to initiate an interlaminar crack opening in

16-ply and 24-ply specimens, respectively, and 9.3–13 J for the crack to propagate the entire span (2L)

of the 16-ply specimen. The results show that delamination crack growth is slow at low energy and increases

very sharply as more energy is pumped into the crack tip. Note that the delamination becomes constant and

independent of impact energy after 9.3 J for I/II = 4/50 and 1/50, and 13 J for both GI/GII = 4/3 and

I/II = 20/50, and approaches a maximum value at incident energy of 13 J. Similarly for the MENF speci-

men, delamination is higher for mixed-mode loading (D = 20 mm) than for pure mode loading (D = 0 mm)and becomes constant at 80 J incident impact energy. It was observed that energy above this value (9.3–13 J

0 5 10 15 20

Impact Energy, Ei (J)

20

30

40

50

60

Del

amin

atio

n C

rack

Len

gth,

a (m

m)

D= 0 mm (I/II=4/3)D = 8 mm (I/II=20/50)D = 16 mm (I/II=4/50)D = 21 mm (I/II=1/50)

MONF, 16-Ply

0 20 40 60 80 100

Impact Energy, Ei (J)

20

30

40

50

60

ENF, 16-ply, (D=0 mm)MENF, 16-ply, (D=20 mm)

Del

amin

atio

n C

rack

Len

gth,

a (m

m)

(a)

(b)

Fig. 8. Effect of impact energy on delamination crack growth for (a) MONF and (b) MENF/ENF specimens.


for MONF and 80 J for MENF) resulted in fragmentation and a reduced delamination length of the spec-

imen as the specimen merely breaks into fragments [28].

4.3. Variation of dynamic delamination with energy absorbed

The delamination crack propagation increases non-linearly as the fracture energy absorption is increased

as shown in Fig. 9(a). A non-linear curve fit to the results shows that the dynamic delamination is a power

function of energy absorbed and is dependent on mode mixing for all the mixed-mode ratios tested. The

higher the mixed-mode ratio, the lower the delamination for the same energy absorbed. Thus, for the same

energy-absorption level, the delamination is greatest at a lower mixed-mode ratios corresponding to highestMode II contribution. That a shearing mode contributed to more delamination than an opening mode for

the same energy absorbed is contrary to our predictions. It implies that shear forces play a more dominant

0 0.5 1 1.5

Mixed Mode Ratio (GI/GII)

0

10

20

30

40

50

60

Del

amin

atio

n C

rack

Len

gth,

a (m

m)

0

5

10

15

20

25

30

Load

ing

Posi

tion

from

the

Cen

ter,

D (m

m)

a @ 9.3 J

a @ 4.0 J

a @ 1.0 J

Loading Position

0 00 0.5 1 1.5


0.5

1

1.5

2

2.5

Peak

Ene

rgy

Abs

orbe

d, E

a(J)

0.5

1

1.5

2

2.5

Ener

gy L

oss

to S

peci

men

, El(J

)

Ea @ 1.0 JEa @ 4.0 JEa @ 9.3 J

EL @ 1.0 JEL @ 4.0 JEL @ 9.3 J

(a)

(b)

Fig. 9. Effect of mixed mode mixing on (a) delamination crack growth and (b) peak energy absorbed and residual energy absorbed by

specimen for varying impact energies.


role in the delamination of uni-directional composite material than tensile forces. An areal plot of Fig. 9(b)

shows the partitioning of energy absorption into critical regions of delamination crack growth for the same(I/II = 4/3) mode ratio. Note the sudden increase in energy absorption after 4.0 J for the same mode ratio.

The areal plot also indicates the main energy-absorption mode for the fracture process. The first region

(labeled I in the figure) represents the internal energy of the composite system due to fracturing and break-

ing of the bonds while the second larger region (II) represents the elastic energy for crack propagation

which appears to increase in proportion to crack propagation and decrease as the crack propagation de-

creases. The sudden jump in region III indicates high kinetic energy as the crack propagates uncontrollably,

indicating the region of unstable crack growth. These observations indicate a smooth increase in crack

propagation for 1.0 6 Ei 6 4.0 J, with beginning of unstable delamination at an impact energy of Ei P 4.0 Jfor this 16-ply specimen.


4.4. Variation of dynamic delamination with Mode I/II mixing

Fig. 10 shows delamination crack length as a function of mixed-mode I/II mixing for 16-ply MONF

specimen. In general, delamination in the MONF specimen configuration decreases non-linearly as the

mixed-mode ratio increases (or loading position decreases from center toward the specimen edge). Atlow incident energy, an increase in impact energy from 1.0 to 4.0 J results in only a 20% increase in delam-

ination length for all the mixed-mode ratios tested. A higher impact energy above 4.0 J (from 4.0 to 9.3 J)

results in a 73% increase in delamination. This observed low delamination growth at lower energy is due

mainly to the greater fraction of the initial energy expended in the early stage to overcome friction and

other effects of inertia, breaking of bonds, opening and propagation of the crack. As more energy is

Fig. 10. (a) Delamination crack growth as a function of peak energy absorbed at 9.3 J impact energy for varying mode ratios and (b)

regions of crack growth and area plot of energy absorbed–delamination curve for varying impact energy showing.


pumped into the crack tip, delamination increases faster as the crack propagates. Fig. 10(a) also shows that

the loading position is a power function of mode mixing. It is observed (Fig. 10(b)) that the energy absorp-

tion as a function of mode mixing follows the same behavior as for delamination. This supports our initial

assertion that dynamic delamination is driven mainly by the amount of energy available at the crack tip.

4.5. Variation of energy release rate with mode mixing

The variations of energy release rates with loading position or mixed-mode ratios determined from Eqs.

(5) and (20) are shown in Fig. 11 for the three impact energies, 1.0 J, 4.0 J and 9.3 J. As predicted, Fig. 11(a)

shows that GmII decreases as mixed-mode ratio increases and loading position decreases. In contrast, Gm

I

0 0.5 1 1.5


0

5

10

15

Tota

l Ene

rgy

Rel

ease

Rat

e, G

T (k

J/m

2 )

0

0.5

1

1.5

2

2.5

3

Dyn

amic

Ene

rgy

Rel

ease

Rat

e, G

d (k

J/m

2 )

Gd @ 9.3 J

GT @ 9.3 J

GT @ 1.0 J

Gd @ 4.0 J

GT @ 4.0 J

Gd @1.0 J

0 0.5 1 1.5


0

5

10

15

Ener

gy R

elea

se R

ate,

Gm

, Gm

(kJ/

m2 )

I-MONF-1.0 JI-MONF-4.0 JI-MONF-9.3 J

II-MONF-1.0 JII-MONF-4.0 JII-MONF-9.3 J

II-MONF-9.3 J

I-MONF-9.3 J

II-MONF-4.0 J

I-MONF-4.0 JII-MONF-1.0 J

I-MONF-1.0 J

III

(a)

(b)

Fig. 11. Comparison of variations of energy release rates (a) GmI and Gm

II and (b) GT and Gd with mixed I/II mode ratio (loading

positions) for MONF 16-ply graphite/epoxy specimen.


increases as mixed-mode ratio increases, and equal to GmII at I/II = 1/1 as predicted by the model. Thus,

Mode I contribution decreases (and Mode II contribution increases) in the direction away from the center

(D = 0), that is, as the crack front moves toward the edge of the specimen (D � L, or I/II = 1/50). The result

shows that GmI and Gm

II are linearly dependent and vary with mixed-mode ratio.

The study postulates that total energy release rate given by the failure criteria, GT, and dynamic energyrelease rate, Gd are materials properties and are therefore expected to be independent of mixed-mode ratio.

This is partly supported by Fig. 11(c) which shows that at low energy below the region of instability, the

dynamic (Gd) and total energy (GT) rates are approximately constant. At higher impact energy, the dynamic

energy release rate decreases slowly with mixed-mode ratio due to an increase in crack velocity and asso-

ciated kinetic energy which reduces the net energy available for crack propagation. This behavior implies

that the resistance for crack growth decreases with particle velocity. However, the GT is observed to

decrease more rapidly since the kinetic energy of the crack extension is neglected. A formulation similar

to the above was first proposed by Sohn et al. [27] with kinetic energy neglected.

4.6. Variation of energy release rate with delamination and energy absorbed

Fig. 12 displays the variation of energy release rate with normalized delamination length, displaying a

typical R-curve under plane stress. The high strain rate energy release rate, Gd increases with normalized

delamination crack extension with a change in slope at above four times the critical crack length for open-

ing of the crack. The curve shows that the energy release rate as function of normalized delamination crack

length is mode dependent, increasing as the loading position decreases (or as mixed-mode ratio increases).The fact that this curve is shifted from zero means that a critical crack initiation point exists above which

the delamination growth will be unstable. The values can be estimated by fitting an appropriate non-linear

function to the Gd-crack extension curve. Such a curve when extrapolated to zero Gd-value gives the critical

values of 4.0 < (a/ac) < 4.4 depending on loading position. In Fig. 12(b), it can be observed that Gd

increases with normalized energy absorbed more slowly than in the case of delamination, with the change

in slope occurring at about two times the critical energy for the crack opening. Below this value, Gd appears

to be independent of energy in agreement with earlier results that show a small variation at energy below

4.0 J. However, in contrast to the delamination case, the result shows that the initial energy for crackgrowth initiation is independent of mixed-mode ratio. In both delamination and energy absorbed curves,

it is clear that the higher the loading position (lower mixed-mode I/II ratio), the lower the dynamic energy

release rate. Since the energy release rate is the ‘‘crack driving force’’, it means that the force required to

sustain a unit length of shearing (represented lower mode I/II mixing) in this uni-directional composite

material is more dependent on crack extension than on the energy absorbed.

4.7. Comparison of fracture laws for MONF and MMB for varying mixed-mode ratios and

impact energies

Variation of GI with GII for varying mode ratios is shown in Fig. 13(a) comparing the MONF and MMB

formulations for various mixed-mode ratios. An attempt was made to eliminate the scaling effect by fabri-

cating the specimen with same span/width (2L/B) ratio. Although the present study compares reasonably

with the Reeder [8] model for GmII at both 4.0 J and 9.3 J incident impact energies, there is a significant dif-

ference between the two formulations in the case of GmI for both energies. The variation of the mixed-mode

ratio with incident impact energy in Fig. 13(b) shows that the ratio decreases slightly with energy in MMB

specimen but independent of energy in MONF specimen. This is because Eq. (4) for MMB included a spec-imen deformation and rotation correction term that depends on energy. As shown in Fig. 13(c), the differ-

ence between mode ratio for MONF model and MMB model is maximum when D is close to L or when the

I/II ratio is the smallest (maximum Mode II contribution).

0

0.5

1

1.5

2

2.5

0 4 10

Normalized Energy Absorbed, Uf/Ec

Dyn

amic

Ene

rgy

Rel

ease

Rat

e, G

d

(kJ/

m2 )

Gd, D=0 mmGd, D= 8 mmGd, D=16 mmGd, D=21 mm

0

0.5

1

1.5

2

2.5

0 6 10

Normalized Delamination Crack Length, a/ac

Dyn

amic

Ene

rgy

Rel

ease

Rat

e, G

d(k

J/m

2 )

Gd, D=0 mmGd, D= 8 mmGd, D=16 mmGd, D=21 mm

2 4 8

2 6 8

(a)

(b)

Fig. 12. Variations of dynamic energy release rate with (a) normalized fracture energy absorbed and (b) normalized delamination

crack extension for various loading positions (mixed mode ratio) for 16-ply MONF specimen.


The mixed-mode energy release rate as function of loading position and mixed-mode ratios are plottedand compared for both MONF and MMB formulations in Fig. 14(a) and (b), respectively. For all the inci-

dent impact energies for the MONF, mixed-mode II contribution increases (and Mode I decreases) with

loading position. It is clear from the figure that this observation is only true for MMB when D 6 8 mm.

Although the variations of GmI and Gm

II energy release rates with mode mixing using MONF formulations

is consistent with behavior with loading positions, Fig. 14(b) shows that both GmI and Gm

II energy release rates

using MMB formulations increase with mixed-mode ratio, reaching a maximum at I/II = 50/50 = 1/1 before

decreasing. It is also observed that the mode mixing for the case of MMB does not have a consistent func-

tionality with loading position, while in contrast in MONF, mode mixing increases with decreasing loadingposition. To understand why the models agree forGm

II but disagree forGmI , it is recalled that the present model

is valid for all values of D 6 L compared to the Reeder [8] MMB model that is valid for DP L/3, and is

particularly true for GmI according to Eqs. (4) and (11). At D = 8 mm (D < L/3), MMB predicts a mode ratio

of zero (GI = 0), implying that Mode I loading was not sufficient to open the crack. This is not the case in

Mode II as been noted by previous investigators [6]. The similarity of fracture laws using MONF and

MMB formulations for mixed-mode II with previous results [8–10] does show that the MONF configuration

Fig. 13. SEM photographs of (a–c) 24-ply MENF and (e–f) 24-ply MCNF delamination fracture surfaces for varying loading

positions at 75 J impact energy.


proposed here can be used for mixed-mode testing using a fracturing Hopkinson bar. However, MONF for-mulation presented here adds the advantage of consistent fracture behavior for both Mode I and Mode II

energy release rates, and the relationships between the loading position and the mode mixing.

4.8. Fractographic analysis

Scanning electron microscope (SEM) techniques have been successful for fractographic studies of graph-

ite/epoxy specimens to relate the detected fracture surface to the type of fracture mode involved [32–39].

Hackles features in SEM photographs are related to fracture induced delamination due to shearing fractureresulting from interlaminar stresses. In the present investigation, the fracture surfaces were generated by a

fracturing split Hopkinson pressure bar under a variety of loading conditions and photographed using a

scanning electron microscope (SEM) at regions indicated in Fig. 1. In mixed-mode testing using the MONF

Fig. 14. SEM photographs of 16-ply MONF fractured surfaces between end of insert and near the edge for varying mixed-mode ratios

at (a–c) 4.0 J and (d–f) 9.3 J impact energies.


specimen, only the loaded upper section was photographed at the regions indicated by numbers in Fig. 1

(where 1 represents near insert end, 3 near the edge, and 2 close to center).

For MENF and MCNF loading configurations in Fig. 15, as the loading shifts from the center

(D = 0 mm) to the edge (D = 20 mm), coarse hackles with some desegregation of very coarse hackles(Fig. 14(b) and (d)) are seen with some resins detached. An increased number of less coarse hackles are

formed when the loading is near the edge (corresponding to low mixed I/II mode ratio) than at the center

(D = 0 mm). The central fracture surfaces at higher energy show fiber pull-out and evidence of fiber break-

age. The hackle marks appear oriented perpendicular to the fiber with their tips bent over along the fiber in

the direction of the relative motion of adjacent plies and with their width approximately equal to the dis-

tance between the fibers. Similarly, Fig. 16 for the MONF specimen shows smooth surface at higher mode

ratios (4/3) indicating the absence of interlaminar shear force. Regularly spaced incipient to medium to fine

hackles are observed at low impact energy (1.0 J). As the energy is increased, the surface is mostly smoothwith some fine to incipient hackles. At 9.3 J at which the crack propagates through the entire specimen

4/3 20/50 1/50

Mixed Mode Ratio

0

0.25

0.5

0.75

1

1.25

1.5H

ackl

e M

arks

Den

sity

(cou

nts/

µm)

0

5

10

15

20

25

Load

ing

Posi

tion

from

Cen

ter,

D(m

m)

Insert-endCenterEdgeTotalLoadingPosition

MONF-16-ply @ 9.3 J

0 4 6 8 1

Impact Energy (J)0

0

0.5

1

1.5

Hac

kle

Mar

ks D

ensi

ty (c

ount

s/µm

)

Insert-endCenter

EdgeTotal

MONF-16-ply, 1/50

2

(a) (b)

Fig. 15. Quantitative summary of effect of (a) mixed-mode ratio and (b) impact energy on SEM hackle marks density for 16-ply

MONF specimen.

0 10 15 20 25

Loading Position from Center, D (mm)

0

1

2

3

4

Hac

kle

Mar

ks D

ensi

ty (c

ount

s/µm

)

MENF-24 at 75 J

0 10 15 20 25

Loading Position from Center, D (mm)

0

1

2

3

4

Hac

kle

Mar

ks D

ensi

ty (c

ount

s/µm

)

CoarseMediumFineTotal

MCNF-24 at 75 J

0 10 15 20 25Loading Position from Center, D (mm)

1

1.5

2

CoarseMediumFineTotal

CoarseMedium

Fine

Total

MONF-16 Ply at 9.3 J

5 5

5

Hac

kle

Mar

ks D

ensi

ty (c

ount

s/µm

)

(a) (b)

(c)

0

0.5

Fig. 16. Quantitative summary of effect of anti-symmetric loading on SEM hackle marks density for 24-ply (a) MCNF, (b) MENF

specimens loaded at 75 J, and (c) 16-ply MONF specimen at 9.3 J.



span, the surface is smoother with more fibers exposed than at lower energy. More fiber exposure is asso-

ciated with less formation of hackle marks. A clean and smooth matrix surface is related to weak interfacial

bonding, and indicates the absence of interlaminar shear forces. Gilchrist et al. [32–34] and Johannesson

et al. [35] showed that hackle marks are generally a matrix feature found in resin-rich regions. The results

show that on the average, increasing the impact energy reduces the hackle marks formation from coarse tofine at low energy to incipient hackles at higher energy. This agrees with the observation that hackles usu-

ally appear smaller at high crack velocity around the crack tip [36–39].

Quantitative non-subjective methods of analyzing the surface morphology were recently reported by

Nwosu and Hui [40] is shown in Fig. 16. The distribution profiles of average hackle marks at insert, center

and edge positions of the crack tip as a function of loading positions (mixed-mode ratios) and incident

0 16 21 0 16 21

Loading Position from Center, D(mm)

0

5

10

15

Ener

gy R

elea

se R

ate,

GI ,

GII (

kJ/m

2 )

II-MONF-9.3 J

I-MONF-9.3 J

II-MMB-4 J

I-MMB-4.0 J

II-MMB-9.3 J

II-MONF-4.0 J

I-MONF-4.0 J II-MONF-1.0 J

I-MMB-9.3 J

II-MMB-1.0 J

1/50 4/50 20/50 4/3 0.25/50 20/50 50/50 4/3


0

5

10

15II-MONF-9.3 J

I-MONF-9.3 J

II-MONF-4.0 J

I-MONF-4.0 J

II-MONF-1.0 J

I-MMB-9.3 J

I-MMB-4.0 J

II-MMB-4.0 J

II--1.0 J

II-MMB-9.3 J

8 8(a)

(b)

Ener

gy R

elea

se R

ate,

GI,

GII (

kJ/m

2 )m

mm

m

Fig. 17. Comparison of variations of energy release rates (GmI and Gm

II) with (a) loading position and (b) mixed I/II mode ratio for

MONF and MMB formulations.


energy are shown in Fig. 17(a) and (b), respectively, for the MONF configuration. While the total hackle

mark density increases with decreases in mode ratio, it decreases linearly with an increase in striker impact

energy. This is because the dominant failure mechanism at higher energy is Mode I fiber breakage and pull-

out. Maximum hackles formation was observed when the crack front is between the specimen edge and

crack initiation point. Thus, the hackle density starts to decrease as the delamination length approachesthe span of the specimen or as the energy approaches the critical energy for unstable delamination. Since

a decrease in I/II ratio implies an increase in the component of bending fracture mode, the result agrees with

our earlier assertion that hackle marks generation is a dominant feature of Mode II fracture. These results

show that the formation of hackles is mode dependent and decreases with increase in impact energy. A

change in slope at 20/50 in the figure may be an indication of change in failure mechanism. In all the loading

configurations (single and multiple modes), the results show that hackle marks are formed and more uni-

formly distributed when the crack front is away from the point of loading. The closer the loading is away

from the center (non-symmetric loading) the higher the hackle density.

10 15

Energy Release Rate, GII (kJ/m2)

0

2

4

6

8

10

12

Ene

rgy

Rel

ease

Rat

e, G

I (k

J/m

2 )

MONF I/II=4/3MONF I/II=20/50MONF I/II=4/50MONF I/II=1/50MMB I/II = 4/3MMB I/II=0.25/50MMB I/II = 20/50MMB I/II = 50/50

20 25 30 35 40 45 50

Delamination Crack Length, a (mm)

0

0.5

1

1.5

2

2.5

GI/G

II

MONF, D=0 mmMMB, D=0 mmMONF, D=8 mm

MMB, D=8 mmMONF, D=21 mmMMB, D=21 mm

5(a)

(b)

m

m

Fig. 18. Comparison of variations of (a) GmI with Gm

II and (b) mixed mode ratio with delamination for MONF and MMB formulations.


Typical plots of the total hackle density as a function of loading position are shown in Fig. 18 for mixed-

mode situations for MCNF, MENF, and MONF configurations. The distribution profile shows a combi-

nation of both medium coarse and fine hackles depending on the mode ratio or impact energy. Greater

frequency of well developed hackles is an indication of high energy absorption and presence of interlaminar

shear forces and (pure Mode II) shearing fracture mode. A lower frequency of coarse hackles or increasedfine or incipient hackles indicate smooth surfaces, weak interfacial bonding, and absence of interlaminar

shear forces (pure Mode I fracture).

An important observation here is why the hackles are more common at the insert point than as the crack

tip as it approaches the edge of the specimen. Marder and Fineberg [29] showed that cracks in brittle mate-

rials suffer a dynamic instability going through some distinct stages of propagation. The motion of the crack

is forbidden at certain ranges of velocities. Close to threshold crack initiation velocity, the crack velocity is

smooth, and increases very slowly, and the motion of the crack is stable. This leaves new and smooth sur-

faces behind. The motion becomes unstable and surfaces become rougher when the velocity is much higherthan the initial threshold velocity. Since the crack is initiated close to the insert point, the crack velocity is

stable at that point. Thus uniform distribution of hackle marks is expected at the point of stable velocity and

delamination. Once the instability has started, higher energy only results in creation of more rough surface

damage than propagation. This also supports Fig. 16(b) that shows a decrease in hackles formation as the

energy is increased.

5. Concluding remarks

A new mixed-mode open-notch flexure (MONF) was successfully applied to investigate dynamic mixed-

mode I/II delamination of unidirectional graphite/epoxy composites using a fracturing split Hopkinson pres-

sure bar (F-SHPB). An expression for dynamic energy released rate Gd is formulated and evaluated. The

important results are summarized below:

1. The energy-released rate results using the MONF configuration are consistent with fracture laws for

graphite/epoxy. Delamination decreases with mixed-mode I/II ratio and increases with impact energy.2. No significant difference in the shape of the wave form is observed at low impact energies less than

4.0 J; the amplitude of the reflected wave increases with a decrease in mode mixing. The peak loading

force is slightly dependent on mode mixing (due to the observed dependency of reflected waves on

mode mixing) but strongly dependent on the incident impact energy. Similarly, the amplitude of the

loading force in the force–displacement curves depends slightly on mode mixing but depends strongly

on the incident energy.

3. Mode mixing above I/II = 1 has no significant effect on the peak fracture energy absorption. A slight

decrease in fracture energy absorption is observed with increasing mode mixing for I/II < 0.5 whereMode I is more dominant mode at the higher impact energy of 9.3 J. The result also shows that

the residual energy retained by the specimen is also more mode dependent at I/II < 0.5. At a higher

impact energy above 4.0 J, approaching unstable crack propagation state, fracture energy decreases

with time and depends strongly on the impact energy, with more energy absorbed at impact energy

high than 4.0 J as Mode II dominates. In contrast, the residual energy absorbed is strongly dependent

on mode mixing.

4. Delamination, once initiated, increases as impact energy is increased until the delamination length

approaches the specimen span and grows slowly at low energy before increasing very sharp as moreenergy is pumped into the crack tip. For the MENF specimen, delamination is higher for the

mixed-mode loading (D = 20 mm) than for the pure mode loading (D = 0 mm) and becomes constant

at 80 J incident impact energy.


5. The delamination crack propagation increases non-linearly as the fracture energy absorption is

increased and is shown to be a power function of energy absorbed and mode mixing for all the

mixed-mode ratios tested. For the same energy-absorption level, the delamination is greatest at a lower

mixed-mode ratios corresponding to highest Mode II contribution implying that shear forces play a

more dominant role in the delamination of uni-directional composite material than tensile forces.6. Mode I contribution decreases (Mode II contribution increases) in the direction away from the center

(D = 0), that is, as the crack front moves toward the edge of the specimen (D � L, or I/II =

1/50). The result shows that GmI and Gm

II are linearly dependent and vary with mixed-mode ratio.

7. Comparison of fracture laws for MONF and MMB for varying mixed-mode ratios and impact ener-

gies show that mode ratio decreases slightly with energy in MMB specimen but independent of energy

in MONF specimen; the difference between mode ratio for MONF model and MMB model is maxi-

mum when D is close to L or when the I/II ratio is the smallest (maximumMode II contribution). Vari-

ations of GmI and Gm

II energy release rates with mode mixing using MONF formulations are consistentwith behavior with loading positions and the Sohn and Hu [27] results.

8. At low energy below the region of instability, the dynamic (Gd) and total energy (GT) release rates

(without kinetic energy) are independent of mixed-mode ratio. At higher impact energy, Gd increases

slowly with mixed-mode ratio while GT is observed to decrease more rapidly. The greatest deviation

between GT and Gd is observed at higher impact energy and lower mode ratio. The dynamic energy

release rate Gd increases more rapidly with increasing delamination than with increasing energy

absorbed. Since Gd and GT are assumed materials properties, it is concluded that interlaminar fail-

ures such as delamination have the effect of changing the integrity of composite structures. The frac-ture behavior as a function of loading position using the present formulation compares very well

with that of Sohn and Hu [27].

9. The profile of hackle marks distribution shows that hackles formation decreases as the impact energy is

increased and increases as the mixed-mode I/II ratio decreases. These results show that the formation

of hackles is mode dependent and decreases with increases in impact energy. Maximum hackle marks

(Mode II feature) mixed-mode testing occur when the crack tip is between the insert end and the edge

of the specimen corresponding to the point of maximum specimen bending.

10. One drawback in the present investigation is in the kinetic energy expression and the associatedassumptions. The results show that the inclusion of the kinetic energy term did not significantly affect

the dynamic results for this low energy up to 9.3 J. It appears that the speed of the crack at the 9.3 J for

this 16-ply composite specimen used is so low that the kinetic energy could be ignored. It is however

noted that in dynamic fracture, the fracture is actually running and an expression that takes this into

consideration is recommended and sought for.

11. The values of the energy release rate obtained using the stress-field loading force Pm(t) = E0Aet(tm)defined in this investigation is an improvement over the peak value, Pm used in our recent paper

[31]. Since this loading force is proportional to the amplitude of the transmitted stress field, the resultsshow that it is a better representation of the real time stress conditions at the crack tip as also observed

by others [19]. However the results in this paper do point to the fact that dynamic fracture phenomena

are controlled mainly by the magnitude of the stress fields around the crack front. Such stress is needed

to determine the true value of the loading force.

Acknowledgment

This research work was supported by Flight Dynamics Directorate, Wright Laboratory, Wright Patter-

son Air Force Base, Ohio. Dr. Arnold Mayer was the Technical monitor.


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