1 23

Experimental MechanicsAn International Journal ISSN 0014-4851 Exp MechDOI 10.1007/s11340-014-9936-5

Fracture Behavior of PrestressedComposites Subjected to Shock Loading: ADIC-Based Study

S. Mallon, B. Koohbor, A. Kidane &M.A. Sutton

1 23

Your article is protected by copyright and

all rights are held exclusively by Society for

Experimental Mechanics. This e-offprint is

for personal use only and shall not be self-

archived in electronic repositories. If you wish

to self-archive your article, please use the

accepted manuscript version for posting on

your own website. You may further deposit

the accepted manuscript version in any

repository, provided it is only made publicly

available 12 months after official publication

or later and provided acknowledgement is

given to the original source of publication

and a link is inserted to the published article

on Springer's website. The link must be

accompanied by the following text: "The final

publication is available at link.springer.com”.

Fracture Behavior of Prestressed Composites Subjected to ShockLoading: A DIC-Based Study

S. Mallon & B. Koohbor & A. Kidane & M.A. Sutton

Received: 30 October 2013 /Accepted: 23 July 2014# Society for Experimental Mechanics 2014

Abstract The dynamic fracture behavior of a prestressedorthogonally woven glass fiber-reinforced composite materialwas experimentally investigated. A shock tube apparatus wasused in conjunction with a tensile pre-loading device to applynominally Mode-I dynamic loading to pre-tensioned, singleedge notched specimens. The specimen response was ob-served with a stereo high speed camera arrangement, and thefull-field displacement and strain distributions near the cracktip were extracted using the 3D digital image correlationtechnique. Critical stress intensity factors for each specimenwere determined from the displacement and strain fields usingan over-deterministic approach. The magnitude of the pre-load applied to the specimens was shown to influence thecrack tip velocity as well as the dynamic stress intensity factorup to the onset of crack propagation. The effect of fiberorientation on both crack tip velocity and dynamic stressintensity factor was also observed.

Keywords Woven composites . Digital image correlation .

Dynamic fracture . Shock tube . Asymptotic analysis

Introduction

The typical stress–strain response of fiber reinforced compos-ite materials has been shown to exhibit an appreciable degreeof strain rate dependence. Similar strain rate dependence hasbeen observed in the fracture behavior of fiber reinforcedcomposites, with interlaminar fracture mechanisms being themost studied phenomenon [1–5]. Interlaminar fracture is pri-marily a matrix property, the study of which typically has little

dependence or relevance to any reinforcing fiber property.Consequently, these results have little applicability in describ-ing behavior relating to other fracture mechanisms. A far morelimited volume of work exists in the study of fracture as a resultof fiber failure, which arises in the form of fiber breakage and/or the physical release of the fiber from the matrix material,referred to as fiber bridging and fiber pull-out, respectively [6].Existing work is further limited regarding the investigation ofdynamic loading combined with a static tensile pre-load, andthe associated effect on the dynamic fracture of this material.

Among notable experimental studies considering the quasi-static fracture of composite materials, Gouda et al. [7] utilizedconventional compact tension specimen geometry and sub-jected the specimens to loading either along or across the fiberdirection. The authors observed appreciably greater Mode-Ifracture toughness for specimens loaded along the fiber direc-tion. In their work, stress intensity factors were calculatedusing load data and specimen geometry [8, 9]. The effect offiber orientation on the quasi-static fracture behavior of com-posites also has also been documented [7, 10, 11]. Dyer et al.[10] observed particulate composite materials reinforced withvarious fibers embedded in different positions and orientationsin three-point bend specimens. His studies showed that theposition and orientation of the reinforcing fibers have a sub-stantial effect on the load and deflection at fracture. Theauthors noted that fiber orientations resulting in fiber tensionyielded the greatest increase in maximum load. Shukla et al.[12] experimentally determined the quasi-static Mode-I stressintensity factors present in orthotropic composite materialsusing strain gages. Khanna and Shukla [13, 14] later adaptedthis method for determining dynamic stress intensity factors,incorporating the use of multiple strain gages. All of thesetechniques fail to yield any full-field data and are also typi-cally difficult or impossible to implement for composite ma-terials subjected to dynamic loading. In this regard, the abilityto obtain full-field data acquisition is particularly

S. Mallon : B. Koohbor :A. Kidane (*) :M. SuttonDepartment of Mechanical Engineering, University of SouthCarolina, 300 Main Street A214, Columbia, SC 29208, USAe-mail: kidanea@cec.sc.edu

Experimental MechanicsDOI 10.1007/s11340-014-9936-5

Author's personal copy

advantageous in the study of fracture mechanisms, as extrac-tion of fracture parameters and crack tip location is betterfacilitated [6].

Attempts at using full-field optical measurements to eval-uate stress intensity factors during dynamic loading are exem-plified in interferometry based studies [1, 15]. Lambros andRosakis [1] observed dynamic crack propagation in unidirec-tional graphite fiber reinforced epoxy composites. Using in-terferometry in conjunction with high speed photography,they were able to obtain stress intensity factors using theout-of-plane displacement component. Substantial strain ratedependence in the elastic modulus of the material and stressintensity factors largely consistent with reported values wereobserved. Crack initiation was shown to occur consistently inthe matrix material, along the reinforcing fiber direction. Suchmethods are able to offer full-field observations; however,extraction of desired measurements may be tedious or impos-sible in some cases.

The development of digital image correlation (DIC) hasfacilitated more detailed optical measurement based experi-mental studies, observed in the works of Sutton et al. [16–21],with the evaluation of stress intensity factors for quasi-staticMode-I loading conditions. Lee et al. [3] employed 2D-DIC ina study using single edge notched specimens constructed ofunidirectional graphite epoxy composites with various fiberorientations. They were able to extract displacement fieldssurrounding the crack tip, subsequently using linear and non-linear over-deterministic least squares methods to computeboth Mode-I and Mode-II stress intensity factors for quasi-static and dynamic loading cases. Stress intensity factorspresent at fracture were found to be consistently lower inquasi-static experiments when compared to similar dynamicloading cases. This may have been due to the reduction fiberbridging that was observed for specimens subjected to dynam-ic loading. It has been further shown that 3D DIC can beeffectively used to extract material properties from orthogo-nally woven, transversely orthotropic fiber reinforced com-posite materials. Pollock et al. [22] used 3D DIC in conjunc-tion with a mechanical extensometer to measure axial strains,further employing digital image correlation to obtain trans-verse, longitudinal, and shear strain fields. Such measure-ments were then shown to be effective in extrapolating acomplete set of mechanical properties for such material.

Robust methods of fracture parameter extraction are ofparticular value in the context of composite materials, espe-cially in the case of dynamic loading [23–25]. The establishedworkmentioned previously has demonstrated the applicabilityof digital image correlation as a viable means of acquiringmaterial response data that is suitable for extracting fractureparameters. However, much of this established work utilizesquasi-static loading rates. Those studies that do examine dy-namic loading conditions typically utilize a Hopkinson pres-sure bar apparatus in conjunction with 2D observations,

assuming negligible out-of-plane displacements. Work ofsuch nature is somewhat established in the examination ofunidirectional fiber-reinforced composite behavior, but quitelimited in the study of woven fiber-reinforced composites.

In the current work, stereo high speed photography isutilized in conjunction with 3D digital image correlation toexamine the fracture behavior of an orthogonally woven com-posite material exposed to combined quasi-static and dynamicMode-I loading. The effects of both fiber orientation andmagnitude of applied tensile prestress are studied. Apprecia-ble out-of-plane displacements, in addition to in-plane dis-placement and strain fields, are measured and stress intensityfactors up to the onset of crack growth are extracted using anover-deterministic least squares method.

Material and Specimen Geometry

The material examined in the present work is NorplexNP130 [26], a five-layer orthogonally woven glass fiberreinforced composite with mechanical properties listed inTable 1. Rectangular specimens measuring 254 mm×127 mm were extracted from 1 mm thick sheets of thecomposite at fiber orientations of 0, 15, 30, 45 and 90°using a FlowTM water jet. The finished specimens weresingle-edge notched specimens with a 46 mm initial notch,having three 13 mm mounting holes on either end. Thetypical specimen geometry is shown in Fig. 1. Beforetesting, each specimen notch was struck with a razor blade,effectively producing a sharp crack ahead of the originalnotch tip with an initial length of approximately 2 mm.

Experimental Methods

In order to examine the effect of pre-loading on the fracturebehavior of single edgenotched specimens, an initial tensileload was applied to each specimen using a specially builtfixture described in Section 3.2. Fracture was then initiatedwith the application of controlled dynamic load, applied usingthe shock tube apparatus described in Section 3.1. With theuse of a stereo high speed camera arrangement, in conjunctionwith 3D digital image correlation, displacement and strainfields were measured and recorded during loading. Using

Table 1 Mechanical properties of composite material examined [20, 24]

β (°) 0 15 30 45 90

E (GPa) 25.9 23.5 16.8 14.6 23.2

υ12 0.15

ρ (kg.m−3) 1,800

Exp Mech

Author's personal copy

these displacement and strain fields, an over-deterministicleast squares method was implemented to extract fractureparameters. In addition, comparable quasi-static experimentswere performed for comparitive purposes.

Loading Apparatus - Shock Tube

A shock tube was used to subject the specimens to a well-controlled dynamic load. A detailed description of the shocktube and its calibration can be found in the literature [27]. Ashock tube is a relatively simple instrument used to replicateblast waves. A typical shock tube consists of a circular tube,open on one end, separated into two sections by a diaphragm.The section open to atmospheric pressure is referred to as thedriven section, while the sealed section, pressurized to someappreciably greater level, is referred to as the driver section.With the application of a pre-determined pressure, the dia-phragm rapidly bursts, thus producing a series of waves that

compress into a shock. This shock wave then propagatesdown the shock tube before it exits the driven section andcontacts the specimen. The shock tube used in the currentwork consisted of a driver section 1.8 m in length and a 5.5 mlong driven section with a constant inside diameter of76.2 mm over the length of the tube. Sheets of Mylar, astretched polyester film, were utilized as the material of choicefor the diaphragm. Figure 2 shows the shock tube apparatusused in the current study. The velocity and magnitude of thepressure wave produced by the shock tube were varied byincreasing or decreasing the number of Mylar sheets compris-ing the diaphragm. Piezoelectronic pressure sensors mountedin the muzzle of the shock tube, very near to the specimen,were used to observe incident and reflected pressures. Thesesensors were also utilized as a reliable means of triggeringboth the data acquisition and image acquisition processes.Typical pressure profiles obtained for different numbers ofMylar sheets are depicted in Fig. 3. It should be noted here thatin the current study all shock tube experiments are conductedusing diaphragms comprised of 3 sheets of Mylar. Often thespecimen can be held in a fixture, depending on the boundaryconditions required. In the current study, the ends of eachspecimen were held in a fixture used to apply a constant pre-tension load. This fixture is described thoroughly in the nextsection.

Prestress Mechanism

The mechanism used to apply a prestress to the specimens isdepicted in Fig. 4. A configuration of steel die springsmounted on the fixture ensures that a consistent pre-load isapplied to the specimen. Since the applied prestress is solelydependent on the displacement of the die springs, the config-uration can be altered in a number of ways to achieve a rangeof possible prestress values. The inner (A) or outer pair (B) ofsprings can be added or removed from the apparatus entirelyand the spring constant can be altered. Two values of pre-loadhave been examined; the first pre-load magnitude has beenachieved by using only the inner pair of die springs, producinga pre-load of approximately 1,750 N, and the second pre-loadmagnitude has been achieved by subsequently adding theouter pair, producing a pre-load of approximately 3,500 N.The springs are compressed by way of a ½-20 bolt (C)that moves the upper specimen mount down to a positionsuch that the specimen can be bolted into the fixture.When the specimen is fastened into the fixture, the ½-20bolt is retracted, thus applying spring tension to thespecimen. Subsequently, a ¼-28 bolt (D) between eachpair of springs that is threaded into the upper specimenmount is snugly tightened, thus locking the mechanismand allowing the specimen to be pre-loaded prior toinitiating the shock loading process.

Fig. 1 Schematic of fracture specimen cut from the original compositesheet using the water jet. β denotes the fiber orientation with respect to thedesignated Cartesian coordinate system. Note that the initial notch for allspecimens is parallel to x axis

Exp Mech

Author's personal copy

Digital Image Correlation System

To facilitate image correlation, a fine speckle pattern wasapplied to the specimens prior to the experiments. To do so,a white paint was first applied on the specimen surface. Then,a black speckle pattern was applied on top of the white paintusing an air gun, resulting in a rather uniform high contrastpattern. A Photron SA-X2 stereo high speed camera systemwas used to capture the full-field three-dimensional specimenresponse in both quasi-static and dynamic loading conditions.In both loading conditions, camera resolution of 384×264was used. Images were captured at 60 fps in the quasi-staticcase, and 96,000 fps in the dynamic loading case.Piezoelectronic pressure sensors mounted in the muzzle ofthe shock tube were employed to trigger image acquisitionwith the use of an oscilloscope, while image acquisition wasmanually triggered in the quasi-static case. The camera ar-rangements for both dynamic and quasi-static cases are shownin Fig. 5. Images taken during the loading were then exportedto the commercial software Vic-3D [28] for further analysis.In this software, subset and step sizes of 17 and 3 pixels,respectively, were used to calculate the displacement andstrain components during the loading stage. Note that theresolution of the measurements in this work was 0.17 mm/pixel in all cases.

Quasi-Static Test

As a benchmark, a quasi-static fracture study was conductedusing identical specimen geometry. The stress intensity factorsfound in this quasi-static study were used as a point of

reference for the evaluation of values obtained in theprestressed specimens exposed to dynamic loading. To facil-itate the quasi-static loading, a 110 kN capacity MTS machinewas employed. Using 101.6 mmwide grips, the specimen wasfastened into the MTS machine as similarly as possible to thepre-load fixture. Specimens were fastened into the tensileframe using 6 mm thick aluminum tabs placed on either sideof the specimen thickness to minimize the damage from

0

50

100

150

200

250

300

350

400

450

500

0 1 2 3 4 5 6 7

Pres

sure

(kPa

)

Time (ms)

1 Mylar sheet

3 Mylar sheets

Fig. 3 Typical pressure profiles as a function of the number of Mylarsheets

Driver Section(High Pressure)

Driven Section(Low Pressure)

Mylar DiaphragmHigh Pressure Source

Shock Propagation

Specimen

Driver SectionDriven Section

SpecimenOscilloscope

Pre-loading

frame

(a)

(b)

Fig. 2 The shock tube apparatusused in this work (a) schematicdrawing and (b) actual apparatus

Exp Mech

Author's personal copy

serrated, hardened steel grips. The quasi-static tests wereconducted at room temperature, under displacement-con t ro l load ing wi th a c ros s head speed of0.0254 mm/s. An imaging procedure identical to thatused in the dynamic experiments was employed, and 3Ddigital image correlation was utilized to measure full-field displacement and strain response. The stress inten-sity factors up to the instanc of crack propagation wereextracted from these displacements using both the over-deterministic approach and load data in conjunctionwith specimen geometry.

Data Analysis

The stress intensity factors for specimens having various fiberorientations loaded under quasi-static and dynamic conditionswere calculated using an over-deterministic procedure basedon a least-square optimization. The detailed procedure can befound elsewhere, [11, 29], and is presented briefly here. Thein-plane displacement components, u and v, for an orthotropiccomposite material subjected toMode I loading can be writtenas [3, 14]:

u ¼ KIffiffiffiπ

p Ac66 −l1αs11 þ p2l3s12

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos2θþ 1

p2sin2θ

sþ cosθ

vuut264

þ pl2l5αql6

s11 þ pql4l5l6

s12

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos2θþ 1

q2sin2θ

sþ cosθ

vuut375 ffiffi

rp

ð1aÞ

v ¼ KIffiffiffiπ

p Ac66 −pl1αs12 þ p2l3s22

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos2θþ 1

p2sin2θ

s−cosθ

vuut264

þqpl2l5αql6

s12 þ pql4l5l6

s22

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos2θþ 1

q2sin2θ

s− cosθ

vuut375 ffiffi

rp

ð1bÞ

where KI is the stress intensity factor for Mode-Ifracture. The terms sij(i,j=1,2,6) in these equations representthe elements of the compliance matrix as shown in Eq. (2)are assumed to be strain rate-independent in this work.

εxxεyyγxy

24

35 ¼

s11 s12 0s21 s22 00 0 s66

24

35 σxx

σyy

τxy

24

35 ð2Þ

Subscripts 1 and 2 in equation (2) denote the axial andtransverse fiber axes of the composite specimen, respectively,as shown schematically in Fig. 1. Quantities r and θ denote theradial and angular coordinates of an arbitrary point withrespect to the original crack tip, respectively. Parameters pand q are defined as:

p ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia1−

ffiffiffiffiffiffiffiffiffiffiffiffia21−a2

qr; q ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia1 þ

ffiffiffiffiffiffiffiffiffiffiffiffia21−a1

qrð3Þ

(b)

Shock tube

Specimen

Springs

(A)- Inner pair

springs

(B)- Outer pair

springs

(a)

(D)- ¼-28 bolt(c)- ½-20 boltFig. 4 The mechanism utilized to

apply the pre-tension to the spec-imen (a) schematic drawing and(b) actual frame with the mountedspecimen

Exp Mech

Author's personal copy

where a1 and a2 are functions of the components of thematerial’s stiffness matrix, cij, and Mach numbers (relativecrack tip velocities), M1 and M2, defined as:

2a1 ¼ αþ α1 − 4β1β2 ; a2 ¼ αα1 ð4aÞ

α ¼ c66c11 1−M2

1

� � α1 ¼ c22c66 1−M 2

2

� � 2β1 ¼c12 þ c66c11 1−M2

1

� �

2β2 ¼c12 þ c66c66 1−M 2

2

� �ð4bÞ

M1 andM2 are defined as the ratio of the crack tip velocitywith respect to longitudinal wave velocity, cl, and shear wavevelocity, cs, respectively, and can be expressed as,

M 1 ¼ c

clM 2 ¼ c

cswith cl ¼

ffiffiffiffiffiffiffic11ρ

rcs ¼

ffiffiffiffiffiffiffic66ρ

rð5Þ

where ρ represents the mass density of the composite.The parameters li(i=1…6) and Ac66 in equation (1a) can be

expressed as:

l1 ¼ 2β1p2

α−p2ð Þ 1−M 21

� � þ 2β−α l2 ¼ 2β1q2

α−q2ð Þ 1−M21

� � þ 2β1−α

l3 ¼ 1 − M 22 −

2β1

α−p3l4 ¼ 1 − M2

2−2β1

α−q2

l5 ¼ − l3− M22 l6 ¼ −l4−M 2

2 Ac66 ¼ l6pql4l5−p2l3l6

ð6Þ

Equation (1b) has originally been proposed for the case ofdynamic crack propagation [3, 14]. In the case of a stationarycrack subjected to either dynamic or quasi-static loading, theabove equation can be simplified by taking c to be zero.

The only unknown parameter in equation (1a) is KI, as uand v at any position r and θ can be obtained from

Fig. 6 A comparison between the evolutions of quasi-static KI valuedetermined from recorded load and DIC data, prior to crack initiation forthe β=45° specimen under quasi-static loading. Note that the crackbegins to grow at τ=1

Table 2 Quasi-static stress intensity factors as a function of fiber orien-tation angle

Fiber orientation ( β ) Stress intensity factor, KI (MPa.m0.5)

Recorded Load DIC data % difference

0° 36.05 38.26 5.7

45° 22.58 24.61 8.2

90° 28.62 30.54 6.2

(b)

(a)

Fig. 5 The camera arrangements for (a) quasi-static and (b) shock tubeexperiments

Exp Mech

Author's personal copy

displacement fields obtained using DIC. The displacementcomponents at arbitrary radial positions in the crack tip vicin-ity, obtained from DIC, were used as input to a computer codewritten on the MATLABTM platform to calculate the stressintensity factor for the material based on the over-deterministic approach detailed in [29–32]. When using theover-deterministic least-square analysis, one should bear inmind that data points selected for the numerical approachshould be sufficiently far from the crack tip area to avoid the

tri-axial stress and local plasticity effects. In this work, datapoints outside the circular region, r>0.5B (with B being thespecimen thickness) were taken for the analysis [3]. A largenumber of data points is required to extract the stress intensityfactor with acceptable accuracy [29, 31]. Accordingly, a min-imum number of 100 data points were considered as the inputfor the analysis to assure the accuracy of the calculated KI.

In attempting to identify the exact moment of crack initia-tion, exclusive use of displacement components may be in-sufficient. This is due to a continuous increase of displacementcomponents, especially opening displacement, v, even aftercrack initiation. Therefore, the sole use of displacement mea-surements may introduce substantial inaccuracy in the calcu-lated values of KI. The uncertainty can be lowered when thevertical strain component εyy is considered, since εyy at alocation behind but very near to the initial crack tip experi-ences a sudden drop in magnitude at the instance of crackpropagation [14]. As such, opening strain εyy was used todetermine the crack initiation time in the case of dynamicloading. The stress intensity factor at the onset of crack growthwas then calculated using both strain and displacement fields.

(b)

-0.128

-0.13225

-0.1365

-0.14075

-0.145

-0.14925

-0.1535

-0.15775

-0.162

-0.16625

-0.1705

-0.17475

-0.179

-0.18325

-0.1875

-0.19175

-0.196

-0.20025

-0.2045

-0.20875

-0.213

u (mm)

0.196

0.1764

0.1568

0.1372

0.1176

0.098

0.0784

0.0588

0.0392

0.0196

0

-0.0196

-0.0392

-0.0588

-0.0784

-0.098

-0.1176

-0.1372

-0.1568

-0.1764

-0.196

v (mm)

(a)Fig. 8 Full field displacementdistributions obtained from DICanalysis for the pre-loaded β=0°specimen, (a) horizontal and (b)vertical displacement components

5 mm

Fig. 7 Crack bridging during early stages of crack propagation forthe β=0° specimen subjected to quasi-static loading

Exp Mech

Author's personal copy

The in plane strain components εxx and εyy are related to thestress intensity factor as [14]:

εxx ¼ KIffiffiffiffiffiffiffi2πr

p cos −θ

2

� �Ac66 −

l1αs11−p2l3s12

� �þ pl2l5

αql6s11 þ pql4l5

l6s12

� �� �

ð7Þ

εyy ¼ KIffiffiffiffiffiffiffi2πr

p cos −θ

2

� �Ac66 −

l1αs12−p2l3s22

� �þ pl2l5

αql6s12 þ pql4l5

l6s22

� �� �

The additional parameters in equation (7) are identicalthose explained earlier for the displacement field, i.e. equa-tions (2) to (6).

Results and Discussions

Quasi-Static Testing

A typical evolution of the quasi-static stress intensity factorprior to crack initiation is shown in Fig. 6. As shown in Fig. 6,reasonable agreement between stress intensity factors extract-ed using DIC and load data has been observed up to the instantof crack propagation. The stress intensity factors for β=0, 45and 90° specimens under quasi-static loading conditions ob-tained using both the recorded load data in conjunction withspecimen geometry and the full-field DIC data are shown inTable 2. In all cases, it is observed that the value calculatedbased on the DIC data is slightly higher than that determinedusing the maximum recorded load. Such a level of discrepan-cy has also been reported previously in [31, 32], especiallywhen single-term asymptotic displacement expressions havebeen utilized. In addition, it has recently been documentedthat, for the case of orthogonally woven composites, calcula-tion of the stress intensity factor using only the far-field loadintroduce some level of uncertainty [11]. Such level of uncer-tainty is due to the difficulty in capturing the exact moment ofcrack initiation in these materials as a result of complicatedfiber/matrix micromechanics. Thus, optical observations arerequired to capture the instant of crack initiation and thecorresponding far field load in order to better estimate thestress intensity factor at the onset of crack growth [11].

The stress intensity factors obtained in this work, shown inTable 2, seem high for a composite material. Wheninterpreting these elevated critical stress intensity factors,there are two key factors that must be understood. First, thesamples are not thick enough to impose plane-strain condi-tions, thus resulting in a substantially increased stress intensityfactor achieved at fracture. [33, 34]. Second, the material is awoven composite, and fracture occurs mainly by fiber break-age, referred to as bridging. Figure 7 shows the bridging effect

Fig. 9 a Crack extension-time plot for a crack subjected to dynamicloading. (Pre-load value is 1,750 N and t=0 indicates the instant of crackinitiation). The fitted dashed lines with their corresponding R2 values arealso shown. b Crack tip velocity as a function of fiber orientations anglefor the specimens subjected to different pre-load values

Table 3 Pre-loaded stress intensity factors as function of fiber orientationangle

Fiber orientation ( β ) Stress intensity factor, KI (MPa.m0.5)

1,750 N pre-load 3,500 N pre-load

0° 10.03 20.03

45° 9.94 16.16

Exp Mech

Author's personal copy

during early stages of crack propagation for a β=0° specimensubjected to quasi-static loading. It has been observed that thefiber bridging is associated with a high stress intensity factor[34, 35].

Stress Intensity Factor Associated With Applied Prestress

Full-field displacement distributions for specimens of eachfiber orientation angle when subjected to pre-loads of 1,750and 3,550 N were obtained using DIC. Typical displacementcontours obtained from the pre-loaded β=0° specimen areshown in Fig. 8. The displacement fields obtained for eachspecimen, along with the analysis detailed in Section 3.5, wereused to extract the stress intensity factor present in eachspecimen subjected to both pre-load values. The results areshown in Table 3. The KI values obtained in this stage can beconsidered as stress intensity factors that already exist in thespecimen prior to being subjected to shock loading. Using theproperty of superposition, this value can be added to the

values calculated from shock loading to yield an estimationof the total KI value of each specimen.

Dynamic Stress Intensity Factor and Crack Velocity

The crack tip velocity during crack propagation was obtainedby carefully tracking the crack tip position. This variation ofcrack tip location as a function of time for different specimenshas been displayed in Fig. 9(a). After extracting the positionsof the moving crack tip, the changes in crack tip position as afunction of timewere used to estimate the crack tip velocity bydifferentiating the linear curve fitted into the crack tipdisplacement-time curve. The crack tip velocity as a functionof fiber orientation angle for two different pre-loads is shownin Fig. 9(b). It is clearly shown that the crack tip velocityincreases continuously as the fiber orientation angle increasesfrom 0 to 45°. Selected images captured at different stages ofcrack propagation for β=0 and 45° specimens are also shownin Fig. 10. As shown in Fig. 11, the crack follows the direction

(a) (b)

10 mm

10 mm

10 mm

10 mm

10 mm

10 mmt = 239 µs

t = 187 µs

t = 0 µs

t = 156 µs

t = 114 µs

t = 0 µsFig. 10 Selected DIC imagescaptured at different stages of thecrack propagation for (a) β=0°and (b) β=45° specimens. Cracktip location has been marked oneach image. t=0 μs indicates theinstant of crack initiation

Exp Mech

Author's personal copy

of fiber orientation as observed by Tippur [3] in the case ofunidirectional fiber reinforced composites. Though the com-posite considered in this work is made of orthogonally wovenreinforcing fibers, crack propagation always takes place in thedirection parallel to the fiber orientation for all the fiberorientations investigated.

A typical history of vertical displacement and strain com-ponents used to detect the crack initiation time is shown inFig. 12. The sudden drop in the vertical strain componentduring the loading stage can be used to accurately determinethe moment at which crack growth initiated. In the currentwork, the crack initiation time has been estimated with anerror<5 μs.

Finally, the dynamic stress intensity factor up to the onsetof crack growth is calculated using the displacement and strainfields obtained from DIC, following the procedure expressedin Section 3.5. To assure that the fracture mode in this work isindeed Mode-I, the out-of-plane displacement component ofeach sample was examined. Selected out-of-plane displace-ment contours both before and after crack initiation for a β=

14o

0o

45o

30o

90o

(b)(a) (c)

(d) (e)

Fig. 11 Crack direction for spec-imens with fiber orientation of (a)β=0° (b) β=15° (c) β=30° (d)β=0°and (e) β 90°, fracturedunder dynamic loading with thepre-load magnitude of 3,500 N

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0 200 400 600 800

Dis

plac

emen

t, v

(mm

)

Stra

in,

yy

Time (µs)

Vertical strain component

Vertical displacment

component

Crack

growth

Fig. 12 History of vertical displacement and strain components beforeand after crack initiation for the β=0° specimen with a 3,500 N pre-loadmagnitude

Exp Mech

Author's personal copy

45° specimen are shown in Fig. 13. It is observed that the out-of-plane displacement component in the vicinity of the cracktip is symmetric along the crack line, indicating that Mode-IIIfracture is minimal or non-existent in the case of a prestressedspecimen subjected to dynamic loading. Since the specimen isvery thin, a plane stress condition is assumed and the effect ofout-of-plane bending on the fracture process can be neglected.The out-of-plane displacement,w, at a location 3 mm ahead ofthe original crack tip for some selected specimens is listed inTable 4. The maximum out-of-plane displacement decreasesby approximately 20 % with the increase in applied pre-loadfrom 1,750 to 3,500 N. It is noted that the stereovision’s depthof field in our studies is greater than the maximum out-of-plane displacement achieved by the specimen. Thus, the im-ages remain in focus during the entirety of the experiment andthe accuracy of the full-field displacement measurements ob-tained from digital image correlation is not affected bydefocus.

Selected strain and displacement contours for the β=0°specimen during the time prior to crack initiation are depicted

in Fig. 14. The evolution of KI up to the onset of crack growthwas calculated using both the displacement and strain fieldsobtained from DIC. This variation of stress intensity factor asa function of time for a specimen exposed to a 3,500 N preloadis shown in Fig. 15. The trend exhibited by the evolution ofKID is irregular, especially during the early stages. This isbelieved to be characteristic of the material, and unrelated tovariations in the loading pulse. As can be seen in a typicalpressure profile obtained at the muzzle of the shock tube,shown in Fig. 3, the loading pulse is nearly constant for almost3 milliseconds. The duration of the experiment, from the

11.745

11.6533

11.5617

11.47

11.3783

11.2867

11.195

11.1033

11.0117

10.92

10.8283

10.7367

10.645

w (mm)

15.52

15.2817

15.0433

14.805

14.5667

14.3283

14.09

13.8517

13.6133

13.375

13.1367

12.8983

12.66

w (mm)

t = 0 µs

t = 150 µs

Fig. 13 3D contour of the out-of-plane displacement component,w, before and after crack initiationfor a β=45° specimen exposed todynamic loading with a pre-loadmagnitude of 3,500 N. Note thatt=0 μs indicates the onset ofcrack growth

Table 4 Maximum out-of-plane displacement, w, at a location 3 mmahead of the crack tip just before crack initiation

Fiber orientation ( β ) Out-of-plane displacement, w (mm)

1,750 N pre-load 3,500 N pre-load

0° 12.233 9.975

45° 13.639 11.630

Exp Mech

Author's personal copy

beginning of loading till crack initiation, is about 800 μs andlies in the middle of this constant region. The irregularitiescould be associated with micro-cracking and other local fail-ure phenomena, which are not considered in this work.

The dynamic stress intensity factor at the onset of crackinitiation for pre-stressed specimens as a function of specimenfiber orientation and pre-load magnitude is shown in Fig. 16.It is observed that the stress intensity factor decreases as theangle of fiber orientation increases from 0 to 45°. Additional-ly, the dynamic stress intensity factor decreases consistently asthe pre-load increases. To provide a clear comparison betweenthe values of quasi-static and dynamic stress intensity factorsobtained in this work, the effective dynamic KI value wasestimated as the summation of KI values calculated from thepre-loading and shock loading stages, as

KeffID ¼ Kpreload

I þ KshockI ð8Þ

where KIDeff is the effective dynamic stress intensity factor,

KIpreload is the pre-load stress intensity factor, and KI

shock is the

stress intensity factor obtained from the shock loading exper-iment. The values calculated for KID

eff are listed in Table 5.Comparing these values with those obtained from the quasi-static loading condition, dynamic loading resulted in an ap-proximate increase of 15 % for the β=0° specimen, and 25 %for the β=45° specimen. An increased value of dynamic stressintensity factor when compared to the quasi-static value wasalso reported in [3], and was attributed to the degree ofbridging present during quasi-static and dynamic loadingconditions.

Regarding the effect of preload on the critical dynamicstress intensity factor, when the fibers are along the primaryloading direction (θ=0°), the preload has negligible effect.However, when the fibers are oriented at θ=45°, the effect ofpreload is to reduce Keff

ID. These experimental results can beunderstood by noting that the material is an orthogonallywoven composite. Thus, growth of a through-thicknesscrack requires that the woven fibers separate. When thefibers are in the principal loading direction and are theprimary loading carrying members, the preload increasesthe tensile loading in these fibers and hence increases the

0.27

0.226667

0.183333

0.14

0.096667

0.053333

0.009999

-0.03333

-0.07666

-0.12

-0.16333

-0.206667

-0.25

v (mm)

0.0059

0.0054041

0.0049083

0.0044125

0.00391667

0.00342083

0.002925

0.00242917

0.00193333

0.0014375

0.00094166

0.00044583

0.00005001

Strain, εyy

(a)

(b)

Fig. 14 Contours of (a) verticaldisplacement component, v and(b) vertical strain component,εyy, at the moment of crack initia-tion for the β=0° specimen sub-jected to shock loading. The pre-load magnitude applied on thespecimen is 3,500 N

Exp Mech

Author's personal copy

initial stress intensity value. When the dynamic loadingprocess initiates, the dynamic component of the stress in-tensity factor is smaller for the larger preload. If one as-sumes that the glass fiber fracture process is the same forour experiments (though the critical values may be ratedependent), then the fibers would fail when the conditions

at the crack tip reach the same critical dynamic stressintensity factor for both preload conditions since they weresubjected to the same dynamic loading conditions.

In the case of off-axis specimen (45°), it is less clear howthe critical effective stress intensity factor evolves with in-creasing preload. One plausible explanation deals with therole of the matrix in the fracture process. Since the fibers areoff-axis, the matrix would initially take much of the load.However, as the loading process progress, the fibers begin toshare the load. The application of preload in the 45° specimenwould stretch and rotate the fibers towards the loading direc-tion and makes the matrix less involved in the fracture resis-tance process. Due to this, the effective stress intensity factorin the case of 45° specimen would tend to decrease as thepreload increases. In this regard, it is noted that a similar trendwas observed for the stress–strain behavior of a similar mate-rial at different fiber orientation angles [11, 22].

Finally, to provide additional insight regarding the effect ofloading rate, variation of dKI/dt, i.e. the time derivative of thestress intensity factor in dynamic and quasi-static conditions,

0

4

8

12

16

20

24

28

32

0 200 400 600 800

KID

(MPa

.m0.

5 )

Time (µs)

Displacement data

Strain data

Crack

growth

Fig. 15 Evolution of dynamic KI value up to the crack initiation, calcu-lated based on displacement as well as stain data for the β=0° specimensubjected to dynamic loading with a pre-load magnitude of 3,500 N

Fig. 16 Dynamic stress intensity factor, KID, obtained for differentspecimens subjected to different pre-load values

Table 5 The effective dynamic stress intensity factor, KIDeff, for different

specimens

Fiber orientation ( β ) effective dynamic stressintensity factor, KID

eff (MPa.m0.5)

1,750 N pre-load 3,500 N pre-load

0° 42.78 43.14

45° 33.03 28.73

Fig. 17 Variation of the rate of change of stress intensity factor (dK/dt)up to the crack initiation, with respect to the stress intensity factor inquasi-static and dynamic loading conditions for the β=0° specimen

Exp Mech

Author's personal copy

was examined. The evolution of dKI/dt was plotted withrespect to KI for a specimen having β=0° as shown inFig. 17. The higher rate observed in the evolution of the stressintensity factor in the dynamic case along with strain ratesensitivity of the material could be taken as the main factorresulting in an increase in SIF during dynamic loadingcondition.

Conclusions

The fracture response of a prestressed orthogonally wovenglass-fiber reinforced composite was investigated using ashock tube apparatus. The full-field displacement and strainswere obtained using 3D digital image correlation, and thefracture parameters were extracted using an over-deterministic approach. It was demonstrated that the shockapparatus can be used to generate Mode-I dynamic fractureloading on pre-stressed specimens. Furthermore, the full field3D digital image correlation method can be used extractdisplacement components at these high rates of loading. Basedon the experiment the following points are observed:

& The crack tip velocity increases as the reinforcing fiberangle increases from 0° to 45°.

& The magnitude of the applied pre-load also significantlyaffects the crack tip velocity, increases with themagnitude.

& The dynamic stress intensity factor decreases as the rein-forcing fiber angle increases from 0° to 45°.

& The material has some strain rate sensitivity for the ratesthat were applied, with the crack initiation stress intensityfactor being higher for dynamic loading when comparedto the quasi-static loading.

& The magnitude of the applied preload has negligible effecton the effective stress intensity factor for 0° fiber orienta-tion, whereas the preload decreases the effective stressintensity factor for 45° fiber orientation.

Acknowledgments The financial support of NASA through EPSCORunder Grant No.21-NE-USC_Kidane-RGP, the College of Engineeringand Computing and the Department of Mechanical Engineering at theUniversity of South Carolina is gratefully acknowledged.

References

1. Lambros J, Rosakis AJ (1997) Dynamic crack initiation and growthin thick unidirectional graphite/epoxy plates. Compos Sci Technol57:55–65

2. Compston P, Jar PYB, Davies P (1998)Matrix effect on the static anddynamic interlaminar fracture toughness of glass-fiber marine com-posites. Compos Part B-Eng 29B:505–516

3. Lee D, Tippur H, Kirugulige M (2009) Experimental study of dy-namic crack growth in unidirectional graphite/epoxy compositesusing digital image correlation method and high-speed photography.J Compos Mater 43:2081–2108

4. Sun CT, Han C (2004) A method for testing interlaminar dynamicfracture toughness of polymeric composites. Compos Part B-Eng35B:647–655

5. Naik NK, Asmelash A, Kavala VR, Veerraju C (2007) Interlaminarshear properties of polymer matrix composites: strain rate effect.Mech Mater 39:1043–1052

6. Lee D, Tippur H, Bogert P (2010) Quasi-static and dynamic fractureof graphite/epoxy composites: an optical study of loading-rate ef-fects. Compos Part B-Eng 41B:462–474

7. Shivakumar Gouda PS, Kudar SK, Prabhuswamy S, Jawali D (2011)Fracture toughness of glass-carbon (0/90)s fiber reinforced polymercomposite – an experimental and numerical study. J Min Mater CharEng 10:671–682

8. Kidane A, Shukla A (2010) Quasi-static and dynamic fracture initi-ation toughness of Ti/TiB layered functionally graded material underthermo-mechanical loading. Eng Fract Mech 77:479–491

9. Kidane A (2013) On the failure and fracture of polymer foamcontaining discontinuities. ISRN Mater Sci, vol. 2013, Article ID408596, 9 pages, doi:10.1155/2013/408596

10. Dyer SR, Lassila LVJ, Jokinen M, Vallittu PK (2004) Effect of fiberposition and orientation on fracture load of fiber-reinforced compos-ite. Dent Mater 20:947–955

11. Koohbor B, Mallon S, Kidane A (2014) Sutton MA (2014) A DIC-based study of in-plane mechanical response and fracture oforthotropic carbon fiber reinforced composite. Compos Part B 66:388–399

12. Shukla A, Agarwal BD, Bhushan B (1989) Determination of stressintensity factor in orthotropic composite materials using strain gages.Eng Fract Mech 32:469–477

13. Khanna SK, Shukla A (1995) On the use of strain gages in dynamicfracture mechanics. Eng Fract Mech 51:933–948

14. Khanna SK, Shukla A (1994) Development of stress fieldequations and determination of stress intensity factor duringdynamic fracture of orthotropic composite materials. Eng FractMech 47:345–359

15. Kokaly MT, Lee J, Kobayashi AS (2003) Moire interferometry fordynamic fracture study. Opt Lasers Eng 40:231–247

16. Sutton MA, Mingqi C, Peters WH, Chao YJ, McNeill SR (1986)Application of an optimized digital correlation method to planardeformation analysis. Image Vision Comput 4:143–150

17. McNeil SR, Peters WH, Sutton MA (1987) Estimation of stressintensity factor by digital image correlation. Eng Fract Mech 28:101–112

18. Chu TC, Ranson WF, Sutton MA, Peters WH (1985) Application ofdigital image correlation technique to experimental mechanics. ExpMech 25:232–245

19. Luo PF, Chao YJ, Sutton MA, Peters WH (1993) Accurate measure-ment of three-dimensional deformations in deformable and rigidbodies using computer vision. Exp Mech 33:123–133

20. Helm JD, McNeill SR, Sutton MA (1996) Improved three-dimensional image correlation for surface displacement measure-ment. Opt Eng 35:1911–1920

21. Sutton MA, Cheng CS, Zavattieri P, Yan J, Deng X (2006) Three-dimensional digital image correlation to quantify deformation andcrack-opening displacement in ductile aluminum under mixed-modeI/III loading. Opt Eng 46:1–17

22. Pollock P, Yu L, Sutton MA, Guo S, Majumdar P, Gresil M (2012)Full field measurements for determining orthotropic elastic parame-ters of woven glass-epoxy composites using off-axis tensile speci-mens. Exp Tech. doi: 10.1111/j.1747-1567.2012.00824.x

23. Fernandez-Canteli A, Arguelles A, Vina J, RamuluM, Kobayashi AS(2002) Dynamic fracture toughness measurements in composites by

Exp Mech

Author's personal copy

instrumented charpy testing: influence of aging. Compos Sci Technol62:1315–1325

24. Wosu SN, Hui D, Dutta PK (2005) Dynamic mixed-mode I/II de-lamination fracture and energy release rate of unidirectional graphite/epoxy composites. Eng Fract Mech 72:1531–1558

25. Heimbs S, Heller S, Middendorf P, Hahnel F, Weisse J (2009) Lowvelocity impact on CRFP plates with compressive preload: test andmodeling. Int J Impact Eng 36:1182–1193

26. http://www.norplex-micarta.com .27. LeBlanc J, Shukla A, Rousseau C, Bogdanovich A (2007) Shock

loading of three dimensional woven composite materials. ComposStruct 79:344–355

28. http://www.correlatedsolutions.com .29. Barker DB, Sanford RJ, Chona R (1985) Determining K and related

stress-field parameters from displacement fields. Exp Mech 25:399–407

30. Yoneyama S, Morimoto Y, Takashi M (2006) Automatic evaluationof mixed-mode stress intensity factors utilizing digital image corre-lation. Strain 42:21–29

31. Yates JR, Zanganeh M, Tai YH (2010) Quantifying crack tip dis-placement fields with DIC. Eng Fract Mech 77:2063–2076

32. Berger JR, Dally JW (1988) An overdeterministic approach formeasuring KI using strain gages. Exp Mech 28:142–145

33. Kim K, Ye L (2004) Effects of thickness and environmental temper-ature on fracture behavior of polyetherimide (PEI). J Mater Sci 39:1267–1276

34. Anderson TL (2005) Fracture mechanics – Fundamentals and appli-cations, 3rd edn. Taylor & Francis, Florida, pp 360–369

35. Yanase K, Ju JW (2013) Toughening behavior of unidirection-al fiber reinforced composites containing a crack-like flaw:matrix crack without fiber break. Int J Damage Mech 22:336–355

Exp Mech

Author's personal copy