research article finite element modeling of mode i...

Hindawi Publishing CorporationJournal of StructuresVolume 2013 Article ID 138617 8 pageshttpdxdoiorg1011552013138617

Research ArticleFinite Element Modeling of Mode I Failure of the SingleContoured Cantilever CFRP-Reinforced Concrete Beam

T Nicholas1 D Boyajian2 S E Chen1 and A Zhou1

1 University of North Carolina at Charlotte Charlotte NC 28223 USA2 Indiana Wesleyan University Upland IN 46989 USA

Correspondence should be addressed to T Nicholas tnicholaunccedu

Received 20 February 2013 Revised 13 October 2013 Accepted 12 November 2013

Academic Editor Domenico Bruno

Copyright copy 2013 T Nicholas et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The single contour cantilever beam (SCCB) test method has been developed with the intent to capture Mode I opening failures ofCFRP-reinforced concrete beams Recent development in the method explores possible shifting damage into the concrete substrateby using the International Concrete Repair Institute (ICRI) Surface Profile LevelThree (SP3) as the desired CFRP bonded interfaceto concrete To validate and explain the interface fracture behavior finite element analysis using special cohesive elements has beenperformed The cohesive element allows separation of the concrete substrate from the CFRPThis paper presents the simulation oflaboratory test results where failure in the substrates has been successfully reproduced The simulation results indicate that finiteelement method using cohesive elements can successfully replicate Mode I critical strain energy release rate and the peak capacityof the laboratory tests and may have the potential to simulate actual applications

1 Introduction

Several laboratory methodologies have been developed overthe past few years to measure Mode I critical strain energyrelease rate involving composite wrapped concrete beamsFailures of representative methodologies designed to isolateMode I opening failure of a fracture interface include themodified double cantilever beam (DCB) method [1] the peeltest method [2] the membrane peeling method [3] and thesingle contour cantilever beam (SCCB) method [4] All theabove methods are variations of each other with differentstrengths and weaknesses depending on the applicationHowever the SCCB method exclusively ensures that thefailure will always be the first mode A second advantageof the SCCB method is the elimination of compliancemeasurements

The SCCB method was first developed by Boyajian [5]and has been utilized to determine the critical strain energyrelease rates at the bonding interface between concrete andcarbon fiber-reinforced polymer (CFRP) [4 6 7] Figure 1shows the schematics of the SCCB test including the testspecimen that consists of concrete base plate CFRP bondedlayer the wood contour and the experimental setup that

includes a steel strap for pulling on the wood contourFigure 2(a) shows the actual test setup within a MTS testapparatus with arrow indicating the direction of pull loadWith the SCCB test the high tensile capacity LVL is loadedwith a normal force P inducingMode I failure behavior of theCFRP to concrete interface and thus avoiding the arm break-off failureThe starter crack is created by debonding theCFRPfrom the concrete substrate for the first fiftymillimeters of thebond length This is achieved by pretreating the starter cracklocation with a substrate with tape or wax paper The startercrack can be seen in Figure 2(c) as the white shaded area onthe substrate

The current study focused on using the InternationalConcrete Repair Institute Surface Preparation 3 (ICRI SP3)[8] method to ensure failure within the substrate In orderto achieve the necessary surface profile the ICRI standardsallow for shot blasting sand blasting or pressurized waterto be used After numerous trials the surface preparationmethod that produced the most consistent results was pres-surized water from a 3447MPa pressure washer Addition-ally a set of surface profile tabs were obtained to assist inclassifying the surface The surface profile tabs are raisedsurface rubber square swatches which illustrate each of the

2 Journal of Structures

Wood contour

Concrete substrate

Loading strap

CFRPepoxy

Starter crack

P

953mm

205mm

Figure 1 Schematic of single contoured cantilever beam test

(a) SCCB test setup (b) Concrete surfaces (left to right) SP1 mould andSP3

Composite FRP wrap

(c) Failed specimen showing exposed substrate

Figure 2 The SCCB test (a) experimental setup (arrow indicating load direction) (b) different concrete surfaces (SP1 mould and SP3) (c)interface surface of failed specimens FRAC1031 T1 and FRAC1031 T2

ICRI surface profiles The common method for classifyingthe surface is to check the target surface tab (SP 3) as wellas the tab above (SP 4) and the tab below (SP 2) Figure 2(b)shows the different surface areas SP1 mould and SP3 Studyof failure in the substrates is important as it may lead topremature failure and brittle failures [9] Figure 2(c) showsthe failed specimens clearly indicating failure within concretesubstrate

This paper reports finite element (FE) simulation of aseries of SCCB tests conducted with concrete specimens pre-pared with SP3 surfaces which was not previously attemptedIn order to develop realistic FE models a damage evolutionapproach has been adopted The results presented shows thatthe approach effectively predicts the critical strain energyrelease rate of the bonded interfaceThemodel also compareswell with the laboratory test results

2 Mode 1 Fracture

Fracture behavior can normally be characterized as begin-ning with crack initiation and intensifying through crackpropagation At the onset of crack initiation the crackpropagation behavior becomes a function of the displacementof the failed interface surfaces [10ndash12] Irwin [13] definedthree failuremodes to describe how the surfaces are displacedby Mode I Mode II and Mode III failures Mode I describesa failure of the interface bond that occurs normal to thefailed surface often referred to as the opening mode While

most fractures can be described by one of the failure modesthe mixing of mode failures such as Mode I-Mode II isalso a possibility The ability of an engineering material toresist these failure modes is frequently referred to as fracturetoughness The commonly accepted method for representingfracture toughness is the critical release strain energy 119866

119862 as

defined by the Irwin-Kies equation [13 14]

119866119862= (

1198752

119862

2119887)(

d119862d119886

) (1)

where 119866119862is the critical strain energy release rate (Jm2) 119875

119862

is the critical load (N) 119887 is the width of the specimen (mm)and dCda is the rate of compliance (119862) with respect to cracklength (119886) (Nminus1)

3 Analytical Modeling of Fracture andthe Cohesive Elements

As it pertains to the current study finite element modeling ofthe SCCB can be divided into two categories compliance ofthe SCCBwood contour and fracture As there exist a numberof methods to model crack propagation it is important toselect an efficient and accurate representation of the failurebehavior While the SCCB has not specifically been modeledfor fracture a number of past studies have focused on thefracture of the double cantilever beam and the peel test Mostrecently Nicholas [15] Huang and Lyons [16] and Diehl [17]

Journal of Structures 3

Elastic limit

K

Trac

tion

t

Separation 120575

tULT

120575ULT120575c

Critical fractureenergy Gc

Figure 3 Damage evolution curve for ABAQUS cohesive element(119905 (MPa) 120575 (mm)) [18]

proposed methodologies for modeling the DCB a modifiedDCB and a peel test respectively For each study the modelwas used to determine the total energy required to propagatethe crack tip The total energy required to fracture concretecan be taken as

119866119891=

1

119861 lowast (119882 minus 119886)int119875119889120575 (2)

where 119866119891is the specific fracture energy (Jm2) 119861 is the

specimen thickness (mm) 119882 is the fracture width (mm) 119886is the initial crack length (mm) 119875 is the point load (N) and120575 is the displacement perpendicular to crack length (mm)

Huang and Lyons [16] employed the 119869-integral algorithmin ABAQUS to model the crack propagation of a modifiedDCB as well as to calculate the critical strain energy releaserate The methodology produced good results compared tothe basic energy equation and laboratory results Howeveraccording toNicholas [15] the cohesive element is an efficientapproach to modeling fracture as well when the crackpropagation is known a priori

Diehl [17] proposed utilizing an ABAQUS cohesiveelement to model the bonded region between elastic andinelasticmaterials namely a thin film In the study a penalty-based approach to debonding was proposed In the penaltyapproach or damage evolution as the elements ultimate stresscapacity (traction (MPa) 119905ULT ) is achieved the element isdeleted from the model and does not provide further resis-tance to load This damage process is illustrated in Figure 3where the ultimate nominal stress serves as the elastic limitand the area under the curve provides the critical fractureenergy 119866119888 This ldquounzippingrdquo behavior closely resembles thebehavior of the SCCB during crack propagation Thereforethe cohesive element was used to model the bond interface inthe current study

ABAQUS assumes that traction separation is linear elasticprior to undergoing complete damage evolution The elasticbehavior is represented by a constitutive matrix in terms of

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6

Criti

cal l

oad

(N)

COD (mm)

FRACT27 T3FRAC1031 T1FRAC1031 T2

Figure 4 Critical strain energy curves for representative specimens

Figure 5 Finite element model of the SCCB utilizing cohesiveelement

nominal stress and strain While ABAQUS provides a three-dimensional model torsional effects will not be presentedhere because only a two-dimensional model was employedIt should be noted that while a mixed mode process maybe present (normal and shear) the SCCB test inherentlyprovides a Mode I failure which is predominantly normal tothe interface

Given that the nominal stress can be written as [18]

119905ULT = 1199050

119899 (3)

where 119905 is the total separation stress and 119905119899is the normal

separation stress and strain can be written as

120576 = 120576119899 (4)

where 120576 is the total separation strain and 120576119899 = (120575119899119879119900) is thenormal separation strain and 119879119900 is the original thicknessof the element the elastic behavior can then be written asfollows

119905ULT = 1199050

119899 = [119870119899] Δ 119899 = 119870120576 (5)

where 119870119899is the stiffness that relates to the nominal stress

(Nm3)The subscripts for the stiffnessmatrix represent againthe normal separation (119899)


CFRP layer

Concrete substrate

Wood contour

Cohesive layer

Figure 6 The finite element SCCB model

Figure 7 Close-up rendering of the damage evolution of thecohesive element

Following the initial elastic response damage is initiatedprovided that one of the user defined criteria ismetThe dam-age initiation criteria can be defined in ABAQUS utilizingstress strain or quadratic functionThe current work utilizeda maximum stress criterion as follows [18]

max⟨119905119899⟩

1199050119899

= 1 (6)

where ⟨119905119899⟩ is the normal stress state and 119905

0

119899is the peak normal

stressOnce the damage criterion is achieved the material

undergoes a softening process or loss of stiffness that perpet-uates the damage evolution ABAQUS [18] represents damageevolution by introducing the damage variable 119863 whichranges in magnitude from 0 to 1 The effect of the damagevariable is given by

1199050

119899=

(1 minus 119863) 119905nd119905nd

(7)

where 119905nd is the predicted normal stress (undamaged) and 119863

is the damage variable

400

350

300

250

200

150

100

50

0

0 002 004 006 008 01 012 014 016

FE results

FE results

COD (mm)

FE no CMZ

Laboratory results

Criti

cal l

oadPc (N

)

Figure 8 Finite element results compared to the companionlaboratory results (straight line indicating nonseparation modelwith no CMZ)

4 Laboratory SCCB Tests

A series of SCCB tests was carried out [7] The singlecantilever contoured beam (SCCB) used for this study is com-prised of a substrate material (reinforced concrete) a fiber-reinforced polymer layer and a wood contour as illustrated inFigure 2This study utilized the previously calibrated contourdeveloped by Lawrence and Boyajian [7] with a rise of 95mm

As previously stated the bonding substrate for the systemis a reinforced concrete beam as illustrated in Figure 2 Thetarget ranges for the concrete compressive strength were2758 plusmn 173MPa 3450 plusmn 173MPa and 4140 plusmn 173MPa


0

02

04

06

08

1

Stiff

ness

deg

rada

tion

pe

rcen

t to

failu

re

Figure 9 Stiffness degradation along the cohesive zone (crackpropagation) including the stiffness degradation behind the crack

among batches for consistency and comparison to previouswork The only derivation in testing protocol from previousstudies was the mix design The previous studies ([6 7])utilized approximately 1 1 1 and 1 2 4 ratios as the mixdesigns so as to increase the workability of the concrete intothe mold and produce a consistent concrete surface For thecurrent work themix design was found using ACI 301 (2005)mix specifications which produced the more commonly used1 3 5 mix design While the issues of workability and aconstant concrete surface are still true for the current studythey were addressed by employing a vibration table to fillvoids and work the concrete into the mold Additionally aslump of 89mm was used to further aid in workability Theonly additive used in the mix design was an air entrainmentagent which was added to achieve 65 percent plusmn1 percentaverage air content The addition of an air entrainment agentwas necessary due to future durability testing

The testing regimen used by the entire study (compressivestrength1198911015840119888 of substrate effects on119866119862) required a total of nineconcrete beam specimens For each batching the concretewas tested for slump air entrainment and compressivestrength The batch was considered successful if it met themix design requirements previously defined The averagecompressive strengths among the batches were 2896MPa(SD = 234MPa) 3689MPa (SD = 010MPa) and 4085MPa(SD = 010MPa) with all batches meeting the compressivestrength standards

41 Fiber-Reinforced Polymer System The fiber-reinforcedpolymer used in the study consists of two parts the carbonfibers and epoxy The system selected for the study wasSikadur 301 two-part epoxy and SikaWrap Hex 103C carbonfiber due to the systemrsquos increasing popularity in industryThehigher demand for the Sika 301 epoxy is a result of a lowercost for material and the lack of a primer coat which in turnallows for faster construction times The material propertiesfor the system are listed in Table 1

Table 1 Fiber-reinforced polymer properties (Sika)

SikaWrap Hex 103C Sikadur 301Tensile strength 3793GPa 520MPaTensile modulus 2345GPa 2000GPaElongation 15 35 at break

42Microllam Laminated Veneer Lumber Thecontourmate-rial used in the study is a wood product 19E MicrollamLVL (laminated veneer lumber) The material was selectedto serve as the contoured member of the SCCB specimendue to the ease by which it could be shaped as required bythe compliance results (refer back to Figure 2) The materialproperties are listed in Table 2

In employing the SCCB testing methodology [5] thesuccess of determining the critical strain energy releaserate is directly related to the accuracy of compliance Asfirst presented in the Irwin-Kies equation compliance 119862is represented by a ratio of displacement to load incrementIn the absence of a contoured cantilever the complianceof the uncontoured beam changes as the crack location 119886propagates along the structural member As a result calcu-lating the critical strain release energy can only be achievedby continuously measuring the crack location during theexperiment which is a difficult task As a means to avoidthe arduous measuring of crack tip location a contouredshape is utilized that causes the compliance to change linearlyin conjunction with crack propagation along the interface[5] This linear relationship removes the dependence of load119875 and strain energy release rate 119866119868 from the crack tiplocation 119886

In determining the optimized contour dimensions andin an effort to simplify the procedure the dimensions ofthe contour are prescribed prior to analysis except for ℎ119891

(the height of the contour given in Figure 1 as 95mm)which will be iterated in a finite element model (FE) toachieve several approximated contour shapes The crack tiplocation begins at 51mm (starter crack) loaded with 448Nand the corresponding contour deformation at the loadlocation is recorded The process is repeated for crack tiplocations at 51mm intervals up to 357mmof specimen lengthThe resulting compliance 119862 (calculated as 119906119875) is plottedas a function of crack tip location 119886 The slope of thelinear relationship provides the compliance gradient dCdaSubsequently for each ℎ

119891that yields acceptable compliance

gradients an experimental calibration must be performed toassist in the final optimization of the contour

This study utilized the previously calibrated contourdeveloped by Lawrence and Boyajian [7] which had an ℎ

119891=

95mm The contour was modeled in ANSYS in an effort tocheck the compliance gradient The resulting gradient usedfor the fracture studies was d119862d119886 = 149 times 10

minus5Nminus1 whichcompares well with Boyajian [5]

From the experimental study three representative speci-mens (closest to 119866

119868119862averages) of the nine pull test results are

presented in Table 3 where 119866119862and 119875

119862for the three different

tests are presented alongwith the averaged values Figure 2(c)


Note location of high stress-initial fracture point

Figure 10 Stress distribution in the nonseparation model

Table 2 19E Microllam LVL properties

Grade 119866

Shear modulus of elasticity119864

Modulus of elasticity119864min

Adjusted modulus of elasticity119865119887

Flexural stress19E 819MPa 13GPa 66GPa 18MPa

Table 3 Representative experimental and analytical results

Specimen Critical load 119875119888

119866119868119888

(initiation) F1015840c

FRAC1031 T1 1494N 384 Jm2 37MPaFRAC1031 T2 1245N 267 Jm2 37MPaFRAC27 T3 1045N 183 Jm2 29MPaAverage 1261N 278 Jm2 34MPaFinite element 1392N 307 Jm2 37MPa

Table 4 Summary of FE material input values

Material Youngrsquosmodulus

Poissonrsquosratio

Fractureenergy

Concrete 30GPa 018 NALVL contour 13GPa 030 NACohesive 102GPa NA 134 Jm2

CFRP 235GPa 015 NA

shows the typical failed specimens where failure planeshowed exposed aggregates embedded in the substrates Thefailure plane for all tests fell within the concrete matrix andlied within the substrate Figure 4 shows the critical loadversus crack opening displacement from the test results

5 SCCB Analytical Model

The SCCB was modeled using 2D plain strain plate quadelements in ABAQUS and represents the LVL contour the

concrete substrate and the CFRP layer (see Table 4) For FRPlaminates typically orthotropic layer elements are used [1]however for the 2D model nondirectional element is used

The interface region was geometrically inputted to rep-resent a mixed layer of concrete and epoxy due to thedeep intrusion of crack propagation into the substrate Thisinterfacial zone was considered to be the cohesive layer andwas modeled using ABAQUS cohesive element COH2D4The material properties required to model the cohesiveelement are 119866119888 119870 nominal stress (traction) 119905 and separa-tion 120575 The system was subjected to a 178mm deflection ofthe contour tip which corresponds to the laboratory resultsfor the crack opening displacement (COD) at the criticalload 119875

119888

Figure 5 shows the FE model Due to the devia-tion in concrete properties averaged material propertiesfrom laboratory tests are used for the cohesive element119866119888

= 13397 Jm2 119870 = 10245Nm3 and nominal stress1551MPa Table 3 provides amaterial summary for the SCCBmodel The one area of concern in utilizing the cohesiveelement as Duan et al [19] pointed out is the element sizeDuan et al [19] and others [12 20] have proposed variousanalytical processes for determining cohesive element sizeand Diehl [17] proposed an element size of one-fifth of themodel The size of the cohesive element was 110 the size ofthe CFRP layer with an aspect ratio of 1 to 5 A close-up viewof the final model is shown in Figure 6 It should be notedthat the stress distribution at the location of the crack tip inFigures 5 and 7 ranged from 0MPa to 4846MPa


6 Results and Discussion

Figure 7 shows the stress distribution at critical load sig-nificant crack propagation has penetrated into the interfaceOver 50 cohesive elements have been removed (delami-nation) immediately after the critical load was achievedAlso illustrated in Figure 5 the stress distribution in thewood layer displayed typical Bernoulli bending behaviorwith compressive stresses of the cantilever at the top andthe tensile stresses at the bottom However during the firstfracture sequence of the SCCB the interface was representedby a region of discontinuity as it pertains to the stress Thediscontinuity is a result of the different material propertiesbetween the cohesive element the concrete and the FRPThemaximum stress in the FRP material is 4846MPa whichoccurs at the crack tip indicating that the composite wrap isbeing stressed

Figure 8 shows the stiffness degradation within the inter-face (cohesive elements) and behind the crack The analyt-ical model produced reasonably close results compared tothe laboratory results (Figure 8) Figure 8 is a rendering ofthe numerical model results as a function of all fracturedspecimens represented by the smeared gray area indicatingthe experimental deviations It should be noted that thelaboratory results actually represent various compressivestrengths of concrete ranging from 290MPa to 414MPaThis will somewhat affect the specific fracture energy of theconcrete as well as the effective stiffness of the cohesive layer

The critical load 119875119888 was determined to be 1392N at acrack opening displacement of 178mmThe averaged criticalload from the laboratory results was 1261N at a crack openingdisplacement of 170mm yielding a percent difference ofapproximately 9 percent and 45 percent respectively Thecritical strain energy release rate from the finite element anal-ysis was then calculated as 307 Jm2 which also correspondedwell with the averaged critical strain energy release rate of278 Jm2 yielding a percent difference of 94 percent Whilethe numerical results are acceptable as the percent differencesare within the laboratory specimen percent differences thebehavior of the modeled fracture varied somewhat from thelaboratory results The fracture produced in the model ismore representative of stable crack propagation rather thanthe moderately unstable fracture pattern produced in thelaboratory experiments

Result from FE model with no cohesive material zone(CMZ) is also investigated which shows significantly largercritical ultimate stress (straight line in Figure 9) Further-more there is a slight but negligible difference in stiffnessbetween the two models Figure 10 shows the stress concen-tration in the nonseparation model where the peak stressat initial fracture point is 716MPa Since the model is notallowed to crack the FRP composite does not demonstraterealistic stress distribution as indicated in Figure 6 It is alsoof interest to note that high stress concentration exists withinthe concrete elements during loading (Figure 5) accuratelyportrayed possible penetrating into the substrate

7 Conclusions

Thepreceding work documents the effectiveness of modelingthe delamination of CFRP that has been bonded to concreteutilizing the Abaqus defined cohesive element The modeldoes accurately predict the critical load 119875119888 as well as thecrack opening displacement COD Furthermore without theuse of the cohesive element the stress distribution at thecrack initiation cannot be modeled properlyThe significanceof the numerical modeling is the accurate portrayal of thedebonding process of SCCB test method with SP3 surface aswas the case with the experiment results the model bears outthe deep penetration into the concrete substrate

Comparing to the nonseparation model (without cohe-sive element) the peak stress is significantly higher than theactual experimental results and the FRP material does notappear to resist the pull loading

There are a few areas need to be addressed to fully definethe SCCB analytically

(1) As multiple materials are contributing to the strengthof the bond it would be intuitive that each of thesematerials could be represented by multiple cohesivelayers

(2) One area of concern is the added concrete materialto the contour during fracture The addition of thismaterial could impact the compliance

(3) The nonhomogeneity of the wood and concretecaused some concern when comparing the numericalresults to the laboratory results

(4) Modeling the cohesive zone as a zero thicknesselement should be investigated for stiffness effects

References

[1] V Giurgiutiu J Lyons M Petrou D Laub and S WhitleyldquoFracture mechanics testing of the bond between compositeoverlays and a concrete substraterdquo Journal of Adhesion Scienceand Technology vol 15 no 11 pp 1351ndash1371 2001

[2] V M Karbhari and M Engineer ldquoInvestigation of bondbetween concrete and composites use of a peel testrdquo Journal ofReinforced Plastics and Composites vol 15 no 2 pp 208ndash2271996

[3] I Kimpara K Kageyama T Suzuki I Osawa and K Yam-aguchi ldquoCharacterization of debonding energy release rateof FRP sheets bonded on mortar and concreterdquo AdvancedComposite Materials vol 8 no 2 pp 177ndash187 1999

[4] D M Boyajian J F Davalos and I Ray ldquoEvaluation ofinterface fracture of concrete externally reinforced with FRPrdquoin Proceedings of the 2nd International Conference on Durabilityof Fiber Reinforced Polymer (FRP) Composites for Construction(CDCC) Montreal Canada 2002

[5] D M Boyajian Mode I fracture and durability of the CFRP-concrete interface bond [PhD thesis] West Virginia University2002

[6] S S Kodkani Interface durability of externally bonded GFRPto normal and high-performance concrete [MS thesis] WestVirginia University 2004


[7] T O Lawrence and D M Boyajian ldquoSurface roughness quasi-static fracture and cyclic fatigue effects on GFRP- And CFRP-concrete bonded interfacesrdquo Journal of ASTM International vol3 no 1 pp 1ndash14 2006

[8] International Concrete Repair InstituteConcrete Surface Prepa-ration for Fiber Reinforced Polymers International ConcreteRepair Institute Des Plains Ill USA 2003

[9] O Buyukozturk O Gunes and E Karaca ldquoProgress on under-standing debonding problems in reinforced concrete and steelmembers strengthened using FRP compositesrdquo Constructionand Building Materials vol 18 no 1 pp 9ndash19 2004

[10] J P Berry ldquoDetermination of fracture surface energies by thecleavage techniquerdquo Journal of Applied Physics vol 34 no 1 pp62ndash68 1963

[11] A Boresi R J Schmidt and O M Sidebottom AdvancedMechanics of Material JohnWiley amp Sons New York NY USA5th edition 1993

[12] A Turon C G Davila P P Camanho and J Costa ldquoAnengineering solution for mesh size effects in the simulation ofdelamination using cohesive zonemodelsrdquoEngineering FractureMechanics vol 74 no 10 pp 1665ndash1682 2007

[13] G R Irwin ldquoFracturerdquo in Encyclopedia of Physics S Flugge Edvol 6 pp 551ndash590 Springer Berlin Germany 1958

[14] G R Irwin and J A Kies ldquoCritical energy rate analysis offracture strengthrdquoWelding Journal Research Supplement vol 33pp 193sndash198s 1954

[15] T Nicholas Mode 1 fatigue and fracture of the carbon fiberreinforced plastic to concrete bond interface region [PhD thesis]University of North Carolina at Charlotte 2010

[16] D Huang and J Lyons ldquoFinite element analysis of test speci-mens to assess compositemdashconcrete bond durabilityrdquo Journal ofReinforced Plastics andComposites vol 24 no 13 pp 1387ndash14052005

[17] T Diehl ldquoOn using a penalty-based cohesive-zone finite ele-ment approachmdashpart I elastic solution benchmarksrdquo Interna-tional Journal of Adhesion and Adhesives vol 28 no 4-5 pp237ndash255 2008

[18] ABAQUSFinite Element CodeHibbitt Karlsson and SorensenInc Providence RI USA 2007

[19] K Duan X Z Hu and F H Wittmann ldquoSize effect on specificfracture energy of concreterdquo Engineering Fracture Mechanicsvol 74 no 1-2 pp 87ndash96 2007

[20] A M Ibrahim and M S Mahmood ldquoFinite element modelingof reinforced concrete beams strengthenedwith FRP laminatesrdquoEuropean Journal of Scientific Research vol 30 no 4 pp 526ndash541 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Wood contour

Concrete substrate

Loading strap

CFRPepoxy

Starter crack

P

953mm

205mm

Figure 1 Schematic of single contoured cantilever beam test

(a) SCCB test setup (b) Concrete surfaces (left to right) SP1 mould andSP3

Composite FRP wrap

(c) Failed specimen showing exposed substrate

Figure 2 The SCCB test (a) experimental setup (arrow indicating load direction) (b) different concrete surfaces (SP1 mould and SP3) (c)interface surface of failed specimens FRAC1031 T1 and FRAC1031 T2

ICRI surface profiles The common method for classifyingthe surface is to check the target surface tab (SP 3) as wellas the tab above (SP 4) and the tab below (SP 2) Figure 2(b)shows the different surface areas SP1 mould and SP3 Studyof failure in the substrates is important as it may lead topremature failure and brittle failures [9] Figure 2(c) showsthe failed specimens clearly indicating failure within concretesubstrate

This paper reports finite element (FE) simulation of aseries of SCCB tests conducted with concrete specimens pre-pared with SP3 surfaces which was not previously attemptedIn order to develop realistic FE models a damage evolutionapproach has been adopted The results presented shows thatthe approach effectively predicts the critical strain energyrelease rate of the bonded interfaceThemodel also compareswell with the laboratory test results

2 Mode 1 Fracture

Fracture behavior can normally be characterized as begin-ning with crack initiation and intensifying through crackpropagation At the onset of crack initiation the crackpropagation behavior becomes a function of the displacementof the failed interface surfaces [10ndash12] Irwin [13] definedthree failuremodes to describe how the surfaces are displacedby Mode I Mode II and Mode III failures Mode I describesa failure of the interface bond that occurs normal to thefailed surface often referred to as the opening mode While

most fractures can be described by one of the failure modesthe mixing of mode failures such as Mode I-Mode II isalso a possibility The ability of an engineering material toresist these failure modes is frequently referred to as fracturetoughness The commonly accepted method for representingfracture toughness is the critical release strain energy 119866

119862 as

defined by the Irwin-Kies equation [13 14]

119866119862= (

1198752

119862

2119887)(

d119862d119886

) (1)

where 119866119862is the critical strain energy release rate (Jm2) 119875

119862

is the critical load (N) 119887 is the width of the specimen (mm)and dCda is the rate of compliance (119862) with respect to cracklength (119886) (Nminus1)

3 Analytical Modeling of Fracture andthe Cohesive Elements

As it pertains to the current study finite element modeling ofthe SCCB can be divided into two categories compliance ofthe SCCBwood contour and fracture As there exist a numberof methods to model crack propagation it is important toselect an efficient and accurate representation of the failurebehavior While the SCCB has not specifically been modeledfor fracture a number of past studies have focused on thefracture of the double cantilever beam and the peel test Mostrecently Nicholas [15] Huang and Lyons [16] and Diehl [17]


Elastic limit

K

Trac

tion

t

Separation 120575

tULT

120575ULT120575c




119866119891=

1

119861 lowast (119882 minus 119886)int119875119889120575 (2)






0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6

Criti

cal l

oad

(N)

COD (mm)






119905ULT = 1199050

119899 (3)



120576 = 120576119899 (4)


119905ULT = 1199050

119899 = [119870119899] Δ 119899 = 119870120576 (5)




CFRP layer

Concrete substrate

Wood contour

Cohesive layer




max⟨119905119899⟩

1199050119899

= 1 (6)


0




1199050

119899=

(1 minus 119863) 119905nd119905nd

(7)



400

350

300

250

200

150

100

50

0

0 002 004 006 008 01 012 014 016

FE results

FE results

COD (mm)

FE no CMZ

Laboratory results

Criti

cal l

oadPc (N

)






0

02

04

06

08

1

Stiff

ness

deg

rada

tion

pe

rcen

t to

failu

re














119891=












Grade 119866







119866119868119888





Poissonrsquosratio

Fractureenergy


CFRP 235GPa 015 NA






119888









7 Conclusions








References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Elastic limit

K

Trac

tion

t

Separation 120575

tULT

120575ULT120575c




119866119891=

1

119861 lowast (119882 minus 119886)int119875119889120575 (2)






0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6

Criti

cal l

oad

(N)

COD (mm)






119905ULT = 1199050

119899 (3)



120576 = 120576119899 (4)


119905ULT = 1199050

119899 = [119870119899] Δ 119899 = 119870120576 (5)




CFRP layer

Concrete substrate

Wood contour

Cohesive layer




max⟨119905119899⟩

1199050119899

= 1 (6)


0




1199050

119899=

(1 minus 119863) 119905nd119905nd

(7)



400

350

300

250

200

150

100

50

0

0 002 004 006 008 01 012 014 016

FE results

FE results

COD (mm)

FE no CMZ

Laboratory results

Criti

cal l

oadPc (N

)






0

02

04

06

08

1

Stiff

ness

deg

rada

tion

pe

rcen

t to

failu

re














119891=












Grade 119866







119866119868119888





Poissonrsquosratio

Fractureenergy


CFRP 235GPa 015 NA






119888









7 Conclusions








References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










CFRP layer

Concrete substrate

Wood contour

Cohesive layer




max⟨119905119899⟩

1199050119899

= 1 (6)


0




1199050

119899=

(1 minus 119863) 119905nd119905nd

(7)



400

350

300

250

200

150

100

50

0

0 002 004 006 008 01 012 014 016

FE results

FE results

COD (mm)

FE no CMZ

Laboratory results

Criti

cal l

oadPc (N

)






0

02

04

06

08

1

Stiff

ness

deg

rada

tion

pe

rcen

t to

failu

re














119891=












Grade 119866







119866119868119888





Poissonrsquosratio

Fractureenergy


CFRP 235GPa 015 NA






119888









7 Conclusions








References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

02

04

06

08

1

Stiff

ness

deg

rada

tion

pe

rcen

t to

failu

re














119891=












Grade 119866







119866119868119888





Poissonrsquosratio

Fractureenergy


CFRP 235GPa 015 NA






119888









7 Conclusions








References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Grade 119866







119866119868119888





Poissonrsquosratio

Fractureenergy


CFRP 235GPa 015 NA






119888









7 Conclusions








References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















7 Conclusions








References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article finite element modeling of mode i...

Documents