fracture of parallel strand bamboo composite under mode i...

Research ArticleFracture of Parallel Strand Bamboo Composite underMode I Loading DCB Test Investigation

Yurong Shen12 Dongsheng Huang 1 Ying Hei Chui2 and Chunping Dai3

1National Engineering Research Center of Biomaterials Nanjing Forestry University Nanjing 210037 China2Department of Civil and Environment Engineering University of Alberta Edmonton T6G 1H9 Canada3Department of Wood Science +e University of British Columbia Vancouver Canada V6T 1Z4

Correspondence should be addressed to Dongsheng Huang dshuangnjfueducn

Received 10 July 2019 Revised 30 August 2019 Accepted 6 September 2019 Published 23 September 2019

Guest Editor Grzegorz Lesiuk

Copyright copy 2019 Yurong Shen et al is 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

is paper describes the experimental studies on Mode I fracture of parallel strand bamboo (PSB) by the double cantilever beam(DCB) test R-curves based on the elementary beam theory and specimen compliance are proposed in order to overcome thedifficulties to monitor the crack propagation during experiments e results demonstrate that the energy release rate (ERR) isinfluenced by the specimen geometry ie the specimen width and initial crack length e ERR at the plateau level is similar forthe range of the analyzed widths (B 20 40 and 60mm) while it decreases with width increasing up to 80mm and 100mm eenergy release rate for PSB specimens would verge to a stable value with the width increasing up to a specific value while the valueof the energy release rate will be influenced by the initial crack length Consequently the DCB tests also show that the obtainedR-curve in this study is not a material property

1 Introduction

Parallel strand bamboo (PSB) is manufactured by parallellygluing bamboo strands together under controlled temper-ature and pressure Because bamboo strips are parallellyglued along the longitudinal direction and uniformly dis-tributed over the transverse direction PSB can be consideredas a unidirectional and orthotropic fibrous composite asshown in Figure 1 [1] More recently PSB wins growinginterests as an alternative of wood composites for con-struction engineering in China due to its fast-growingfeature and excellent structural performance Aimed at thestructural use the failure modes of combined compressionand bending PSB members were studied by Huang et al[2ndash4] It was found that the fracture along the fiber interfaceswas one of the major failure modes of PSB composites Oncea PSB member subjected to an increasing external load theinitial deflects such asmicrovoids andmicrocracks could beadvancing or growing into macrocracks and consequentlyresult in catastrophic failure of structures erefore the

fracture of PSB composite is one of the major concerns inPSB structural design

e objective of the present study is to investigate theModeI fracture properties and to measure the fracture toughness ofthe PSB composite through DCB experiments which is one ofthe necessities for establishing design allowable values used indamage tolerance analysis of PSB structures

e double cantilever beam (DCB) test [5ndash7] a standardtest procedure prescribed in ASTM D5528-13 [8] wasemployed as the test procedure in this study e test uses arectangular specimen with different widths different initialcrack lengths and constant thickness It contains a pre-implanted nonadhesive insert or crack as an initial de-laminatione opening load is applied perpendicular to theinitial crack surface to induce the Mode I crack Such a testanalysis is based on the beam theory and the fracturetoughness can be measured through the energy release rate(ERR) for orthotropic fibrous composites e ERR can beobtained by various methods including direct area in-tegration of loading-unloading curves or by means of

HindawiAdvances in Materials Science and EngineeringVolume 2019 Article ID 7657234 10 pageshttpsdoiorg10115520197657234

compliance measurements [9] Since the data reduction ofDCB test is easier than the other test approaches [10 11] it isnow the most popular method used to determine Mode Ifracture toughness

Recommended by ASTM and ISO standards [9 12 13]the energy release rate can be estimated through the changeof compliance eoretically it can be obtained by differ-entiating the specimen compliance C with respect to thecrack length a ie G (P22B)(zCza) [14ndash18] where P isthe applied load and B the width of the specimen In theframe of linear fracture mechanics the root condition issupposed to be fully built-in hence the compliance equationcan be given by simple beam theory ie C 8a3BEh3 [9]Nevertheless because of the fuzzy boundary conditions atthe end of opening arms the compliance equation C(a)cannot be determined without controversy On the otherhand the crack length cannot be measured either withdesired precision erefore various data reductionmethods were developed to overcome this disadvantagesuch as the area method in which the compliance equationwas built through data fitting for tests [19 20] Hashemi et al[21] compared the different data reduction methods forobtaining the energy release rate of fibrous composites eyproposed that the correction of crack length was necessary inthe beam theory-based method because the end of openingarms was not perfectly clamped ey developed the cor-rected beam theory (CBT) providing a correction in thecrack length based on a compliance calibration Howeverthe fracture mechanism of fibrous composite is muchcomplicated than that of brittle materials e major aspectis that the microvoids coalescing fine cracks extending andfiber bridging lead to a large fracture process zone (FPZ) infront of the crack tip which makes the clear location of thecrack tip impracticable [22ndash25] Furthermore the devel-opment of the large FPZ in the crack-tip front delays thefracture of specimen which consequently makes the built-inassumption no longer valid It has been well recognized thatthe use of elementary beam theory with the built-in as-sumption at the crack tip has a significant error for calcu-lating the energy release rate of fibrous composites [26] Todate there is no method available to exactly identify thecrack tip for the DCB test of fibrous composites For thisreason extensive researches have been carried out to avoidlocating the crack tip [27ndash32] Among these researches the

concept of equivalent linear elastic fracture mechanics(LEFM) was widely accepted to deal with the fracture with alarge FPZ [31] According to the concept of equivalentLEFM the increasing of compliance owing to the devel-opment of FPZ or main crack propagation with FPZ isattributed to the elastic crack which equals to the actualcrack with its FPZ [33] erefore the crack length can beestimated according to the associated compliance obtainedby experiments Furthermore the R-curve can also bemeasured using only amonotonic load-displacement record

In the present study the data reduction method was basedon the theory of equivalent LEFM Compliance calibration wasintroduced to determine the crack length e direct integralapproach was adopted to calculate the energy release rate

2 Data Reduction Scheme

Figure 2 illustrates the principle of evaluating energy releaserate based on the theory of equivalent LEFM In the sche-matic load-displacement curve (F δ) two consecutivepoints M1(δ(a1) F(a1)) and M2(δ(a2) F(a2)) corre-sponding to two different crack lengths a1 and a2 re-spectively are selected Suppose that the crack extends fromlength a1 to a2 with a small amount of propagation in-crement Δa and that the load-displacement trajectory goesfrom M1 to M2 thus the shadow area circulated by thedashed lines OM1 and OM2 and the segment of load-dis-placementM1M2 must be equal to the energy released as thecrack growth of the extension Δa [19] erefore the energyrelease rate can be calculated by

GR 1

bΔa12

P a1( 1113857δ a2( 1113857 minus12

P a2( 1113857δ a1( 11138571113876 1113877 (1)

where P and δ stand for the applied load and associateddisplacement at loading position respectively e cracklength ai(i 1 2) can be determined from the test com-pliance C(ai) (δ(ai))(P(ai)) According to the beamtheory the compliance can be calculated by [34]

C(a) a3

ELI+

6a

5GLTA (2)

where EL is the longitudinal elastic modulus GLT is the shearmodulus in LT plane ie the 12 or 13 plane as shown inFigure 1(b) I is the inertia moment of the cross section and

Long

itudi

nal d

irecti

on

Para

llel-t

o-gr

ain di

recti

on

(a)

1 (Longitudinal)

3 (Transverse)

2 (Transverse)

(b)

Figure 1 (a) Photograph of PSB (b) Principal directions of PSB

2 Advances in Materials Science and Engineering

A is the area of cross section Once the compliance C(ai)isobtained by experiment and the crack length can be de-termined by resolving equation (2) or by numerical iterationin terms of the following equation

ai 3ELIλC ai( 1113857

2 1 + 3ELh210GLTa2iminus 1( 1113857( 1113857

1113890 1113891

(13)

(3)

where λ C0C0 is the calibration parameter to eliminatethe system error of the experiment in which C0 is the testcompliance corresponding to the initial crack length a0 andC0 stands for the theoretical compliance corresponding tothe initial crack length calculated by equation (2)

3 Experimental Investigation

31 Materials e test PSB was provided by FeiyuBamboo Products Jianghxi China e material densitywas 126 gcm3 and the moisture content was 11 Me-chanical properties in parallel-to-grain direction whichare involved in test analysis were pretested following themethod recommended in ASTM D143-14 [35] and theresults are collected in Table 1 where the subscripts L andTare the parallel-to-grain direction and perpendicular-to-grain direction respectively and υ represents Poissonrsquosratio of PSB

32 Specimen Preparation e geometry of DCB specimenis shown in Figure 3e dimensions of DCB specimen weredetermined referring to the standard test procedureaddressed in ASTM D5528-13 [8] In this method the DCBdimension was designed to ensure the damage zone ornonlinear deformation developed along the delaminationfront and the stable crack growth can be achieved

Totally four groups of specimens with different initialcrack lengths and different widths were prepared as il-lustrated in Table 2 in which each group consists of thesame initial crack length and 5 types of specimens withdifferent widths A label system was designed to identify thespecimen In this system the latter A B C and D

correspond to the initial crack length of 34mm 67mm100mm and 134mm respectively e number prior tothe letter of the group name stands for the width of thespecimen as shown in Table 2 e initial crack was firstlyintroduced by a 15mm thick saw kerf afterwards precrackwith length about 1mm was extended by using a cuttingblade [10] At the end of the DCB test two bolt holes of8mm in diameter were drilled for the sake of joining DCBspecimen to the actuator of the test machine as illustratedin Figure 3

33 Test Procedure e fracture tests were performed on aservo-hydraulic universal test machine of 20 kN capacity inroom ambient circumstance e test setup is illustrated inFigure 4(a) e specimen was joined to the load actuatorthrough two steel rods of 75mm diameter as shown inFigure 4(b) Loading was controlled by the displacement of amoveable actuator at the speed of 10mmmin A micro-scope digital camera was mounted in front of the specimento monitor the crack propagation and take the images of thecrack tip e applied load and the displacement at loadingposition were simultaneously recorded at a frequency of10Hz e opening displacement at the initial crack tip wasmeasured by using a clip-on gauge (COD gauge) symmet-rically fixed at the two sides of the crack tip through em-bedded aluminum flakes (Figure 4(b)) e crack lengthduring propagation can be observed by using the micro-scopic camera as shown in Figure 4(b)

4 Test Results

41 Load-Displacement Curve Figure 5 illustrates a typicalload-displacement curve Roughly three stages can be ob-servede first one (stage I) is no-damage stage from originto the proportional limit point where the curve deviates fromits original direction e load-displacement curve exhibitsperfect linearity in this stage Once the load exceeds the pointof proportional limit (stage II) damage onset extends andcoalesces to form the fracture process zone (FPZ) andconsequently leads to the compliance augment and the curvecontinuously deviates from its original direction as the loadincreases Hence this stage can be understood as the stage ofFPZ development When the FPZ fully developed the load-displacement curve would reach its critical point where theload reached its maximum value and the crack propagationbegan Hence the third stage (stage III) is the crack prop-agation stage

Figure 6 presents the load-displacement profiles of thespecimens For the specimens of Group A the load-dis-placement curve sharply declines once the load reaches themaximum value which indicates that the crack

Table 1 Mechanical properties of PSB composites in parallel-to-grain direction

Items EL (MPa) GLT (MPa) υLT υTLMean 15363 4890 032 005CV () 9575 1231 123 256

M2

M1Pi

Pi+1

δi δi+10

1200

2400

Load

(N)

5 10 150δ (mm)

Figure 2 Schematic diagram of the evaluation of the resistance tocrack growth (GR)

Advances in Materials Science and Engineering 3

propagation is unstable For the specimens in Groups B Cand D with longer initial crack length the load-displace-ment profile slowly declines in post-summit segmentsFurthermore the load-displacement profile declined moreslowly with longer initial crack length which indicated thatthe stability of crack propagation is sensitive to the initialcrack length erefore enough initial crack length isneeded for obtaining stable crack propagation In thepresent study the ratios of initial crack length to ligamentlength of Groups B C and D are 0191 0286 and 0383respectively and their crack propagates in a stable andductile manner which means specimens with the ratio ofGroups B C and D can be used to determine the fractureproperties

e second factor is the width scaling which has asignificant influence on fiber bridging in the wake of thecrack consequently affecting the delamination behaviorAs shown in Figure 7 the load-displacement curves forpartial specimens are presented with the same initial cracklength but different widths It can be concluded that thecrack grows in a ldquothumbnailrdquo shape [36] under constant or

decreasing load while the overall displacement is in-creased e ldquothumbnailrdquo theory means that the crackextends mainly from the center of the thickness of speci-mens while the edge regions are plastically deformederefore with the width increasing the energy release rate

1~1

51212

16

L

B

H

T (2)

L (1)

R4

T (3)

1~2 mm

a0

Figure 3 e configurations of DCB specimens

Table 2 Dimensions of DCB specimens

Group Label a0(mm)

L(mm)

B(mm)

H(mm)

a0(L) Number

A

20-A

34 350

20

50 0097 340-A 4060-A 6080-A 80100-A 100

B

20-B

67 350

20

50 0191 340-B 4060-B 6080-B 80100-B 100

C

20-C

100 350

20

50 0286 340-C 4060-C 6080-C 80100-C 100

D

20-D

134 350

20

50 0383 340-D 4060-D 6080-D 80100-D 100

TransparentCOD

Microscope

Loading

(a)

F

F

Aluminium flakeCOD gauge

DCB specimen

Loading actuator

Tensile clamp

Crack tip

T (2)L (1)

Steel rods

(b)

Figure 4 (a) Experimental setup of the DCB test (b) Schematicdiagram of the DCB test


DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

0

300

600

900

1200

1500

1800

Load

(N)

4 8 12 16 200Displacement (mm)

(a)

DCB-40-ADCB-40-B

DCB-40-CDCB-40-D

0

500

1000

1500

2000

2500Lo

ad (N

)


(b)

DCB-80-ADCB-80-B

DCB-80-CDCB-80-D

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Load

(N)


(c)

DCB-100-ADCB-100-B

DCB-100-CDCB-100-D


0

600

1200

1800

2400

3000

3600

4200

4800

Load

(N)

(d)

Figure 6 Load-displacement curves of all tested DCB specimens with different initial crack lengths in the same width (a) width B 20mm(b) width B 40mm (c) width B 80mm and (d) width B 100mm

FPZ development Crack propagationNo damage

IIII II

0

500

1000

1500

2000

2500

Load

(N)


Figure 5 A typical load-displacement curve


of DCB specimens for PSB composite would converge to astable value

It is worth mentioning that only partial specimens ex-hibit their load-displacement curves or R-curves in lateranalysis due to the similar tendency of these curvesMoreover because of the manufacturing defects for somePSB specimens the data cannot be used to analyze theenergy release rate in the DCB test erefore some spec-imens present two lines in partial load-displacement curvesor R-curves

42FractureProcessZone Damage begins when the externalload exceeds its proportional limit which is characterized bylocal microcracks at the crack tip front zone is damagedzone is comprised of microcracks between the grains orthrough the grains e microcracks are consequently ex-tended and coalesced to form macrocracks and localmicrocracks at the advancing crack tip front as the externalload increases is fracture process and damaged zone canbe called fracture process zone (FPZ) Before the loadreaches its maximum value the crack interfaces are bondedby fiber bridges which either rupture or peel off from thecrack surfaces is fracture mechanism leads to a large FPZwhich can be observed at the crack tip front before crackpropagation as shown in Figure 8 Due to the restriction offiber bridges the strain energy is smoothly consumedthrough the fibrous rupture or pull-off which leads to stablecrack propagation and a rising R-curve

Several micrographs were taken from the testedspecimens at the fracture surfaces using the scanningelectron microscope (SEM) as shown in Figure 9Figure 9(a) exhibits the typical fracture surface with alimited amount of fiber pull-out in the debonding plieswhich is presented with higher magnitude in Figure 9(b)

e pull-out process could have created a fibre-bridgedzone in the wake of the advancing crack tip During thewhole experiment the growth and eventual stabilization ofthis fibre-bridged zone could account for the tendencyobserved in later R-curves

43 R-Curve Measurement Energy release rate for each testspecimen was measured by the method addressed in Section2 e R-curves of partial DCB specimens with differentwidths and different initial crack lengths corresponding tospecific thickness are presented in Figures 10 and 11 It wasobserved that the energy release rate increases up to a steady-state toughness after the initiation of delamination As il-lustrated in Section 42 the fiber bridging effect during thewhole crack propagation led to eventual stabilization ofcrack growths for all tested specimens Meanwhile the re-sults also implied that the R-curve obtained in this study wasnot a material property ie it depended on specimen ge-ometry Consequently when the crack starts to propagatethe bridging zone is created By developing the bridging zonelength the strain energy release rate increases up to thesteady-state fracture toughnesse length between the initialcrack length and crack length corresponding to the steady-state fracture toughness is called as the steady-state bridgingzone length From Figure 10 the value of the energy releaserate was always affected by the initial crack length e majorreason may be that the steady-state bridging zone of PSBspecimens was always influenced by the preimbedded crack

From Figure 11 it can also be concluded that the energyrelease rate of DCB specimens for the PSB composite wouldverge to a stable value with the width increasing up to aspecific value which will be identified in the futureDCB tests for PSB specimens As illustrated in theabovementioned ldquothumbnailrdquo theory the width scaling has

DCB-20-CDCB-40-CDCB-60-C

DCB-80-CDCB-100-C

0

500

1000

1500

2000

2500

3000

3500Lo

ad (N

)


(a)

DCB-20-DDCB-40-DDCB-60-D

DCB-80-DDCB-100-D

0

500

1000

1500

2000

2500

Load

(N)


(b)

Figure 7 Load-displacement curves of DCB specimens with different widths in the same initial crack length (a) initial crack lengtha0 100mm (b) initial crack length a0 134mm


a significant effect on fiber bridging in the wake of thecrack which make the crack grow in a ldquothumbnailrdquo shapeie the crack extends mainly from the center of specimenswhile the edge regions are plastically deformed erefore

the energy release rate of DCB specimens for the PSBcomposite would converge to a stable value with the in-creasing width Table 3 gives the average fracture toughnessfor partial test samples

Fiber pull-out

(a) (b)

Figure 9 (a) SEM micrograph of the DCB specimensrsquo fracture surface for PSB composite (b) Fiber pull-out with higher magnitude

Fiber bridging

Figure 8 e fiber bridging phenomenon of DCB specimens

DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

00

05

10

15

20

25

30

35

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(a)

DCB-60-ADCB-60-B

DCB-60-CDCB-60-D

00

05

10

15

20

25

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(b)

Figure 10 R-curves of DCB specimens with different initial crack lengths on the same width (a) width B 20mm (b) width B 40mm


5 Conclusion

is paper has investigated an experimental procedure toobtain the energy release rate (ERR) using DCB tests forparallel strand bamboo (PSB) composites e effects ofspecimen width and initial crack length on large-scale fiberbridging in Mode I fracture of unidirectional PSB compositeswere investigated e R-curve measurements for the range ofthe analyzed widths (B 20 40 60 80 and 100mm) and initialcrack lengths (a0 34 67 100 and 134mm) show that theenergy release rate is influenced by both the width and initialcrack length of specimens in that the ERR at the plateau leveldecreased with an increasing width and initial crack lengthConsequently the DCB tests imply that the R-curve obtainedin the present study is not a material property because itdepends on the specimen geometry However the ERR at theplateau level is decreased to similar values as the width in-creases up to 80mm and 100mm It may be concluded that theenergy release rate would verge to a stable value with the widthincreasing up to more than a specific value which can beclarified in the future DCB tests for PSB composites

Nomenclature

B Specimen widthC Specimen compliancea Crack lengthP Applied loadG Energy release rateE Youngrsquos modulush Height of the cantilever portion H2H Specimen thicknessδ Loading-line displacementΔa Crack extensionEL Elastic modulus in longitudinal directionGLT Shear modulus in LT planeI Inertia moment of cross sectionA Area of cross sectionλ Calibration parameter to eliminate errors from

experimentsC0 eoretical compliance corresponding to initial crack

lengthC0 Test compliance corresponding to the initial crack

lengtha0 Initial crack lengthυ Poissonrsquos ratioL Specimen length

Data Availability

e data of the DCB test for PSB composites used to supportthe findings of this study are available from the corre-sponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest


DCB-80-CDCB-100-C

00

05

10

15

20G R

times103 Jm

2

150 200 250100a (mm)

(a)


DCB-80-DDCB-100-D

00

05

10

15

20

25

30

G Rtimes1

03 Jm2

200 250150a (mm)

(b)

Figure 11 R-curves of DCB specimens with different widths in the same initial crack lengths (a) Initial crack length a0 100mm (b)Initial crack length a0 134mm

Table 3 e average fracture toughness for partial test samples(H 50mm)

Specimens a0 (mm) B (mm) L (mm) P (N) GR (Jm2)

DCB-C 100

20

350

839 174040 1535 150560 2364 155080 2149 630100 2952 820

DCB-D 134

20

350

745 260040 1332 257060 2081 196080 2009 950100 2233 870


Acknowledgments

e research was supported by the National Natural ScienceFoundation of China (no 51778299) and the Priority Ac-ademic Program Development of Jiangsu Higher EducationInstitutions

References

[1] D Huang Y Bian A Zhou and B Sheng ldquoExperimentalstudy on stress-strain relationships and failure mechanisms ofparallel strand bamboo made from phyllostachysrdquo Con-struction and Building Materials vol 77 pp 130ndash138 2015

[2] D S Huang A P Zhou H T Li Y Su and G ChenldquoExperimental study on the tensile properties of bamboorelated to its distribution of vascular bundlesrdquo Key Engi-neering Materials vol 517 pp 112ndash117 2012

[3] D Huang A Zhou and Y Bian ldquoExperimental and analyticalstudy on the nonlinear bending of parallel strand bamboobeamsrdquo Construction and Building Materials vol 44pp 585ndash592 2013

[4] D Huang Y Bian D Huang A Zhou and B Sheng ldquoAnultimate-state-based-model for inelastic analysis of in-termediate slenderness PSB columns under eccentricallycompressive loadrdquo Construction and Building Materialsvol 94 pp 306ndash314 2015

[5] M F Kanninen ldquoAn augmented double cantilever beammodel for studying crack propagation and arrestrdquo In-ternational Journal of Fracture vol 9 pp 83ndash92 1973

[6] R Olsson ldquoA simplified improved beam analysis of the DCBspecimenrdquo Composites Science and Technology vol 43 no 4pp 329ndash338 1992

[7] F Ozdil and L A Carlsson ldquoBeam analysis of angle-plylaminate DCB specimensrdquo Composites Science amp Technologyvol 59 no 2 pp 305ndash315 1999

[8] American Society for Test Materials (ASTM) ASTM D5528-13 Standard Test Method for Mode I Interlaminar FractureToughness of Unidirectional Fiber-Reinforced Polymer MatrixComposite ASTM West Conshohocken PA USA 2013

[9] H Yoshihara and T Kawamura ldquoMode I fracture toughnessestimation of wood by DCB testrdquo Composites Part A AppliedScience and Manufacturing vol 37 no 11 pp 2105ndash21132006

[10] M F S F de Moura J J L Morais and N Dourado ldquoA newdata reduction scheme for mode I wood fracture character-ization using the double cantilever beam testrdquo EngineeringFracture Mechanics vol 75 no 13 pp 3852ndash3865 2008

[11] J De Gracia A Boyano A Arrese and F Mujika ldquoA newapproach for determining the R-curve in DCB tests withoutoptical measurementsrdquo Engineering Fracture Mechanicsvol 135 pp 274ndash285 2015

[12] American Society for TestMaterials (ASTM)ASTMD6671M-19 Standard Test Method for Mixed Mode I-Mode II In-terlaminar Fracture Toughness of Unidirectional Fiber Rein-forced Polymer Matrix Composites ASTM WestConshohocken PA USA 2019

[13] International Organization for Standardization (ISO) ISO15024-2001 Fiber-reinforced Composite - Determination ofMode I Interlaminar Fracture Toughness GIc for Unidirec-tional Reinforced Materials ISO Geneva Switzerland 2001

[14] W Xu and Z Z Guo ldquoA simple method for determining themode I interlaminar fracture toughness of composite withoutmeasuring the growing crack lengthrdquo Engineering FractureMechanics vol 191 pp 476ndash485 2018

[15] D Huang B Sheng Y Shen and Y-H Chui ldquoAn analyticalsolution for double cantilever beam based on elastic-plasticbilinear cohesive law analysis for mode I fracture of fibrouscompositesrdquo Engineering Fracture Mechanics vol 193pp 66ndash76 2018

[16] S Hofmann ldquoMode I delamination onset in carbon fibrereinforced SiC double cantilever beam testing and cohesivezone modellingrdquo Engineering Fracture Mechanics vol 182pp 506ndash520 2017

[17] E Farmand-Ashtiani J Cugnoni and J Botsis ldquoSpecimenthickness dependence of large scale fiber bridging in mode Iinterlaminar fracture of carbon epoxy compositerdquo In-ternational Journal of Solids and Structures vol 55 pp 58ndash652015

[18] A Jyoti R F Gibson and G M Newaz ldquoExperimentalstudies of Mode I energy release rate in adhesively bondedwidth tapered composite DCB specimensrdquo Composites Sci-ence and Technology vol 65 no 1 pp 9ndash18 2005

[19] N A Plan S Morel and M Chaplain ldquoMixed-mode fracturein a quasi-brittle material R-curve and fracture criter-ionmdashapplication to woodrdquo Engineering Fracture Mechanicsvol 156 pp 96ndash113 2016

[20] S Bennati and P S Valvo ldquoAn experimental compliancecalibration strategy for mixed-mode bending testsrdquo ProcediaMaterials Science vol 3 pp 1988ndash1993 2014

[21] S Hashemi A J Kinloch and J G Williams ldquoCorrectionsneeded in double-cantilever beam tests for assessing the in-terlaminar failure of fibrous-compositesrdquo Journal of MaterialScience Letters vol 8 no 2 pp 125ndash129 1989

[22] B F Soslashrensen and T K Jacobsen ldquoLarge scale bridging incomposites R-curve and bridging lawsrdquo Composites Part Avol 29 no 11 pp 1443ndash1451 1998

[23] B F Soslashrensen E K Gamstedt R C Oslashstergaard andS Goutianous ldquoMicromechanical model of cross-over fibrebridging-prediction of mixedmode bridging lawsrdquoMechanicsof Materials vol 40 no 4-5 pp 220ndash234 2008

[24] K R Pradeep B N Rao S M Srinivasan andK Balasubramaniam ldquoInterface fracture assessment onhoneycomb sandwich composite DCB specimensrdquo Engi-neering Fracture Mechanics vol 93 pp 108ndash118 2012

[25] U Stigh ldquoDamage and crack growth analysis of the doublecantilever beam specimenrdquo International Journal of Fracturevol 37 no 1 pp R13ndashR18 1988

[26] J GWilliams ldquoEnd corrects for orthotropic DCB specimensrdquoComposite Science and Technology vol 35 no 4 pp 367ndash3761989

[27] L P Canal M Alfano and J Botsis ldquoA multi-scale basedcohesive zone model for the analysis of thickness scaling effectin fiber bridgingrdquo Composites Science and Technologyvol 139 pp 90ndash98 2017

[28] B D Manshadi E Farmand-Ashtiani J Botsis andA P Vassilopoulos ldquoAn iterative analyticalexperimentalstudy of bridging in delamination of the double cantileverbeam specimenrdquo Composites Part A Applied Science andManufacturing vol 61 pp 43ndash50 2014

[29] H Danielsson and P J Gustafsson ldquoA three dimensionalplasticity model for perpendicular to grain cohesive fracturein woodrdquo Engineering Fracture Mechanics vol 98 pp 137ndash152 2013

[30] A B de Morais ldquoA new fibre bridging based analysis of thedouble cantilever beam (DCB) testrdquo Composites Part Avol 42 no 10 pp 1361ndash1368 2011

[31] S Morel C Lespine J L Coureau J Planas and N DouradoldquoBilinear softening parameters and equivalent LEFM R-curve


in quasibrittle failurerdquo International Journal of Solids andStructures vol 47 no 6 pp 837ndash850 2010

[32] J-L Coureau S Morel and N Dourado ldquoCohesive zonemodel and quasibrittle failure of wood a new light on theadapted specimen geometries for fracture testsrdquo EngineeringFracture Mechanics vol 109 pp 328ndash340 2013

[33] Z P Bazant and M T Kazemi ldquoSize effect in fracture ofceramics and its use to determine fracture energy and effectiveprocess zone lengthrdquo Journal of the American Ceramic Societyvol 73 no 7 pp 1841ndash1851 1990

[34] F A M Pereira M F S F de Moura D DouradoJ J L Morais J Xavier and M I R Dias ldquoDirect and inversemethod to the determination of cohesive law of bovinecortical bone using the DCB testrdquo International Journal ofSolids and Structures vol 128 pp 210ndash220 2017

[35] American Society for Test Materials (ASTM) ASTMD143-14Standard Test Methods for Small Clear Specimens of TimberASTM West Conshohocken PA USA 2014

[36] H D Bui Fracture Mechanics Springer Berlin Germany2006


CorrosionInternational Journal of

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Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018


Journal of

Chemistry

Analytical ChemistryInternational Journal of


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compliance measurements [9] Since the data reduction ofDCB test is easier than the other test approaches [10 11] it isnow the most popular method used to determine Mode Ifracture toughness

Recommended by ASTM and ISO standards [9 12 13]the energy release rate can be estimated through the changeof compliance eoretically it can be obtained by differ-entiating the specimen compliance C with respect to thecrack length a ie G (P22B)(zCza) [14ndash18] where P isthe applied load and B the width of the specimen In theframe of linear fracture mechanics the root condition issupposed to be fully built-in hence the compliance equationcan be given by simple beam theory ie C 8a3BEh3 [9]Nevertheless because of the fuzzy boundary conditions atthe end of opening arms the compliance equation C(a)cannot be determined without controversy On the otherhand the crack length cannot be measured either withdesired precision erefore various data reductionmethods were developed to overcome this disadvantagesuch as the area method in which the compliance equationwas built through data fitting for tests [19 20] Hashemi et al[21] compared the different data reduction methods forobtaining the energy release rate of fibrous composites eyproposed that the correction of crack length was necessary inthe beam theory-based method because the end of openingarms was not perfectly clamped ey developed the cor-rected beam theory (CBT) providing a correction in thecrack length based on a compliance calibration Howeverthe fracture mechanism of fibrous composite is muchcomplicated than that of brittle materials e major aspectis that the microvoids coalescing fine cracks extending andfiber bridging lead to a large fracture process zone (FPZ) infront of the crack tip which makes the clear location of thecrack tip impracticable [22ndash25] Furthermore the devel-opment of the large FPZ in the crack-tip front delays thefracture of specimen which consequently makes the built-inassumption no longer valid It has been well recognized thatthe use of elementary beam theory with the built-in as-sumption at the crack tip has a significant error for calcu-lating the energy release rate of fibrous composites [26] Todate there is no method available to exactly identify thecrack tip for the DCB test of fibrous composites For thisreason extensive researches have been carried out to avoidlocating the crack tip [27ndash32] Among these researches the

concept of equivalent linear elastic fracture mechanics(LEFM) was widely accepted to deal with the fracture with alarge FPZ [31] According to the concept of equivalentLEFM the increasing of compliance owing to the devel-opment of FPZ or main crack propagation with FPZ isattributed to the elastic crack which equals to the actualcrack with its FPZ [33] erefore the crack length can beestimated according to the associated compliance obtainedby experiments Furthermore the R-curve can also bemeasured using only amonotonic load-displacement record

In the present study the data reduction method was basedon the theory of equivalent LEFM Compliance calibration wasintroduced to determine the crack length e direct integralapproach was adopted to calculate the energy release rate

2 Data Reduction Scheme

Figure 2 illustrates the principle of evaluating energy releaserate based on the theory of equivalent LEFM In the sche-matic load-displacement curve (F δ) two consecutivepoints M1(δ(a1) F(a1)) and M2(δ(a2) F(a2)) corre-sponding to two different crack lengths a1 and a2 re-spectively are selected Suppose that the crack extends fromlength a1 to a2 with a small amount of propagation in-crement Δa and that the load-displacement trajectory goesfrom M1 to M2 thus the shadow area circulated by thedashed lines OM1 and OM2 and the segment of load-dis-placementM1M2 must be equal to the energy released as thecrack growth of the extension Δa [19] erefore the energyrelease rate can be calculated by

GR 1

bΔa12

P a1( 1113857δ a2( 1113857 minus12

P a2( 1113857δ a1( 11138571113876 1113877 (1)

where P and δ stand for the applied load and associateddisplacement at loading position respectively e cracklength ai(i 1 2) can be determined from the test com-pliance C(ai) (δ(ai))(P(ai)) According to the beamtheory the compliance can be calculated by [34]

C(a) a3

ELI+

6a

5GLTA (2)

where EL is the longitudinal elastic modulus GLT is the shearmodulus in LT plane ie the 12 or 13 plane as shown inFigure 1(b) I is the inertia moment of the cross section and

Long

itudi

nal d

irecti

on

Para

llel-t

o-gr

ain di

recti

on

(a)

1 (Longitudinal)

3 (Transverse)

2 (Transverse)

(b)

Figure 1 (a) Photograph of PSB (b) Principal directions of PSB




2 1 + 3ELh210GLTa2iminus 1( 1113857( 1113857

1113890 1113891

(13)

(3)








4 Test Results





M2

M1Pi

Pi+1

δi δi+10

1200

2400

Load

(N)

5 10 150δ (mm)






1~1

51212

16

L

B

H

T (2)

L (1)

R4

T (3)

1~2 mm

a0



Group Label a0(mm)

L(mm)

B(mm)

H(mm)

a0(L) Number

A

20-A

34 350

20

50 0097 340-A 4060-A 6080-A 80100-A 100

B

20-B

67 350

20

50 0191 340-B 4060-B 6080-B 80100-B 100

C

20-C

100 350

20

50 0286 340-C 4060-C 6080-C 80100-C 100

D

20-D

134 350

20

50 0383 340-D 4060-D 6080-D 80100-D 100

TransparentCOD

Microscope

Loading

(a)

F

F


DCB specimen

Loading actuator

Tensile clamp

Crack tip

T (2)L (1)

Steel rods

(b)



DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

0

300

600

900

1200

1500

1800

Load

(N)


(a)

DCB-40-ADCB-40-B

DCB-40-CDCB-40-D

0

500

1000

1500

2000

2500Lo

ad (N

)


(b)

DCB-80-ADCB-80-B

DCB-80-CDCB-80-D

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Load

(N)


(c)

DCB-100-ADCB-100-B

DCB-100-CDCB-100-D


0

600

1200

1800

2400

3000

3600

4200

4800

Load

(N)

(d)



IIII II

0

500

1000

1500

2000

2500

Load

(N)












DCB-80-CDCB-100-C

0

500

1000

1500

2000

2500

3000

3500Lo

ad (N

)


(a)


DCB-80-DDCB-100-D

0

500

1000

1500

2000

2500

Load

(N)


(b)





Fiber pull-out

(a) (b)


Fiber bridging


DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

00

05

10

15

20

25

30

35

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(a)

DCB-60-ADCB-60-B

DCB-60-CDCB-60-D

00

05

10

15

20

25

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(b)



5 Conclusion


Nomenclature





Data Availability





DCB-80-CDCB-100-C

00

05

10

15

20G R

times103 Jm

2

150 200 250100a (mm)

(a)


DCB-80-DDCB-100-D

00

05

10

15

20

25

30

G Rtimes1

03 Jm2

200 250150a (mm)

(b)




DCB-C 100

20

350

839 174040 1535 150560 2364 155080 2149 630100 2952 820

DCB-D 134

20

350

745 260040 1332 257060 2081 196080 2009 950100 2233 870


Acknowledgments


References










































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






2 1 + 3ELh210GLTa2iminus 1( 1113857( 1113857

1113890 1113891

(13)

(3)








4 Test Results





M2

M1Pi

Pi+1

δi δi+10

1200

2400

Load

(N)

5 10 150δ (mm)






1~1

51212

16

L

B

H

T (2)

L (1)

R4

T (3)

1~2 mm

a0



Group Label a0(mm)

L(mm)

B(mm)

H(mm)

a0(L) Number

A

20-A

34 350

20

50 0097 340-A 4060-A 6080-A 80100-A 100

B

20-B

67 350

20

50 0191 340-B 4060-B 6080-B 80100-B 100

C

20-C

100 350

20

50 0286 340-C 4060-C 6080-C 80100-C 100

D

20-D

134 350

20

50 0383 340-D 4060-D 6080-D 80100-D 100

TransparentCOD

Microscope

Loading

(a)

F

F


DCB specimen

Loading actuator

Tensile clamp

Crack tip

T (2)L (1)

Steel rods

(b)



DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

0

300

600

900

1200

1500

1800

Load

(N)


(a)

DCB-40-ADCB-40-B

DCB-40-CDCB-40-D

0

500

1000

1500

2000

2500Lo

ad (N

)


(b)

DCB-80-ADCB-80-B

DCB-80-CDCB-80-D

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Load

(N)


(c)

DCB-100-ADCB-100-B

DCB-100-CDCB-100-D


0

600

1200

1800

2400

3000

3600

4200

4800

Load

(N)

(d)



IIII II

0

500

1000

1500

2000

2500

Load

(N)












DCB-80-CDCB-100-C

0

500

1000

1500

2000

2500

3000

3500Lo

ad (N

)


(a)


DCB-80-DDCB-100-D

0

500

1000

1500

2000

2500

Load

(N)


(b)





Fiber pull-out

(a) (b)


Fiber bridging


DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

00

05

10

15

20

25

30

35

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(a)

DCB-60-ADCB-60-B

DCB-60-CDCB-60-D

00

05

10

15

20

25

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(b)



5 Conclusion


Nomenclature





Data Availability





DCB-80-CDCB-100-C

00

05

10

15

20G R

times103 Jm

2

150 200 250100a (mm)

(a)


DCB-80-DDCB-100-D

00

05

10

15

20

25

30

G Rtimes1

03 Jm2

200 250150a (mm)

(b)




DCB-C 100

20

350

839 174040 1535 150560 2364 155080 2149 630100 2952 820

DCB-D 134

20

350

745 260040 1332 257060 2081 196080 2009 950100 2233 870


Acknowledgments


References










































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







1~1

51212

16

L

B

H

T (2)

L (1)

R4

T (3)

1~2 mm

a0



Group Label a0(mm)

L(mm)

B(mm)

H(mm)

a0(L) Number

A

20-A

34 350

20

50 0097 340-A 4060-A 6080-A 80100-A 100

B

20-B

67 350

20

50 0191 340-B 4060-B 6080-B 80100-B 100

C

20-C

100 350

20

50 0286 340-C 4060-C 6080-C 80100-C 100

D

20-D

134 350

20

50 0383 340-D 4060-D 6080-D 80100-D 100

TransparentCOD

Microscope

Loading

(a)

F

F


DCB specimen

Loading actuator

Tensile clamp

Crack tip

T (2)L (1)

Steel rods

(b)



DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

0

300

600

900

1200

1500

1800

Load

(N)


(a)

DCB-40-ADCB-40-B

DCB-40-CDCB-40-D

0

500

1000

1500

2000

2500Lo

ad (N

)


(b)

DCB-80-ADCB-80-B

DCB-80-CDCB-80-D

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Load

(N)


(c)

DCB-100-ADCB-100-B

DCB-100-CDCB-100-D


0

600

1200

1800

2400

3000

3600

4200

4800

Load

(N)

(d)



IIII II

0

500

1000

1500

2000

2500

Load

(N)












DCB-80-CDCB-100-C

0

500

1000

1500

2000

2500

3000

3500Lo

ad (N

)


(a)


DCB-80-DDCB-100-D

0

500

1000

1500

2000

2500

Load

(N)


(b)





Fiber pull-out

(a) (b)


Fiber bridging


DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

00

05

10

15

20

25

30

35

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(a)

DCB-60-ADCB-60-B

DCB-60-CDCB-60-D

00

05

10

15

20

25

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(b)



5 Conclusion


Nomenclature





Data Availability





DCB-80-CDCB-100-C

00

05

10

15

20G R

times103 Jm

2

150 200 250100a (mm)

(a)


DCB-80-DDCB-100-D

00

05

10

15

20

25

30

G Rtimes1

03 Jm2

200 250150a (mm)

(b)




DCB-C 100

20

350

839 174040 1535 150560 2364 155080 2149 630100 2952 820

DCB-D 134

20

350

745 260040 1332 257060 2081 196080 2009 950100 2233 870


Acknowledgments


References










































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

0

300

600

900

1200

1500

1800

Load

(N)


(a)

DCB-40-ADCB-40-B

DCB-40-CDCB-40-D

0

500

1000

1500

2000

2500Lo

ad (N

)


(b)

DCB-80-ADCB-80-B

DCB-80-CDCB-80-D

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Load

(N)


(c)

DCB-100-ADCB-100-B

DCB-100-CDCB-100-D


0

600

1200

1800

2400

3000

3600

4200

4800

Load

(N)

(d)



IIII II

0

500

1000

1500

2000

2500

Load

(N)












DCB-80-CDCB-100-C

0

500

1000

1500

2000

2500

3000

3500Lo

ad (N

)


(a)


DCB-80-DDCB-100-D

0

500

1000

1500

2000

2500

Load

(N)


(b)





Fiber pull-out

(a) (b)


Fiber bridging


DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

00

05

10

15

20

25

30

35

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(a)

DCB-60-ADCB-60-B

DCB-60-CDCB-60-D

00

05

10

15

20

25

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(b)



5 Conclusion


Nomenclature





Data Availability





DCB-80-CDCB-100-C

00

05

10

15

20G R

times103 Jm

2

150 200 250100a (mm)

(a)


DCB-80-DDCB-100-D

00

05

10

15

20

25

30

G Rtimes1

03 Jm2

200 250150a (mm)

(b)




DCB-C 100

20

350

839 174040 1535 150560 2364 155080 2149 630100 2952 820

DCB-D 134

20

350

745 260040 1332 257060 2081 196080 2009 950100 2233 870


Acknowledgments


References










































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls












DCB-80-CDCB-100-C

0

500

1000

1500

2000

2500

3000

3500Lo

ad (N

)


(a)


DCB-80-DDCB-100-D

0

500

1000

1500

2000

2500

Load

(N)


(b)





Fiber pull-out

(a) (b)


Fiber bridging


DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

00

05

10

15

20

25

30

35

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(a)

DCB-60-ADCB-60-B

DCB-60-CDCB-60-D

00

05

10

15

20

25

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(b)



5 Conclusion


Nomenclature





Data Availability





DCB-80-CDCB-100-C

00

05

10

15

20G R

times103 Jm

2

150 200 250100a (mm)

(a)


DCB-80-DDCB-100-D

00

05

10

15

20

25

30

G Rtimes1

03 Jm2

200 250150a (mm)

(b)




DCB-C 100

20

350

839 174040 1535 150560 2364 155080 2149 630100 2952 820

DCB-D 134

20

350

745 260040 1332 257060 2081 196080 2009 950100 2233 870


Acknowledgments


References










































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Fiber pull-out

(a) (b)


Fiber bridging


DCB-20-ADCB-20-B

DCB-20-CDCB-20-D

00

05

10

15

20

25

30

35

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(a)

DCB-60-ADCB-60-B

DCB-60-CDCB-60-D

00

05

10

15

20

25

G Rtimes1

03 Jm2

100 150 200 25050a (mm)

(b)



5 Conclusion


Nomenclature





Data Availability





DCB-80-CDCB-100-C

00

05

10

15

20G R

times103 Jm

2

150 200 250100a (mm)

(a)


DCB-80-DDCB-100-D

00

05

10

15

20

25

30

G Rtimes1

03 Jm2

200 250150a (mm)

(b)




DCB-C 100

20

350

839 174040 1535 150560 2364 155080 2149 630100 2952 820

DCB-D 134

20

350

745 260040 1332 257060 2081 196080 2009 950100 2233 870


Acknowledgments


References










































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




5 Conclusion


Nomenclature





Data Availability





DCB-80-CDCB-100-C

00

05

10

15

20G R

times103 Jm

2

150 200 250100a (mm)

(a)


DCB-80-DDCB-100-D

00

05

10

15

20

25

30

G Rtimes1

03 Jm2

200 250150a (mm)

(b)




DCB-C 100

20

350

839 174040 1535 150560 2364 155080 2149 630100 2952 820

DCB-D 134

20

350

745 260040 1332 257060 2081 196080 2009 950100 2233 870


Acknowledgments


References










































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




Acknowledgments


References










































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls













Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




fracture of parallel strand bamboo composite under mode i...

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