8
Effect of geometric factor, winding angle and pre-crack angle on quasi-static crushing behavior of filament wound CFRP cylinder Xiaolong Jia a , Gang Chen a , Yunhua Yu a , Gang Li b , Jinming Zhu a , Xiangpeng Luo b , Chenghong Duan b , Xiaoping Yang a,, David Hui c,a State Key Laboratory of Organic–Inorganic Composites, College of Materials Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, PR China b College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, PR China c Department of Mechanical Engineering, University of New Orleans, New Orleans, LA 70148, USA article info Article history: Received 29 April 2012 Received in revised form 11 September 2012 Accepted 12 September 2012 Available online 27 September 2012 Keywords: A. Carbon fiber B. Buckling B. Fracture E. Filament winding abstract Effect of geometric factor, winding angle and pre-crack angle on quasi-static crushing behavior of fila- ment wound CFRP cylinder was systematically evaluated in details. The cylinder with end reinforcing layer had higher compressive properties and sequentially showed brittle fracturing mode, local buckling mode and transverse shearing mode with winding angles increasing, respectively. Additionally, crack propagation initiated by pre-crack and subsequent failure in the cylinder were strongly dependent of pre-crack angle due to deflection and penetration competition of crack evolution. The simulated and experimental results of loads–displacement curve, crushing load and failure mode were compared to elu- cidate quasi-static crushing behavior of the cylinder. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction With potential advantages over cylinders made of conventional materials, such as high strength, light weight and resistance to cor- rosion, carbon fiber reinforced plastics (CFRPs) cylinders have been increasingly used for a variety of applications, including chemical plants and high pressure containers [1–3]. The filament winding process was an efficient technique, commonly used in the mass production of high performance CFRP cylinders. The properties and performance of the filament wound products like cylinders were mainly affected by geometric and winding factors such as end reinforcing layer and winding angle [3–5]. The practical appli- cations of CFRP cylinders required adequate assessment of their response under severe conditions like high compression loading. Specifically, crushing failure was of much interest, which often limited engineering applications of CFRP cylinders due to the lower compressive strength relative to tensile strength. However, crush- ing failure of filament wound CFRP cylinders was inherently com- plex. At present, there was a large uncertainty of understanding about effect of end reinforcing layer and winding angle on crushing failure behavior of these cylinders. On the other hand, many fundamental researches reported that the crushing failure for cylinders occurred initially from the cracks existing in their structures [6–10]. These cracks have been viewed in different forms, orientations, locations, size and types, for in- stance, through thickness cracks, from single or double edge cracks and surface cracks [6,7]. For glass/epoxy filament wound pipes, the effect of a surface cracks on the tensile strength and fatigue behav- iors under internal pressure has been investigated by Tarakcioglu and Samanci et al. [7–10], as well as the effect of surface crack an- gle on the tensile strength has been studied by Arikan [6]. Among these cracks, through thickness crack problems resulted in more serious failures of the cylinders than other crack problems. More- over, practically applying CFRP cylinders required a complete understanding of through thickness cracks, especially with respect to the effect of their angle on crushing failure behavior of the cylinders. Noticeably, finite element model was an efficient and economic method for simulating the crushing failure mode of the cylinders. With those numeral simulations, the complicated crushing behav- ior of the cylinders was better understood by analyzing the dis- crepancy between the experimental and predicted results. However, only a few literatures reported the numerical studies on the axial crushing response of CFRP cylinders up to now. For in- stance, Mamalis et al. [11] used a three-layer finite element model to predict the axial crushing response of carbon woven fabric rein- forced epoxy square cylinders without cracks. McGregor et al. [12] reported a continuum damage mechanics based model to simulate failure propagation of braided composite cylinders without cracks 1359-8368/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2012.09.060 Corresponding authors. Fax: +86 10 64412084. E-mail addresses: [email protected] (X. Yang), [email protected] (D. Hui). Composites: Part B 45 (2013) 1336–1343 Contents lists available at SciVerse ScienceDirect Composites: Part B journal homepage: www.elsevier.com/locate/compositesb

Effect of geometric factor, winding angle and pre-crack ...site.icce-nano.org/Clients/iccenanoorg/effect of geometric factor... · Effect of geometric factor, winding angle and pre-crack

  • Upload
    others

  • View
    2

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Effect of geometric factor, winding angle and pre-crack ...site.icce-nano.org/Clients/iccenanoorg/effect of geometric factor... · Effect of geometric factor, winding angle and pre-crack

Composites: Part B 45 (2013) 1336–1343

Contents lists available at SciVerse ScienceDirect

Composites: Part B

journal homepage: www.elsevier .com/locate /composi tesb

Effect of geometric factor, winding angle and pre-crack angle onquasi-static crushing behavior of filament wound CFRP cylinder

Xiaolong Jia a, Gang Chen a, Yunhua Yu a, Gang Li b, Jinming Zhu a, Xiangpeng Luo b, Chenghong Duan b,Xiaoping Yang a,⇑, David Hui c,⇑a State Key Laboratory of Organic–Inorganic Composites, College of Materials Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, PR Chinab College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, PR Chinac Department of Mechanical Engineering, University of New Orleans, New Orleans, LA 70148, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 29 April 2012Received in revised form 11 September2012Accepted 12 September 2012Available online 27 September 2012

Keywords:A. Carbon fiberB. BucklingB. FractureE. Filament winding

1359-8368/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.compositesb.2012.09.060

⇑ Corresponding authors. Fax: +86 10 64412084.E-mail addresses: [email protected] (X. Ya

Effect of geometric factor, winding angle and pre-crack angle on quasi-static crushing behavior of fila-ment wound CFRP cylinder was systematically evaluated in details. The cylinder with end reinforcinglayer had higher compressive properties and sequentially showed brittle fracturing mode, local bucklingmode and transverse shearing mode with winding angles increasing, respectively. Additionally, crackpropagation initiated by pre-crack and subsequent failure in the cylinder were strongly dependent ofpre-crack angle due to deflection and penetration competition of crack evolution. The simulated andexperimental results of loads–displacement curve, crushing load and failure mode were compared to elu-cidate quasi-static crushing behavior of the cylinder.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

With potential advantages over cylinders made of conventionalmaterials, such as high strength, light weight and resistance to cor-rosion, carbon fiber reinforced plastics (CFRPs) cylinders have beenincreasingly used for a variety of applications, including chemicalplants and high pressure containers [1–3]. The filament windingprocess was an efficient technique, commonly used in the massproduction of high performance CFRP cylinders. The propertiesand performance of the filament wound products like cylinderswere mainly affected by geometric and winding factors such asend reinforcing layer and winding angle [3–5]. The practical appli-cations of CFRP cylinders required adequate assessment of theirresponse under severe conditions like high compression loading.Specifically, crushing failure was of much interest, which oftenlimited engineering applications of CFRP cylinders due to the lowercompressive strength relative to tensile strength. However, crush-ing failure of filament wound CFRP cylinders was inherently com-plex. At present, there was a large uncertainty of understandingabout effect of end reinforcing layer and winding angle on crushingfailure behavior of these cylinders.

On the other hand, many fundamental researches reported thatthe crushing failure for cylinders occurred initially from the cracks

ll rights reserved.

ng), [email protected] (D. Hui).

existing in their structures [6–10]. These cracks have been viewedin different forms, orientations, locations, size and types, for in-stance, through thickness cracks, from single or double edge cracksand surface cracks [6,7]. For glass/epoxy filament wound pipes, theeffect of a surface cracks on the tensile strength and fatigue behav-iors under internal pressure has been investigated by Tarakciogluand Samanci et al. [7–10], as well as the effect of surface crack an-gle on the tensile strength has been studied by Arikan [6]. Amongthese cracks, through thickness crack problems resulted in moreserious failures of the cylinders than other crack problems. More-over, practically applying CFRP cylinders required a completeunderstanding of through thickness cracks, especially with respectto the effect of their angle on crushing failure behavior of thecylinders.

Noticeably, finite element model was an efficient and economicmethod for simulating the crushing failure mode of the cylinders.With those numeral simulations, the complicated crushing behav-ior of the cylinders was better understood by analyzing the dis-crepancy between the experimental and predicted results.However, only a few literatures reported the numerical studieson the axial crushing response of CFRP cylinders up to now. For in-stance, Mamalis et al. [11] used a three-layer finite element modelto predict the axial crushing response of carbon woven fabric rein-forced epoxy square cylinders without cracks. McGregor et al. [12]reported a continuum damage mechanics based model to simulatefailure propagation of braided composite cylinders without cracks

Page 2: Effect of geometric factor, winding angle and pre-crack ...site.icce-nano.org/Clients/iccenanoorg/effect of geometric factor... · Effect of geometric factor, winding angle and pre-crack

X. Jia et al. / Composites: Part B 45 (2013) 1336–1343 1337

under axial compression. However, practical test results revealedthat the crushing mechanism was far more complex for thecylinders with through thickness cracks than for conventionalmaterials, including matrix cracking, fiber–matrix debonding,delamination and fiber breakage. These reported numerical modelsin the literatures could hardly simulate crushing failure mode ofthe cylinders with through thickness cracks. Therefore, the vitalissue of simulating crushing failure mode of such cylinders wasto establish an effective numerical model.

To bridge this gap, the effect of geometric factor, winding angleand through thickness crack (which were pre-made in the cylinderand named pre-crack in this work) angle on crushing behavior offilament wound CFRP cylinder under quasi-static compressioncondition were investigated in details. To this end, (i) the effectof geometric factor such as end reinforcing layer on compressiveproperties of CFRP cylinders was discussed; (ii) the variation ofcompressive strengths of CFRP cylinders with various windingangles was evaluated, and the related crushing mechanism andcrushing efficiency were analyzed on the basis of optical andSEM observations on fractured CFRP cylinders with various wind-ing angles; (iii) and the effect of pre-crack angle on compressiveproperties of CFRP cylinders were also studied, as well as thenumeral simulation based on Chang–Chang failure criteria wasperformed and compared with the experimental results to eluci-date the effect of pre-crack angle on the crushing behavior of thecylinders.

2. Experimental section

2.1. Materials

The resin matrix, diglycidyl ester of aliphatic cyclo (DGEAC)type epoxy resin (epoxy value, 0.85) was supplied by Tianjin Jin-dong Chem, China. The diluter, diglycidyl ether of butanediol(epoxy value, 0.65–0.75) was synthesized by authors to reducethe viscosity of DGEAC resin. The harders, DDM and DETDA (74–80% 3,5-diethyltoluene-2,4-diamine and 20–26% 3,5-diethyltolu-ene-2,6-diamine) were obtained from Tianjin Synthetic MaterialResearch Institute, China and from Lonza, Switzerland, respec-tively. The reinforcement, T700 carbon fibers (CFs) were purchasedfrom Toray Co., Japan. T700 CFs possess a diameter of 7 lm, a ten-sile strength of 4.9 GPa, a modulus of 240 GPa and an elongation of2.1%.

2.2. Sample preparation

The epoxy resin system was obtained by uniformly mixingDGEAC resin, DGEB, DDM, DETDA and 2,4-EMI with a weight ratioof 100:20:24:19:1 at 40 �C, as following our previous works [13].Filament wound CFRP cylinders with the winding angles of 20�,40�, 60� and 90� were prepared with four CF layers by the filamentwinding machine (MAW 20-LS1-6, MIKROSAM Co.) after a bundleof CFs were coated with the epoxy resin systems. These cylinderswere cured at 80 �C/1 h + 120 �C/2 h + 150 �C/3 h on a mandrel ina slow motion rotary oven. After pulling out the mandrel, theobtained cylinders with dimensions of 65 mm inside diameterand 1 mm average thickness were cut into 130 mm length,respectively.

The end reinforcing layers with dimensions of 72 mm widthand 2.25 mm average thickness were also prepared on theobtained cylinders with the winding machine. Then, the final cylin-ders with the end reinforcing layers were obtained by re-curing theresulted cylinders at the aforementioned conditions. In addition,

the 15 mm pre-cracks with angles of 0�, 20�, 40�, 60�, 80� and90� relative to the cylinder axis were carved on the final cylinders.

2.3. Characterizations

2.3.1. Compression propertiesThe axial compression tests of specimen cylinders were per-

formed between two flat platens on a testing machine (Instron1121) at a crosshead speed of 0.5 mm/min. Load platens were setparallel to each other before testing and all cylinders were com-pressed until limited crush. The final values were averages of fivemeasurements.

The compressive strengths of the cylinders were calculated bythe following equation:

rc ¼4P

pðD2 � d2Þ

where P is the crush load, D and d are the outside and inside diam-eters of the cylinders, respectively.

The compressive modulus of the cylinders were obtained fromthe following equation:

E ¼ F=Ae

where F is the load along the longitudinal axis of the cylinders, A isthe transverse cross-section area of the cylinders and e is the max-imum strain along the longitudinal axis of the cylinders.

Stroke efficiency of the compression on the cylinders was calcu-lated from the following equation [14]:

SE ¼ U�=L

where U� is the stroke length that is the distance the cylinder iscrushed before the cylinder ‘‘bottoms out’’ and the load sharply in-creases. L is the length of the cylinders.

2.3.2. Morphology observationMorphologies of fractured surfaces of CFRP cylinders were

observed by scanning electron microscopy (S4700, HITACHI Co.,Tokyo, Japan). The composite specimens of the cylinders werecoated with a thin layer of a gold alloy.

Morphologies of the debris of fractured CFRP cylinders wereobserved by optical microscopy (CK � 41, OLYMPUS Co., Tokyo,Japan). The debris of the composite specimens were placed onthe glass slide during optical observation.

2.3.3. Modeling of crushing behaviorFailure criteria were only intended as a useful tool for material

characterization and estimating the load carrying capacity of astructure. The failure mode of CFRP cylinder was predicted withMaterial type 54 in LS-DYNA, using the Chang–Chang failure crite-rion. This criterion was given as follows [15–17]:For the tensilelongitudinal direction,

rxx > 0 then e2f ¼

rxx

Xt

� �2

þ brxy

Sc

� �� 1

P 0 failed

< 0 elastic

8>><>>:

If failed, then Ex ¼ Ey ¼ Gxy ¼ vyx ¼ vxy ¼ 0.For the compressive longitudinal direction,

rxx < 0 then e2c ¼

rxx

Xc

� �2

� 1

P 0 failed

< 0 elastic

8>><>>:

If failed, then Ex ¼ vyx ¼ vxy ¼ 0; for the tensile transverse direction,

Page 3: Effect of geometric factor, winding angle and pre-crack ...site.icce-nano.org/Clients/iccenanoorg/effect of geometric factor... · Effect of geometric factor, winding angle and pre-crack

Fig. 2. Optical images of fractured CFRP cylinders (a) without and (b) with endreinforcing layers.

Fig. 3. Effect of winding angle on compressive strength and modulus of CFRPcylinders.

1338 X. Jia et al. / Composites: Part B 45 (2013) 1336–1343

ryy > 0 then e2m ¼

ryy

Yt

� �2

þ rxy

Sc

� �2

� 1P 0 failed< 0 elastic

8><>:

If failed, then Ex ¼ vyx ¼ Gxy ¼ 0; and for the compressive transversedirection,

ryy < 0 then e2d ¼

ryy

2Sc

� �2

þ Yc

2Sc

� �2

� 1

" #ryy

Ycþ rxy

Sc

� �2

� 1P 0 failed< 0 elastic

If failed, then Ex ¼ Ey ¼ Gxy ¼ vyx ¼ vxy ¼ 0; where rij is stress in the(ij) direction, Ei is Young’s modulus in the (i) direction, Gij is in planeshear modulus in the (ij) direction, tij is Poisson’s ratio in the (ij)direction, S is shear strength and X, Y is strength, respectively.

3. Results and discussion

3.1. Effect of geometric factors

Fig. 1 shows the effect of end reinforcing layer on compressivestrength and modulus of CFRP cylinders with winding angle of60� (without cracks). The compressive strength and modulus weremuch higher for CFRP cylinders with end reinforcing layer thanthose without end reinforcing layer, which was strongly relatedwith their failure mode. Fig. 2 shows optical images of the final fail-ure of CFRP cylinders with and without end reinforcing layers(without cracks). As shown in Fig. 2, the failure of CFRP cylinderswith end reinforcing layer took place with the crack propagationin the central circumference as a result of load transfer along thelongitudinal axis, while the failure of those without end reinforcinglayers occurred at both ends in the form of fiber and matrix break-age due to large transverse stress and strain at both ends of the cyl-inders. Actually, it was found that adding end reinforcing layerswere beneficial to enhancing the strength efficiency of the fibersand corresponding mechanical properties of the cylinders. There-fore, CFRP cylinders with end reinforcing layers were used in thefollowing parts of this study.

3.2. Effect of winding angle

3.2.1. Compressive propertiesFig. 3 shows the effect of winding angle on the compressive

strength and modulus of CFRP cylinders (without cracks). Withwinding angle increasing, the compressive strength generallyexhibited the decreasing trend as shown in Fig. 3, while thestrength value was minimum at the winding angle of 40�, whichagreed with similar studies on glass fiber reinforced pipes by other

Fig. 1. Effect of end reinforcing layer on compressive strength and modulus of CFRPcylinders with winding angle of 60�: (a) without end reinforcing layers and (b) withend reinforcing layers.

researchers [18–20]. The decreasing trend was obviously attrib-uted to the reduction of load bearing by the fiber and the resultantenhancement of longitudinal deformation because of the decreas-ing of fiber alignment along the longitudinal axis with windingangle increasing. However, the minimum value of compressivestrength was related with the local buckling crushing mode ofthe cylinder with the winding angle of 40�, which would be dis-cussed in details in the following parts of this study. Furthermore,the compressive modulus of the cylinders linearly decreased withthe winding angles as shown in Fig. 3, which was consistent withvariation trend of compressive strength and also resulted fromthe decreasing of the fiber alignment along the longitudinal axis.

3.2.2. Crushing mechanismFig. 4 shows optical images of fractured CFRP cylinders with

various winding angles (without cracks). It could be seen that themacro-cracks propagated just along the direction of winding an-gles for 20�, 60� and 80�, implying that the cracks perpendicularto the fiber direction were inhibited effectively by the fibers.However, for the cylinder with winding angle of 40�, the failureoccurred along with the plastic deformation in the central circum-ference and no fractured fibers were observed. Thus, the morphol-ogies of fracturing cracks of these cylinders were quite different,which was strongly related with the crushing mechanisms atdifferent winding angles. According to the literatures [21,22], thecrushing behaviors of the continuous fiber reinforced composites

Page 4: Effect of geometric factor, winding angle and pre-crack ...site.icce-nano.org/Clients/iccenanoorg/effect of geometric factor... · Effect of geometric factor, winding angle and pre-crack

Fig. 4. Optical images of fractured CFRP cylinders with winding angles of (a) 20�, (b) 40�, (c) 60� and (d) 80�. Images of (a1), (b1), (c1) and (d1) show the corresponding high-resolution optical images of the cracks, respectively.

Fig. 5. SEM images of fractured surfaces of CFRP cylinders with winding angles of (a) 20�, (b) 40�, (c) 60� and (d) 80�.

X. Jia et al. / Composites: Part B 45 (2013) 1336–1343 1339

were dominated by four main mechanisms: (1) transverse shear-ing, (2) lamina bending, (3) local buckling and (4) brittle fracturing.Actually, the brittle fracturing was normally considered as a mixedmode of the transverse shearing and lamina bending modes.

Fig. 5 shows SEM images of fractured surfaces of CFRP cylinderswith various winding angles (without cracks). At the winding angleof 20�, the fractured surfaces were scalloped and a large number ofinterlaminar and longitudinal cracks were found as shown inFigs. 4a and 5a, which were the characteristics of brittle fracturingmode [21]. At the higher angles of 60� and 80�, the wedge-shaped

cross-section of the laminate with interlaminar and longitudinalcracks were clearly observed from Fig. 5c and d, which manifestedthe typical feature of transverse shearing crushing mode [22]. Thelamina bundles which consisted of a single lamina or multiplelaminae were resulted from interlaminar and longitudinal cracks.It was found that these bundles behaved as integrated elementto bear the load and the interlaminar crack propagation endedafter the edges of these bundles were fractured, finally producinga wedge-shaped cross-section. According to the literatures [21],the number, location, and length of the cracks were dependent of

Page 5: Effect of geometric factor, winding angle and pre-crack ...site.icce-nano.org/Clients/iccenanoorg/effect of geometric factor... · Effect of geometric factor, winding angle and pre-crack

Fig. 6. Effect of winding angle on stroke efficiency and crack length of CFRPcylinders.

1340 X. Jia et al. / Composites: Part B 45 (2013) 1336–1343

the structure of the specimen and the basic properties of materialconstituents.

However, the crushing behavior was much different at thewinding angle of 40� compared to other angles. As shown inFig. 4b, the plastic deformation of the cylinder occurred in the re-gion of a buckle. The deformation of the material between adjacentbuckle nodes showed elastic characteristics, while the plasticdeformation of the material at a buckle node was not uniformlydistributed through the thickness of the cylinder. On the convexand concave sides of the buckle node, the material was in a stateof tension and compression, respectively. It was worth noting thatthe obvious failure associated with fiber breakage was not ob-served from Figs. 4b and 5b. All these features implied that thecrushing behavior of the cylinder with winding angle of 40� waspredominated by the local buckling crushing mode. This modewas attributed to the smaller interlaminar stresses relative to thestrength of the matrix when the winding angle was close to 45�

Fig. 7. Optical microscope images of the debris of fractured CFRP cylinders with wind

[18,19]. At this condition, the epoxy matrix with the higher failurestrain than the carbon fiber exhibited plastic deformation underthe load [23]. The interlaminar cracks were reduced or prohibitedby the matrix with higher failure strain during the compression.Thus, the interlaminar cracks were just generated at the buckleswhere the local interlaminar cracks did not propagated to adjacentbuckles. Therefore, it concluded that the crushing behavior of thecylinder was dominated by brittle fracturing mode at low windingangle of 20� and by transverse shearing crushing mode at highwinding angles from 60� to 80�, while it was controlled by localbuckling mode at moderate winding angle of 40�.

3.2.3. Crushing efficiencyThe crushing efficiency of composite cylinders was a measure of

the effectiveness of energy absorption during crushing, which alsocould provide some information about the crushing mode of thecylinders. Practically, stroke efficiency along with the debris sizeand crack length were often used to measure crushing efficiency[24,25]. Stroke efficiency was obtained by dividing the strokelength with the original length of the cylinder. Usually, the higherstroke efficiency along with the smaller the debris size and cracklength indicated the more efficient crushing process. Fig. 6 showsthe effect of winding angle on the stroke efficiency and cracklength of CFRP cylinders and Fig. 7 shows optical microscopeimages of the debris of fractured CFRP cylinders with various wind-ing angles after the test of stroke efficiency. With winding angleincreasing, the stroke efficiency increased distinctively as shownin Fig. 6, while the debris size and crack length showed the oppo-site trend as shown in Figs. 6 and 7, which indicated that the en-ergy absorption was effectively enhanced at the higher windingangles. In addition, as observed from Fig. 7, the crushing debris ex-isted in form of pieces with large dimension at the low winding an-gle for the brittle fracturing mode, whereas the debris size rangedfrom lengths equal to lamina bundle thickness to near powders atthe high winding angles for the transverse shearing mode, whichmeant that more materials were destroyed in the crushing process.At the moderate winding angle for the local buckling mode, the

ing angles of (a) 20�, (b) 40�, (c) 60� and (d) 80� after the test of stroke efficiency.

Page 6: Effect of geometric factor, winding angle and pre-crack ...site.icce-nano.org/Clients/iccenanoorg/effect of geometric factor... · Effect of geometric factor, winding angle and pre-crack

Fig. 8. Effect of pre-crack angle on compressive strength and modulus of CFRPcylinders.

X. Jia et al. / Composites: Part B 45 (2013) 1336–1343 1341

debris was the mixture of small powders and large pieces. Coupledwith the aforementioned crushing mechanism, it concluded thatthe transverse shearing mode showed highest crushing efficiency,sequentially followed by the local buckling mode and brittle frac-turing mode, respectively.

3.3. Effect of pre-crack angle

3.3.1. Compressive propertiesWith the aims of better understanding crushing behavior of the

cylinder under compression loads, the pre-cracks (through thick-ness cracks) were caved in the cylinder and used as the crushinginitiator. Meanwhile, the performance of cylinders with windingangle close to 60� was much of interest to many researchers[6,8,9]. Thus, the effect of pre-crack angle on crushing behaviorof the cylinders with winding angle of 60� were investigated in thispart of our study in order to expose the relationship of crushingmechanism with the structural defects of the cylinders. Fig. 8shows the effect of pre-crack angle on compressive strength andmodulus of CFRP cylinders. As expected, the strength and modulusvalues of the cylinders with pre-cracks were lower than those ofthe cylinders without pre-cracks. With the pre-crack angle increas-ing, the compressive strength and modulus initially decreased tothe minimum values when the pre-crack angle equaled or closeto the winding angle, and subsequently increased. This variationtrend was attributed to the decrease and increase of depression

Fig. 9. (a) Experimental and simulated loads–displacement curves of CFRP cylinders witcylinders with various pre-crack angles.

effect of the fibers on the crack propagation in the cylinder withthe included angle variation between pre-crack angle and windingangle. Specifically, the cracks initiated from the pre-crack propa-gated more easily in the condition of the pre-crack angle parallelto the winding angle.

3.3.2. Modeling of crushing behaviorFig. 9 shows experimental and simulated loads–displacement

curves and crushing loads of CFRP cylinders. It was clearly seenfrom Fig. 9a that the simulated loads–displacement curve corre-lated well with the experimental result for CFRP cylinders withpre-crack angle of 60�. The loads reached initial peak values alongwith the failure of the cylinders and abruptly dropped to level-offvalues due to the formation of the crush zone in the cylinders.Actually, for CFRP cylinders with various pre-crack angles, experi-mental and simulated loads–displacement curves also correlatedwell and showed the similar trend. Additionally, conforming tothe variation trend of compressive strength and modulus shownin Fig. 8, the crushing loads decreased distinctively with thepre-crack angle increasing up to the angle of 60�, and subsequentlyincreased as shown in Fig. 9b.

Fig. 10 shows experimental failure images and simulated com-pression strain distribution of CFRP cylinders with various pre-crack angles. The materials failed when the maximum principalcompression strain in a material element exceeded the uniaxialcompression strength of materials. As shown in simulated com-pression strain distribution in Fig. 10, the cylinders would be dam-aged from the location with maximum compression strain.Noticeably, the simulated failure model generally conformed toexperimental crushing behaviors for CFRP cylinders with variouspre-crack angles, which proved that the Chang–Chang failure crite-ria could accurately represent the quasi-static crushing failure oflaminates in the cylinder. However, the crushing behavior of thecylinders with various pre-crack angles was quite different, judg-ing from the experimental failure images and simulated compres-sion strain distribution.

At the pre-crack angle of 60�, the interfacial adhesion surround-ing the pre-crack was poor since the pre-crack angle was parallel tothe winding angle and the region formed at the interface betweenthe fiber and the matrix at the location of the pre-crack was max-imum. As shown in Fig. 10d, it was noted that the significant stressconcentration clearly occurred in the circumferential area close tothe pre-crack in the simulated model due to the circumferentialtension during crush, resulting in the crack propagation of the cyl-inder, which was quite consistent with the observed experimentalfailure mode. At this case, the pre-crack acted as the crack initiator

h pre-crack angle of 60� and (b) experimental and simulated crushing loads of CFRP

Page 7: Effect of geometric factor, winding angle and pre-crack ...site.icce-nano.org/Clients/iccenanoorg/effect of geometric factor... · Effect of geometric factor, winding angle and pre-crack

Fig. 10. Experimental failure images and simulated compression strain distribution of CFRP cylinders with pre-crack angles of (a) 0�, (b) 20�, (c) 40�, (d) 60�, (e) 80�, and (f)90�.

1342 X. Jia et al. / Composites: Part B 45 (2013) 1336–1343

and resulted in the final fracture of the cylinder under lower loads.When the cracks in the matrix grew and reached the interface, thecrack deflection occurred along the interface and led to the delam-ination of the interface. According to the literatures [26,27], thecrack propagation at the interface of composites was characterizedby two competing effects of crack evolution: deflection and pene-tration. Thus, the crack propagation was predominated by deflec-tion effect for the cylinder with pre-crack angle of 60�, and thefailure band was formed by increasing delamination. Followingthe band separation, the failure ended with sudden seepage inthe crack zone.

At the lower pre-crack angle such as 0�, the failure of the cylin-der was not initiated by the pre-crack as shown in Fig. 10a. Thiswas because the fracture region formed at the interface at the loca-tion of the pre-crack was small when the pre-crack angle wasmuch different from winding angle. At this case, the fracture ofthe cylinder occurred randomly at the site of the biggest defectsin the matrix under the higher loads. With the loads furtherincreasing, the cracks grew in the matrix and penetrated the fibersat the interface, showing the brittle fracture perpendicular to theload direction. As the pre-crack angle increased to 90�, the fractureregion formed at the interface around the pre-crack was reducedand the interfacial adhesion surrounding the pre-crack was strongdue to the relatively smaller deviation between pre-crack angleand winding angle. The cracks were initiated by the pre-crackand the fracture of the cylinder started from the matrix at theend of the pre-crack under lower loads. When the cracks in the ma-trix grew and reached the interface, the deflection effect competedwith the penetration effect, thus making that the fracture synchro-nously occurred in the directions parallel to the fiber alignmentand perpendicular to load direction as shown in Fig. 10f.

4. Conclusions

The CFRP cylinder with end reinforcing layer showed highercompressive properties along with failure mode of crack propagat-ing in its central circumference. With winding angle increasing, thecompressive strength, compressive modulus and crack length ofthe cylinder generally exhibited the decreasing trend, whereasthe crushing efficiency showed the opposite trend. At the lowerwinding angle of 20�, the cylinder showed the brittle fracturingmode, whereas the cylinder showed transverse shearing crushingmode at the higher winding angles of 60� and 80�. Particularly,the crushing behavior of the cylinder was predominated by the lo-cal buckling crushing mode at the moderate angle of 40�. Besides,with pre-crack angle increasing, the compressive strength andmodulus of the cylinder initially decreased to the minimum valueswhen the pre-crack angle equaled or close to the winding angle,and subsequently increased. Moreover, the crack propagation initi-ated by pre-crack and the fracture region formed at the interface inthe cylinder were strongly dependent of pre-crack angle as a resultof the competition between deflection effect and penetration effectof crack evolution. The simulated loads–displacement curve,crushing load and failure mode correlated well with the experi-mental results, indicating that the Chang–Chang failure criteriaused in this study was effective in representing the quasi-staticcrushing behavior of CFRP cylinder.

Acknowledgement

The authors are very pleased to acknowledge financial supportfrom the National High Technology Research and DevelopmentProgram of China (Grant No. 2012AA03A203).

Page 8: Effect of geometric factor, winding angle and pre-crack ...site.icce-nano.org/Clients/iccenanoorg/effect of geometric factor... · Effect of geometric factor, winding angle and pre-crack

X. Jia et al. / Composites: Part B 45 (2013) 1336–1343 1343

References

[1] Hwang TK, Hong CS, Kim CG. Probabilistic deformation and strengthprediction for a filament wound pressure vessel. Composites Part B 2003;34:481–97.

[2] Kobayashi S. Effect of autofrettage on durability of CFRP composite cylinderssubjected to out-of-plane loading. Composites Part B 2012;43(4):1720–6.

[3] Morozov EV. The effect of filament winding mosaic patterns on the strength ofthin-walled composite shells. Compos Struct 2006;76(1/2):123–9.

[4] Rousseau J, Perreux D, Verdietre N. The influence of winding patterns on thedamage behaviour of filament-wound pipes. Compos Sci Technol 1999;59(9):1439–49.

[5] Spencer B, Hull D. Effect of winding angle on the failure of filament woundpipe. Composites 1978;9:263–70.

[6] Arikan H. Failure analysis of (±55) filament wound composite pipes with aninclined surface crack under static internal pressure. Compos Struct2010;92:182–7.

[7] Samanci A, Tarakçioglu N, Akdemir A. Fatigue failure analysis of surface-cracked (±45�)3 filament-wound GRP pipes under internal pressure. J ComposMater 2011;46:1041–50.

[8] Tarakcioglu N, Samanci A, Arikan H. The fatigue behavior of (±55) filamentwound GRP pipes with a surface crack under internal pressure. Compos Struct2007;80:207–11.

[9] Tarakcioglu N, Gemi L, Yapici A. Fatigue failure behavior of glass/epoxy ±55filament wound pipes under internal pressure. Compos Sci Technol 2005;65:703–8.

[10] Samanci A, Avci A, Tarakcioglu N, Sahin OS. Fatigue crack growth of filamentwound GRP pipes with a surface crack under cyclic internal pressure. J MaterSci 2008;43:5569–73 [2007;38:1192–9].

[11] Mamalis AG, Manolakos DE, Ioannidis MB. The static and dynamic axialcollapse of CFRP square tubes: finite element modelling. Compos Struct 2006;74:213–25.

[12] McGregor CJ, Vaziri R, Poursartip A. Simulation of progressive damagedevelopment in braided composite tubes under axial compression.Composites Part A 2007;38(11):2247–59.

[13] Chen WM, Yu YH, Li P, Wang CZ, Yang XP. Effect of new epoxy matrix for T800carbon fiber/epoxy filament wound composites. Compos Sci Technol 2007;67:2261–70.

[14] Harte AM, Fleck NA, Ashby MF. Energy absorption of foam-filled circular tubeswith braided composite walls. Eur J Mech A/Solids 2000;19:31–50.

[15] Chang FK, Chang KY. Post-failure analysis of bolted composite joints in tensionor shear-out mode failure. J Compos Mater 1987;21:809–33.

[16] Chang FK, Chang KY. A progressive damage model for laminated compositescontaining stress concentrations. J Compos Mater 1987;21:834–55.

[17] Labeas G, Belesis S, Stamatelos D. Interaction of damage failure and post-buckling behaviour of composite plates with cut-outs by progressive damagemodeling. Composites Part B 2008;39:304–15.

[18] Moon CJ, Kim IH, Choi BH, Kweon JH, Choi JH. Buckling of filament-woundcomposite cylinders subjected to hydrostatic pressure for underwater vehicleapplications. Compos Struct 2010;92:2241–51.

[19] Liu HK, Tai NH, Chen CC. Compression strength of concrete columns reinforcedby non-adhesive filament wound hybrid composites. Composites Part A 2000;31:221–33.

[20] Liu HK, Liao WC, Tseng L, Lee WH, Sawada Y. Compression strength of pre-damaged concrete cylinders reinforced by non-adhesive filament woundcomposites. Composites Part A 2004;35:281–92.

[21] Farley GL, Jones RM. Crushing characteristics of continuous fiber-reinforcedcomposite tubes. J Compos Mater 1992;26(1):37–50.

[22] Mamalis AG, Manolakas DE. Crashworthy behavior of thin-walled tubes offiberglass composite materials subjected to axial loading. J Compos Mater1990;24:72–91.

[23] Farley GL, Jones RM. Energy-absorption capability of composite tubes andbeams. NASA, TM 101634; 1989.

[24] Sen JK, Dremann CC. Design development tests for composite crashworthyhelicopter fuselage. SAMPE Quarterly 1985;17(1):29–39.

[25] Kindervater CM. Quasi-static and dynamic crushing of energy absorbingmaterials and structural components with the aim of improving helicoptercrashworthiness. In: Proceedings of seventh European rotorcraft and poweredlift aircraft forum. Garmisch-Partenkirchen, Federal Republic of Germany;1981. p. 66.1–66.25.

[26] Erkendirci OF, Haque BZ. Quasi-static penetration resistance behavior of glassfiber reinforced thermoplastic composites. Composites Part 2012;43(8):3391–405.

[27] Sirichantra J, Ogin SL, Jesson DA. The use of a controlled multiple quasi-staticindentation test to characterize through-thickness penetration of compositepanels. Composites Part B 2012;43:655–62.