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Article history:Received 15 August 2014Received in revised form 18 December 2014Accepted 27 January 2015Available online 4 February 2015

Keywords:BambooFlexural behaviorFunctionally graded structure

a b s t r a c t

rior mechanical properties and unique hierarchical structure. Bam-boo culms are essentially optimized unidirectional ber-reinforcedcomposites with cellular parenchyma as the matrix (see Fig. 1).They also perfectly demonstrate the concept of functionally graded

es for synthd the relatiand its me

cal behavior (particularly its impressive exibility) has rattracted considerable attentions [713]. In an attempt, Oet al. [8] demonstrated that the bamboo culm is exible when itsstiff outer layer is strained while softer inner layer is compressed.Basically, they attributed the excellent exural ductility of splitbamboo culm to the combination of ber rich outer parts and com-pressible inner parts. In a different study, Tan et al. [11] showedthat, in the course of bending deformation on a single edge notchedspecimen, the crack growth occurs by deection into interlaminar

Corresponding author at: Department of Mechanical and Biomedical Engineer-ing, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China.Tel.: +852 3442 4061.

E-mail address: yanglu@cityu.edu.hk (Y. Lu).

Acta Biomaterialia 16 (2015) 178186

Contents lists availab

Acta Biom

sevavailability and mechanical performance [1], but also are excellentcandidates for the mimicking purposes to design new bio-inspiredmaterials for structural purposes [2,3]. Among biological materials,bamboo is one of the most procient candidates owing to its supe-

[4,6].With the notion of mimicking natural structur

new structural materials, the quest to understanbetween bamboos hierarchical graded structurehttp://dx.doi.org/10.1016/j.actbio.2015.01.0381742-7061/ 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.esis ofonshipchani-ecentlybataya1. Introduction

Biological materials, such as plants and animal bones, tend to beoptimized for the loading conditions they are subjected to. Theyare not only promising for engineering applications owing to their

materials (FGMs) in which continuously graded properties arespecied by spatially varying microstructure stemmed out fromnon-uniform distribution of different constituents [4,5]. By havingsmooth variation in properties, FGMs may offer advantages such asreduction of stress concentration and increased bonding strengthAsymmetryBio-inspired structural materialsAs one of the most renewable resources on Earth, bamboo has recently attracted increasing interest for itspromising applications in sustainable structural purposes. Its superior mechanical properties arising fromthe unique functionally-graded (FG) hierarchical structure also make bamboo an excellent candidate forbio-mimicking purposes in advanced material design. However, despite its well-documented, impressivemechanical characteristics, the intriguing asymmetry in exural behavior of bamboo, alongside itsunderlying mechanisms, has not yet been fully understood. Here, we used multi-scale mechanical char-acterizations assisted with advanced environmental scanning electron microscopy (ESEM) to investigatethe asymmetric exural responses of natural bamboo (Phyllostachys edulis) strips under different loadingcongurations, during elastic bending and fracture failure stages, with their respective deformationmechanisms at microstructural level. Results showed that the gradient distribution of the vascularbundles along the thickness direction is mainly responsible for the exhibited asymmetry, whereas thehierarchical ber/parenchyma cellular structure plays a critical role in alternating the dominant factorsfor determining the distinctly different failure mechanisms. A numerical model has been likewiseadopted to validate the effective exural moduli of bamboo strips as a function of their FG parameters,while additional experiments on uniaxial loading of bamboo specimens were performed to assess thetensioncompression asymmetry, for further understanding of the microstructure evolution of bamboosouter and innermost layers under different bending states. This work could provide insights to help theprocessing of novel bamboo-based composites and enable the bio-inspired design of advanced structuralmaterials with desired exural behavior.

2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.Asymmetric exural behavior from bambhierarchical structure: Underlying mecha

Meisam K. Habibi a, Arash T. Samaei a, Behnam GhesaDepartment of Mechanical and Biomedical Engineering, City University of Hong Kong,bCentre for Advanced Structural Materials (CASM), City University of Hong Kong, 83 Ta

journal homepage: www.elos functionally gradedisms

ghi a, Jian Lu a,b, Yang Lu a,b,at Chee Avenue, Kowloon, Hong Kong, Chinaee Avenue, Kowloon, Hong Kong, China

le at ScienceDirect

aterialia

ier .com/locate /ac tabiomat

boundaries. Low et al. [5] also demonstrated that the excellentdamage tolerance of bamboo can be mainly attributed to the inter-play and concurrent display of crack-deection, ber-debondingand crack bridging as the major energy dissipative processes.

In light of the earlier studies, it appears that the asymmetric ex-ural behavior of bamboo strips along with its underlying deforma-tion mechanisms at the microstructural level has not yet been fullyexplored, despite a very recent research dealing with bamboomaterials anisotropic gradient mechanical behavior [2]. Even,among those limited efforts on bending characterization of bamboostrips, it appears that investigations pertaining to the FG structureof bamboo have been paid great attention to [2,8], whereas theimportant fracture behavior, alongside their corresponding failuremechanisms interacted with the hierarchical structure of bamboo,has been often underrated [14]. Likewise, to facilitate the imple-mentation of experimental results for bio-mimicking purposes,there is a need for developing a proper numerical model to predictthe gradient exural behavior of bamboo strips along their thick-nesses with full consideration of their hierarchical biological struc-tures. Together with the inputs from the experimental studies, sucha model could be also used for further development of FG-structureinduced asymmetry for desired structural purposes.

2. Samples and experimental procedures

The Moso or Mao Zhu bamboos (belonging to Phyllostachysedulis species), collected from bamboo plantations located in

Jiangsu and Zhejiang provinces in China were selected as the rawmaterials for this study. They were all mature bamboo (5 yearsold), cut from the middle section of stalk, and were kept at roomtemperature of 23 C and relative humidity of 5570% (closeto the humidity level of bamboos natural habitat 6080%).

To evaluate the exural behavior of bamboo, bamboo stripswere prepared along the culm thickness with different ber vol-ume fractions. As demonstrated in Fig. 2, strips prepared fromthe outer part (Red: 4 4.2 mm2) comprised the highest amountof bers, whereas the ber volume fraction kept diminishing asthe thickness of the strips approached the entire thickness of bam-boo culm (Blue: 6 6.2 mm2 and Green: 8 8.2 mm2). The bam-boo strips, with ambient humidity level, were subsequentlysubjected to Three-Point (3-P) bending by using Tinius Olsen50KT Material Testing System (MTS) with displacement rate of0.01 mm/s. The ambient humidity (5570%) and temperature(23 C) level were chosen for the mechanical characterizationsto stimulate the actual working condition of bamboo alongsideavoiding any drying artifacts. The exural modulus of each stripwas nally extracted from the stressstrain curve through Eq. (1)which is given below [15]:

Ef L3m

4wd31

where Ef is the exural modulus of elasticity, m is the gradient (i.e.,slope) of the initial portion of the loaddeection curve, L is thesupport span, w is the width of the specimen and d is the thickness.

M.K. Habibi et al. / Acta Biomaterialia 16 (2015) 178186 179Fig. 1. Functionally graded (FG) hierarchical structure of bamboo: optical and SEM micconstituents; (c) parenchyma cells and (d) bamboo bers (viewed in transverse directionbers in longitudinal direction, respectively.rographs (a and b) representing the microstructure of bamboo culm with different). The insets in (c) and (d) show the microstructure of parenchyma cells and bamboo

ng sss, r

matTo obtain the necessary materials properties data for thenumerical analysis, load controlled nano-indentation experimentswere conducted [16,17] on bamboo bers along with parenchymacells, respectively, to measure their youngs moduli. To assure thevalidity of the results, 50 indentations were conducted, separately,on both bers and parenchyma cells. A Hysitron TI 750 Ubi nano-indenter with a cube corner tip (Radius 100 nm) was employedfor this purpose. A maximum force of 700 lN was achieved inthe course of 5 s. Following 10 s holding period, the load was thenreleased over 5 s. The reduced moduli (Er) along with its subse-quent youngs moduli (Es), dened as below [18], were nallyextracted from the unloading region of loaddisplacement curves.

Er 1bp

p2

1Ap

p dpdh

2

Fig. 2. Samples and experimental conguration: schematic representation of bendithickness (8 mm), whereas blue and red refer to 75% and 50% of the culm thickne

180 M.K. Habibi et al. / Acta Bio1Er 1 m

2i

Ei 1 m

2s

Es3

where AP is the projected contact area, b is a geometrical constantthat is 1.034 for a cube corner tip [16], and dpdh is the initial stiffnessat the onset of unloading. In Eq. (3), the subscripts i and s standfor the indenter and substrate, respectively and m is the Poissonsratio. For the diamond indenter tip, the Ei and mi are 1140 GPa and0.07, respectively, whereas the m for bamboo bers is found to be0.22 [19]. In view of lack of experimental data on the Poissons ratioof bamboos parenchyma cells, the reported value for the paren-chyma cells of other biological species, 0.4, is considered here [20].

The microstructural characterizations were conducted by FEIQuanta 450 FEG Scanning Electron Microscope with ESEM mode,which allows the revelation of bamboos different constituents aswell as its functionally graded hierarchical structure at high reso-lution, along with an Olympus/SZX12 Stereo Optical Microscopefor fracture surface examinations.

3. Results

3.1. Gradient exural behavior

In view of bamboo strips hierarchical functionally graded (FG)structure, as displayed in Fig. 1, bers are densely distributed inthe outer part while sparsely dispersed in the inner part, whereasparenchyma cells are densely and sparsely distributed in inner andouter parts, respectively. The exhibited graded distribution ofbers and parenchyma cells naturally aroused a functionally gradi-ent mechanical behavior along the thickness of the strips which isschematically depicted in Figs. 3 and 4 and summarized in Table 1,respectively (Mode A refers to loading on higher ber density side,whereas Mode B stands for loading on lower ber density side).Our mechanical characterizations demonstrated that bamboostrips prepared from the outer part (Red color: 4 4.2 mm2), withhigh ber volume fraction, exhibited high exural moduli andstrengths. However, as the thickness of the strips approached theentire thickness of bamboo culm (Blue: 6 6.2 mm2 and Green:8 8.2 mm2), their respective exural moduli and strengthsdiminished (see Figs. 3a and 4ab), which is mainly owing to thereduction in ber volume fraction (see Table 1).

amples prepared from longitudinal section of bamboo culm (green refers to wholeespectively).erialia 16 (2015) 178186Similarly, bamboo strips exhibited a graded exural behavior interms of their exibility and exural toughness, which could beonce again attributed mainly to graded distribution of bers andparenchyma cells along the thickness of the strips. Flexibility, here,was dened as the exural strain at the fracture point, whereasexural toughness was considered as the area under the stressstrain curves up to the failure point. Since, bamboo strips exhibiteda non-catastrophic fracture with extensive delamination, similar tober reinforced polymer composites and laminates [5,21], 40%drop in the loading was considered as the materials failure point,here. As depicted and listed in Fig. 4cd and Table 1, respectively,strips prepared from near the outer part, with high ber volumefraction, exhibited considerably large exibility and toughness.However, as the thickness of the strips approached the entirethickness of bamboo culm, their respective exibility and exuraltoughness diminished.

3.2. Asymmetric exural behavior

In addition to the exhibited gradient exural behavior due tothe FG distribution of bers and parenchyma cells along the thick-ness of the strips, more interestingly, the exural behavior of bam-boo strips also changed as the bending conguration changed. Asdemonstrated and listed in Figs. 3 and 4 and Table 1, respectively,bamboo strips exhibited relatively larger exural modulus andstrength in the case of Mode A bending conguration compared

matM.K. Habibi et al. / Acta Bioto Mode B. On the contrary, they demonstrated much larger exi-bility and exural toughness in the case of Mode B compared toMode A.

The demonstrated asymmetry in exural behavior of bamboostrips can be further evidenced by comparing the shape of thestressstrain curves from their respective loading modes. Thestressstrain curves were thus compared in terms of two distinct

Fig. 3. Selective three-point bending stressstrain curves of bamboo strips, prepared alonand (b) Mode B (loading on lower ber density side) bending congurations. The crossgreen diamonds stand for bamboo strips failure points (namely, the point where the loa

Fig. 4. Asymmetric exural properties of bamboo strips under Mode A and Mode B bendexural toughness as a function of strips thickness.erialia 16 (2015) 178186 181regimes, namely elastic bending and fracture failure stages(i.e., before and after fracture point), which are distinguished bythe cross marks in Fig. 3. As displayed, in the course of Mode A ex-ural loading (see Fig. 3a), bamboo strips exhibited a relatively nar-row linear region up to the fracture point, whereas theydemonstrated a wider linear regime followed by a non-linearregion in the course of Mode B. Also, stressstrain curves showed

g the culm thickness, in the case of: (a) Mode A (loading on higher ber density side)symbols () represent the fracture points, whereas the red circles, blue cubes, andding drops down to 40%).

ing congurations: (a) exural modulus; (b) exural strength; (c) exibility and (d)

ndin

matTable 1Flexural properties of bamboo strips subjected to different be

182 M.K. Habibi et al. / Acta Bioless serration in the case of Mode A compared to Mode B. Here, theserrations in the stressstrain curves stand for the occurrence ofdelamination or debonding of the ber bundles. Therefore, the dif-ferent extent of serrations in the case of each loading mode couldreveal part of the underlying mechanisms, which might be respon-sible for the asymmetric exural behavior of bamboo strips.

Fig. 5. Fracture mechanisms in different bending congurations: (a) schematic represenacts to restrain the crack opening); for Mode A bending conguration (b and c), optical mthe compressively deformed areas in the top layer; for Mode B bending conguration (d a(d) reveals the deformed parenchyma cells in the top layer. (The insets in (c) and (e) srespectively).g modes.

erialia 16 (2015) 1781864. Discussions

4.1. Mechanisms and modeling of the gradient exural behavior

The exhibited gradient behavior, especially the exural modu-lus and strength of bamboo strips, as listed in Fig. 4ab and Table 1,

tation of ber bridging and debonding (red arrows represent the bridging tractionicrograph (c) shows the bers bridging in the fractured samples, while (b) displaysnd e), optical micrograph (e) shows the delamination in the fractured samples, whilehow the extent of ber bridging and delamination from the bottom surface view,

matM.K. Habibi et al. / Acta Biocould be mainly attributed to the graded distribution of vascularbundles, mainly bamboo bers, along the thickness of the strips.It is already demonstrated that, compared to parenchyma cells(elastic modulus Ep = 3.7 0.4 GPa) [23], bers are signicantlystronger (elastic modulus Ef = 22.8 2.8 GPa) [14,23] and any var-iation in their volume fraction can affect the overall strength andmodulus of bamboo strips, accordingly. The triggered tougheningmechanisms such as bers bridging (schematically depicted inFig. 5a) and crack deection (or so called tortuous crack propaga-tion) [14] are also partly responsible for the gradient and remark-able exural strength and toughness of bamboo strips. Hence, asthe overall volume fraction of ber decreased (thickness of thestrips approached the entire thickness of bamboo culm), the con-tribution of triggered toughening mechanisms, due to the presenceof bers, also diminished which resulted in minimizing the exuralstrength and toughness of bamboo strips.

In light of the exhibited graded exural behavior along thethickness of the bamboo strips, a numerical model, capable of pre-dicting the exural behavior during the elastic bending stage, wasprimarily introduced here, which could be useful for the imple-mentation of graded structure induced asymmetry from the (bam-boo) strips level to bamboo culm level. In this regard, theexperimentally derived exural moduli (see Fig. 4a) were t intoa mathematical method by treating bamboo strip as a FG beam.The necessary material properties were also measured by conduct-ing nano-indentation on bamboo bers as well as parenchymacells, individually, to provide estimation for innermost and outer-most exural moduli of bamboo strip, respectively, which were

Fig. 6. Occurrence of interfacial fractures within the bamboo bers and paren-chyma cells: (a) in the delaminated areas of a fractured sample; (b) shows thehigher magnication view of the wall structure of the intact parenchyma cells.found to be Ef 22:8 2:8 and Ep 3:1 0:4 GPa for bers andparenchyma cells, respectively.

As far as a functionally graded beam with specied width of w,thickness of h and length of L is concerned (see Fig. 7a), the varia-tion of exural modulus along the thickness can be expressed bythe exponential law introduced by Wakashima et al. [25] as below:

Ez Ei Eo zh12

k Eo 4

where Ei and Eo are the exural modulus at the innermost and out-ermost layers of bamboo strips, respectively; and k is a FG exponentvarying with volume fraction of ber along the thickness of thestrips. Here, we introduced the expression representing the equiva-lent bending rigidity of bamboo in static equilibrium as following:

Z h2

h2

Ezwz2 dz Px3

12 C1x C2 0 x 12

Z h2

h2

Ezwz2 dz Px3

12 PLx

3

4 C3x C4 L2 x L

5

where C1 Pl216, C2 = 0, C3 34PL2, C4 PL3

48 and P is the externalstatic loading.

By using Eqs. (4) and (5) via an iterative manner as well as t-ting Eq. (5) to the average value of exural modulus derived for thelargest bamboo strip (8 8.2 mm2), the parameters in the theoret-ical model (i.e., Ei, E0 and k) were measured to be Ei = 2.78 GPa,E0 = 15.21 GPa, and k = 0.43. The nally introduced model, sche-matically depicted in Fig. 7b, predicted exural moduli close tothe experimentally derived values for other cross sections(6 6.2 mm2 and 4 4.2 mm2). So, in view of the demonstratedclose compatibility between the experimentally achieved values(during elastic bending) and their numerically derived counter-parts (see Fig. 7bc), the validity and capability of the introducednumerical model could be veried. This numerical model couldalso demonstrate how the exural moduli distribution should beoptimized along the thickness in a functionally graded compositestructure in order to reach an overall exural behavior similar toor even better than that of bamboo strip.

4.2. Mechanisms of the asymmetric exural behavior

4.2.1. Asymmetry during elastic bendingFirstly, under different bending congurations, bamboo strips

demonstrated a signicant asymmetric behavior during the elas-tic bending stage, i.e., before fracture occurred, showing differentmodulus and exibility. As displayed in Figs. 4ac and listed inTable 1, bamboo strips demonstrated larger exural modulus inthe course of Mode A compared to Mode B, which could be easilyunderstood that more bers were elastically strained while berswere the major constituent to take load (compared to parenchymaground). On the contrary, they demonstrated an even larger differ-ence in the exibility for Mode B compared to Mode A, which couldbe explained by the fact that more parenchyma cells allow toaccommodate much larger deformation by getting squeezed inthe compressively deformed areas of the strips in the top layer ofMode B than that of Mode A (see Fig. 5d) while bers are appar-ently less elastic deformable. This could be also inferred by a com-parison among the shape of the stressstrain curves in the case ofeach loading mode. Compared to Mode A, stressstrain curves inthe case of Mode B (see Fig. 3) exhibited a non-linear deformationregime before the fracture point (see Fig. 3b), which was believedto be associated with the squeezing of parenchyma cells in the

erialia 16 (2015) 178186 183course of exural loading (that is why we called this stage beforefracture as elastic bending rather than simply elastic stage).Lastly, it might be noted that the higher content of parenchyma

mat184 M.K. Habibi et al. / Acta Biocells in the bottom layer in the case of Mode A also increases thestrain heterogeneity and the possibility of crack initiation (as frac-ture always occurred at the bottom side, as shown in Fig. 5c) andsubsequent catastrophic failure than that of Mode B, resulted infurther lower exibility.

4.2.2. Asymmetry during fracture failureFurthermore, bent bamboo strips also demonstrated signicant

asymmetric behavior in the course of fracture failure, i.e., duringand after fracture occurred, displaying different strength andtoughness. However, the associated underlying mechanisms hereare very different, and more complicated compared to the asym-metry during elastic bending stage. As displayed and listed inFig. 4bd and Table 1, respectively, bamboo strips exhibitedrelatively larger exural strength and much smaller toughness,respectively, in the course of Mode A compared to Mode B. Thiscould be understood that, for Mode A fracture, the crack bridging,due to the bers bridging (see Fig 5c), alongside its resultant bersdebonding is the most signicant toughening mechanism which is

Fig. 7. Distribution of exural moduli along the bamboo strip thickness: (a) schematic ralong with distribution of exural moduli along the bamboo strip thickness derived froerialia 16 (2015) 178186responsible for the exhibited strength asymmetry. As demon-strated in Fig. 5a, separation of a matrix crack which is bridgedby uniaxially aligned bers requires sliding of the matrix overthe bers [26]. The sliding however is restricted by frictional forcesthat consequently lead to a reduction in the crack surface displace-ment, which is equivalent to applying a closure stress on the cracksurfaces. Hence, owing to crack bridging, higher load needs to beapplied to initiate the crack. This reduction in stress at the cracktip can be expressed as [26]:

Ktip Ka Ks 6

where Ktip is the local stress intensity factor at the crack tip, Ka is theapplied stress intensity factor and Ks is the shielding stress intensityfactor.

It is moreover remarkable to note that the inuence of bers oncrack bridging amplies with a decrease in the distance of bersfrom the crack tip; in a way that if during crack propagation thecrack encounters a second row of bers, the crack growth resis-tance would be enhanced further. However, in the case of very

epresentation of a functionally graded beam used to develop the numerical modelm (b) the introduced numerical model and (c) the experimental characterizations.

c anhe dthe

matlarge ber volume fraction, the occurrence of crack bridging along-side its resultant bers debonding diminishes owing to reducedmatrix spacing [11,25]. Accordingly, the layers with very large vol-ume fraction of bers result in very low extent of crack bridgingand bers debonding in Mode B, because delamination occurred

Fig. 8. Tensioncompression asymmetry: (a and b) stressstrain curves along with (of tensile and compressive loading, respectively (The schematic demonstration of tevolution of strain heterogeneity and distribution of the load within the samples, in

M.K. Habibi et al. / Acta Biomore often (see Fig. 5e), which considerably reduce the exuralstrength. This could be also inferred by a comparison among theexhibited serrations in the stressstrain curves during each loadingmode (see Fig. 3). The presence of more serrations in the stressstrain curves of bamboo strips subjected to Mode B rather thanMode A is an evidence of more delamination occurrence in thecourse of Mode B compared to Mode A.

For the higher toughness in Mode A than that in Mode B, it canbe largely attributed to the role of foam-like parenchyma cells onaccommodating the large deformation by getting squeezed, duringelastic bending, resulted in much larger exural ductility (exibil-ity) for Mode B than Mode A. More importantly, by inducing tor-tuous crack propagation [14] along their interfacial areas duringfracture failure, parenchyma cells could further enhance thebamboos superior exural toughnessalthough it is a generalmechanism for enhancing the fracture toughness [14], the muchlarger interface areas created by delamination processes in ModeB considerably increased the interfacial fracture occurrences(Fig. 6a) between delaminated parenchyma cells (as evidenced bythe intact parenchyma cells in Fig. 6b), making the tortuous crackpropagation a dominating factor for differentiating the toughnessduring Mode B fracture failure stage. So even the overallstrengths of Mode B were lower than that of Mode A, its fracturetoughness could be still higher than that of Mode A.

4.3. Tensioncompression asymmetry

From the results and above discussions, it has been shown thatthe exhibited asymmetry in the elastic bending depends more onthe deformation mechanisms from the top layer of bamboo strips(loading side), whereas the asymmetry during fracture failureseemed to be more related with the characteristics from the bot-tom layer (as fracture always occurred from the bottom layer).Considering standard three-point bending model (Fig. 2) wherethe top layer should be under compression while the bottom layershould under tension, we additionally performed tensile and com-pressive experiments along the longitudinal direction (bers

d d) schematic representations of deformation behavior of bamboo culm in the caseeformed specimens and the arrows across the samples cross section indicate thecase of each loading mode, respectively).erialia 16 (2015) 178186 185direction) of the bamboo culm specimen, to assess the differencein accommodating large deformation and its possible relation withthe origin of the exural asymmetry. Interestingly, we againobserved asymmetric responses from the uniaxial tension andcompression tests (see Fig. 8). As displayed in Fig. 8ab, bambooculm demonstrated larger strength but smaller ductility in thecourse of tension than that of compression. The developed strainheterogeneity, as shown in Fig. 8cd was mostly from the gradientdistribution of load due to bamboos FG structure. The disclosedasymmetry in strength could be basically justied by the existenceof crack bridging and deection mechanisms in the case of tension,whereas the demonstrated asymmetry in failure strain (ductility)could be mainly attributed to the squeezing of the parenchymacells during the compression, which were both very similar to thatof exural bending. However, unlike in bending tests fracturemostly occurs in tension area, we discovered very different fracturemechanism in severe compressed specimenthe formation ofshear band (see Fig. 9a), due to the bers buckling (see Fig. 9b),as well as crack initiated and nucleated when shear band metthe interface of ber bundle and parenchyma ground (as displayedin Fig. 9c). Lastly, the signicant larger compression ductility (up to1520%) than that in tension and bending (a few percentages)conrmed that bamboo materials can indeed sustain much largerdeformation in compression than in tension, resulted in the oftenoccurrences of fracture failure at the bottom layer of the bent bam-boo strips.

5. Conclusions

In summary, bamboo materials remarkable exural propertiesare stemmed out from the concurrent graded distribution of

186 M.K. Habibi et al. / Acta Biomattougher constituent (mainly bers), along with weaker constituent(such as parenchyma cells). Induced by their FG hierarchical struc-ture, bamboo strips demonstrate signicant asymmetric exuralbehavior and distinctly different underlying mechanisms whenloaded from the inner and outer sides during the elastic bendingand fracture failure stages. Similar asymmetric behavior has beenalso disclosed in uniaxial loading of bamboo culm specimen, indi-cating the important role of the microstructural features in deter-mining the macroscopic asymmetry in bamboos mechanicalbehavior. The insights obtained from this systematic experimentalstudy, along with the numerical model, shall be useful for the bio-mimicking purposes in fabrication and processing of advancedstructural materials with desired exural behavior.

Fig. 9. Shear band formation in the compressively deformed specimen: (a) opticaland (b and c) SEM micrographs representing the formation of shear bands inbamboo culm, subjected to longitudinal compression; (c) represents the bersbuckling as well as crack formation at the matrix-bers interfaces.Acknowledgments

The authors gratefully acknowledge the nancial support fromCity University of Hong Kong under the Grants # 7003021,# 9610288 and # 9667098, as well as the CityU InternationalTransition Team Scheme (ITT-GTA) postdoctoral fellowship.

Appendix A. Figures with essential color discrimination

Certain gures in this article, particularly Figs. 19, are difcultto interpret in black and white. The full color images can be foundin the on-line version, at http://dx.doi.org/10.1016/j.actbio.2015.01.038.

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Asymmetric flexural behavior from bamboos functionally graded hierarchical structure: Underlying mechanisms1 Introduction2 Samples and experimental procedures3 Results3.1 Gradient flexural behavior3.2 Asymmetric flexural behavior

4 Discussions4.1 Mechanisms and modeling of the gradient flexural behavior4.2 Mechanisms of the asymmetric flexural behavior4.2.1 Asymmetry during elastic bending4.2.2 Asymmetry during fracture failure

4.3 Tensioncompression asymmetry

5 ConclusionsAcknowledgmentsAppendix A Figures with essential color discriminationReferences