Radial and longitudinal variation of the mechanical properties of bamboo
by
Lina M. Garcia
Submitted to the
Department of Materials Science and Engineering
in Partial Fulfillment of the Requirements for the Degree of
Bachelor of Science
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Signature of Author ..............................
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Department of Materials Science and Engineering
May 10, 2011
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C ertified by ...................................................................................................Loma J. Gibson
Matoula S. Salapatas Professor of Materials Science and Engineering
Thesis Supervisor
Signature redacted
Accepted by ..........................................
Lionel C. I'dimerling
Professor of Materials Science and Engineering
Chairman, Undergraduate Committee
2
Radial and longitudinal variation of the mechanical properties of bamboo
by
Lina M. Garcia
Submitted to the Department of Materials Science and Engineering
on May 10, 2011 in partial fulfillment of the requirements for the
degree of Bachelor of Science in Materials Science and Engineering
ABSTRACT
Although used for millennia, only recently has there been an increased interest in bamboo as a
construction material for its economic, social and environmental benefits. For bamboo to be
widely implemented in construction, however, there is a need to better understand the variation
in the plant's mechanical properties. The microstructure of bamboo and the mechanical
properties of the solid cell wall material of bamboo were characterized for use in models for the
variation of the overall mechanical properties of bamboo as a function of radial and longitudinal
position. The density of bamboo and the volume fraction of vascular bundles in the bamboo
increases with radial position (away from the center of the culm) and decreases with height.
Tensile tests follow the trends predicted by the models. Young's modulus and strength increase
with radial position (away from the center of the culm). Values for Young's modulus were in the
range of 5 to 40 GPa and values for strength varied from 100 to 400 MPa.
Thesis Supervisor: Loma J. Gibson
Title: Matoula S. Salapatas Professor of Materials Science and Engineering
3
ACKNOWLEDGEMENTS
This thesis project would not have been possible without the invaluable time and support of
numerous individuals. Special thanks to:
-
Professor Lorna J. Gibson for her support, patience and guidance;
-
Alan Schwartzmann for teaching me everything I know about nanoindentation, and for
his advice and stories about San Francisco;
-
David Bono, Matthew Humbert and Michael Tarkanian for their guidance and creativity;
-
Donald Galler for fixing the scanning electron microscope on time for this thesis;
-
Ken Stone and Brian Chan at the MIT Hobby Shop for remaining optimistic about
machining bamboo;
-
Dr. Michael Dosmann and The Arnold Arboretum of Harvard University for supplying
bamboo; and
-
Tatiana Kish for making the lab a happier place.
4
TABLE OF CONTENTS
Background.....................................................................................................................................
8
Bam boo life cycle .....................................................................................................................
12
Anatomy of bam boo .................................................................................................................
13
Cellular m aterials ......................................................................................................................
16
Tensile properties......................................................................................................................
17
M aterials and M ethods..................................................................................................................
19
Nom enclature ............................................................................................................................
19
Optical m icroscopy ...................................................................................................................
20
Scanning electron m icroscopy ...............................................................................................
21
N anoindentation........................................................................................................................
23
Tension tests..............................................................................................................................
25
Results and Discussion .................................................................................................................
30
M acrostructure ..........................................................................................................................
30
M icrostructure...........................................................................................................................
31
M echanical properties of bamboo solid cell wall fiber.........................................................
35
M odels for cellular materials .................................................................................................
38
Tensile properties of bamboo..................................................................................................
39
Strength and failure of bamboo.................................................................................................
42
Conclusion ....................................................................................................................................
46
W orks Cited ..................................................................................................................................
47
Appendix........................................................................................................................................
49
A.
Retrieval sites for bamboo specim ens........................................................................
49
B.
CellProfiler pipeline for analysis of vascular bundle density .....................................
50
C.
Derivation of cellular m aterial models for bam boo ....................................................
51
D.
Stress-strain curves for specimen 2.............................................................................
54
5
LIST OF FIGURES
Figure 1. Bamboo structures across the world.............................................................................
8
Figure 2. Apparent consumption of industrial roundwood in China ...........................................
9
Figure 3. Bamboo forms a network of rhizomes ..........................................................................
11
Figure 4. Modem bamboo constructions ...................................................................................
12
Figure 5. World distribution of woody bamboos......................................................................
13
Figure 6. Scanning electron microgaph of bamboo microstructure...........................................
15
Figure 7. Layering patterns in the phloem fibers......................................................................
16
Figure 8. Internode nom enclature ............................................................................................
20
Figure 9. Scanning Electron M icroscope...................................................................................
21
Figure 10. Scanning electron microscope images of incorrectly prepared bamboo surfaces....... 22
Figure 11. Specimen deformation during nanoindentation loading and unloading..................
25
Figure 12.Bamboo slicing technique with knife ........................................................................
26
Figure 13. Carving of dog bones from bamboo slivers ............................................................
27
Figure 14. Bam boo dog bone sam ples......................................................................................
29
Figure 15. Bamboo culm length, outer diameter, and wall thickness...................
31
Figure 16. Scanning electron micrograph of bamboo...............................................................
32
Figure 17. Radial variation of area fraction occupied by vascular bundles at internode 2.11...... 33
Figure 18. Longitudinal variation of area fraction occupied by vascular bundles.....................
33
Figure 19. Radial variation of bamboo density for different heights of specimen 2................. 34
Figure 20. Longitudinal cross-section of metaxylem (voids) in bamboo ..................................
34
Figure 21. Scanning electron micrograph of the porous matrix. ..............................................
35
Figure 22. Longitudinal force-depth curve of nanoindentation...............................................
36
Figure 23. M odeling bamboo....................................................................................................
39
6
Figure 24. Tension test results for internode 2.12. ....................................................................
41
Figure 25. Young's modulus vs. radial position for different internodes of specimen 2. ......... 41
Figure 26. Density variation of Young's modulus at various heights of specimen 2 ................ 42
Figure 27. Scanning electron micrograph of failure by tension of internode 2.2......................
43
Figure 28. Scanning electron micrographs of failure by tension...............................................
43
Figure 29. Radial variation of strength for different heights of specimen 2.............................
44
Figure 30. Density variation of strength for different heights of specimen 2...........................
44
Figure 31. Strength vs. volume fraction of vascular bundles ...................................................
45
Figure 32. Stress-strain curves for all specimens of internode 2.4. ..........................................
54
Figure 33. Stress-strain curves for all specimens of internode 2.5............................................
54
Figure 34. Stress-strain curves for all specimens of internode 2.12..........................................
55
Figure 35. Stress-strain curves for all specimens of internode 2.12..........................................
55
7
BACKGROUND
Bamboo has gained great appeal as a structural material in construction because of its
mechanical properties as well as its economic, social and environmental benefits. In fact, it has
been used in construction for millennia. Around 200 BC, Chinese craftsmen built a palace out of
bamboo for Emperor Hanwudi of the Han Dynasty (1). In Colombia, guadua bamboo was
responsible for much of the development of the coffee-growing zone, where Spanish colonizers
constructed houses, bridges and aqueducts out of bamboo (2). Evidence of the use of bamboo in
construction has also been found in India, Philippines, and Ecuador, among other countries (3).
Figure 1 shows traditional bamboo houses in Philippines and Colombia.
(a)
(b)
(c)
Figure 1. Bamboo structures across the world: (a) traditional bamboo house in the
Phillippines, (b) plastered bamboo house in Colombia, and (c) load truck testing
of bridge made with laminated bamboo girders. (3), (4)
Amidst growing concerns about environmental sustainability, bamboo presents itself as a viable
alternative to common construction materials like wood, concrete and, in some cases, steel,
especially in the developing world where bamboo grows in abundance. Fast growing nations like
Brazil, China and India can greatly benefit from the development of bamboo. It is estimated that
there are close to 8 million ha of bamboo in India and in Brazil (5), (6). China, for instance,
imports around 25% of its industrial round wood with a trend towards increasing use (Figure 2).
8
Most importantly, while national production has remained constant throughout the years,
apparent consumption' has increased, a trend sustained by increased imports. As a developing
nation with approximately one fifth of the world population, housing and infrastructure projects
are projected to increase the demand for roundwood. This presents a challenge for the supply
140
-
security of construction materials in China and, thus, the country's development.
120
E
80
60
P
40
~20_-_
_
__
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Year
--
-C0-National production
Apparent consumption
-*-National exports
-X-National imports
Figure 2. Apparent consumption of industrial roundwood in China based on
national production, imports and exports from 2000 through 2009. While national
production has been constant through the years, consumption has grown through
increased imports. (7)
While self sustenance may not be possible because of land and climate limitations, import
substitution can help alleviate the problem. Bamboo can replace part of the round wood, and
even concrete and steel, in construction contributing to the local economy, reducing negative
impacts in the environment, and aiding in disaster relief.
1 Apparent consumption is calculated from the difference between national production and imports, and exports.
This does not take into account any inventory material.
9
In construction, bamboo can be used in its raw form as seen in the house in Figure IA, or as a
fiber-reinforced composite as used in the bridge in Figure 1 C. In its raw form, bamboo is
appealing because of its high specific strength and specific stiffness, comparable and sometimes
higher than those for glass-reinforced polymers and steel as seen in Table 1. As a fiberreinforced composite, bamboo's strength is even more appealing since, due to its porous
microstructure, the bamboo fiber itself is estimated to be up to 2.5 times stronger than the
bamboo culm (8).
Table 1. Mechanical properties of different construction materials. (9), (10)
Density
gm/cm 3
Tensile
strength
Young's
modulus
MPa
GPa
MPa/(gm/cm 3 )
GPa/(gm/cm 3
400
40
200
4
51
36
25
3.6
Specific
strength
Specific
stiffness
)
Material
Mild steel
Polyester resin
7.9
1.1
GRP with WR and CSM 2
1.45
150
7.2
103
50
Unidirectional GRP
Eastern White Pine
Bamboo
1.8
0.35
0.9
450
34
193
41.3
6.8
20.6
250
97
214
23
19
23
Growing, harvesting and processing bamboo are all low-cost processes, especially when
compared to alternative products. The plant grows with little care to the point that bamboo care
guides provide advice on how to control the spread of bamboo. Bamboo grows at a surprising
speed of up to 5 meters per month (11). The plant reaches its full maturity within four or five
years whereas traditional hardwood requires ten times the amount of time (5). During harvest,
bamboo can be easily transported without the use of special equipment, and its transformation to
a finished product requires less energy to produce than other alternative products. For example,
production of bamboo fiberboard consumes 80% as much energy as production of glass-fiber
reinforced plastics (12).
2 Glass-reinforced
polymer (GRP) with woven roving (WR) and chopped-strand mat (CSM)
10
Moreover, development of bamboo stimulates the local economy as it creates demand for labor
and generates opportunities for local craftsmen and women. The plant can also be used as fuel
and food by local communities. In bamboo producing economies, like China, it can further
contribute to export-led growth and import substitution.
Beside employment generation, bamboo has important benefits in disaster prevention and relief.
Due to its reproductive nature, bamboo helps in erosion control. Bamboo has one single root
called the rhizome from which others branch out creating a dense network of rhizomes as seen in
Figure 3. In Brazil, for instance, this can help manage and prevent floods. Because of this and its
rapid growth rate, bamboo is also ideal for land rehabilitation. The plant's energy absorption and
high bending strength also make it a suitable material for earthquake resistant structures.
Figure 3. Bamboo forms a network of rhizomes below the ground that helps in
erosion control. (13)
11
(b)
(a)
Figure 4. Modem bamboo constructions: (a) marginal neighborhood in Manizales,
Colombia built out of bamboo after disaster in less than a month, and (b) bamboo
ceiling in Madrid's Barajas airport. (2), (14)
Some of the main appeals of bamboo are its environmental benefits in water flow regulation, and
carbon sequestration. As described above, its network of rhizomes makes it good for erosion
control. Furthermore, bamboo forests have high carbon fixation because of the plant's fast
growth and reproduction. Finally, substitution of timber products by bamboo may reduce
deforestation in tropical jungles and rainforests.
Bamboo life cycle
Bamboo grows naturally in every continent except Europe. There are more than 1100 species of
bamboo in the world, which can be divided into two main groups: herbaceous and woody
bamboos. Both belong to the bambusoideae subfamily of grasses. For construction, woody
bamboos are of greater interest. They have lignified culms, leaves and strong rhizomes. Figure 5
shows the world distribution of woody bamboos. One of the most studied species is moso
bamboo (Phyllostachyspubescens) since it is the most widely grown species in China, used in
both construction and cuisine. This project comprised the study of two woody bamboo species:
sweetshoot bamboo (phyllostachys dulcis) and japanese timber bamboo (phyllostachys
bambusoides).
12
Figure 5. World distribution of woody bamboos. (14)
Bamboos grow from bulbs at the rhizome of an already-existing bamboo. These bulbs develop
shoots containing all the nodes that will be present in the mature bamboo. The bamboo then
elongates by cell division at the intemodes. In a few months, the bamboo has reached its fullest
height and begins a process of densification and lignification, which lasts five to nine years and
increases the stiffness and strength of the bamboo. Afterward, the bamboo weakens mostly due
to fungus and mould infection. As a result, the structure and properties of the bamboo are
dependent on age. Typically, bamboo is harvested after five years for maximum mechanical
properties. Although their exact age is not known, the bamboos studied in this project are
estimated to be around one or two years old. (16) (17)
Anatomy of bamboo
Bamboo has an uncommon structure, perfected to withstand forces exerted by the wind. The
main stem, or culm, is a hollow cylinder with solid disks, or nodes, intermittently along the stem.
Nodes are the only solid sections of the bamboo and the space between them is called an
internode. Because of geometry, the hollow shape allows bamboo to withstand higher forces than
a solid cylinder of the same material volume, by increasing its moment of inertia. Overall, the
13
bottom internodes are usually longer, have greater outside diameters and greater wall thickness
than the top internodes, as the former are subject to greater internal forces and moments than the
latter (18).
The outer shell of the bamboo has a yet more engineered structure, for it has to provide
mechanical support as well as nutrient transport and storage capacity. The most distinct feature is
the vascular bundles, regions of solid fiber surrounding the conductive tissue, contained within a
porous matrix (also called the ground tissue in botany). The density and shape of the vascular
bundles varies as a function of the radius and height. The outer-most layer of bamboo is known
as the epidermis or cortex, a porous layer protecting the bamboo from the environment. This is
followed by the peripheral zone, distinguished by multiple small, mostly circular and tightly
packed vascular bundles with little or no conductive tissue. This is followed by a transitional
zone of disperse vascular bundles with conductive tissue in their centers. Finally, the inner-most
sections of the bamboo contain no vascular bundles and are entirely composed of the porous
matrix (2). Nogata et al. measured vascular bundle density as a function of relative radial
position. Density increased exponentially toward the periphery of the culm with no vascular
bundles in the inner 5-10% of the radius or the epidermis which accounted for ~-% of the radius.
Furthermore, the literature indicates that the overall area fraction of vascular bundles increases
with height to account for the decreased wall thickness of the bamboo (8).
Vascular bundles are made of bamboo fibers arranged in a distinct shape (Figure 6). For the most
part, they are shaped like four adjacent lobes surrounding three circular voids for nutrient and
substance transport. The two voids, or channels, opposite each other are called metaxylem and
are responsible for water transport. The third channel, identified by the sclerenchyma fibers in
the middle for mechanical support, is the phloem vessel and is responsible for sugar and nutrient
14
transport (19). The bamboo fibers are arranged in two to six 5-pm layers to form a multilayered
cell wall (Figure 7). The diameter, cell wall thickness and number of layers vary with position
within the bamboo and age, with some studies reporting an additional variation with the position
within the vascular bundle (20).
The porous matrix surrounding the vascular bundles is made of parenchyma cells, which have
cell walls that have been measured to be around one-third as stiff as bamboo solid cell wall fibers
in the vascular bundles (21). The porous matrix as a whole is even less stiff than the fiber
because of its cellular nature. In fact, Amada et al. report porous matrix stiffness around 5% of
that of the bamboo fibers. (21)
Porous matrix
Pr >jtoxylem
Metaxylem
Vascular bundle
0*100
Phloemn
Scle
anchyma
Figure 6. Scanning electron microgaph of bamboo microstructure.
The fibers in bamboo are the primary contributor to its mechanical stiffness and strength even
though they only account for around 40% of the volume. Separate nanoindentation tests on moso
bamboo report bamboo solid fiber modulus of elasticity and hardness in the range of 10-26 GPa
and 0.2-0.6 GPa in the longitudinal direction, respectively (18), (21) while estimates of the fiber
stiffness from the rule of mixtures yield solid fiber Young's modulus in the order of 55 GPa (8).
15
Figure 7. Layering patterns in the phloem fibers (under polarized light) of a
mature culm (20)
Cellular materials
The mechanical properties of cellular materials depend on three different parameters: (a) the
volume fraction of solid, (b) the mechanical properties of the cell wall material, and (c) the cell
geometry (22). For honeycomb geometries, the out-of-plane properties vary with relative density
as follows:
E*
_p
=
Equation 1
Ps
where E* and p* are the Young's modulus and density of the honeycomb, and Es and ps the
Young's modulus and density of the solid cell wall material (or fiber in the case of bamboo).
Because Es and ps are constant throughout a bamboo specimen, its Young's modulus should vary
linearly with density (18).
In his study of grasses, J.F.V. Vincent (23) determined the strength of grasses depended on the
volume fraction of sclerenchyma fiber (Equation 2).
16
- (MPa) = 144 - Vf + 1.53
Equation 2
where crf is the failure strength, and Vf is the volume fraction of sclerenchyma fiber. Similarly,
bamboo strength should depend linearly on the volume fraction of bamboo fiber. Because
vascular bundles run continuously throughout the length of the bamboo culm, strength should
then vary linearly with area fraction of vascular bundles. For the case of bamboo, divergence
from this model is expected as the strength of sclerenchyma cells from grass leafs is 150 MPa
(24) while the strength of bamboo fiber is 341 to 503 MPa (25).
Tensile properties
The macroscopic mechanical properties of bamboo will depend on the loading direction, radial
and longitudinal position of the specimen within the bamboo culm, and the mechanical
properties of the cell wall material, which in turn is influenced by the bamboo species and its
state of maturity. Furthermore, mechanical properties can be influenced by the moisture content
of the bamboo at the time of testing. For the study of bamboo as a construction material, the dry
state is of greater relevance.
Nogata et al. measured the tensile properties of bamboo as a function of radial and longitudinal
position. In the radial direction, stiffness varied exponentially from 10 to 20 GPa as follows:
E = Aexp (bf)
Equation 3
where A and b are constants, and P is the relative radial position (8). When comparing the radial
variation at two different heights, b was constant at 2.2 and A varied. Similarly, strength also
varied exponentially from 50 to 200 MPa. Results by Amada et al. also reveal the same
exponential behavior of the tensile stiffness (24). Furthermore, tensile strength increased linearly
17
with volume fraction of fiber and intemodal number. Internodal number is the number assigned
to each internode in a bamboo specimen in order of increasing height and starting at the base
internode closest to the ground.
The economic, social and environmental benefits of the development of bamboo are well
recognized, yet further progress in structural bamboo products (eg. Bamboo glulam beams,
plywood) and their use has to be made. In an effort to develop building codes for bamboo, one
must first examine of the product's mechanical, thermal and chemical properties. In particular,
for the design and fabrication of bamboo composite products, further understanding of the
plant's mechanical properties is needed. Of main interest is the variation of stiffness and strength
with loading direction, position and density. This thesis aims to determine and model the
longitudinal and radial variation of the mechanical properties of bamboo by analyzing the cellwall mechanical properties, microstructure and mechanical properties of the plant.
18
MATERIALS AND METHODS
Imaging, modeling and mechanical testing techniques were employed to examine the positional
variation of the mechanical properties of bamboo.
Table 2 outlines the methods used for each one of the objectives in this thesis. To characterize
the microstructure of the bamboo, images obtained from optical microscopy and scanning
electron microscopy were analyzed. The mechanical properties of the cell wall were evaluated
through nanoindentation. The results from these two steps were then used to model the
macroscopic mechanical properties of bamboo based on models for cellular materials. Finally,
the actual mechanical properties of the bamboo were tested in tension tests.
Table 2. Objectives and methods
Methods
Objective
Structural characterization
*
*
*
Mechanical properties of the cell wall
Models for the mechanical properties
Mechanical properties of bamboo
*
0
1
Optical microscopy
Scanning electron microscopy (SEM)
Image analysis
Nanoindentation
Models for cellular materials
Instron tension tests
Evaluations and experiments were performed on three specimens of two species: Sweetshoot
Bamboo (Phyllostachysdulcis) and Japanese timber bamboo (Phyllostachys bambusoides). All
species were obtained from The Arnold Arboretum of Harvard University. Please refer to
Appendix A for the location from which species were retrieved.
Nomenclature
Figure 8 shows the nomenclature used throughout the project. Specimens 1 and 2 are of the same
species, sweetshoot bamboo, and specimen 3 is of the second species, Japanese timber bamboo.
19
Internodes are numbered in order of increasing height starting at the internode in contact with the
ground as zero. Nodes are also labeled in order of increasing height, starting at the first node
above the ground as one. This way, the second specimen from the 14th internode of specimen 2
is referred to as specimen 2.14 B.
Internode n
+I
- Node n
Internode 2
Internode 1-+
Internode 0
+
Node 3
+-
Node 2
4-
Node 1
-+
-+
Figure 8. Internode nomenclature
Optical microscopy
Optical microscope images were used to evaluate the fraction of cross-sectional area occupied by
vascular bundles. Therefore, images were taken at 2.5 times magnification to show the entire
thickness of the bamboo cross-section and the light contrast adjusted to achieve the greatest
contrast between vascular bundles and porous matrix. An MVI optical microscope with Nikon
lens L-4EPI (Japan) and Pixelink model PL-A642 were used.
For sample preparation, please refer to sample preparation for Nanoindentation.
Image analysis was done with CellProfiler (25). A detailed description of the procedure used for
image analysis can be found in Appendix B. Images were first converted to grey scale through a
20
combine conversion method. Vascular bundles were identified on the grey image based on
intensity. An appropriate range of object diameters was set to ensure selection of desired objects
only. Finally, the image area occupied by the identified objects was measured as a percentage of
the total image area. Therefore, analyzed images had to show bamboo in its entire area. To
ensure this, images were first cropped using an image editor. Images were cropped at different
locations along the radius of the bamboo to analyze the vascular bundle density as a function of
radial position. Scale bars are not relevant in this analysis since measured quantities are all
relative (e.g. fractional, not absolute, area occupied by vascular bundles).
Scanning electron microscopy
Scanning electron microscopy was used to image the surface of the bamboo in its undeformed
and deformed states. Because of the organic nature of bamboo and to avoid coating with gold,
images were taken in variable pressure mode (10-20 Pa) using backscattered electrons. Images
were taken with a LEO VP438 SEM at various magnifications to study the microstructure of the
bamboo.
electron gun
electron beam
anode
magnetic lens
backscattered
electron detector
secondary
electron detector
specimen
stage
0 2008 Encyclopada Britannica, Inc.
Figure 9. Scanning Electron Microscope (26)
21
Samples for scanning electron microscopy had to be carefully prepared to preserve the
microstructure of the bamboo. For this, samples of the approximate desired size were cut from
the bamboo using a hand saw. Cut samples were then soaked in water for four hours to soften the
surface tissue. A thin slice of the surface of the face was then cut using a new steel alloy blade
each time. Finally, samples were allowed to dry for two days before placing inside the SEM.
This ensures the microstructure returns to its dry state and prevents any damage to the
microscope itself.
Unsuccessful sample preparation procedures for scanning electron microscopy include sanding,
polishing and laser cutting. Surfaces that were cut with a band saw and/or sanded but not
polished looked like smeared sheets of fiber on top of each other and revealed no microstructural
details of the bamboo. Surfaces polished for nanoindentation (Figure lOB) did show the
microstructure yet pores were covered with material removed during polishing, which made it
hard to analyze the shape and size of pores afterwards. Finally, laser-cut surfaces (Figure 1 OA)
also revealed the microstructure but some edges had melted and were rounded off, once again
altering any analysis and measurements.
(b)
(a)
Figure 10. Scanning electron microscope images of incorrectly prepared bamboo
surfaces: (a) melted edges of internode 1.16 after laser cutting and (b) clogged up
pores of internode 3.18 after polishing.
22
Nanoindentation
Nanoindentation was performed using a Berkovich tip on a Hysitron triboindenter. Typical radii
of Berkovich tips are 100 to 150 nm. Because of use and wear, the one used in this project is
estimated to be blunter with radius in the order of 200 nm. The area function and machine
compliance were first calculated by indenting the surface of a fused silica sample of known
mechanical properties. Then, indentations were performed on vascular bundles at different
heights and radial positions. Indentation areas were selected in situ with the optical microscope
embedded in the Hysitron triboindenter so that they were away from the porous matrix. Each
indentation area contained thirty six indents in a six by six grid. Indents were spaced 5 ptm apart
to avoid interaction between the stress fields of each indent. A trapezoidal load function was
followed as done by Yu et al. (18) yet modified to allow for a representative indent depth. Load
and unload rate was 50 pN/s to a peak load of 500 pN and hold time of 5 seconds. The same load
function was used for both axial and longitudinal indentation.
The unloading curve was analyzed to obtain hardness and modulus of elasticity of the material
through Oliver-Pharr analysis (29). The initial slope of the unloading curve, S, is used to
calculate the reduced Young's modulus, Er, as follows:
Er
where
= fl
2 JAp(hc)
Equation 4
P is a constant, h, is the contact depth and Ap(hc) is the area function or projected area of
the indenter tip at h. The reduced modulus is a combination of the mechanical properties of the
indenter tip and the indented material. Therefore, the Young's modulus of bamboo was then
calculated using the following relationship:
23
Er
Ei
+
Es
S
Equation 5
where E is the Young's modulus and v is the Poisson's ratio. The subscripts r, i and s designate
the reduced, indenter and sample properties, respectively. The indenter tip properties are those of
diamond. Therefore, Ei is 1141 GPa and vi is 0.07. For bamboo, v was assumed to be 0.3.
Hardness is defined as the ratio of maximum load to the projected area in contact with the
sample.
H=
Equation 6
Pax
A(hc)
where H is hardness, Pmax is the maximum load obtained from the force-depth curve. The contact
area, A(h), is a function of the depth along which contact is made, which is calculated from the
maximum depth of the indenter tip and the amount of sink-in as follows:
hc = hmax-E
Equation 7
where hc is the depth along which contact is made between the indenter and the specimen, hmax is
the maximum depth obtained from the force-depth curve, E is a constant given by the geometry
of the indenter, and S is the slope of the unloading curve. For a conical punch, E= 0.72. Figure 11
shows the difference between contact and maximum depths.
24
initial surface
a
-
indenter
hs
h
unloaded
jhc
loaded
Figure 11. Specimen deformation during nanoindentation loading and unloading
illustrating the difference between maximum depth, and contact depth (29).
In the final statistical analysis of all indents, no points were discarded as outliers.
For nanoindentation, the surface was polished down to 0.04 tm using Struers method 368 for
polishing woods (30) on a Struers Tegrapol-21 automatic plusher (Cleveland, OH). A hand saw
was used to cut bamboo cross-sections smaller than one inch in any dimension. These were done
mounted on Epofix and allowed to dry for fourteen hours. Samples were finally polished
following Struers method for polishing woods. In this method, the samples are first sanded using
four different Si-C papers in order of decreasing particle grain size and then polished using
colloidal silica abrasive of 0.04 ptm on an MD-Chem polishing surface. This same procedure can
be used for preparing samples for optical microscopy even though it is possible to skip the last
polishing step for this technique.
Tension tests
Tension tests were done with an Instron Model 4206 and a static extensometer model number
2630-104 Instron (Norwood, MA). Strain rate was 1 mm/min and samples were tested to failure
or to a maximum extension of 5 mm, whichever came first, to avoid damage to the extensometer.
25
Figure 12.Bamboo slicing technique with knife: (1) An initial cut is created by
pressing and rotating the knife against the bamboo, and (2) press knife along
bamboo fiber to complete slice.
Dog bone samples for tension tests were created using a sharp exacto knife (Figure 12). First, 3inch long segments of bamboo were cut with a band saw. Then, bamboo culms were axially
sliced into flat, long rectangular slivers comprising a segment of the radial thickness. To induce
an initial cut in the bamboo, knife can be pressed against the bamboo, parallel to the axis of
symmetry, and pressed while rotating back and forth about the center of pressure against the
bamboo. Once the initial crack is created, the bamboo will easily crack open by continuing to
apply downward pressure. It is especially important to keep track of the slivers that are cut off
from the same circumferential position. Slivers from the same circumferential direction were
annotated with the same letter after the internode number and a differentiating number with
decreasing radial position. For instance, the first sliver from the outside to the inside of the
bamboo, out of four, taken at one circumferential position from internode 3.2 was labeled 3.2A1.
In this example, 3.2A1 is the sliver closest to the outside bamboo surface and 3.2A4 is closest to
the inside bamboo surface. Then, slivers can be shaped into dog bones with the same knife
following the technique shown in Figure 13. In this method, dog bones are shaped by
26
1
2
---------------------I---- -------------- --------
3
--
---
-
44
6
-
5
------------
7
8
9
Figure 13. Carving of dog bones from bamboo slivers (1)start with bamboo
slivers created in preceding step; (2) draw dog bone shape onto bamboo; (3) begin
carving out the surplus material by scraping the surface of the bamboo but
without cutting all the way through; (4) remove fibers by scraping from the other
side; (5) repeat step 4 at greater depth; (6) repeat step 4; (7) repeat steps 3 and 4
until you remove all of the desired material from one side; (8) repeat steps 3
through 7 to remove the material on the other side; and (9) finalize with your
bamboo dog bone sample.
27
progressively carving out the surplus material from each side of the sliver. Carving occurs from
both sides of the opening to be created to prevent propagating cracks along the fiber direction.
Each sliver is associated with a value for relative radial position in the zero to one range. This
way, zero represents the inside surface and one represents the outside bamboo surface. Relative
radial position is calculated from the thicknesses of the slivers as follows:
A
= 1 -
rnXflnax
where
4^ is the relative radial position,
ti
Equation 8
inmax is the number of slivers at that circumferential
position and t is thickness of sliver n. Values for thickness and width for each sliver were
calculated as the average of four measurements along the length of the test area of the dog bone
shape. Because of the curved wall of the bamboo, this method overestimates the thickness of the
outside-most and inner-most slivers of the bamboo.
Unsuccessful procedures to make dog bone samples of different radial position include use of the
lathe and laser-cutter. A lathe was used to reduce the thickness of the bamboo culm by removing
material from either the inside or outside of the bamboo, or a combination thereof. Afterward,
circumferential segments were taken from the culm and sanded to shape into dog bones.
However, bamboo culms are not perfectly circular or of even thickness throughout the entire
circumference, so only a few of the culms can be shaped with this process. Furthermore, lathe
cutting stresses the material causing cracks to form during the process, yet, most importantly, the
final surfaces are still curved and crack when gripped by the Instron. Finally, laser-cutting works
well to create dog bone shapes, yet testing theses samples presents other challenges because of
the circular nature of bamboo.
28
7T
Figure 14. Bamboo dog bone samples. Total length (L) is -75 mm, test length (1)
is between 15 and 30 mm, thickness (t) between 0.6 and 3 mm, and width (w)
between 1 and 4 mm. Width and length measurements were within 7% of the
average measurement for each sample.
Bamboo density was calculated from volume and mass measurements. A rectangular piece was
cut from each dog bone specimen after the tension test, making sure it suffered the least
deformation during the tensile test. Volume was calculated from length, width and height
measurements and mass was measured with a Sartorius scale model CP225D with a 0.01 mg
resolution.
29
RESULTS AND DISCUSSION
The structural and mechanical properties of bamboo were evaluated on two different samples:
sweetshoot bamboo (phyllostachys dulcis) and Japanese timber bamboo (phyllostachys
bambusoides). Specimens 1 and 2 correspond to sweetshoot bamboo and specimen 3 is Japanese
timber bamboo. Please refer to the section on methods for information on the nomenclature used
throughout the results.
Macrostructure
The internode, outer diameter and wall thickness, as a function of internode number, are shown
for each bamboo specimen in Figure 15. For sweetshoot bamboo, the culm length increases from
~15 cm up to 30 cm halfway up the bamboo and then decreases to around the initial length of 15
cm. The outer diameter starts at 15 and 20 mm, and only increases 1 to 4 mm at around one third
of the height of the bamboo. The diameter decreases with intermodal number to about half of the
initial diameter. Finally, the wall thickness decreases almost linearly from 5 mm to ~1.5mm.
Specimen 1 was probably younger than specimen 2 because its culm length and outer diameter
were almost always lower than the measurements for specimen 2.
The macrostructure for Japanese timber bamboo follows the same general trend with some
differences. The culm length at the bottom of the bamboo is 25 cm and increases to ~30 cm at
one third of the height. Then, it decreases to about half the peak length. The outer diameter is 45
mm at the bottom of the bamboo and decreases from then to less than 15 mm at the highest
internode. The wall thickness is not significantly different from sweetshoot bamboo; it also starts
around 5 mm at the bottom and decreases to ~2 mm at the top.
30
All results for culm length and wall thickness are consistent with those of Amada et al. Only the
outer diameter trend for Japanese timber bamboo is consistent with the literature, which means
that sweetshoot bamboo could simply have a different macrostructure from other species or these
particular specimens were not fully mature.
-
30
-
E
-
45
-_
0
40
25
--
000
20
0
as-
S35
0Oe
00
30
0
*
15
U
50
(b)
35
Specimen
* Specimen:
10
0
* Specimen 3
25
0 0
220
U.
10
000000060
5
---J-_
0
0
0
Specimen 1
rn
0
20
15
10
5
* Specimen 2
S.
Specimen:
-
(a)
5
0
15
20
Internode number
Internode number
(c)
10
6
U
5
E 4
I**
**4*
a
3
am
2
* Specimen 3
* Specimen 2
a
O Specimen 1
10
0
5
15
10
20
Internode number
Figure 15. Bamboo culm length, outer diameter, and wall thickness as a function
of internode number for each specimen.
Microstructure
The microstructure of bamboo is characterized by a varying volume fraction of vascular bundles
along the radius surrounded by a porous matrix (Figure 16).
31
Figure 16. Scanning electron micrograph of bamboo. Top: cross-sectional view
from top of internode 3.2. Bottom: longitudinal view of internode 1.5. Radius
increases from left to right.
The area fraction of vascular bundles varies exponentially with radial position except at the
inner-most 10-15% and outer-most 2-5% of the bamboo thickness, which have no vascular
bundles (Figure 17). Contrary to the results reported by Nogata and Amada, the overall area
fraction occupied by vascular bundles, p, at a given height decreases logarithmically by 5-10
percentage points from the bottom to the top of the bamboo. For specimen 2 (Figure 18), T
decreases from 34% at internode 2 to 28% at internode 18.
With the exception of internode 2.5, density also increases exponentially with relative radial
.
position (Figure 19). Overall, density varies from 0.7 to 0.9 g/cm3
Following the models for cellular materials, and the findings by J.F.V. Vincent (23), density,
stiffness and strength should vary similarly to vascular bundle area fraction, increasing with
radial position and decreasing with height. This allows the bamboo to have a higher bending
stiffness at the lowest internodes to resist loads exerted by the wind while at the same time
remaining light weight.
32
Furthermore, the walls of vascular bundles are porous in nature, with pore radii in the order of a
few micrometers (Figure 20). This is most likely to facilitate nutrient transport in the radial
direction.
100%
90%
%n
80%
2904
y = 0.0833e 2. x
70%
~0
60%
.0
a
50%
C
.0
40%
0*
30%
*~0-~~'~~'
0
0
20%
10%
0%
0*
0
a **
0.2
0.6
0.4
0.8
1
Relative radial position
Figure 17. Radial variation of area fraction occupied by vascular bundles at
internode 2.11
40%
35%
30%
0%
25%
y
=
-0.0261n(x) + 0.35
20%
0
10
5
15
20
Internode number
Figure 18. Longitudinal variation of area fraction occupied by vascular bundles
for specimen 2
33
1.0
0.9
xX
0.8
IptX X
0.7
0
X
A0
E 0.6
0.4
o 2.4
A 2.5
X 2.12
0.3
* 2.18
0.5
0.2
0.1
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Relative radial position
Figure 19. Radial variation of bamboo density for different heights of specimen 2
Figure 20. Longitudinal cross-section of metaxylem (voids) in bamboo. Walls
have pores in the order of microns. Pores are organized in rectangular clusters.
In the porous matrix, pores are not continuous throughout the height but cylindrical for added
structural support. Pores closest to the inner surface are more spherical in shape while the pores
closest to the outer surface are more cylindrical. The walls of the porous matrix, made of
parenchyma cells, are multi-layered (Figure 21). Pore radius is in the order of 20-50 pm while
the thickness of the pore wall is in the order of 5-8 gm. On the inside, pores are filled with
globular particles, which are most likely starch as the same can be observed for other
34
parenchyma cell such as potato. Finally, the heights of pores are on the order of 50-100 pm, or
approximately double the radius.
While the porous matrix is neglected in modeling the mechanical properties of bamboo, the latter
will also depend on the properties of the parenchyma cells in the porous matrix and the adhesion
forces between the walls of adjacent pores. As can be seen in Figure 21, the walls of each pore
are independent of each other; adjacent pores don't share walls. Furthermore, the pressure inside
pores might not be ambient pressure and may vary with temperature, affecting the overall
mechanical properties of bamboo.
(b)
(a)
Figure 21. Scanning electron micrograph of the porous matrix of internode 3.2:
the walls of pores are multi-layered, and the spherical particles inside the pores
are most likely starch.
Mechanical properties of bamboo solid cell wall fiber
The mechanical properties of bamboo will be most influenced by the fraction of bamboo fibers,
discussed earlier, and the mechanical properties of bamboo fiber itself since this is the strongest
and stiffest component of bamboo. The mechanical properties of bamboo fiber were evaluated
through nanoindentation of vascular bundles. Figure 22 shows the longitudinal force-depth curve
for the inner section of internode 3.18. During loading, force increases exponentially with depth.
In the figure, depth increases at nearly constant force at around 45 pN. This is most likely due to
35
internal voids and defects that make the material more resilient at this specific point. The plateau
at the top of the curve corresponds to the hold time of 5 seconds, revealing the viscoelastic
properties of bamboo fiber. Although not evaluated, these may depend on the temperature and
moisture content of the material. At a peak force of -130 pN, maximum depth is 120 nm.
Finally, the unloading curve was used to determine the modulus of elasticity of bamboo fiber.
Table 3 though Table 5 summarize the longitudinal, radial and tangential properties of both
species being analyzed.
140
120
100
80
,
60
40
20
0
0
20
40
60
80
100
120
140
Depth (nm)
Figure 22. Longitudinal force-depth curve of nanoindentation on the inner section
of internode 3.18.
The modulus of elasticity and hardness of bamboo fiber do not vary significantly with radial
position but do with height. For example, the modulus of elasticity of Japanese timber bamboo
(specimen 3) in the longitudinal direction is 14.5 GPa at the bottom and 10.5 GPa at the top.
Similarly, hardness is -480 MPa at the bottom and -430 MPa at the top. The modulus of
elasticity in the radial and tangential directions is almost 50% lower than in the longitudinal
direction while the hardness is about the same.
36
Table 3. Modulus of elasticity and hardness of bamboo solid cell wall fibers from
nanoindentation tests in the longitudinal direction
Species
Height
(cm)
20
Phyllostachis
bambusoideae
450
Phyllostachis
10
280
dulcis
Hardness (MPa)
Min Avg
Max
443
1083
244
505
331
599
482
385
565
418
567
225
Modulus of elasticity (GPa)
Max
Min
Avg std
11.1
14.5 2.3
25.6
14.9 1.1
12.5
18.0
14.1 0.8
12.5
16.3
10.6 0.9
8.2
12.1
Radial
position
Inner
Middle
Outer
Inner
std
127
46
40
68
Middle
15.9
6.7
10.5
1.6
647
224
421
80
Outer
12.2
9.0
10.6
0.8
588
337
458
48
Inner
17.6
11.5
15.1
1.3
653
414
527 48
13.6
1.8
615
168
415
Inner
Outer
20.6
17.0
4.5
10.4
14.0
14.0
3.4
1.6
861
742
138
277
490 165
476 72
8.5
17.4
Outer
83
Table 4. Modulus of elasticity and hardness of bamboo solid cell wall fibers from
nanoindentation tests in the radial direction
Species
Height
Modulus of elasticity
(cm)
(GPa)
Hardness (MPa)
Max
Min
Avg
std
Max
Min
Avg
std
Bambusoideae
10
9.4
5.8
7.0
0.9
804
289
451
127
Phyllostachis
Dulcis
30
250
13.4
21.6
5.1
1.9
7.9
9.9
2.1
5.6
865
2043
205
37
405
719
157
488
Table 5. Modulus of elasticity and hardness of bamboo solid cell wall fibers from
nanoindentation tests in the tangential direction
Species
Height
Modulus of elasticity (GPa)
Hardness (MPa)
(cm)
Max
Min
Avg
std
Max
Min
Avg
std
Bambusoideae
Phyllostachis
10
30
14.2
20.2
2.2
7.2
8.4 2.9
12.4 3.6
1128
1563
77
531
259
279
849
341
Dulcis
250
15.6
3.1
8.4
1221
129
563
276
3.1
These results are consistent with those presented by Yu et al. (18) and Linhua (21), but are not as
high as predicted by Nogata et al (8). Theoretically, the modulus of elasticity obtained for
bamboo solid cell wall fiber is the maximum theoretical stiffness of bamboo, so the tensile
37
properties obtained through Instron tests should not exceed this value. However, the properties
obtained through nanoindentation can be an over or underestimate of the true properties of
bamboo fiber. While the Oliver-Pharr analysis to obtain modulus of elasticity assumes the
material being tested is isotropic, bamboo fiber is not. As seen in the results, bamboo fiber is
stiffer in the longitudinal direction than in the radial and tangential directions. In
nanoindentation, an indent induces a stress field in all directions, not only the direction being
tested. Therefore, the properties in all directions influence the measurement of reduced modulus,
which will lead to an underestimate of the properties in the stiffest direction and an overestimate
of the properties in the softest direction.
While no data points were discarded as outliers, some of them might not be representative of the
material's properties. For instance, indents at or near one of the smaller pores observed in the
walls of vascular bundles will misrepresent the properties of the material as well as indents at or
near the interface of cell walls.
Models for cellular materials
Following the models for cellular materials presented by Gibson and Ashby, the out-of-plane
properties of bamboo will depend on the properties of its components by the rule of mixtures. As
seen in Figure 23, bamboo can be modeled as a two-phase system of vascular bundles and a
porous matrix. The overall properties of bamboo will depend on the properties of these two
phases and their relative composition. In the model for Young's modulus, the properties of the
porous matrix are considered negligible since the bamboo fibers in the vascular bundles are
much stiffer. Therefore, the model can be simplified to:
E1 = Ep
38
Equation 9
where El is the overall Young's modulus of bamboo in the longitudinal direction, Ef is the
Young's modulus of bamboo fiber and EZ is the previously-calculated total area fraction occupied
by the vascular bundles. A complete derivation of the model for Young's modulus, taking the
porous matrix into consideration, can be found in Appendix C.
From the analysis above, the area fraction of vascular bundles increases exponentially by seven
times from the inner to the outer-most layers of the bamboo. Thus, the Young's modulus should
follow this same pattern. The porous matrix has several failure mechanisms not completely
studied in this project: failure of the pore cell walls, and cell detachment of the porous matrix.
Both are expected to occur before failure of the vascular bundles.
Fr
F,
Porous
Vascular
matrix (p)
bundles (f)
r
t
d
(b)
(a)
Figure 23. Modeling bamboo: (a) two-phase system of vascular bundles
surrounded by a porous matrix; (b) the porous matrix is made of circular pores in
contact with each other.
Tensile properties of bamboo
The tension stress-strain behavior of bamboo (Figure 24) is characterized by an initial linear
deformation followed by failure before yield. Throughout the period of linear deformation,
abrupt decreases in stress can sometimes be observed. These correspond to some sections of the
39
bamboo failing before others. As mentioned before, bamboo is a two-phase system of vascular
bundles and porous matrix, which fail at different stress values.
Figure 25 summarizes the variation in Young's modulus as a function of relative radial position
for different heights of specimen 2. Appendix D includes stress-strain curves for all samples
tested. Overall, Young's modulus increased exponentially from ~6 GPa to ~35 GPa with relative
radial position. Contrary to the literature, there was no significant variation with height although
this was expected for this particular specimen as the area fraction of vascular bundles does not
vary drastically along the height of the bamboo. While this could be the true nature of this
species of bamboo, it could also be influenced by the maturity stage of the bamboo specimen.
Still, as predicted by the model, Young's modulus increased exponentially. If the data points are
extrapolated to cover the entire thickness covered by vascular bundles, on average, Young's
modulus did increase by a factor of seven from 5 to 35 GPa as expected.
Exponential fitting of Young's modulus versus relative radial position matches the data
presented by Nogata et al. For all heights, the exponent coefficient (b) in equation 3 was within
ten per cent of 2.2, the value reported by Nogata. Similarly, following the rule of mixtures from
equation 9 and using the data in Figure 17 and Figure 25, the Young's modulus of the bamboo
fiber should be in the order of 55 GPa as estimated by Nogata from similar measurements.
Therefore, the modulus of elasticity obtained from nanoindentation is not truly representative of
the properties of the bamboo fibers and a different test will be needed for greater accuracy.
As expected, Young's modulus also increases with density (Figure 26) although the trend is not
as clear as with radial position.
40
45
350
40
300
y=
35
250
5.3148e. 10 93x
x
30
x
x
325
200
x
20
150
x
15
100
x
10
X-
50
0
0.0%
0.2%
0.6%
Strain
0.4%
0.8%
1.0%
0.0
1.2%
0.6
0.4
0.2
0.8
Relative radial position
(b)
(a)
Figure 24. Tension test results for internode 2.12: (a) tensile stress strain curve at
relative radial position 0.77; and (b) Young's modulus vs. radial position for all
samples of internode 2.12.
45
40
x
35
DAX
30
x
x
s25
o 2.4
0
ox
2 20
A 2.5
X 2.12
* 2.18
JA
0
5
0
0.0
0.2
0.6
0.4
0.8
1.0
Relative radial position
Figure 25. Young's modulus vs. radial positic n for different internodes of
specimen 2.
41
1.0
45
x
40
A
35
Ax
0
525
*
0 2.4
IAA
2.5
AA
U)20
x 2.12
x
.2.18
15
10
A
5
0
0.4
0.5
0.6
0.8
0.7
1.0
)
Density (g/cm
0.9
3
Figure 26. Density variation of Young's modulus at various heights of specimen 2
Strength and failure of bamboo
During the tensile tests, bamboo samples failed through different modes. The most influential
factor in the failure mode was the area fraction of the porous matrix. The failure surface is less
rough for the porous matrix than that for the vascular bundles as vascular bundles are continuous
and each fails wherever it is weakest and not necessarily at the same location along the length.
There are two failure mechanisms in bamboo which lead to the overall failure of the bamboo
specimen, all shown in Figure 28: (1) vascular bundle failure, and (2) failure of the porous matrix
by either delamination or cell wall failure.
Figure 29 and Figure 30 show the variation of strength with radial position and density,
respectively. Although the data is not conclusive to a specific trend, strength does increase with
both variables, as expected.
42
Figure 27. Scanning electron micrograph of failure by tension of internode 2.2
(b)
(a)
Figure 28. Scanning electron micrographs of failure by tension of internode 2.6:
the sample failed by failure of the porous matrix, (a) Vascular bundles remain
intact within a matrix of pores that failed, (b) different failure mechanisms: 1)
vascular bundle failure, and 2) failure of the porous matrix by either delamination
or cell wall failure.
Finally, Figure 31 shows strength versus volume fraction of vascular bundles as measured and
predicted by the Vincent model (23). Results are not consistent with the values predicted by the
model because the bamboo solid cell wall fiber is 2 to 3 times stronger than sclerenchyma cells,
for which the value was developed (24), (25). Following a rule of mixtures, the coefficient of the
strength versus volume fraction of vascular bundles relationship should be 2 to 3 times greater
for bamboo than it is in the model. A linear fit of results shows a coefficient of 4.62, or 3.2 times
Vincent's coefficient of 1.44 (23).
43
450
A
350
.
400
0*
x
300
A
250
~200
A 2.5
A X
x 2.12
50x
M150
X
* 2.18
Ct tg*'
100
50
0
0.0
1.0
0.8
0.6
0.4
0.2
Relative radial position
Figure 29. Radial variation of strength for different heights of specimen 2
450
400
350
A
300
*x
A
x
AL
250
02.4
o
20X
A 2.5
15
x 2.12
o2.18
A
4A
*
100
x
X
50
0
0.4
0.5
0.6
0.8
0.7
0.9
1.0
)
Density (g/cm3
Figure 30. Density variation of strength for different heights of specimen 2
A final factor to consider when interpreting the results is that volume fraction was not calculated
in situ for every sample. Instead, it was inferred from the radial position using the volume
fraction versus radial position relationships developed earlier. Therefore, there might be some
local variability in the volume fraction of a specific specimen that was not calculated.
44
450
400
y
350
=
4.62(Vf*100)
+
46.15
0
0
300
r
i
250
2.5
200
* 2.18
Model
150
100
0
0
50
y = 1.44(V *100) + 1.53
0
0%
10%
20%
30%
40%
50%
60%
70%
Volume fraction of vascular bundles
Figure 31. Strength vs. volume fraction of vascular bundles as measured at two
internodes of specimen 2 and as predicted by the Vincent model
45
CONCLUSION
Bamboo has gained wide recognition for its economic, social and environmental benefits when
used as a construction material. To see an increase in the use of bamboo for construction, a
greater understanding of the variation of its mechanical properties is still needed.
Bamboo is composed of vascular bundles within a porous matrix. The fraction of vascular
bundles increases exponentially with increasing radial position and decrease logarithmically with
increasing height. The second trend does not agree with the results from other authors, for which
further evaluation is needed. While this may be the true nature of the specific species being
tested, the maturity stage of the bamboo might also be an influencing factor.
Following cellular materials models for Gibson and Ashby, and Vincent, one can establish a
relationship between Young's modulus and strength, and relative density, radial position and
volume fraction of vascular bundles, all of which are consistent with the experimental results.
Overall, Young's modulus increased with density, radial position and volume fraction of
vascular bundles. Strength also increased with radial position and density. Volume fraction of
vascular bundles increased with radial position and moderately decreased with height.
Further modeling and testing should include mechanical properties in the radial and tangential
directions, as well as compression tests. It would also be beneficial to understand the influence of
age and temperature on the properties of bamboo. Finally, when carrying out tests, it is important
to consider possible internal stresses in the bamboo, especially when the specimens have been
subjected to changes in moisture content or temperature, as these stresses can lead to misleading
results of the mechanical properties of the bamboo.
46
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for Western Europe. [Online] 2009.
http://www.bambooteam.com/pablo/200810%2INBAR%20TR%2030%20v2.7%20incl%20figu
res%20SMALL.pdf>.
12. Sustainable ManufacturingSystem Focusingon the Natural Growth of Bamboo. Ogawa,
Keiji, et al. 2010, Journal of Advanced Mechanical Design, Systems, and Manufacturing, pp.
531-542.
13. Bamboo as a building material. Rwth Aachen University. [Online] [Cited: April 4, 2011.]
http://bambus.rwth-aachen.de/eng/reports/buildingmaterial/buildingmaterial.html.
14. Bamboo Ceiling. [Online] [Cited: April 5, 2011.] http://www.bamboo-ceiling.com.
47
15. Maps, Bamboo Biodiversity. Iowa State University. [Online] [Cited: April 5, 2011.]
http://www.eeob.iastate.edu/research/bamboo/maps.html.
16. Physicaland mechanicalproperties of strandboardmade from Moso bamboo. Lee, AWC,
Bai, X and Peralta, PN. 1996, Forest Products Journal, Vol. 46, pp. 84-88.
17. Moso Bamboo in China. Fu, J. s.l. : American Bamboo Society Magazine, 2000, Vol. 21, pp.
12-17.
18. Cell-wall mechanicalpropertiesof bamboo investigatedby in-situ imaging nanoindentation.
Yu, Yan, et al. 2006, Wood and Fiber Science, pp. 527-535.
19. The effect offiber density on the strength capacity of bamboo. Lo, Tommy Y., Cui, HZ and
Leung, HC. 2004, Materials Letters, Vol. 58, pp. 2595-2598.
20. Developmental Changes in Cell Wall Structure of Phloem Fibres of Bamboo Dendrocalamus
asper. Gritsch, Cristina Sanchis, Kleist, Gunnar and Murphy, Richard J. 2004 : s.n., Annals
of Botany, Vol. 94, pp. 497-505.
21. Nanoscale structuraland mechanical characterizationof the cell wall of bamboo fibers.
Zou, Linhua, et al. 2009, Materials Science and Engineering C, Vol. 29, pp. 1375-1379.
22. Gibson, Lorna J. and Ashby, Michael F. Cellular Solids. 2nd Edition. Cambridge
University Press : Cambridge, UK, 1997.
23. Strength andfractureofgrasses. Vincent, J.F.V. 1947-1950, Journal of Materials Science,
Vol. 26.
24. Roberts, Keith, [ed.]. Handbook ofPlantScience. s.l. : Wiley, 2007. p. 204. Vol. 2.
25. Extraction and tensile properties of naturalfibers:Vakka, date and bamboo. Rao, K. Murali
Mohan and Rao, K. Mohana. 2007, Composite Structures, Vol. 77, pp. 288-295.
26. Fiber texture and mechanical graded structure of bamboo. Amada, Shigeyasu, et al. 1997,
Composites Part B, Vol. 28B, pp. 13-20.
27. CellProfiler. [Online] http://www.cellprofiler.org/.
28. Encyclopedia Britannica, s.l. : 2008.
29. Measurement of hardness and elastic modulus by instrumentedindentation: Advances in
understandingand refinements to methodology. Oliver, W.C. and Pharr, G.M. 1, January
2004, J. Mater. Res., Vol. 19.
30. Preparation Parameters, Method 368. Struers. [Online] http://www.struers.com.
48
APPENDIX
A. Retrieval sites for bamboo specimens
4,
ARNOLD
ARBORETUM
WUCNE WELL
ITOR CENTO
RSITY
f HARVARD UNIVE
ARaowAy
GATE
Entrance)
(WAin
125 Arborway
Boston, MA
02130-3500
tel:617-524-1718
www.arboretum.harvard.edu
t2
3
4
E5
6
&
/leventrittShru
Vine Garden (L,)
Larz Anderson
Bonsai (LARZ)
\
FOREST
5
Bradfey
CIENTRE STRE!
GATE
DTE
Rosaceous
l6Colection(BR)
14
-
.
9 an
reenhouse
(GB)
17
stHil
?AVU0514C5 11
Bussey
'213
2
Hill
-'22
1982f
-3
Forest
Hills
tubway
6A041450&4
J2
25
27
26
AQ,
WA
I
3
[29
Qq
3
oUT
STRIET
35
34
WALT
I
Explorers Garden
Chin ese Path
RS
Hemlock Hill 170 ft.
39
STEE41
43
42
RSM ILL
SATE
:46
44
49f'
50
TE
5
PIer
3
47
Da Wl
240 ft.
54
55
56
ter Grid Map
58
SSTREET
4T
64
rid quadrants
a)9-
NW
SW
6
63
65
49
NE
SE
No oil50
ETIET
B. CellProfiler pipeline for analysis of vascular bundle density
The following parameters specify the pipeline used for analysis of vascular bundle density. The
CellProfiler program can be downloaded from <http://cellprofiler.org>.
1. LoadImages
2. ColorToGray
a. Conversion method: Combine
b. Image type: RGB
c. Relative weight of the red channel: 1
d. Relative weight of the green channel: 1
e. Relative weight of the blue channel: 1
3. IdentifyPrimaryObjects
a. Typical diameter of objectis, in pixel units (Min, Max): 5, 50
b. Discard objects outside the diameter range? Yes
c. Try to merge too small objects with nearby larger objects? No
d. Discard objects touching the border of the image? No
e. Thresholding method: Otsu Global
f.
Two-class thresholding
g. Minimize the weighted variance or the entropy? Weighted variance
h. Threshold correction factor: 1
i.
Lower and upper bounds on threshold: 0.0, 1.0
j.
Method to distinguish clumped objects: Intensity
k. Automatically calculate size of smoothing filter? Yes
1.
Automatically calculate minimum allowed distance between local maxima? Yes
m. Speed up by using lower-resolution image to find local maxima? Yes
n. Retain outlines of the identified objects? Yes
o. Fill holes in identified objects? No
p. Handling of objects if excessive number of objects identified: Continue
4. MeasurelmageAreaOccupied
50
C. Derivation of cellular material models for bamboo
Bamboo can be described as a two phase system with different Young's modulus for each phase:
the first phase is the dense vascular bundles and the second phase is the porous matrix. A global
Young's modulus, E1 , can then be derived based on the moduli and geometry of the two phases.
The force total force exerted on the material has to equal the sum of the forces on the vascular
bundles and porous matrix:
Equation 1
F1 = F + Fp,
where F is force and the subscripts (1), (f) and (p) denote properties in the z direction, of the
vascular bundles and of the porous matrix, respectively. The total strain, s, and strains for each
element are all the same since they act in parallel:
Equation 2
El = Ef = EP
From the definition of stress, a, we know:
Equation 3
F = uA
where A is area. Substituting equation 3 into equation 1, we get:
ujAj = afAf + apAp
Equation 4
If E (r) is the fraction of vascular bundles as a function of radius, r, the total area covered by the
vascular bundles can be defined as:
Af =f
<p(r) dr A1 = 9pA 1
Equation 5A
Equation 5B
Af = (1 - <p)Aj
51
Substituting into equation 4 yields:
a1 A 1 = or pAj + up(1 - p)Aj
Equation 6A
a1 = fcp + p,(' - (p)
Equation 6B
From the definition of Young's modulus, we know:
Equation 7
a = eE
Substituting equation 7 into equation 6B:
E1 E 1 = Ef Ef
EjEj
p + pEp(1 - p)
Equation 8A
p)
Equation 8B
= EjEfqp + e1 Ep(1 -
Ei = E9p + E(1 - p)
Equation 8C
To determine Ep we follow a similar method but for a different geometry based on the structure
for the porous matrix. In this model, we are assuming the pores are not closed while in reality
there might be some internal pressure. From the rule of mixtures, we know:
Equation 9
Ep = EeY
where E, is the Young's modulus of parenchyma cells and y is the area fraction covered by the
cell wall of the porous matrix. This can be computed from the geometry of the pores as follows:
Sd+-t
Equation 10
(d+2t)2
where d is the average pore inner diameter and t is the average pore wall thickness. We can then
simplify equation 10 and obtain:
52
=dd-t
Equation 11
Yd 2+4dt+4t 2
Assuming t<<d, we get:
=
y = 2 d-t
d +4dt
Equation 12A
=
rt
d+4t
Equation 12B
We then substitute equation 12B into equation 9:
Ep = Ee
Equation 13
lt
ed+4t
Finally, substituting equation 13 into equation 8C:
El = Ef Tp + Ee Ir(1 -qp)
d+4t
53
Equation 14
D. Stress-strain curves for specimen 2
450
400
350
300
0.83
0.77
250
*
200
o05
*0.54
iso
'.0.25
* 0.27
0.75
100
w
-f
0.21
ao,
50
0
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
Strain
Figure 32. Stress-strain curves for all specimens of internode 2.4. Values in the
graph key represent relative radial position.
400
350
0.83
300
0.79
0.78
250
.0.76
S200
. 0.72
0.56
4-0
ISO0*
0.29
0.28
100
* 0.26
'0.23
50
* 0.22
0
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
Strain
Figure 33. Stress-strain curves for all specimens of internode 2.5. Values in the
graph key represent relative radial position.
54
350
300
* 0.89
250
0.89
-
W0.85
200
-
0.77
~
-
0.63
-150-+
0.60
0.31
+ 0.27
100
50
0.24
-
0.22
0
0.5%
0.0%
2.0%
1.5%
1.0%
Strain
Figure 34. Stress-strain curves for all specimens of internode 2.12. Values in the
graph key represent relative radial position.
400
-
-
--0.81
350
300
0.80
250
.0.78
'U
-0.78
#A200
*0.77
9K
A
150
0.30
* 0.28
100
A0.28
0.27
50
00.0%
0.5%
1.0%
1.5%
2.0%
Strain
Figure 35. Stress-strain curves for all specimens of internode 2.12. Values in the
graph key represent relative radial position.
55