Mode II Fracture Mechanics of Moso Bamboo for
Application in Novel Engineering Materials
by
MASSACHUSETTS INSTITUTE
OF TECHNOLOLGY
Rachel Ellison
JUN 16 2015
LIBRARIES
Submitted to the
Department of Materials Science and Engineering
in Partial Fulfillment of the Requirements for the Degree of
Bachelor of Science
at the
Massachusetts Institute of Technology
June 2015
2015 Rachel Ellison
All rights reserved
The author hereby grants MIT permission to reproduce and to
distribute publicly paper and electronic copies of this thesis document in whole or in part
in any medium known or hereafter created
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Signature
.. /....<.....
Signature of the Author..g ...
........ * ......................................
De artment of Materials Science and Engineering
March 20, 2015
Certified by..............................................
Matoula
Accepted by...................
Signature redacted
Lorna J. Gibson
lapatas Professor of Materials Science and Engineering
Thesis Supervisor
Signature redacted
...................
Geoffi'y-S-D. Beach
Department of Materials Science and Engineering
Undergraduate Committee Chairman
Mode II Fracture Mechanics of Moso Bamboo for
Application in Novel Engineering Materials
by
Rachel Ellison
Submitted to the Department of Materials Science and Engineering
on March 20, 2015 in Partial Fulfillment of the
Requirements for the Degree of Bachelor of Science in
Materials Science and Engineering
ABSTRACT
Bamboo has been used as a structural material for thousands of years. Recently there has
been increasing interest in its use as a modem construction material. In this study, as part of a
larger project to characterize the mechanical properties of Moso bamboo for application in the
production of structural bamboo products (SBP), end-notched flexure (ENF) tests and three-point
bending tests were performed to obtain the mode II interlaminar toughness (GIe) and
longitudinal Young's modulus (EL). It was found that known values for G 1, include the pith
(innermost layer) and cortex (outermost layer) of the bamboo culm in their calculations. The
resulting value is, to a statistically significant degree (t = 5.0 x 106), higher than that with the pith
and cortex removed, as they typically will be in processing SBP. A new value, G11, = 630 155
J/m 2 , was established for specimens lacking the pith and cortex. Although no correlation was
found between G 1, and specimen density, it is suspected that a relationship does exist, and
recommendations for further investigation are given.
Thesis Supervisor: Lorna Gibson
Title: Matoula S. Salapatas Professor of Materials Science and Engineering
2
Acknowledgements
This thesis is the capstone of my undergraduate education, during which I've had the
opportunity to learn from and with some of the most amazing people I've ever met. I'd like
to extend special thanks to Dr. Gibson, who has been the most supportive of mentors as I've
been working on this project, and to Patrick Dixon, the ever-patient PhD student I've had
the pleasure of working with. Patrick and Dr. Gibson have helped me immensely with
shaping this work.
I'd also like to recognize various instructors for Course 3 undergraduates. I had the
privilege of learning under many great teachers, and have been especially influenced by Dr.
Michael Rubner, Dr. Polina Anikeeva, and, of course, Dr. Gibson. I also owe a lot to Mike
Tarkanian, Chris di Perna, and the rest of the LEM instruction team, who taught me to work
not just with my mind, but with my hands.
I'd like to thank Brian Chan, Ken Stone, and the rest of the MIT Hobby Shop staff for their
help with specimen manufacture and preparation.
I'd like to thank Victoria Borland, my roommate and best friend, who has been infinitely
patient and supportive of the work I do.
I'd like to thank Dr. Linn Hobbs, who helped me pilot the Course 3 exchange with Imperial
College London-this cultural experience taught me a lot about my interests and priorities,
and my MIT education would be less valuable without it.
And, finally, I'd like to put in a thanks to the Course 3 Undergraduate Committee, who have
made it possible for me to both complete my thesis and leap into my new career on an
unusual schedule. I have always felt that the Department of Materials Science and
Engineering was supportive of me, and I will remember this expression of that support for
a long, long time.
3
Contents
1. Introduction .......................................................................................................................................
7
1.1. Bam boo in the Developing W orld..................................................................................
7
1.2. Structural Bam boo Products...........................................................................................
10
2. M aterials an d Experim ental M eth ods..........................................................................
13
2.1. Macrostructure and Microstructure of Phyllostachyspubescens......................13
2.2. Specim en Preparation and Processing.............................................................................15
2.3. End-N otched Flexure Test.................................................................................................
16
2.4. Three-Point Bending Test.................................................................................................
18
3. A nalytical M ethods ......................................................................................................................
19
3.1. Data Processing...........................................................................................................................19
3.2. Substitutional M ethod for Obtaining G c........................................... . ... ... .. ... ... ... ... .. . . 21
3.3. Young's Modulus and Modulus of Rupture Calculations......................................21
3.4. Tim oshenko M ethod for Obtaining G &...........................................
... ... .. .... ... ... .. ... ... . . .
23
4 . R esu lts and D iscussion ...............................................................................................................
4.1.
4.2.
4.3.
4.4.
4.5.
24
Impact of Pith and Cortex Inclusion on Fracture Properties..............................24
G jcvs. Density...............................................................................................................................26
Gi, vs. H eight.................................................................................................................................27
Pith vs. Cortex in increasing Gui value..........................................................................
28
Im pact of Other Factors...........................................................................................................30
5. Con clu sion s an d O utlook .....................................................................................................
31
W orks Cited.............................................................................................................................................
32
A p pen dix..................................................................................................................................................35
A . M oisture content calculations...........................................................................................
35
B. F j, and 6 cj approxim ations...................................................................................................36
C. M odulus of rupture calculations.....................................................................................
4
37
Figures
Figure 1.1: Global distribution of woody bamboos. Note the prevalence in developing areas
such as China, India, the Philippines, South America and Central Africa (Gardner and
Vogel 2006)
Figure 1.2: Traditional full-culm bamboo construction. The cylindrical shape of the culms
causes difficulties when using nails or screws; hence, ropes and notches are the
primary methods of binding. (Holcim Foundation 2012)
Figure 1.3: "Passive House," in Bessancourt, France, by Karawitz Architecture. Passive
House is a demonstration of sustainable building materials and methods, and uses
bamboo for its exterior cladding. The project was labeled the best performance low
consumption house in France in 2010. (ArchDaily)
Figure 1.4: Structural bamboo products (SPBs). Left: WeaveCore" by Lamboo®, Inc. Right:
Bamboo oriented strand board produced by Greg Smith (University of British
Columbia), developed in tandem with the Gibson lab.
Figure 2.1: Moso bamboo. Left: Phyllostachyspubescens garden by the American Bamboo
Society. Right: dried moso culms ready for use (Alibaba)
Figure 2.2. Left: Vascular bundle in Phyllostachyspubescens showing dense sclerenchyma
surrounding vessels for fluid transport. Right: Moso bamboo cross-section. Note that
the density of vascular bundles increases significantly between the inner wall (pith)
and the outer wall (cortex). (De Vos 2010)
Figure 2.3: Orientation of specimens cut from the culm
Figure 2.4: A double-cantilever beam specimen. Axes indicate the orientation of DCB
specimens relative to the bamboo culm. The crack is made in the r-z plane, also
known as the TL plane, so as not to sequester the radial gradient on one side or the
other (which would confer disparate mechanical properties).
Figure 2.5: Typical ENF setup. (Adapted from Yoshihara 2000)
Figure 3.1: Typical F-6 curve for an ENF test, divided into stages: a) initial loading; b) stable
crack propagation; c) unstable crack propagation and failure
Figure 3.2: F-6 curve with secant line approximation (black), corresponding to 95% of the
original slope (red) (i.e. y = 0.95 Cox). The point of intersection, annotated in yellow,
defines Fcrit and 6 crit
Figure 3.3: Typical beam bending curve. The initial slope (dashed black lines) is used to
calculate Young's modulus (equation 4). The peak load and displacement, Fcrit and
Scrit (annotated in yellow), are used to calculate modulus of rupture (MOR)
5
Figure 4.1: No trend was observed between interlaminar toughness and density. Note the
impressively low R 2 value.
Figure 4.2: No trend was observed between interlaminar fracture and height. On this chart,
blue diamonds represent G,,, calculated by the substitutional method for specimens
without pith and cortex; green triangles represent the substitutional Gil, value with
pith and cortex still intact. Red squares represent G11, calculated by the Timoshenko
method for specimens without pith and cortex; purple hatchmarks represent the
Timoshenko Gi1, value with pith and cortex still intact.
Figure 4.3: Comparison between specimens with various pith and cortex configurations.
The cortex only samples have a significantly higher value than the pith only or no
pith and cortex specimens. It appears that the inclusion of the cortex makes the
difference between the no pith and cortex specimens and the both pith and cortex
specimens (shown to be significantly different from each other in section 4.1)
Tables
Table 4.1: Calculated values for Gic for samples without pith and cortex.
Table 4.2: Calculated values for Giic for samples with pith and cortex intact.
Table 4.3: Calculated values of Young's modulus, EL. Note the much-higher mean value for
the cortex-only specimens compared to the average for all specimens.
6
Chapter 1: Introduction
1.1: Bamboo in the Developing World
Bamboo has been used as a structural material for thousands of years, particularly by the
indigenous groups of Central and South America, Asia, and Africa. It is a favorable construction
material for many reasons: it is one of the fastest growing plants in existence, it is locally sourced,
and it has mechanical properties similar to those of traditional Western timbers. It is also
abundantly available: according to the FAO's 2010 Forest Resource Assessment, there are 31.4
million hectares of bamboo worldwide ("Global Forest Resource Assessment" 2010). Nearly
60% of global bamboo production is concentrated in India, China, and Brazil, where timber is
scarce, and rapid urban development has created a great need for affordable construction material.
Figure
1.1: Global distribution of woody bamboos. Note the prevalence in developing areas such as China,
India, the Philippines, South America and Central Africa (Gardner and Vogel 2006)
Bamboo is an excellent choice for load-bearing applications. Having evolved over
millennia to withstand the forces incurred by high-speed winds, it has a high elastic modulus and
a high strength-to-weight ratio (Aijazi 2013). These features, being highly desirable for structural
7
materials, have caused bamboo to be a source of inspiration for novel materials for the last forty
years.
Bamboo is also both ecologically and economically sustainable. It has a much higher
growth rate than timber, being ready for harvest in ten years or less; tree species, by contrast,
mature over a broad spectrum of periods, ranging from thirty to more than hundred years (Fu
2000; Ding et al. 2007). Bamboo also has a greater yield per hectare than traditional timber
sources-some species of bamboo produce up to 6 times the mass of woody material per hectare
as conventional timber species such as southern pine (Hodge 1961). There is also the issue of
negative carbon impact: a well-managed Moso bamboo plantation sequesters more carbon over a
60-year period than an equivalent area of Chinese fir (Lou et al. 2010). In modem China,
meanwhile, the primary structural material in residential buildings is concrete, whose production
accounts for nearly 5% of the world's carbon emissions (Samarin 1999).
Figure 1.2: Traditional full-culm bamboo construction. The cylindrical shape of the culms causes difficulties
when using nails or screws; hence, ropes and notches are the primary methods of binding. (Holcim
Foundation 2012)
8
However, several challenges arise when working with bamboo. Like wood, it is an
anisotropic material, with its greatest mechanical properties along its longitudinal axis. Unlike
wood, however, bamboo contains a significant density gradient in the radial direction, due to
anatomical variation in the position and density of load-bearing structures in the plant. This leads
to large changes in its mechanical properties: within a single plant, the tensile Young's modulus
can vary from 5 to 25 GPa, and the tensile strength from 100-800 MPa (Amada et al. 1997;
Nogata and Takahashi 1995).
Traditional bamboo construction uses the entire culm, or stem of the plant, and thus
features the entire range of mechanical properties present. This issue makes quality control of the
material difficult, and hampers its widespread use in modem construction. Thus, at present
bamboo is a niche product, used by high-end Western architects interested in ecological
friendliness. It is also used by natives of Asia and South America who cannot afford concrete or
other more "modern" building materials. This study aims to narrow the gap between the low-cost
but nonstandard bamboo already in widespread use, and the robust but expensive engineered
bamboo products used by Western architects.
Figure 1.3: "Passive House," in Bessancourt, France, by Karawitz Architecture. Passive House is a
demonstration of sustainable building materials and methods, and uses bamboo for its exterior cladding. The
project was labeled the best performance low consumption house in France in 2010. (ArchDaily)
9
1.2: Structural Bamboo Products
One solution to the issue of material and mechanical inconsistency is the development of
structural bamboo products (SBPs). These are analogous to timber products such as plywood,
glue-laminated timber, and oriented strandboard. SBPs are formed by breaking down bamboo
culms into smaller components, and reassembling them in a composite structure. In doing so, the
differences in mechanical properties due to natural variation in the density of the bamboo, the
culm wall thickness, the height, and other variables are minimized, resulting in a far more
standard product than full-culm bamboo. SBP can also be made into beams and plates of
relatively large dimensions.
Figure 1.4: Structural bamboo products (SPBs). Left: WeaveCore" by Lamboo®, Inc. Right: Bamboo oriented
strand board produced by Greg Smith (University of British Columbia), developed in tandem with the Gibson
lab.
Several projects have already demonstrated the small-scale viability of SBP as a building
solution. GluBam &, a product pioneered at the University of Southern California, is a composite
made by coating strips of bamboo with an adhesive and compressing them into boards. So far, it
has been used in China to construct a concept house (USC Viterbi School of Engineering News
2009), modem bamboo bridges, and emergency earthquake shelters (Xiao 2007). Lamboo@
10
WeaveCoreTM, a laminate made of multiple pressed layers of interwoven bamboo slats, is a
commercially available product that is advertised as being better suited to changes in ambient
conditions (e.g. variable temperature and humidity) than standard plywood (Lamboo Industrial
Solutions). Lamboo also offers CrossCoreTM, a thicker version of WeaveCoreTM that is sold in
planks and advertised as an alternative to timber structural parts.
However, though Lamboo has been relatively successful financially, its product is used
primarily as a wall and ceiling cladding-the company has a quite successful partnership with
Pier I Imports, for whom it provides the paneling to storefront entranceways (Moloney). This
superficial use of the material is the norm: Lamboo's other product lines include flooring panels,
handrails, and interior furnishing boards for private jets (Lamboo Design). The company, based
out of Illinois, has failed to meaningfully break into the market for structural construction
materials. This is likely due in part to the price point, which would fall if greater quantities were
produced, and in part to the lack of building codes governing SBP usage, which makes use of the
product for structural components a risky decision for potential buyers.
Since the academic examples of SBP are relatively few, and work done by "green"
companies such as Lamboo, Inc is privatized, little information is available about the
manufacture and properties of SBP. To broaden that knowledge base, Professor Gibson's lab has
joined a cross-university collaborative effort, which aims to develop processing methods for SBP
creation, characterize the structural, thermal and moisture performance of SBPs, create building
codes for SBP use, and perform life cycle assessment of the material.
Most of the work done to date, both in the literature and in Professor Gibson's lab, has
focused on measurement of the Young's modulus, the tensile and compressive strength, and the
bending response (modulus of rupture). Little data exists for the fracture properties of bamboo,
11
which is a critical consideration for a structural material. This study aims to correct that oversight,
examining the Mode II (sliding mode) fracture properties of bamboo in depth, and relating them
to the physical structure of the plant.
12
Chapter 2: Materials and Experimental Methods
The species of interest to this study is Phyllostachyspubescens, or Moso bamboo, the
most commercially important bamboo species in China. This species was chosen due to
connections some members of the research team have with building projects in China; hopefully,
the conclusions drawn from the study overall can be applied to bamboos of similar size and
abundance in other regions of the world (such as Guadua angustifoliain South America, and
Yushania alpinain Africa.)
For this study, sections of Moso bamboo were obtained from Bamboo Craftsman
Company (Portland, OR, USA). For ease of shipping, the bamboo had been pre-cut into sections
approximately 1.5 meters in length, and had been labeled by the merchant to indicate the position
of the segments along the height of the culm. The bamboo had been air-dried, and treated with
boric acid to protect against insect and fungal attack. The age of the bamboo at harvest is
uncertain. Moisture content, determined by relating mass as-received to mass after 24 hours of
incubation at 103 'C, was 5%. (Appendix A)
2.1: Macrostructure and Microstructure of Phyllostachys pubescens
Moso bamboo is striking mostly because of its impressive size: it grows up to 28 meters
in height and 20 centimeters in diameter (Lewis 2008). It reaches these staggering proportions
within its first few months of life, making it one of the fastest-growing plants in the world. Over
the next few years, it densifies to its adult mass, maturing for harvest by year four (Wang et al.
2013; Shao et al. 2010).
Moso has the same macroscopic structure as most bamboos: its culm is a long, hollow
cylinder, with walls 1-2 cm thick around a large cavity called the lacuna. The culm is
13
interspersed with solid disks called nodes, which are distributed increasing intervals along the
height of the plant (Aijazi 2013). The culm sections between nodes are called internodes.
Figure 2.1: Moso bamboo. Left: Phyllostachys pubescens garden by the American Bamboo Society. Right: dried
Moso culms ready for use (Alibaba)
Most of bamboo's impressive mechanical properties come from its microstructure. It is a
naturally occurring unidirectional fiber composite, comprised of load-bearing vascular bundles
embedded in a porous matrix of parenchyma cells (Liese 1987). Vascular bundles primarily
consist of dense, darkly-colored sclerenchyma fibers, which support the plant's water-conducting
tissues. The sclerenchyma fibers run longitudinally through the intemodes, and contribute the
majority of bamboo's mechanical strength and stiffness (Shao et al. 2010). By volume, the culm
consists of approximately 50% parenchyma, 40% sclerenchyma fiber, and 10% conducting tissue
by volume (Liese 1987).
Vascular bundles are distributed by radial position, with a higher number of fibrous
bundles at the outer edge of the culm. A cross-sectional view of a typical internode showcases
the change in density and shape of vascular bundles from the outer to inner wall. (Figure 2.2)
14
W-
V
4: j:o k:v
v
-J
C,
-W.-V
Gjj-
Y,; 0.VV
V,
Q V
C
~.- i.,
C,
Figure 2.2. Left: Vascular bundle in Phyllostachys pubescens showing dense sclerenchyma
surrounding vessels for fluid transport. Right: Moso bamboo cross-section. Note that the density of
vascular bundles increases significantly between the inner wall (pith) and the outer wall (cortex).
(De Vos 2010)
Previous studies have related the variation in microstructure to variation in bamboo's
compressive and flexural moduli and strengths (Aijazi 2013; Dixon and Gibson 2014). This
study will examine the contributions of the cortex and pith specifically to fracture properties.
2.2: Sample Preparation and Processing
Sample specimens were prepared from the lowest 16 internodes of the as-received Moso
culm. The internodes were labeled beginning with 0, at ground level, and ascended to internode
16 over a height of approximately 3 meters. Specimens were cut from the node 7, the lowest
node that was physically tall enough to accommodate samples of the requisite size, nodes 10
through 12, and node 16, in order to provide data at a variety of heights.
Figure 2.3: Orientation of specimens cut from the culm
15
The culm was cut into its component internodes using a woodworking bandsaw. The
uppermost and lowermost half centimeter of each internode were then further removed to
minimize specimen curvature. From the resulting hollow cylinder, specimens were split using a
knife and mallet, and then sanded with an electric belt sander to form right-angled edges.
Specimens were prepared with special attention to the innermost and outermost shells of
the bamboo. Four kinds of specimens were made: pith and cortex both removed, only cortex
removed, only pith removed, and pith and cortex both intact. These specimen types were
manufactured for both DCB (double cantilever beam) and simple beam specimens.
2.3: End-Notched Flexure Test
The end-notched flexure (ENF) test was first proposed as a method of measuring mode I
fracture by Barrett and Foschi (1977). It has since undergone improvements by many different
groups: the original proposal relied on precise measurement of the crack tip as it propagated
through the specimen, which in practice is quite difficult to do. This study will explore several
routes to obtain G 1c, the mode II interlaminar toughness, in chapter 3.
For ENF testing, a double cantilever beam (DCB) specimen is required (Figure 2.4). As
the specimen undergoes three-point bending, one cantilever beam slides past the other in an
expression of Mode II deformation. A typical ENF setup is shown in Figure 2.5.
r
Figure 2.4: A double-cantilever beam specimen. Axes indicate the orientation of DCB specimens relative to
the bamboo culm. The crack is made in the r-z plane, also known as the TL plane, so as not to sequester the
radial gradient on one side or the other (which would confer disparate mechanical properties).
16
LI
2L
Figure 2.5: Typical ENF setup. (Adapted from Yoshihara and Ohta 2000)
These specimens are prepared as described in section 2, with the addition of a crack
running in the radial-longitudinal plane. The crack was made by splitting with a mallet and
razorblade, forming a naturally sharp tip. The nominal dimensions of these specimens ranged
from: length, 115 - 130 mm (in the longitudinal direction); width, 11 - 15 mm (in the tangential
direction); and thickness, 7 - 13 mm (in the radial direction). These sample sizes are similar to
those used in other studies (Wang et al. 2013). Span to depth ratios were no less than 7.5. In total,
20 specimens with both pith and cortex were produced; 15 specimens with neither pith nor
cortex; 5 specimens with pith only; and 5 specimens with cortex only.
Specimens were measured with calipers to determine their dimensions, and weighed on a
Cole-Parmer Symmetry ECII balance (Cole Parmer, Vernon Hills, IL). From these
measurements, the density was calculated. Specimens were then mounted on a three-point
bending experimental span and subjected to bending at 2 mm/min by an Instron 4206 with a 5kN
load cell (Instron, Norwood, MA). Span length (2L) was 110 mm. Bending continued until
specimen failure.
The load was measured using the Instron's load cell, and specimen displacement was
measured using a direct-current linear variable differential transformer (LVDT) model 0243-
17
0000 (Trans-Tek Inc., Elington, CT). The LVDT was connected to a DC power supply (HewlettPackard model E3612A, Palo Alto, CA) and outputted at approximately 10 V. The load and
displacement were recorded using a National Instruments data acquisition module (NI USB6211) and LabView software (National Instruments, Austin, TX).
Samples were positioned so that the radial axis of the culm pointed outward, i.e. so that
the radial gradient was directed into the page in Figure 2.4. This prevented partial fracture of the
specimens due to density-induced differences in mechanical strength.
2.4: Three-Point Bending Test
In order to perform most kinds of ENF analysis, an estimate of Young's Modulus in the
longitudinal direction (EL) is required. To accomplish this, simple beam specimens (length = 120
m, width = 5.8 -7.2 mm, thickness [determined by the culm wall thickness]= 7-13 mm) were
also prepared. These specimens were then subjected to 2 mm/min Instron three point bending
tests until failure.
18
Chapter 3: Analytical Methods
The interlaminar toughness, G 1e, is perhaps the most critical materials parameter for
predicting bamboo failure. Because bamboo has such profound anisotropy in its tensile
strength-hundreds of MPa in the longitudinal direction, but much lower along other axes-the
propagation of cracks is determined by the material's propensity to delaminate (Wang et al.
2013). Thus, the interlaminar toughness, not the strength, is the key parameter. Previous studies
have examined the mode I fracture characteristics of Moso bamboo by calculating G, in the LR
plane: Shao et. al found Gk= 358 J/m 2 (2009). This study examined longitudinally propagating
cracks in the TL plane.
For application in structural bamboo products, the sliding mode is expected to be the
most relevant. Hence, this study focused on mode I fracture, calculating the value of G 1 e by two
different analytical routes.
3.1: Data processing
During ENF testing, the force-displacement curve of the sample was measured until
fracture. However, in calculation of G11 , it is not the maximum load the material withstands that
is important; it is the point at which crack propagation, caused by loading, moves from the stable
regime to the unstable regime (de Moura 2006). During the initial stage of loading, the crack
remains stable, as the material elastically deforms; then, as shown in Figure 3.1, the slope of the
F-6 curve decreases, signaling the beginning of crack propagation. As the load increases, crack
propagation becomes unstable, followed shortly thereafter by specimen failure (Wang et al.
2013).
19
Load vs. Dishcomen
400
Figure 3.1: Typical F-6 curve for an ENF test, divided into stages: a) initial loading; b) stable crack
propagation; c) unstable crack propagation and failure
A secant line approximation is used to determine this critical transition (Figure 3.2). In
this method, used by industry standard in China (Janssen 1991) and by many researchers (Lo et
7e
Yu et al. 2007), the initial slope of the F-6 curve is measured by
al. 2004; Chung and Yu 2002;
Soo
regression of the linear section of the curve (usually between 0 and 0.25F.,,,). Then, a secant line
with 95% of that slope is drawn on the F-6 curve. When the point of intersection of the secant
point is taken as the critical
line with the F-6 curve is before the maximum load, the intersection
4
3'
3
-ci
0
'S
I
AS
2
2'5
load, Ferj. When the intersection is beyond F.,,x, Fcru is approximated as F.,,,.
Load vs. Displacement
900
300
-
700-
200
Displacemrpa
(mm)
to 95% of the original slope
corresponding
(black),
Figure 3.2: F- curve with secant line approximation
catt
defines Fft and
yellow,
in
annotated
intersection,
of
(red) (i.e. y = 0.95 Co x). The point
20
3.2: Substitutional Method
Once Fe,,i, and 6 c,,i,were established for each sample (Appendix B), Gmc was calculated.
The first method used, dubbed the substitutional method, is so-called because it requires no
materials parameters from outside the experiment. Wang et. al found that Gmc could be calculated
from Equation 1 (2013).
_
2
9Fcrita Scrit
2b(2L 3 + 303
)
subs =9U
G HC
bOa
where a is the crack length, b is the thickness of the specimen, and L is half the support span, as
illustrated in Figure 2.5.
3.3: Young's Modulus and Modulus of Rupture Calculations
Classical beam-bending experiments were undertaken to determine values for the
longitudinal Young's modulus, EL. For these experiments, EL was determined from the initial
slope of the F-6 curve, using equations 2 through 4:
FL3
j
48
ELIbeam
Ibeam=bh
3
(3)
12
where
'beam
is the moment of inertia for a beam, and h is the height of the specimen. Combining
these two expressions, we find:
21
E
=
4b 6~
m
(4)
L=
3
84b3
"
where mF-j is the initial slope as marked in Figure 3.3. By measuring F,,, it was further possible
to calculate the modulus of rupture (MOR, or Ofle) to correlate the experiments with those
reported in the literature. Details of this comparison can be found in Appendix C.
3FL
MOR = 2bh2
(5)
The average longitudinal Young's modulus was found to be 12 GPa, in good
agreement with known literature values (Dixon and Gibson 2014). The Young's modulus did not
vary much with sample sheathing (i.e. pith vs. cortex removed), suggesting that, as a bulk
property, it is not much affected by the outermost layers of the sample.
Load vs. Dhlacament
21
218
y =58.4x + 9.3
R^2 = 0.994
ISOC~m
Displacement (mm)
Figure 3.3: Typical beam bending curve. The initial slope (dashed black lines) is used to calculate Young's
modulus (equation 4). The peak load and displacement, FeaI and dent (annotated in yellow), are used to
calculate modulus of rupture (MOR)
22
3.4: Timoshenko Method
The Timoshenko method, derived from Timoshenko beam theory, takes into account the
effect of the transverse shear. For this method, the EL used was from the experiments above,
taken as EL = 12.0 (standard deviation: 1.1); density values for beams were 600-680 GPa, in
good agreement with the densities calculated for ENF samples. GJ3 was taken from literature
values for
GTL,
the relevant direction for our specimens. In 1999, Bai et. al found that
GTL
for
Moso bamboo was 900 MPa.
c
G LO-9Fcita'
2 3
-
2ELb h
EL (h 2]
+ 0.2
a(6)
where h is the specimen half-height (as illustrated in Figure 2.5).
Wang et. al claims that the Timoshenko method is less accurate than the substitutional
method (2013). In the case of this study, particularly since
GTL
was not directly measured, it is
provided simply as a point of comparison for the substitutional method.
23
Chapter 4: Results and Discussion
In the manufacture of structural bamboo products, the bamboo culm is sliced into strands
or wafers (Dixon and Gibson 2014). During this process, many of its macroscopic properties are
equalized: the density gradient becomes much less pronounced; the material can be made more
isotropic by layering it in a crisscross fashion; the material may be strengthened by densification,
hot-pressing, or other manufacturing methods; and the addition of a glue or resin adds a whole
new dimension of properties to consider.
During processing, the bamboo also loses its structural hallmarks: nodes, internodes, pith,
and cortex. The nodes are sometimes said to be mechanically robust and biologically
instrumental to bamboo's high strength, but recent research has shown that they are generally
points of mechanical weakness (Taylor et al. 2015). The role of the pith and cortex, from a
mechanical perspective, is even less well understood.
This study measures the interlaminar toughness (Gil,) of Moso bamboo, comparing
results from specimens with: both the pith and cortex intact; the pith removed; the cortex
removed; and both pith and cortex removed. The other axes of comparison explored are the
density (which ranged from 530-720 kg/M 3) and the height of on the culm, with specimens cut
from the
7 th, 1 0
th 12 th,
and
1 6 th
nodes.
4.1: Impact of Pith and Cortex Inclusion on Fracture Properties
Given that bamboo is sliced in the preparation of SBPs, it is expected that the typical
element of material within an SBP does not have its pith or cortex intact. We will thus treat the
bare case-no pith and no cortex-as the "baseline" for our GIc calculations. Twenty of these
baseline specimens were tested in ENF.
24
Table 4.1: Calculated values for Giic for samples without pith and cortex.
Glic (j/M2
Timoshenko Method
)
Glic (J/m 2 )
Substitutional Method
Internode
Average
694
708
7 (n=5)
Std Dev
83
108
Internode
10 (n=10)
Average
Std Dev
673
163
666
103
Internode
16 (n=5)
Average
Std Dev
485
109
703
179
Average
All (n = 20) Std Dev
631
155
686
121
Wang et
Average
1303
1108
al.(n= 43)
Std Dev
116
127
The values obtained were substantially lower than those reported by Wang et al. (2013),
who finds G 1c to be in the 1050-1370 J/m 2 range. But close reading of the Wang et al. study
suggests that the methodology used left the pith and cortex both intact. If we do the same, we
find the following:
)
Table 4.2: Calculated values for G 1c for samples with pith and cortex intact.
Glic (J/m 2 )
GlIc (j/M2
Substitutional Method
Timoshenko Method
Internode
10 (n=10)
Average
Std Dev
911
103
751
83
Internode
12 (n=5)
Average
Std Dev
924
195
823
179
All (n = 15)
Average
Std Dev
916
133
775
121
25
The discrepancy between these value ranges (t = 5.0 x 106 for the substitutional method;
t = 0.029 for the Timoshenko method) confirms that the mechanical properties of each subset of
specimens are quite different. Since Wang et. al's values are significantly higher than even the
specimens that include the pith and cortex, we believe that they left the pith and cortex on their
specimens. Hence, it does not accurately reflect the anatomy of bamboo elements used in SBP.
.
From our data, we established a new baseline value: G1 c = 630 t 155 J/m 2
4.2: Gi, vs. Density
We shall now explore the relationship between Guc and other parameters. Other studies
have correlated mechanical properties such as Young's modulus, the tensile strength, the
compressive strength and other parameters to density (Dixon and Gibson 2014; Aijazi 2013;
Shao et al. 2009; Amada et al. 1997). It thus seems fitting to map our data against calculated
densities (Figure 4.2). In doing so, however, we do not see any meaningful trend.
GII, vs. Density
1200
1000
y= 0.7508x + 286.48
800
R 2 =0.03824
600
S
400
200
100
200
300
400
500
3
Density (kg/M
600
700
800
)
0
Figure 4.1: No trend was observed between interlaminar toughness and density. Note the impressively low
R2 value.
26
It is possible that no trend is observed because the samples measured were too thick to
capture the density gradient in the radial direction. If it were possible to manufacture much
thinner specimens, we might observe a more pronounced trend. However, the specimens used in
this study are already on the small end of the spectrum for ENF testing; more typical sample
dimensions are 500 mm x 25 mm x 25 mm (de Moura 2006; Yoshihara and Ohta 2000). Future
studies would need to consider the feasibility of measuring from a substantially smaller sample.
4.3: Guc vs. Height
Since a density gradient also exists along the longitudinal axis for Moso, it is observed
that properties that vary with density also vary with height. Since Glic does not vary with density,
we do not expect a variation with height. And, indeed, we do not see one:
G1II vs. Height
1000
900
800
700
600
500
400
*Subs w/o p+c
300
lITimo w/o p+c
200
Subs w/ p+c
X Timo w/ p+c
0
0
50
100
150
200
Height from base of plant (cm)
250
300
Figure 4.2: No trend was observed between interlaminar toughness and height. On this chart, blue diamonds
represent Gil calculated by the substitutional method for specimens without pith and cortex; green triangles
represent the substitutional G 1, value with pith and cortex still intact. Red squares represent Gu calculated
by the Timoshenko method for specimens without pith and cortex; purple hatchmarks represent the
Timoshenko G 1evalue with pith and cortex still intact
27
4.4: Pith vs. Cortex in increasing G, value
,
In section 4.1, we established a statistically significant discrepancy between G 1
measured with the pith and cortex intact, and Gjjc measured with both removed. It is also
interesting to consider the question of which component-the pith or the cortex-is the greater
contributor to this discrepancy. In order to answer this question, samples missing either the pith
or the cortex were prepared from internode 11, and tested for comparison with the other
specimens.
Interlaminar Toughness Varies with Pith and Cortex Inclusion
1000
U
U Timoshenko
800
E
U
Substitutional
600
400
200
0
(/'0)
*70)
Figure 4.3: Comparison between specimens with various pith and cortex configurations. The cortex only
samples have a significantly higher value than the pith only or no pith and cortex specimens. It appears that
the inclusion of the cortex makes the difference between the no pith and cortex specimens and the both pith
and cortex specimens (shown to be significantly different from each other in section 4.1)
From these values, it appears that the cortex, or outermost layer, is the primary
contributor to increased G 1e. This finding is counterintuitive, however: the pith, or innermost
layer, is made up of isotropic stone cells, which perhaps should impede motion of the crack more
28
effectively than the thin, waxy cortex does (Wang et al. 2013). It was qualitatively observed that
more visible propagation of the crack does occur in the pith, both in this study and that by Wang
et. al.
If the cortex itself does not, in fact, contribute meaningfully, this data suggests that in fact
Gi1, is a function of density, but that our specimens were so large in the radial direction that it
could not be captured in this study. In this interpretation of the data, the pith-only specimens
have an artificially low Glic measurement, due to the fact that their outermost layers were
removed to in order to remove the cortex. In doing so, the tissue most densely populated with
schlerenchyma fibers was also removed, weakening the remaining specimen.
This interpretation of the data is supported by the pith-only and cortex-only Young's
modulus data from the beam-bending experiments. The cortex-only specimens, which through
removal of their innermost layer have an inflated volume fraction of sclerenchyma fibers, are
calculated to have an EL value that is anomalously high compared to the rest of the specimens.
Table 4.3: Calculated values of Young's modulus, EL. Note the much-higher mean value for
the cortex-only specimens compared to the average for all specimens.
Average
Standard
dev
EL (GPa)
without pith +
cortex (n=9)
12.2
EL (GPa)
pith only
(n = 4)
12.4
EL (GPa)
cortex only
(n = 3)
15.0
EL (GPa)
with pith +
cortex (n = 3)
13.1
EL (GPa)
All, except cortex
only (n=16)
12.2
1.0
0.6
1.3
0.6
0.9
A preliminary t-test gives t = 0.044 between the cortex-only specimens and the others.
With only three cortex-only specimens, this is not sufficient information to make a verdict. But it
once again suggests, since Young's modulus is known to vary with density, that there may be a
density gradient issue at hand.
29
4.5: Impact of Other Factors
It should be noted that some of the calculations made in this study may differ from
literature values due to atypically low moisture content (4.5-5% for this study; 10-12% is more
typical). This disparity led to higher specimen density overall. Lower moisture content is
generally associated with higher values for mechanical strength and Young's modulus (Dixon
and Gibson 2014), but may have led to brittleness in fracture. Further experimentation with a
wider variety of cuirn samples would clarify this issue.
30
Chapter 5: Conclusions and Outlook
As part of a larger project to characterize the mechanical properties of Moso bamboo and
translate them into the practical understanding and application of structural bamboo products
(SBPs), this study examined the mode II interlaminar toughness (Gil,) of Moso bamboo by
performing end-notched flexure (ENF) tests. It was found that literature values include the pith
(innermost layer) and cortex (outermost layer) of the bamboo culm in their calculations. Our
measurements indicate that the resulting value is, to a statistically significant degree (t = 5.0 x
106), higher than that with the pith and cortex removed. In the context of SBP, the pith and
cortex will often be removed as a consequence of processing. A new value, GmI, = 630 t 155
J/m 2 , was established for specimens lacking the pith and cortex. This value could be altered by
specimen densification, hot-pressing, or one of the other processing modes used in the
production of SBPs.
Although no correlation was found between GIc and specimen density, it is suspected
that a relationship does exist. Many properties of Moso bamboo vary with the volume fraction of
load-bearing sclerenchyma fibers throughout the plant, which increases several-fold from the
pith to the cortex. The specimens used in this study were too large to adequately capture that
density gradient, but a future study could consider the use of smaller samples.
Through a standardized application of bamboo's mechanical properties, SBPs could turn
bamboo from a niche material to one widely used in modern construction. The production of
SBPs is an especially favorable proposition in the developing world, where most of the world's
woody bamboo grows: for countries such as China and India, SBPs could provide an
ecologically and economically sustainable solution to need for timber-like materials.
31
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34
Appendix
Appendix A: Moisture Content
Moisture content was calculated by comparing the mass of the as-received specimen to
the mass of the specimen after 24 hours of incubation at 103 'C. More explicitly,
%H20
where mo is the as-received mass, and
- mdried x100%
mdried
rndried
(lA)
is the mass after incubation. This
calculation gave
an average moisture content of 4.68%, with a standard deviation of 0.24%, with
n = 35. No difference was noted between the specimens including the pith and cortex vs. the
specimens with neither pith nor cortex.
35
Appendix B: F,,it and
'cri,
approximations
This section gives the exact values determined for Feri,and deit of each specimen
measured. Specimens are numbered by internode and then by specimen number (i.e. 10-1 is the
first specimen cut from the tenth internode up.) Some specimens are labeled "b," for "both
removed," in order to differentiate them from other specimens taken from the same node.
I dcrit (mm)
Sample I Fcrit (N)
Neither pith nor cortex
3.06
799
7-1
2.23
819
7-2
2.55
977
7-3
2.00
748
7-4
2.55
779
7-5
2.12
601
10-bi
2.05
534
10-b2
3.11
630
10-b3
1.87
574
10-b4
2.04
622
10-b5
2.73
567
10-b6
2.55
771
10-b7
2.48
513
10-b8
1.85
703
10-b9
1.89
567
12-bi
1.89
548
16-1
1.70
611
16-2
1.85
483
16-3
1.80
452
16-4
1.50
586
16-5
only)
No cortex (pith
1.98
951
11-cl
2.48
694
11-c2
2.37
710
11-c3
I
Sample I Fcrit (N)
I dcrit (mm)
No pith (cortex only)
11-p1
781
2.42
11-p2
869
1.72
11-p3
897
1.83
11-p4
1099
1.77
11-p5
1171
1.76
Both pith and cortex
10-1
888
2.03
10-2
745
2.13
2.09
842
10-3
10-4
771
2.26
10-5
770
2.48
10-6
832
2.12
2.30
811
10-7
10-8
934
1.97
1139
2.12
10-9
10-10
967
2.11
12-1
875
2.02
12-2
934
2.28
12-3
831
2.32
12-4
846
2.55
12-5
730
1.93
No cortex (pith only)
11-c4
786
1.87
11-c5
813 1
1.74
These are the values from which the substitutional and Timoshenko method measurements for
Guc were taken.
36
Appendix C: Modulus of Rupture
Although the modulus of rupture (MOR) was not examined in-depth in this study, it is
useful to compare values for our specimens to values in the literature. A comparison shows that
our MOR values match up well with those found in an investigation by Lin et al. (2006):
Sample
without pith +
cortex (n = 9)
Avg
Std dev
MOR (MPa)
139.10
12.53
pith only (n =
4)
Avg
Std dev
118.57
16.19
cortex only (n
= 3)
Avg
Std dev
158.29
5.14
both pith and
cortex (n = 3)
Avg
Std dev
139.60
5.49
Lin et al. (n=
30)
Avg
Std dev
144.3
9.6
Since increasing MOR is correlated with increasing density, the cortex only specimens show the
same bias identified in Young's modulus in section 4.4. (i.e. artificially inflated value due to
increased volume fraction of sclerenchyma fibers).
37