Wavy Sycamore Maple Relationships Between Anatomical, Physical, Mechanical, And Vibrational Properties
WAVY SYCAMORE MAPLE: RELATIONSHIPS BETWEEN
ANATOMICAL, PHYSICAL, MECHANICAL, AND
VIBRATIONAL PROPERTIES
AHMAD ALKADRI
GRADUATE SCHOOL
BOGOR AGRICULTURAL UNIVERSITY
BOGOR
2017
ii
iii
COPYRIGHTS STATEMENT
I declare that this thesis, entitled Wavy Sycamore Maple: Relationships between Anatomical, Physical, Mechanical, and Vibrational Properties is my own
work with the direction of the supervising committee and has not been submitted
in any form for any college except in AgroParisTech centre de Nancy and Université de Lorraine, France (required by the Double Degree Master Program—the
joint Master program held between the Program Study of Forest Products Science
and Technology of Bogor Agricultural University and Bois Forêt et Développement Durable of AgroParisTech centre de Nancy and Université de Lorraine).
Information and quotes from journals and books have been acknowledged and
mentioned in the parts of the thesis where they appear. All complete references
are given at the end of the paper.
I understand that my thesis will become part of the collection of Bogor Agricultural University. My signature below gives the copyright of my thesis to Bogor Agricultural University.
Bogor, January 2017
Ahmad Alkadri
NIM E251140041
iv
SUMMARY
AHMAD ALKADRI. Wavy Sycamore Maple: Relationships between Anatomical, Physical, Mechanical, and Vibrational Properties. Supervised by IMAM
WAHYUDI and IRIS BRÉMAUD.
Sycamore maple (Acer pseudoplatanus L.) is a wood species particularly
known for its wavy grain figures and its high-value utilization among luthiers and
craftsmen for musical instruments or furniture making. Although past separate
studies had determined its properties, little had been done in order to quantify the
waviness characteristics of its unique patterns and the correlations between its
properties which include the anatomical, physical, mechanical, and vibrational or
acoustical characteristics. Backed by its high degree of valuation and utilization,
this research was conducted in order to study the characteristics of sycamore maple and how they correlate with each other.
The specimens taken for the measurements were procured from different
trees with various surface figures. Vibrational and mechanical measurements were
conducted using Vybris, a semi-automated device developed by Gifu and Kyoto
University, Japan and manufactured in LMGC (Laboratoire de Mécanique et Génie Civil) in Montpellier, France by taking into account the radial and longitudinal
directions and its local variations. Waviness’ characteristics were quantified by
measuring the wood blocks which were splitted parallel to the grain, while anatomical properties such as microfibril angle and rays’ dimensions were measured
using light microscopy.
Results from this study provide a dataset regarding the properties of wavy
sycamore maple. Through statistical analysis, it can be concluded that there are
significant correlations between the measured parameters, particularly between
waviness, microfibril angle, the specific modulus elasticity, and damping coefficient by internal friction of the wood in longitudinal direction. The anisotropy
properties were found to be very low but was not satisfactorily explained by the
anatomical features studied. Future studies using similar methods should be conducted with larger number of speciments and refined statistical analysis models.
Analysis regarding the mechanical model of wavy-grain wood, which may include
variables such as MFA, grain angle, and waviness, should be conducted.
Keywords: anisotropy, damping, microfibril angle, modulus of elasticity, rays,
wavy grain
v
RINGKASAN
AHMAD ALKADRI. Maple Sycamore Bergelombang: Hubungan antara Sifat
Anatomi, Fisis, Mekanis, dan Akustik. Dibimbing oleh IMAM WAHYUDI dan
IRIS BRÉMAUD.
Maple sycamore (Acer pseudoplatanus L.) adalah spesies kayu yang dikenal
karena pola seratnya yang bergelombang dan pemakaiannya sebagai bahan baku
furnitur serta alat musik. Walaupun banyak penelitian terdahulu telah berhasil
menentukan berbagai macam karakteristiknya, sedikit di antaranya yang telah
melakukan kuantifikasi pola gelombang seratnya dan hubungan antar sifatsifatnya yang mencakup dari anatomis, fisis, mekanis, hingga akustik. Mengingat
penggunaannya yang intensif dan nilai ekonominya yang tinggi, penelitian ini pun
dilakukan untuk menentukan sifat-sifat kayu maple sycamore dan korelasinya antara satu sama lain.
Spesimen yang digunakan dalam pengukuran diperoleh dari berbagai pohon
yang memiliki pola permukaan bergelombang yang berbeda-beda. Penentuan sifat
mekanis dan akustik dilakukan dengan menggunakan Vybris, alat semi-otomatis
yang dikembangkan oleh Universitas Gifu dan Kyoto di Jepang serta dirakit di
LMGC (Laboratoire de Mécanique et Génie Civil) di kota Montpellier, Perancis
pada arah orientasi radial dan longitudinal. Variasi lokal untuk kedua arah orientasi tersebut juga ditentukan. Kuantifikasi karakteristik pola serat gelombang dilaksanakan dengan mengukur spesimen balok yang dibelah pada arah sejajar
dengan serat, sedangkan sifat-sifat anatomi seperti sudut mikrofibril dan dimensi
jari-jari diukur menggunakan mikroskop cahaya.
Penelitian ini menghasilkan set data hasil pengukuran sifat-sifat kayu maple
sycamore bergelombang. Melalui analisis statistik, korelasi signifikan antar parameter berhasil ditentukan, terutama antara derajat kegelombangan dengan sudut
mikrofibril, dan antara sifat-sifat anatomi dengan modulus elastisitas spesifik serta
peredaman oleh friksi internal kayu pada arah longitudinal. Pada penelitian ini,
nilai sifat-sifat anisotropi kayu yang diamati sangat rendah dan tidak bisa dijelaskan dengan cukup memuaskan menggunakan sifat-sifat anatomi yang telah ditentukan. Penelitian berikutnya yang menggunakan metode serupa harus dilakukan
dengan jumlah spesimen lebih besar dan model analisis statistik yang lebih mendalam. Analisis model mekanis kayu bergelombang, yang dapat mencakup variabel-variabel seperti MFA, sudut serat, dan derajat kegelombangan serat, pun
sebaiknya dilakukan.
Kata kunci: anisotropi, jari-jari, modulus elastisitas, peredaman, serat bergelombang, sudut mikrofibril
vi
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without a permission from IPB
WAVY SYCAMORE MAPLE: RELATIONSHIPS BETWEEN
ANATOMICAL, PHYSICAL, MECHANICAL, AND
VIBRATIONAL PROPERTIES
AHMAD ALKADRI
Thesis
In partial fulfillment of the requirements for the degree of
Master of Science
at
Forest Products Science and Technology Study Program
GRADUATE SCHOOL
BOGOR AGRICULTURAL UNIVERSITY
BOGOR
2017
External Examiner: Dr Ratih Damayanti, SHut, MSi
x
FOREWORD
The author would like to thank the administration of Master of Science program of Forest Products Science and Technology of Bogor Agricultural University and Master Program of Bois Forêts et Développement Durable (BFD) of AgroParisTech centre de Nancy and Université de Lorraine for their academic cooperation in the form of Double Degree Master Program, supported with the
scholarships of Beasiswa Unggulan from Ministry of Education and Culture of
Indonesia and Bourse de couverture social de gouvernement Française from
French’s Ministry of Foreign Affairs. Without said cooperation, such chance to
conduct this research will not come into fruitition.
The author is grateful to LMGC (Laboratoire de Mécanique et Génie Civil)
and Cirad (Centre international de cooperation et recherche en agronomie) in the
city of Montpellier, France, who offered the information and opportunity for this
research. Without all their supports, both in materials, equipment, and financial,
this research would not be able to be conducted. The authors would also like to
thank La Région Languedoc-Roussillon for the financial support, as part of the
project “Chercheur(se)s d’Avenir” awarded to Dr. Iris Brémaud.
Special thanks to Professor Joseph Gril, the head of Wood Research Group
at LMGC; to Dr. Iris Brémaud and Dr. Patrick Langbour who supervised this research in Montpellier. Special thanks also directed to Professor Imam Wahyudi,
the author’s supervisor in the Department of Forest Products, Faculty of Forestry,
Bogor Agricultural University, Indonesia; to Professor I Wayan Darmawan, the
coordinator of the double degree Master program of Bogor Agricultural University, Indonesia; and to Professor Mériem Fournier, the director and coordinator of
double degree Master program of AgroParisTech centre de Nancy. Special thanks
are also directed to Capucine Carlier, the PhD student in LMGC’s Wood Research
Group, who worked on the violin-making tonewood, for sharing and exchanging
the scientific information about the subject.
Finally, the author would like to express his gratitude to his friends and colleagues: Capucine (again), Agnès, and Vivien for their companionships, high spirit attitude, great work ethos, positive outlooks, and the bicycle; to Anna for the
guitar; to Alban, Daniel, and Marie-France Thèvenon for their help and hospitality
during the course of this research at the laboratory of wood anatomy at Cirad; and
to all other professors, researchers, staff, technicians, Post-Docs, PhD students, interns and any other individuals at LMGC, Cirad, AgroParisTech, and Bogor Agricultural University who have helped the author, both directly and indirectly, in
conducting this research.
The author recognizes that this research is still far from perfect. Thus, suggestions and constructive criticisms are expected in order to improve this work.
Bogor, December 2016
Ahmad Alkadri
xi
TABLE OF CONTENTS
SUMMARY
iv
RINGKASAN
v
SHEET OF APPROVAL
ix
FOREWORD
x
TABLE OF CONTENTS
xi
LIST OF TABLES
xii
LIST OF FIGURES
xii
1 INTRODUCTION
Background
Formulation
Objective
Benefits
1
1
2
2
2
2 MATERIALS AND METHODS
Location and Period of Research
Materials Preparations
Measurements
Data Analysis
3
3
3
4
8
3 RESULTS
Vibrational Properties
Microfibril Angle
Waviness
Ray Dimensions
Correlation Between Parameters
10
10
11
12
14
14
4 DISCUSSIONS
21
5 CONCLUSIONS AND SUGGESTIONS
Conclusions
Suggestions
24
24
24
REFERENCES
24
CURRICULUM VITAE
27
xii
LIST OF TABLES
1
2
3
4
5
6
Measurement results of the sycamore maple wood’s physical and
vibrational properties
Measurement results of the sycamore maple wood’s anatomy features
Measurement results of the sycamore maple wood’s wavy grain
properties
r and p-value of pearson-product moment correlation between paired
parameters
Coefficients of regression of tanδL with MFA and waviness
Coefficients of regression of E’L/ρ with MFA and waviness
16
17
18
19
20
20
LIST OF FIGURES
1
Specimen preparation from the back plates toward the small blocks
needed for MFA and ray dimensions measurements
2 Preparation of specimens used in vibrational measurement
3 Depiction of split block specimen, from which two parameters can be
measured: the wavelength (λ) and amplitude (A=2A/2)
4 Illustration of grain angle measurement.
5 Vibrational properties results for both R and L directions.
6 Local variations (of specimens from each plate) of E’/ρ and tanδ of L
and R specimens.
7 MFA measurement methods
8 Microfibril angle (MFA) results for the twelve plates/specimens
9 Waviness (w) results for the twelve original plates/specimens
10 Example of waviness figures of the sycamore maple wood
11 Rays of the waviest wood and the least wavy one (specimen H, images
on the right)
12 MFA plotted against waviness (w), E’L/ρ and tanδL against MFA, and
E’L/ρ and tanδL against mean grain angle or θaverage.
3
4
7
8
10
11
12
13
13
14
15
22
1
1 INTRODUCTION
Background
Sycamore maple (Acer pseudoplatanus L.) is a hardwood tree species welladapted for cold temperatures and mountainous climate and broadly distributed
throughout European land (Krabel and Wolf 2013). Because of its rapid growth
and high versatility (it can grow almost everywhere as long as the soil is not too
dry or poor), it is considered as an invasive species in several regions (Peterken
2001; Chytrý et al. 2008; Morecroft et al. 2008). Although its low biological durability makes it unsuitable for outdoor construction purposes, its creamy timber and
excellent wood surface make it aesthetically pleasing, and it is mainly used in furniture, flooring, and musical instruments (Bucur 2006; Krabel and Wolf 2013).
Sycamore maple is particularly favored by luthiers and craftsmen in manufacturing the violin, guitar, mandolin, and other musical instruments (Bucur 2006;
Wegst 2006). Several factors contribute in the favorability of sycamore maple as a
material in musical instrument making. Although some studies such as Wegst
(2006) suggest that its acoustical properties are what make it highly suitable for
the back-board of several types of musical instruments such as violin or guitar,
others have suggested that craftsmen tend to determine the selectability of wood
based on more multi-factorial criteria including also visual or cultural preferences
(Brémaud 2012; Buksnowitz et al. 2012).
Psychosensory study on this subject is currently still limited; however, it has
been suggested that there is a correlation between the wood’s physical appearance—or, in the case of sycamore maple, its wavy-grain—with its mechanicalacoustical properties (Kudela and Kunštár 2011). It needs to be noted that, in their
study, Kudela and Kunštár (2011) compared the physical-mechanical-acoustical
characteristics of wavy maple wood with those of the control (non-wavy wood).
Thus, even though they have determined that there are significant differences in
characteristics between wavy and non-wavy or normal wood, the degree of correlation, or the depth of the relationships between the wood’s wavy-figure characteristics and physical-mechanical-acoustical properties, such as the factors causing
and being affected, has still not been determined.
Although little is known on the relations between the wavy grain characteristics and physical-mechanical-acoustical properties, several studies have tried to
determine the factors causing the formation of this particular trait in order to reproduce it. Various studies have shown the possibility of giving external stresses,
for the wavy grain is also known as another form of reaction wood, to stimulate
the specific genetical agents within the tree to produce phytohormones like auxin
and ethylene for prompting the formation of wavy grain (Nelson and Hillis 1978;
Rohr and Hanus 1987; Ewald and Naujoks 2015). These studies have also shown
that the formation of wavy grain are affected by genes and phytohormones, which
is also the case with the formation of wood on microstructural level (Pilate et al.
2004). However, study on the anatomical characteristics of sycamore maple with
wavy wood characteristics is still very limited.
In the past, others have studied the relationships between the anatomical
properties of the wood with its physical and mechanical properties (Yang and
2
Evans 2003; Beery et al. 2007). Several anatomical factors affecting wood mechanical properties have been determined. Along the grain (longitudinal direction
of wood), microfibril angle (MFA), is known as the main determinant of modulus
of elasticity (MOE, or E’, or Young’s Modulus) and specific modulus (E’/ρ), as
well as of internal friction (or damping, tanδ) (Obataya et al. 2000). Fiber angle
has a similar effect on mechanical-vibrational properties (Brémaud et al. 2011).
The rays may affect the mechanical and physical properties on radial section
(Burgert and Eckstein 2001; Reiterer et al. 2002) and possibly also, to a lower
extent, on longitudinal direction (Tippner et al. 2013). In short, the relationships
between anatomical and physical-mechanical-acoustical properties of the wood
have been well-documented. However, in sycamore maple with wavy grain wood,
the correlations between those characteristics have not yet been well-studied.
Formulation
Interested by the high value and utilization of wavy sycamore maple, many
researchers had conducted studies in order to better understand its properties.
However, the correlations between its physical, mechanical, acoustical, and anatomical properties (including the wavy grain) have not been clearly determined.
Therefore, the questions that needed to be asked: how do said properties of sycamore maple correlate with each other? Which characteristics are related with others, and how much of those relationships are significant?
Objective
This research aims to better characterise sycamore maple wood presenting a
gradient of wavy figure and to determine the potential correlations among anatomical (wavy grain, MFA, rays’ characteristics), physical, mechanical, and acoustical
properties (including specific modulus of elasticity, damping coefficient, and their
anisotropy). The sample selection included a wide variability of wood surface
with varying level of grain waviness, making it possible to determine the relationships between those parameters by using statistical analysis.
Benefits
The results of this study are expected to provide the scientific informations,
original data, and statistical analysis of the properties of wavy sycamore maple
wood. Said data are expected to be beneficial for the development of study in the
field of acoustic science, materials, biology, and sylviculture. Further benefits
could also be reaped by the musical instruments industry, especially by the violin
makers, artists, and other interested parties.
3
2 MATERIALS AND METHODS
Location and Period of Research
This research was conducted at the Laboratory of Mechanics and Civil Engineering (Laboratoire de Mécanique et Génie Civil) and French Agricultural Research Centre for International Development (Centre international de cooperation
et recherche en agronomie) in Montpellier, France from February to July 2016.
Materials Preparations
Specimens Preparations for Anatomical Measurements
Twelve quarter-cut wedge shaped boards for violin back plates, labelled A to
L, were used in this study, with the approximate dimensions of ± 40 cm × 13 cm ×
2.5 cm (connecting side) or 1 cm (edge). They were obtained from several violin
makers and specialized wood suppliers from Romania, Bosnia, and France. Specimens from each plate were prepared according to Figure 1. The first cut produced
a trapesium-shaped block 2.5—3 cm high, named block i. From block i, second
cuttings were conducted to produce block ii and block iii, with dimensions 2 × 2.5
× 3 cm3. Each block ii from each specimens were used for waviness measurement.
Block iii were then cut to produce block iv and block v used for MFA and ray dimensions measurements, respectively.
Figure 1 Specimen preparation from the back plates toward the small blocks
needed for MFA and ray dimensions measurements
4
Specimens Preparations for Vibrational Measurements
For vibrational properties measurement, using the existing sampling plan
that was also used in other assessments of within-plate variability using vibrational tests (Brémaud et al. 2010, 2012), the back plates were cut into small strip
specimens with the dimension of 150×12×2 mm3 (L×R×T) for longitudinal specimens, and 120×12×2 mm3 (R×L×T) for radial specimens (Figure 2). The sampling plan allows to study the distribution of properties within plates.The variation
of specimen thickness must be reduced as much as possible for it provides a primary source of errors in the measurement of the specific modulus (E’/ρ) (Brémaud et al. 2012). Thus, after being procured, all specimens for vibrational testing
were conditioned for at least 2 weeks in standard air-dry conditions (20±1°C and
65±5% relative humidity-RH) in order for them to reach dimensional stabilization.
Figure 2 Preparation of specimens used in vibrational measurement
Measurements
MFA Measurements
Specimens for MFA measurement were prepared based on the light microscopy MFA methods described by Senft and Bendtsen (1985). The blocks used for
MFA measurements were those of block iv. Each of them were submerged in water, taken out, oven dried, and then re-submerged again. This cycle was conducted
at least two times in order to create cracks within the wood cells which will enhance the appearance of MFA.
Slicings were conducted on the blocks’ radial surface using a rotary-slide
microtome to produce small thin sections approximately 5 µm thick. The resulting
sections were stored in 50% alcohol. Afterward, the sections were dehydrated in a
solution of absolute (>99%) alcohol for 5 minutes, twice. The sections were then
5
immersed in a solution of 2% iodine-potassium iodide (IKI) for 2 to 10 seconds.
Then, sections were placed on a slide and excess solution were blotted using a
paper towel. Two drops of 60% nitric acid (HNO3) were added to the section
before applying a coverslip. The iodine filled the cracks between the microfibrils,
thus making the MFA visible as dark streaks along the cell wall. Pictures of the
MFA were taken using a light microscope with 600× enlargement and the angles
were measured using ImageJ.
During the course of the measurements, because of the different surface cut
condition of each sample, the angles measurements were not always conducted
according to the same strict rule. The MFA themselves are very hard to be observed directly using light microscopy because the fibrils in the cell walls, especially in S2 layer, are tightly formed (Long et al. 2000). The pretreatment given
before the slicings relieved the tightness a little, but not by a wide margin, and
thus the resulting surfaces made it necessary to measure the MFA using one of the
following techniques:
a. the MFA was measured according to the angle of the cracks between
microfibrils and complemented by the angle of the pits (Donaldson
2007),
b. the MFA was measured according to the MFA directly. This rarely
occured, for in order to be able to observe and measure the MFA
using light microscopy, the “crackings” or defibrilation between the
microfibrils must happened exactly between each one of them within
one fiber cells. These rare occurences could be chalked up to the low
tightness between the microfibrils and the low amount of lignin or
bonds between the MFA,
c. the MFA was measured based on the angle of the pits within the
fiber (Donaldson 2007). This is an acceptable method of MFA
measurement, but it has to be conducted very carefully because the
angle of the pits does not always correspond perfectly with the
MFA. Thus, it is necessary to measure more than one pits’ angle
within the same fiber, and to check with the occurring cracks,
however small they are, within the same or neighbouring cells. If the
angles between them are consistent and not vary by a high amount,
then the angle of the pits can be said to be similar, or the same, with
the MFA. Also observed were the “tails” of the pits, or the elonged
lines from both end of the pits, which normally correspond more
with the MFA than the “body” of the pits.
Examples of each of the mentioned MFA measurement methods can be seen
in Figure 7.
Rays Dimensions Measurement
The blocks used for rays dimensions measurements were those of block v.
Each blocks’ tangential surfaces were sliced using a rotary-slide microtome to
small sections 15—17.5 µm thick. The resulting sections were stored in 50%
alcohol. Afterwards, sections were immersed in sodium hypochlorite for 30
minutes in order to solubilize the extractives. Sections were then immersed in
colorant (green iode, prepared with 1 g Iodine powder + 30 cc distilled water and
70 cc ethanol), giving it a green color, in order to enhance the observation. Next,
6
sections were dehydrated in several levels of alcohol solution, starting from 25%,
50%, 75%, towards absolute (>99%). Fully dehydrated, the sections were placed
on a slide and given a coverslip. Pictures were taken using a light microscope with
40× enlargement and the rays’ dimensions were measured using ImageJ. Measured parameters were the height and width of, respectively, large rays and small
rays, and the percentage of the surface of the section they represent.
Wavy Figure and Grain Angle Measurement
Block ii were splitted parallel to the grain direction (Figure 3). The resulting
splits show clear wave-like figures which were then scanned and measured using
ImageJ. To measure the wavy grain, it was assumed that: a) the wave-like figures
were consistent throughout the part of the wood which possesses it, b) the wavelike figures followed the standard equation form of a sinusoidal wave (formula 1)
with two parameters taken into account: the amplitude (A) and wavelength (l).
⎛ 2π x ⎞
y = A ⋅ sin ⎜
⎟
⎝ λ ⎠
(formula 1)
In a sinusoidal wave function, the slope of a specific point (x,y) can be
calculated as dy/dx (Figure 4). Slope = tanθ with θ in radians (rad) unit. Thus:
⎛ 180 ⎞
⎛ dy ⎞
θ =⎜
⎟ ⋅ arctan ⎜ ⎟ for θ in degrees (º) unit.
⎝ π ⎠
⎝ dx ⎠
(formula 2)
When the slope is small, or if dy/dx |t|)
Intercept
0.007122
0.002337
3.048
0.0138*
MFA
0.000145
0.000261
0.556
0.5919
Waviness
0.063876
0.054615
1.170
0.2722
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Multiple R2 = 0.6757 ; adjusted R2 = 0.6037 ; p-value = 0.006295
Table 6 Coefficients of regression of E’L/ρ with MFA and waviness
Independent
variable
Estimate
Standard Error
t-value
Pr (>|t|)
Intercept
19.9896
3.5103
5.695
MFA
-0.2328
0.3920
-0.594
0.567182
-64.3900
82.0482
-0.785
0.452742
Waviness
0.000296***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1
Multiple R2 = 0.5699 ; adjusted R2 = 0.4743 ; p-value = 0.02245
From the multivariate regression analysis of tanδL with MFA and w (Table
5), the output shows that p = 0.006295, indicating that the null hypothesis that the
variables MFA and w collectively have no effect on tanδL should be rejected
(confidence level = 95%). Results also show that variable MFA is not
significantly controlling for the variable w (p = 0.5919), and that the variable w is
not significant controlling for the MFA (p = 0.2722). However, overall it can be
seen that collectively, MFA and w indeed affect the tanδL with the R2 = 0.6757
and R2adjusted = 0.6037. Thus, the equation can be written as follow:
tanδL = 0.007122 + 0.000145MFA + 0.063876w
(formula 5)
From the multivariate regression analysis of E’L/ρ with MFA and w (Table
6), the output shows the p-value = 0.02245, indicatng the the null hypothesis that
the variables MFA and w collectively have no effect on E’L/ρ should be rejected
(confidence level also = 95%). The results also show that the MFA is not
significantly controlling for the w (p = 0.567182) and that w is not significantly
controlling the MFA (p = 0.452742). Similar with the results of table 5,
collectively, MFA and w affect the E’L/ρ with the R2 = 0.5699 and R2adjusted =
0.4743. Thus, the equation can be written as follow:
E’L/ρ = 19.9896 – 0.2328MFA – 64.3900w
(formula 6)
21
4 DISCUSSIONS
From the results, it can be seen that there is a high intra-species variability
of w (waviness, formula 6) and θaverage (mean angle, formula 4). Among wavy maple trees, some possess low to no wavy grain, while others possess a grain so
wavy that it forms stripes-like figures on the radial plane of the wood, called
‘wave front’ (Harris 1989). Although the methods of waviness measurements
used in the present study differ from some previous research, the average values
of wave amplitude (≈0.21 mm) and of wavelength (10 mm) are comparable with
other recent results on a different and wide sampling (Krajnc et al. 2015).
In the present results, the degree of waviness is not correlated with the wood
density. This is in contrast with other findings, on reduced samplings, which suggested that wavy wood would have higher density than non-figured one (Bucur
2006; Kudela and Kunstar 2011). Anatomical features related to rays also show
nearly no correlation with waviness.
Positively correlated with the θaverage (or waviness), according to the statistical analysis that has been conducted, is MFA (Table 4, Figure 12). This original
finding is important because both the MFA and the grain angle (here caused by
wavy grain) are known to strongly affect mechanical properties in the longitudinal
direction of wood, both lowering E’/ρ and increasing tanδ (Obataya et al. 2000,
Brémaud et al. 2011). One can wonder about the origin of this strong correlation
between MFA and waviness, for past studies have shown that the MFA has to be
ruled out from the list of possible factors causing the existence of spiral grain
(Harris 1989). This suggestion was brought forward given that the grain angles
are almost certainly determined by cambial orientation in the early formation of
the fi
ANATOMICAL, PHYSICAL, MECHANICAL, AND
VIBRATIONAL PROPERTIES
AHMAD ALKADRI
GRADUATE SCHOOL
BOGOR AGRICULTURAL UNIVERSITY
BOGOR
2017
ii
iii
COPYRIGHTS STATEMENT
I declare that this thesis, entitled Wavy Sycamore Maple: Relationships between Anatomical, Physical, Mechanical, and Vibrational Properties is my own
work with the direction of the supervising committee and has not been submitted
in any form for any college except in AgroParisTech centre de Nancy and Université de Lorraine, France (required by the Double Degree Master Program—the
joint Master program held between the Program Study of Forest Products Science
and Technology of Bogor Agricultural University and Bois Forêt et Développement Durable of AgroParisTech centre de Nancy and Université de Lorraine).
Information and quotes from journals and books have been acknowledged and
mentioned in the parts of the thesis where they appear. All complete references
are given at the end of the paper.
I understand that my thesis will become part of the collection of Bogor Agricultural University. My signature below gives the copyright of my thesis to Bogor Agricultural University.
Bogor, January 2017
Ahmad Alkadri
NIM E251140041
iv
SUMMARY
AHMAD ALKADRI. Wavy Sycamore Maple: Relationships between Anatomical, Physical, Mechanical, and Vibrational Properties. Supervised by IMAM
WAHYUDI and IRIS BRÉMAUD.
Sycamore maple (Acer pseudoplatanus L.) is a wood species particularly
known for its wavy grain figures and its high-value utilization among luthiers and
craftsmen for musical instruments or furniture making. Although past separate
studies had determined its properties, little had been done in order to quantify the
waviness characteristics of its unique patterns and the correlations between its
properties which include the anatomical, physical, mechanical, and vibrational or
acoustical characteristics. Backed by its high degree of valuation and utilization,
this research was conducted in order to study the characteristics of sycamore maple and how they correlate with each other.
The specimens taken for the measurements were procured from different
trees with various surface figures. Vibrational and mechanical measurements were
conducted using Vybris, a semi-automated device developed by Gifu and Kyoto
University, Japan and manufactured in LMGC (Laboratoire de Mécanique et Génie Civil) in Montpellier, France by taking into account the radial and longitudinal
directions and its local variations. Waviness’ characteristics were quantified by
measuring the wood blocks which were splitted parallel to the grain, while anatomical properties such as microfibril angle and rays’ dimensions were measured
using light microscopy.
Results from this study provide a dataset regarding the properties of wavy
sycamore maple. Through statistical analysis, it can be concluded that there are
significant correlations between the measured parameters, particularly between
waviness, microfibril angle, the specific modulus elasticity, and damping coefficient by internal friction of the wood in longitudinal direction. The anisotropy
properties were found to be very low but was not satisfactorily explained by the
anatomical features studied. Future studies using similar methods should be conducted with larger number of speciments and refined statistical analysis models.
Analysis regarding the mechanical model of wavy-grain wood, which may include
variables such as MFA, grain angle, and waviness, should be conducted.
Keywords: anisotropy, damping, microfibril angle, modulus of elasticity, rays,
wavy grain
v
RINGKASAN
AHMAD ALKADRI. Maple Sycamore Bergelombang: Hubungan antara Sifat
Anatomi, Fisis, Mekanis, dan Akustik. Dibimbing oleh IMAM WAHYUDI dan
IRIS BRÉMAUD.
Maple sycamore (Acer pseudoplatanus L.) adalah spesies kayu yang dikenal
karena pola seratnya yang bergelombang dan pemakaiannya sebagai bahan baku
furnitur serta alat musik. Walaupun banyak penelitian terdahulu telah berhasil
menentukan berbagai macam karakteristiknya, sedikit di antaranya yang telah
melakukan kuantifikasi pola gelombang seratnya dan hubungan antar sifatsifatnya yang mencakup dari anatomis, fisis, mekanis, hingga akustik. Mengingat
penggunaannya yang intensif dan nilai ekonominya yang tinggi, penelitian ini pun
dilakukan untuk menentukan sifat-sifat kayu maple sycamore dan korelasinya antara satu sama lain.
Spesimen yang digunakan dalam pengukuran diperoleh dari berbagai pohon
yang memiliki pola permukaan bergelombang yang berbeda-beda. Penentuan sifat
mekanis dan akustik dilakukan dengan menggunakan Vybris, alat semi-otomatis
yang dikembangkan oleh Universitas Gifu dan Kyoto di Jepang serta dirakit di
LMGC (Laboratoire de Mécanique et Génie Civil) di kota Montpellier, Perancis
pada arah orientasi radial dan longitudinal. Variasi lokal untuk kedua arah orientasi tersebut juga ditentukan. Kuantifikasi karakteristik pola serat gelombang dilaksanakan dengan mengukur spesimen balok yang dibelah pada arah sejajar
dengan serat, sedangkan sifat-sifat anatomi seperti sudut mikrofibril dan dimensi
jari-jari diukur menggunakan mikroskop cahaya.
Penelitian ini menghasilkan set data hasil pengukuran sifat-sifat kayu maple
sycamore bergelombang. Melalui analisis statistik, korelasi signifikan antar parameter berhasil ditentukan, terutama antara derajat kegelombangan dengan sudut
mikrofibril, dan antara sifat-sifat anatomi dengan modulus elastisitas spesifik serta
peredaman oleh friksi internal kayu pada arah longitudinal. Pada penelitian ini,
nilai sifat-sifat anisotropi kayu yang diamati sangat rendah dan tidak bisa dijelaskan dengan cukup memuaskan menggunakan sifat-sifat anatomi yang telah ditentukan. Penelitian berikutnya yang menggunakan metode serupa harus dilakukan
dengan jumlah spesimen lebih besar dan model analisis statistik yang lebih mendalam. Analisis model mekanis kayu bergelombang, yang dapat mencakup variabel-variabel seperti MFA, sudut serat, dan derajat kegelombangan serat, pun
sebaiknya dilakukan.
Kata kunci: anisotropi, jari-jari, modulus elastisitas, peredaman, serat bergelombang, sudut mikrofibril
vi
© Copyright 2017, Bogor Agricultural University (IPB)
All Rights Reserved by Law
It is prohibited to quote part or all of this paper without mentioning or citing the
sources. Quotation is allowed only for educational purposes, research, writing
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It is prohibited to publish and reproduce part or all of this paper in any form
without a permission from IPB
WAVY SYCAMORE MAPLE: RELATIONSHIPS BETWEEN
ANATOMICAL, PHYSICAL, MECHANICAL, AND
VIBRATIONAL PROPERTIES
AHMAD ALKADRI
Thesis
In partial fulfillment of the requirements for the degree of
Master of Science
at
Forest Products Science and Technology Study Program
GRADUATE SCHOOL
BOGOR AGRICULTURAL UNIVERSITY
BOGOR
2017
External Examiner: Dr Ratih Damayanti, SHut, MSi
x
FOREWORD
The author would like to thank the administration of Master of Science program of Forest Products Science and Technology of Bogor Agricultural University and Master Program of Bois Forêts et Développement Durable (BFD) of AgroParisTech centre de Nancy and Université de Lorraine for their academic cooperation in the form of Double Degree Master Program, supported with the
scholarships of Beasiswa Unggulan from Ministry of Education and Culture of
Indonesia and Bourse de couverture social de gouvernement Française from
French’s Ministry of Foreign Affairs. Without said cooperation, such chance to
conduct this research will not come into fruitition.
The author is grateful to LMGC (Laboratoire de Mécanique et Génie Civil)
and Cirad (Centre international de cooperation et recherche en agronomie) in the
city of Montpellier, France, who offered the information and opportunity for this
research. Without all their supports, both in materials, equipment, and financial,
this research would not be able to be conducted. The authors would also like to
thank La Région Languedoc-Roussillon for the financial support, as part of the
project “Chercheur(se)s d’Avenir” awarded to Dr. Iris Brémaud.
Special thanks to Professor Joseph Gril, the head of Wood Research Group
at LMGC; to Dr. Iris Brémaud and Dr. Patrick Langbour who supervised this research in Montpellier. Special thanks also directed to Professor Imam Wahyudi,
the author’s supervisor in the Department of Forest Products, Faculty of Forestry,
Bogor Agricultural University, Indonesia; to Professor I Wayan Darmawan, the
coordinator of the double degree Master program of Bogor Agricultural University, Indonesia; and to Professor Mériem Fournier, the director and coordinator of
double degree Master program of AgroParisTech centre de Nancy. Special thanks
are also directed to Capucine Carlier, the PhD student in LMGC’s Wood Research
Group, who worked on the violin-making tonewood, for sharing and exchanging
the scientific information about the subject.
Finally, the author would like to express his gratitude to his friends and colleagues: Capucine (again), Agnès, and Vivien for their companionships, high spirit attitude, great work ethos, positive outlooks, and the bicycle; to Anna for the
guitar; to Alban, Daniel, and Marie-France Thèvenon for their help and hospitality
during the course of this research at the laboratory of wood anatomy at Cirad; and
to all other professors, researchers, staff, technicians, Post-Docs, PhD students, interns and any other individuals at LMGC, Cirad, AgroParisTech, and Bogor Agricultural University who have helped the author, both directly and indirectly, in
conducting this research.
The author recognizes that this research is still far from perfect. Thus, suggestions and constructive criticisms are expected in order to improve this work.
Bogor, December 2016
Ahmad Alkadri
xi
TABLE OF CONTENTS
SUMMARY
iv
RINGKASAN
v
SHEET OF APPROVAL
ix
FOREWORD
x
TABLE OF CONTENTS
xi
LIST OF TABLES
xii
LIST OF FIGURES
xii
1 INTRODUCTION
Background
Formulation
Objective
Benefits
1
1
2
2
2
2 MATERIALS AND METHODS
Location and Period of Research
Materials Preparations
Measurements
Data Analysis
3
3
3
4
8
3 RESULTS
Vibrational Properties
Microfibril Angle
Waviness
Ray Dimensions
Correlation Between Parameters
10
10
11
12
14
14
4 DISCUSSIONS
21
5 CONCLUSIONS AND SUGGESTIONS
Conclusions
Suggestions
24
24
24
REFERENCES
24
CURRICULUM VITAE
27
xii
LIST OF TABLES
1
2
3
4
5
6
Measurement results of the sycamore maple wood’s physical and
vibrational properties
Measurement results of the sycamore maple wood’s anatomy features
Measurement results of the sycamore maple wood’s wavy grain
properties
r and p-value of pearson-product moment correlation between paired
parameters
Coefficients of regression of tanδL with MFA and waviness
Coefficients of regression of E’L/ρ with MFA and waviness
16
17
18
19
20
20
LIST OF FIGURES
1
Specimen preparation from the back plates toward the small blocks
needed for MFA and ray dimensions measurements
2 Preparation of specimens used in vibrational measurement
3 Depiction of split block specimen, from which two parameters can be
measured: the wavelength (λ) and amplitude (A=2A/2)
4 Illustration of grain angle measurement.
5 Vibrational properties results for both R and L directions.
6 Local variations (of specimens from each plate) of E’/ρ and tanδ of L
and R specimens.
7 MFA measurement methods
8 Microfibril angle (MFA) results for the twelve plates/specimens
9 Waviness (w) results for the twelve original plates/specimens
10 Example of waviness figures of the sycamore maple wood
11 Rays of the waviest wood and the least wavy one (specimen H, images
on the right)
12 MFA plotted against waviness (w), E’L/ρ and tanδL against MFA, and
E’L/ρ and tanδL against mean grain angle or θaverage.
3
4
7
8
10
11
12
13
13
14
15
22
1
1 INTRODUCTION
Background
Sycamore maple (Acer pseudoplatanus L.) is a hardwood tree species welladapted for cold temperatures and mountainous climate and broadly distributed
throughout European land (Krabel and Wolf 2013). Because of its rapid growth
and high versatility (it can grow almost everywhere as long as the soil is not too
dry or poor), it is considered as an invasive species in several regions (Peterken
2001; Chytrý et al. 2008; Morecroft et al. 2008). Although its low biological durability makes it unsuitable for outdoor construction purposes, its creamy timber and
excellent wood surface make it aesthetically pleasing, and it is mainly used in furniture, flooring, and musical instruments (Bucur 2006; Krabel and Wolf 2013).
Sycamore maple is particularly favored by luthiers and craftsmen in manufacturing the violin, guitar, mandolin, and other musical instruments (Bucur 2006;
Wegst 2006). Several factors contribute in the favorability of sycamore maple as a
material in musical instrument making. Although some studies such as Wegst
(2006) suggest that its acoustical properties are what make it highly suitable for
the back-board of several types of musical instruments such as violin or guitar,
others have suggested that craftsmen tend to determine the selectability of wood
based on more multi-factorial criteria including also visual or cultural preferences
(Brémaud 2012; Buksnowitz et al. 2012).
Psychosensory study on this subject is currently still limited; however, it has
been suggested that there is a correlation between the wood’s physical appearance—or, in the case of sycamore maple, its wavy-grain—with its mechanicalacoustical properties (Kudela and Kunštár 2011). It needs to be noted that, in their
study, Kudela and Kunštár (2011) compared the physical-mechanical-acoustical
characteristics of wavy maple wood with those of the control (non-wavy wood).
Thus, even though they have determined that there are significant differences in
characteristics between wavy and non-wavy or normal wood, the degree of correlation, or the depth of the relationships between the wood’s wavy-figure characteristics and physical-mechanical-acoustical properties, such as the factors causing
and being affected, has still not been determined.
Although little is known on the relations between the wavy grain characteristics and physical-mechanical-acoustical properties, several studies have tried to
determine the factors causing the formation of this particular trait in order to reproduce it. Various studies have shown the possibility of giving external stresses,
for the wavy grain is also known as another form of reaction wood, to stimulate
the specific genetical agents within the tree to produce phytohormones like auxin
and ethylene for prompting the formation of wavy grain (Nelson and Hillis 1978;
Rohr and Hanus 1987; Ewald and Naujoks 2015). These studies have also shown
that the formation of wavy grain are affected by genes and phytohormones, which
is also the case with the formation of wood on microstructural level (Pilate et al.
2004). However, study on the anatomical characteristics of sycamore maple with
wavy wood characteristics is still very limited.
In the past, others have studied the relationships between the anatomical
properties of the wood with its physical and mechanical properties (Yang and
2
Evans 2003; Beery et al. 2007). Several anatomical factors affecting wood mechanical properties have been determined. Along the grain (longitudinal direction
of wood), microfibril angle (MFA), is known as the main determinant of modulus
of elasticity (MOE, or E’, or Young’s Modulus) and specific modulus (E’/ρ), as
well as of internal friction (or damping, tanδ) (Obataya et al. 2000). Fiber angle
has a similar effect on mechanical-vibrational properties (Brémaud et al. 2011).
The rays may affect the mechanical and physical properties on radial section
(Burgert and Eckstein 2001; Reiterer et al. 2002) and possibly also, to a lower
extent, on longitudinal direction (Tippner et al. 2013). In short, the relationships
between anatomical and physical-mechanical-acoustical properties of the wood
have been well-documented. However, in sycamore maple with wavy grain wood,
the correlations between those characteristics have not yet been well-studied.
Formulation
Interested by the high value and utilization of wavy sycamore maple, many
researchers had conducted studies in order to better understand its properties.
However, the correlations between its physical, mechanical, acoustical, and anatomical properties (including the wavy grain) have not been clearly determined.
Therefore, the questions that needed to be asked: how do said properties of sycamore maple correlate with each other? Which characteristics are related with others, and how much of those relationships are significant?
Objective
This research aims to better characterise sycamore maple wood presenting a
gradient of wavy figure and to determine the potential correlations among anatomical (wavy grain, MFA, rays’ characteristics), physical, mechanical, and acoustical
properties (including specific modulus of elasticity, damping coefficient, and their
anisotropy). The sample selection included a wide variability of wood surface
with varying level of grain waviness, making it possible to determine the relationships between those parameters by using statistical analysis.
Benefits
The results of this study are expected to provide the scientific informations,
original data, and statistical analysis of the properties of wavy sycamore maple
wood. Said data are expected to be beneficial for the development of study in the
field of acoustic science, materials, biology, and sylviculture. Further benefits
could also be reaped by the musical instruments industry, especially by the violin
makers, artists, and other interested parties.
3
2 MATERIALS AND METHODS
Location and Period of Research
This research was conducted at the Laboratory of Mechanics and Civil Engineering (Laboratoire de Mécanique et Génie Civil) and French Agricultural Research Centre for International Development (Centre international de cooperation
et recherche en agronomie) in Montpellier, France from February to July 2016.
Materials Preparations
Specimens Preparations for Anatomical Measurements
Twelve quarter-cut wedge shaped boards for violin back plates, labelled A to
L, were used in this study, with the approximate dimensions of ± 40 cm × 13 cm ×
2.5 cm (connecting side) or 1 cm (edge). They were obtained from several violin
makers and specialized wood suppliers from Romania, Bosnia, and France. Specimens from each plate were prepared according to Figure 1. The first cut produced
a trapesium-shaped block 2.5—3 cm high, named block i. From block i, second
cuttings were conducted to produce block ii and block iii, with dimensions 2 × 2.5
× 3 cm3. Each block ii from each specimens were used for waviness measurement.
Block iii were then cut to produce block iv and block v used for MFA and ray dimensions measurements, respectively.
Figure 1 Specimen preparation from the back plates toward the small blocks
needed for MFA and ray dimensions measurements
4
Specimens Preparations for Vibrational Measurements
For vibrational properties measurement, using the existing sampling plan
that was also used in other assessments of within-plate variability using vibrational tests (Brémaud et al. 2010, 2012), the back plates were cut into small strip
specimens with the dimension of 150×12×2 mm3 (L×R×T) for longitudinal specimens, and 120×12×2 mm3 (R×L×T) for radial specimens (Figure 2). The sampling plan allows to study the distribution of properties within plates.The variation
of specimen thickness must be reduced as much as possible for it provides a primary source of errors in the measurement of the specific modulus (E’/ρ) (Brémaud et al. 2012). Thus, after being procured, all specimens for vibrational testing
were conditioned for at least 2 weeks in standard air-dry conditions (20±1°C and
65±5% relative humidity-RH) in order for them to reach dimensional stabilization.
Figure 2 Preparation of specimens used in vibrational measurement
Measurements
MFA Measurements
Specimens for MFA measurement were prepared based on the light microscopy MFA methods described by Senft and Bendtsen (1985). The blocks used for
MFA measurements were those of block iv. Each of them were submerged in water, taken out, oven dried, and then re-submerged again. This cycle was conducted
at least two times in order to create cracks within the wood cells which will enhance the appearance of MFA.
Slicings were conducted on the blocks’ radial surface using a rotary-slide
microtome to produce small thin sections approximately 5 µm thick. The resulting
sections were stored in 50% alcohol. Afterward, the sections were dehydrated in a
solution of absolute (>99%) alcohol for 5 minutes, twice. The sections were then
5
immersed in a solution of 2% iodine-potassium iodide (IKI) for 2 to 10 seconds.
Then, sections were placed on a slide and excess solution were blotted using a
paper towel. Two drops of 60% nitric acid (HNO3) were added to the section
before applying a coverslip. The iodine filled the cracks between the microfibrils,
thus making the MFA visible as dark streaks along the cell wall. Pictures of the
MFA were taken using a light microscope with 600× enlargement and the angles
were measured using ImageJ.
During the course of the measurements, because of the different surface cut
condition of each sample, the angles measurements were not always conducted
according to the same strict rule. The MFA themselves are very hard to be observed directly using light microscopy because the fibrils in the cell walls, especially in S2 layer, are tightly formed (Long et al. 2000). The pretreatment given
before the slicings relieved the tightness a little, but not by a wide margin, and
thus the resulting surfaces made it necessary to measure the MFA using one of the
following techniques:
a. the MFA was measured according to the angle of the cracks between
microfibrils and complemented by the angle of the pits (Donaldson
2007),
b. the MFA was measured according to the MFA directly. This rarely
occured, for in order to be able to observe and measure the MFA
using light microscopy, the “crackings” or defibrilation between the
microfibrils must happened exactly between each one of them within
one fiber cells. These rare occurences could be chalked up to the low
tightness between the microfibrils and the low amount of lignin or
bonds between the MFA,
c. the MFA was measured based on the angle of the pits within the
fiber (Donaldson 2007). This is an acceptable method of MFA
measurement, but it has to be conducted very carefully because the
angle of the pits does not always correspond perfectly with the
MFA. Thus, it is necessary to measure more than one pits’ angle
within the same fiber, and to check with the occurring cracks,
however small they are, within the same or neighbouring cells. If the
angles between them are consistent and not vary by a high amount,
then the angle of the pits can be said to be similar, or the same, with
the MFA. Also observed were the “tails” of the pits, or the elonged
lines from both end of the pits, which normally correspond more
with the MFA than the “body” of the pits.
Examples of each of the mentioned MFA measurement methods can be seen
in Figure 7.
Rays Dimensions Measurement
The blocks used for rays dimensions measurements were those of block v.
Each blocks’ tangential surfaces were sliced using a rotary-slide microtome to
small sections 15—17.5 µm thick. The resulting sections were stored in 50%
alcohol. Afterwards, sections were immersed in sodium hypochlorite for 30
minutes in order to solubilize the extractives. Sections were then immersed in
colorant (green iode, prepared with 1 g Iodine powder + 30 cc distilled water and
70 cc ethanol), giving it a green color, in order to enhance the observation. Next,
6
sections were dehydrated in several levels of alcohol solution, starting from 25%,
50%, 75%, towards absolute (>99%). Fully dehydrated, the sections were placed
on a slide and given a coverslip. Pictures were taken using a light microscope with
40× enlargement and the rays’ dimensions were measured using ImageJ. Measured parameters were the height and width of, respectively, large rays and small
rays, and the percentage of the surface of the section they represent.
Wavy Figure and Grain Angle Measurement
Block ii were splitted parallel to the grain direction (Figure 3). The resulting
splits show clear wave-like figures which were then scanned and measured using
ImageJ. To measure the wavy grain, it was assumed that: a) the wave-like figures
were consistent throughout the part of the wood which possesses it, b) the wavelike figures followed the standard equation form of a sinusoidal wave (formula 1)
with two parameters taken into account: the amplitude (A) and wavelength (l).
⎛ 2π x ⎞
y = A ⋅ sin ⎜
⎟
⎝ λ ⎠
(formula 1)
In a sinusoidal wave function, the slope of a specific point (x,y) can be
calculated as dy/dx (Figure 4). Slope = tanθ with θ in radians (rad) unit. Thus:
⎛ 180 ⎞
⎛ dy ⎞
θ =⎜
⎟ ⋅ arctan ⎜ ⎟ for θ in degrees (º) unit.
⎝ π ⎠
⎝ dx ⎠
(formula 2)
When the slope is small, or if dy/dx |t|)
Intercept
0.007122
0.002337
3.048
0.0138*
MFA
0.000145
0.000261
0.556
0.5919
Waviness
0.063876
0.054615
1.170
0.2722
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Multiple R2 = 0.6757 ; adjusted R2 = 0.6037 ; p-value = 0.006295
Table 6 Coefficients of regression of E’L/ρ with MFA and waviness
Independent
variable
Estimate
Standard Error
t-value
Pr (>|t|)
Intercept
19.9896
3.5103
5.695
MFA
-0.2328
0.3920
-0.594
0.567182
-64.3900
82.0482
-0.785
0.452742
Waviness
0.000296***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1
Multiple R2 = 0.5699 ; adjusted R2 = 0.4743 ; p-value = 0.02245
From the multivariate regression analysis of tanδL with MFA and w (Table
5), the output shows that p = 0.006295, indicating that the null hypothesis that the
variables MFA and w collectively have no effect on tanδL should be rejected
(confidence level = 95%). Results also show that variable MFA is not
significantly controlling for the variable w (p = 0.5919), and that the variable w is
not significant controlling for the MFA (p = 0.2722). However, overall it can be
seen that collectively, MFA and w indeed affect the tanδL with the R2 = 0.6757
and R2adjusted = 0.6037. Thus, the equation can be written as follow:
tanδL = 0.007122 + 0.000145MFA + 0.063876w
(formula 5)
From the multivariate regression analysis of E’L/ρ with MFA and w (Table
6), the output shows the p-value = 0.02245, indicatng the the null hypothesis that
the variables MFA and w collectively have no effect on E’L/ρ should be rejected
(confidence level also = 95%). The results also show that the MFA is not
significantly controlling for the w (p = 0.567182) and that w is not significantly
controlling the MFA (p = 0.452742). Similar with the results of table 5,
collectively, MFA and w affect the E’L/ρ with the R2 = 0.5699 and R2adjusted =
0.4743. Thus, the equation can be written as follow:
E’L/ρ = 19.9896 – 0.2328MFA – 64.3900w
(formula 6)
21
4 DISCUSSIONS
From the results, it can be seen that there is a high intra-species variability
of w (waviness, formula 6) and θaverage (mean angle, formula 4). Among wavy maple trees, some possess low to no wavy grain, while others possess a grain so
wavy that it forms stripes-like figures on the radial plane of the wood, called
‘wave front’ (Harris 1989). Although the methods of waviness measurements
used in the present study differ from some previous research, the average values
of wave amplitude (≈0.21 mm) and of wavelength (10 mm) are comparable with
other recent results on a different and wide sampling (Krajnc et al. 2015).
In the present results, the degree of waviness is not correlated with the wood
density. This is in contrast with other findings, on reduced samplings, which suggested that wavy wood would have higher density than non-figured one (Bucur
2006; Kudela and Kunstar 2011). Anatomical features related to rays also show
nearly no correlation with waviness.
Positively correlated with the θaverage (or waviness), according to the statistical analysis that has been conducted, is MFA (Table 4, Figure 12). This original
finding is important because both the MFA and the grain angle (here caused by
wavy grain) are known to strongly affect mechanical properties in the longitudinal
direction of wood, both lowering E’/ρ and increasing tanδ (Obataya et al. 2000,
Brémaud et al. 2011). One can wonder about the origin of this strong correlation
between MFA and waviness, for past studies have shown that the MFA has to be
ruled out from the list of possible factors causing the existence of spiral grain
(Harris 1989). This suggestion was brought forward given that the grain angles
are almost certainly determined by cambial orientation in the early formation of
the fi