Composites: Part A 38 (2007) 945–953
www.elsevier.com/locate/compositesa
Nanoindentation of wood cell walls: Continuous stiffness
and hardness measurements q
W.T.Y. Tze
a,*
, S. Wang a, T.G. Rials a, G.M. Pharr
b,c
, S.S. Kelley
a,d
a
Forest Products Center, The University of Tennessee, Knoxville, TN 37996-4570, USA
Department of Material Science, The University of Tennessee, Knoxville, TN 37996-2200, USA
c
Metals and Ceramic Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6116, USA
d
Department of Wood and Paper Science, North Carolina State University, Raleigh, NC 27695, USA
b
Received 25 April 2005; received in revised form 28 June 2006; accepted 30 June 2006
Abstract
The objective of this study was to measure the mechanical properties of individual, native wood fibers using the continuous nanoindentation measurement technique. The indentation depth profile exhibited a small length-scale effect, which was confirmed using
the size-effect index derived from the indentation loading curve. The hardness (Hu) or stiffness (Eu) values determined from indentation
unloading were also examined for 10 different annual rings of a loblolly pine, with microfibril angles (MFA) between 14 and 36. A
predictable pattern of Eu values was found as a function of MFA, and hence Eu can at least be considered a relative measure of the longitudinal stiffness properties of wood cell walls. For Hu values, a dependence on orientation was observed, and there is a preliminary
indication that the dependence could be affected by cell-wall extractives. It is thus desirable, for cell-wall modification studies, to minimize any unintended variations by using samples that are from the same growth ring, so that any treatment-induced changes in the cellwall hardness can be identified.
2006 Elsevier Ltd. All rights reserved.
Keywords: A. Wood; B. Mechanical properties; Nanoindentation
1. Introduction
Nanoindentation testing is a technique that determines
the mechanical properties of a material in the micron or
sub-micron scale. The test involves penetrating a sample
material using an indenter, while the penetration depth
and load are recorded so that the stiffness and hardness
of the indented location can be subsequently calculated.
The indenter head can be 100 nm in radius (in the case of
a Berkovich indenter), and the penetration can be up to 1
or 2 lm in depth, with the resulting indent having a linear
dimension in the order of micrometers. This dimension is in
q
Part of this work was performed at the Department of Bio-based
Products, University of Minnesota (St. Paul, MN 55108, USA), where the
corresponding author (W.T.Y. Tze) is currently affiliated.
*
Corresponding author. Tel.: +1 612 6242383; fax: +1 612 6256286.
E-mail address: [email protected] (W.T.Y. Tze).
1359-835X/$ - see front matter 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compositesa.2006.06.018
the same order of magnitude of the wood cell-wall thickness. The wood cell walls were reported to be 5–6 lm
and 9–13 lm in thickness, respectively, for earlywood and
latewood of loblolly pine [1]. Therefore, the local mechanical properties of wood cell walls can be probed using
nanoindentation tests. More specifically, the test detects
the mechanical properties of the cell-wall S-2 layer, which
constitutes about 80% of the total cell-wall thickness and
is the major contributor to the mechanical properties of
wood cell walls.
The micron spatial (lateral) resolution in nanoindentation tests renders the technique very useful in the investigation of the wood cell-wall level as a result of growth
processes or utilization operations. To date, a few studies
have used nanoindentation to investigate the effects of seasonal growth response (earlywood versus latewood) [2],
cell-wall lignification [3], melamine modification [4], and
adhesive bonding [5] on the mechanical properties of single
W.T.Y. Tze et al. / Composites: Part A 38 (2007) 945–953
cell walls. An attractive feature demonstrated in these studies is that the measurements were made without requiring
chemical or mechanical modifications to isolate individual
wood fibers as required in single-fiber tensile tests. These
chemical and mechanical modifications change the
mechanical properties of the wood fibers in poorly defined
ways.
Accompanying the promise of nanoindentation for
studying the mechanical properties of wood, there are also
uncertainties in the analysis of the raw data. The first of
these uncertainties is that the stiffness values (13–21 GPa;
compiled in [6]) obtained from the nanoindentation test,
which is usually performed in the longitudinal direction
of wood, is less than half the value of the tensile modulus
obtained from single wood-fiber tensile test (60–80 GPa)
[7]. Gindl and Schöberl [6] attempted to identify the origin
of the underestimation by modeling the longitudinal modulus of the cell-wall S-2 layer using the laminate theory,
assuming that the S-2 layer is a composite of lignin-hemicellulose matrix reinforced with variations in the microfibril angle (MFA) of the crystalline cellulose. These
researchers observed that the modeled stiffness values at
an MFA of 25 approximated the experimental (nanoindentation) stiffness values. Gindl and Schöberl [6] attributed the observation to the loading angle (which is also
25) owing to the geometry of a Berkovich indenter. This
finding led the researchers to conclude that the nanoindentation test data is influenced by the anisotropy of wood,
where in off-axis loading of the tracheid (either due to
indenter face angle or cell-wall microfibril angle), the lower
transverse modulus contributes to reducing the observed
stiffness value in nanoindentation experiments.
Experience with materials other than wood also reveals
that the nanoindentation test data are influenced by the
penetration size effect – the variations of modulus or (more
commonly) hardness with the penetration depth (area).
This phenomenon, which is more pronounced in materials
of low hardness, also occurs in isotropic materials especially those that are crystalline [8]. The size-effect phenomenon has been ascribed to several mechanisms related to
sample polishing (work hardening and surface-microcracks
formation), test artifacts (indenter bluntness and indenter/
surface friction), and material properties [9]. The materialrelated size effects can be explained in the perspective of the
strain gradients that exist in the vicinity of the indentation.
The strain gradient (or the density of dislocations) is larger
at a smaller indentation depth; the resulting increase in the
effective yield strength is projected as an increased hardness
near the surface [8]. The penetration size effect complicates
the comparisons of indentation properties of different
materials, and this issue has not been addressed for nanoindentation of wood.
The continuous measurement technique offers a tool to
probe stiffness as a function of indentation depth in one
single experiment [10]. Commonly, a discrete indentation
loading, with a targeted penetration load or depth, provides only one value of hardness (from the maximum load)
1.2
dP
dh
1
Load (mN)
946
0.8
0.6
0.4
0.2
0
0
100
200
300
Displacement (nm)
400
Fig. 1. The load–displacement curve during indentation. Note: The initial
slope of the unloading curve was used to calculate stiffness (Eu).
or stiffness (from the slope of the unloading curve) as
shown in Fig. 1. In the continuous measurement technique,
cycles of indentation, each of which consists of incremental
loading and partial unloading, are performed until a final
desired depth is attained. Each loading-and-partial unloading cycle provides a value of hardness and stiffness; hence
as the penetration progresses, various hardness or stiffness
values were determined as a function of the indentation
depth. Such a feature is particularly attractive in examining
graded materials, for instance multilayer films, where hardness or stiffness differs in different layers under the surface
[10]. The continuous measurement technique is also potentially useful for investigating penetration size effects, and it
has not been applied to the indentation studies of wood.
The objective of this study was to measure the mechanical properties of wood fibers using nanoindentation with
the continuous measurement technique. The study also
examines the effects of microfibril angle on the stiffness
and hardness values determined from nanoindentation
experiments.
2. Materials and methods
The wood samples were collected from a loblolly pine
stem. This tree was part of a study of the relationship
between the Near Infrared spectra and the MFA (from Xray diffraction measurements), moduli of elasticity (MOE;
from three-point bending experiments), and moduli of rupture (MOR; also from three-point bending) of wood [11].
Five different annual rings (number 2, 5, 16, 32, and 50;
counted from the pith), with MFA values ranging from
15 to 36, were selected from the portion of the tree stem
that was 0.3 m above the ground. The latewood portion of
these annual rings were cut to 2 mm · 5 mm · 5 mm in
radial, tangential, and longitudinal dimensions, respectively.
The wood samples were soaked in the Spur epoxy resin
[12], which is commonly used as an embedding medium for
electron microscopy of biological samples. The soaking
was performed in a desiccator and under vacuum for
W.T.Y. Tze et al. / Composites: Part A 38 (2007) 945–953
overnight. On the next day, the resin-impregnated samples
were removed from the desiccator and transferred to a flat
mould, which was subsequently filled with freshly prepared
epoxy resin. The mould containing both wood samples and
epoxy resin was then placed in an oven at 70 C for 12 h.
The embedding epoxy, once cured, was intended to allow
a smooth surface cut (ultra-microtoming), to insure the
wood cellular structure to be intact during microtoming,
and to keep the wood cell walls from buckling during the
indentation of the cell walls.
The resin-embedded samples were glued to an acrylic
block using a five-minute epoxy. The acrylic block was then
mounted onto an ultra-microtome. The transverse (crosssectional) surface of the wood was leveled using a glass
knife, and then smoothed using a diamond knife. The
smoothed samples were conditioned for at least 24 h at
21 C and 60% relative humidity in a room that housed
the nanoindenter.
To begin indenting, the indenter was positioned, using an
attached microscope, onto the cell wall in the longitudinal
direction of the tracheid. A continuous measurement was
performed at a displacement rate of 2 nm/s until a final penetration depth of 300 nm. At this depth, the loading was
held for 50 s prior to the ultimate unloading. The unloading
was then performed at a rate of 100 nm/s until 90% of the
load was removed. At the end of the indentation experiment, the sample was examined under the microscope to
evaluate the position and quality of the indentation.
Five indents were made on the cell wall of each tracheid
in its longitudinal direction. To reduce variability, only the
cell wall at the tangential side of the tracheid was examined
although a previous study [2] observed no differences in
longitudinal stiffness or hardness between the radial and
tangential walls. The indents were made on the mid-width
of the cell wall, so that it could be soundly assumed that
only the S-2 layer was probed. Five tracheids were examined for each annual ring, and hence there were 25 measurements for each of the rings investigated in this study.
The load–displacement data from the nanoindentation
tests were used to calculate hardness and elastic modulus.
The hardness (H) of the samples for an indentation depth
(h) can be calculated from the following equation:
P max
;
A
1 1 m2i
Er
Ei
1
ð3Þ
;
ð4Þ
where in this case, h is the microfibril angle of the wood
sample, while E1, E2, G12, and t12 are elastic constants
16
14
ð1Þ
where Pmax refers to the load measured at a maximum
depth of penetration (h) in an indentation cycle, while A refers to the projected area of contact between the indenter
and sample at Pmax. The combined modulus of the system,
or reduced indentation modulus (Er) was determined from
the following expression [13]:
pffiffiffi
dP 1 p
pffiffiffi ;
Er ¼
ð2Þ
dh 2 A
dP
dh
where ms and mi are the Poisson’s ratios of the specimen and
indenter, respectively, while Ei is the modulus of the indenter. Here, it is worth mentioning that the data reduction for
hardness and stiffness mentioned above, which is commonly employed in nanoindentation studies, assumes an
isotropic elastic–plastic behavior. Since wood cell walls exhibit inelastic and anisotropic behaviors, the moduli and
hardness values determined in this study should be viewed
as effective values, rather than the absolute material properties of the wood cell wall. These effective values provided
the data that were used to compare different cell-wall materials in the present study.
The continuous measurement technique employed in
this study produces a series of hardness and modulus
values as a function of indentation depth. To express
the (effective) hardness or moduli of a sample, various
approaches (Fig. 2) were used – taking the values corresponding to 100 nm (H100 or E100) and 200 nm (H200 or
E200) indentation depth, or averaging the values for a depth
of more than 200 nm (Have,>200 or Eave,>200). In addition,
the hardness and modulus values (Hu or Eu) were also
determined from the ultimate unloading curve (Fig. 1),
an approach used by Gindl and co-workers in their studies
on nanoindentation of wood [3–6].
The moduli (Eu) derived from nanoindentation studies
of the samples from different annual rings were then correlated to the theoretical value (Ex) of cell-wall longitudinal
modulus. The Ex value can be computed from the transformation of stiffness tensor for orthotropic materials
1
1
1
2t12
1
¼
cos4 h þ
sin4 h;
sin2 h cos2 h þ
Ex E1
G12
E2
E1
is the slope of the line in tangent to the initial
where
unloading curve in the load–displacement plot (Fig. 1).
The sample modulus (Es) can then be calculated as follows:
Stiffness (GPa)
H¼
Es ¼ ð1 m2s Þ
947
12
Eave, >200
10
8
6
E100
E200
4
0
50
100
150
200
250
300
350
Displacement (nm)
Fig. 2. The depth-dependent longitudinal stiffness, and various approaches
to express the sample stiffness.
948
W.T.Y. Tze et al. / Composites: Part A 38 (2007) 945–953
of cell-wall elastic constants would be resulted. The effects
of these input values and volume fraction will be discussed
in the following section.
Table 1
Volume fractions (f) of cellulose and matrix, and the elastic constants of
the S-2 cell-wall layer
Modela
1
2a
2b
2c
Remark on the
adopted values
of cellulose and
matrix moduli
fcellulose:
fmatrix
E1
(GPa)
–
Low valuesd
High valuesd
High valuesd
0.45:0.55
0.50:0.50
0.50:0.50
0.60:0.40
63.96
66.50
86.75
102.9
E2
(GPa)
G12
(GPa)
m12
3. Results and discussion
9.51b
5.00
10.03
11.58
3.2c
2.0
2.4
2.5
3.1. Approach comparisons
0.33
0.17
0.17
0.16
The variability of the data was first examined to ascertain that any potential differences observed in the longitudinal hardness and moduli could be genuinely attributed
to differences between the samples. A mean value was
obtained from the longitudinal hardness or moduli of five
locations on a tracheid S-2 cell wall. The mean values for
five adjacent tracheids were compared using single-factor
analyses of variance (ANOVA). The analyses detected no
significant differences (at a confidence level of 0.95) in
either hardness or modulus values among the five tracheids
of the same growth ring regardless of the estimation
approach. An exception was observed for wood ring 32,
where tracheid-to-tracheid differences within the growth
ring were pronounced for cell-wall hardness or moduli
expressed at 100- and 200-nm indentation depth, but not
when the values were determined from the ultimate unloading curve (Hu or Eu). This particular sample had a high surface roughness compared to the other samples, as observed
under the microscope. It is also noteworthy that for the
(rough) sample ring 32, data from the ‘‘unloading’’
approach (Hu or Eu) exhibits coefficients of variation or
CV (up to 14%; Table 2) that are smaller than other
approaches (CV up to 21%; Table 2). On the other hand,
when the sample surfaces were smooth, the Hu or Eu data
exhibit low CV values (2–8%; Tables 2 and 3) that are quite
a
Model 1 was derived for radiata pine [14], while models 2a and 2b were
used in [6] for spruce.
b
The E2 value for model 1 was averaged from the values of tangential
and radial Young’s moduli tabulated in [14].
c
The G12 value for model 1 was averaged from the values of G1t and G1r,
where t and r, respectively, stand for tangential and radial directions [14].
d
Refer to [6] for the two different sets of values (low and high) for the
moduli (including Young’s and shear moduli) of cellulose and matrix.
These values, in additional to the Poisson ratio (m12), were used in [6] to
calculate the elastic constants (model 2a and 2b) of the laminate (S-2 cell
wall) at fcellulose:fmatrix = 0.50:0.50. The high moduli values of the cellulose
and matrix were also used in the present study to determine the elastic
constants (model 2c) of the S-2 cell wall at fcellulose:fmatrix = 0.60:0.40.
for the S-2 cell wall. Four different sets of elastic constant
values (presented in Table 1) were used in this study. These
elastic constants were determined by various researchers
[6,14], using the laminate theory, with the assumption that
the cell-wall layer consists of cellulose embedded in a matrix of hemicellulose and lignin. The laminate calculation
requires input of elastic constant values of cellulose, hemicellulose, and lignin, which had been estimated in different
reports, some of which were compiled by Bergander and
Salmén [15]. Using different input values and adopting different cellulose:matrix volume fraction ratio, different sets
Table 2
Cell-wall longitudinal hardness (in GPa) of tracheids expressed using different approaches
H100
H200
Havg,>200
Hu
Ring no. 2 [MFA 36]
Ring no. 5 [MFA 35]
Ring no. 16 [MFA 30]
Ring no. 32 [MFA 28]
Ring no. 50 [MFA 15]
0.54
0.53
0.53
0.46
0.50
0.48
0.48
0.42
0.44
0.44
0.44
0.38
0.42
0.40
0.40
0.34
0.41
0.43
0.43
0.38
(3)
(2)
(1)
(2)
A
A
A
B
(5)
(5)
(4)
(4)
A
B
B
C
(6)
(5)
(5)
(5)
A
A
A
B
(21) #
(17) #
(16) #
(14)
(12) A
(7) A
(7) A
(7) B
Note: Values were averaged from the mean hardness of five tracheids. The coefficient of variation (in bracket; units in percentage) represents the variability
of the mean hardness of the five tracheids. The values assigned with the same letter in a column are indications that the approaches provide hardness values
that are insignificantly different at a confidence level of 0.95. The hardness value followed by a ‘‘#’’ symbol had significant within-ring data variability, and
hence no comparisons of the approaches were made for ring no. 32.
Table 3
Cell-wall longitudinal modulus (in GPa) of tracheids expressed using different approaches
E100
E200
Eavg,>200
Eu
Ring no. 2
Ring no. 5
Ring no. 16
Ring no. 32
Ring no. 50
16.3
16.0
15.9
15.9
15.7
16.2
16.2
16.3
13.8
14.2
14.3
14.3
12.7
12.8
13.0
13.3
16.3
17.6
17.8
17.9
(2)
(1)
(2)
(3)
A
AB
B
B
(5)
(5)
(4)
(5)
C
AB
AB
A
(8)
(7)
(7)
(8)
B
A
A
A
(19)
(15)
(13)
(10)
#
#
A
A
(8)
(5)
(5)
(4)
C
B
A
A
Note: Values were averaged from the mean moduli of five tracheids. The coefficient of variation (in bracket; units in percentage) represents the variability
of the mean moduli of the five tracheids. The values assigned with the same letter in a column are indications that the approaches provide moduli values
that are insignificantly different at a confidence level of 0.95. The moduli value followed by a ‘‘#’’ symbol was not included in the comparisons of the
approaches due to the significant within-ring variability.
W.T.Y. Tze et al. / Composites: Part A 38 (2007) 945–953
Table 4
Indices for indentation size effects
0.6
Ring no. 2 Ring no. 5 Ring no. 16 Ring no. 32 Ring no. 50
Hardness (GPa)
0.5
0.4
n from
Eq. (5)
0.3
Note: Values were averaged from five tracheids. The ± sign indicates the
95% confidence interval of the respective data sets.
1.74 ± 0.02 1.79 ± 0.05 1.81 ± 0.05 1.75 ± 0.06 1.86 ± 0.07
0.2
0.1
0.0
0
50
100
150
200
250
300
350
Displacement (nm)
Fig. 3. An example of the depth-dependent longitudinal hardness.
similar to the CV values of other approaches for corresponding samples. Hence, Hu or Eu, whose data are relatively reproducible, will be used in subsequent discussions
whenever a discrete expression of cell-wall (effective) longitudinal stiffness or hardness value is required.
A close examination of the hardness and stiffness measurements at different depths suggests that there is little if
any indentation size effect. The hardness values below
100-nm indentation were highly variable (Fig. 3) due to
surface roughness. Table 2 shows that in most cases H100,
H200, and Have,>200 are not statistically different. The
depth-dependent changes in stiffness were generally small
and not consistent (Table 3). To further examine the penetration size effect, a power-law equation was used to relate
(P) to the indentation depth (h):
P ¼ Bhn ;
ð5Þ
where B is a constant and n is the size-effect index [16]. The
parameter n bears the value of 2 if there are no indentation
size effects (Fig. 4). Hence, the amount of deviations of n
1.6
With size effects
Ideal
1.4
1.2
1.0
P (mN)
949
n =2
0.8
n <2
0.6
0.4
0.2
0.0
0
50
100
150
200
250
300
350
h (nm)
Fig. 4. Loading curve for illustrating size effects based on Eq. (5):
P = Bhn. Note: the curve for n < 2 was plotted from one of the data set in
the present study.
from the value of 2 would indicate the extent of the size-effect contributions. For polymeric materials (which includes
wood cell walls), the deviation from the ideal relation of
P = Bh2 could also be contributed by viscoelastic effects
such as stress relaxation (or creep) [17], which result in a
low load (P) value at a given displacement (h), as compared
to the case of n = 2 (Fig. 4). Table 4 shows that the n values
range from 1.69 (the lower limit of ring 32) to 1.93 (the
upper limit of ring 50). Hence, our n values are closer to
the value of 2 when compared to the published data [16]
on single crystals of copper (n = 1.59) and steel (n =
1.66), which are primarily influenced by penetration size
effects (i.e., no viscoelastic contributions). Where viscoelastic effects are present, expectedly in our samples, the small
deviation of n from the value of 2 is an even stronger indication that the penetration size effect is considerably small
for wood cell walls. To summarize the above discussion,
the n values show that the indentation size effects are considerably little, hence in agreement with the observation inferred earlier from the indentation depth profile (Fig. 3,
Table 2).
To complete the exploratory study, the significance of
the embedding resin in modifying cell-wall mechanical
properties was also examined. For obtaining the hardness
and moduli of the Spur epoxy resin, eight separate indents
were made on the cured resin that embedded the wood
sample. The Hu and Eu values were, respectively, 0.17 ±
0.01 GPa and 3.6 ± 0.1 GPa, at a 95% confidence interval.
The values obtained from nanoindentation are close to the
microindentation hardness (0.10 GPa; [18]) and tensile
moduli (3.2 ± 0.4 GPa; [19]) of the bisphenol-A epoxy.
The observed Hu and Eu values of the Spur epoxy are
low compared to the values for wood cell walls examined
in the present study (with MFA 6 36; Tables 2 and 3).
The Eu value of the cured epoxy is also low compared to
the calculated transverse elastic moduli (E2; Table 1) of
the S-2 cell wall. Similarly low values of hardness and moduli were also observed by Gindl et al. [3] for the cured Spur
epoxy resin. Based on this observation, the researchers
deduced that the resin imposes a negligible influence on
the cell-wall nanoindentation test data [3]. Further supporting this argument is the study of Hepworth et al.
[20], who made flax fiber composites using a slow-curing
(48 h) epoxy as the matrix. These researches reported that
the low-viscosity epoxy resin (molecular weight <700) did
not penetrate into the fiber cell wall unless the fibers were
pre-swollen with chemicals (urea solution) that, compared
to water, swell lignocellulosics to a larger extent.
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W.T.Y. Tze et al. / Composites: Part A 38 (2007) 945–953
3.2. Examination of longitudinal stiffness: relations
to microfibril angles (MFA)
It was acknowledged, in the methodology section, that
the current practice of deducing stiffness and hardness values from nanoindentation data does not result in absolute
material properties for anisotropic materials such as wood
cell walls. Recognizing this constraint, no specific efforts
were made to compare (or match) Eu or Hu with the ‘‘true’’
moduli or hardness values. Instead, attempts were made to
compare the trends between the effective values (from nanoindentation) and the reference (modeled) values as a
response to changes in microfibril angle (MFA). More relevantly, the subsequent effort of this report is to identify if
the effective values (Eu or Hu) can be considered a reasonable relative measure of the S-2 longitudinal moduli and
hardness.
To better discern the changes in Eu values as a response
to microfibril angle changes, five more samples (MFA values ranged from 14 to 30) were added to the study. These
samples (annual rings 2, 5, 9, 16, and 32; counted from the
pith) were cut from a wood disk (labeled as disk 2)
obtained from the portion of the stem five meters above
the position where the initial samples (from disk 1) were
obtained. The newly added samples, together with the
initial five samples analyzed for calculation approaches,
provided 10 experimental data points for subsequent observations. The effective modulus values from nanoindentation studies, as anticipated, do not entirely match the
modeled values although these two data sets are in the
same order of magnitude (Fig. 5). Conventional wisdom,
as illustrated by the S-2 cell-wall model calculation, indicates that as the microfibril angle (MFA) increases (to a
value up to 90), the longitudinal stiffness would decrease.
The effective moduli from nanoindentation show a somewhat similar trend. This trend, however, exhibits a gentler
40
(I) Nanoindentation
(II) Model for radiata pine
(III) Model for spruce
(IV) Model for radiata pine (horizontal shifted)
(V) Model for spruce (horizontal shifted)
(VI) Vertical shifting of curve (V)
Longitudinal modulus (GPa)
(II)
35
(III)
30
25
(I)
(VI)
20
15
(IV)
(V)
10
5
0
5
10
15
20
25
30
35
40
45
Microfibril angle (degree)
Fig. 5. The S-2 cell-wall longitudinal stiffness as a function of microfibril
angles: experimental and modeled values. Note: curve II was from model 1
(refer to Table 1), and curve III was from model 2b (Table 1). Error bars
refer to the 95% confidence intervals of the respective data points.
slope (at a given MFA value) compared to the modeled
values (curves II and III; Fig. 5), indicating that altering
the MFA values would result in a change in the longitudinal stiffness, but the change would be smaller than that predicted by either model 1 (for radiate pine) or model 2b (for
spruce) described in Table 1.
It has been discussed in [6] that when MFA is 0, each of
the three faces of the Berkovich indenter will form an angle
of about 25 with the longitudinal axis of the load-bearing
microfibrils to result in a 25 off-axis loading. For an MFA
value larger than 0, however, the individual faces of the
indenter will form different angle values in relation to the
longitudinal axis of the microfibrils [6], hence the resultant
off-axis loading becomes complicated to analyze. While the
use of 3D finite element analyses seems to be a sensible way
to tackle this complication, there are however, according to
our experience in applying the technique for nanoindentation [21], uncertainties in assuming the boundary conditions. Such uncertainties present an even bigger challenge
for the case of wood cell walls, whose micron-scale properties are not well understood, and so we opt to keep finite
element analyses for a detailed study in the future. For
now, it is hypothesized that an effective loading angle that
is larger than the MFA was responsible for influencing the
cell-wall longitudinal moduli observed in the present study.
To pragmatically represent this situation, an effective loading angle was determined by increasing the cell-wall MFA
value by an arbitrary 20, i.e. a horizontal shift along the xaxis of the stiffness–MFA plot (Fig. 5). As an example, the
modulus value plotted for curve IV at 10 MFA was calculated, based on Eq. (4), using an effective (loading) angle
value of 30. The resultant curves (IV and V in Fig. 5) exhibit trend lines that are very similar in shape to the experimental data trend. Indeed, a reasonable expression (curve
VI) for the data trend can be obtained by performing an
upward shift of curve V. This observation agrees with
our hypothesis that the orientation dependence of the
cell-wall stiffness from nanoindentation is influenced by
an effective (off-axis) loading angle that is larger than the
MFA value. The similar trend line exhibited by curves IV
and V also implies that at a large (effective) loading angle,
the predicted dependence of the nanoindentation stiffness
on MFA was not noticeably different for using models that
were adopted for different wood species (radiata pine versus spruce). Based on the predictable response of Eu on
MFA, it is inferred that Eu can be considered relative quantities to discern the stiffness properties of one cell wall from
another.
To expand the findings reported in the preceding
paragraph, it is desirable to investigate some factors that
potentially reconcile the predicted modulus values with
the experimental values. First, the spruce cell-wall model
(model 2a) was plotted (curve B in Fig. 6) using effective
loading angle values that are 20 larger than the corresponding MFA, as described in the preceding paragraph.
Then, high values of elastic constants were used for the
cell-wall polymer (model 2b) in determining the S-2 proper-
W.T.Y. Tze et al. / Composites: Part A 38 (2007) 945–953
(A) Experiment: nanoindentation
(B) Modeled: horizontal shifted (low elastic constant; 50:50)
(C) Modeled: horizontal shifted (high elastic constant; 50:50)
(D) Modeled: horizontal shifted (high elastic constant; 60:40)
(E) Modeled: horizontal shifted (high elastic constant; 60:40; low MC)
(F) Arbitrary trend line for data points: vertical shifting of curve (E)
35
30
25
(F)
(A)
20
15
(E)
10
(D)
(C)
(B)
5
0
5
10
15
20
25
30
35
40
45
Microfibril angle (degree)
Fig. 6. The S-2 cell-wall longitudinal stiffness as a function of microfibril
angles: examining some factors that cause the difference between experimental and modeled values. Note: Error bars refer to the 95% confidence
intervals of the respective data points.
ties. A considerable vertical shift was observed as a consequence, i.e. the predicted longitudinal moduli become
higher (curve C), and relatively closer to the experimental
data points. When the cellulose:matrix volume ratio is
increased from 50:50 to 60:40 (model 2c), the vertical shift
(curve D) is small. At this point, it is in order to mention
that the cell-wall polymer elastic constants, which are used
as input values for the calculation of S-2 cell-wall properties, were derived in the literature for 12% moisture content
level. In contrast, the wood sample used in the experiment
of this present study had an initial moisture content of
8.0%. Vacuum (impregnation) and subsequent heating in
an oven (with the presence of epoxy resin) would reduce
the moisture content level. The moisture change, though
difficult to determine for wood samples that were finally
embedded in the cured epoxy, should be consistent for all
the samples, given that they were prepared using the same
protocol. With a conservative assumption of 4% as the
moisture content level of wood during the nanoindentation
test, the longitudinal moduli were corrected from 12% MC
to 4% MC using the following formula [22]:
x
MMt M
E12 p 12
Ex ¼ Et
;
ð6Þ
Eg
where E and M, respectively, represents the stiffness (or Eu;
in GPa) and moisture content (MC) level (in %) of the cellwall sample, with Et referring to the E value (at Mt = 12%)
that needs to be adjusted to Ex (at Mx = 4%). The symbol
Mp refers to the fiber saturation point (21% for loblolly
pine; [22]) at which mechanical properties begin to change
when wood is dried from a higher MC level. The ratio of
cell-wall stiffness values at air-dry condition
(MC = 12%)
in relation to the green condition,
E12
Eg
, was estimated
from the values
[22] ofbending moduli of loblolly pine
MOE12
wood, i.e. MOEg ¼ 1:27 . The resulting values, plotted as
curve E, exhibit a substantial upward shift from curve D
(12% MC). Hence the cell-wall polymer elastic constant
values and moisture content levels are among the important factors that are responsible for the differences in the
experimental and predicted values.
To put things into perspective, it should be reinstated
that the present study did not attempt to quantitatively
match nanoindentation data with modeled values that
themselves are determined from estimated input values.
Instead, the aforementioned discussions were meant to
show that the modeled values would indeed be different if
different values were used for the cell-wall polymer elastic
constants. Additionally the moisture content effects need
to be taken into account in the modeling before fair comparisons between the modeled and nanoindentation values
can be made. More relevantly, our preceding discussion
concludes that the longitudinal moduli from nanoindentation, though not absolute in values, can be considered relative quantities. It follows these moduli (Eu) values can
potentially be used for comparisons aimed at probing
cell-wall mechanical changes associated with plant growth
and processing.
3.3. Examination of longitudinal hardness: relations to
microfibril angles
Corresponding to the 10 wood samples in the longitudinal stiffness measurements, 10 values of longitudinal
hardness were obtained from nanoindentation. At first
glance, the S-2 longitudinal hardness appears to be influenced by the microfibril angle (Fig. 7). This behavior seems
to agree with the reported observation at the macroscopic
level, where the Brinell hardness of wood decreases
with the increase in grain angles in accordance with the
0.8
Longitudinal hardness (GPa)
Longitudinal modulus (GPa)
40
951
0.7
0.6
Ring 2
(disk 2)
0.5
Ring 50
(disk 1)
0.4
Ring 5
(disk 1)
Ring 2
(disk 1)
0.3
0.2
Nanoindentation
0.1
Curve fitting (Hankinson formula)
0.0
5
15
25
35
Microfibril angle (degree)
Fig. 7. The longitudinal hardness (Hu) of wood as a function of
microfibril angles: experimental values and curve fitting. Note: Error bars
refer to the 95% confidence intervals of the respective data points. Eq. (7)
was used for curve fitting of the data points using N = 2. The curve fitting,
which excluded the four outlying data points, resulted in a R2 of 0.88, with
HL iterated to be 0.71 GPa, and HT 0.14 GPa.
952
W.T.Y. Tze et al. / Composites: Part A 38 (2007) 945–953
Hankinson-type formula [23]. The Hankinson-type formula has been commonly used in the field of wood science
to express the (two-dimensional) orientation dependence of
wood properties. In the present study, the same formula
was used to perform a curve fitting on the plot of cell-wall
(effective) longitudinal hardness as a function of MFA [22]:
Hh ¼
ðH L ÞðH T Þ
;
H L sinN h þ H T cosN h
ð7Þ
where H is the (effective) cell-wall longitudinal hardness (or
Hu), h is the microfibril angle (MFA), HL is the (effective)
hardness value at 0 MFA, HT is the (effective) hardness
value at 90 MFA, and N is an empirically determined constant which ranges between 2 and 2.5 for compressive
strength properties [22]. The fitted curve (Fig. 7) demonstrates a tendency of longitudinal hardness to decrease
when MFA increases, with several exceptional data points
deviating from the trend line. This behavior suggests that
although there are some unaccounted variations in the
data, the effective longitudinal hardness values from nanoindentation tests are generally orientation dependent.
Whether this dependence is entirely on MFA or on its
interaction with the indenter faces is not evident because
the trend line was obtained by mere curve fitting, instead
of theoretical calculations.
A subtle decrease in the average indentation hardness
with increasing MFA (values ranged from 0 to 50) was
also observed by Gindl et al. [24]. The researchers, nevertheless, concluded from the lack of statistical differences
that the indentation hardness is governed by the yielding
of the cell-wall matrix (i.e. lignin and hemicelluloses),
instead of the property of the microfibrils (or their alignment). These previous findings do not necessarily contradict our observations because the yielding of the cell-wall
matrix, if indeed influential for nanoindentation test data,
could partially explain the deviation of data points from
the trend line in the present study. It is worth mentioning
that the three outlying data points above the trend line
(Fig. 7) are in correspondence to the three samples collected from the inner most (heartwood) region (rings 2
and 5), which are known to be rich in extractives. On the
other hand, the remaining data point, lying below the trend
line, is of ring 50, the outermost (sapwood; normally less
extractive) region of the wood disks examined in this study.
Extractives in the wood cell walls have been ascribed [25] to
contribute to the compression properties of wood, as evidenced from the decreased maximum crushing strength
upon removal of extractives, even when the accompanying
density changes had been taken into account. A co-incidence was also observed between a lowered (cold water soluble) extractive content and the reduced parallel-to-grain
compression strength property of fire-impacted loblolly
pine wood [26]. Based on these findings, it is reasonable
to expect that the yielding of the cell-wall matrix in the
present study would vary depending on the extractive concentration in the cell wall. The variation in yielding should
affect the indentation hardness in different extents, accord-
ing to the classic work of Tabor [27] and the postulation of
Gindl et al. in Ref. [24]. The net effect is hence an additional source of variation that influences the dependence
of Hu on MFA.
Overall, an orientation dependence of Hu values was
observed, and there is a preliminary indication that the
dependence could be affected by variations in extractive
contents. This postulated, additional source of variation,
once verified in future studies, would add merits to using
nanoindentation hardness as a relative parameter to probe
the mechanical changes of cell walls as a response to physiological changes in living trees. In the context of cell-wall
modification for enhanced wood utilization, any unintended variations can be minimized by using starting materials that are similar for both control and treatment
experiments. One example is to use, for both the control
and treated samples, wood of the same growth ring to minimize the effects of MFA and possibly the influence of
cell-wall extraneous materials (extractives), so that any
treatment-induced changes in the cell-wall hardness can
be clearly identified from the nanoindentation data.
4. Conclusions
This study reports the continuous nanoindentation measurement of longitudinal stiffness and hardness of wood
cell walls as the indentation progresses. The indentation
depth profile exhibited a small length-scale effect, which
was confirmed using the size-effect index derived from the
indentation loading curve. The ultimate unloading curve
was used to determine the (discrete) modulus and hardness
values (Eu and Hu) for different wood annual ring samples.
A predictable pattern of Eu values was found as a function
of MFA, but the Eu values were lower than the corresponding moduli estimated from the cell-wall models. Further
observations indicate a high possibility that the longitudinal stiffness determined by nanoindentation was influenced
by an effective (off-axis) loading angle that is larger than
the MFA value of the corresponding wood sample. While
3D finite element analyses are recommended for the future
to verify this phenomenon, it is sufficed to conclude at present that Eu can be considered a relative measure of the
wood cell-wall longitudinal stiffness. Results from additional analyses also suggest that the differences in the
experimental (Eu) and predicted (modeled) values were largely influenced by the input values of the models (e.g. the
elastic constant values of cell-wall constituents) and the
moisture content levels of the samples during indentation.
For cell-wall longitudinal hardness (Hu), a dependence on
orientation was observed, and there is a preliminary indication that the dependence could be affected by variations in
extractive contents. Further investigations are needed to
verify the extractive effects. Meanwhile, for cell-wall modification studies, it is desirable to minimize any unintended
variations by using samples that are from the same growth
ring, so that any treatment-induced changes in the cell-wall
hardness can be identified from nanoindentation data.
W.T.Y. Tze et al. / Composites: Part A 38 (2007) 945–953
Acknowledgements
The authors would like to acknowledge financial supports from the USDA Wood Utilization Research Program, the National Research Initiative (grant number
2003-35103-13638) of the USDA Cooperative State Research, Education and Extension Service and the Tennessee
Agricultural Experiment Station (Project MS #83). Instrumentation for the nanoindentation work was provided
through the SHaRE Program at the Oak Ridge National
Laboratory, which was sponsored by the Division of Materials Science and Engineering, US Department of Energy,
under contract DE-AC05-000R22725 with UT-Battelle,
LLC. The authors also thank Dr. John Dunlap of the University of Tennessee Electron Microscopy Laboratory for
assisting in the microtome sectioning of the samples, and
Dr. Andrei Rar of the Oak Ridge National Laboratory
for technical supports in nanoindentation tests.
References
[1] Barefoot AC, Hitchings RG, Ellwood EL. Wood characteristics of
kraft paper properties of four selected loblolly pines. III. Effect of
fiber morphology on pulp. Tappi 1965;49:137–47.
[2] Wimmer R, Lucas BN, Tsui TY, Oliver WC. Longitudinal hardness
and Young’s modulus of spruce tracheid secondary walls using
nanoindentation technique. Wood Sci Technol 1997;31:131–41.
[3] Gindl W, Gupta HS, Grünwald C. Lignification of spruce tracheid
secondary cell walls related to longitudinal hardness and modulus of
elasticity using nano-indentation. Can J Bot 2002;80:1029–33.
[4] Gindl W, Gupta HS. Cell-wall hardness and Young’s modulus of
melamine-modified spruce wood by nano-indentation. Composites:
Part A 2002;33:1141–5.
[5] Gindl W, Schöberl T, Jeronimidis G. The interphase in phenolformaldehyde and polymeric methylene diphenyl-di-isocyanate glue
lines in wood. Int J Adhes Adhes 2004;24:279–86.
[6] Gindl W, Schöberl T. The significance of the elastic modulus of wood
cell walls obtained from nanoindentation measurements. Composites:
Part A 2004;35:1345–9.
[7] Page DH, El-Hosseiny F, Winkler K, Lancaster APS. Elastic
modulus of single wood pulp fibres. Tappi 1977;60:114–7.
[8] Nix WD, Gao H. Indentation size effects in crystalline materials: a
law for strain gradient plasticity. J Mech Phys Solids 1998;46(3):
411–25.
[9] Bull SJ. On the origins and mechanisms of the indentation size effect.
Z Metall 2003;94(7):787–92.
953
[10] Li X, Bhushan B. A review of nanoindentation continuous stiffness
measurement technique and its applications. Mater Charact 2002;48:
11–36.
[11] Kelley SS, Rials TG, Snell R, Groom LH, Sluiter A. Use of near
infrared spectroscopy to measure the chemical and mechanical
properties of solid wood. Wood Sci Technol 2004;38:257–76.
[12] Spur AR. A low-viscosity epoxy resin embedding medium for
electron microscope. J Ultrastruct Res 1969;26:31–43.
[13] Oliver WC, Pharr GM. An improved technique for determining
hardness and elastic modulus using load and displacement sensing
indentation experiments. J Mater Res 1992;7:1564–83.
[14] Harrington JJ, Booker R, Astley RJ. Modelling the elastic properties
of softwood. Part I: The cell-wall lamellae. Holz Roh- Werkst 1998;
56:37–41.
[15] Bergander A, Salmén L. Cell wall properties and their effects on the
mechanical properties of fibers. J Mater Sci 2002:151–6.
[16] Hainsworth SV, Chandler HW, Page TF. Analysis of nanoindentation of load–displacement loading curves. J Mater Res 1996;11:
1987–95.
[17] Tjernlund JA, Gamstedt EK, Xu Z. Influence of molecular weight on
strain-gradient yielding in polystyrene. Polym Eng Sci 2004;44:
1987–97.
[18] Low IM, Shi C. Vickers indentation responses of epoxy polymers.
J Mater Sci Lett 1998;17:1181–3.
[19] Rosso P, Ye L, Friedrich K, Sprenger S. A toughened epoxy resin by
silica nanoparticle reinforcement. J Appl Polym Sci 2006;100:
1849–55.
[20] Hepworth DG, Vincent JFV, Jeronimidis G, Bruce DM. The
penetration of epoxy resin into plant fibre cell walls increases the
stiffness of plant fibre composites. Composites: Part A 2000;31:
599–601.
[21] Shim S, Oliver WC, Pharr GM. A critical examination of the
Berkovich vs. conical indentation based on 3D finite element
calculation. Mater Res Soc Symp Proc 2005;841:39–44.
[22] Wood handbook: wood as an engineered material. Madison, WI,
USA: Forest Products Society; 1999.
[23] Holmberg H. Influence of grain angle on Brinell hardness of Scots
pine (Pinus sylvestris L.). Holz Roh- Werkst 2000;58:91–5.
[24] Gindl W, Gupta HS, Schöberl T, Lichtenegger HC, Fratzl P.
Mechanical properties of spruce wood cell walls by nanoindentation.
Appl Phys A 2004;79:2069–73.
[25] Luxford RF. Effect of extractives on the strength of wood. J Agric
Res 1931;42:801–26.
[26] Bortoletto Júnior G, Moreschi JC. Physical-mechanical properties
and chemical composition of Pinus taeda mature wood following a
forest fire. Bioresour Tech 2003;87:231–8.
[27] Tabor D. Indentation hardness and its measurement: some cautionary comments. In: Blau PJ, Lawn BR, editors. Microindentation
techniques in materials science and engineering. Philadelphia,
USA: American Society for Testing and Materials; 1985. p. 129–59.