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Temperature-Stress Equivalancy in Nonlinear Visco-elastic Creep Characterization of Thermoplastic/Agro-Fiber Composites

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The viscoelastic characterization of agro-filler based plastic composites is of paramount importance for the material’s long-term commercial success. To predict creep, it is important to derive a relationship between deformation, time, temperature, relative humidity, and stress. Since temperature shift can interfere with stress shift in creep, the predictive model should incorporate the relationship between these two shifts. Rice husk-HDPE beams were subjected to creep and recovery in the flexural mode and stress/time/temperature-related creep behavior of the same was studied. Temperature-related creep constants and shift factors were determined for the material and the constants were compared against theoretical two-phase constants. The combined effect of temperature and stress on creep strain was accommodated in a single analytical function where the interaction was shown to be additive. This means that the stress equivalency of temperature is possible. This constitutive equation can predict creep in the long run. Although stress dependency is nonlinear, temperature dependency is linear and thermorheologically complex. The ‘single-phase’ material behavior (creep constants) was also compared with a ‘two-phase’ predictive model, where the creep constants were estimated with the ‘theory of mixtures’.
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Composite Materials
Journal of Thermoplastic
http://jtc.sagepub.com/content/19/1/35
The online version of this article can be found at:
DOI: 10.1177/0892705706055443
2006 19: 35Journal of Thermoplastic Composite Materials
A. Pramanick and M. Sain
Characterization of Thermoplastic/Agro-fiber Composites
Temperature-Stress Equivalency in Nonlinear Viscoelastic Creep
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Temperature–Stress Equivalency in
Nonlinear Viscoelastic Creep
Characterization of
Thermoplastic/Agro-fiber Composites
A. PRAMANICK AND M. SAIN*
Faculty of Forestry, 33 Willcocks Street
University of Toronto, Toronto, Ontario
M5S 3B3, Canada
ABSTRACT: The viscoelastic characterization of agro-filler based plastic compo-
sites is of paramount importance for the material’s long-term commercial success.
To predict creep, it is important to derive a relationship between deformation, time,
temperature, relative humidity, and stress. Since temperature shift can interfere with
stress shift in creep, the predictive model should incorporate the relationship between
these two shifts. Rice husk–HDPE beams were subjected to creep and recovery in the
flexural mode and stress/time/temperature-related creep behavior of the same was
studied. Temperature-related creep constants and shift factors were determined
for the material and the constants were compared against theoretical two-phase
constants. The combined effect of temperature and stress on creep strain was
accommodated in a single analytical function where the interaction was shown to
be additive. This means that the stress equivalency of temperature is possible. This
constitutive equation can predict creep in the long run. Although stress dependency
is nonlinear, temperature dependency is linear and thermorheologically complex.
The ‘single-phase’ material behavior (creep constants) was also compared with a
‘two-phase’ predictive model, where the creep constants were estimated with the
‘theory of mixtures’.
KEY WORDS: HDPE–rice husk composites, creep, viscoelastic, temperature–stress,
nonlinear, two phase.
Journal of T
HERMOPLASTIC COMPOSITE MATERIALS, Vol. 19—January 2006 35
0892-7057/06/01 0035–26 $10.00/0 DOI: 10.1177/0892705706055443
ß 2006 SAGE Publications
*Author to whom correspondence should be addressed. E-mail: m.sain@utoronto.ca
at UNIV OF TORONTO on June 25, 2014jtc.sagepub.comDownloaded from
INTRODUCTION
A
GRO-BASED FIBERS AND particles are being considered as fillers for
thermoplastic composites. In these composites, typically 40–60%
agro-particles are blended with thermoplastics such as HDPE, PP, PVC,
etc. These composites have various uses: as deck-boards, railings, railway
ties, automotive parts, etc. In future, this material may replace both
wood and plastics. When used in building applications, plastic composite
can creep in the long run. Since creep is affected both by load and
temperature, any predictive model should consider the interactive effects
of these two factors among others. A study of the stress/temperature inter-
action is imperative for the prediction of creep under changing temperature
and load. ASTM standard defines some procedures to standardize the
performance of wood–plastic lumber; according to this standard, compli-
ance (stiffness/stress) of wood–plastic lumber should be used as one of the
creep-related performance parameters. Incidentally, compli ance has been
used as the measure of creep strain of plastic materials by many authors,
e.g., W oo [1]. ASTM D 6112 [2] also suggests that wood–plastic lumber,
when used as load bearing material, should be tested in four-point flexural/
bending mode rather than tensile mode for their creep properties. All
plastic-based materials and wood exhibit viscoelastic behavior and creep
under stress. In many plastic materials, creep is nonlinear with respect to
stress in the sense that compliance is a function of stress. Temperature and
moisture [3] can also induce nonlinearity. An issue with temperature is its
influence on stre ss, i.e., whether the combined stress–temperature effect
could be additive or interactive.
Individual temperature and stress-related creep issues have been dealt
with in the field of thermosetting-based composites [1,4]. It is imperative
to deal with the effect of these factors, when they occur concomitantly. We
have shown in our earlier work that creep of HDPE–rice husk deck-boards
show nonlinear behavior with respect to stress [5] and follow the power
law. Authors have proven that pure HDPE creep exhibits nonlinear
behavior under stress [6]. Xu et al. [7] showed that with an increase in fiber
content, the creep of wood particles-filled plastic composite decreas es. This
proves the influence of natural fiber on creep of plastic, but it has not been
clarified whether this influence is due to its reduction in plastic content or
due to the rigidity of the filler as there is a question of interfacial bond
energy. Martinez-Guerrero [8] suggests that stress infl uences compliance
in creep of wood–plastic lumber. Knauss and Emory [9] attributed stress-
related nonlinearity to changes in the free volume during deformation.
Rangaraj and Smith [10,11] ascribed nonlinearity to micro-damages
from deformation, and used power law to link damage with nonlinearity.
36
A. PRAMANICK AND M. SAIN
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Many authors have used the power law to express creep behavior of
plastic-based materials [10–12]. Schapery showed that a thermodynamic
approach to a nonlinear viscoe lastic model is similar to the Boltzman
superposition principle, where the power law concept can fit in [13].
Another popular model to be considered is the Kelvin–Maxwell model
[14–16]. Kelvin–Maxwell, in conjunction with the Boltzman superposition
principle yield s an expression that actually resembles Schapery’s expression.
Martinez-Guerrero concludes that plastic lumber does not follow the
Kelvin–Maxwell model [8]. However, Pooler [17] suggests that a modif ica-
tion of this model, which is the Prony series, fits the creep behavior of wood
particle-filled plastic well. Pooler, however, did not try to explore Schap ery’s
model analytically. The Prony series model application calls for numerical
calculations and is very material specific. All of the above models predict
creep through the determination of creep constants (and stress shift factors),
which treat the materials as ‘single-phase’ ones.
Temperature may influence compliance in a similar way as stress.
Crissman [20] has pointed out that stress and temperature dilations are
responsible for easier movement of the plastic macromolecules in
amorphous regions. The theory of temperature dilation has led to the
famous WLF (Williams–Landel–Ferry) equation, the activation energy
concept, and the TTSP ( time–temperature superposition principle)
proposition. According to these assertions, temperature effects may be
described by altering the timescale of the viscoelastic response. That means,
if D is creep strain (per unit stress) at a temperature of T
1
and time t, the
creep at a temperature of T
2
can be described as follows:
Dðt, T
1
Þ¼D
t
a
T
, T
2

where a
T
is a shift factor.
For thermorheologically complex material such as semicrystalline
plastics, a vertical shift of the data plots along the Y-axis should be
considered [17 ]. The fam ous WLF [21] assertion states that for an
amorphous plastic, the shift factor can predict the change in creep strain
corresponding to a temperature:
log a
T
¼
c
1
ðT T
g
Þ
c
2
þ T T
g
:
An Arrhenius relationship is also typically used [16]:
ln a
T
¼
E
a
R
1
T
1
T
ref

:
Viscoelastic Characterization of Agro-based Plastic Composites 37
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In this eq uation E
a
is the activation energy of chain relaxation, and T
ref
is
the reference temperature. Both of these equations are valid when there is a
linear temperature shift in creep strain due to a change in the tempe rature.
Elahi and Weitsman [18,19] used the concept of TTSP in their chopped
glass/urethane composites, which implies the ap plicability and universali ty
of this concept to composites. Many authors used the concept of vertical
shift in semicrystalline plastics in conjunction with horizontal shift (TTSP),
but the real cause for the vertical shift is not very clear [22]. While the
vertical shift factor had been thought to be a representation of the change
in crystallinity, crystallinity may not change at such a low temperature as
around 60
C [24]. However, both vertical and horizontal shift factors are
needed to model viscoelastic behavior of HDPE and composites. In the
studies involving temperatur e effect on creep, the prediction of creep is done
through the calculations of shift factors. Like the current stress models,
temperature models are also used to calculate shift factors with a ‘single-
phase’ approach.
Through the perusal of the literature, one would notice that the power law
and Schapery mod els have been used to describe stress-related nonlinearity
in thermosetting composites and pure thermoplastics. The studies on
temperature shif ts never looked at the interactive shift factors due to
concomitant changes in temperature and stress. We have proven that
Schapery models can be used to describe the nonlinear creep of rice-based
HDPE composite creep [25]. Here, we would like to incorporate the
temperature shift factor into the power law/Schapery equation and generat e
constitutive equations that define, characterize, and predict long-t erm creep
of the material. So with a single analytical function, which is nonexisting at
the moment, we will be able to encompass both stress- and tempe rature-
related shift factors. The constants, thus determined, will be validated
through rigorous step loading and long-term creep experiments. The
emphasis here is on the temperature effect, but becau se the temperature
and stress are both acting on creep, a cursory look at the stress effect also
will be taken. This work is also the vanguard to use power law concept in
step loading of temperature/stress.
We follow a two-step approach in this study. In the first step, which is a
‘single-phase’ approach, we characterize the material in hand (rice husk/
HDPE composite) for creep, and develop creep prediction equations
thereof. Here we determine creep constants, i.e., stress–temperature shift
factors for the experimental material. Extensively modified Schapery’s
concept is adhered to, because this concept is a blend of several creep
concepts, to develop the equation describing the validation material. The
predictive equation in the first step is actually a validation for the theory
developed in the second step. In the second step we strive to predict the said
38
A. PRAMANICK AND M. SAIN
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constants with those of the constituent materials (wood particle and HDPE)
from the literature. The second step is a generic ‘two-phase’ model, but in
this article we only emphasize the first step. However, a discussion about the
‘two-phase’ model is also included in the text. We mu st also emphasize that
no article exists to date on the ‘two-phase’ creep approach in composites.
For the ‘two-phase’ model, the HDPE and wood rheological data are
obtained from literature [26–29]. In the literature, HDPE and wood
behaviors were studied at different conditions, and shifts were calculated.
Wood also creeps in a nonlinear fashion and exhibits temperature shift.
There is a conspicuous absence of rice husk creep data. However, since
wood particles and rice husk are both lignocellulosic materials with similar
adhesion properties against HDPE, we propose to use the shift factor values
of wood as a substitute for rice husk.
THEORETICAL CONSIDERATIONS
Theory of Flexural Deformatio n
When a beam is loaded in four-point bending mode (Figure 1), maximum
tensile stress occurs at the bottom surface of the beam, whereas, compressive
stress occurs at the top. The ultimate tensile stress occurring at the bottom
can be calculated using the formula:
¼
PLI
1
bd
2
I
2
,
where is the stress at the bottom of the beam; I
1
¼ bd
3
/12, I
2
¼ðbd
3
b
1
d
3
1
Þ=12; P, load; L, span; b, breadth; and d, depth of the material. Also
note that I
1
, I
2
represent the moments of inertia of cross sections of solid and
Figure 1. A typical four-point bending setup.
Viscoelastic Characterization of Agro-based Plastic Composites 39
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hollow bars, respectively (Figure 2). The corresponding strain in the bottom
surface of the material can be calculated using the formula [2]:
" ¼
4:7d
L
2
,
where is the deflection of the beam.
Many studies [7,13,15] prefer to use normalized deformation, creep
or instantaneous, over absolute deformation, where normalized defor-
mation ¼ "/. This parameter, known as compliance, is useful in the study of
changes due to stress variation.
Theory of Creep
STRESS FACTOR
In the present work, creep is defined as the total strain at the bottom
surface of the beam. In order to quantify the effect of stress on the material,
throughout this article, creep has been normalized:
DðtÞ¼
"ðtÞ
¼ compliance ð1Þ
where represents a constant applied load and "(t) is the time-depend ent
strain. The thermodynamic theory permits us to express the nonlinear
material properties in strain [13] as follows:
"ðtÞ¼g
0
D
0
þ g
1
Z
t
0
Dð
0
Þ
dg
2
d
d ð2Þ
where
D
0
Dð0Þ and Dð
0
ÞDð
0
ÞD
0
ð3Þ
d, b
b1, d1
Figure 2. Cross-sectional schematic view of the beam.
40 A. PRAMANICK AND M. SAIN
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In Equation (3), D
0
is the init ial value of the creep compliance, Dð
0
Þ
is the transient component of the creep compliance, and (at a constant
temperature) is the reduced time calculated as follows:
¼
Z
dt
a
for a
> 0 ð4Þ
0
¼ ðÞ¼
Z
dt
a
ð5Þ
In the above equations, g
0
, g
1
, g
2
, and a
are the material properties as a
function of stress. In general, these stress-dependent properties have specific
thermodynamic significance and the changes in g
0
, g
1
,andg
2
reflect third-
and higher- order dependence of the Gibb’s free energy on the applied stress
[13]. Equation (2) can be simplified in a single-step load, where the value of
is assumed to be constant, to the following form :
"ðtÞ¼g
0
D
0
þ g
1
g
2
D ðÞ ð6Þ
By substituting a constant stress into Equation (2), d g
2
=d ¼ 0 (except
when ¼ 0, where d ¼ ). Equation (2) morphs into:
"ðtÞ¼g
0
D
0
þ g
1
g
2
D
t
a

n
ð7Þ
For nonlinear creep Equation (7) shows that the initial elast ic response is
particularly linear even though the creep is strongly nonlinear and the
transient component of the creep D( ) is modeled by the log power law:
D
t
a

¼ D
1
log
t
a

n
ð8Þ
Determination of Stress-related Creep Coefficients
A full nonlinear viscoelastic theory presents a constitutive behavior ,
a stress–strain relation, of polymeric materials (Figure 3) through the
following equations:
"ðtÞ¼g
0
D
0
þ g
1
g
2
D
1
log
t
a

n

þ "
p
ðtÞð9Þ
Viscoelastic Characterization of Agro-based Plastic Composites 41
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where a
is a timescale shift factor. It mathematically (and horizontally)
shifts the creep data parallel to the time axis relative to a master curve for
creep strain versus time, n is the index that determines the shape of the creep
curve, and "
p
is the plasticity that occurs during creep. It should be noted
that for linear viscoelastic strain, Equation (9) reduces into the following
equation (g
1
, g
2
, and a
are equal to unity in the linear region):
"ðtÞ¼DðtÞ ¼ðD
0
þ D
1
ðtÞðlog tÞ
n
Þ ð10Þ
Equation (9) relates stress with strain through material constants; so in
order to predict creep for a given level of stress we estimate the creep
coefficients as a function of stress. According to the data reduction method
proposed by Papanicolaou et al. [12] for ‘carbon–epoxy resin’ composite,
the constants can be calculated through solving Equations (9) and (10) along
with the following equation for recovery (Figure 3):
"
r
ðtÞ¼g
2
D
1
log
t
a
þ t t
a

n
D
1
logðt t
a
ðÞÞ
n

þ "
p
ðt
a
Þð11Þ
Equation (11) for recovery assumes that at zero stress the a
, g
0
, g
1
, g
2
are
all unity.
Calculation of the Basic Creep Constants
The value D
0
can be determ ined from the instantaneous deflection data of
the creep/time curve in the linear range. According to Equation (2), g
0
could
be calculated from the creep plot when t is equal to zero. The following
formula may be employed to calculate compliance:
"ð0Þ¼Dð0Þ ¼ D
0
g
0
) g
0
¼
"ð0Þ
D
0
ð12Þ
ε
or
Strain
ε
oc
ε
c
(t)
0
0
Time
ε
r
(t)
∆ε
c
Figure 3. A typical creep diagram depicting strain–time relationship.
42 A. PRAMANICK AND M. SAIN
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The n and D
1
values can be calculated through curve fitting of Equation (9)
in the linear region. We may calculate g
1
with the following equation:
g
1
¼ ("
c
(t
a
) g
0
D
0
"
p
)/"
r
(t
a
). In order to calculate a
, we can use the
recovery equation (11) to obtain a fit; g
2
can be calculated from the
following equation where the assumption is that g
2
¼ 1 in the linear region:
"
c
ðt
a
Þ"
p
g
1
log
n
ðt
a
Þ

nl
g
1
log
n
ðt
a
Þ
"
c
ðt
a
Þ"
p
ðt
a
Þ

l
¼ g
2
ð13Þ
where the subscript l means linear and nl means nonlinear.
Validation of the Model with a ‘Two-step’ Loading
When stress is applied stepwise in time with the following con ditions:
¼
a
, for 0 < t < t
a
¼
b
, for t
a
< t < t
b
¼
b
¼
c
ð14Þ
where the superscripts refer to the properties associated with the corre-
sponding stress levels. Equation (2) morphs into the following:
"
c
ðtÞ¼
b
g
b
0
D
0
þ
a
g
b
1
g
b
2
D
1
log
t
a
a
a
þ
t t
a
a
b

n
þðg
b
2
b
g
a
2
a
ÞD
1
log
t t
a
a
b

n
ð15Þ
"
r
ðtÞ¼
a
g
b
1
g
b
2
D
1
log
t
a
a
a
þ
t
b
t
a
a
b
þ
t t
b
a
c

n
þðg
b
2
b
g
a
2
a
Þ
D
1
log
t
b
t
a
a
b
þ
t t
b
a
c

n
b
D
1
g
b
2
log
t t
b
a
c

n
ð16Þ
TEMPERATURE FACTOR
We assumed that temperature and stress act additively. So the tem-
perature acts upon time factor of the constitutive equation (6) as follows:
"ðtÞ¼ðg
0
D
0
ÞFðT Þ þ g
1
g
2
D
t
a
a
T

n
þ "
p
ð17Þ
Viscoelastic Characterization of Agro-based Plastic Composites 43
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or
"ðtÞ¼ðg
0
D
0
ÞFðT Þ þ g
1
g
2
D
t
a

n
E
a
RT
þ "
p
ð18Þ
where E
a
is the activation energy of chain relaxation. In the semicrystall ine
materials, there could be an instantaneous deformation due to the
temperature change, which is known as the vertical shift factor. In
the above equation, F(T ) denotes the vertical shift factor. If temperature
is changed dur ing the course of creep, we may call the activity as the step
loading of temperatures. If at the time t
1
the temperature is changed from T
1
to T
2
, the following relationships will hold:
For t t
1
, when a
T
¼ a
1T
"
c
ðtÞ"
p
¼ ðg
0
D
0
ÞFðT
1
Þþg
1
g
2
D
1
log
t
a
1T

n
ð19Þ
For t>t
1
, when a
T
¼ a
2T
"
c
ðtÞ¼ðg
0
D
0
ÞFðT
2
Þþg
1
g
2
D
1
log
t
1
a
a
1T
þ
t t
1
a
a
2T

n
þ"
p
ð20Þ
If the load is withdrawn at time t
a
while the temperature remains same,
the following relationship should hold:
"
r
¼ D
1
log
t
a
a
a
T
þ
t
a
T
t
a
a
T

n

D
1
log
t
a
T
t
a
a
T

n

g
2
þ "
p
ðt
a
Þ
ð21Þ
‘TWO-PHASE’ APPROACH WITH ‘THE THEORY OF MIXTURE’
In this approach the number of parameters needs to be limited, or else the
calculations will be cumbersome. So Equation (6) needs simplification, where
we assume that D
0
g
0
¼ "
0
and g
1
g
2
D
1
¼ g"
1
. Now, for discontinuous fibers
with a low aspect ratio, the composite stiffness can be expressed in terms of
the following equation where is the volume fraction of the fiber, is the
factor for shortness of the fibers, E
f
is the modulus of the fiber, E
m
is the
modulus of the matrix, "
0
is the compliance [16]:
E ¼
1
E
f
þ E
m
ð1 Þ
and "
0
¼
1
E
ð22Þ
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A. PRAMANICK AND M. SAIN
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The assumption for Equation (22) is that when under stress the fibers
and the matrix must undergo the same strain as the whole composite does
at low stress. Thus, we prop ose the following creep equation (based on
Equation (6)):
Creep ¼
"
c
ðtÞ
¼ "
0
þ g"
1
log½t
n
ð23Þ
where g"
1
¼ 1=ð=g
1
f
"
1, f
þ 1=g
2
m
"
1, m
Þ and g
1
f
¼ g
2
m
¼ g: Also,
1
and
2
are incremental stress distrib ution in fibers and matrix, respectively.
If we incorporate temperature shift and temperature stress shifts are
additive:
Creep ¼
"
c
ðtÞ
¼ "
0
a
0
þ
g"
1
log½t
n
a
ð24Þ
where g"
1
=a
¼ 1=ða
,f
=g
1
f
"
1, f
þ a
,m
=g
2
m
"
1, m
Þ, a
¼ exp(E
a
(1/T 1/T
0
)/R).
The difference between a
and a
0
is that the latter (vertical shift) is measured
with respect to "
0
, not "
1
. However, these two values depict the same shifts.
The value of can be calculated as follows [16]:
¼ 1 tanh
na
na

where n ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2G
m
=E
f
lnð2R=d Þ
p
, G
m
is the matrix shear stress, E
f
is the fiber
modulus, 2R is the distan ce between two adjacent fibers, d is the diameter of
each fiber, and a is the aspect ratio.
Using Equation (23), the stress shift per unit stress is calculated as follows:
¼
1
þ
2
¼ 2 MPa ðfor 50% volume of particles Þ
g
1
m
¼
g
f

2
¼ increase in length per 1 MPa stress
where g
m
¼ g
f
¼ 1.12 (Table 4). Solving for g values, we obtain g
1
m
¼ 1:21:
The temperature shift (Equation (24)) can be calculated as follows:
Stress generated due to temperature shift on the composite ¼ ¼
(1/a
1)"
1
¼ 0.5(
f
þ
m
), where
f
and
m
are the stresses on the fiber
and matrix respectively. But the strain on the composite ¼ strain on the
constituents ) 1/a
,f
1 ¼ 1/a
,m
1 ¼ 1/a
1 ¼
f
"
f
¼
m
"
m
¼ "
1
(Table
6), where "
1
¼ 1=ð1="
f
þ "
m
Þ:
Viscoelastic Characterization of Agro-based Plastic Composites 45
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METHODOLOGY
Materials
Material for this experiment was acquired from Extendex Inc., Barrie,
Canada. This material is commercially marketed as deck-boards and railings
(Figure 4). The railings are our focus and they contain 60% rice husk
and 40% HDPE. A ‘two-step’ procedure was followed to process these
materials compounding and extrus ion. In the first step, rice husk goes
through a sieve of mesh size 16–80 with the moisture content of 10%. The
husks at the outlet of the dr ier achieve a moisture content of 1%. The dried
husk is sent through a heated co-rotating twin-screw extruder, where HDPE
pellets are mixed thoroughly and are ejected as compounded pellets. These
pellets are subsequently passed through a conical profile extruder. While
the profile is pulled out of the extruder, a mist is used to cool the product
down. MAPE (maleated polyethylene) is used as the coupling agent, which
is mixed during the pelletization in the twin-extruder. The dimension of the
cross-section of these rails is 600 40 40 mm
3
, whereas the thickness of the
same is 5 mm.
Experimental Setup
Two types of tests (creep and instantaneous) were carried out and both
were done in the flexural mode. A flexural creep testing rack was de signed
based on ASTM D 6112. ASTM uses the four-point loading configuration
(Figure 1) because plastic lumbers are relatively ductile and do not fail by
the maximum strain (3%) under the three-point loading. The span length
for the test was 600 mm (¼ L) and the crosshead speed of 10 mm/min. The
noses of both the support and loading beams were configured with
cylindrical surfaces with a radius of 1.27 mm in order to avoid excessive
indentation of the specimen. In order to allow for overhanging, at least
10% of the support span were maintained at each test specimen ends.
Figure 4. Composite railings and deck-board.
46 A. PRAMANICK AND M. SAIN
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The deflection of the specimen was measured at the midpoint of the load
span at the bottom face of the specimen.
The instantaneous failure test (four-point flexural) was done by a Zwick
‘strength testing’ machine. A load was applied to the object in the middle of
the span and stress/strain diagram was plotted until the material failed. The
purpose of this test was to determine the strength of the material. The peak
stress was determined from the ensuing stress–strain curve.
Both short-term and 1000-h tests (Figure 5) were performed at various
stress levels (14–50%) of the maximum stress level (ultimate stress,
u
).
The temperature was also varied for the purpose of determining the
temperature shift of the plots (20–60
C). The creep tests were also followed
up with retraction of the load when full or a part of the strain/creep was
recovered. Step loading was carried out by adding an extra load during the
process and with respect to temperature in the sense that temperature was
varied in some cases. A transducer was placed at the bottom of the beams
(Figure 5) to note the voltage of the transducer with respect to the creep
level. The whole setup was ensconced in a kiln room where the temperature
and humidity could be altered with a control panel.
RESULTS AND DISCUSSION
Stress Effect on Creep
The composi te beams tested for strength did not show extreme variations
in the stress/strain properties (Figure 6). This lack of variation proves
uniformity of its strength and stiffness properties amongst specimens. The
maximum force level to break the beams was about 1900 N. At this force,
the ultimate stress (
u
) is in between 25 and 20 MPa.
NONLINEARITY IN CREEP
The composite creep showed a significant stress dependency, as is evident
from Figure 7. The compliance went up consistently with the applied
Figure 5. Creep setup according to ASTM standards.
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stress level. The composite also showed a low plasticity, about 2–5% of the
total strain. The stress-related constants were determined to develop a basic
empirical equation for the ambie nt conditions. D
0
and g
0
values were
calculated according to Equation (12) and are shown in Tabl e 1. It was
assumed that the value of g
0
was 1 at 14% stress (base line creep). The g
0
value in general increases with stress. However, the increase is prominent
only from 14 to 27%. Beyond that, the average g
0
value hovers at
around 1.50. We propose to use this value for the stress level abo ve 27%.
0
0.02
0.04
0.06
0.08
0.1
0.12
0 200 400 600 800 1000 1200 1400 1600
Time
(
min
)
Strain (%/MPa)
5.2 MPa 11 MPa
3.39 MPa 8.39 MPa
Figure 7. Stress dependency of the composite.
Figure 6. Stress/strain diagram.
Table 1. Stress-related creep coefficients (single phase).
Stress
level (%)
Compliance
(MPa
1
) g
0
D
0
g
1
D
1
10
2
n
14 0.00035 1.00 0.00035 1.66 0.0036 1.45
22 0.00040 1.14 0.00035 1.50 0.0036 1.45
27 0.00054 1.55 0.00035 1.45 0.0036 1.45
30 0.00056 1.60 0.00035 1.00 0.0036 1.45
50 0.00045 1.30 0.00035 1.00 0.0036 1.45
40 0.00054 1.54 0.00035 1.00 0.0036 1.45
48 A. PRAMANICK AND M. SAIN
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No error was introduced because our long-term tests were based on low
stress where g
0
was close to 1. In the cases where high stresses were used,
the exact values were chosen for g
0
from Table 1.
The g
1
values represent the part of creep that is recoverable after the load
is withdrawn. This value is important only if we are interested in the recovery
part of the creep process. It is observed that the values of g
1
(Table 1)
decrease with the increase in load. A high value of g
1
suggests quickness
in recovery. This implies that at low stress (and low strain), as the load is
retracted, the recovery may behave like elastic recovery. But g
1
plateaus
after 30% stress levels off to a value of 1 (Figure 8). Therefore, for practical
purposes, a value of 1 is justifiable at high stress level (>30% ultimate stress
level). Below this we must use the appropriate values.
Using Equation (9), the value of n was estimated, as we obtained a
straight line between log "(t) and log(log(t)). So the slope of this plot is
n and it does not change with time because of this straight line relationshi p.
The values of n and D
1
are presented in Table 1. Equation (11) was validated
with a
value as unity and that means the stress-related nonlinearity is a
function of g
2
only [9,30]. The g
2
values were calculated using Equation (13)
(Table 2). The values of g
2
go up with the stress level. The g
2
values are also
0
0.5
1
1.5
2
0 204060
Stress level (%)
g
1
values
Figure 8. Stress dependency of g
1
values.
Table 2. Estimation of g
2
values.
Stress
% max
stress
t
a
(min) "
c
/g
1
g
2
3.5 14 1537 0.01988 1
5.2 22 1483 0.027333 1.376317
6.71 27 2849 0.042727 1.901831
11 50 77 0.041818 4.448346
8.83 40 252 0.044545 3.043111
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linearly related with the stress level (Figure 9). This makes it simple to make
prediction based on the creep level.
MODEL VALIDATION FOR STRESS NONLINEARITY
At ambient conditions, the final equation assum es the following form:
ð"
c
ðtÞ"
p
Þ= ¼ g
0
ð0:035Þþg
1
g
2
ð0:0036 log½t
1:45
Þ %MPa:
For some stresses log power law models were verified through Figures 10–12,
where creep and recovery were studied. It is evident from Figures 11 and 12
that the model works very well for long-term creep. In this case, a linear
model was adopted. In the case of step loading, which is followed up with the
load retraction, the log power law model fit excellently well (Figure 13).
Temperature Effect
TEMPERATURE STR ESS INTERACTION
In one set of experiments, temperature was varied from 20 to 60
C and
the stress level was also concomitantly varied, but in the reverse order
0
1
2
3
4
5
0 2 4 6 8 10 12
Stress (MPa)
g
2
Log based Linear (log based)
Figure 9. The g
2
–stress relationship.
0
0.02
0.04
0.06
0.08
0 500 1000 1500 2000 2500 3000 3500
Time (min)
Strain (%/MPa)
Lo
g
power law Expt.
Figure 10. Creep and recovery data for 14% stress level.
50 A. PRAMANICK AND M. SAIN
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0
0.02
0.04
0.06
0.08
0.1
0.12
1 10 100 1000 10,000
Time (min)
Strain (%/MPa)
Experimental Log power law
Figure 11. Creep data for 27% ultimate stress.
0.01
0.1
1
1 10 100 100
0
Time (min)
Strain (%/MPa)
Expt. Lo
g
power law
Figure 12. Creep data for 40% ultimate stress.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 1000 2000 3000 4000 5000 6000
Time (min)
Strain (%)
Experimental
Predicted
Figure 13. Creep and recovery plot for step loading.
Viscoelastic Characterization of Agro-based Plastic Composites 51
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i.e., from 6.5 to 3.4 MPa respectively. Figure 14 depicts the temperature/
stress effect on creep. In order to segregate the temperature effect from the
stress dilation an extension of Equation (17) was used:
log
ð"ðtÞðg
0
D
0
ÞFðT Þ"pÞ
g
1
g
2
¼ log D
t
a
a
T

n
ð25Þ
In Figure 14, log((""
0
"
p
)/(g
1
g
2
)) values were plotted along the Y-axis
and log t values were plotted along the X-axis for the composite. In this
particular experiment the total creep increased with increase in temperature,
although at higher temperatures applied stresses were lower. Although the
creep strain was affected by both temperature and stress, the normalized
plots with respect to stress factors (g
1
and g
2
) showed a horizontal shift
along the time axis. The shift factor a
T
, that depicts horizontal shift, seems
to increase uniformly with temperature. A point per point time–temperature
shifting too was attempted on the experimental compliance data. The creep
compliance curve of Figure 14 was shifted point by point to obtain a smooth
master curve in Figure 15. This master curve confirms that a creep test result
at 60
C and 1000 min is equivalent to that at 20
C and 2 years.
It has already been mentioned that activation energy (E
a
) indicates a shift
of the creep curves along the X-axis due to the changes in temperature.
As described by Equation (18), a plot of 1/T versus log(""
0
)/(g
1
g
2
)at
371 min of creep yields us a straight line (Figure 16) for the composite,
where the line yields a slope of about –3200. After we equated this slope
value with E
a
/R, we obtained a value of 30 kJ/mol for the E
a
. The value
of E
a
can be converted into a
T
through Equations (17) and (18). Thus we
obtain a value of 0.15 for a
T
for an increase of 10
C. Using this value we
obtain Figure 17 where the experimental values show conformation with
-3
-2.75
-2.5
-2.25
-2
-1.75
-1.5
-1.25
-1
-0.75
-0.5
-0.25
0
0 0.5 1 1.5 2 2.5 3 3.5 4
Log (time, min)
Log (normalized strain, %/MPa)
20°C, 6.5 MPa 30°C, 5.7 MPa 40°C, 4.93 MPa 50°C, 4.15 MPa 60°C, 3.4 MPa
Figure 14. Effects of temperature and str ess on creep.
52 A. PRAMANICK AND M. SAIN
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y = -3297.7 x +6.9837
R
2
= 0.9946
-5
-4
-3
-2
-1
0
0.0029 0.003 0.0031 0.0032 0.0033 0.0034 0.003
5
1/T (K)
Log(e-e
0
)/g
1
/g
2
Figure 16. Energy of activation.
-3
-2.5
-2
-1.5
-1
-0.5
0
0.1
1
1
0
Time (log(t/a
T
), min)
Strain (%/MPa,
normalized)
20°C 30°C 40°C 50°C 60°C
Figure 15. Master curve for time–temperature–stress superposition.
0
0.05
0.1
0.15
0.2
0.25
0 1000 2000 3000 4000 5000 600
0
Time (min)
Strain (%/MPa)
20°C 30°C 40°C 50°C
Figure 17. Constitutive equation and experimental data.
Viscoelastic Characterization of Agro-based Plastic Composites 53
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the model (Equation (17)). From various literatures, it is clear that a pur e
HDPE has an E
a
value of 90 kJ/mol [22,24]. A high value of E
a
signifies a
higher sensitivity to temperature, so it is no surprise that the value of this
composite turns out to be only 30 kJ/mol. This attests to the fact that the
incorporation of the rice husk particles has reduced the creep. The T
g
value
of the composite was also estimated through the W LF equation, where the
universal co nstants c
1
and c
2
were assumed to be 17 and 52 respectively. For
pure HDPE the T
g
value is close to 125
C. The value we obtained for the
composite is given in Tabl e 3. This value indicates that the effective T
g
of
the composite is way higher than pure HDPE.
A vertical shift factor was also observed for these materials, as the matrix
is made of a semicrystalline material. The instantaneous deformation
was actually linear with respect to temperature with the formula: F(T ) ¼
(0.0015T 0.4K )/0.04 (Table 3, Figure 18).
VALIDATION OF THE CREEP MODEL FOR THE
MATERIAL AS ‘SINGLE PH ASE’
Figure 17 shows a comparison of experimental data and Equation (17),
where the temperature was varied from 20 to 50
C and stress was varied
from 6.5 to 4.15 MPa respectively for the composite. The a
T
and g values as
per the described in the theory and in Tables 1–3 were incorporated into
Equation (17) and this equation can describe the related creep behavior.
y = 0.0015 x -0.4052
R
2
= 0.9919
0
0.02
0.04
0.06
0.08
0.1
0.12
290 300 310 320 330 340
Temperature (K)
Momentary strain (%/MPa)
Figure 18. Vertical shifts at several temperatures.
Table 3. Temperature-dependent creep coefficients (single phase).
Material Model type a
T
F(T ) E
a
T
g
Rice husk
plastic composites
Log power law 0.15/10
C (0.0015T0.4)/0.04 30 kJ/mol 25
C
54 A. PRAMANICK AND M. SAIN
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Figure 19 shows the plots for two stress levels, 4.1 and 4.9 MPa. With
respect to an ambient condition of T ¼ 20
CandRH¼ 58%, the stress-
related vertical shift factor g
2
should be around 1.2. By comparing model
equation values (Equation (20)) and experimental data in this figure, it is
obvious that the theory of additivity holds well. Figure 19 also testifies that
the same g
2
value holds at 50 and 60
C as well regarding the stress level.
Figure 19 also represents a step-temperature loading experiment where the
temperature was elevated to 60
C from 50
C during the creep at 60 min
(while the stress level was also changed). As expected from Equation (20),
the creep went up followed by an increase in the instantaneous deformation.
The increase in instantaneous deformation at the start of 60
C suggests
an increase in the vertical shift factor. But due to the slow increase in
temperature, the instantaneous creep increase does not take place abruptly.
However, the overall creep in the long run can be predicted well with
Equation (20).
A three-step loading of temperature, keeping the stress level same depicts
a slightly different picture where temperature was maintained as follows:
60
C for 1600 min, 40
C for 1600–6000 min, 60
C for 6000–8000 min.
The three-step temperature loading (Figure 20) experiment sho ws that
Equation (20) is valid for a general prediction of creep at varying
temperatures. It is valid only when the vertical shift factor is considered
as F(T
1
) rather than as F(T
2
) for a decrease in the temperature. It is not valid
if the instantaneous drop in modulus due to temperature dro p (from 60 to
40
C) is considered in the equation. That is probably due to the fact that
at lower temperature the recovery is slowed down just like creep. So it is
difficult for the beam to recover to the full potential. Due to the fact that not
many articles exist about this aspect, this aspect may be investigated in
greater detail.
The validity of this additivity theory is also checked through a set of creep
and relaxation experiments. Plotted data at three temperatures conform
0
0.05
0.1
0.15
0.2
0.25
0 20406080100120
Time (min)
Strain (%/MPa)
4.1 MPa, 50°C, %RH
4.9 MPa, 60°C, %RH
Model
Figure 19. Effect of step loading of temperature and str ess on the creep strain.
Viscoelastic Characterization of Agro-based Plastic Composites 55
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to Equation (21). This reinforces the asser tion that the creep stress-related
constants are independent of temperatur e (Figure 21).
Long-term tests (Figure 23) for the composite, acco rding to the ASTM
standard for a thousand hours, were performed with 4.55 MPa and at
40
C and variable RH. A model plot for a temperature of 40
C/60% RH/
4.55 MPa is also plotted with the experimental data in the background
in Figure 23. The model data points are ensconced in between the data of
72 and 51% showing the validity of the model for 1000 h test:
"
c
ðtÞ"
p
ðtÞ
¼ g
0
ð0:035ÞFðT Þþg
1
g
2
ð0:0036Þ log
t
a
T

1:45
%
Since the creep rate is extremely low and the plasticity of the material is only
2–5%, it is expecte d that the material viscoe lastic property will not change
much for moderate conditions like this. So a 1000 h test should suffice for
moderate conditions. At least it shows that the shape of the model curve is
0
0.05
0.1
0.15
0.2
0.25
0 2000 4000 6000 8000
Time (min)
Strain (%/MPa)
Expt. Model
Figure 20. A three-step temperature loading experiment.
0
0.05
0.1
0.15
0.2
0.25
0 20 40 60 80 100 120 140
Time (min)
Strain (%/MPa)
40°C, %RH 50°C, %RH 60°C, %RH model model model
Figure 21. Creep and relaxation at several temperatures.
56 A. PRAMANICK AND M. SAIN
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similar to that of the experimental plots and these curves plateau after
certain hours of creep. So the model is definitely valid in the long run.
In fact, it is better suited for long-term test because of some inaccuracies in
the first few minutes of data collection.
VALIDATION OF THE CREEP MODEL
FOR ‘TWO-PHASE’ MATERIALS
In this model both g and a
values are culled from literatures for wood
and HDPE creep experiments. The a
0
value is related to a
through the
ratio of "
1
and "
0
. Tables 4–6 display the predicted calculated shift values for
the composites and the constituents. Based on Equation (24) and Tables 4–6
we construct the following equations to describe ‘two-phase’ creep behavior
under 40
C/72% RH/4.5 MPa:
Creep ¼
"
c
ðtÞ
¼ "
0
1:2
2
þ 1:2 1:05"
1
log½t
1:45
1:4
2
Table 4. Creep properties of the constituents.
Compliance
(MPa
1
)
Modulus (E)
(GPa)
Shear
modulus
(Gm) n
Creep
modulus,
1/"
1
g
f
, g
m
/unit
stress
Aspect
ratio (a)
Wood
(for rice husk)
8 NA 0.3 1.45 1/0.0008 1.12 2
HDPE 1.2 0.6 GPa NA 1.45 1/0.05 1.12 NA
Table 6. Theoretical ‘two-phase’ a
value calculations.
Material
E
a
(activation
energy)
(kJ/mol)
(1 þ 1/a
)/
10
C
1/"
1
(¼ 1/creep
compliance)
(MPa) ¼ stress
distribution
HDPE 90 2.36 20 (1/"
1
, m) 47.2
Wood 20 0.30 375 (1/"
1
, f ) 112.5
Composite 30 0.41 197.5 (1/"
1
)80
Table 5. Comparison of experimental and theoretical creep constants
(stress related).
Methods
D
0
g
0
¼ "
0
(%/MPa)
D
1
g
1
g
2
¼ g"
1
(%/(MPa min
1.45
))
g/unit
stress
Theory of mixture 0.05 0.0050 1.20
Experimental 0.052 (average) 0.0060 (for 14% stress) 1.25
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The above equation is validated in Figure 22 where 1/a
value at 400
Cis
1.4
2
and g value is 1.2. Since RH was 72% and the moisture shift is about
1.2/20% RH change (Figure 23), we had to include a 1.05 shift in the above
final expression. A cursory look at Figure 23 testifies that the shift due to the
changes in RH is uniform at low RH (21–72%). But it changes dramatically
at 90% RH. So the 1.2 value per 20% change in RH is valid only in the
limited range. We must recall that all the shifts are based on 20
C/58% RH/
3.5 MPa.
CONCLUSION
We characterized and modeled creep behavior of agro-based plastic
composites with respect to stress and temperature. We selected a rice-based
HDPE composite for that purpose. Since this material is a ‘two-phase’ one,
0
0.05
0.1
0.15
0.2
0.25
0.3
0 10,000 20,000 30,000 40,000 50,000 60,000
Time (min)
Strain (%/MPa)
23.5°C/58% RH 40°C, 21% RH 40°C, 72% RH
40°C, 51% RH 40°C, 93% RH Theoretical plot
Figure 23. Long-term depiction of model and experiment.
0
0.05
0.1
0.15
0.2
0 10,000 20,000 30,000 40,000
Time (min)
Compliance (%/MPa)
Expt. data, 40°C, 72% RH
Prediciton
Figure 22. Validation for creep at 40
C, 72% RH.
58 A. PRAMANICK AND M. SAIN
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we took a two-step approach. In the first, the temperature–stress equivalence
was studied for the material, where the material was considered as ‘single
phase’. The material constants were determined with the help of extensively
modified Schapery’s model, where the temperature shift factor was also
incorporated. The constants in the model were validated against step- loaded
(temperature and stress) creep and recovery data. In this so-called ‘single-
phase’ characterization, the temperature effect was found to be linear but was
thermorheologically complex exhibiting vertical shifts. The activation energy
of creep chain relaxation is lower than the literature E
a
value of HDPE in
general. Despite being a two-phase composite material this composite shows
time–temperature superposition behavior. The interaction between tempera-
ture and stress is additive within a limited range of temperature and stress.
A cursory look at the moisture effect also was taken.
The second step of creep prediction consisted of applying ‘the theory of
mixture’ to the predictive model. In this case the material is considered as
‘two phase’ and the model has a universal application. We have touched
upon the fact that creep data for HDPE and wood from literature can be
used to predict the behavior of this composite when put into the said theory.
The experimental constants determined with the modified Schapery model
actually conforms well to the theoretically predicted constants even for
long-term creep.
REFERENCES
1. Woo, E.M. (1994). Moistur e Temperature Equivalency in Creep Analysis of a
Heterogeneous-matrix Carbon Fire/Epoxy Composites, Composites, 25: 425–430.
2. Standard Test Methods for Compressive and Flexural Creep and Creep Ruptures of Plastic
Lumber and Shapes, ASTM D 6112-97, pp. 821–838.
3. Tuttle, M.E., Pasricha, A. and Emery, A.F. (1995). The Nonlinear Visco-elastic-viscoplastic
Behavior of IM7/5260 Composites Subjected to Cyclic Loading, Journal of Composite
Materials, 29(15): 2025–2044.
4. Lu, H. and Knauss, W.G. (1999). The Role of Dilatation in the Nonlinearly Viscoelastic
Behavior of PMMA under Multiaxial Stress States, Mechanics of Time-Dependent
Materials, 2: 307–334.
5. Lin, W.S., Pramanick, A.K. and Sain, M. (2004). Determination of Material Constants for
Nonlinear Viscoelastic Predictive Model, Journal of Composite Materials, 38(1): 19–29.
6. Lai, J. and Bakker, A. (1995). Analysis of Nonlinear Creep of High Density Polyethylene,
Polymer, 36(1): 93–99.
7. Xu, B., Simonsen, J. and Rochefort, W.E. (2001). Creep Resistance of Wood-filled
Polystyrene/High Density Polyethylene Blends, J. of Applied Polymer Science, 79: 418–425.
8. Martinez-Guerrero, J.N. (1998). Flexural Creep Analysis of Recycled Polymeric Structural
Elements, PhD Thesis, Louisiana Sate University.
9. Knauss, W.G. and Emri, I. (1987). Volume Change and the Nonlinear Thermo-visco-elastic
Constitution of Polymers, Polymer Engineering Science, 27: 86–100.
10. Rangaraj, V.S. and Smith, V.L. (1999). The Nonlinear Visco-elastic Response of Wood
Thermoplastic Composite, Mechanics of Time Dependent Materials, 3: 125–139.
Viscoelastic Characterization of Agro-based Plastic Composites 59
at UNIV OF TORONTO on June 25, 2014jtc.sagepub.comDownloaded from
11. Rangaraj, V.S. (1999). Durability Assessment and Modeling of Wood-Thermoplastic
Composites, MS Thesis, School of Mechanical and Materials Engineering, Washington
State University.
12. Papanicolaou, G.C., Zaoutsos, S.P. and Cardon, A.H. (1999). Further Development
of a Data Reduction Method for the Nonlinear Visco-elastic Characterization of FRPs,
Composites: Part A, 30: 839–848.
13. Schapery, R.A. (1969). On the Characterization of Nonlinear Visco-elastic Materials,
Polymer Engineering and Science, 9(4): 295–309.
14. Schapery, R.A. (1997). Nonlinear Visco-elastic and Visco-plastic Constitutive Equations
based on Thermodynamics, Mechanics of Time Dependent Materials, 1: 209–240.
15. Tschoegl, N.W. (1997). Time Dependence in Material Properties, An Overview, Mechanics
of Time Dependent Materials, 1: 3–31.
16. Mcrum, N.G., Buckley, C.P. and Bucknall, C.B. (1992). Principles of Polymer Engineering,
Chapter 6.4 (The Mechanics of Fiber Reinforcement). Published in the United States by
Oxford University Press, New York.
17. Pooler, D.J. (1999). The Temperature Dependent Non-linear Response of a Wood Plastic
Composite, MS Thesis, School of Mechanical and Materials Engineering, Washington
State University.
18. Elahi, M. and Weitsman, Y.J. (1999). On the Mechanical Response of a Random Chopped
Fiber Mat/Polymeric Resin Composites: Data and Model, Mechanics of Time Dependent
Material, 3: 219–244.
19. Elahi, M. and Weitsman, Y.J. (October 1999). On the Mechanical Response of P4 Chopped
Glass/Urethane Resin Composite: Data and Model, Oak Ridge National Laboratory,
ORNL-6955.
20. Crissman, J.M. (1986). Creep and Recovery Behavior of a Linear H igh Density
Polyethylene and an Ethylene-Hexene Copolymer in the Region of Small Uniaxial
Deformations, Polymer Engineering and Science, 26(15): 1050–1059.
21. Williams, M.L., Landel, R.F. and Ferry, J.D. (1955). The Temperature Dependence of
Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids,
Journal of the American Chemical Society, 77: 3701.
22. Penn, R.W. (1966). Dynamic Mechanical Properties of Crystalline, Linear Polyethylene,
Journal of Polymer Science: Part A-2, 4: 545–557.
23. Onogi, S., Sato, T., Asada, T. and Fukui, Y. (1970). Rheo-Optical Studies of High
Polymers, XVIII. Significance of the Vertical Shift in the Time Temperature Superposition
of RheoOptical and Viscoelastic Properties, Journal of Polymer Science: Part A-2,
8: 1211–1255.
24. Fukui, Y., Sato, T., Ushirokawa, M., Asada, T. and Onogi, S. (1970). Rheo-Optical Studies
of High Polymers. XVII. Time-Temperature Superpo sition o f Time-depe ndent
Birefringence for High-Density Polyethylene, Journal of Polymer Science: Part A-2,
8: 1195–1209.
25. Pramanick, A.K. and Sain, M. Nonlinear Visco-elastic Creep Characterization of HDPE-
Rice Husk Composites, Polymer & Polymer Composites (in press).
26. Gerhards, C.C. (2000). Bending Creep and Load Duration of Douglus-fir 2 by 4s under
Constant Load for up to 12 Plus Years, Wood and Fiber Science, 32(4): 489–501.
27. Popelar, C.F. (1990). Visco-elastic Characterization and Modeling for Polyethylene,
Polymer Engineering and Science, 30(10): 577–586.
28. Green, D.W., Winandy, J.E. and Kretschmann, D.E. (1999). Mechanical Properties of
Wood, Wood Handbook, pp. 4/1–4/45, Forest Products Society, Madison.
29. Tissaoui, J. (1996). Effects of Long-Term Creep on the Integrity of Modern Wood
Structures, PhD Thesis, Virginia Poly technic Institute and Stat e University, Civil
Engineering.
60 A. PRAMANICK AND M. SAIN
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... In four-points bending, the maximum tensile stress occurs at the mid-zone of the bottom area of the beam and compressive stress at the top. Also, in this zone, the deflection is maximum [8][9][10]. In the figure below, P is the applied load, L the span of beam and a = L/3 distance between the points of application of load and the support. ...
... Neglecting the viscoelasticy term in the constitutive law [11] we obtain In the above equations, g 1 , and g 2 are material properties as a function of stress. These parameters have a specific thermodynamic significance and the changes in g 1 and g 2 reflect third and higher order dependence on the Gibb's free energy on the applied stress [8], is the time-scale shift factor, which is a function of stress, temperature, and humidity in the case of the biomaterial. However, the tests where performed at constant laboratory conditions, so that is a function of the stress only. ...
... Firstly, we study the effect of the flexural span on the instantaneous deflexion for beams of 38 mm diameter subjected to a load of 225 N. In this case, for each beam, we chose the spans of respective values 360, 420, 480, 600 and 720 mm as represented on figure 4 [7][8][19][20]. One will take the average of the values of the deflexion obtained for the increasing and decreasing variations of the span. ...
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Length affects both the deflection and the viscoelastic behaviour of materials. The bending of raffia Vinifera is studied at an average room temperature of about 24 °C and a relative humidity of 70 %. The material is raffia Vinifera referred to as "raffia bamboo". A review of the existing laws on the deflection and creep of material is made. We did the bending tests on six samples. In the first stage, each test-sample was tested five times with increasing and decreasing values of the span of the beam loaded at 225 N. From the curves obtained, we deduced that, the relation between the deflection and the flexural span of the beam obeys a power function. In the second stage, we did the bending creep test on the same six samples, and each sample was tested at five different flexural spans. From the curves obtained, we deduced: the power function between the span of the beam and the creep rate; and we calculated the parameters of the rheological model of Schapery, used to represent the creep behaviour of the material. The power relation between the span of the beam and the creep rate on the one hand, and, moreover, the polynomial relation between the span and the nonlinear parameter of Schapery, permit us to confirm the nonlinearity of the effect of the span of the beam on the creep behaviour of raffia bamboo.
... However, due to the constituents, intrinsic viscoelastic properties of WPCs would become an important concern when being used as a load-bearing member, especially time-and temperature-dependent behaviors. In the past, many researches have discussed time-and temperature-dependent behaviors of WPCs, particularly about creep (Pooler and Smith 2004;Tajvidi et al. 2005;Pramanick and Sain 2006;Dastoorian et al. 2010;Chang et al. 2013Chang et al. , 2014Wang et al. 2015;Pulngern et al. 2016). Some of them attempted to adopt accelerated or short-term creep tests to construct master curves based on time-temperature superposition principle (TTSP) in order to obtain useful information within a reasonable period. ...
... A sequence of different rate loading segments was fitted to the Prony series and then integrated as an overall curve. Furthermore, the Prony series model application calls for numerical calculations and is materialspecific (Pramanick and Sain 2006). Moreover, obtaining these data fits can be difficult when the data were spread over a wide range of time (Chambers 1997). ...
... As to the temperature issue, in previous studies, the reduced time with the temperature shift factor and the theory of activation energy were employed to deal with the issue of varying temperatures (Findley et al. 1989;Pramanick and Sain 2006). Their methods may also be possible solutions for this issue. ...
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To investigate the effect of fluctuating temperatures on the creep strain of wood–plastic composites, a full-scale, long-term creep test was conducted in an unconditioned environment. However, the effect of elevating temperature caused unexpected additional increases in strain. In this study, the previously developed stress–temperature incorporated creep model and the proposed temperature-induced strain superposition method were employed in combination. The temperature-induced additional strain was successfully simulated, indicating that the creep test under an ambient environment could successfully simulate long-term creep with increasing temperatures. This approach and the concept can be applied to comparable future studies.
... Frequently, it is used to obtain the activation energy associated with the glass transition event. However, both WLF and Arrhenius equations are valid when there is a linear temperature shift in creep strain due to a change in the temperature [Pramanick and Sain 2006b]. ...
... Pooler and Smith [1999] suggested a modification of the Schapery modelthe Prony series, the general form of which is the same as the generalized Zener model, which fits the creep behaviour of wood particle-filled plastics wellusing 5 elements over the temperature range of 23°C to 65°C. The Prony series model application calls for numerical calculations and is very material specific [Pramanick and Sain 2006b]. ...
... An issue with temperature is its influence on stress, i.e. whether the combined stresstemperature effect is additive or interactive [Pramanick and Sain 2006b]. Individual moisture, temperature and stress related creep issues have been dealt with in the field of thermosetting based composites [Woo 1994]. ...
... Thus, time is accelerated by elevating temperature [14]. Farrag [11], Thornton et al. [42], Zornberg et al. [47], Hsuan et al. [17], Elleuch and TakTak [9], Pramanick and Sain [38], and Chen et al. [8] studied the creep behavior of HDPE by elevating temperature and employing an Arrhenius model to extrapolate the results to field temperature. Thermal acceleration methods are hampered by changes in the mechanical properties of polymers due to temperature. ...
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Remanufacturing has achieved viability in a diversity of industrial markets as a means to both maintain the value of products and minimize waste. From carpet tiling to manufacturing robots, a wide range of goods have presently established supply and consumer networks that support remanufacturing, and thus offer a point of entry into a more circular industrial economy. Based on this performance, it is reasonable to expect that remanufacturing can in some cases be made an iterative endeavor; that existing networks may be leveraged to create additional lifecycles for previously remanufactured goods at net environmental and economic gain over virgin production. This case study identifies and explores factors of Davies Office, Inc. (Davies) remanufacturing processes for office furniture that affect the economic and environmental practicality of creating multiple remanufacturing cycles. Specifically, we use Life Cycle Assessment (LCA) to estimate the impacts of multiple remanufacturing cycles and how these are affected by “adaptive remanufacturing,” a neologism to describe the use of an end-of-life (EOL) product core to create a similar, but non-identical product. LCA results suggest that adaptive remanufacturing is both an environmentally preferable and economically viable business strategy. Specifically, the ability to update, reconfigure, and customize previously obsolete products to meet present market demands enables lifecycle extension beyond what is achievable with traditional remanufacturing. In this, the study posits that such adaptive remanufacturing techniques not only expand the potential environmental benefits of remanufacturing, but enhances the long-term economic viability of remanufacturing in durable product markets.
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... However, the tensile specimen requires the use of loading tabs on the end of the specimen, which may cause debonding problems at elevated temperatures. In view of this, a few works (Ha and Springer,1989;Guedes, et al, 1999;Pramanick and Sain 2006) ...
... Thus, time is accelerated by elevating temperature [14]. Farrag [11], Thornton et al. [42], Zornberg et al. [47], Hsuan et al. [17], Elleuch and TakTak [9], Pramanick and Sain [38], and Chen et al. [8] studied the creep behavior of HDPE by elevating temperature and employing an Arrhenius model to extrapolate the results to field temperature. Thermal acceleration methods are hampered by changes in the mechanical properties of polymers due to temperature. ...
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The creep properties of wood-plastic composites limit their application, particularly in temperature variations affecting long-term performance. In this study, the effect of temperature was studied based on dynamic mechanical analysis spectra and isochrones and a newly developed stress-temperature incorporated creep equation. According to the dynamic mechanical analysis spectra, the addition of a higher content of wood flour resulted in higher moduli, indicating increased stiffness and lower mechanical loss factor. According to the isochrones, the creep strain of wood-plastic composites increased with elevated temperatures and stresses at the same time point. Moreover, the strain increased almost linearly with increasing stress at lower temperatures but became nonlinear with elevated temperature. With these findings, a stress-temperature incorporated creep equation was developed based on short-term creep tests. This empirical equation incorporates the effect of temperature in a power law equation. Good agreement was observed between the equation and experimental results.
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Rice husk based plastic composites are increasingly being used as deck-boards, railings and other load-bearing materials. Since this material typically contains 40% plastic, and plastics creep with respect to time when they carry load, creep is an important issue here. So the viscoelastic characterization of this material and the prediction of creep as a function time is of paramount importance for the material's long-term commercial success. Creep is a time related deformation but it can also be affected by the stress level and environmental conditions, such as time and temperature. In order to predict the creep of this composite, it is important to derive a relationship between deformation, time, temperature, relative humidity and stress. Nonlinearity can exist in the stress, temperature, and moisture related deformation. In this study, hollow extruded rice husk -HOPE beams were subjected to creep and recovery in flexural mode and the stress related nonlinear creep behaviour of the same was studied phenomenologically. Both linear and non-linear region constants were determined with modified models, and a predictive model was developed. These constants will be used to define, model and predict long-term creep deformation.
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This paper finalizes research on graded Douglas-fir 2 by 4 beams subjected to constant bending loads of various levels and durations. Compared to results for testing in a controlled environment, results confirm that load duration did not appear to be shortened by tests in an uncontrolled environ-ment, at least extending out to 12-plus years. By the same comparison, relative creep was considerably increased, however. The extended data also confirm that no evidence was found for a threshold below which stress levels for lumber can be maintained indefinitely. Based on the finalized prediction equations of this study and those of two previous studies, a factor of 2.0 for a 10-year load duration is more appropriate for Douglas-fir bending allowable properties than the 1.62 factor currently recommended. Also, bending deflections due to creep doubled sooner than commonly accepted. This research is important to structural engineers and code groups respon-sible for the safe design of wood structures when establishing new design criteria for load duration and deflection limits.
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Creep in the nonlinear zone of wood plastic composite can be described by a few material constants. The purpose of this study was to determine these creep related material constants for 60% wood flour reinforced extruded HDPE samples. Creep and recovery data in flexural bending mode were analyzed. Schapery's theory was used to simulate creep data. The creep related material constants varied according to the stress level. The experiment was short term and the values of these constants will be used to characterize, simulate, and model long-term creep under varying temperature and moisture in our ongoing project.
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A constitutive model consisting of a combination of the Schapery nonlinear viscoelastic heredity integral and a nonlinear viscoplastic functional employed by Zapas and Crissman is described. Material constants associated with the constitutive models are measured for graphite-bismaleimide (IM7/5260) composites at elevated temperatures and stress levels. These results are then combined with classical lamination theory, so as to predict the response of a multi-angle laminate to cyclic thermomechanical loadings. Predictions are favorably compared with measurements obtained during a 50-hr test involving ten 5-hr loading cycles.
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This report presents data on the creep response of a polymeric composite that is a candidate material for automotive applications. The above data were used to establish the basis for the mechanical characterization of the material's response over a wide range of stresses and temperatures, as well as under cyclic loading and due to exposure to distilled water. A constitutive model based upon fundamental principles of irreversible thermodynamics and continuum mechanics was employed to encompass the above mentioned database and to predict the response under more complex inputs. These latter tests verified the validity of the model.
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The results of creep and recovery experiments are reported for two types of polyethylene—one a linear high density homopolymer, and the other an ethylene-hexene copolymer. Data were obtained at temperatures in the range 23°C to 57°C and creep times of 10 s to 4.33 × 105 s. In order to approximate constant true stress conditions, all of the experiments were carried out at the same value of applied stress (4 MPa) and the change in strain during creep was in all cases less than 2 percent. Comparison of these results with the results from earlier work on an ultra high molecular weight polyethylene shows that there is a great similarity in the behavior of all three materials, and the behavior of all three can be described quite well by a one-dimensional equation consisting of two terms—one a hereditary term and the other a plasticity term. It is further shown that to a very good approximation the idea of time-temperature superposition can be applied to the description of the hereditary term.
To determine the true reason for the increase in birefringence and the decrease in relaxation modulus for high-density polyethylene with rising temperature, changes in crystalline structure as well as in thermal, viscoelastic, and rheo-optical properties with temperature were measured, by several techniques, including DSC, DLI, infrared dichroism, x-ray diffraction, and NMR. The values for degree of crystallinity obtained from the DSC fusion curve, density, and infrared absorbances coincide very well and show almost no divergence till about 80°C. The optical vertical shift factor pT can be related to the ratio of the orientation function for the crystal c axis at an arbitrary temperature to that at the references temperature, fε/fε0. The mechanical vertical shift factor bT, on the other hand, is associated with the temperature dependence of the mobile fraction, as determined by NMR measurements, but not with variations in degree of crystallinity.
Two sets of dynamic mechanical property data and some stress relaxation data for semicrystalline, linear polyethylene are treated by data reduction methods previously described. These data can be represented by a master plot of reduced modulus versus reduced frequency and two sets of temperature-dependent shift factors. The first of these factors reflects the change of viscoelastic relaxation times with temperature. The second represents a separable change of modulus with temperature which applies over the entire time or frequency range of the experiments. This change is larger and in the opposite direction to that found applicable in the behavior of noncrystalline plastics and rubbers. The two sets of dynamic data show the same frequency–temperature dependence which can be represented by an activation energy of 22 kcal./mole. Small differences in the modulus–temperature dependence are attributed to differences in molecular weight or annealing conditions. The stress relaxation data superposes to a curve in good agreement with the dynamic data but with a factor of 20 difference in time scale. This difference is attributed to the finite strains used in the stress relaxation measurements. Such strains might be expected to increase free volume in simple extension deformations and so accelerate the relaxation.