Viscoelastic Properties of Wood-Fiber
Reinforced Polyethylene: Stress Relaxation,
Creep and Threaded Joints
Syed Imran Farid
A thesis submitted in conforrnity with the requirernents for the
degree of Master of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
O Copyright by Syed Imran Farid ZOO0
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Viscoelastic Properties of Wood-Fiber Reinforced Polyethylene: Stress Relaxation, Creep and Threaded Joints
By: Syed Imran Farid
Master of Applied Science
Year 2000
Department of Mechanical and Industrial Engineering, University of Toronto
Abstract
Tensile stress relaxation and flexural creep experiments were performed to evaluate
the viscoelastic properties of WFRP. nie effect of time. temperature and loading conditions
were investigated. In stress relaxation experiments. the modulus rela~ed rapidly within a
short period of time and then a slow relaxation was observed. In creep experiments. at lower
stress and temperature. the strain increased rapidly within the short period of time and then
slow creep was observed. At higher stress and temperature. the specimen niptured a
rapid increase in strain to a maximum of 3% strain. W R P perfonned better than low-density
polyethylene but the long-term effects did not match those of wood. The Power Law was
f o n d to be appropriate to describe the viscoelastic behavior of the material but at the same
time it suggests that the modulus relaxes infinitely.
Wood screw and Plastite screw were found to be better than post molded inserts. The
pullout force was also found linearly dependent on the engagement len-gh. The pullout force
for WFRP was found comparable with spruce. The clamping force relaved rapidly within the
short period of time and then a slow relaxation was observed
Acknowledgement
Fint. 1 am thankful to God for giving me the ability to pursue my goals. I am
especially gratefùl to my supervisors. Professor J. K. Spelt. Professor M. T. Kortschot and
Professor J. J. Balatinecz. for their support. encouragement and guidance throughout this
work. Special thanks go to Professor C. E. Chaffey for his valuable advice. precious time and
guidance
The assistance and advice of Afsaneh Akhtarkhavari and Shaing Law were a great
help. I would like to thank al1 my fiiends and colleague. Saeed Douroudiani. Wei Ding. Steve
Hu. Sanjiv Sinha. Baohua Shen and Ryo Okada for their interesting and inspiring
conversation and discussion.
1 am also grateful to the Manufacturing and Materials Ontario and Royal EcoProducts
for their financial support
Last but not least. many thanks to my parents. brother and sisters for t k i r continuous
moral support. patience and understanding.
Table of Contents
. . ................................................................................................................... Acknowledgement 11 ...
Table of Contents ................................................................................................................... rit
List of Figures .......................................................................................................................... v
List of Tables .......................................................................................................................... Lx Nomenclature .......................................................................................................................... x
....... 1 Introduction ................................................................. 1-1
2 Literature review .......................................................................................................... 2-1 3 . ? 2.1 Wood Fiber Reinforced Composites .......................................................................... - - 3-3 2.2 Viscoelasticity .............................................................................................................
.................................................................................................... 2.3 Threaded Joints 3 - 11
............................................................................................................... 3.1 Introduction 3-1
........................................................................................................ 3.2 Stress Relaxation 3-2 4 4 .......................................................................................................................... 3 3 Creep J -J
3.4 Time-Temperature Superposition .............................................................................. 3 4
4 Experimental ................... ...................................................................................... 4-1
...................................................................................................................... 4.1 Material 4-2
4.2 S pecimen Preparation ................................................................................................ 4-3
4.2.1 Kinetic Mixing .............................................................................................. 4-3
4.2.3 Compression molding ........................................................................................ 4-3
.................................................................................................... 4.3 Mechanical Testing 4 4
4.3.1 Tende testing ................................................................................................... 4 4
................................................................................................... 4.3.1 Flexural testing 4 6
4.4 Tensile stress relaxation ............................................................................................. 4-9
......................................................................................... 4.4.1 Specimen preparation 1-9
............................................................................................ 4.4.2 Experimental setup 4 -9
4.5 Creep ...................................................................................................................... 4-10
4.5.1 Specimen preparation .................................................................................... 4-10
............................................................................................. 4.6 Fastener performance 4 - 1 2
4.6.1 Specimen preparation .................................................................................... 4 - 1 2
.................................................... 4.6.2 Quasi-static pullout and engagement length 4-1 3
........................................................................................... 4.6.3 Experimentai setup 1- 13
4.6.4 Stripping force and torque ............................................................................... 4-1 5
4.6.5 Backout Torque ................................................................................................ 4- 19
4.7 Clamping force relaxation ........................................................................................ 4- 19
.......................................................................................... 4.7.1 Experimental Setup 1- 19
5 Results ................... ............................................ ...... ................................................. 5-1
................................................................................................................ 5.1 Introduction 5-1
............................................................................................... 5.2 Mechanical Properties 5 - 2
5.3 T'ensile stress relaxation .......................................................................................... 5 -4
5.1 Creep .......................................................................................................................... 5-8 - - .............................................................................................. 3.3 Fastener Performance 5 - 1 1
5 -6 Fastener backout torque ........................................................................................... 5- 17
5.7 Fastener clarnping force relaxation .......................................................................... 5- 18
5.8 Fastener re-tightening ....................................................................................... 5 - 2 5
6 iModel and Discussion .................................................................................................. 6-1
................................................................................................................ 6.1 Introduction 6-1
6.2 Tensile Stress Relaxation ........................................................................................... 6-3
6.3 Flexural Creep ............................................................................................................ 6-8
6.4 Screw Clamping Force ............................................................................................. 6- 14 - . ......................................................................................................... 6.3 Time Exponent 6- 18
6.6 Specific Modulusl Cornpliance1 Force ..................................................................... 6-10
6.7 Time-Temperature Superposition ......................................................................... 6 - 2 2
7 Conclusion ................... ................................................. 7- 1
.......................................................................................................... 8 Recommendation 8-1
Reference
Appendix A
Appendix B
Appendix C
Appendix D
List of Figures
Figure 1 - 1. Typical stress-time and strain-time curves for time-dependent mechanicd properties (a) creep and (b) stress relaxation.
Figure 1-2. Schematic of torque and clamping forcr as a function of time at constant driving speed
Figure 4-1. Specirnen configuration for tensile and stress relavation experiments (a) LDPE. (b) WFRP (al1 dimensions in mm)
Figure 4-2. Experimental arrangement for tensile and stress relaxation experiments (al1 dimensions in mm).
Figure 4-3. Specimen configuration for flexural and creep expenments (a) LDPE and (b) WFRP (al1 dimensions in mm)
Figure 44 . Experimental arrangement for three-point flexural espenment.
Figure 4-5. Experiinentai arrangement for tlexural creep esperiments.
F i ç w 4-6. Typical specirnen ~ o ~ g u r a t i o n for fastener performance testing (al1 dimension in mm).
Figure 4-7. Experimental arrangement for fastener pullout (a) for inserts. (b) for scrrw.
Figure 4-8. Specimen configuration for effect of engagement length on fastener pullout force (a11 dimensions are in mm).
Figure 4-9. Load ce11 for measuring clamping forcr of screw
Figure 4-10. Experimental arrangement for torque and pullout measurements (a) for simultaneous measurement of driving torque and stripping force (b) for the measurement of dnving torque only
Figure 4-1 1. Typical arrangement for clarnping force relaxation experirnents
Figure 5-1 Stress i s t r a h curve in simple tension at different strain rates for 50% WFRP
Figure 5-2. Tensile modulus as a hnction of time at different temperatures and 0.5% strain
Figure 5-3. In-ln plot of tensile modulus as a function of time at difierent temperatures and 0.5% strain
Figure 54. In-In plot of tensile modulus as a fûnction of time at 33C temperature and 0.5% main for pure LDPE and 50% WFRP.
Figure 5-5.
Figure 5-6.
Figure 5-7.
Figure 5-8.
Figure 5-9.
Figure 5-10.
Figure 5- 1 1.
Figure 5- 12.
Figure 5-13,
Figure 5- 14.
Figure 5-15.
Figure 5- 1 6.
Figure 5- 17.
Figure 5-18.
Figure 5- 19.
Figure 5-20.
Figure 5-2 1.
Figure 5-22.
Percentage drop in modulus as a function of time with reference to initial modulus at different temperature and strain
Flexurai strain as a function of time at different temperature and 25% UFS stress
Flexurai Strain as a function of time at different temperature and 10% UFS stress
Flexural strain as a function of time at various stresses and 23' C temperature
Double log plot of stain and time at different condition of stress and temperature
Driving torque and clamping force for the wood screw as a function of time (100 rpm)
Driving torque for various fasteners as a tùnction of timr (n=100 rpm)
Static pullout and specific pullout force for various fasteners and inserts in WFRP and spruce wood
Static pullout force as a function of thread engagement length
Plastite and wood screw after pullout from WTRP in screw pullout experiment.
Backout torque as a hnction of time at room temperature.
Clamping force as a function of time for wood screw in WFRP at different initial clamping force (Fpo = Pullout Force) at 23 'C temperature
Clamping force as a function of time for wood screw in WFRP at different initial clarnping force (Fpo = Pullout Force) at JO "C temperature
Clamping force as a function of timr for wood screw in W R P at different initial clarnping force (F', = Pullout Force) at 60 O C temperature
Clarnping force as a function of time for the wood screw in WFW at different temperatures and 17% of pullout force
Clamping force as a fimction of time for the wood screw in WFRP at different temperatures and 53% of pullout force
In-ln plot of clamping force as a funcion of time at differemt initial clamping force and temperame
Clamping force relaxation for WFRP and Spruce at 23 O C and 33% of Pullout Force
vii
Fikg.ue 5-23.
Figure 5-24.
Figure 5-25.
Figure 6- 1.
Figure 6-2.
Figure 6-3.
Figure 6-11.
Figure 6-5.
Figure 6-6.
Figure 6-7.
Figure 6-8.
Figure 6-9.
Figure 6- 10.
Figure 6- 1 1.
Clarnping force as a function of t h e after re-tightening the screw to the initial clamping force after 3600 s at 23 "C.
Clamping force as a function of time after re-tightening the screw to the initial clamping force after 7200 s at 23 OC.
In-ln piot of clamping force as a fùnction of time afier re tighten the screw to the initial clamping force after 3600 s at 23C temperature
Expimental and calculated tende modulus at 23'C temperature and two strains
In-In graph of experimental and calculated tensile modulus at 0.5% strain
Corn parison of three di fferent models at O. 5% strain and various temperatures (PL=Power Law. FL=Findleyts Law. KWW=Kohlrausch-William-Watts model)
Confidence limits of time exponent (n) at 95% CI . constant specific Modulus (Es) and 0.5% strain.
Esperimental and calculated values of flexural compliance at 25% UFS
Experimental and calculated values of flexural compliance at 25% LFS at 3 temperatures
Esperimental and calculated values of flesural compliance at 23°C temperature and three stress
Confidence limits of time exponent (n) at 95% CI . constant spccific compliance (I,) and 25% UFS
Long-term flexural creep expenments at 20% ultimate flesural stress (C'FS)
Expenmental and calculated values of clamping force at 23C temperature and three initial clamping force as a percentage of pullout force
In-ln graph of experimental and calculated values of clarnping force at 23C temperature and three initial clarnping force
Figure 6-1I.Confidence limits of time exponent (n) at 95% CI . constant specific clarnping force (F,) and 23C ternperature
Figure 6- 13. Time exponent for stress relaxation at different initial strain
Figure 6-14. Time exponent fkom creep expenments at three initiai stress
Figure 6- 15. Time exponent fiom clamping force esperiments at three initial clamping force
viii
Figure 6-16. Specific modulus from Stress relaxation experiments
Figure 6-1 7. Specific Cornpliance from creep experiments at three initial stress
Figure 6-1 8. Specific clamping force fIom clamping relaxation expenments at three initial clamping force
Figure 6-1 9. Time temperature superposition at 0.5% Strain
Figure 6-20. Time temperature superposition at 1 .O% strain and three temperature
Figure 6-2 1 . Time-temperature superposition using vertical and horizontai shifi
Figure 6-22. Time dependent factor as a h c t i o n of temperature at two strains
List of Tables
Table 5- 1 :
Table 5-2.
Table 6- 1.
Table 6-2.
Table 6-3.
TabIe 6-4.
Table 6-5.
Table 6-6.
Table 6-7.
Mechanical Properties of LDPE and 50% WFRP at 23 C (number of specimens = 6. standard deviation is shown as upper and lower values)
Pullout force and charactenstic torque for different fasteners
Power law model fitting results at different conditions of strain and temperature (ts = 1 sec)
Estimation of power law fittinç parameters at 95% CI
Power Law model for flewral creep cornpliance
Estimation of power law fitting parameters at 95% CI
Power law model for screw clamping force.
Variation estimation of power law fitting parameten at 95% CI
Enthalpp and time-dependent constant from Arrhenius equation.
A. B = Material constants
a< = Arhennius (horizontal) shift factor
b, = Vertical shift facor
d = Deflection in specimen
D = Tensile compliance
D, = Depth of specimen
E = Tensile modulus (MPa)
E(t) = Time-dependent tensile modulus
E, = Modulus at time t=O
Es = Specific Tensile modulus
F = Force (N)
F(t) = time dependent ciamping force
Fc = Screw clarnping force
F, = Screw pullout load
G = Flexural modulus
G(t) = Tirne-dependent flexural modulus
J = Flexural cornpliance
J(t) = Tirne-dependent tlexural compliance
Js = Specific flexural compliance
k = Material constant for Andrade Equation
2 = length of specimen
2, = initial len+d of specimens
m = mass in kg
n = time exponent
R = gas constant
s = span of the test
T = Temperature
t = time
Tb = Backout torque
Td = Driving torque
Tf = Forming Torque
T, = Reference temperature
4 = Specific time ( 4 s )
Ts = Stripping torque
v = specific volume
V = Volume
w = width of specimen
< = reduced time
E = Strain in specimen
~ ( t ) = time-dependent strain
E+ = specific strain
E' = Strain in specimen at time=O
o = Tensile stress
~ ( t ) = Time-dependent tensile mess
os = Specific tensile stress
p = Viscoelastic constant for Andrade Equation
AH = Activation enthalpy
Introduction
Reinforcing materials are widely used to improve the mechanical properties of
thermoplastics. Wood fiber reinforced thennoplastic composites have attracted a great deal of
interest in recent years because wood fibers (WF) have numerous advantages over
conventional fibers. The low cost. wide availability and low density of WF can lower the
overall cost of a composite and increase production volumes. Wood fibers are less abrasive
than other minerai tillers. which increase the life of the mold. In addition. wood fiber
reinforced composites are easy to process by most of the conventional methods. In recent
yrars. a steady increase in production of polyolefins and wood products and increasing
pressure from government and environmental protection agencies have also dnvrn the
industp to recycle these materials in a cost effective and environmentally friendly process.
Generally. the addition of wood fiben does not have an. signiticant rffect on the
strength of a composite. but the modulus increases marginally [ I l . However. the impact
strength typically decreases as the wood fiber concentration increases. Surface
incompatibility between hydrophilic w o d tiber and hydrophobie thermoplastics is
responsible for poor interfacial adhesion between fibers and matrix and poor dispersion of
wood fiben in the matrix. This increases the probability of an early failure during impact [2].
Processing rnethods. wood fiber (W) concentration. fiber aspect ratio. and wood species
also effect the overall mechanical properties of the composites 13.41.
Short-tenn mechanical properties (strength and modulus) c m be used for the
selection of matenal for a particular application. but are not mou& to detemine the
effective life cycle of any product. Thermoplastic composites exhibit time-
dependent mechanical properties. and changes in strain and 1 or stress have been observed
even after decades [S. 4. A good understanding of shon and long-term viscoeIastic
properties is necessary to design for adequate long-term performance. Material composition,
temperature. stress-strain condition. environment. processing and loading history are some of
the factors that affect the viscoelastic properties of the composite. Most of the research on
wood-fiber reinforced polyethplene (WFRP) conducted in the past has focussed on the eKect
of various processing parameten and matrix and filler material on the short-term mechanical
properties of the composite. Few experimental results are available on the long-rem
variation of mechanical properties of WFRP.
For the characterization of long-term behavior of polymer composites. two kinds of
expenments are usually conducted: creep. and stress relaxation. In a creep rsprrimrnt. a
constant stress (or force) is maintained. and the strain is rneasured as a Function of time. The
results are expressed as a time-dependent cornpliance (strainistress). D(t) in tensile and J(t) in
flexurai loading conditions. Typical stress-time and strain-tirne curves for creep esperiments
are s h o m in Figure 1-l(a). In a stress relaxation experiment. the strain is applied and
maintained constant. and the stress required to maintain the strain is measured as a h c t i o n
of time. The results are expressed as a time-dependent modulus E(t) in tensile and G(t) in
flexural loading conditions. The stress-time and strain-time curves for a typical stress
relaxation expenments are s h o w in Figure 1 - 1 (b).
Time
Time
( a )
Time
Figure 1 - 1. Typical stress-time and strain-time curves for time-dependent mechanical
properties (a) creep and (b) stress relaxation.
Most polymeric materials exhibit linear or nearly lincar viscorlastic behavior for
srnall deformations or stresses. The theop of linear viscoelasticity yields a simple
mathematical representation for stress-stnin-time relations. Conventionally. the linear
viscoelastic properties are modrled usinç different combinations of spnng and dashpot
elements. The spring represents the prrfectly elastic behavior whilr the dashpot represents
perfectly viscous behavior. The strain or stress where the behavior can be approximated as
linear. however. is often small cornpared with the total strain or stress bcfore yielding or
fracture. Furthemore. at higher temperatures polymers becorne mcre ductile. and non-
linearity can be observed even at very low strains (less than 0.2%). Thcrefore. linear
viscoelastic theory ofien does not yield a generalized solution for a wide range of time.
Introduction id
Ioading conditions and temperatures. In recent years, two different approaches
have been widely used to address non-linear viscoelasticity. The first approach use
continuum mechanics to derive constitutive equations for non-linear viscoelasticity [7, 81,
while the second uses the thermodynarnics theory for irreversible processes [9] .
Time-temperature superposition (TTS) is widely used to describe the long-term
viscoelastic behavior on the b a i s of short-term experiments. Time-temperature superposition
is based on the assumption that the effect of temperature on the time dependent brhavior of a
material is equivalent to a stretching or shrinking of the real time for temperatures above or
beiow a rrference temperature [IO]. This technique was originally developed for pure
polymers but later expanded for use with fiber-reinforced composites.
Mechanical fasteners provide a fast and effective mrthod for joining wood-fiber-
reinforced composites. Varieties of fasteners are available for the assembly or joining of
composites. Many of the fasteners were originally developed to join metal or wood and have
simply been adopted for use with polymer composites. while others have been developed
specifically for polymeric materials. Self-threading screws. used in applications where
lirnited reassembly is required. can be categonzed into two broad types: thread cutting and
thread forminp. Thread cutting screws cut or tap mating threads as the. are dnven into the
composites. while thread-forming screws displace material as they are driven.
The overall performance of threaded joints c m be affected by many factors:
including: thread geometry, thread root-tip diameter ratio. pilot hole diameter. driving speed.
Introduction 1-5
driving torque. direction and magnitude of applied Ioading. temperature and
environment. Thread cutting or forming causes localized regions of high stress. which often
results in the early failure of the joints. Thread geometry is also very important in composites
as the material flows inside the gaps created during thread installation. If the threads are too
close. over a long period of time cracks are created at notch sensitive areas at the tip of
threads and failure can occur due to crack propagation between threads [II]. Some of the
performance criteria for screwed joints are illustrated in Figure 1-2 and discussed below.
Screw pullout force (Fpo): The tende force required to pull the screw from the
composite.
Driving torque (Td): The torque required to tum or drive die screw into the predrillrd
pilot hole. It is the torque required to overcome the frictional resistance due ro thread cutting
or forming.
Stripping torque (T,): The torque required to cause failure of the joint either by composite
cracking. thread stripping or screw shearing.
Strip-to-drive torque ntio: The ntio of the stripping torque to the driving torque. A
higher ratio is desirable to effectively control the clamping force and to avoid joint failure
during tightening.
Screw clamping force relaxation: The relavation of clamping force over a period of time.
Vibration resistance: The resistance of a joint to variable and vibratory loading. The
fatigue life of a joint may be important as many joints are not loaded under static conditions.
Introduction
- - A - - - - 120 - Torque
- Clamphg force -- 100
-- 80
-- 60
Driving torque (Td) lm ;
1 1.5
T h e (s)
Figure 1-2. Schematic of torque and clarnping force as a function of time
driving speed (values are for illustration purpose only)
at constant
Unfortunateiy. most of these performance parameters are coupled. Screw pullout
resistance and strip-to-drive torque ratios are highly dependent upon variables such as screw
type. size. surface finish. drive speed. pilot hole diarneter and engagement len-@. Torque
charactenstics are also highly dependent upon the coefficient of fiction benveen the metal
screw and the plastic material which is in tum. dependent upon the surface temperature.
normal stress and surface quality of the fastener. Due to cornplex relation between physical
parameters. it very difficult to predict fastener performance on the b a i s of available data. and
a series of tests are needed for every combination of fastener and composite.
Introduction I- 7
Objectives
The objective of die present research was two fold: 1) To determine the viscoelastic
properties of wood fiber reinforced polyethylene and present an appropriaie model to predict
the viscoelastic behavior of WFRP and. 2) To e v a l ~ t e diflerent threaded fasteners and
extend the theory of viscoelasticity to determine the effect of these parameters on the
relaxation of the clamping force in a joint.
Emphasis was placed on the most critical conditions for viscoelastic behavior and
experiments were done at room and higher temperatures. .Appropriate loading conditions
were also chosen to cover the practical range for desired applications. Non-linear viscoelastic
theory was used to model the behavior of the material? to reduce the deficiencies of linear
models and to increase the reliability of long-term predictions. Both creep and stress
relaxation experiments were carried out. Only one wood fiber concentration and polymer
matrix were used in al1 the experiments to reduce the time required to conduct the
experiments.
Static pullout force and the effects of different driving parameters were also
investigated for threaded joints. Four different threaded fasteners were investigated and
commercial grade spruce was used as a baseline. Relaxation in clamping force was also
studied for various temperatures and loading conditions.
Literature Review 2-1
Literature review
Thermoplastic composites reinforced with natural fibers are becomingly increasingly
important non-load bearing materials. Wood fiber reinforced thennopiastic composites are
used for various applications as deck surfaces. uindow and door components. tùmiture and
automotive components. As these materials become more common. an improved
understanding of the physical. mechanical and chernical properties is necessary to utilize the
full potential of these materials. Many of the applications are designed for extended prriods
of time during which components are subjected to various combinations of mechanical and
environmental loads. Polymer based composites are viscoelastic. making time dependent
behavior one of the most important factors for use in analysis and design. Joining and
fastenine of composites is also an important factor in design. Thrradrd joints provide a t'aster
and easier way to join the composites. Understanding the basic mechanism of threaded joints
and long trrm performance is necrssary for optimum design.
Unfortunatel-. most of the research related to wood-fibçr reinforced composites was
done to understand the structure-process-properties relationship. Very few resrarchers have
investigated the Long-term mechanical properties of wood-fibrr reinforced polyethylene
(WFRP). This literature review is divided into three main sections: Wood fiber reinforced
composites. viscoelasticity and threaded joints performance.
Wood Fiber Reinforced Composites
In 1992 approximately 5.1 million tons of low density and Iinear low-density
polyethylene (LILLDPE) was produced in United States [I t] , while the world market
estimate was about 25.3 million tons [I3]. An annual grow-th rate to 7005 is estimated to be
2.7%/year [12]. In 1992. wood consumption as timber. and related products in various
markets. was approximately 572 million tons (air dry weight) [14. In the united States. wood
and wood fiber represent the largest material component of municipal solid waste. arnounting
to more than half of the total amount of 178 million tons per year in 1997 [ l q . Depletinç
resources. increasing demands for wood and polymer related products and increasing
economic and environmental pressure has attracted a great deal of interest in recycling these
materials.
In addition to the economical and environmentai benefits. wood fiber also offers
various benefits over conventional filler materîals. ïhey are low cost and low-drnsity fillers
available in abundant quantity. After comparing the rhcoiogical properties of polymer melt
containing cellulose fiber. g l a s and aramid fibers. Czarnecki and White [16] observed that
cellulosic fiben showed the least damage during - processinç. When wood fiber is mised with
polyethylene. it increases the stiffness of the composite. but tends to reduce the strength and
toughness [ l . 171. Man); researchers have investigated the effects of particle s ix . wood
species and fiber concentration on the overall mechanical performance of WTRP [3]. Various
methods have been used to evaluate and increase the adhesion between wood fiber and
polyethylene. Different coupling agents proved to be effective in increasing the adhesion and
consequently the mechanical properties of the composites [M. 191.
Wood waste from various sources can be harnmer-milied to low aspect ratio fibers.
Compounding wood fiber or flour with a polymer is a challenging task. Wood fibers are light
and tend to bundle and bridge. making continuous metering with even distribution very
dii3cult. Two methods are generally used to process WFW. In the first the wood fibers and
polymer are mixed. melted and pelletized using buss kneaders or similar machines [JO]. The
pellets can then be used in injection molding or extrusion. In the second method. a kinetic
mixer is used to mix the polymer and matrix and the molten material can be compression
rnolded instantly. or pelletized for injection moldinç or extrusion. Moisture content in wood
is also an important factor in reducing the adhesion between the polymer and the wood-
fibers. Mixing and processing of composites in both ways reduces the moisture content of the
fibers.
The nest section will discuss the viscoelastic properties of composites with an
introduction of the basic theory of viscoelasticity and the genrral form of models and data
reduction methods to predict long-term properties using relatively short-term experirnents.
Viscoelasticity
With recent advances in materials science and polymer engineering and the estensive
industriai demands for polymer based composires. the subject of viscoelasticity has
progresscd rapidl y.
The classical theory of elasticity deals with mechanical properties of perfectly elastic
solids. According to Hooke's Law the stress is always directly proporticnal to strain but
Lirerature Review 2-4
independent of the rate of strain. On the other hand. the classical theory of fluid dçmamics
deals with the properties of perfectly viscous fluids. According to Newton's Law. the stress is
always directlp proportional to the rate of strain but independent of strain itself. When a
Newtonian Buid is subjected to a sinusoidally oscillating load. the deformation is found to be
90' out of phase with the load.
The classical theories of linear elasticity and Newtonian tluid rnechanics do not
adequately describe the response of real materials over a wide range of loading. There are
two important types of deviations [21]. First. the strain (in solid) or the rate of strain (in fluid)
may not be directiy proportional to the stress. but may depend on stress in a more
complicated manncr. Such stress anomalies are familiar when elastic limits are exceeded in
solids. Second. the stress may depend on both the strain and the rate of strain together. as
well as higher time derivatives of the strain. Such time anomalies evidently reflect a behavior
that combines 1 iquid and sol id li ke c haracteristics. and are there fore called iiscoeiasiic. In
general. when a viscoelastic materid is subjected to a constant stress. it does not hold a
constant defonnation. but continues to tlotv with time.
Both stress and time anomalies may of course coexist. If only the latter is present. we
have linear viscoelastic behavior and the change in strain is a Function of time only and not of
the stress rna~gitude. When both anomalies esists. we have non-lincar viscoelastic behavior
Vicat was the first to systematically nudy viscoelasticity in metais in 1834 [22]. The
experimental aspects of the creep of metals have been treated in many publications.
beginning with Norton [23] and Tapsell [24. .hirade [25l u;is the first researcher who
made a systematic investigation of the creep of lead wires under constant load and proposed
that
where 1, and 1 are the initial and current length of a specimen. respectively. t is the
time under load and P and k are material constants which depend on stress.
As compared to metals. where the viscoelasticity can be observed at high
temperature. polymers and polymer-based composites are viscoelastic at al1 temperatures
[2q. These materials are highly time and temperature dependent and hence. in considering
the strains and stress induced in service. it is always required to consider the time for which
loads are applied and the corresponding oprrating temperature.
Polymers consists of long lengths of molecular chains undergoing thermal motion
[26]. #en the polymer is subjected to externa1 stress. two types of chain moïement are
normally obsewed: first. the elastic response against the applied force. and second. the time-
drpendent tlow of polymer chains. Below the g l a s transition temperature the polymer chains
are largely immobilized due to lack of thermal enrrgy. it is in the transition zone between
glass-like and rubber-like consistency that the dependence of viscoelastic functions on
temperature is significant [ J I ] .
To understand viscoelastic behavior it is necessary to understand the relation m o n g
stress. strain and time for a particular type of deformation and Ioading. Various experimental
techniques have been developed to study different patterns in both static and dynamic
loading. No single erperiment can describe the behavior of composites completely, and most
loading conditions are a combination of the experiments described below.
In creep. the stress is suddenly applied and maintained constant. and the strain is
measured as a hnction of time. The result is expressed as a tirne-dependent compliance. In
stress relaxation. the sarnple is subjected to a constant strain and the stress required to
maintain the strain is measured as a function of time. The result is expressed as a time
dependent modulus.
In deformation with constant rate of strain. the strain is increased linearly ~vit l i time
and the stress is rneasured as a function of time. In case of linear viscoelasticity the results
can be converted to relaxation modulus. but if the behavior is non-linear. analysis of the data
is very difficult. In deformation with constant rate of stress loading. the stress is increased
linearly with time and the strain is measurrd as a function of tirne. In the case of linear
viscoelasticity. the results c m be converted to a creep compliance.
In dyamic or cyclic loading. the stress is varied periodically. usually with a
sinusoidal fom. If the viscoelastic behavior is lineu. the strain wiIl also alternate
sinusoidally but will be out of phase with the stress. Wlen the stress is decomposed into two
vector components and divided by the suain. the modulus will then be separated into two
components: red and imaginas..
Though al1 these esperiments are important. due to the scope of the present research
only creep and stress relaxation experiments are discussed in detail below.
L iterature Revie w 2- 7
Creep
Creep is the slow continuous deformation of a material under constant stress. The
creep snain as r function of time can be descnbed in terms of three different stages [27l. ïhe
first stage. in which creep occm at a decreasing rate. is called primmy creep: the secondary
creep proceeds at a nearly constant rate: and the third or rerriary creep occurs at an
increasing rate and terminates in rupture.
The creep curves for many polymer composites are similar to those for metals:
however. they usually do not eshibit a pronounced secondary stage. Leaderman [A was the
first who proposed the viscoelastic response of Bakelite under constant torque as descnbed
beio w
where E'. A and B are fûnctions of stress. temperature and material
A number of investigators have also represented creep by using suitable combinations
of a spring which obeys Hooke's Law and a dashpot which obeys Newton's Law. The mon
common models are the Zener and Mamvell models. To simulate the real materiai behavior
these models may require an infinite numbrr of spring and dash-pot combinations. but in
most of the Iinear viscoelastic range when the stress is small the model can be approximated
by a smaller number of combinations.
The power law model developed by Findley [28] has become one of the most widely
used ana1ytica.i models for describing the ~bcoelastic behavior of fiber reinforced polyrner
composites under constant stress. Many different researchers [29. JO. 311 have used this
Lirerature Review 2-8
mode1 to characterize and predict the time-dependent behavior of fiber-reinforced polymer
composites. The model has been recommended by the Amencan Society of Civil Ençineers
(ASCE) structural Plastic Design Manual [32] for the use and analysis of fiber reinforced
polymer composites (FRPC) sections with regards to long-term behavior.
Read et al. [33] investigated the effect of fiber orientation on the viscoelastic behavior
of the composites and f o n d that a substantial anisotropy rxists in oriented injection molded
specimens. The Power Law model was used to predict the long-tenn behavior of glass-fiber
reinforced polypropylene composites. and çood agreement was found between rxperimcntal
and predicted values. Findley [5. 6] investigated the effect of time on long-term creep using
short-term data. Rrsults of tensile creep çxperiments of 16 years (230.000 h) duration on
polyvinyl chlotide (PVC) and polyethylene show that long term behavior cm be well
predictrd from short term (1 900h) data using the Power Law.
The creep behavior in randomly oriented tiber reinforced composites is largely
controlled by matris behavior as opposed ro unidirectionally oriented composites where
fibers control the viscorlastic behavior in the fiber direction. Weidmann and Ogorkiewicz
[34 tested a filament wound unidirectional glass/epoq- composite at fiber angles of O". 45"
and 90'. These tests showed that the creep behavior for 45" and 90' loading was nearly
identical and very similar to the creep of the rnatrir. On the other hand. for randomly oriented
short-fiber reinforced composites Silverman [3q and Mallick 134 showed that matrîx creep
and the nature of stress m s f e r between the fibers andthe matnx largely controlled the creep
behavior.
Temperature, moisture. degree of crystallinity. molecula. weight of polymeric
material. fiber concentration and the adhesion between fiber and matrix are some of the
factors that affect the creep behavior of unreinforced and reinforced composites. The failure
of creep specimens at clevated temperatures occurs in a time-dependent marner. and time to
failure is accelerated dong with viscoelastic behavior at high temperatures [37l. Moisture
also has negative effect on the long-term creep of FRPC with the composites tending to creep
more at higher moisture contents [38]. Increasing molecular weight and crystallinity make
composite more rigid and less creep is generally observed [39]. Increasing the fiber
concentration and the adhesion between fiber and matrix was found to increase crerp
resistance [#O]. Emri [41]. and Read et al. [42] studied the effects of pressure and physical
aging. respectively. on long-term creep and found that increasing pressure and physical age
of the material tends to retard creep.
Stress Relaxation
Viscoelastic materials subjected to a constant strain will relax and as a result the
stress decreases gradually. Creep experiments are simple to perform. because it is easy to
maintain a constant load. Stress relaxation experiments in cornparison are more difficult to do
without expensive experimental setups. However. matenals are often subjected to a constant
smin as opposed to constant stress such as threaded joints. Understanding the stress
relaxation behavior of wood-fiber reinforced composites along with creep beha~ior is
important to understanding the broad range of viscoelasticity.
Literature Revie w 2-1 0
Find1ey.s Power Law model has also been used by many researches to model short
and long-terni stress relaxation behavior. and \vas found to be in good agreement with
experimental data [43].
Stress relaxation behavior of short pineapple-fiber reinforced polyethylene
composites \vas investigated by George et. al. [ 44 . The addition of natural fiber had a
decreased stress relaxation. Fiber-matrix interface bonding has a great effect on the overall
behavior. Several surface modification techniques increase the interfacial adhesion and hence
decrease the relavation of stress [451. Surpnsingly. stress relaxation increases with an
increase in fiber length. This c m be evplained in ternis of insufficient stress transfer due to
fiber bending and curling as well as higher fiber-to-fiber interaction [451. It is also very
important to determine the optimal fiber length where the low relaxation modulus may be
observed becausr of insufficient stress transfer as well as pullout of fiber from the matrk by
the application of strain [46]. Fiber orientation and strain level also affect the stress
relaxation behavior. The effect of environmental and chemical factors on stress relaxation in
polyester-fiberglass composite was investigated by Gutman et. al. 1471. Cenain chemical
environrnents deteriorate the polymer composite structure and an increase in relaxation \vas
observed when the specimens were exposed to acidic and basic environments. Mechanical
and viscoelastic properties decreased afier exposure to watrr. depending on time of water
immersion. fiber loading and fiber surface modification [48].
The determination of the long-term performance on the fiber-reinforced polymers has
ofien been hindered by the expensive and time-consuming experimentation necessary to
obtain reliable results. Therefore. much effort has been expended in the pursuit of accelerated
procedures for the viscoelastic characterization of composite systems. One of the most
widely used technique. time-tempreature superposition (TTS). was developed in mid 1950s
and takes advantage of the relationship between temperature and viscoelastic behavior in
fiber-reinforced composites [21. 491. nie technique was further expanded by Yeow et al.
[SOI for use with fiber reinforced composites systems. It is based on the assumption that the
effects of temperature a d o r strain on the time-dependent behavior of a material are
equivalent to a stretching or shrinking of the real time for temperature a d o r strain above or
below the reference temperature and/or strain. Thus. when plotted on graphs where the
abscissa is defined as log-tirne. the individual relaxation curves obtained at elevated
temperatures a d o r svain c m be shifted to the lefi to obtain a continuous master curve
which spans a much longer time period. For superposition of various stress level vertical
shifts can be used in conjunction with horizontal shift to achieve a master curve for both time
and stress superposition. Therefore. a procedure c m br developed wliere series of short-term
stress relaxation tests are performed at elevated temperature and/or strain leading to the
eeneration of a family of c w e s for a given type of composite system. This technique was C
used successfÙlly to predict the long-term stress relauation behavior of polymer composites
using horizontal and vertical shifi in the curves [SI. 521.
Threaded Joints
Varieties of mechanical fastenen are available for the assembly of plastic products.
Many of these fasteners were originally developed to join metai or wood components and
have simply been adopted for use with plastic materials. while others have been developed
specifically to provide an effective means of assembling plastic parts.
Screws are the most widely used category of mechanical fastening device for the
assembly of plastic products. Screws are generally used in applications where operable or
reverse assernbly is required. They provide a simple. fast and effective method of joining
similar and dissimiiar rnaterials.
Metals screws are generally stronger and stiffer than the matinç plastic components.
Unfortunately. rnost screws were designed for metals and not enough literature is available
describing joint behavior in short fiber reinforcrd composites.
There are man? parameters that c m affect the overall joint performance: Pilot holr
diameter. drive torque. strip torqur. failure torqur. tightening torque. prestressing torque.
loosening torque. screw engagement length. thread depth utilization. pull out force. screw
driving speed [53]. Thread geometry and size are also major factors in determining the joint
performance.
Some of the recent research investigated the performance of threaded joints for
unfilled and filled composites. Dratschmidt [54] investigated V ~ ~ O U S fastewrs and evduated
the effects of different parameten on joint performance. Determination of optimum thread
engagement length. pilot hole diarneter and driving speed is necessay during the design
process [5q. However. due to the complex nature of joint configuration. experimental
methods are necessary to obtain these optimum conditions. A poorly designed joint c m fail
even during assembly. High speed driving of threaded fastcnen in composites can result in
scattered data and high percentage of joint failure. Environmental conditions of temperature
and moisture c m be more sikglificant nith plastic metal joints than al1 metal joints. Thermal
conductivity, thermal expansion and moisture absorption of the dissimilar materials can
promote excess stress and material degradation. leading to a joint failure or looseness [5q.
In conclusion. the need to understand the long-term viscoelastic behavior of WFRP
and to propose theoretical mode1 predicting long-tem properties on the basic of short-term
expenments is obvious. A fundamental understanding of viscoelastic behavior and the rffects
of various environmental and loading conditions is necessary to utilize WFRP to its full
potential. Understanding of threaded joints is also necessary to use these materials in various
automotive and building applications.
Theoretical
Introduction
In polymeric materials. the pnmary molecular chains are held together bp weak
cohesive forces. These chains are constantly rearranging their configurations by random
thermal motion. The driving force for these motions is the thermal energy contained in the
system [21]. When subjected to an external stress. rearrangement on a local scale takes place
rapidly but that on a larger scale occun rather slowly. This in tum leads to a wide range of
time spans where changes in mechanical proprrties are observed. This behavior is termed
viscoclasrici~. The amount of crystaiinity. cross-linking and chah structure also affects the
overall behavior [571. In wood-fiber reinforced polyethylene. the viscoelastic behavior is
mainly controlled by the matrix and the adhesion between randomly oriented @id fibers and
the polyeth~lene mauix. The O bjectivr of this study was to investigate the macromechanical
0-term behavior of the composite and to propose a suitable hypothesis to predict the Ion,
viscoelastic properties of the composites.
Various researchers have proposed empincal relations to describe the viscoelastic
behavior of fiber-reinforcrd composites. The Findley power law mode1 [28] is one of the
most widely used analytical models for describing the viscoelastic behavior of fîber-
reinforced polymer composites. The general form of the power Iaw for creep is given as
where go. E- and n are funciions of stress that can be determined by experimental data.
ïhe equation for stress relaxation cm be obtained by replacing strain E with stress o. In most
cases. E* cm be eliminated to get a more simplified fom of the mode1 known as the Power
Law.
Stress Relaxation
Short-term time-dependent stress at constant strain c m be generalized according to
Equation 3 2:
where the specific stress. a,. and the erponent. n. are constants which rnust be
determined from esperiments. The specific tirne t, is just a non-dimensionalizing constant
normally taken as 1 S. In general. n is independent of strain and temperature whereas o, is
svain and temperature dependent. Normally. n is less than one and is negative because of the
decreasing modulus. In stress relaxation experiments. the strain is constant and the power law
can be w-ritten in terms of modulus. E. as shown such that:
3.3 Creep
Time dependent flexural strain c m be generalized according to Equation 3.4 with
good accuracy over a wide span of time within the primary creep stage:
I t is important to understand that the power law mode1 cannot generalize creep
behavior in rupture. because of the change in the creep rate. The valid time span to apply a
power law c m vary depending on the stress and tempenture condition. Using stress as a
constant. Equation 3.4 c m be w-ritten in tems of a time-dependent flesural compliance J(t) as
folIows:
The specific compliance. J,. and time exponent. n. are constants which must be
determined fiom esperiments. Generally. n is independent of stress and temperature whereas
J, is temperature and stress dependent. t, is again just a constant. usually taken as 1 S.
Time-Temperature Superposition
The determination of the long-term performance of reinforced composites has often
been hindered by the expensive and time-consurning experimentation necessary to obtain
reliable results. The time-temperature superposition (TTS) principle was originally developed
in the mid-1950s for use with unreinforced plastics [49]. In late 1970's this method was
expandrd for use with fiber-reinforced composites [S8].
Tirne-temperature superposition is based on the assumption that the effect of
temperature on the time-dependent behavior of a material is equivalent to a stretching or
shnnking of the real time for temperatures abovc or below the reference temperature. Tnus.
when piotted on graphs where the abscissa is defined as ln(timc). the individual creep/ stress
relaxation curves obtained at different temperatures c m be shified to the lefV right to obtain a
continuous master curve which spans a much longer time penod than actually was empioped
in testing . The master curve is then used to predict the long-term behavior of the composites.
The relation between the shift factor. a,. and tempenture is normally govemed by the
Arhenius equation as shoun in Equation 3.6:
where AH is the activation enthalpy of the relaxation. R is the gas constant. T is the
testing temperature and T, is the reference temperature.
Theoretical 3-5
Modulus at time t and temperature T can be w-ritten as E(t.T) and can be calculated
according to Equation 3.7:
Where
with t being the real time of observation. T is the temperature. T, is the reference
temperature and is the reduced time.
Experimental 4-1
Experimental
Most previous experirnental studies of wood fiber reinforced plastics (WFRP) have
focused on manix and filler materiais. filler particle size. and the effect of mixing and
processing parameters on the mechanical properties of the composite. The present snidy
focussed more on the long-term viscoelastic properties and threaded joint performance of
WFRP.
In this study. the experirnental work was divided into two sections: The first section
was designed to investigate the mechanical properties and viscoelastic behavior of the
WFRP. Tende and flexural tests were performed to evaluate the mechanical properties of
the composites. Flexurai creep and tensiie stress relaxation rxperiments were performed to
study the effect of time and temperature on the mechanical properties of the composite.
Testing conditions were chosen to be representative of service conditions and to address the
most critical conditions of temperature and loading.
The second part of the work was desiçned to investigate the performance of threadrd
fastener and post moldrd inserts in WFRP. Experiments were designed to investifate the
effect of time and temperature on the clampinç force and backout torque of the tàstener
different types of fastenen. A detaiied description of the espenmental work is presented in
the foliowing sections.
4.1 Material
Recycled low-density polyethylene (LDPE) was used as matrix material in dl the
experiments. The melt flow index (MFI) was measured at 2.5 g/10 min when determined
according to ASTM Dl 238 at 1 90°C and 2.16 kgf. Royal Ecoproducts supplied LDPE chips
in a large cardboard container. The material was mixed thoroughlp and stored at room
temperature to avoid any variance in the quality of the test specimens throughout the period
of research. Royal Ecoproducts also provided compression moided specimens of WFRP.
prepared at their facility. using wood pellets. These specimens were used to replicate the
actual molding parameters in the laboratory and to compare the laboratory results with
typicai commercial products.
The laboratory test specimens used wood-flour (WF) as the reinforcing fillers in the
polymer matrix to promote homogeneous distribution and random orientation of fibers.
Wood flour of mesh size 40-60 was supplied by Northem Fibers in paper bags. The bags
were stored at room temperature in the sarne lab at approximately 50% relative humidity.
Four different fasteners were used to evaluate the fastening properties of WTRP.
General-purpose fasteners for wood (# 1 0 { size 1 - 1 2 (thread/inch) . $3 2 [ root diameter) )
manufactured by Crovtn Bolts. California USA were purchased from Canadian Tire Ltd.
Camcar Textron. Ontario. Canada provided specially designed plastiteK (#IO-1 7. 43.23)
fasteners for plastic. Penn Engineering and Manufacturing Corporation. Pemsylvania USA
provided NFPC ' (# 10-32. $6.2 (outer diameter)) and PPB" (8 10-32. $6.35) series post-
molded insens. Post-moldrd inserts can be installed by simply pressing them into pre-molded
or dnlled holes. Using post-molded inserts reduces installation time and eliminates the need
for heat or ultrasonic installation. Detailed dimensions and drawings of fasteners and inserts
are show in Appendix C. Commercial grade spruce wood was purchased from Home
Hardware as a baseline material for the screw pullout tests.
4.2 Specimen Preparation
4.2.1 Kinetic Mixing
For al1 the experiments conducted on WRP. 50 percent by weight wood tlour was
mixed with LDPE in a kinetic mixer (Werner and Pfleiderer. Grlimat). The typical batch size
was 200 gram. The discharge temperature was set at 18j°C a l th a maximum tip speed of
22.8 m / s (3300 rpm). The temperature inside the kinetic chamber was monitored with an
infia-red thermocouple. which controlled the pneumatic controlled discharge mechanism.
42.2 Compression molding
Matenal discharged from the kinetic mixer was immediately compressed at 3.5 MPa
(360 psi) pressure and 20°C temperature in a 50-ton press (Wabash 50). Pressure was
released autornatically from the molded specimens after 5 minutes. The specimens were
removed manually from the mold and flash was trimmed. Water was circulated inside the
tubes of the compression plates to maintain the temperature of the mold throughout the
process at roorn temperature. Details for individual specimen preparation are discussed in the
respective sections.
4.3 Mechanical Testing
4.3.1 Tensile testing
Tensile tests were performed to determine the tensile strength. modulus and breaking
strain of the LDPE and WFRP. These tests were also performed to establish testing
conditions for tensile stress relaxation experiments.
1.3.1.1 Specimen preparation
Tensile expetiments were done on the injection molded LDPE and compression
molded WFRP. Dog-bone shape specimens as shoun in Figure 4-l(a) were usrd to test
LDPE. The specimens were molded in an injection molding machine (ENGEL ES 80/18)
according to ASTM D638-98 type 1 standard specirnen. An injection pressure of 4.84 MPa
was used to inject LDPE into the mold at 205'C. The cycle timrs were 15 s for injection. 25 s
for cooling and 2 s for mold opening. Typical specimens were 150 mm in overall length and
3.2 mm in thickness. The lengtli and width of the test section were 50 mm and 12.75 mm.
respectively.
To test WRP. 150 x 150 .u 4 mm plaques were molded in a compression mold as
desctibed earlier. Standard specimens were cut from the plaque in the dimension of 150 x
12.75 x 4 mm by hi@-speed circula cutting saw as show-n in F i g w 4-1 (b). The distance
between grips was 100 mm while the length and width of the test section of the specimen
were 50 mm and 12.75 mm. respectively. Due to the random orientation of the short wood
fibers in the molded plates no consideration was made for the orientation of the test section.
Figure 4-1. Specimen configuration for tensile and stress relauation esperiments (a)
LDPE. (b) WFRP (al1 dimensions in mm)
4.3.1.2 Experirnental setup
Tensile tests were conducted in accordance with the ,\SIX1 D 638-98. Standard Test
Method for Tensile Properties of Plastic. Al1 tests were performed at room temperature on a
computer-controllrd screw-drivrn Sintech 20 terisile trsting machine using Testworks 3.1
software m i n g under DOS 6.12. on a 486 micro-processor based compter.
The experimental setup for tensile testing is shown in Figure 4-2. For accurate
measurement. strain in the specimen was detected using an MTS estensorneter (632.25B-50).
The extensometer was aitached to the specimen bg two springs lightly acting on two knife-
edges. A cross-head speed of 12.5 mrn/min was used to load the specimens till break. A load
cell (Sintech 3 133-149. 10001b) attached to the upper _&p was used to rneasure the applied
load. Testworks 2.1 calculated the yield stress. modulus and breaking strain using the data
collected from the load-ce11 and extensorneter. For al1 conditions. six specimens were tested.
P Upper Gnp
Figure 4-1. Esperimental arrangement for tensile and stress relaxation experiments (al1
dimensions in mm).
4.3.2 Flerural testing
Flexural tests were performed to evaiuate flesurai modulus. strength and break
deflection of the LDPE and WFRP. These tests were aiso performed to establish testing
conditions for flexural creep experiments
4.3.2.1 Specimen preparation
Flexural experiments were performed on the injection rnolded LDPE and
compression molded WFRP. Injection molded rectangular shape specimens were used to test
LDPE as shown in Figure 4-3(a). Standard specimens accordinç to ASTM D790 were
molded using injection molding machine (ENGEL ES 80128). Molding procedures and
conditions were the same as described in Section 4.3.1.1. Typical specimens were 130 mm in
overall length and 5.2 mm in thickness. The length and width of the support section were 50
mm and 12.75 mm. respectively.
Figure 4-3. Specimen configuration for flexural and creep experiments (a) LDPE and (b)
WFRP (al1 dimensions in mm)
To test WTW. 150 x 150 x 4 mm plaques were molded in a compression mold as
descnbed in Section 4.2. Specimens ( 150 .u 12.75 x 4 mm ) were cut from the plaque using
high-speed circular cutting saw as shoun in Figure 4-3(b). The [enb& and width of the
support section of the specimen were 50 mm and i 3.75 mm. respectively.
4.3.2.2 Experimental setup
The tests were perforrned according to ASTM Standard Test Method for Flexural
Properties of Unreinforced and Reinforced Plastics and Elecaical Insulating Materials D790-
98. A three-point bending fixture with a test span of 2". aaached to a Sintech 20 machine.
was used for flexural testing as s h o w in Figure 14.
The specimen was loaded uith a cross-head speed of 12.5 m d r n i n until the final
fracture or 10% deflection is achieved. Deflection was monitored by cross head motion of the
machine while the load was measured by ioad ce11 attached to the cross head.
Force t
Figure 44. Expenmental amgement for three-point flexural experiment.
4.4 Tensile stress relaxation
Tensile stress relaxation experiments were performed on the WFRP to evaluate the
effect of time and temperature on the tensile moduius of the composite.
4.4.1 Specimen preparation
Standard specimens were compression molded and cut as described earlier in Section
4.3.1.1. Typical specimens were 150 x 17.5 x 4 mm in dimensions as shown in Figure 4-1 (b).
The length and width of the test section of the specimen were 50 mm and 12.75 mm.
respectively.
4.42 Experimental setup
Tensile stress relaxation expenments were done on WFRP usinç the same Sintech 10
machine as described in Section 4.3.1.7. The machine was equipped with an environmental
chamber capable of controlling the temperature between -20 and 160 OC to within k1 "C. The
tensile stress relaxation esperiments were performed according to ASTM E328-96. Standard
Practice for Testing Stress-Relaxation for Materiais and Structures.
The extensometer. grips and specimen were preconditioned for two hours at each test
temperature. Specimens were held between grips afier preconditioning as shown in Figure
4-2. An extensometer was used to measure the displacernent accurately as described earlier in
Section 4.3.1.2. Cross-head speed was 12.5 rnm/min and a 1000 Ib (4300 N) load cell was
used to rneasure the load. At a prescribed displacement. the cross-head was stopped
automatically and the load readinp was recorded manually. The cross-head was held
Experimen fa1 4-1 0
stationary for the next 48 hrs and load relaxation was recorded manually according to the
time schedule as shown in Appendix Al . The load was thrn used to calculate the tirne-
dependent modulus. At the end of 48 hours. the extensometer was removed and the specimen
was unloaded and discarded. Four specimens were tested for each condition of temperature
and strain.
Creep
Creep experirnents were also prrformed on 50% WFRP to determine the effect of
time and stress on the tlexural strain of the composites. The esperiments were prrformed in
flexural loading conditions io determine the effect of time and temperature on deformation
during loads in bending
4.5.1 Specimen preparation
Standard specimens were compression moided and cut as described earlier in Section
4.3.2.1. TypicaI specimens were 150 x 12.5 x 4 mm as show in Figue 4- l (b). The length
and width of the support section of the specimen were 5Omm and 12.75 mm. respectivrl~.
Experimen ta1 setup
The flrsural creep esperiments were performed according to ASTM D2990-95.
Standard Test Methods for Tende. Compressive. and Flesural Creep and Creep-Rupture of
Plastics. AI1 experiments were perfomed on a testing rig specially desiçned for creep tening
of WFRP. This ng consisted of five linear displacement transducers and flexural test rigs and
as shown in Figure 4-5. The construction of the test rig! the calibration of the transducers and
the method used to calculate displacements are descnbed in reference [40].
LVDT tans ducer
Figure 4-5. Exprrimental arrangement for flexural creep experiments.
The linear displacement transducers were c o ~ e c t e d to an IBM XT computer throuçh
an ND converter and signal amplifier. A computer propram was witten in BASIC to read
the voltage and convert this into displacement (listing c m be found in Appendix D). The
creep machine was equipped with a temperature controller capable of controlling temperature
between 23 "C (room temperature) and 80 O C to nithin f l OC. The specimens and creep
machine were conditioned for two hours at each testing temperature prior to testing. After
loading the specimens with a constant load. the voltage reading was acquired automatically
from each LVDT every 30 sec and converted into displacement. Creep strain w3s calculated
using the standard relationship as described in ASTM D-2990. Each test uiis done on four
specimens for 48 houn.
4.6 Fastener performance
4.6.1 Specirnen preparation
For screw performance testing. block type specimens were compression molded
according to the same procedure as described in Section 1.2 Typical specimens were 120 x
70 x 30 mm. and were conditioned at room temperature for 24 hours before 5 pilot holes
were ddled as shown in Figure 4-6 using a drill press. The diameters of the holes were 2.1
mm (70% of root diameter) for screws and 6.4 mm for inserts. The screws were driven into
the pilot holes manually unless othenvise mentioned. Inserts were installed by pressing thrrn
into the pilot hole using a hydraulic press. Care was taken to keep the screws perpendicular
to the specimen surface. A11 the screws and inserts were inspected to scrern out an. major
thread defects. The specimens were conditioned at room temperature for 74 hows pnor to
static pullout. and backout toque tests.
Experimental 4-13
Figure 4-6. Typical specimen configuration for fastener peiiormance testing (al1
dimension in mm).
4.6.2 Quasi-static pullout and engagement length
Fastener pullout was performed to evaluate the strength of joints using different
fastenen as a Function of thread engagement length.
4.6.3 Experimental setup
The quasi-static pullout test was performed according to ASTM D6 1 17-97. Standard
Test Method for Mechanical Fasteners in Plastic Lurnber and Shapes. All tests were
performed on the Sintech 20 tensile testing machine by using a special pullout fisture (4 23.4
mm) designed for fastener pullout tests. The tvpical experimental arrangement is s h o w in
Figure 4-7
The screw specimen was placed inside the specimen holder and the head of the screw
was slid inside the slot of the pullout fixture. A cross-head speed of 12.5 rnmhin was used
to pull the fastener from the specimen. For each type of fastener. 5 specimens were tested at
room temperature.
To determine the effect of engagement length on the pullout force. the specimens
were drilled in steps to Vary the engagement length. The typical specimen is shown in Fi jure
4-8. The pullout tests were perfomed as described above.
Load c e 1
Pin iomt
1
/ / / / / / / /
Figure 4-7. Expenmental arrangement for fastener pullout (a) for inserts. (b) for screw.
! ! 1 engagement iength I t
I I I I I Ill
.t+i-l CV
I I I I
Figure 4-8. Specimen configuration for effect of engagement length on fastrner pullout force (al1 dimensions are in mm).
Stripping force and torque
Stripping force and torque measurements were made to determine different
characteristic torque. This experiment was divided into two parts. In the first part. wood
screws were used to determine the driving and failure torque and the effect of torque on the
clamping and stripping load. In the second part. only torque measurements were done to
determine different characteristic torque. The following section describes the apparatus used
to measure clamping force and di-iving torque.
4.6.4.1 Data acquisition and load cells
Button-type load cells and a data acquisition systern were built to study the fastening
characteristics. A total of six load cells were designed and manufactured as s h o w in Figure
4-9. Each load ce11 was designed for a maximum load of 5.000 N. Large. flat. rigid plates
were used on both the top and bottom ends of a cylindrical tube to distribute pressure evenly
on the specimen surface. Two 90' tee stack rosette strain gages (CEA-13-062WT-350.
Intertechnology. Ontario. Canada) were glued on the cylindrical tube to measure applied
compressive load. Two gages were used to reduce the effect of bending and misalignment
and to increase the voltage output of the signais. Construction details are shoun in Appendix
D.
Figure 4-9. Load cell for measuring clamping force of screw
The data acquisition card (AT M016-XEjO) was purchased from National
Instruments Ltd.. Austin. TX. USA. The system was capable of acquirîng 8 differential
inputs at a total rate of 20.000 samples/sec with a resolution of 16 bits. The card was installed
on a 486DX.1 cornputer running under ~ i n d o w s ' 95. A device driver was also purchased
fiom National Instruments to install the software for the card.
The strain gage accessory (SC-2043-SG) was also purchased to connect the strain
gage to the data acquisition card. The strain gage accessory was capable of conditioning and
ampliQing 8 inputs directly on the board and was powered by an extemal 10V power supply.
A reaction torque sensor (S WS- 1 O) was purchased by Transducrr Techniques.
Teemeecula CA. USA. and was used to measure torque. The sensor was capable of measuring a
maximum torque of 13.5 N-m (10 fi-lb). The sensor was attached to the data acquisition card
via the main gage accessory. Details of the card and setup are given in Appendis D.
Software was written using Visual Basic V6.0 to acquire data fiom the strain gages.
convert the voltage into force and &-rite the data to an output file. Standard modules provided
by National Instruments were used to acquire the data calibrate the load cells and write the
output files. Details of software are given in Xppendix D.
4.6.4.2 Experimental setup
Simultaneous measurements of driving torque and clamping force were made to
determine the effect of driving torque on stripping load. The experimental setup is shown in
Figure 4-10 (a). The screw was driven into the specimen using variable speed electric
screwdriver. Torque and load measurement were recorded automatically by the data
acquisition system at a rate of 10 readingskc. The screw was driven into the specimen m i l
a sudden drop in torque or failure in the specimen was observed.
Torque sensor I I Screwdnver
Torque sensor
Figure 4- 10. Experimental arrangement for torque and pullout measuremçnts (a) for
simultanrous measurement of driving torque and stripping force (b) for the
measurement of driving torqur only
To measure the characteristic torque only the torque sensor was used during the
driving of the screw. The experirnental setup is shomm in Figure 4-10(b). The post molded
inserts were installed 24 hours prior to testing.
4.6.5 Backout Torque
Expenments were conducted to determine the effecr of time on the relaxation of the
initial tightening torque. Wood screws wvee driven to a certain torque according to the
arrangement shown in Figure 4-10 (b). Mer a certain penod of time. the screw was
untightened and the maximum torque was measured.
4.7 Clamping force relaxation
Experiments were conducted to study the effect of initial clamping force. time and
temperature on the clamping force of wood screw in WFRP.
4.7.1 Experimental Setup
The clamping force relaxation experimeni. ivas done using wood screws to determine
the effect of tirne. temperature and initial clamping force on the overall behavior. Relavation
in the clarnping force was measured with the data acquisition systern as descnbed earlier in
Section 46.4. The typical arrangement is shown in Figure 4-1 1. The manual method of
driving the screw uas chosen afier the initia1 failure in controlling the clarnping force when
the variable speed screwdriver was used. The clamping force increased so rapidly that it \vas
almost impossible to conuol it using the electric screw-driver.
Al1 the experiments were done inside a convection oven capable of controlling the
temperature from 73 *C to 160 "C within +l°C. The specimens. load cell. and screws were
conditioned for 2 hours prior to testing.
The experiment was divided into two parts: In the fint part. the screw was dnven
manually into the pilot hole of the specirnen and the force was measured using the data
acquisition system. The cornputer program was set to beep at 90% of the required clamping
force to prevent overtightening. Afier tightening the screw to the desired clarnping force, the
0s were screw was left in the controlled environment for the next 48 hours and the readin,
recorded automatically.
Figure 1-1 1. Tppical arrangement for clamping force relaxation esperiments
In the second part of the experiment the clamping force was dlowed to relax for a
certain period of tirne. after which period the screw was retightened to the initial clarnping
force and the relaxation in the clamping was again observed for the next 48 hours. This
experiment was conducted to study the effect of retightening on the overall performance on
the composite and to compare the result with the initial clamping force relaxation.
Results 5-1
Results
Introduction
In this study. the viscoelastic properties of wood-fiber reinforced polyethplene were
studied. and a model was developed to predict the long-term stress relaxation and creep
properties of the composites using short-term experiments. The performance of self-
threading screws and inserts was studied and the model was hrther expanded to assess the
relaxation in fastener clamping force and backout torque.
To study the viscorlastic behavior of WFRP. flexural creep and tensile stress
relaxation experiments were perfomed. Stress in creep and strain in stress relix~ation were
chosen caretùlly to cover a broad range of loading conditions. The cffrct of time and
temperature on the mechanical properties was studied in both esperiments. Tende and
flexural tests were done to assess the mechanical properties of the composites.
Threaded joint performance was evaluated for five different fasteners and insrrts.
Static pullout force. driving and stripping torque and the effect of thread engagement length
on pullout force were studied to evaluate the static performance of the fasteners. Relavation
in clamping force and backout torque was also studied to evaluate the joint performance over
an extended period of time.
Only one WFRP composition was used in a11 the experiments to reduce the time
required to conduct creep and relaxation experiments and also to replicate the processing and
fiber content requirement of a typical product.
Mechaoical Properties
The results from tensile and flexural tests of unreinforced and reinforced recycled low
density polyethylene (LDPE) with wood fibers (WF) are listed in Table 5-1. The tensile
strength of the composite was 20% higher than that of the unfilled polymer but the results
were more scattered. Generally. poor adhesion between the wood fiber and the polymer
matrix caused scatter. The addition of wood fiber in LDPE increased the tensile modulus by
350%. The elongation at break in WFRP was 1.7%. which was much lower than that in
LDPE where no break was detected at 10% elongation strain.
An increase of about 25% was observed in the tlexural strength of the composite. The
flexural modulus was also increased by 250% with a much lower dcflection at break than
LDPE where no break was detected at 10% deflection strain.
Table 5- 1 : Mechanical Properties of LDPE and 50% WFRP at 23 C (number of
specimrns = 6. standard deviation is shom as upper and lower values)
LDPE WFEW
Tensile strength (MPa) 10.6 i 0.2
Elongation at break (%) No break (> 1 0%)
Tensile Modulus (GPa) 0.3 = 0.01
Fiexural Strenpth (MPa) 13.7 i 0.5
Deflection at break (%) No break (> 10%)
Flexural Modulus (GPa) 0.3 i 0.02
In general. the addition of wood fiber in LDPE increased the stiffness and modulus
but had very little effect on the stren*@ of the composites. In this study the main objective
was to determine the viscoelastic propenies of the composite and no effort was made to
optimize the mechanical properties of the composite.
The effect of strain rate on the tensile strength \vas also studied as shown in Figure
5-1. The composite showed normal süain rate sensitivity and the stress level increased with
higher strain rate. This change in stress level caused by the strain rate implied that the
deformation properties of the composite are mainly due to the viscous and non-Iinear
behavior of the composite.
0.5 1 .O 1.5 Strain (mm / mm x 100)
Figure 5-1 Stress ! strain curve in simple tension at different strain rates for 50% WFRP
Tensile stress relaxation
Stress relaxation experiments were performed on 50% WFRP to investigate the effect
of strain. temperature and time on the tende modulus. Some of the graphs are s h o w here to
discuss the results. The complete set of expenmental data and figures can be found in
Appendix A. Figure 5-2 shows the modulus as a function of time at different temperatures
and 0.5% strain. As expected. the initial modulus was higher at Iow temperature than at high
temperatures. At 0.5% strain the initial modulus at 13°C (1 460 MPa) was 35% and 50%
higher than at 40°C (935 MPa) and 50°C (746 MPa) respectively. At 1% strain the difference
becarne smaller and the initial modulus at 23'C (980 MPa) was 20% and 35% higher than at
40°C (750 MPa) and 50°C (630 MPa).
0.OEi-O0 6.OE+04 1 .3E+05 1.8E+05 Tirne (s)
Fi-me 5-2. Tensile modulus as a function of time at different temperatures and 0.5%
strain
The modulus was highly time-dependent and decreased rapidly within a short period
of time. Slow but continuous relaxation was then observed till the end of the experiments at
172800s (48 hrs). Figure 5-3 shows the In-ln plot of modulus as a function of Ume at three
different temperatures and 0.5% strain. The curves are aimost linear with a negative slope.
The negative slope represents the decreasing modulus as a function of time. The slopes are
not the sarne for all the conditions and are dependent on temperature.
6 1 O In Time (s)
Figure 5-3. in-ln plot of tensile modulus as a funcrion of rime at different temperatures
and 0.5% main
The efect of the addition of wood fiber (MF) on the tensile modulus is shown as a In-
In plot in Figure 5 4 . The graph shows an almosr parallel relation between LDPE and WFW.
The addition of WF increased the initial modulus of rhe composites but did not change the
relaxation behavior. The LDPE matrix govemed the main relaxation behavior and WF acted
as a ngid and immobile mass that does not interact strongly with the LDPE.
6 1 O 14 In Time (s)
Figure 5-4. In-ln plot of tensile modulus as a function of time at 23C temperature and
0.5% strain for pure LDPE and 50% W R P .
Figure 5-5 shows the percentage drop in modulus with refercnce to initial modulus as
a function of time at various temperatures and strains. Percentage drops in modulus at
diKerent temperatures and strains were aimost equal and were not affected by initial
modulus. which was different for al1 conditions. Initially the modulus relased very rapidly
and during the fint 30 minutes almost 30% of the modulus relaxed. Afier 2 hours the value
dropped to about 40% and an average of 50% was observed at the end of 172800 s (48
hours).
6.0E+04 Time (s) 1.2E+03
a ! 4
8
Figure 5-3. Prrcentage drop in modulus as a function of tirne with referencr to initia1
modulus at different tempenture and strain
10
The stress relavation behavior of WTRP is highly dependent on testing temperature
and loading condition. The WTRP also exhibits non-linear relaxation with reducing modulus
at increasing strain. The highest modulus was observed at 23'C but at the same time the
highest relaxation. in absolute terms. was also observed at 2j0C. The addition of WF
increased the stiflhess but had no signifiant effect on the relaxation behavior. The
percentage drop in modulus was found to be nearly independent of initial n a i n or
temperature. The relaxation behavior was found to be exponentially dependent on testing
time.
0 23 C. 0.5% a 40 C. 0.5% a 50 C, 0.5% + 23 C. 1% x 40C. 1% 0 5OC. 1% - Average
Results 5-8
5.4 Creep
The percentage flexural strains at different temperature are shown in Figure 5-6 and
F i g w 5-7 for loading equal to 25% and 10% of ultimate flexural strength (UFS).
respectively. A complete set of data and figures can be found in Appendix A. At the end of
the experiment the strain at 25% UFS was under 1% at 23°C and reached a value of about
1.25% at 40°C. At 60°C the strain reached a value of around 2% and creep rupture was
observed before 157000 s (42 hours). At 35% UFS the strain was just above 1% at Z ° C and
reached a value of about 1.3% at 40°C aiter a penod of 172800s. At 60°C the specimen
ruptured before 129600 s (36 hours) with a maximum strain of 2.8%. At 40% UFS the strain
was around 1.4% at X°C d e r 172800 s (48 hours) but the specimen ruptured at 152000s (42
hours) at 40°C with a mavirnum stnin of 2.9%. At 60°C the composite creeped very rapidly
and rupture occurred within 7200s (2 hours) with a mavirnum main of around 3% deîlection.
Figure 5-6. Flexural strain as a function of time at different temperature and 25% UFS
stress
Resui. 5-9
Figure 5-7. Flexural Strain as a function of tirne at different temperature and 40% UFS
stress
O.OE+OO 6'0E+04 Time (s) 1.2E+O3 1,8E+05
Figure 5-8. Flexural svain as a function of time at various stresses and 73' C temperature
The percentage strain as a function of time at various stresses and 23" C is shown in
Figure 5-8. At 25% of UFS the WFRP was well under the creep rupture limit after 172800s
(48 hours) but the creep was proceeding at almost a constant rate. At 30% of UFS the creep
was higher than observed for 75% UFS and at 60C the specimen rupture around 152000s (42
hrs). At a stress 10% of UFS. a high rate of creep was observed and al1 specimens rupnired in
less than 48 hours.
3 L. 4 6 8 10 12 14
In Time (s)
Figure 5-9. Double log plot of nain and time at different condition of stress and temperature
Figure 5-9 shows the double logarithic plot of strain as a fimction of time for
various combinations of initial stress and temperature. The curves at lower strain and
temperature were aimost linear and in the range of prirnary creep. When the temperature and
stress increased. accelerated creep was observed and the materiai started with primary creep
but soon tended to creep with a higher raie in the tertiary creep region. resulting in creep
rupture.
At lotver suain and temperature. the strain increases rapidly m-ithin a short period of
time and then proceeds at a nearly constant. slow rate. At highrr stress and temperature.
creep increases rapidly within a short period of rime and then after a period of constant creep.
strain proceeded with an increasing rate and terminated in creep rupture.
5.5 Fastener Performance
Figure 5-10 shows the torqur and clamping force in a stripping test for the wood
screw as a hinction of tightening time at a driving speed of 100 rpm in WFRP. Figure 5-1 1
shows the curve of driving torque as a h c t i o n of tightening time for different fasteners at
the sarne rotational speed. Fi_we 5-12 shows the static pullout force and specific pullout
force (pullout force / engagement length) for different fasteners and inserts. The
characteristic values of thread forming torque (T,;). ciriving torque (Td). stripping torque (7,).
pullout force (Fp ). and specific pullout force (F,) were obtained from curves and are
tabulated in Table 5-2.
++ Load 4 Torque
O - 3 4 6 8 10 12
Time (sec)
Figure 5-10. Driving torque and clamping force for the wood screw as a function of time
- .. -
-e- NFPCS Insert 4 P P B 8 lnserts
O - 3 4 6 8 10 Time (sec)
Figure 5-1 1. Driving torque for various fasteners as a Function of tirne (n=100 rpm)
Figure 5- 12.
O Pullout Force 0
Specific Pullout Wmm)
NFPCB PPBB Plasthe@ Wood screw Wood screw insert inserts screw in Wood
Static pullout and specific pullout force for various fasteners and inserts in
WFRP and spnice wood
Table 5-2. Pullout force and characteristic torque for different fasteners
Wood screw Plastite@ NFPCB PPB@
Engagement length (mm)
Thread pitch diameter
Pilot hole diameter
Pullout load (N)
Specific Pullout load (N!m)
Forming Torque (N-m)
Driving Torque (N-rn)
Stripping Torque (N-m)
Strip/Drive torque ratio
Static pullout force (Fp) was around 2700 N for the wood screw and the Plastite
screw. The pullout force for the post-molded inserts was in the range of 10-20% of that of the
wood screw. but inserts offer virtually unlimited possibility of repeated assembly. The
pullout force for the wood sciews in the torque stripping expenments was found to be 2630
N. which was 3% less than the static pullout force. Screw pullout tests were also performed
on spmce wood to compare the results. The pullout force for wood screws in spruce was
20 12 N. which was 10% l e s than for the same screw in the composite.
Because of different thread engagement lengths for different façteners. the pullout
force per unit thread engagement length wwas calculated to provide a bencr comparison. The
specific pullout force (pullout force/engagement length) was highesr at 181 Nimm for the
wood screw in the composite. The specific pullout load for the wood screw was about 10%
higher than for Plastite screw. 250% larger than that of the NFPC inserts and 450% more
than with PPB inserts.
The characteristic torque-clarnping force-iurn behavior of wood screw is shown in
Figure 5-10. Initial value of torque was due to thread cutting into the WFRP. The torque
continues to climb as the screw is driven deeper into the WFEW due to added frictional
resistance associated with deeper engagement. The torque and clamping force climbs rapidly
as the head of the screw mates with the load ce11 surface. Continued driving of the screw
results in shear loading levels on the composite threads that rsceed their yield value and
eventualiy the threads fail. The torque-turn behavior of varioils fasteners is shown in Fibpre
5 4 1 . Wood screws showed around 10% less dnving torque and 20% less stripping torque
than Plastite screws. Due to the construction of the post-molded inserts. the driving torque
was very low and almost negligible when compared to that observed for the Plastite screw.
The stripping torque for NFPC and PPB inserts was approximately 40% and 50% less than
for the Plastite screw. respectively. As mentioned above a significant difference between the
dnving and stripping torque (Ts - T') is desirable to effectively control the screw clarnping
force and to avoid failure during tightening. Tne difference between the dnving and stripping
torque was 25% higher for the Plastite screw than for the wood screws. For insens. the
difference was almost equal ro the stripping torque. as very l o a torque was required to drive
the screw in the inserts.
O 5 10 15 20
Engagement Length (mm)
500
Figure 5-1 3. Static pullout force as a function of thread engagement length
4 Wood Screw + Plastite Screw O
Figure 5-14. Plastite and wood screw afier pullout from WFRP in screw pullout
The large difference between the tensile modulus of the screw material and the
WFRP resulted in an even force distribution dong the length of the screw engagement
length. This caused a linear dependence of the pullout force on the engagement length.
Figure 5-13 shows the linear effect of engagement length on the static pullout force for the
wood and Plastite screws. The effective pullout force for a certain application c m be easily
determined using this relation. An engagement length of more than 120 mm would result in
pullout forces on the order of the screw tensilr strength.
The preferred mode of failure is thread stripping since this mode of failure can be
avoided easily using longer or Iarger diarneter screws or repaired after failure using a gap-
filling adhesive. Shear deformation in stripping causes a plug of material to be removed
during a pullout test as s h o w in Figure 5- 14.
Results 5-2 7
Wood screws and Plastite screws perfom almost equally well in puilout force. but the
Plastite screw had a higher strip to drive torque ratio. The pullout force for wood screLvs was
higher in composite when compared with spruce and also highly dependent on thread
engagement length. The relation between torque. engagement length. pilot hole diameter. and
driving speed is highly dependent on screw size. shape. dimension and surface finish. It is
important to determine these relation by experiments for every combination of screw and
WFRE'.
Fastener backout torque
Results From the backout torque measurement are shoun in Figure 5-15. About 6%
of the torque relaxes within 172800s (24 hrs) and afier that no significant relaxation was
observed. Afier the screw is seated. the polymer cold flows back into the relief areas created
dunng the thread cutting process to conform ro the shapt: of the screw. This enhances the
mechanical interlocking contact between the screw and polymer and no signifiant relauation
in backout torque was observed when compared to stress relaxation and creep results.
O.OE+OO 5.OEi-OS 1 .OE+O6 Z.5E+06 3.OE+06
Time (s)
Figure 5-1 5 . Backout torque as a function of time at room temperature.
Fastener clamping force relaxation
The static pullout experiments produced bener results for WFRP than for spruce. Due
to the highly viscoelastic behavior of WFRP it was important to study the effect of time and
temperature on the clamping force relaxation. The viscoelastic behavior in threadrd joints is
complex and lot of work remains to be done ro understand the exact phenomenon. Different
thread geometries also affect the loading behavior inside the composite and consequently the
relaxation mechanism. Only the wood screw was used in this study 10 determine the behavior
of the clamping force as a function of time and temperature.
Three initial clamping forces (17. 33 and 50% of pullout force. Fpo) were used to
study the relaxation in the clamping force of wood screws. The loading conditions were
0. 17Fp 0.33Fp0 and O.jF, for 17%. 33% and 50% of pullout force (F,). respectively. The
relaxation of clamping force for the wood screw as a function of time is shown in Figure
5- 16. Figure 5-1 7. and Figure 5- 18 at three different percentages of pullout force and 23. JO
and 60 O C temperature. respectively. .At 23 OC temperature and 0.17FP. the force relaved io
70% of the initial force within 3600s. 60% within 64800s ( 1 8 h) and around 50% at the end
of experiment (48 h). At 0.33Fp and O.jF, the relaxation response was alrnost same and
around 50% of the clamping force relaved after 172800 s (48 h). At 40 O C the mavimum
relaxation was observed at 0.1 7F, where the force relaxrd to a value of 44% of the initial
clamping force after 177800s (48 h). The relmed force reached a value of 46% at 0.33Fpo
and 50% at O.jF,. .4t 60 "C the relased force reached a value of 40% at 0.1 7FP0 after 172800
(48 h). The value reached 42% at 0.33 Fpo and 48% at 0.5 Fp.
1500 4 0.17 Fpo ++ 0.35 Fpo x O . 5 0 Fpo
O.OE+OO 5.OE+04 1 .OE+O5 1.5E+05 2.OEa05 Time (s)
Figure 5-16. Clamping force as a function of time for wood scren in WFRP at different
initial clamping force ( F p = Pullout Force) at 23 'C temperature
1500 ,O. 17 Fpo .+ 0.35 Fpo - 0.50 Fpo
O.OE+OO 5.OE+04 1 .OE+03 1.5Et-O5 2.OE-05 Time (s)
Figure 5-17. Clamping force as a function of time for wood screw in WFRP at different
initial clamping force (Fpo = Pullout Force) at 40 O C temperature
+- 0.17 Fpo 4 0 . 3 Fpo -b 0.50 Fpo
5.OE+04 1 .OE+05
Time (s)
Figure 5-18. Clamping force as a huiction of time for wood screw in WFRP at different
initial clarnping force (Fpo = Pullout Force) at 60 O C temperature
The effect of temperature on clamping force relavation at 0.1 7Fp0 and 0.5 Fpa is shown
in Figure 5- 19 and Figure 5-20, respectively. The relaxation in clamping force was greater at
higher temperatures. At 0.17FP the force relaved to 52% of the initial force after 172800s
(48 h) at 23 OC. the value reached 44% at 40 "C and 38% at 60 'C temperature. At O.jF, the
effect of temperature was less than at O. 1 7Fp. The force relaved to 5 1% of the initial force
after 172800s (48 h) at 3 C . it reached to 50% at JO "C and 48% at 60 O C .
Initially. the force relaved rapidly to approx 70% of the initial force within 500s.
dropping to 60% at 7200s (2 h) and 50% at 84600s (24 h). The average relaxation of 47%
was observrd after 172800s with a maximum of 37% at 60C and 0.1 7F, loading condition
and minimum 53% at 23C and 0.1 7Fp0.
O.OE-O0 5.OE+04 1 .OE+05 1.5Et05 2.OE+O5
Time (s)
Figure 5-19. Clamping force as a function of time for the wood screw in WFRP at different
temperatures and 17% of pullout force
O.OE+OO 5.OE44 2 .OE+05 1 .SE+05 2.OE+05
Tirne (s)
Figure 5-20. Clarnping force as a function of tirne for the wood screw in WTRP at different
temperatures and 50% of pullout force
No arrangement was made to measure the deformation in the composite between the
threads nor the shear de formation bctween the thread outrr diarneter and the composites.
The results showed that temperature doesn't have any significant effect on the
ciarnping force relaxation behavior of the composites. At ail conditions the drop ranged from
52 to 37% of the initial clamping force. In creep the stress was held constant while in stress
relaxation the strain was held constant. In the clarnping force relaxation experiment at
different loading and temperature condition the WFRP was allowed to strain as much as
possible while at the same tirne the clamping Ioad was allowed to decrease over a period of
time. This experiment is thus a combination of creep and stress relaxation and the results
cannot be compared with stress relaxation or creep behavior where the temperature ef5ect
was much larger.
O - 7 4 6 8 10 12 14 ln Xrne (s)
Figure 5-21. In-ln plot of clamping force as a function of time at differemt initial clamping
force and temperature
O.OE+OO 6.OEi04 1.2E+05 1.8E+05 Time (s)
Figure 5-22. Clamping force relaxation for WFRP and Spruce at 23 O C and 33% of Pullout
Force
Figure 5-21 shows the double logarithmic plot of clamping force as a hinction of time
at different initial clamping force and temperature The curves are almost straiçht lines at al1
conditions of clamping force and temperature. At higher clarnping force (O-jF,) the curves
are almost overlapping each other at al1 temperatures but at lower clamping force (0.17Fp,)
the differences become more prominent and the curves become separated at different
tempenture.
The clamping force relaxation cornparison between spruce and WFRP is s h o m in
Figure 5-22 for the wood screw at Zj°C and 33% of screw pullout force in WRP. The
WFRP produced a higher pullout force than spruce but only 25% relaxation was observed in
spruce as cornparrd to 50% in WFRP.
5.8 Fastener re-tightening
The effect of re-tightening of the screws was investiçated to undersrand the relaxation
brhavior and to test the superposition principle. Figure 5-23 and Figure 5-24 show the effect
of re-tightening on screw clamping force relaxation d e r 3600s and 7700s respectively at
23 O C . At O.33FP the clamping force relaved to about 52% of the initial force after 5600s.
Then the screw was re-tightened to the initial ciamping force and the relaxation behavior was
again observed. The clarnping force relaxed to 68% afier 3600s (tirne &er re-tightening).
65% after 7200s and reached a minimum of 55% after 173800s (48 h) after re-tightening. At
O.jF,. the clamping force rekued to 55% of the initial force at 3600s. Afier re-tightening the
clamping force relaved to 72% afler 3600s. 70% d e r 7200s and reached a minimum of 60%
at the end of 172800s.
At O.33FP,. the clamping force relaved to about 50% of the initial force afier 7200s.
Afier re-tightening the screw to the initial clarnping force. the relauation was measured at
67% at 3600s. 64% at 7200s and reached a minimum of 54% after 172800s (48 h). .At O.jF,.
the clamping force relaxed to about 53% at 7200s. M e r re-tightening the force was relased
to 69% at 3600s. 67% at 7200s and reached to a minimum of 56% afier 172800s.
The re-tightening of the screw afier a certain penod of timr affects the relaxation
behavior. and the relaxation in clarnping force afier 177800s was less than the simple screw
clarnping force relaxation experiments where the initial force relaxrd to an average value of
47% of the initial clamping force. Also the relaxation at the end of the expenment (48 h) kvas
less than the initial relaxation be fo te re-tightening.
5.OE+O4 1 .OE+OS
Time (s)
Figure 5-23. Clamping force as a function of time after re-tightcning the screw to the initial
clamping force after 3600 s at 23 O C .
Tirne (s)
Figure 5-24. Clamping force as a function of time atier re-tightening the screw to the initial
clamping force after 7200 s at 23 O C .
Figure 5-25 shows the double logarithmic plot of clamping force as a fûnction of time
at two different initial clamping force value with ce-tightening after 3600s (1 h). The plots
clearly show the change in the relaxation behavior of the material afier re-tightening. Before
re-tightening the plots are almost straight lines. but after re-tightening the screw to its initial
clamping force the relaxation behavior deviates from the original path.
Figure 3-25. ln-ln plot of clamping force as a function of time after re tighten the screw to
the initial clamping force after 3600 s at 23C temperature
7.5
7.0 L w O
2 O ZL
6.5 .L
E s G s - 6.0
5.5
Retightening of the screw after a specified period of time enhance the joint
performance and the reduction in clamping force relaxation was observed. The relaxation in
clamping force afier 48 hours was less than the relaxation after 2 hours. This leads to a
,+O.~;FPO -0.sFp0
O - 3 4 6 8 10 12 14 In T h e (s)
Resulîs 5-28
conclusion that the composites have a memory effect and retightening decrease the chance of
loosening.
The experiment was done to explore the behavior of the relaxation spectrum after re-
tightening of the screw. A series of experiments is required to characterize the relaxation
behavior and to deduce any fùrther result from thrse experiments. which is beyond the scope
of the present studies.
Mode1 and Discussion
Introduction
Once the data fiorn tensile stress relaxation. Bexural creep and fastener clamping
force relaxation were obtained from the respective experiments. a linear regression technique
was used to fit the experimental data to Equation 3.3 and Equation 3.5 (Power Law modrl).
Microsoft Excel was used to estimate the viscoelastic parameters. The results from the Power
Law modeling are given in the following sections. ï h e Kohlrausch-William-Watts (KWW)
equation and Findley's Law (FL). as shown in Equation 6.1 and 6.2. respectively. were also
investigated for stress relaxation experiments and the results were cornparrd with the power
Law model.
A long-term flexural creep esperiment (4000 hours) was also performed and the
validity of the Power Law model based on relatively short-term experiments (48 hours) was
verified. Time-temperature superposition was done for the sness relaxation experiments to
study the long-term relaxation in modulus and a master curve was dmm for IWO different
constant strains. The effect of temperature and loading condition on the viscoelastic
parameters are discussed.
Mode[ and Dkcussion 6-2
6.2 Tensile Stress Relaxation
The ln-ln plot of calculated and experimental tensile modulus is s h o w in Figure 6-1 as a
fimction of time at 73 O C temperature and various strains. Figure 6-2 shows the In-in plot of
modulus as a fùnction of tirne at 0.5% strain and various temperatures. The complete set of
figures is shown in Appendix B. Experimental data at al1 conditions were wrll-fitted to the
Power Law mode1 with good regression coefficients. The Power Law parameters Es and n are
tabulated in Table 6-1. Since the initial modulus is hiphly dependent on temperature and
strain. the power law equation is estimated for each condition individually.
The generalized non-linear power law proposed by Findley [28] requires twelve
kemel functions that must be determined by a series of rsperiments at different strains and
temperatures. No effort was made to address this generalized non-linear viscoelastic solution.
Figure 6-1. E.xprimentai and calculated tensile modulus at 23°C temperature and two
strains
Model and Dkcussion 6-4
Table 6-1. Power law mode1 fiaing results at diRerent conditions of s t r a i n and
temperature (t, = 1 sec)
Temperature C S train Power Law mode1 R"
The modulus after one second (1s) or Es was found to be around 90% of the initial
modulus. The value of n was found to be slightly temperature dependent but independent of
strain. The effect of temperature on Es and n is discussea in Section 6.5 and 6.6
The Kohlrausch-William-Watts (KWW) equation and the Findley Law (FL) were
also investigated and the results are shown in Figure 6-3. The difference between the power
law and the Findley Law is negligible. which confirms the radier assumption made in
Section 3.1 to eliminate E,. The KWW equation fits well for short-term data but a deviation
fiom the experimental data was observed after 6 hours. The predicted values Kere higher
than the experimental data making this model inappropriate to predict long-term relaxation
behavior.
Mode1 and Discussion 6-6
The major drawback of using the Power Law is the long-term behavior of the c u v e
that leads to a continuous relaxation in modulus for infinite time. However. the exponential
nature of the cuwe predicts that the decrease in modulus afier long periods of time bill be
very small and cm be considered negligible when compared with the initiai relaxation (-50%
in 48 hours).
Stress relaxation in WFRP must be considered in design for non-load bearing
structural applications. In most cases. the product remains in service for an extended penod
of time. usually longer than it's practical to run experiments. Thus it is necessary to
extrapolate the results O btained from reiativel y short-tenn laboratop tests. Hence. the
accuracy with which a stress relaxation equation describes the time dependrnce is an
important consideration. A statistical analysis \vas performed on actual data to evaluate the
variations in fitting parameters at a 95% Confidence Interval (CI). Results from the statistical
analysis are shoun in Table 6-2. The upper and lower confidence limits for timr rsponent. n.
are plotted at various tempentures and 0.5% suain in Figure 6-4. Escept for a couple of
points at the beginning of tlie experiments. almost al1 of tlie data points lie within the limits.
The initial divergence was rnainly due to the effects of Ioading and the sudden stoppage of
the cross-head.
Mode1 and Dkcussion 6- 7
Table 6-2. Estimation of power law fitting parameters at 95% CI
Temperature ( O C ) Strain (%) Specific Modulus. Es (MPa) Time exponent. n
Figure 64 . Confildence limits of tirne exponent (n) at 95% CI . constant specific modulus
(Es) and 0.5% strain.
Mode[ and Discussion 6-8
Flexural Creep
The ln-ln plot of calculated and experimentd flexurd compliance at various
temperatures and 25% ultimate flexurai strength (UFS) is shown in Figure 6-5. Cornplete sets
of plots cm be found in Appendix B. Power Law parameterss Js and n are tabulated in Table
6.3. Experimental data at lower strains and temperatures were well fitted by the Power Law
with good regression coefficients. At higher temperatures. WFRP tends to creep rapidly
within 24 hours and creep rupture was observed. This made it difficult to fit the Power Law
mode1 at higher levels of temperature and stress.
l o 23C A 4OC CI 60C - Calculated
Figure 6-5.
Tirne/ t,
Experimental and calculated values of flexural compliance at 25% UFS
Mode1 and Dkcussion 6-9
Table 6-3. Power Law mode1 for flexurd creep compliance
Temperature (C) Stress (% UFS) Power Law RL
23 (296 K ) 25 794.7 (th,) 0.993
40 (3 13 K) 35 1039.7 (th,) 0.07827 0.995
60 (333 K) 25 1181.5 (Uts) O. 1 1036 0.97 I
23 (296 K) 30 922.0 (th,) 0.058 1 7 0.983
40 (3 13 K) 30 928.6 (Ut,) 0.07776 0.992
60 (333 K) 30 1399.5 (Ut,) o. IO304 0.982
23 (296 K) 50 86 3.1 (thr) 0-06269 0.978
40 (3 13 K) 50 898.0 (th,) 0.1 1769 0.995
60 (333 K) 50 1133.1 (Ut,) 0.07293 O. 940
UFS = Ultimate Flexural Stress
The specific compliance J, (compliance after 1 s) was found to be approximately 80%
of compliance at 30 sec. The values of n were not only dependent on temperature. but also on
applied stress. This contrasted with the stress relavation experiments where n was almost
independent of mess. Higher values of n were observed in creep (- 0.07 - 0.1
uith stress relaxation (- 0.4 - 0.6). The higher value of n leads to a conc
1 ) as compared
lusion tiiat the
material showed more viscous behavior at constant stress (creep) tlian at constant strain
(stress relaxation). The effects of temperature and stress on n and J, are discussed in Sections
6.3.1 and 6.3.2.
Modef and Dkcussion 6-10
Figure 6-6.
Figure 6-7.
Experimental
temperatures
6
and calculated
ln t / t,
values of
1 O
flexural cornpliance
14
at 23% UFS at 3
O 25 UFS A 30 UFS u 50 UFS - Calculated
3 5 7 9 11 13 In t f t ,
Experimental and calculated values of flexural cornpliance at 23°C
temperature and three stress
Mode[ and Discussion 6- 11
Figure 6-7 shows the In-ln plot of flexural modulus at 23 O C temperature. The curves
are very close at different initial constant stress as conpared to Figure 6-6 where the curves
are separate at different temperatmes. The effect of temperature on creep behavior is more
pronounced than the effect of stress. This makes the material more wlnerable to creep
rupture at extended periods at elevated temprratures.
The statistical analysis was dso prrformed on rxperimental data to evaluate the
variations in fitting parmeters nt 95% CI and to validate the appropriateness of the model.
The results are tabulated in Table 6.4. The upper and lower confidence limits for n are plotted
at various temperature and 25% UFS in Figure 6-8. The experimental data lies within the
limits except at the beginning of the experiments where the effects of loading the specimens
were obsemed.
Table 6-4. Estimation of power law fitting parameters at 95% CI
Temperature ( O C ) Strain (%) Specific Cornpliance. Js (MPa-l) Time exponent. n
23 (296 K) 25 794.7 1 1,0179 0.07227 5 2.246E-03
40 (313 K) 25 1039.7 i 1.0158 0.07827 k 1.98 1 E-03
60 (333 K) 35 1181.5 1 1.0575 0.1 1 036 I 7.2 1 1 E-03
23 (296 K) 30 922.0 -t 1 .O22 1 0.058 17 k 2.765E-03
ciO(313 K) 30 928.7 i 1 .O206 0.07777 F 2.579E-O3
60 (333 K) 30 1399.5 i 1 .O41 5 0.10305 5 5.372E-05
33 (296 K) 50 865.2 I 1 .O275 0.06270 2 3 .43OE-03
40 (313 K) 50 898.1 1 1 .O243 0.1 1769 I3 .091E-03
60 (333 K) 50 1133.1 + 1.0924 0.07293 t 1.169E-02
Mode/ and Dkcussion
Figure6-8. Confidence Iimits of time esponent (n) at 95% CI. constant specific
cornpliance (J,) and 25% UFS
Long-term fleura1 creep experiments were also done to validate the Power Law fit.
The constants. time exponent and specific strain. were calculated based on 24 hour creep and
then the model was used to predict the long-term flexural creep strain. The esperiment was
conducted for a duration of 2.25E+07s (260 days). The results from the exprrimental and
calculated values at 20% UFS are s h o w in Figure 6-9. The model predicted the long-term
values within &IO%. which is a fairly good agreement with experimental data.
c. C ri)
f d
x 9
Screw Clamping Force
The experimental and predicted relaxation clarnping force at 23'C temperature are
shown in Figure 6-10 and 6.1 1. respectively. ï h e complete set of plots can be found in
Appendix B. Power Law parametes F, and n are tabulated in Table 6-5. The experirnental
data were well fiaed by the Power Law fits. The regression values are somewhat lower than
in the stress relavation experiments. but well above the acceptable range in genrral. Some
deviation was also observed near the end of the experiments. which was
electrical interference and heating of the strain gages.
1250 o 17% A 33% O 50% - Calculated
mainly due to the
Figure 6- 10. Experimental and calculated values of clamping force at 23C temperature and
three initial clarnping force as a percentage of pullout force
Mode1 and Discussio~t 6-15
Figure 6-1 1. In-In graph of experimental and calculated values of clamping force at 23C
temperature and three values of the initial clarnping force
The specific-clamping force was found to be approximateiy 90% of the original
clarnping force. The average value of n \vas found to be around 0.5 which was comparable
with that in stress relaxation experiments. Almost identical values of fitting parameten
supported that stress relaxation is the mechanism that causes the relaxation in the clamping
force. The effects of temperature and loading condition on n and Fs are discussed in Sections
6.6 and 6.7.
Model und Dkcusion 6-16
Table 6-5. Power Law for screw clamping force.
Temperature (C) Clamping Force Power Law Modei R"
23 (296K) 17% Fpo 457.4 (t/&) *a+Y1 0.9606
40 (3 13K) 17% Fpo 392.2 (Us) -0.ojzj 0.97 18
60 (333K) 17% Fpo 429.0 (t/t,) -0.0758 0.96 1 O
23 (296K) 33% Fpo 830.6 (th,) -0.0507 0.9703
40 (3 I X ) 33% Fpo 839.1 (th,) -0.058 I 0.980 1
60 (333K) 33% Fpo 93 1.1 (th,) -0.0719 0.96 1 O
23 (296K) 50% Fpo 1245.5 (th,) -0.0509 0.9923
40 (3 13K) 50% Fpo 1 149.4 (th,) 4.0527 0.9935
60 (333K) 50% Fpo 1250.8 (th,) -0.0536 0.9853
Again. to validate the accuracp of the model. statistical analysis vas perforrned using
actual data at 95% CI. The results are tabulated in Table 6-6. The upper and lower confidence
limits for n are ploaed at 23 "C temperature and various initial clarnping forces in Figure
6-12. The experimental data lie within the limits çxcept at the end where deviation was
O bsewed due to draft current in stnin gage.
Model and Dhcussion 6 1 7
Table 6-6. Variation estimation of power law fitting parameters at 95% CI
Temperature Clamping Force %F, Specific Clamping force (N) Time Exponent
F, = Fastener Pullout Force
o 0.17 Fpo a 0.35 Fpo O 0.50 Fpo - min - mau
Figure 6-12. Confidence limits of tirne exponent (n) at 95% CI . constant specific clamping
force (Fs) and 23C temperature
Model and Dkcussion 6-18
Time Exponent
According to Findley [28] and other researchers. n is normally independent of loading
conditions and temperature. ï h e values of n for the stress relaxation experiment are shoun in
Figure 6-13 and were found to be dependent on temperature but the value of applied strain
did not have much effect on n. Normally. with increasing temperature. n increases. but in
these stress relaxation esperiments the trend was slightly different: the mavimum value was
observed at 40 OC. Lking the average value of 0.055 for n would lead to an error of 1 1
percent in the force prediction at the end of 1 year. and 14 percent after 10 yrars.
290 300 3 10 320 330 340 Temperature (K)
Figure 6- 13. Time esponent for stress relaxation at di fferent initial strain
Figure 6-11 and Figure 6-1 5 show the value of the tirne exponent as a b c t i o n of
time at different loading conditions for the creep and screw clamping force experiments.
respectively. The values for creep increase with increasing temperature except at 50% UFS
Model and Dkcussion 6- 19
where the trend changed abruptly. The main reason was the early creep rupture in the
composite. which failed within 6 hours. The stress did not have much effect on n. In the
clamping force relavation experiments the values of n also follow the same trend w-ith a
higher deviation in values of n at higher temperature. The clarnping force did not have a large
effect on n while the temperature tends to increase it.
The effect of temperature on n is more important to understand because it changes the
dope of the In-ln curve and ultimately affect to a larger extent on the overall behavior.
290 300 3 IO 320 330 340
Temperature (K)
Figure 6-14. Tirne exponent frorn creep experiments at three initial stress
Mo& and Discussion 6-20
390 300 310 320 330 340 Temperature (K)
Figure 6-15. Time rxponent from clamping force experiments at three initial clamping
forces
Specific Modulus/ Corn pliance/ Force
The values of the specific constants Es. J, and F, are shown as a function of
temperature in Figure 6- 16. Figure 6- 17 and Figure 6-1 8 for stress relaxation. creep and
clamping force relaxation experiments. respectively. The specific constant is dependent
mainly on the initial value of modulus or compliance. In stress relaxation experiments. the
initial modulus was non-linear and dependent on both temperature and strain. The specific
modulus showed the same trend. In the creep experiments. the compliance behaved in the
same way and the specific cornpliance was observed to increase with increasing temperature.
The clamping force experiment showed different behavior than both the creep and stress
relaxation experiment. In the clamping force relaxation. the initial clamping force was
~'Model and Discussion 6-21
allowed to relax while no constraint was put on either stress or strain. This led to almost the
same specific modulus at initial clamping force and temperature.
290 295 300 305 310 315 320 325 Temperature (K)
Figure 6-1 6. Specific modulus from stress relaxation experirnents
-
O 25UFS O 30 UFS A - 40 UFS
300 310 320 330
Temperature (K)
Figure 6-1 7. Specific cornpliance fiom creep experirnents at three initial values of stress
Motlel and Discussion 6-22
Temperature (K)
Figure 6- 18. Specitic clamping force frorn clamping relaxation esperiments
6.7 Time-Temperature Superposition
The master curves are constructed with respect to the highest temperature (50 O C ) at
0.5 and 1.0% strain as shown in Figure 6-19 and Figure 6-20 respectivrly. The stress
relaxation curves are superimposed to a single smooth curve using a horizontal shifi factor a,.
The construction of a master curve enables prediction of the long-term behavior of the
composites. Both curves can be combined together using both horizontal and vertical shift
factors as show-n in Figure 6-2 1.
Model and Dkcmsion 6-23
O 5 In th, (s)
Figure 6- 19. Time temperature superposition at 0.5% Strain
Figure 6-20. Time temperature superposition at 1 .O% suain and three temperature
Mode1 and Dkcussion 6-24
Figure 6-2 1. Time-temperature superposition using vertical and horizontal shift
The enthalpy and shifr factors are tabulated in Table 6-7. The horizontal shifi factor is
ploned against temperature as showm in Figure 6-22. The shift factor obeys the .\rhennius
equation and values can be interpolated for any temperature.
t em stress The construction of a master cuve allows for the prediction of the ion,-
relaxation behavior of WFRP. The time scale can be extendeci to about 25 years on the basis
of only 48 hour stress relaxation experiments at three values of temperatures. Using the
master c w e . the approximate relaxation in modulus can be predicted to a minimum of 68%
at room temperature. For the ekqolation values. care should be taken as the relaxation
behavior changes quickly with changing temperatures and loading temperature.
Model and Discussion 6-25
290 300 310 320
Tempe nature (K)
Figure 6-22. Time dcpendent factor as a function of temperature at two strains
Table 6-7. Enthalpy and tirne-dependent constant tiom Arrhenius equation.
AH (Enthalpy)
Model and Dkcussion 19-26
Every efforts were made to reduce the errors in preparation of samples, experimental
procedure and data acquisition. To avoid the variability in composition specimens were
prepared in the begiming of the research. Same condition of temperature and pressure were
used on the sarne machines. The specimens were stored at room temperature in sealed
polyethylene bags to avoid moisture absorption. During the mechanical testing. speciai care
was taken to avoid any misaligrnent during sample loading. Strain gages were used to
measure actual strain during stress relaxation experiments. Creep specimens were loaded
manually and spnng jack was used to avoid shocks. All samples were condition for 3 hours
before loading to avoid any variation of temperature between the cross section of specimen.
The possible reasons of error in al1 of the experiment were drift curent in strain gages.
moisture absorption during storage and small variation of temperature during the penod of
experiment.
Conclusion 7-1
Conclusions
In recent years. extensive research has been conducted on many aspects of
mechanical and processing properties of WFRP. However. few studies have exmined
viscoelasticity and long-term properties. In this study. a cornprehensive experimental
progmm of research was carried out to investigate the stress relaxation and creep behavior
and to propose appropriate mode1 for long-term prediction of Mscoelastic properties of
WFRP. The investigation was hirther rxtended to study the threaded joint performance and
relaxation in clamping force was studied along with the basic joint performance evaluation
experiments.
Stress relaxation and creep esperiments suggested that the material is tempenture
dependent and showed non-linear viscoelastic behavior. High initial relaxation in stress was
observed in stress relaxation experiments. which continues with a constant êsponrntial rate
till the end of experimrnt. Creep strain also behaves in the sarne manner and was
exponentially dependent on time. Creep rupture was observed at higher stress and
temperature within 74 hours afier the loading. The effect of temperature on the viscoelastic
behavior was much more pronounced than the çffect of loading conditions.
Threaded joints were also evaluated with simple pullout and driving tests. Thread
engagement length and pilot hole diameter were found to be important in determining the
clamping or pullout load. The torque- clamping force relation was also investigated and
Camcar Plastite was found to be better than al1 other screws tested. Relaxation in screw
clamping force was also investigated for different condirion. Stress relaxation was found to
be the main mechanism dnving the relaxation in clarnping force. When the screw was
Conclusion 7-2
retightened after 2 hours the effect of memory was observed and the relaxation was much
lower than in original experiments.
A Power law model was proposed for stress relaxation. creep and clamping force
relaxation experiments. Good agreement benveen the proposed model and experimental data
was found for al1 experiments. Statisticai anaiysis was also done to validate the model and
eood results were obtained with 95% CI. The proposed model was used quite satisfactorily in C
various previous studies for as long as 26 years of creep prediction. Time-Tempcrature
superposition for stress relaxation experiments was donc as a data reduction method for long
term prediction. A smooth master curve was obtained using horizontal and vertical shih. The
horizontal shift factor obeys the Arhenius equation and it can br interpolated for intermediate
temperatures.
Recommendations
1. More extensive experimental should be done to charactenze the material
over a uide range of temperature and loading. A temperature range of -30 O C to +60°C
would heip us in determining the widest range of operating temperature.
2. Fatigue experiments and relaxation under dynamic load should be
performed to evaluate the mechanical properties under dymamic conditions.
3. More experiments should be performed for screw pullout and stripping
experiments. Various parameter should be considered such as driving speed.
misaiignment. screw boss design. pilot hole diarneter and engagement length.
4 Fastener clamping force relaxation should be done under wide range of
temperature and initial clamping force. A temperature range of -30 "C to +6O0C will give
us a practical range of operating remperature.
5. Fastener clamping force relaxation under dynarnic conditions should be
done to evaluate the effects of dynarnic loading and fatigue life
Reference 1
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B. E. Read and P. E. Tomlin (1997) "Creep and physical aging of injection molded
fiber reinforced polypropy lene". Pol ymer Engineering and Science. Vol 37. p 1572-
158 1
G . W. Weidmann and R M. Orgorkiewicz (1974) "Trnsile creep of a
midirectional glas fiber-epoxy laminate".
M. Silverman (1985) "Creep and impact resistance of reinforced thennoplastic: Long
fiber vs short fiben". ?Ofh Annual conference. Reinforced Plastic/ Composites
Institute. Society of Plastic Industry. 4-E. 1
P. K. Mallick (1988) "Fiber reinforced composites: materials. manufacturing and
design". Marcel Dekker. p270-27 1
K. C. Grarnoll, D. A. Dilliard and H. F. Brinson (1990). "Thennoviscoelastic
characterization and prediction of kevlad Epoxy composites laminates". Composite
Matenal: Testing and Design. Vol 9. p477-493
R F. Gibson, S. J. Hwang, G. R. Kathawate and C. H. Sheppard (1991).
"Measurement of compressive creep behavior of Glassi PPS composites using the
frequencyltime transformation methods". 23" International SAMPE Technical
Conference. p208-2 18
J. Plazek (199 1) "A mpopic review of the viscoelastic behavior of polymers". Journal
of non-crysalline solids. Vol 13 1. p836-85 1
Reference 5 a
B. D. Park and J. J. Balatinen ( 1 998) "Short term flexural creep behavior of wood-
fiber/polypropylene composites", Polymer composites. Vol 19. p3 77-3 82
Emri (1 996) Tirne-dependent phenornena related to the durability analysis of
composite stmctures", Durability Analysis of structural composite systems. Ed Albert
H. Cardon, A. A. Bakema, Rotterdam, Brook Field
B. E. Read, G. D. Dean and P. E. Tomlins (1988) Effects of physical ageing on
creep in pol ypropylene". Polymer. Vol 29. p2 1 59-2 169
J. S. Lai and W. N. Findley (1968) "Stress relaxation of non-linear viscoelastic
material under uniaxial strain. Transaction of the Society of Rheolog. Vol 12. pZ59-
280
J. George, M. S. Sreekala, S. Thomas, S. S. Bhagawan and N. R. Neelakantan
( 1 998) "Stress relaxation behavior of short pineapple fiber reinforced polyrthy lene
composites". Journal of reinforced plastics and composites. Vol 1 7. p65 1 -672
Thomas, J. George and S. S. Bhagawan (1998) "Improved interactions in
chemically modified pineapple leaf fiber reinforced polyethylene composites".
Composites Interfaces. Vol 5. pZO 1-723
S. Thomas, J. George, S. S. Bhawagan, N. Prabhakaran (1995) "Short pineapple-
leaf-fiber-reinforced low-density polyethylene composites". Journal of Applied
Polymer Science. Vol 57. p843-854
M. Gutman and R. Soncino (1995) Environmental effects on stress relaxation in
polyester-fiberglass composites. P o l p e r Composites. Vol 16. p j 18-52 1
S. Thomas, J. George, S. S. Bhawagan (1998) "Effects of environment on the
properties of low-density polyethylene composites reinforced with pineapple-leaf
fiber". Composites Science and Technology. Vol 58. pl4714485
Reference 6
M. L. William, R F. Lande1 and J. D. Ferry (1955) "The temperanüe dependence
of relaxation mechanism in amorphous polymer and other glass-liquids", Journal of
the Amencan chernical society, Vol 77. p370
T., Yeow, D. H. Morris and H. F. Brinson (1978) "A new experimentai method for
the accelerated characterization of composites material". VPI-E-78-3
J. Wortmann and K. V. Schulz (1995) "Stress relaxation and time temperature
superposition of polypropylene fibers". Polymer. Vol 36. p3 15-32 1
P. A. O'Connel1 and G. B. McKenna (1997) "Large deformation response or
polycarbonate: time-temperature. time aging time. and time-strain superposition".
Polymer Engineering and Science. Vol 37, p 1485- 14%
R. A. Malloy (1 994) *'Plastic part design of injection molding". Hanscr Publication
F. Dratschmidt and G. W. Ehrenstein (1997) "Threaded joints in g las fiber
reinforced polyamide". Polymer Engineering and Science. Vol 37. p74-I-755
R A. Malloy, S. A. Orroth and E. S. Arnold (1981) "Self threading screw boss
design". ANTEC. p744
C. L. Clark, R. Florence, D. J. Locke, C. Batros, R. Rozmus and M. Trapp
(1996) "Understanding the mechanical behavior of threaded fastenen in thennoplastic
bosses under load". SAE Transaction: Journal of Material and Manufachring. Vol
105. p294-398
Aniod A. Ogale (199 1) "Creep behavior of thermoplastic composites". Thermoplastic
composites materials. ed. Leif A. Carlsson. Elsevier Science Publisher. 705-232
Yeow, Y . T., D. 8. Morris and H. F. Brinson (1978) "The time-temperature
behavior of a unidirectional graphite/ epoxy composite materials" VPI-E-78-4.
A Experimental Data
A.1. Stress Relaxation
Table A-1. Tensile force at 0.5% strain
-~em~erature("C) 2 23 23 23 40 40 40 40 50 50 50 50
Width (mm) 12.88 13.25 12.98 12-93 11.8 13.05 12.8 11.8 13.03 12.9 13.35 13.23
Thickness (mm) 4.13 4.25 4 . U 4.57 4.5 4.25 4.36 4.37 4.35 4.47 4.99 4.35
Tirne (sec) Tensile Force (N)
O 366.1 396.0 462.4 434.5 252.0 215.2 301.4 137.8 268.7 21 1.1 2 19.8 186.1
Table A-2. Tensile force at 1 .O% strain
' ~em~ermre( 'C) 23 23 23 U 40 40 40 40 50 50 50 50
W idth (mm 12.8 12.93 13.83 12.14 12.8 13.01 13.2 12.78 12.82 12.84 12.89 12.91
Thickness(mm) 4.26 4.21 4.4 4-29 4.2 4.31 4 , a 4.32 4.56 1.28 4.52 4.22
Time (sec) Tensiie Force (N)
O 434.9 608.0 612.0 478.9 379.5 448.5 491.5 394.1 394.0 395.0 297.2 339.1
30 334.5 467.0 469.9 363.0 288.4 342.4 378.7 31 1.0 303.1 516.9 243.3 273.7
60 321.8 137.3 450.3 343.4 274.7 327.7 366.9 297.2 282.5 306.1 233.5 263.2
90 315.9 437.5 439.5 338.4 268.8 319.8 358.1 291.4 269.8 300.2 229.6 260.4 120 312.0 430.7 433.6 333.5 262.9 3 13.9 353.2 286.5 260.9 294.3 226.6 257.4
150 309.0 425.8 427.7 329.6 260.0 310.0 348.3 283.5 255.1 289.4 224.6 254.9
180 306.1 421.8 423.8 225.7 256.0 307.1 345.3 380.6 252.1 284.5 222.7 252.8
2 10 305.1 418.9 419.9 323.7 253.1 304.1 342.4 278.6 249.2 280.6 220.7 251.0 340 303.1 415.9 416.9 320.8 251.1 301.2 339.4 276.6 248.2 277.6 219.7 349.6
270 302.1 - I I 4.0 41 5.0 3 18.8 250.3 300.2 328.4 274.7 247.2 276.6 218.8 248.7
300 300.2 412.0 4 12.0 3 17.8 248.2 298.2 336.5 273.7 246.2 274.9 217.8 247.6
360 298.2 409.1 408.1 314.9 245.3 294.3 333.5 271.7 245.3 273.4 216.8 245.5
420 296.3 405.2 405.2 312.0 242.3 291.4 330.6 269.8 245.3 272.2 214.8 243.0
480 295.3 403.2 402.2 310.0 240.3 789.4 328.6 267.8 244.3 371.3 213.9 240.9
540 293.3 401.2 399.3 308.0 238.4 287.4 325.7 265.9 241.3 270.9 213.9 239.2
600 292.3 399.3 397.3 306.1 236.4 284.5 323.7 264.9 238.4 269.4 212.9 237.1
900 287.4 392.4 589.5 300.2 229.6 276.9 315.9 258.0 237.4 263.2 208.0 232.2
1200 283.5 386.5 384.6 295.3 223.9 271.7 3 12.0 255.1 237.4 259.8 204.0 237.8 1 500 280.6 382.6 379.6 292.3 220.7 267.8 304.1 252.4 336.4 237.1 202.1 224.6
1800 277.6 378.7 576.7 289.3 217.2 263.9 503.1 245.3 233.5 253.8 200.1 222.4
3 600 268.8 365.9 362.0 277.6 200.4 249.6 289.4 233.9 228.6 244.3 194.2 213.0 5400 263.9 355.1 356.1 269.8 196.9 239.7 281.5 228.3 223.7 339.4 186.4 208.7
7200 258.0 351.2 349.2 260.9 193.2 234.8 275.7 236.6 221.7 234.5 184.4 206.0
9000 253.1 348.3 36.3 258.0 189.6 230.1 271.7 223.3 218.8 231.5 183.4 203.1
IO800 250.2 543.4 342.4 255.1 187.6 224.3 267.8 222.6 216.8 230.5 182.5 201.1
1 U O O 246.7 338.4 336.5 352.6 183.8 220.0 262.5 223.7 215.8 229.6 181.5 198.2
18000 242.3 334.5 330.6 250.2 182.4 215.8 258.4 219.3 213.9 228.6 178.5 196.7
2 1600 240.3 530.6 327.7 248.2 t 8 1.5 213.9 256.0 216.8 2 10.9 227.2 176.6 194.4
86300 211.9 299.2 303.1 224.6 164.0 197.6 230.0 198.9 192.3 206.6 162.8 178.4
172800 197.2 287.4 284.5 212.9 162.6 188.5 219.2 196.2 183.4 199.6 154.3 170.0
- -- -
0.0EIOO 6.0Eto.1 1.2E+û5 I .8E+û5
Time (s )
(a)
Figure A-1. Tensile modulus at 0.5% suain (a) E vs t (b) in E vs in t
O.OE+OO 6.0E-04 ! . X 4 5 1.8EM5
Tirne (s)
(a)
5.5 1 I 2 6 10 14
ln Time (s)
@)
Figure .4-2. Tensile modulus at 1 .O% saain (a) E vs t (b) ln E vs ln t
A.2. Flexural creep
Table A-3. Flexural deflection at 25% ultimate flexurai stress (UFS)
'emperature (C) 23 23 23 23 40 JO JO 10 60 60 60 60
.oad (w) 1346 1346 1346 1346 1346 1336 1346 f 346 1346 1346 1346 1346
Vidth (mm) 12.30 12.17 12.10 12.19 12.20 12.25 12.20 12.22 12.10 11.30 11.90 11.90
lepth (mm) 4.20 1.20 4-15 4.18 4-10 4.20 4.20 4.20 4.28 4.30 4.25 4.30
ïme Flexural deflection (mm) 1
O
10
'O
20
50
8 O
! I O
!40
!70
ioo i60
120
180
500
JO0
1200
1500
1800
; 600
5400
7300
9000
10800
14400
18000
2 1600
86400
1 O8000
129600
15 1200
L 72800
ilppendix A-5
Table A 4 Flexural deflection at 30% UFS 'em perature ( C) 23 23 23 23 40 JO 40 40 60 60 60 60
.oad (gm) 1874 1874 1874 1874 1874 1874 1574 1874 1874 1874 1874 1874
Y idth (mm) 12.80 12.95 12.85 12.96 13.00 12.88 12.80 12.72 13.15 12.97 12.71 12.84
lepth (mm) 4-31 4-20 4.35 4-26 4.42 4.58 4.30 4.27 4.17 4.24 4-36 4-31 -. . ime Deflection (mm) I O O O O O O O O O O O O
!10
1-10
? 70
N O S60 120
180
540
500
900
l ZOO 1500
1800
j 600
5400
7200
9000
10800
1400
18000
2 1600
86400
1 O8000
129600
15 1200
172800
Appendir A-6
Table A-5. Flexural deflection at 40% UFS
'emperature ( C) 23 23 23 23 40 40 40 40 60 60 60 60
-0ad (w) 3408 2408 2408 2408 2408 2408 2408 2408 2408 2408 2408 2408 Vidth (mm) 11.65 12.16 12.40 12-07 12.25 12.28 12.15 12.15 12-19 12-18 12.24 12.30
lepth (mm) 4.34 4.45 4.40 4.40 4.19 4.21 4.38 4.31 7 4.40 4.33 4.50
ime Deflection (mm)
0.OEtOO 6.0E-W 1 .X45 i .8E+05
Tirne (s)
(a) (b)
Figure A-3. Creep cornpliance at 25% UFS (a) J(t) vs t. (b) ln J(t) vs ln t
e -
0.0E-tOO 6.0E'OJ 12E+û5 1.8EMj l i m e (s)
(a)
O 23C a JOC O 60C
0 23C 0 40C a 60C 6.5
2 61n Time (s) 10 14
(b)
6.5 - i - InTime (r) 1 O 14
Figure A 4 . Creep cornpliance at 30% UFS (a) J(t) vs t. (b) ln J(t) vs Ln t
61n Timc (r) 1 O
(b)
Figure A-5. Creep cornpliance at JO% UFS (a) J(t) vs t. (b) In J(t) vs In t
A 3 . Clam ping force relaxation
Table A-6. Clamping force relaxation at Z ° C temperature (F, = maximum pullout orce)
Initial Load 17F, I7F, 17F, 17F, ;3F, 33F, 33F,,,, 33FP 50FV 5OFP 50Fp 5OFP
Time (s) Clamping Force (N)
Appendix A-I O
Time (s) Clamping Force (N)
232.8 341.2 501.2 506.4 510.2 496.5 689.7
230.9 338.3 496.4 497.6 504.5 492.5 687.7
230.0 335.4 486.9 4903 495.5 485.9 685.6
226.3 333.0 479.8 484.6 487.5 481.7 684.8
223.6 228.2 476.6 480.5 484.8 478.4 690.1
220.8 326.6 477.5 480.2 483.3 478.3 691.6
320.8 325.6 474.9 480.6 482.0 177.4 686.9
219.6 325.8 471.5 480.7 479.2 475.8 687.8
220.3 325.4 468.1 478.6 477.1 473.5 689.3
219.3 324.5 465.0 479.0 474.4 470.4 692.6
219.7 323.3 462.4 480.5 473.5 469.4 691.4
318.1 522.6 466.9 487.5 477.8 471.2 692.3
216.8 1 . 8 465.5 484.8 476.2 467.1 691.8
218.1 3 19.8 459.6 183.4 473.9 464.7 690.8
215.7 5 19.4 457.2 481.9 472.4 461.9 687.6
215.5 2 17.9 456.7 481.2 471.6 461.1 682.0
209.6 3 13.3 453.5 480.1 469.6 455.7 653.5
211.4 311.2 444.0 6 1 . 453.1 447.5 634.4
209.6 304.1 429.0 438.7 433.9 437.7 634.1
210.9 305.1 423.4 441.0 434.8 435.9 673.3
216.6 295.4 447.9 495.1 474.2 459.5 681.5
225.3 264.5 446.0 493.6 472.7 454.9 656.3
722.3
7 18.6
716.2
713.7
7 14.7
714.5
709.2
708.8
709.9
71 1.3
7 IO. 1
710.1
709.8
707.9
704.6
700.6
675.2
659.6
668.1
692.5
693.1
673.0
Figure Ad. Clarnping force at 2j°C temperature (a) F, vs t (b) In F, vs ln t
1.100 7.5
1 200 - 7.0
Io00 t O
5 a L P) O 6.5
800 CL 3 M L - e 2 600 .- E 6.0 E Cu E G = JO0 s t - 5.5
200
5 .O
, 0 17Fpo 0 35Fpo a SOFpo
a .. .-..i4
O O 0 '--%.
O Q o O----%
O--\
O 2 6 1 O 14
O.O.E-00 6.0.E-04 1 LE105 1 -8.E-05 In Time (s) Erne (s) (b)
(a)
iippendix A-2 1
Table A-7. Clamping force relaxation at 40°C temperature - --
Initial Load 17F, 17F, 17F, 17F, 33F, 33F, 33Fp 33F, 50Fp jOF, SOF, 5OF,
Time (s) Clamping Force (N)
rime (s) CIamping Force (N)
$9600 246.5 202.6 219.9 229.8 j94.8 463.9 439.1 497.3 734.7 718.3 694.6 699.9
O 1 0 . 0 . E a 6.0.Eto.l I3.E"05 1.8.E+05
Erne (s)
(a)
2 6 1 O 14 In Time (s)
Figure A-7. Clarnping force at 40°C temperature (a) Fpo vs t (b) ln Fpo vs In t
Table A-8. Clamping force relaxation at 60°C temperature
l~irne (s) 1 Clamping Force (N)
Initial Load 17F, 1 17F, 1 17F, j 17F, 1 33F, 1 33F, i 33F, / 33F, 1 jOF, / jOF, 1 jOF, 1 SOF, I
Time (s) 1 Clamping Force (N)
t I7Fpo a 35Fpo , 50Fpo l ZOO
Figure A-8. Clamphg force 3t 60°C temperature (a) Fpo vs t (b) In Fpo vs ln t
.
d
7.5 r
A 7 .O 5 O tr L
3
30 e U
62i
Ê " 6.0 G c -
5.5
5 .O
1
o 1 7Fpo 0 3 5Fpo b SOFpo 1
A b A-
-"\ O "
0-
\
0.O.EtOO 6.0.E-OS I . X t 0 5 1.8.E+05 2
-OO\
,
61n Time (s) 10 14
Tirne (s)
(a) (b)
B.1. Stress Relaxation 1 7 M
lated
Figure B-l Experimental and calculated Tende modulus at 0.5% Strain (a) E vs t. (b) ln E vs In
- calculated O 23C A K O 5 o c - calculated
A
Figure B-2. Experimental and calculated tende modulus at 1 .O% strain (a) E vs t. (b) ln E vs In t
Appendix B-2
Table B-1 . Power law model for tende stress relaxation (t, = 1 sec)
Temperature C S train Power Law mode1 R~
B.2. Creep
jaX) J
O.OE4û 6.0E-OJ 13E45 1.8EM5 - 9 6 10 13
t / tr l n t l t s
(a) (b)
Figure B-3. Experimental and calculated creep cornpliance at 25% UFS (a) J vs t (b) In J vs ln t
O 0 6oc - Catculated
0 23C A J0C
O 60C - Calculated
Figure B-1. Experirnental and calculated creep compliance at 30% CiFS (a) J vs t (b) ln J vs ln t
1 0 13C A MC- Calculated 0 23C A UK: - Calculated
Figure B-5. Experirnental and calculated creep compliance at 50% UFS (a) J vs t (b) In J vs In t
Table B-2. Power law mode1 for flexural creep cornpliance
Temperature (C) Stress (% UFS) Power law R~
23 (296 K) 25 794.7 (tt&) 0.07226 0.993
40 (3 13 K) 25 1039.7 (t/&) 0.07827 O .995
60 (333 K) 25 1 18 1.5 (th,) O. 1 IO36 0.97 1
23 (296 K) 30 922.0 (t/&) 0.058 17 0.984
40 (313 K) 30 928.6 (Uh) 0.07776 0.992
60 (333 K) 30 1399.5 (Ut,) 0.1 O3W 0.982
23 (296 K) 50 865.1 (LI&) 0.06269 0.978
40 (313 K) 50 898.0 (t/&) 0. II769 0.995
60 (333 K) 50 1133.1 (Ut,) 0.07'293 0.940
B.3. Clamping force relaxation
0 I70G a 3396 0 5096 - Calculated
17% 33% O 5W.b - Calculated
Figure B-6. Experimentai and calculated clamping force at 17% F, (a) F, vs t (b) In F, v s h t
1250 0 17?h A 33% 0 50% - Calculated
IF! 33%
a 5OO/o - Calculated
Figure 8-7. Experimentai and calculated clamping force at 33% F, (a) F, vs t (b) ln F, vs ln t
1250 0 IP'O A 33% 0 5096 - Calculated
m
a 50% - Calculated
Figure B-8. Expenmental and caiculated clamping force at 50% F, (a) F, vs t (b) ln F, vs In t,
Table B-3. Power law rnodel for screw clamping force.
Temperature (C) Clamping Force Power Law Mode1 R~
23 (296K) 17% Fpo 457.4 (ths) -0.049 1 0.9606
17% Fpo
60 (333K) 17% Fpo 429.0 (tls) -0.0758 0.96 1 O
33% Fpo
40 (313K) 33% Fpo 829.1 (Vk) -0.0581 0.980 1
33% Fpo
23 (296K) 50% Fpo 1 245.5 (th,) -0.0509 0.9923
60 ( 3 3 K ) 50% Fpo 1250.8 (Vt,) 4.0536 0.9853
C Screw Dimensions
(a) @)
Figure C-1. Screws (a) General purpose Screw for wood [ I l (b) Plastitea Screw [t]
Table C-l. Typical dimensions of screw (ail dimension are in mm)
Wood Screws Plastitea
Root Diameter (d, ) 3.2 3.23 (max)
5-12 (min)
Outer Diameter (4) 4.75 4.5
Head Diarneter (dh) 8 8
Thread Angle (a,) 60 48
Helix Angle (ah) 120 110
Thread per inch 12 16
' Crown bolts. California USA ' Carncar Textron. Gananoque. ON. Canada
Figure C-2. Post modeled inserts [II] (a) NFPAB (b) PPB8 (Interna1 threads are $10-32 and al1 dimensions are in mm)
3 PENN Engineering and Manufacturîng, Danboro. Pennsylvania USA
D Data Acquisition System for Screw Testing
D.1 Load Ce11
Button-type load ce11 was designed and manufactured to measure different performance
characreristics of fasteners. Detailed dnwings are s h o w in Figure D-l
Figure D- 1. Load ce11 (a) Cylinder. (b) Plate and (c) Complete load ce11 (al1 dimensions are in mm and not to scale)
Two element. 90' tee stack rosette gages (CEA-13-062WT-350) were purchased from
Intertechnology Inc.. Toronto. Canada. Two gages were used in each load cell to reduce the effect of
misalignment and bending and to increase the output voltage. The strain gages were glued on
opposite side of the cylinder using the standard procedure as described in Catalog A-110-4, Bulletin
PB-108. 309A. Intertechnology Inc.). The upper and Iower plates were glue to the cylinder f i e r the
saain gage tabs were soldered to shielded electricai cables.
Appendu D-2
D.2 Data Acquisition Hardware
A multifunction 1/0 card (ATMIO-16XE-50) was purchased fiom National Instruments Inc.. The
system was capable of acquinng total of 20.000 sarnples/sec at 16-bit resoiution fonn 16 single ended
or 8 differential analog inputs. !? i s o had the capability of data uansfer via a 2 channel analog
output. 8 channel digital I/O. and two up down counters. Strain gage accessory SC 2043-SG was also
purchased from National Instruments to connect the load cells and torque sensor directly to the card.
The suain gage accessory was capable of conditioning 8 load cells usine a regulated 5V intemal or
10V extemai power supply.
The torque sensor (S WS- 1 O) was purchased from Transducer Techniques. California. USA. It was
capable of measwïng a maximum of 120 in-lb (13.6 N-m) torque. The data acquisition hardware
system was installed on a 486 computer running under WindowB 95 via an [SA bus as shown in
Figure D-2
Power Supply sws -10
AC 110V O 0
AT M O 16X-E50 .
0 n
SC 2043-SG =A/ ISBJ AT bus
Figure D-2. Data Acquisition Hardware
D.3 Data Acquisition Software
Software for data acquisition was designed on Visual Basic 6.0 using standard modules provided by
National Instruments. The screen shots are shown in Figure D-3 to D-5
- .Th- fort- [-for &hanneQI - - -- --.. -.-- .---- -- -- -4- -. .-- - - ---- ---- I
Second Third Fwth Fdth I
Durution [minj
Figure D-3. Main Screen
Appendix D-d
Press Channel number to adivate data acquisition . .-Fi-,+ ..-- A . .
Lod one qell at a Cme .h"f 6/99 1 :26:a .. -:. . . .- *- * ..'C . . . K i * - -**.-
Channal - L d @ m t a n t intoryds Toque r -2 .. a . T o t a I i ~ i ' < : 1 4%, r+ac;fy . A d - . . - . . Z.?.?.Y> 11 -301 736496373 10.1 2641 nsm4356 S. -... - a. c- 19.5445556640625 ::?Fi,
. . c. - - . rn - . , .- '~,:'*y,,"~' ' . * ' . 7
. -*, ,S.- . WdMCLosd OK J .-
. . r t . . <-, ... .i.i 7. il-
. . . .-,:.- '. - -
.,. . +,=<i.;;-.:s Unit - +.-...-.*--.
&Acqirisiti#i . : . . 1 '.-. . . .. : ,
A0 1 ~ & t t D o n e ( S t i w t h ~ 12n6/991:2552PM i; 19,4867256637169.' -. - - . . . - - . - . I I . . ,
Figure D-5. Data Acquisition Screen