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