The mechanical behaviour of particle filled thermoplastics
Citation for published version (APA):
Vollenberg, P. H. T. (1987). The mechanical behaviour of particle filled thermoplastics. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR272161
DOI:
10.6100/IR272161
Document status and date: Published: 01/01/1987
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The Mechanical Behaviour
of
P~rticle
Fitled Thermoplastics
The Mechanical Behaviour
of Partiele Fitled Thermoplastics
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnificus, Prof. dr. F.N. Hooge, voor een commissie aangewezen door het college van dekanen in het openbaar te verdedigen op
dinsdag 29 september 1987 te 14.00 uur door
Peter Hendrilws Theodorus Vollenberg
Dit proefschrift is goedgekeurd door de promotoren:
Prof.dr. D. Heikens en
CONTENTS Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Introduetion Preliminary experiments
The machanical properties of chalk filled polypropylene
The dewetting stress of glass bead filled polystyrene and polypropylene The dewetting stress of polystyrene filled with irregularly shaped chalk particles
The dewetting stress of polystyrene filled with submicron titanium-dioxide particles
Partiele size dependenee of the Young•s modulus of filled polymers ·Part 1
Partiele size dependenee of the elastic modulus of filled polymers Part 2
The ultimata properties of glass bead filled SAN 1 5 25 45 56 61 80 101
Summary Samenvatting Dankwoord Curriculum Vitae 116 118 120 122
CHAPTER 1
INTRODUCTION
1.1. BACKGROUND OF THE INVESTIGATION
Plastics are important potential substitutes for the traditional materials. In general. the advantages of polymerie materials are: the easy processability, the low density and the corrosion persistancy. A serious drawback of plastics is that for a large number of applications the mechanica! properties do not come up to the requirements. For this ~eason special attention is being paid, in particular by industrial research departments, to the improvement of the mechanica! properties of polymerie materials.
One of the methods to reach this goal is the addition of a second phase to polymers [1-7]. In this way a
composite material is created. A benefit of composites is that by a variation of the kind and amount of the filler, and the degree of adhesion between the filler and the polymer, the mechanica! properties can be optimized for a certain application.
Also in our group at the Eindhoven University of Technology the mechanica! behaviour of polymer composites is being studied. This investigation has a fundamental character and is performed mainly with model-fillers dispersed in model-polymers [8-10].
1.2. AIK OF THE PRESENT STUDY
During the investigation the effects of inorganic fillers on the machanical properties of composite
materials were studied. The aim of this investigation was to gain insight into the deformation mechanisms that are responsible for the machanical properties of a composite.
The effects of a varlation of the partiele size of the filler, the filler content, the shape of the filler
particles and the interfacial adhesion on the properties of four different thermoplastics were examined. It was the intention to explain the observed differences
qualitatively and where possible quantitatively on basis of a study of the microdeformations.
1.3. SURVEY OF THIS THESIS
In chapter 2 the results are discussed of the machanical tests on chalk filled polypropylene. This
investigation had a preliminary character and was aimed at locating points of interest for further research.
One of the results discuseed in chapter 2 is that the dewetting stress seems to depend on the partiele size of the filler. In chapter 3 a quantitative model is given which describes this behaviour. The equation was checked experimentally and fo.und to hold true for glass bead filled polypropylene and polystyrene.
In chapter 4 this equation is modified in order to make it applicable to irregularly shaped filler particles. As demonstrated by the results of the experiments with chalk filled polystyrene, also in that case the agreement between the theory and the experiments is excellent.
An implication of the dewetting stress equation is that for very small filler particles the theoretica!
dewetting stress is higher than the fracture stress of the material. As is ·shown in chapter 5 for polystyrene filled with submicron titaniumdioxide particles, the filler behaves as i f it were chemically bonded to the P,olymer
matrix.
The results of a study of the Younq•s modulus as a function of the partiele size of the filler are discussed in chapter 6. Unexpectedly, the Younq's modulus appears to increase with decreasinq partiele size of the filler. Five possible explanations for this behaviour are examined, of which all but one could be ruled out.
The remaininq explanation is based on the assumption of a special morpholoqy of the polymer matrix surroundinq the filler particles. This explanation is sustained in chapter 7 with the results of annealing- and solid state NMR experiments.
From chapter 8 it appears that the fracture properties of a composite depend on the partiele size of the filler. An optimum in the fracture properties is reached at a certain filler partiele size to sample thickness ratio. An adhoc explanation is presented.
REFERENCES
1. L.E. Nielsen. "Mechanica1 Properties of Polymers and Composites. Vol. 1 and 2" (Marcel Dekker. New York. 1974).
2. C.B. Bucknal1, "Touqhened Plastics" (Applied Science Publishers. London, 1977).
3. D. Hull. "An Introduetion to Composite Materials" (Cambridge University Press. cambridqe, 1981). 4. M.O.W. Richardson, "Polymer Engineering Composites"
(Applied Science Publishers. London. 1977).
s. D.R. Paul and
s.
Newman, "Polymer Blends, Vol. 1 and 2" (Academie Press, New York. 1978).6. J.A. Manson and L.H. Sperling, "Po1ymer Blends and Composites" (Plenum Press, New York, 1976).
7. D.R. Pau1 and L.H. Sperling, "Multicomponent Polymer Materials" (American Chemica! Society, Washington, 1986).
8. W.M. Barentsen. "Some Machanical Properties of Polymer Blends" (Ph.D. Thesis, Eindhoven, 1972).
9. S.D. Sjoerdsma, "The Deformation Behaviour of Polystyrene-Low Density Polyethylene Blends" (Ph.D. Thesis, Eindhoven, 1981).
10. M.E.J. Dekkers, "The Deformation Behaviour of Glass Bead-Filled Glassy Polymere" (Ph.D. Thesis, Eindhoven, 1985).
CHAPTER 2
PRELIMINARY EXPERIM!NTS
THE MECHANICAL PROPERTIES OF CHALK PILLED POLYPROPYLENE
2.1. INTRODUCTION
Polypropylene (PP) is a commercially important polymer [1], which is of practical utility in a wide variety of applications. Because of its morphology [2,3] the
mechanical properties of PP are moderate, but if one wants to extend the field of application of this material. an impravement of the mechanica! properties is mostly
necessary. A relatively easy way to imprave the mechanical properties of a polymer is the addition of filler
mateiials. In general, inorganic fillers or short glass fibers are applied to imprave tbe stiffness [4,5],
whereas tbe addition of a rubbery phase is favourable to tbe toughness of a polymer [6. 7].
In tbe present study the impravement of the modulus of PP, through the addition of particulate chalk, a
commercial filler, was investigated. The chalk particles are very irregularly shaped. but tbeir average aspect ratio's were close to unity. The mechanica! behaviour of chalk filled PP has been investigated, both under low speed and high speed testing conditions. as a function of the size of the chalk particles, tbe volume fraction of the filler and tbe degree of adhesion between the polymer
and the filler.
Because of the preliminary character of this study, the aim was not so much as to explain in all depth the observed phenomena, as to locate points of interest for further research.
2.2. EXPERIMENTAL
As matrix material a special moulding type of PP, HM6100 (Shell), was used. As filler three different types of chalk particles. with respect to their mean partiele diameter, were used: Queenfil 120 {ECC), diamet,er 3. 5
~m. Durcal 40 (Omya), diameter 30 ~. Durcal 130 (Omya), diameter 130 ~. Pure chalk particles were
applied in order to obtain a system in which the adhesion between the filler particles and the polymer matrix was very poor. Perfect adhesion between the filler and the polymer was created by treating the chalk particles with the adhesion promotor (CH30)3 Si(CH2) 3 NH(CH2) 2'NHCH2 -C6H4 - CH = CH2.HC1, Silane Z6032 (Dow Corning) [8]. The adhesion promotor was applied in the following pre-treatment.
To a suspension of 50 g chalk in 85 ml methanol, 15 ml Z6032, 1 ml water and 1 ml acidic acid was added. This mixture was stirred for 4 hours, after which it was centrifuged to obtain a sediment of chalk. The sediment was wasbed with 85 ml methanol, centrifuged again and dried at room temperature. In this way a very thin layer of coupling agent on the particles was obtained.
The polymer and the filler were mixed on a two roll mill at 190°C. The filler content was varied in the range of 0 to 25 vol.\. Tensile bars and notched Izod bars were machined from compression moulded sheets. in accordance with ASTM D638 III and D256. The tensile tes.ts were
performed on an Instron tensile tester, which was equipped with an extensometer (1
0
=
50 mm), at a strain rate of 0.02/min. A Zwick impact tester was used to determine thewere performed in a conditioned room at 20°C and 50\ rel. humidity. The degree of crystallinity of PP was determined with a DuPont DSC/DTA. The effectiveness of Z6032 as a coupling agent as well as the dispersion were checked by taking micrographs of fracture surfaces with a Cambridge scanning electron microscope (SEM). Before fracture the samples were immersed in liquid nitrogen for a few minutes. 2.3. RESULTS AND DISCUSSION
2.3.1. Degree of adhesion
The micrographs of the fracture surfaces in Figure 1 show clearly the effect of the pre-treatment with Z6032 on the interfacial adhesion between the chalk particles and PP.
Figure 1.
A
B
The fracture surfaces of PP filled with pure chalk (A) and of PP filled with chalk treated with Z6032 (B).
lt is quite obvious that the pre-treatment with the coupling agent causes an excellent adhesion between PP and the particles (Figure lb). whereas the absence of this treatment renders a system in which the adhesion is very poor (Figure la).
2.3.2. Stress-strain behaviour
There was a clear distinction between the results of the tensile tests of the composites which contain poorly adhering and excellently adhering chalk particles.
Therefore these two systems are discussed seperately. P9orly adherJnq chalk
The stress-strain diagrams in Figure 2 of PP filled with poorly adhering chalk reveal that the beh.viour is a function of the partiele size of the filler.
In the case of a poorly adhering filler. tnree successive stages occur during a tensile test [9-11]: lineair elastic behaviour. dewetting of the filler particles and plastic deformation. It is to be expected that the second stage, dewetting, occurs as soon as the strass-strain curve turns off from the elastic line.
It is possible to apply the Griffith theory [12} to the phenomenon of dewetting. If we assume that the size of the dewetting cavity at the filler partiele is
proportional to the radius r of the particle, the Griffith theory prediets that the cavity is formed at a stress which obeys a formula of the form:
-%
0dewetting
=
A · r (1)A is a constant that depends on the system. Therefore this theory prediets that in the case of large particles
dewetting will take place at a lower stress than in the case of small filler partic1es. This is in agreement with the observed strass-strain behaviour (Figure 2).
It is noteworthy that the process of dewetting in the material filled with 3.5 1J.IIl particles is initiated at about the same stress level at which also in the case of the raferenee PP the turning off from the elastic line is observed. From this the preliminary conclusion could be drawn that in case of still smaller filler particles dewetting does not occur, as in that case the plastic
Figure 2. 30 20 10 A 0 0 5 10 15 é <X> '0 20 Q. 5 b B 0 0 5 10 15 E<X> ~ 20 5 b 10
c
o~---~---~---0 5 10 é (%)Stress-strain diagramsof pure PP (A), of PP filled witb 20 vol., of poorly adbering 130 wm cbalk particles (B}. and of PP filled witb 20 vol., of poorly adbering 3.5 ~m
cbalk particles (C). Fracture is indicated by a vertical arrow.
deformation processas are initiated at a lower stress than dewetting and become responsible for the bending off of the curves.
As the used chalk particles have a very broad partiele size distribution, it is not justified to apply equation {1) guantitatively. For this reason further research is necessary with filler materials that have a narrow
partiele size distribution (e.g. glass spheres), so that final conclusions can be drawn on the applicability of a Griffith-like theory.
At the applied strain rate, a material like PP usually displays necking from a strain of about 20%. As can be seen from Figure 2, in the case of the filled polymer the materials break before a strain of 20\ is reached and therefore necking does not occur. This will be discussed in more detail in a following section.
g~cellently adherinq chalk
In Figure 3 the stress-strain diaqrams of PP filled with excellently adhering chalk are shown as a function of the partiele size of the filler. It can be seen that the turning off from the elastic line for all three strass-strain curves takes place at about the same stress level. At this point the local plastic deformation processas and
the diffuse shearing as in pure PP are initiated. As a result of the stress concentration at the chalkiparticles, the local processes will start at the partiele matrix interface.
According to Goodier [13] the stress concentration at a spherical filler partiele is independent of the radius of that particle. As a first approximation the chalk particles can be considered to be spherical.
Therefore the stress at which the plastic deformation is initiated should be independent of the size of the chalk particles. This is in agreement with the experimental results .
. From Figure 3 and 4 it can be concluaed that the yield stress depends on the chalk concentration and on the
Figure 3.
~
20 10 o~---~---o 5 ~ 20'
10 0~---r---P ~ 20 0 ~ 10 0 5 10 E C%) A Bc
o~---~---~---~---0 5 10 15 E C%)Stress-strain diagrams of PP filled with 15 vol.% of excellently adhering 3.5
wm
(A). 30wm
(B) and 130 'IJ.m (C) chalk particles. Fracture is indicated by a vertical arrow.Figure 4. 29
.-0 ·----Q_ 25'
~ ()') ()') 11;!....
()') .---6-c 21 ...J w~
;;:: 17.,
13 0 10 20 30 VOL.% FILLERThe yield stress as a function of the volume fraction of the filler for 3. 5 )LIII ( • ) , 30 vm ( D.) and 130 lLm ( •) chalk partieles.
partiele size. The yield stress is defined bere as the maximum in the a-E diagram. From Figure 4 it appears
that tbe yield stress of PP filled with adhering particles is always lower than for pure PP.
This can be explained as follows. The strain e of a material during a tensile test can be divided into the strains caused by the different microdeformation processes: elastic deformation (ee1}. local microdeformat~on
(e10c) and diffuse microdeformation (ediff). erazes
and sbear bands are eonsidered as local microdeformations, whereas the process of diffuse shearing in PP, whieh oceurs in the bulk of the matrix in relatively large volume elements, is a typical example of a diffuse microdeformation process. As a first approximation the total strain e ean be assumed to consist of a series conneetion of tbe three strains [14]:
(2)
The amount of strain caused by the microdeformation processes is of course a function of the applied stress and the deformation time. Moreover. the presence of local microdeformations has effects on the propagation of the diffuse microdeformation process. Therefore, equation (2) can be rewritten into:
(3)
(4)
It is to be expected that at large deformations, as is the case at the yield point of PP. the contribution of the local microdeformations to the total strain is neglegible [15,16]. For this reason equation (4) can be reduced to:
(5)
From equation (5) it appears that. given a total strain e, the stress a tends to be higher in case of a diminishing strain caused by diffuse microdeformations. Consequently, an exp1anation for the increasing ay
with decreasing filler partiele size could be that in the case of the smaller filler particles the diffuse
microdeformation process is greatly hampered, which causes ediff to be small.
The hamparing of the diffuse microdeformation could be due to the presenee of the local microdeformations.
Assuming that the area of a craze or shear band is proportional to the area of the filler particle, a "blocking area" (BA) can be introduced:
BA
where
c
1 is a constant and n is the number of filler particles with a radius r. Combination of equation (6)with eguation (7):
n
where ~ is the volume fraction of the filler and c2 is a constant. gives:
c3 is a constant.
(7)
(8)
According to eguation (8) the blocking area is
inversely proportional to the filler partiele size. which supports the above mentioned explanation.
2.3.3. Necking in chalk filled PP
From experiments it appears that the strain. at which necking is initiated in chalk filled PP. depends on the volume fraction chalk. As larger volume fractions of chalk are applied, the strain at which necking occurs increases, until at about 10-20 vol.\ filler necking even no longer takes place at all (see Table 1).
This can be explained as follows. Necking is a process of shearing {bulk flow) that spans the whole cross-section of a tensile bar. As said before, in the case of a filled polymer, the filler particles act as stress concentrators and therefore the local microdeformation processes
shearband formation and/or erazing take place at these filler particles at rather low applied stresses.
These microdeformation processes are initiated
throughout the whole tensile bar and disturb the diffuse process of necking in the way discussed before. This makes necking impossible in more highly filled polymers.
vol.\ filler 0 5 15 poor adhesion filler partiele size
3.5~m 130~
23\ 21\
fr.l6\ fr.23\
excellent adhesion filler partiele size
3.5~ 130~
23\ 22\
fr.9\ fr.l8\
Table 1. Strain at which necking is initiated or fracture occurs (indicated as fr.) inchalk filled PP.
2.3.4. Young•s modulus
The Young•s modulus of a composita. consisting of a matrix material and a dispersed phase that are both structureless (continuous). is independent of the
dimension of the dispersed phase. The local stresses in the composita under load are only dependent on the ratio of the distance between particles of the dispersed phase to the dimension of these particles. At a certain volume fraction of dispersed phase. this ratio is constant and therefore independent of the dimension of the dispersed phase.
Kerner [17] has derived an equation. which has been modified for the maximum packing density of spheres by Nielsen and Lewis [18]. that describes the Young•s
modulus of particulate filled polymers quite accurately. In this equation the Young•s modulus is of course
Fiqure 5. 3. 7
~
3. 1 A/
til ::::> _, ::::>i
2.5 I IJJ 1. 9/
A 1.3 0 10 20 30 VOL. % F ILLER 3. 7 'êi 3. 1 ~ ~ =Ii
2.5 I IJJ B 1. 9 1. 3 0 10 20 30 VOL% FILLERThe Younq•s modulus of PP filled with
excellently (A) and poorly adhering (B) chalk particles as a function of the volume fraction of the filler for 3.5 lUil ( e ) . 30 lUil {~)
and 130 lUil ( • ) chalk particles. In A the curve is calculated with the Kerner equation.
pp chalk Young•s modulus (MPa) 1560 35000
maximum packing density +m á 0.64
Poisson•s ratio
0.42 0.20
Table 2. Data used for the calculations according to the modified Kerner equation
In Figure 5 the experimental Young•s moduli of PP filled with excellently adhering chalk and poorly adhering chalk are plotted as a function of the volume fraction filler.
The Young's moduli of PP filled with excellently adhering chalk particles fit the modified Kerner equation very satisfactory. The data needed for the calculations are listed in Table 2.
surprisingly, the Young•s moduli of PP filled with poorly adhering chalk particles appeared to be dependent on the partiele size of the filler. In the case of the 30
~m chalk particles the modulus is in accordance with the predictions according to the Kerner equation, but the 3.5
~m chalk particles cause bigher and the 130 ~ chalk particles cause lower Young•s moduli. Because of the semi-crystalline character of PP it was investigated if the morphology and/or the crystallinity of the PP-matrix was affected by the presence of the chalk particles. With DSC the degree of crystallinity was determined of filled PP as a function of the volume fraction of 3.5 ~mand
130 ~m chalk particles. In Figure 6 the results are shown.
Fiqure 6. 70
8
65>-....
~ ..J ..J 60•
•
<--·
.... .-(/)•
5
•
A•
55 50 +---,,---,.----...., 0 10 20 30 VOL.% FILLER !50 E .3-LIJ 100 !::! (/) LIJi
B 50 '---0 0 10 20 30 VOL.% FlLLERThe crystallinity (A) and the size of the spherulites (B) of PP as a function of the volume fraction of the filler for 3.5 ~
Within the ranges of experimental error, the degree of crystallinity appeared to be independent of partiele size and volume fraction of the filler, and equal to that of pure PP. So the partiele size dependenee of the Young•s modulus is obviously not caused by differences in the degree of crystallinity as such.
Another explanation was that a certain layer of PP at a filler particle. e.g. the first row of spherulites, acts as an interphase. If the size of this interphase is small enough. say about 1 ~m. its Young•s modulus can be assumed to have a value between those of PP and chalk. If the thickness of the interphase is assumed to depend hardly on the size of the filler particles. the amount of inter-phase along with the Young•s modulus of the material in its entirety. would increase with decreasing partiele size.
The application of a
o
2-plasma etching technique made it possible to study the size of the spherulites of PP filled with 3.5 ~ chalk particles with the SEM. The introduetion of chalk particles in PP causès a
considerable drop in the size of the spherulites (Figure 6), but the particles always appeared to be much smaller than the spherulites, which is in contradiction with the assumption of an interphase.
It is therefore not clear whether. and how. the size of the spherulites plays a part in the explanation of the partiele size dependenee of the Young•s modulus. Further research is necessary, e.g. with an amorphous polymer as a matrix material, to answer the question if the partiele size dependenee is caused by the semi-crystalline
character of PP.
2.3.5. Notched Izod Impact Strength
The results of the impact tests of PP filled with poorly adhering and excellently adhering chalk particles are presented in Figure 7. In the case of perfect adhesion an increasing amount of filler results in a decreasing impact strength, whereas in the case of poor adhesion a
F'igure 7. 3. 7 ti'
f"\
:::E 3.1'
A ..., 0\
Clo,o/o
\
0 !::::! Cl 2. 5 LIJ 0 -:r: u ·~ 0 -.... 0 z ·---1.9•
1. 3 +---.---.---., 3. 7 ~ ..., 3.1 0 8 !::::! Cl 2.5 ~ u .... !i 0 0 10 20 30 VOL.% FILLER 0~•
o-_0
----o-10 20 30 VOL.% FILLER BThe notched Izod impact strength of PP filled with excellently (A) and poorly adhering (B) chalk particles as a function of the volume fraction of the filler for 3. 5 1Lm ( •) and 130 1Lm ( o ) chalk particles.
maximum in the impact strength is observed at a certain volume fraction of the filler. The location of this maximum depends on the particle size of the filler.
The difference in behaviour of PP filled with
excellently and poorty adhering chalk has to be explained with a fundamental difference in deformation behaviour. Very special equipment is needed to observe the
deformation mechanisms during a Izod impact test. Unfortunately those facilities were not available. Instead, the deformation mechanisms were studied under a light microscope during a (slow) tensile test.
At this point i t should be admitted that i t is well possible that the deformation behaviour depends on the speed of testing. Therefore, the explanations based on this study have to be considered as preliminary, and a study of the deformation mechanisms at high speed should eventually lead to final conclusions.
The microscopic study showed that at perfectly adhering chalk particles exclusively crazes are created. This could explain its decreasing effect on the impact strength.
1
A
B
Figure 8. Crazes formed at an excellently adhering chalk
particle (A) and cavitation at a poorly adhering chalk particle (B), both in a
PP-matrix. The arrow indicates the direction of the applied stress.
By increasing the amount of perfect adhering chalk the "tough" deformation mechanism shearing of PP is
increasingly replaced by the "brittle" mechanism erazing (see Figure Sa), in the same way as discuseed in the section "stress-strain behaviour".
During a tensile test excessive cavitation takes place at poorly adhering chalk particles (Figure Sb), which involves shearing processas in the PP at these spots. Therefore, when PP is filled with poorly adhering chalk particles the "tough" deformation process of diffuse shearing is partially replaced by another "tough"
mechanism, the formation of local shear bands. It is well possible that these two "tough" deformation mechanisme create a maximum in the impact strength at a certain combinat ion.
In Figure 7 it can be seen that the locatioh of this maximum depends on the partiele size of the filler. In the same way as discuseed in the explanation of the partiele size dependenee of the yield stress, this may be due to an increasing hamparing of the diffuse shear processas in the case of smaller filler particles.
Again we should make it very clear that a study of the deformation mechanisme at high speed, or at low
temperature testing is necessary to confirm the above explanation.
2.4. CONCLUSIONS
The stress at which dewetting takes place i~ PP filled with poorly adhering chalk particles can probably be
I
described by a Griffith-like theory. Further research, applying fillers with a narrow partiele size distribution, is necessary to confirm this conclusion.
The increase of the yield stress with decreasing partiele size can be explained by the hamparing of the diffuse shear processas by the presence of a large amount of .shear bands and erazes at the filler particles. The fact that necking does no langer occur in PP filled with
more than 10-20 vol., of chalk can be accounted for in a similar way.
The modified Kerner equation provides a satisfactory description of the Younq's modulus of PP filled with
excellently adherinq chalk particles. However, the Younq•s modulus of PP filled with poorly adherinq chalk particles appears to exhibit a partiele size dependence. The
explanation for this behaviour is still unknown.
The notched Izod impact strenqth of PP filled with poorly adherinq chalk is higher than that of PP filled with excellently adhering chalk. In the former case there even appears to be a maximum in the impact strength that depends on the partiele size of the filler. This maximum may be due to a favourable combination of two shearing processes: diffuse shearing and the formation of shear bands. Therefore it also appears useful to investigate the deformation behaviour. which eventually may lead to the optimal properties of filled polymers as a function of the partiele size of the filler.
HEFERENCES
1.
w.
Glenz. Kunststoffe, 76 (1984) 834.2. H.P. Frank. "Polypropylene" (MacDonald Polymer Monographs, vol. 2. 1968}.
3. F.L. Binsbergen. "Nucleation in the Crystallization of Polyolefins" (thesis Univarsity Groningen. 1969). 4. L.E. Nielsen. "Mechanica! Properties of Polymers and
Composi tes Vol. 1 and 2", ( Marcel Dekker. New York, 1974).
5. F. Bueche. "Physical Properties of Polymers". (Interscience Publishers. New York, 1962).
6. C.B. Bucknall. "Toughened Plastics". (Applied Science Publishers. London. 1977).
7. D.R. Paul and L.H. Sperling, "Multicomponent Polymer Mate.rials". (American Chemical Society. Washington. 1986).
8. E.P. Plueddemann, "Silane Coupling Agents", (Plenum Press, New York, 1982).
9. M.E.J. Dekkers and D. Heikens, J. Mat. Sci., 18 (1983} 3281.
10. Ibid., J. Mat. Sci. Lett., ~ (1984) 307. 11. Ibid., J. Mat. Sci., 19 (1984) 3271.
12. A.A. Griffith, Phil. Trans. Royal Soc., London, A221 (1920) 163.
13. J.N. Goodier, J. Appl. Mech. (Trans ASME), 55 (1933) A39.
14. D. Heikens, S.D. Sjoerdsma and W.J. Coumans, J. Mat. Sci .• 16 (1981) 429.
15. M.E.J. Dekkers and D. Heikens. J. Appl. Pol. Sci., 30 (1985) 2389.
16. E.J. Kramer. J. MacromoL Sci., BlO (1974) 191. 17. E.H. Kerner, Proc. Phys. Soc., 69B (1956) 808. 18. T.B. Lewis and L.E. Nielsen. J. Appl. Pol. Sci., 14
CHAPTBR 3
THE DEWETTING STRESS OP GLASS BEAD PILLED POLYSTYRENE AND POLYPROPYLENE
3.1. INTRODUeTION
During a tensile test, a composita material wbicb consists of a polymer matrix filled with a poorly adhering filler. generally exhibita dewetting during a tensile test after an initia! elastic behaviour. By dewetting is meant the partial loss of contact between the filler and the polymer [1-6]. The loss of contact bacomes visible if one observes the behaviour of sucb a material with a light-microscope. Beyond a certain strain. a shadow appears at the filler particles around the two poles directed to the applied stress. The shadow is caused by total reflection of tbe light at the polymer-cavity interface. As the strain increases. the cap shaped
cavities grow until both shadows span about 120° along the circumference of the particle. After that
microdeformations (crazes or shear bands) are created at the tip of the cavi ty [4-B].
In the present study it is investigated whicb
parameters determine the dewetting stress. The fact tbat a certain stress is needed to induce dewetting indicates the presence of an adhesion energy and possibly other local stress energies.
3.2. EXPERIMENTAL
The experiments were performed with two different polymers as matrix material: polystyrene and
polypropylene. Three types of glass beads with respect to their mean partiele size, were chosen as fillers. The specifications are shown in Table 1.
Matrices polystyrene Styron 634 (Dow Chemical)
polypropylene HM6100 (Snell)
mean diameter range
glass beads 41J.m 0.4~-lOllm (Louwers)
301J.m lOlJ.m-50~ (Tamson)
l001J.m 801J.m-1101J.m (Tamson)
Table l. Specifications of the used materials
Because of the fact that the glass surface is polar whereas the polymers are both nonpolar, the adhesion energy between the filler and the matrix will b~ rather small.
The composites were prepared on a two-roll ~ill. The mixing time was kept constant at 13 minutes. Th~
processing temperature was 190°C. Tensile bars ~ere
machined from compression moulded sheets in accQrdance wi th ASTM 0256. The tensi le tests we re performed' on a
Instron tensile tester at a strain rate of 2 mm/min. The strain was measured by means of a separate exten1someter {Instron, L
0
=
50 mm). To diminish and to standardize the thermal stresses, the polystyrene composites were annealed 24 hours at 80°C. The tests were performed in a conditioned room at 20°C and 50% relativa humidity.3.3. RBSULTS
Stress-strain diagrams were measured of polystyrene and polypropylene filled with the three different types of glass beads, of which the content was varied between o and 25 volume percent (vol.\). The composites filled with more than 5 vol.\ of the larger types of glass beads (30 ~m
and 100 ~m) showed a typical stress-strain behaviour. After an initial elastic behaviour. characterized by the Young•s modulus, the stress-straio diagrams of these materials exhibit a well observable "kink" whicb is
followed by a second linear part. At still bigher stresses a gradually turning off is observed, whicb is to be
expected during plastic deformation (initiation and propagation of erazes and shear bands). Figure 1 gives examples of tbe stress-strain diagrams of polystyrene filled witb glass beads, Figure 2 of filled polypropylene.
It is remarkable that for botb polystyrene and
polypropylene. tbe "kink" appears at a lower stress in the
30 4pm b 20 '0 CL ! 10 E (%)
Figure 1. Stress-strain diagrams of PS filled witb 25 vol.\ of non-adbering glass beads of different diameters.
E. (%)
Figure 2. Stress-strain diaqràms of PP filled witb 25 vol.% of non-adbering glass beads of different diameters.
case of the material filled with 100 ~ glass beads tban in the case of tbe 30 ~m glass bead composites. It is also noteworthy that wben 4 ~m glass beads are used as a filler no distinct kink can be observed.
To check whether tbe initiation of tbe dewetting process coincides with tbe change in slope of the strass-strain curve qlass bead filled samples were obs.erved
during straining in a micro tensile tester witb the aid of a light microscope.
The microscopie study sbowed that for the samples witb the 30 ~ and the 100 ~ glass beads tbe strain at
which dewetting occurs is equal to the strain at which tbe kink in the strass-strain diagram of tbe same material is found. At higher strains microdeformations are initiated at the edges of the cavities. From this it can be
concluded that in tbe case of polystyrene and
polypropylene filled with glass beads, tbe dewetting
stress tends to be bigher with decreasing partiele size of the filler. Unfortunately, the 4 ~ glass beads appeared too small for such an investigation. In tbat case it was
impossible to discriminate between the initiation of
microdeformations (crazes) and the occurrence of dewetting. If the results of the microscopie study are combined with the stress-strain experiments. it is possible to distinquish the different stadia in diagram. which bas been done in Figure 3.
2 3
Figure 3. Different stadia in a stress-strain diagram: 1. elastic behaviour: 2. dewettinq; 3. shearing and/or crazinq.
3.4. THEORY
3.4.1. Dewetting Stress
The process of dewetting can be looked upon in two different ways. It can be considered as a process of growth, in which the debonded region enlarges from an initial very small debonded region [9-LO]. In the second approach one assumes that at the same time the whole interface debonds, and the whole cavity is created
instantaneously [11]. Both considerations are to a great deal based on the Griffith-theory [12] on the initiation of a crack in a materia1. Neither of the
considerations is theoretically perfect. For the creation of the initial small debonded region in the case of the process of growth, theoretica11y a very high stress is needed, so that it bas to be assumed that this region already exists "by nature". In the one-step approach it is not clear how it is possib1e that a re1atively large
interface debonds in one motion, unless an equal stress is applied to the who1e area.
The consideration that wil1 be derived bere is a combination of both mentioned ones and seems to have a more realistic basis. If it is assumed that very small but sharp cracks are always present at the polymer-filler interface, the initiation of the dewetting process is always possible. But for the creation of a larger free surface enough potentlal energy must be present in order to transform this energy in surface energy. From
calculations it appears [4] that up to about 25d from the pole of a glass bead the 1ocal stress is constant and approximately 1.8 times the applied stress. Beyond 25° the stress rapidly decreases. Therefore, the first region that will exhibit dewetting during a tensile test will be the part between 0 and 25° from the pole of a glass bead. This proceeds as a one-step process at a certain critica! local stress and involves the turning off of the stress-strain curve. At higher stresses the dewetting cavity enlarges,
Figure 4. 5ituation at the pole of a glass bead.
until at about 60° from the pole the plastic deformation processes shearing and/or erazing occur.
An equation for the stress at which the process of dewetting is initiated can be derived as follows. At the moment of dewetting. potential energy that is created during the tensile test is transformed into adhesion energy. The potential energy from volume V (see Figure 4)
is needed to create surface 5. potential energy adhesion energy
5.A (1)
with a
1 oe E A
local stress at the pole of the sphere Young's modulus of the polymer matrix adhesion energy per unit area
The volume V and the surface 5 are related to the size of the sphere:
V
s
4 3
3"r
where K1 and K2 are constants and r is tbe radius of (2)
(3)
the sphere. Combination of the eguations (1), (2) and (3) gives:
(4)
In the direction parallel to the applied tensile load, two stresses act on the sphere which are directed opposite to one another: the stress that is caused by the tensile load and the thermal stress (see Figure 5). This thermal stress is created during the cooling cycle of the
production process of the material.
Figure 5.
au
au
App1ied stress a and tbermal stress aT
working on a filler particle. a is the stress concentration factor.
Because of stress concentration at a rigid sphere [4,13] the applied stress is increased at the pole of
the sphere by the stress concentration factor a. If the applied stress a eguals the overall dewetting stress a0, the local stress at the pole of the sphere . a10c is given by equation (5).
Equation (5) can be substituted into equation (4):
Therefore. according to equation (7) in which c 1 and c
2 are constante for a certain polymer/filler system.
(5)
(6)
(7)
the dewetting stress is dependent on the partiele size of the filler. The dewetting stress tends to be higher with deereasing partiele size.
3.4.2. Estimation of Parameters
In this section estimations will be made of the
parameters that determine. according to equation (6}. the dewetting stress.
Estimation of aT
The thermal stress is created during the cooling cyele of the production process of the compression moulded
sheets. During this cycle the composita is cooled down from approximately 200°C to room temperature in about three minutes. Because of the fact that the coefficient of thermal expansion of the polymer is about ten times higher than that of the filler, the thermal compression stress acts on the filler. The thermal stress can be calculated with the equation of Laszlo [14].
The polystyrene/glass composites were annealed for 24 hours at 80°C, so that we may assume that the thermal
PS pp glass volume coefficient of thermal expansion 1.9*10- 4 1. 6*10- 4 2*10-S (K-1) Young•s modulus 3450 1480 70000 (MPa) Poisson•s ratio 0.34 0.40 0.~2
Table 2. Data used to calcu1ate the thermal stress
stress is created by the cooling down from 80°C to room temperature. The polypropylene/glass composites,were not annealed and therefore. as a first approximatio~. the temperature difference was calcu1ated from the yrystal melt temperature (about 170°C). With these data,and those of Table 2 the thermal stress can be calculated. The
vol.\. filler 10 15 20 25 Table 3. O'T(PS-glass) aT(PP-glass) (MPa) (MPa) 14 13 13 12 12 11 11 10
The thermal stress in glass-polymer composites as a function of the filler content. calculated with the equation of Laszlo [14]
results are shown in Table 3.
These thermal stresses are independent of the partiele size and weakly dependent on the volume fraction of the filler. It is to be expected that these stresses will relax slowly at room temperature.
Estimation of K 2 The constant K
2 is the factor that indicates which part of the surface of the sphere debonds. From the
paragraph "Dewetting Stress" it appears that the debonded region covers an area up to a polar angle of 25°.
Therefore K
2 bas to be:
surface area between 0 and 25°
K2 = 0.094 (9)
surface area between 0 and goo
Estimation of K 1
The volume of which the potential energy is used to create the adhesion energy, is related to the volume of the sphere by the factor K
1• From general principles of stress theory it follows that, as a,first approximation, the volume can be assumed to consist of two half spheres with a radius proportional to sin $. where $ is the angle of dewetting. It therefore appears:
0.075 (10)
Estimation of A
The energy absorbed in debonding a unit area of the interface between the glass beads and the polymer is called A. The energy A can be calculated using the following equation [15]:
d
where Ysi
=
nonpolar component of the surface energy of substance ipolystyrene qlass polypropylene 0.0414 0.078 0.0335 0.0006 0.209 0.0041 reference {:1,5] [16] [15]
Table 4. Data used to calculate the adhesion enerqy A
polar component of the surface enerqy of substance i
ysi surface enerqy of substance i
Combination of equation (11) and the data of Table 4 qives: A (PS-glass) 0.14 Jtm2
A (PP-glass) = 0.16 Jtm2
3.5. COMPARISON OF THEORY WITH EXPERIMENT 3.5.2. The constant
c
2
The dewetting stress is determined experimentally as the intersection of the two tangents of the linear parts of the a-t diagram before and after the kink. As
already mentioned, the composites that contain 4~m glass beads do not exhibit a kink in the a-t diagram, so
that the dewetting stress could not be determined. In the case of the composites filled with 5 vol.% of 30~ and
100~ qlass beads, the kink could be observed with dif.ficulty but is was impossible to appoint a dewetting stress with reasonable accuracy.
Dewetting stress of glass bead filled polystyrene
vol.\ O'D (3 OlUD) 0' D (1 OOlUD) cl c2
filler (MPa) (MPa) (MPa) (kPa.m%)
10 10.6 7.1 2.9 30
15 10.4 7.1 3.1 28
20 11.3 6.9 1.5 38
25 11.4 6.4 0.5 42
Dewetting stress of glass bead filled polypropylene
vol.\ O'D(30lUD) ·aD(lOOlUD) cl c2
filler (MPa) (MPa) (MPa) (kPa.m%)
10 8.5 6.6 4.3 16
15 8.8 6.2 3.1 22
20 8.1 5.6 2.6 21
25 7.3 5.2 2.7 18
Table 5. Experimentally determined dewetting stresses. The constants c1 and c2 are calculated using equation (7).
Each value of O'D in Table 5 is the average of six measurements. and the standard deviation in this average is approximately 0.4 MPa. The calculation of c
2 is based on the difference O'D(30lUD)-O'D(lOO~m). a
difference that amounts to just a few MPa's and is
afflicted with a possible error of two times 0.4 MPa. For this reason the standard deviation of c2 reaches a value of 20\. In fact. if one strikes the average of the c
going witb tbe different filler volume fractions, sucb a value of tbe standard deviation is found. Prom this it can
be concluded that
c
2 is independent of tbe volume fraction of tbe filler.polystyrene c2 polypropylene: c2
35 ± 7 (kPa .m%) 19 ± 3 {ltPa.m%) Prom equations {6) and {7) it appears:
where a. K
1 and K2 are independent of the matrix material. Also bas been found that:
A (PS-glass) - A (PP-glass)
Using equations (12) and 13) and data from Table 2, the theoretica! gradient ratio can be derived:
1.53
(12)
{13)
(14)
On basis of data from Table 5, the experimental ratio can be calculated:
1.8 ± 0.6
which corresponds satisfactorily to the result of equation
{14).
Prom equation (12) it appears that the dependenee of
c
2 on the filler content is caused by the dependenee of a on the filler content. The experimental results show thatc
2 is constant within the range of themeasurements. From this it appears that a is constant. which seems logically because overlap of stress
concentration fields in the vicinity of the glass beads takes place only at relatively high filler loadings. In the experiments therefore a is equal to the value that holds true for low filler loadings:
a
= 1.8
The value of K
1• the constant that relates the volume
{15)
from which the potenttal energy is drawn to the volume of the sphere. can be calculated using equation {12).
According to the theory K1 is independent of the matrix material. which is also proved by the validity of equation
(14). and so it is sufficient to make a calculation on basis of the data of the polystyrene composites:
c2
=
35 {kPa.m*> K2 0.094 a=
1.8 E 3450 {MPa) A = 0.14 (J/m2) 0.069As a first approximation. according to equation (10), a value of 0.075 was predicted. So it can be stated that there is a good agreement between the theory and the expertmental results.
3.5.2. The constant
c
1The constant c
1 is according to equations (6) and (7) related to the thermal stress:
(16) In a previous section the thermal stress has been
polymer-filler systems. Because a too is known, c 1 has
to correspond to: 5 MPa <
c
1 < 7 MPa
The experimentally determined values of c
1• see Table 5, agree as far as the order of magnitude is concerned fairly well with the calculated value. The experimentally determined values are all lower .than the calculated thermal stresses, which could mean that the
!
assumed temperature differences, used in the calculations, were too high, or that already some relaxation has taken place.
From Table 5 it also appeàrs that the thermal stress is a function of the volume fraction of the filler. At higher filler loadings a lower value of the thermal stress is found. This is in good agreement with the predictions according to the equation of Laszlo {see Table 3).
3.5.3. The dewetting stress of 4 ~ glass beads Since
c
1 andc
2 are known, the theoretica!dewetting stress of composites filled with 4 ~ glass beads can be calculated. Of these composites the dewetting stress could not be determined from the stress-strain diagrams. The calculated values of a
0 are llste~ in Table 6, along with the stress at which in the same
material the initiation of plastic deformation takes place (ai). Figure 6 is a graphical representation of'these data.
From Table 6 and Figure 6 it appears that for all materials the calculated value of the dewetting stress is higher than the stress at which initiation of plastic deformation occurs. Therefore, as the dewetting stress is reached, the deformation mechanisme erazing and/or
shearing are already in progress and the stress
concentratien is no longer located at the poles of the glass beads. For this reason it is very unlikely that in
this case dewetting will occur. This is in agreement with the observation that the stress-strain diagrams of these materials do not exhibit a kink. From this the practically important conclusion may be drawn that these composites. consisting of a polymer filled with glass beads of 4 ~
or smaller. do not undergo dewetting during a tensile test.
polystyrene filled with 4 ~m glass beads
vol. 't. a
0(cal) a1(exp)
filler (MPa) (MPa)
10 28 23
15 28 23
20 27 20
25 26 20
polypropylene filled with 4~m glass beads
vol.\ a
0(cal.) a 1 ( exp.)
filler (MPa) (MPa)
10 18 14
15 17 14
20 16 12
25 16 12
Table 6. Comparison of the calculated dewetting stress a0 (cal) with the stress at which in the same material the initiation of plastic deformation a
1 (exp) takes place. for both
polystyrene as well as polypropylene filled with 4 ~ glass beads.
35 0 28 a.. ~ tf) tf) 21 UJ +
""
1--tf) 14 7 0 0 • 1 • 2 .3 .4 . 5 .• 6 r-1/2 (,um-1121 20 0 16 a.. ~"'
tf) 12 + UJ""
....
(J) 8A~
4~
0 0 . I .2 • 3 • 4 .5 .8 r-1/2 l:«m-1121Figure 6. Representation of the partiele size dependenee of tbe dewetting stress of glass bead filled PS (Figure A) and PP (Figure B) in accordance witb equation (7). Indicated are tbe experimental determined dewetting stresses ( • ) • the calculated dewetting stresses ( A ) . and the stress at whicb shearing and erazing are ini tiated (
+).
3.6. CONCLUSIONS
An equation is derived whicb enables us to calculate the dewetting stress of bead filled composites. This equation is extensively experimentally tested. Two matrix materials are investigated, the volume fraction of the filler is varied and three different filler partiele sizes are applied. From all these experiments it appeared that tbe model delivers an excellent desaribtion of tbe reality.
A second partically important conclusion is that in the case of the two systems studied, dewetting does not occur if the filler partiele size is equal to or smaller than 4 1dl in diameter.
HEFERENCES
1. L.E. Nielsen, "Mechanica! Properties of Polymers and Composites". Volume 2 (Marcel Dekker, New York, 1974). 2. T.L. Smith, Trans. Soc. Rheol., ~ (1959) 113.
3. L. Nicolais and R.A. Mashelkar. Intern. J. Polymerie Mater.,
á
(1977) 317.4. M.E.J. Dekkers and D. Heikens. J. Mat. Sci., 18 (1985) 3281.
s.
6. 7. 8. Ibid. Ibid. Ibid. Ibid, J. J. J. J. Mat. Mat. Mat. Appl. Sc i. Lett .• ~ (1984) 307. Sc i .• 19 {1984) 3271. Sci.. 20 {1985) 3865. Polym. Sci .• 30 (1985) 2389. 9. A.N. Gent, J. Mat. Sci., 15 (1980) 2884.10. A.N. Gentand Byoungkyeupark, J. Mat. Sci., 19 (1984) 1947.
11. D.W. Nicbolson. J. Adhesion, 10 (1979) 255.
12. A.A. Griffitb, Pbil. Trans. Royal Soc .• London, A22l (1920-21) 163.
13. J.N. Goodier. J. Appl. Mech. (Trans ASME).
ss
{1933) 39.15. D.W. van Krevelen. "Properties of Polymers" (Elseviers, Amsterdam, 1972).
16. L.H. Lee, "Adhesion science and Technology". Volume 9B, 647 (Plenum Press, New York. 1975).
CHAPTER 4
TRB DBWBTTING STRESS OP POLYSTYRBNB PILLED WITH IRRBGULARLY SHAPED CHALK PARTICLES
4.1. INTRODUeTION
In a previous chapter·[1) a theory is described
which makes it possible to calculate the dewetting stress of spherical particles in a polymer matrix. èalculations on the basis of this model were compared with
experimentally determined dewetting stresses, and it was found that the equation holds true for glass bead filled polymers [1].
However, the industrial applications of glass beads as a filling material are rather limited, and for this reason in the present investigation the usefulness of the above mentioned theory is checked for a more practically used fi1ler. In this study irregularly shaped chalk particles were cbosen as the filling material.
In order to be applicable to composites filled with irregularly shaped particles, the dewetting stress equation had to be modified slightly.
4.2. BXPERIMENTAL
In order to investigate the influence of the partiele size of the filler on the dewetting stress. irregularly shaped chalk particles (Durcal 130. Boekamp), with a
partiele size ranging trom 10 to 300 ~. were sieved into three fractions with an Alpine Air Jet sieve. Within the fractions the partiele diameter ranged trom 200-250
~m. B0-100 ~m and 40-60 ~ respective1y. composites of these fractions and the matrix material polystyrene
(Styron 634, Dow Chemical) were prepared at two filler loadings: 10 vol.% and 20 vol.% of filler.
The composites were melt mixed with the matrix material at 190°C on a lahoratory mill. The processing time was kept constant. Tensile bars were machined from compression moulded sheets in accordance with ASTM D 638. The composites were annealed 24 hours at 80°C.
The tensile tests were performed on an Instron tensile tester, which was equipped with an extensometer (1
0
=
50 mm), at a strain rate of 0.02/min.4.3. MODIFICATION OF THE DEWETTING STRESS EQUATION In a previous chapter [1] an equation bas been
derived for tbe dewetting stress of a bead filled polymer. This equation was founded on the assumption that at tbe moment of dewetting, the potential energy from the volume V (see Figure 1.1} is transformed into the adhésion energy of the interface S.
For both tbe spherical and the irregularly shaped partiele the volume V can be assumed to be proportional to the volume of the particle:
4 3
V
=
K1 .3
w r (1)where K1 is a constant and r the radius of the particle. But, as appears from Figure 1, tbe debonded area of an irregularly shaped partiele is larger than the debonded area of a spherical partiele with an equal radi~s. For this reason a correction term R, indicating the
irregularity of the surface of the filler particle, is introduced:
Figure 1.
u
loc 1.1r
I
I
I I
I
I
u toe 1.2l
The process of dewetting: potential energy is transformed into surface energy, for 1.1 a spherical partic1e, and for 1.2 an irregular1y shaped partiele
s
(2)where K2 is a constant.
Of a perfectly smooth sp.herical partiele the term R is
o.
and in the case of irregularly shaped particles R is larger than 0. For a certain type of filler. produced under fixed conditions. R is assumed to be constant and independent of the radius of the particle.The dewetting stress of a polymer filled with spherical particles bas been found to be [1]:
aT 1 [ K2 .4nr2
p
aD - + - 2.E.A 4 3
(X a K
1 •
3
'1Trwhere: aD dewetting stress O'T thermal stress
a. stress concentration factor E Young's modulus of the polymer
(3)
A adhesion energy between filler and polymer
The introduetion of the term R. indicating the irregularity of the surface of the particles. gives:
crT 1 [ 2. E.A K 2.4'1T{ (l+R)r} 2
l
12
crD - + 4 3 (X (X K 1 •3
1rrwhich can be rewritten into:
A simplification of this equation is:
(4)
(5)
where: (7) (8)
4.4. EXPERIMENTAL RESULTS
In order to check the validity of equation (5) the dewetting stresses were determined of PS filled with chalk particles of three different sizes: 200-250 ~. 80-100
~ and 40-60 ~ respectively. The composites were produced at filler loadings of 10 and 20 vol.%.
Because of the fact that the partiele size
distributions were rather narrow, the dewetting stresses could be determined from the "kink~ in the stress-strain diagram in question [1]. In Figure 2 a stress-straio diagram of PS filled with 20 vol.\ of 80-100 ~ chalk particles is shown. Clearly visible is the "kink~ which is caused by the process of dewetting.
u
jMPa)
0 2
E (%1
Figure 2. Stress-strain diagram of PS filled with 20 vol.\ of 80-100 ~m chalk particles. The
moment of dewetting becomes visible as a "kink" in the diagram
partiele diameter
<wm>
40-60 80-100 200-250 vol.'\ o 0 filler (MPa) O'D (MPa) cl (MPa) 10 15. 3 13.0 11.9 10.8 10.1 ~.3 5.3 45 45 20 l4 .1 Table 1. Fiqure 3.Experimentally determined dewettinq stresses. The constants
c
1 andc
2 are calculated usinqequation (6). The experimental error is about 5'\.
20
..,
16 / c.. ~x/ ~ 'Ö 12~~~0
/~~
8 //
/ . / / 4 0 0 .05 .I • 15 .2 .25 r-112 (,um-112)The dewettinq stress plotted as a function of the partiele size. The data of the 10 vol.'\ filled composites are indicated with x. the 20 vol.'\ filled composites with
o.
In Table 1 the experimentally determined dewetting stresses of the different composites are shown. These data are plotted in Figure 3 as
~D
versus r-%. whichshould render. according to equation (6). a straight line. Indeed. within the limits of experimental error. for both the 10 vol.\ and the 20 vol.\ filled composites a linear relation is found.
4.5. DISCUSSION
In order to be able to compare the experimental data. listed in Table 1. with the theoretical predictions. all the parameters of the eguations (7) and (8) should be known.
The thermal stress ~T and the adhesion energy A can be calculated with the following eguations [2.3]:
where E a 6T ~ $ d y yh 2E Ef(a -af)~T . p p
=
Young•s modulus=
linear coefficient of tbermal expansion temperature intervalPoisson•s ratio
= volume fraction of the filler
= nonpolar component of the surface energy
=
polar component of the surface energy(9)
(10)
the subscripts p and f refer to the polymer and the filler respectively
Using the data from Table 2 it appears:
O'T (10% filler) 13 MPa (11)
aT (20% filler)
=
11 MPa (12) A{PS-Caco3)=
0.15 ~ 0.01 Jtm2 (13) PS Chalk Young' s modulus 3450 [1] 50*103 {5] [MP a] Poisson's ratio 0. 34 [1] 0.25 [5) volume coefficient of thermal expansion 1. 9*10-4 [4] 3.51*10-5 [5) [K-1] surface energy 0.0420 [3] 0.23 [6) [J /m2] nonpolar component of surface energy 0.0414 [3] 0.09-0.ll [7] [J /m2] temperature interval 60 [°C]Table 2. Data used to calculate the thermal stress and the adhesion energy at the PS-chalk interface. The nonpolar component of the surface energy of chalk is estimated based on data of similar compounds
