The deformation behaviour of polystyrene-low density
polyethylene blends
Citation for published version (APA):
Sjoerdsma, S. D. (1981). The deformation behaviour of polystyrene-low density polyethylene blends. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR33444
DOI:
10.6100/IR33444
Document status and date: Published: 01/01/1981 Document Version:
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THE DEFORMATION BEHAVIOUR OF
POLYSTYRENE-LOW DENSITY
POLYETHYLENE BLENDS
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN, OP GEZAG VAN DE RECTOR MAGNIFICUS, PROF. IR. J. ERKELENS, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN IN HET OPENBAAFJ, TE VERDEDIGEN OP
VRIJDAG 11 DECEMBER 198lTE 16.00 UUR
DOOR
SJOERD DIRK SJOERDSMA
GEBOREN TE ALMELODit proefschrift is goedgekeurd door de promotoren
Prof.dr. D. Heikens en
A an de nagedachtenis van mijn vader
a an mijn moeder a an Mar go
CONTENTS
1. Introduction
1.1. Aim of investigation 1.2. Deformation mechanisms
1.3. Toughening of glassy polymers 1.4. Viscoelastic properties of blends 1.5. Survey of the thesis
1.6. References
2. Volume strain, elongational strain and stress in homogeneous deformation 2.1. Introduction 1 1 1 2 5 6 8 11 11 2.2. Crazing and elastic deformation 13 2.3. Crazing, shear flow and elastic deformation 16
2.4. References 17
3. Dilatometric investigation of deformation mecha-nisms in polystyrene/low density polyethylene
blends 18
3.1. Introduction 19
3.2. Experimental 22
3.2.1. Volume, stress and strain measurements 22 3.2.2. Materials and tensile specimens 23
3.3. Results and discussion 23
3.3.1. Presentation of results 23 3.3.2. Blends from P~ and ldPE 26 3.3.3. Blends from PS and blockcopolymer 28
3.3.4. Blends containing PS, ldPE and
block-copolymer 29
3.3.4.1. Poisson's ratio and adhesion 29 3.3.4,2. Brittle-tough behaviour 30
3.4. Conclusion 33
3.5. References 34
4. The Poisson's ratio of polymer blends, effects of adhesion and correlation with the Kerner packed grains model
4 .1. Introduction 4.2. Experimental
4.3. Results and discussion 4.4. Conclusion
4.5. References
5. Dynamic mechanical properties of polystyrene/low 35 35 35 41 47 48
density polyethylene blends 49
5.1. Introduction 50
.5. 2. Experimental 50
5.3. Results and discussion 51
5.3.1. Polystyrene, low density polyethylene and polystyrene-polyethylene diblock
copolymer 51
5.3.2. Polystyrene/low density polyethylene
homopolymer blends 54
5.3.3. Polystyrene/low density polyethylene blends, containing
polystyrene-poly-ethylene diblock copolymer 63
5.4. Conclusion 65
5.5. References 65
6. A model for the stress-strain behaviour of toughened polystyrene I 6.1. Introduction 6. 2. Theory 6.2.1. Deformation characteristics of toughened polystyrene 66 66 68 68
6.2.2. Modeling of the stress-strain behaviour
6.2.3. Elaboration of the model 6.3. Experimental
6.4. Results and discussion
6.4.1. Validity of the model~
Determination of the craze modulus and 69 69 72 73
the expansion factor 73
6.4.2. Time dependence of the rates of craze
initiation and growth 76
6.5. Conclusion 78
6.6. References 79
7. A model for the stress-strain behaviour of toughened polystyrene II
7.1. Introduction 7.2. Experimental
7.3. Results and discussion
7.3.1. Stress dependence of crazing in
con-81 81 83 83
stant strain-rate experiments 83
7.3.2. Constant stress-rate experiments 85
7.3.3. Temperature dependence of crazing 88
7.4. Conclusion 90
7.5. References 91
8. The constant stress behaviour of polystyrene/low
density polyethylene blends 92
8.1. Introduction 92
8.2. Experimental 94
8.3. Constant stress behaviour 95
8.3.1. General features of the creep curves 95 8.3.2. The concave part of the creep curves 96 8.3.3. The linear part of the strain-time
curves, craze termination 97
8.4. Results from constant stress experiments 99
8.4.1. Results from the analysis of the con-cave part of .t:he strain-time curve 99
8.4.2. Results from the analysis of the
linear part of the strain-time curve 101 8.4.3. Results from the analysis of the
con-stant stress part of concon-stant strain-rate curves
8.4.4. Application of the Eyring activated flow equation
8.5. Conclusion 8.6. References
9. The effect of varying the polyethylene content and the copolymer content on crazing in
poly-102
104 106 106
styrene/low density polyethylene blends 108
9.1. Introduction 109
9.2. Experimental 110
9.3. Results 110
9.3.1. Apparent craze modulus 110
9.3.2. PS/PE homopolymer blends 111
9.3.3. Blends containing PS-PE copolymer 116
9.4. Discussion 117
9.4.1. Variation of the ldPE content in
PS/ldPE homopolymer blends 117
9.4.2. Clusters 118
9.4.3. Copolymer modified blends 123
9.5. Conclusions 123 9.6. References 124 Summary 126 Samenvatting 130 Dankwoord 134 Levensbericht 136
CHAPTER 1
INTRODUCTION
1. 1. AIM OF INVESTIGATION
Previous studies1-5on the mechanical properties of polystyrene/low density polyethylene (PS/ldPE) blends showed that the addition of certain PS-PE copolymers to this system results in an enhanced impact strength and tensile strength. This effect was attributed to the im-proved interfacial.adhesion caused by copolymer addition. High copolymer concentrations, however, were found to re-sult in a rather strong decrease in the tensile modulus. This was ascribed to changes in morphology, i.e. phase reversal induced by the presence of copolymer 4 .
The investigations described in this thesis aim at a better understanding of the elastic and plastic properties of PS/ldPE blends, and the effect of varying the PS-PE copolymer and ldPE content thereupon.
1.2. DEFORMATION MECHANISMS
At: low strains, and at sufficiently low tempera-tures and sufficiently high deformation rates, glassy polymers like polystyrene and toughened polystyrene can be l?egarded as linear viscoelastic materials6• However, at higher strains g!assy polymers begin to show evidence
of plastic deformation. Plastic deformation in general is caused by shear flow and/or voiding.
Shear flow is caused by sometimes highly localised cooperative movements of molecular segments. These move-ments may result in shear yielding, which, depending on the degree of localisation, may give rise to readily ob-servable shear bands. The degree of localisation is in-fluenced by the tyoe of loading and by the properties of the material itself. Shear flow is a deformation process that does not involve volume changes.
Voiding is usually a consequence of crazing, to be discussed later. However, for instance, Cornes et al.7 showed that this is not necessarily so. Voiding, of course, causes a volume increase, and thus can be detected in a relatively simple manner.
1.3. TOUGHENING OF GLASSY POLYMERS
Many glassy thermoplastic polymers have a set of attractive oroperties like high tensile strength, high tensile modulus and good dimensional stability which ren-ders these materials in principle suitable for a large number of applications. However, many of these polymers, including polystyrene, behave brittly, which is a serious drawback that prevents many applications. Since 1927 it has been recognized that the brittle polymer polystyrene
(PS) could be made tough by the incorporation of a rubber. Though the rubber incorporation reduces tensile strength and modulus, many of the good characteristics of PS are retained. Thus rubber toughened PS (TPS) is a material with an excellent set of properties. It was commercialized in the 1940's and it has been a highly successful product eversince8•
Many new and improved types of toughened (glassy) polymers have been developed. This was mostly an empirical matter until the first hypotheses on toughening were ad-vanced. The first important hypothesis was based on the
two phase nature of TPS, suggested by Buchdahl and Niel-sen9•10. Claver and Merz 11 provided evidence for this suggestion. The two-phase nature of TPS gave the first clue to the toughening mechanism advanced by Merz et al.12:
An analysis of the stress distribution around an isolated sphere in a solid body by Goodier13 can be ap-plied to calculate the stress around a rubber particle embedded in PS. These calculations show that if a solid body consisting of PS is subjected to an unaxial tension cr then the stress at the equator of the embedded rubber sphere is approximately 2cr. Defining the stress concen-tration as the ratio of the major principal stress and the applied stress the maximum stress concentration is then "'2.
This concept of a locally increased stress was 12
further developed by Merz et al. • They proposed that this locally increased stress causes the formation and growth of microcracks. The energy absorption resulting from this process could then impart toughness. Merz et al. showed that after tensile deformation the density of TPS had decreased, which confirmed void formation.
Another important aspect that resulted in a better understanding of the toughening mechanism was the dis-covery of crazes. Many glassy polymers develop, often under tensile stress, crack-like defects called crazes. Unlike cracks, where no material connects the separated surfaces, crazes contain oriented polymer fibrils that span the distance between the separated surfaces14•15 • Thus a specimen of a polymer containing a craze that spreads across the whole cross-section area is still load bearing lG-l ~ Crazes are initiated by stress concentrating flaws in the material18-20• They expand by an increase of the craze area normal to the stress direction2~ and by growth in the stress direction. The last process, craze thickening, is made possible by elongation of the polymer fibrils spanning the craze22•23.
Both the craze initiation and craze growth proc-esses absorb energy. This aspect, combined with the
evidence obtained by Merz et a1.12 that deformation of TPS is accompanied by void formation, forms the basis of the multiple crazing mechanism put forward by Bucknall and Smith24• They proposed that voiding of TPS under stress does not result from the formation of microcracks, but from crazes, that are initiated by the stress concentra-tions around the rubber particles. Optical microscopy24 and electron microscopy25 studies indeed showed this to be true.
According to Bucknall and Smith, the toughening effect of the rubber particles results from the energy absorbing mechanisms of multiple craze initiation and growth. However, there are still questions that remain unanswered by the multiple crazing mechanism, thus in-voking a search for additional mechanisms. For instance, it is not clear why interfacial adhesion between PS and the rubber is such an important factor in toughness26• Bucknall8 assumes that a bonded rubber particle stabilizes a craze in some fashion. However, though the toughness of-TPS with unbonded rubber at high deformation rates is low, it is quite high1'4 at low deformation rates. This dis-crepancy cannot be explained by the craze stabilizing mechanism proposed by Bucknall. Schmitt27 demonstrated that failure of interfacial adhesion takes place during impact tests, and proposed that the energy absorbed by this failure mechanism contributes to the toughness. Fol-lowing this train of thought toughness at low strain rates would be due to the energy absorbing multiple crazing, while at high rates crazing is the cause of energy absorb-ing interfacial failure or even fracture of the rubber
t . 1 28 par ~c es •
Another interesting feature that can have a thor-ough effect on the tthor-oughness of a material is the possi-bility of a combination of deformation by crazing and by
(localised) shear flow. This has in effect been observed in TPS/poly(2.6-dimethyl-1.4-phenylene oxide) blends29 as well as in ABS30• Concluding, the occurrence of multiple crazing has been verified experimentally in many ways and
is a sound concept to explain toughening, although other factors may play quite an important role as well.
1. 4. VISCOELASTIC ·PROPERTIES OF BLENDS
It has already been mentioned that incorporation of a rubber in a glassy polymer results in a decrease of the modulus. Indeed the presence of the rubber affects all (visco)elastic properties of the glassy polymer. The way in which and the extent to which it does so is deter-mined strongly by the properties of the two phases and of the interphase, by the blend composition and by the mor-phology. Deviations in the (visco)elastic properties of a blend from the expected properties can be useful to gain an insight into the blend morphology. Therefore much work has been done to predict the (visco)elastic properties of a blend from the properties of the components and the structure of these blends. Exact solutions have been ob-tained in only a few cases, but many empirical and
semi-31
empirical formulae have been developed • There are three groups of models that can be applied to predict the (vis-co)elastic properties of binary blends32:
1. mechanical coupling models.
These models are basically generalizations of the spring and dashpot models. Well-known examples are.the series and parallel models by Pau133 , the combined series and parallel model by Takayanaki34, and the three-dimensional combined series and parallel model
1
by Barentsen • These models are applicable for dis-persed systems1'~ Furthermore by using these models as curve fitting methods they can be useful to detect orientation effects.
2. self consistent models.
Here the mechanical response of a representative struc-ture of the blend is compared with that of a homoge-neous body that has the same (visco)elastic properties as the blend. The representative structure.of the blend
consists of a spherical dispersed particle in a matrix shell that is embedded in a homogeneous body with the same (visco)elastic properties as the blend, Well-known
35 36
examples are the models by Bruggeman , Van der Poel and Kerner37 . The predictive behaviour of these models is usually good for binary blends consisting of a ma-trix with spherical inclusions31•
3. models that predict upper and lower bounds on (visco)-elastic properties of blends,
The series and parallel model by Paul33 provide such bounds though they are too widely.· separated for accu-rate predictions. The most restrictive bounds without specification of blend morphology are those derived by Hashin and Shtrikman38•
Applications of these models to predict the (visco}elastic properties of TPS are greatly hampered by the presence of PS subinclusions in the rubber39'40. Bucknall41 applied the Hashin equations42 to calculate bounds on the shear mod-ulus of TPS. However, the bounds were too widely separated to be discriminative to the effect of those sub-inclusions. Generally it appears that until today the bounds derived from this type of model are not restrictive enough to be of much predictive value.
1.5. SURVEY OF THE THESIS
In chapter 2 a model is presented to describe the volume behaviour of a material deforming homogeneously during a tensile test. It is shown that this model accu-rately predicts the volume strain of samples that deform by crazing, An important application of the model is the determination of the contributions of respectively shear flow and crazing to strain.
Chapter 3 deals with the tensi.le deformation be-haviour of blends of PS and ldPE; modified with a PS-PE blockcopolymer, By using a dilatometer to monitor volume changes during tensile tests and by applying the model
described in chapter 2 the effect of varying the ldPE con-tent and the PS-PE blockcopolymer concon-tent on the deforma-tion mechanism is determined. The results are explained by copolymer induced changes in morphology. The dependence of the low strain rate toughness on the ldPE content and the PS-PE blockcopolymer content is discussed in terms of craze density. Furthermore some attention will be paid to the dependence of the Poisson's ratio on interfacial ad-hesion.
Chapter 4 gives an explanation for the low de-pendence of the shear modulus on interfacial adhesion in PS/ldPE blends, contrasting with the strong effect that interfacial adhesion has on the Poisson's ratio. The Kerner packed grains equations are applied to predict the shear modulus and Poisson's ratio of PS/ldPE(/PS-PE co-polymer) blends. The cause of the discrepancies between the Kerner predictions and experimental results will be specified,
In chapter 5 the dynamic mechanical properties of PS/ldPE blends are discussed. Anomalies in the ldPE con-tent dependence of the shear modulus at low temperatures and the high value of the loss modulus of PS/ldPE homo-polymer blends with a 50/50 composition are explained in terms of interfacial adhesion and mechanical interactions between the phases.
In order to gain information about crazing in PS/ldPE blends a model is developed in chapter 6 that de-scribes stress-strain behaviour as a function of the rates of craze initiation and craze growth.
In chapter 7 this model is applied to analyse con-stant strain-rate and concon-stant stress-rate experiments. From these analyses the stress, time and temperature de-pendence of the rates of craze initiation and craze growth are determined. The predictive value of the model is veri-fied by subsituting these rates in the model.
Application of the model to constant stress ten-sile tests on PS/ldPE blends as described in chapter 8 confirms the validity of the model and the results for
craze growth and initiation rates obtained in chapter 7. The results allow the separate determination of the stress dependence of the rate of craze growth. Furthermore the nature of craze termination will be specified.
In chapter 9 the effects of copolymer addition and of changes in the ldPE content on the crazing behaviour of PS/ldPE blends are analysed using the stress-strain model.
Parts of this thesis have been published elsewhere
* * * * 43-46
(chapters 2 , 3 , 4 and 5 ) or have been accepted for publication (chapters 6 and 7)47•48• Furthermore some papers on related research, not presented in this thesis, have
. 49-51 been published, or have been accepted for publicatkon .
* Most of the theoretical work and part of the experimental work has been performed by the present author.
1.6. REFERENCES
1. W.M. Barentsen, Thesis, Eindhoven University of Technology, Eindhoven, 1972.
2. ·w.M. Barentsen, D. Heikens, Polymer
!!
(1973) 579.3. W.M. Barentsen, D. Heikens, P. Piet, Polymer ~ (1974) 119. 4. N.G.M. Hoen, Thesis, Eindhoven University of Technology,
Eind-hoven, 1977
5. D, Heikens, N, Hoen,
w.
Barentsen, P. Piet, H. Ladan, J, Polym. Sci, (Polym. Symp.) 62 (1978) 309.6. C.B. Bucknall, D. Clayton, J, Mater, Sci. 7 {1972) 303,
7. P,L, Cornes, K. Smith, R.N. Haward, J, Polym, Sci, {Polym. Phys. Ed.) ~ {1977) 955,
8, C,B, Bucknall, "Toughened Plastics" {Applied Science Publishers Ltd., London, 1977).
9. R. Buchdahl, L.E. Nielsen, J, Polym, Sci, ~ (1955) 1. 10. L.E. Nielsen, J. Am. Chem. Sci. ~ (1953) 1435,
11. G.C. Claver, E,H, Merz, Official Digest, Fed, Paint Varnish Prod. Clubs 28 (1956) 858,
12. E.H. Merz, G,C, Claver, M. Baer, J, Polym. Sci, 22 (1956) 325, 13. J.N. Goodier, J. Appl. Mech. ~ (1933) 39,
14. G.K. Spurr, W.D. Niegisch, J. Appl. Polym. Sci. ~ (1962) 585. 15, R,P, Kambour, Polymer ~ (1964) 143.
16, J,A, Sauer, J, Marin, C,C, Hsiao, J, Appl. Phys, (1949) 507. 17. c.c. Hsiao, J.A. Sauer, J. Appl. Phys.
3!
(1950) 1071,18. G.P. Marshall, L,E, Culver, J.G. Williams, Proc. Roy. Soc. ~ (1970) 165.
19. E,H, Andrews, in "The Physics of Glassy Polymers", R.N. Haward ed. (Applied Science Publishers Ltd., Barking, Essex, 1973), 20. A.S. Argon, Pure and Appl. Chemistry~ (1975) 247.
21. R.P. Kambour, J. Polym. Sci.: Macromol. Rev. 7 {1973) 1.
22, N, Verheulpen-Heymans, J.C. Bauwens, J. Mater. Sci. ~ (1976) 7. 23, B,D, Lauterwasser, E.J. Kramer, Philos. Mag. A39-4 (1979) 469. 24, C,B. Bucknall, R.R. Smith, Polymer~ (1965) 437,
25. M. Matsuo, Polymer
I
(1966) 421.26. L. Morbitzer, D. Krantz, G. Humme, K.H. Ott, J. Appl. Polym, Sci, 20 (1976) 2691.
27. J.A, Schmitt, J. Appl. Polym. Sci. ~ (1968) 533.
28, J,A, Manson, R.W. Hertzberg, J. Polym. Sci. (Polym, Phys. Ed,)
.!.!..
(1973) 2483,29. C.B. Bucknall, D. Clayton, W,E, Keast, J. Mater. Sci, 7 (1972) 1443.
30, C,B, Bucknall, I.C. Drinkwater, J. Mater, Sci, ~ (1973) 1800. 31. L,E,,Nielsen, "Predicting the Properties of Mixtures", (Marcel
32. R.A. Dickie, in "Polymer Blends", Vol. 1, D.R. Paul and S. Newman eds. (Academic Press, Inc., New York, 1978). 33. B. Paul, Met. Soc. AIME 218 (1960) 36.
34. H. Takayanaki, T. Okamoto, J. Polym. Sci. C23 (1968) 597. 35. D.A.G. Bruggeman, Ann. Phys. 29 (1937) 160.
36. C. van der Poel, Rheol. Acta
!
(1958) 198. 37. E.H. Kerner, Proc. Phys. Soc. 69B (1956) 808.38.
z.
Hashin, S. Shtrikman, J. Mech. Phys. Solids 11 (1963) 127. 39. C.M. Thomas, British Plastics 36 (1963) 645.40. B.J. Spit, Polymer! (1963) 109.
41. C.B. Bucknall, J. Materials (ASTM) ! (1969) 214. 42. Z. Hashin, J. Appl. Mech. ~ (1962) 143.
43. D. Heikens, S.D. Sjoerdsma, W.J. Coumans, J. Mater. Sci. 16 (1981) 429.
44. W.J. Coumans, D. Heikens, S.D. Sjoerdsma, Polymer
3!
(1980) 103. 45. S.D. Sjoerdsma, A.C.A.M. Bleijenberg, D. Heikens, Polymer 22(1981) 619.
46. S.D. Sjoerdsma, J. Dalmolen, A.C.A.M. Bleijenberg, D. Heikens, Polymer
3!
(1980) 1469.47. S.D. Sjoerdsma, D. Heikens, J. Mater. Sci., in press. 48. S.D. Sjoerdsma, D. Heikens, J. Mater. Sci., in press.
49. S.D. Sjoerdsma, A.C.A.M. Bleijenberg, D. Heikens, in "Polymer Blends", E. Martuscelli, R. Palumbo and M. Kryszewski eds.
(Plenum Press, New York, 1980).
50. S.D. Sjoerdsma, D. Heikens, in "Polymer Compatibility and Incompatibility" (MMI Press Symposium Series, 1980, in press). 51. S.D. Sjoerdsma, D. Heikens, J.J.A.M. Brands, J. Mater. Sci.,
in press.
CHAPTER 2
VOLUME STRAIN, ELONGATIONAL STRAIN AND
STRESS IN HOMOGENEOUS DEFORMATION
A model is presented for the volume strain of a t~o phase blend ~hiah elongates homogeneously during a tensile test. If only elastic deformation and crazing take plaee the volume strain against elongation curve can be calculated from the data of the stress-strain curve. When elastic deformation, crazing and deformation by shear flo~ take place, the stress versus elongation aurve and the volume-strain versus elongation curve aan be used to aaZculate the separate contributions of the three deformation mech-anisms at any elongation. In principle, the model aan be used for any material that deforms homogeneously and ~here
one or more deformation mechanisms are present.
2 • L INTRODUCTION
In order to study the mechanical deformation be-haviour of polystyrene (PS)/low density polyethylene (ldPE) blends a dilatometer was developed to determine volume strain during tensile deformation1-3. The results prompted the development of a simple model that describes the vol-ume strain as a function of stress and strain for constant strain-rate experiments. Assuming additivity of volume strain and elongational strain caused by elasticity,
4-6
crazing and shear flow, as suggested by Bucknall , it is possible to write
( 2. 1)
where ~V is the change in volume strain, V
0 is the zero strain volume, and ~Vel' 6Vsh and ~Vcr are the change in components of volume strain caused by elasticity, shear flow and crazing.
Further:
eel+esh+ecr' (2.2)
where e is the elongational strain, 61 is the change in length, 10 is the zero strain length, 6lel' 6lsh' ~lcr' and eel' esh and e:cr are the changes in respectively
length and elongational strain caused by elasticity, shear flow and crazing.
From the definition of the Poisson's ratio v:
while
a
E'
where a is the stress and E is Young's modulus.
(2. 3)
(2.4)
The contribution of crazing to the volume strain is given by:
ecr' (2.5)
while
0. (2.6)
Thus i t follows that
(2.7)
or
{ 2. 8)
where Eel may be set equal to a/E for all values of Esh and £er when the amount of material subjected to elastic deformation is constant.
In case of the PS/ldPE blends the total elonga-tion-to-break is at low strain rates about 10 per cent, of which 1-2 per cent is elastic. In case of crazing only, the void content is then ultimately about 8 per cent. Assuming that an approximately equal fraction of the sam-ple material is transformed into craze-filling material, the amount of matrix available to deform elastically will always be higher than 92 per cent. This means that the elongation Eel should be corrected by a factor with a value between 0.92 and 1. When the matrix also deforms by shear flow the same factors must be considered, but for many cases equation 2.8 will be a good approximation.
2.2. CRAZING AND ELASTIC DEFORMATION
In many high-impact polystyrenes deformation by shear flow is negligible and equation 2.8 reduces to:
~V/V0
=
(1-2~)a/E+£-a/E. (2.9)Again, the first term represents the elastic contribution to the volume strain and the following two terms the con-tribution of crazing. Rearrangement gives
~V/V
0
= e-2~ ajE. (2.10)Equation 2.10 can be used to calculate the volume strain versus elongational strain curve from a stress-strain curve, provided the Poisson's ratio and Young's modulus are known.
The general features predicted by the model are confirmed by experimental curves of PS/ldPE blends. In
figures 2.1 and 2.2 the experimental results are presented for a commercial high-impact polystyrene and for a PS/ldPE
af
t~%)
0
2
6
Figure 2.1. Experimental curves of engineering stress and of volume strain versus elongational strain of a high impact poly-styrene (Dow Chemical eo.) are represented by the full lines. The volume strain calculated from the stress-strain curve using equation 2.9 is represented by dots.
af
t
J\' ' \b (%) (MP a) 4 10 4Figure 2.2. Experimental curves and model predictions as in figure
2.1 for a 92.5/7.5 {wt %) PS/ldPE blend.
blend1• The full curves have been experimentally deter-mined whereas the dots have bV and c as coordinates and are calculated from equation 2.9. As the true stress de-viates by less than one per cent from the engineering stress, values for the engineering stress were used in-stead of true stress values. E and v were calculated from the initial slopes of the stress and volume strain curve. The agreement between the model and the experimental re-sults is very good.
2.3. CRAZING, SHEAR FLOW AND ELASTIC DEFORMATION
For some PS/ldPE blends containing certain block-copolymers evidence of the occurrence of both crazing and shear flow have been. obtained1: Rearrangement of equation 2.8 gives:
(1-2v)cr/E+(e-cr/E)-6V/V
0 (2.11)
Thus esh can be calculated by combining the data from the stress-strain curve and the volume-strain curve.
Also, ecr can be calculated by combining equations' 2.4 and 2.7:
(2.12)
Of special interest are the parts of a stress versus elongation curve where
da/de = 0. (2.13)
Differentiating equations 2.11 and 2.12 with respect to strain yields
(2.14)
This shows that for cases where dcr/de ~ 0, for instance at the yield-point or at high elongations, the slope of the volume strain curve is a direct measure of the in-cremental contributions desh/de and deer/de: at the cor-responding elongation. For creep experiments, where dcr/de is practically zero, the slope at any point on the volume stra·in against elongational strain curve is a measure of the strain contributions of the two deformation mecha-nisms. This principle has been applied by Bucknall for a
7 number of materials •
The model developed for heterogeneous systems should be applicable to any material that deforms homoge-neously, provided that deformation by shear flow and/or crazing does not greatly diminish the volume of the mate-rial that is deforming elastically. However, as the volume changes resulting from elastic deformation are usually rather small in the region of crazing, deviations from the model will still be small, and the model will there-fore still be applicable.
2.4. REFERENCES
1 • Chapter 3.
2. W.J. Coumans and D. Heikens, Polymer~ (1980) 957.
3. W.J. Coumans, D. Heikens and S.D. Sjoerdsma, IUPAC 26 Inter-national Symposium on Macromolecules 1979, Mainz.
4. C.B. Bucknall and D. Clayton, Nature (Phys. Sci.) 231 (1971) 107.
5. C.B. Bucknall and D. Clayton, J. Mater. Sci.
I
(1972) 202. 6. C. B. Bucknall, D. Clayton and W. E. Keast, J. Mater. Sci. 7{ 1972) 1443.
7. C.B. Bucknall, "Toughened Plastics" (Applied Science Publishers Ltd., London, 1977).
CHAPTER 3
DILATOMETRIC INVESTIGATION OF DEFORMATION MECHANISMS
IN POLYSTYRENE/LOW DENSITY POLYETHYLENE BLENDS
To gain more insight into the deformation behaviour of blends containing polystyrene (PS), low density polyeth-ylene (ldPE) and PS-PE blockcopolymer (BC), tensi tests have been performed with simultaneous volume measurements. It is shown that, after yielding, crazing is the only de-formation mechanism of blends with a low ldPE and blockco-polymer content. Shear flow becomes important at
relative-ly high coporelative-lymer concentrations. This is explained by the formation of a semi-continuous low-modulus phase. The decrease of the Poisson's ratio with the ldPE content in PS/ldPE homopolymer blends and the increase of the Pais-son's ratio in case copolymer is present in these blends show the sensitivity of the Poisson's ratio to adhesion between the components. Toughness of PS/ldPE blends is discussed in terms of craze density. If the craze density is too low brittle failure will take place as a tow num-ber of crazes cannot take over much of the deformation of the matrix. Too high a craze density causes brittle fail-ure because the chance of fatal crack formation due to combination of crazes is high. Therefore high toughness is only obtained at intermediate craze densities. The craz'e density is shown to be dependent on the nu'mber of dispersed particles and on the adhesion between these particles and the matrix.
3.1. INTRODUCTION
1-8
In earlier research , normal blockcopolymers of polystyrene (PS) and polybutadiene (PB) and blockcopoly-mers with a tapered structure containing a random styrene-butadiene block between a PS block and a PB block were hydrogenated to obtain PS-polyolefine blockcopolymers. On addition of these blockcopolymers in concentrations of about 2 (wt)% to polystyrene/low density polyethylene blends (PS/ldPE) by meltblending, the range of dimensions of the spherical ldPE particles diminished from 10-40 pm to 1-10 pm. This indicated that blockcopolymer was situ-ated at the interface between the ldPE particles and the PS matrix (figure 3 .. 1). Thus the blockcopolymers behaved as PS-ldPE blockcopolymers. In accordance with this inter-pretation the tensile strength, the yield stress and the impact strength of samples with these low concentrations
Figure 3 .1. A particle of low density ~lyethylene (A) dispersed in a matrix of polystyrene (B) with blockcopolymer at the interface.
(relative to the concentration of the ldPE) of normal and tapered blockcopolymers were higher than that of corre-sponding PS/ldPE blends without copolymer. Scanning elec-tron micrographs of impact fracture surfaces of these samples gave evidence of craze planes (figure 3.2a). How-ever, at higher concentrations of the tapered blockcopoly-mers (BC) the fracture surfaces showed signs of shear flow
(figure 3.2b). Micrographs showed that in blends that con-tain more than 20% of total dispersed phase, (semi-)con-tinuous ldPE/BC phases are formed. Comparison of the mod-ulus-concentration behaviour of these samples with simple models indicated that at low concentrations of BC !(rela-tive to ldPE) the blockcopolymer was situated at the inter-face between the ldPE particles and the PS matrix. How-ever, at higher concentrations of BC relative to ldPE and if the total dispersed phase concentration exceeded 20% the excessively low modulus values suggested that most of the deformation takes place within a low modulus (semi-) continuous phase. It may well be that this phase also gives rise to the evidence of shear flow that was found on the fracture surfaces of these blends.
To gain more insight into the deformation mecha-nism it was necessary to determine the contribution of crazing and shear flow to the deformation. Determination of volume changes during creep experiments is a well-known method to distinguish shear flow and crazing9-12. Crazing produces an increase in volume that is proportional to the elongation, whereas the contribution of shear flow to vol-ume changes can be assvol-umed to be negligible. As this in-vestigation aims at strain rates that are higher than those attainable in creep experiments a dilatometer for use with a tensile tester was developed. It must be re-marked here that the volume changes during tensile test can only arise from craze formation. Void formation in the soft phase has never been observed in PS/ldP~ blends.
a
b
Figure 3.2. a) Scanning electron micrograph of a fracture surface of a blend of PS/BC/ldPE (80/2.25/17.5 by weight)
indi-cating crazing (400x) .
b) Scanning electron microscope picture of a fracture
surface of a blend of PS/BC/ldPE (60/30/10 by weight) indicating shear flow (1600x).
3. 2. EXPERIMENTAL
3. 2 .1. Volume, stress and strain measurements
A detailed description of the dilatometer has been published elsewhere1~ but some general principles
will be given here. The dilatometer allows continuous de-termination of the volume change of a sample during its
G D
A
B
F
Figure 3.3. Dilatometer for measuring the volume change of a sample during a tensile test.
22
A dilatometer vessel filled with water;
B sample;
c stationary clamp;
D bar attached to stress gauge;
E attachment to cross-bar of tensile tester;
F compensation bar with same diameter as bar D;
elongation in a tensile tester. This is achieved by meas-uring the waterlevel in a capillary G that is attached to the vessel A which encloses the sample (figure 3.3). The load is measured by the tensile tester. The elongation of the sample is measured by monitoring the displacement of the lower sample-clamp relative to the compensation bar F
that is connected to the upper stationary clamp C. On an xyy'plotter, load and volume are recorded simultaneously as a function of the elongation.
3.2.2. Materials and tensile specimens
The blends consisting of PS, ldPE and/or block-copolymer BC were prepared by meltmixing on a laboratory mill. The PS used was Styron 666 (Dow Chemical) with a Mn of about 100 000. The ldPE was Stamylan 1500 (DSM, Holland) with an estimated Mn of 30 000 to 40 000 and a broad mole-cular distribution: Mw/Mn ~ 30. The blockcopolymer BC is obtained by hydrogenating Solprene 410 (Phillips Petroleum Company, u.s.A.), which is a linear partial diblockcopoly-mer of PS and PB1'2 •
The tension test specimens were rectangular com-pr.ession moulded bars, with a span of 50 mm and with cross-sectional dimensions of 13 x 3 mm.
3.3. RESULTS AND DISCUSSION
3.3.1. Presentation of results
The results presented here have been obtained from a series of blends containing 7.5, 15 or 25 (wt)% of ldPE in PS, and from a derived series in which 5, 30, 60 or 100% of the free ldPE is replaced by bound PE (by add-ing appropriate amounts of blockcopolymer BC to the blends). Results are presented in figures ·3. 4, 3. 5, 3. 6 and in
tables 3.1 and 3.2. They have been obtained by averaging the results of five samples of every composition. The
results are conveniently discussed by comparing data on blends containing PS and ldPE with those from blends con-taining PS and blockcopolymer only. In a latter part blends containing all three components will be considered.
5 6
Figure 3.4. Engineering stress ~nd volume strain measured as function of elongational strain. Curves of PS blends containing in total 7.5% of ldPE. In these blends 0, 5, 30, 60 and 100% of the free ldPE is replaced by ldPE bound by the block-copolymer BC, as indicated by the numbers at the curves.
0 3 4 5 6 7 8
t(Ofo)
Figure 3.5. Engineering stress and volume strain measured as function of elongational strain, Curves of PS blends containing in total 15% of ldPE. In these blends 0, 5, 30, 60 and 100% of the free ldPE is replaced by ldPE bound by the block-copolymer BC, as indicated by the numbers at the curves.
30,---, 5
Figure 3,6. Engineering stress and volume strain measured as function of elongational strain. Curves of PS blends containing in total 25% of ldPE. In these blends 0, 5, 30, 60 and 100%
of the free ldPE is replaced by ldPE bound by the block-copolymer BC, as indicated by the numbers at the curves.
3.3.2. Blends from PS and ldPE
Blends containing 7.5, 15 and 25% ldPE (figures 3•4, 3.5 and 3.6, curves 0) have Poisson's ratios of 0.33, 0.32 and 0.31 respectively (table 3.1).
An increase of Poisson's ratios should be ex-pected in case of adhesion between ldPE and PS, as the phase ldPE has a Poisson's ratio of 0.48. The decrease of the Poisson's ratio with increasing ldPE content may be explained by void formation around the ldPE particles that do not adhere to the matrix.
At that elongation of a sample containing 7;5% ldPE where the slope of the stress strain curve dcr/de starts to decrease, the slope of volume strain curve d(~V/V
0
)/de starts to increase and becomes approximately one (figure 3.4). Apparently this decrease in the slope of the stress-strain curve corresponds with the onset of the craze growth mechanism. Beyond the yield-point the stress decreases rapidly to a relatively small value of 75-80% of the yield stress, reflecting the increase of the volume of the crazes. When the stress has reached a more or less constant value the slope of the volume strain curve goes asymptotically to one, indicating an equilibrium between volume strain rate (void content increase) and elonga-tional strain rate.By comparing the results of samples 4.0, 5.0 and 6.0, it is seen that the elongation at break diminishes from 6 to 1% as the ldPE concentration increases from 7.5 to 25%. The samples with 25% ldPE 6.0 (table 3.1, figure 3.6, number 0) break before yielding takes place. The de-crease of elongation at break with increasing ldPE content can be explained by the increase of the number of crazes. In a blend with a high craze density( crazes can easily comblne to form a fatal crack, which causes premature failure.
Table 3.1. Comparison of blends containing PS and ldPE and blends containing PS and blockcopolymer (BC) with respect to their mechanical data, dilatometric data and deformation mechanism.
Dispersed Poisson's
Sample a) phase b) E c) Eb c) ratio d) Slope e) Mechanism f) y (wt %) (%) {%) Blends of PS andldPE 4.0 7.5 1.8 6.0 0.33 1.13-1.04 cr. 5.0 15.0 1.8 4.0 0.32 1.04 cr. 6.0 25.0 1.0 1.0 0.31 g cr. Blends of PS and BC 4.100 14.4 1.7 1.7 0.36 g cr. 5.100 29.0 2.55 2.60 0.41 0.68 cr.+sh. 6.100 48.0 h 18 0.47 0.04 sh.
a) The first number of this notation refers to figur'e 3.4, 3.5 or 3·.6. The second number corresponds to the curve numbers in these figures and indicates the percentage of free ldPE being replaced by bound ldPE of the blockcopolymer;
b) ldPE plus blockcopolymer; c)
Elongational strains at yield-point (e:Y) and at break {e:b) ; d)
Derived from initial slope of volume strain/elongational strain curve {elastic behaviour) ;
e)
Relates to second part of volume strain/elongational strain curve (post-yielding behaviour) ;
f)
cr. = crazing and sh.
=
shearing; g) Breaks just at yield-point; h) No stress maximum observed.3.3.3. Blends from PS and bloakcopolymer
The deformation behaviour of PS/BC blends will be compared with the deformation behaviour of PS/ldPE blends. Attention will be paid in particular to the effects of ad-hesion on the Poisson's ratio of the blends and on the number of crazes formed during tensile tests.
Adhesion seems to be reflected by the increase of the Poisson's ratio from 0.36 to 0.41 and 0.47 at respec-tively 14.4, 29 and 48 (wt)% concentration of blockcopoly-mer (table 3.1, figures 3,41 3.5 and ·3.6, curves lOO).
These copolymer concentrations correspond to bound ldPE concentrations of 7.5, 15 and 25% and thus can be compared with the samples 4.0, 5.0 and 6.0 with equal concentrations of free ldPE. In the blockcopolymer containing blends co-polymer particles will adhere to the matrix and will cause an increase of the Poisson's ratio of the system. As the Poisson's ratio of the blockcopolymer is 0.48, an increase from 0.36 to 0.41 can be expected on the basis of simple rules of mixtures. Thus comparison of the results for PS/ ldPE and for the PS/blockcopolymer blends indicates that the presence of interfacial adhesion can be shown by meas-urements of the Poisson's ratio of these blends. However, at the highest blockcopolymer concentration (48%), the blockcop(,lymer forms a more or less continuous low modulus
1 2
phase ' . The volume change may then be determined almost exclusively by the Poisson's ratio of the blockcopolymer.
Microscopic observations in earlier work2'4
showed that adhesion causes a strong reduction in the num-ber of crazes in PS/ldPE blends. In the case of PS/block-copolymer blends adhesion between the phases will exist and therefore fewer crazes will be initiated. In case of a small number of crazes, fatal crack formation in the elastically strained PS matrix can be expected before the yield stress is reached and such a sample breaks brittly. This seems to be the case for the 14.4% blockcopolymer containing sample 4.100. At higher concentrations (29% blockcopolymer, figure 3.5, curve lOO) more crazes will
be formed since more craze initiating particles are pres-ent. This results in the attainment of the yield-point. The beginning of a strong volume increase beyond the yield-point (slope = 0.68) indicates that crazing takes place12• Assuming that shear flow does not produce an ap-preciable volume increase, this value also indicates that deformation by shear flow contributes 32% to the yielding deformation, while crazing contributes 68%. According to microscopic observations, the blockcopolymer in this blend
forms a semi-continuous network. This network can suppress fatal craze growth by acting as a craze stopper and makes shear flow possible. The occurrence of shear flow is more pronounced in the sample containing 47% of blockcopolymer
(figure 3.6, curve 100). Here the Poisson's ratio is ap-proximately 0.47, indicating that deformation mainly takes place in the low modulus phase. The very low volume in-crease with a slope of only 0.04 at high elongations also shows that here shear flow is the only deformation mecha-nism.
3.3.4. Blends containing ZdPE and blookaopolymer
The results are presented in figures 3.4, 3.5 and 3.6 and in table 3.2. The mechanical properties of blends containing PS, ldPE and blockcopolymer are in between those of PS/ldPE and PS/BC blends.
3.3.4.1. Poisson's ratio and adhesion
In samples containing 7.5% free plus bound ldPE (samples 4.5, 4.30 and 4.60) the ldPE phase will adhere to the matrix due the presence of the blockcopolymer at the interface. Adhesion is confirmed by the increase of the Poisson•s ratio from 0.33 to 0.37 as the total per-centage of dispersed material increases from 7.9-11.6. Still higher Poisson 's ratios are· found for the 5 and 6 series as compared with the 4 series. This must result from the higher concentration of dispersed phase in these series.
At concentrations higher than about 20-25% of total dispersed material a semi.-continuous or continuous
phase of ldPE and blockcopolymer is formed. The samples 5.60, 6.30 and 6.60 that contain these (semi-)continuous phases have rather low moduli of 13.7-7.7 102 MPa and high Poisson's ratios of 0.43-0.47 due to the fact that most of the deformation takes place in the low modulus phase.
Thus it may be concluded that adhesion, concen-tration and morphology strongly determine the values of modulus and Poisson's ratio of the blends. At low concen-trations of the dispersed phase (sample 4.5, 4.30, 4.60), adhesion can be deduced from the dependence of the Pois-son's ratio on the concentration. ~t high concentrations
(samples 5.60, 6.30, 6.60), both modulus and Poisson's ratio of the blends are strongly influenced by the pres-ence of a (semi-)continuous low modulus phase.
3.3.4.2. Brittle-tough behaviour
In describing the brittle-tough behaviour of blends in which no deformation by shear flow takes place, the craze density appears to be a crucial parameter. A qualitative relation between the craze density and brittle-tough behaviour is shown in figure 3.7.
At low craze densities catastrophic cracks are formed due to the large size of the crazes, whereas at high craze densities crazes can easily combine to form cracks. At medium craze densities excessive growth of the crazes is stopped by stress release mechanisms as pointed out by Nielsen14.
In series.4 from 4.5 onward, low concentrations of dispersed material are combined with a good adhesion. This results in a low craze density causing brittle fail-ure. Samples 4.5 serves as an example for this behaviour, and thus is placed at the low craze densi.ty side of th.e curve of figur>e 3.7. Sample 4.0, which does not contain blockcopolymer, will have a higher craze density and shows a tough behaviour (figure 3.7).
w
...
Table 3.2. Mechanical data, diiatometric data and deformation mechanism of PS/blockcopolymer (BC)/ldPE blends.
E-modulus Total Dispersed Poisson's
Sample a) X 10-2 PE phase b) c) E:b cl ratio d) Slope e) Mechanism f) (MP a} (wt %) (wt %} (%} (%) 4.5 29.3 7.5 7.9 g 1.5 0.33 g cr. 4.30 23.9 7.5 9.6 g 1.7 0.34 g cr. 4.60 22.0 7.5 11.6 g 1.4 0.37 g cr. 5.5 19.4 15.0 15.7 2.1 7.6 0.35 0.99 cr. 5.30 19.3 15.0 19.2 2.2 2.4 0.39 1.15 cr. 5.60 13.7 15.0 23.3 2.6 2.8 0.43 0.75 cr.+sh. 6.5 15.8 25.0 26.1 2.3 7.2 0.38 0.87 cr.+sh. 6.30 11.2 25.0 32.0 4.5 6.3 0.44 0.67 cr.+sh. 6.60 7.7 25.0 38.8 h >18 0.47 0.07 sh.
.c gi 0 ' lCraze density -Yield point present No yield point
Figure 3.7. A schematic presentation of the relation between craze density and brittle-tough behaviour. The numbers in the graph refer to the samples in tables 3.1 and 3.2 and to · the figures 3.4, 3.5 and 3.6.
In series 5 (tables 3.1 and 3.2) the concentra-tion of dispersed material in the samples 5.0, 5.5 and 5.30 varies only from 15 to 19.2%. As indicated by,the slope of the volume strain curve crazing is the only yielding deformation mechanism. All these samples show a yield-point but their elongation at break varies respec-tively from 4.0 to 7.6 to 2.4%. In the order 5.0, 5.5, 5.30 the particle dimensions decrease and the number of particles increases so a higher craze density is expected. However, the formation of crazes is much more strongly reduced by the increased adhesion that accompanies the reduction of particle size2'4 • Apparently the samples are qualitatively situated on the curve as shown in figure
3.7.
In sample 5.60, containing 24% ductile material, some shear flow (24%) takes place due to the formation of a
(semi-)continuous phase. Shear flow will tend to enhance the elongation at break. But at the .same time craze for-mation is suppressed by adhesion, which tends to lower the elongation at break. The net result here is that this ma-terial breaks just beyond the yield-point.
In series 6 the increase of the concentration of dispersed material (> 26%) results in more shear flow. The elongation at break will increase by the formation of a
(semi-)continuous phase. This phase will act as a craze stopper in all three samples and thus even in sample 6.5, which still deforms 87% by crazing, catastrophic crazing does not occur at low elongation. If shear flow is the only deformation mechanism (sample 6.60) a high Poisson's ratio is combined with a low slope of the volume strain curve and a very low modulus. In this sample most of the deformation takes place in the (semi-)continuous low mod-ulus phase.
3.4. CONCLUSION
During a tensile test, low modulus particles (ldPE and/or blockcopolymer) dispersed in a stiff matrix (PS) can cause crazing. At higher concentrations the soft phase tends to form a more or less continuous phase and yielding will take place by shear flow. At intermediate concentrations a combination of both mechanisms occurs.
In blends where the occurrence of shear flow does not take place, a low craze density causes brittle fail-ure. However, a high craze density also causes brittle behaviour, as the many crazes now can combine to form a crack. Tough behaviour can be expected at intermediate craze densities. The craze density will be determined to some extent by the number of dispersed particles and is high if the adhesive forces acting between the particles and the matrix are weak. Addition of blockcopolymer to the blends reduces the ease of formation of crazes and this effect overcompensates the increase in the number of particles by emulsifying action. Adhesion can be deter-mined from the experimental deterdeter-mined dependence of the Poisson's ratio on the concentration of the low modulus material.
Higher concentrations of the low modulus material results. in the formation of a more or less continuous phase and in this case the phase borders will act as craze stoppers. However, shear flow can occur in the low modulus phase and rather large elongations at break can result. By choosing a correct ratio of blockcopolymer and low mod-ulus polymer (added in suitable concentration to the ·stiff polymer) attractive combinations of modulus and toughness are attainable.
3.5. REFERENCES
1. N.G.M. Hoen, Thesis, Eindhoven University of Technology, Eind-boven, 1977.
2. D. Heikens, N. Hoen,
w.
Barentsen, P. Piet and H. Ladan, J. Polym. Sci. (Polymer Symp.) §!. (1978) 309.3. W.M. Barentsen and D. Heikens, Z. fur Werkstofftechnik
!1!L
{1970) 49.4. W.M. Barentsen, Thesis, Eindhoven University of Technology, Eindhoven, 1972.
5. W.M. Barentsen and D. Heikens, Polymer!! (1973) 579.
6. W.M. Barentsen, D. Heikens and P. Piet, Polymer~ (1974) 119. 7. D. Heikens and W.M. Barentsen, Polymer (1977) 69.
8. W.M. Barentsen, P.J. Heijdenrijk, D. Heikens and P. Piet, Br. Polym. J. 10 (1978) 17.
9. C.B. Bucknall and D. Clayton, Nature (Phys. Sci.) ~ (1971) 107. 10. C.B. Bucknall and D. Clayton, J, Mater, Sci.
2
(1972) 202. 11. C.B. Bucknall, "Toughened Plastics" (Applied Science Publishers,London, 1977). 12. Chapter 2,
13. W.J. Coumans and D. Heikens, Polymer
3!
(1980) 957,14. L.E. Nielsen, "Mechanical Properties of Polymers" (Reinhold Publishing Corporation, New York, 1963).
CHAPTER 4
THF POISSON
1S RATIO OF POLYMER
BLENDS~EFFECTS OF ADHESION
AND CORRELATION WITH THE KERNER PACKED GRAINS MODEL
The moduli and Poisson's ratios of polystyrene/low density polyethylene blends with different aompositions have been determined. In some cases a po tyrene-polyethylene co-polymer was added to the blends to provide for adhesion between the components. It is shown that the Kerner packed grains model aan be used to predict aaaurately both modu-lus and Poisson's ratio of these blends. Deviations of both modulus and Poisson's ratio from the values occur in some blockaopolymer containing blends as a con-sequence of the aopolymer-induaed formation of a contin-uous low modulus phase at a relatively low concentration of the low modulus material. In aase of non-adhesion be-tween the components only the Poisson's ratio was found to deviate significantly from the prediated value. This is explained by assuming hole-like behaviour of the low den-sity polyethylene particles due to non-adhesion and the misfit of the coefficients of thermal expansion of poly-styrene and low density polyethylene.
4.1. INTRODUCTION
In the course of a research project on styrene (PS) plastics toughened with low density ethylene (ldPE) and in some cases modified with a
poly-1 2
styrene-polyethylene (PS-PE) copolymer ' , an apparatus
suitable for observing volume changes during tensile tests has been developed3. The object was primarily to study crazing phenomena. However, pre-crazing volume changes, measured by the Poisson's ratio, could be determined quite accurately as well. This is of interest, since theoreti-cally the Poisson's ratio of a blend can reflect proper-ties of the components that the modulus, for example, can-not. The Kerner packed grains equations4 for a two phase blend show that this is true, particularly for blends that
Figure 4.1. ~dulus of blends predicted by the Kerner equations, show-ing the relative insensitivity of the modulus of the blend compared with the Poisson's ratio of the blend (figure 4.2) to changes in the modulus of the ductile component at low volume fractions of the ductile component.
consist of a stiff matrix and a ductile dispersed phase: 0 GO-G1 GO-G2 (7-sv0)G 0+(8-10v0)G1 fl + (7-Sv0)G0+(8-10v0)G2 f2 where K
0, K1 and K2 are the bulk moduli of the blend, com-ponent 1 and 2 respectively; G0, G1 and G2 are the corre-sponding shear moduli, v0 is the Poisson's ratio of the blend and f1 and f 2 are the volume fractions of components 1 and 2.
For two kinds of blends, A and B, the modulus and the Poisson's ratio have been calculated using these Kerner equations (figures 4.1 and 4.2). Blend A consists of a component 1 {modulus G1
=
109 Pa, Poisson's ratio v1 0.30) and a component 2 (modulus G2=
108 Pa, Poisson's ratio v2
=
0.45). The components of blend B have the same elastic constants, except that the modulus of component 2 is G2=
0.5 108 Pa. Figure 4.1 shows the relative insen-sitivity of the modulus of a blend to a change in the mod-ulus of the ductile dispersed phase if the volume fraction of the low modulus phase does not exceed 0.2. The Poisson's ratio, however, is much more sensitive to a change in mod-ulus in this concentration range (figure 4.2).The aim of this study is to explore whether the modulus and the Poisson's ratio of PS/ldPE blends can be described by the Kerner packed grains equations, and, secondly, whether the sensitivity attributed to the Pais-son's ratio as described above, can be verified experi-mentally.
The Kerner packed grains equations were chosen to compare the experimental data with since they predict the moduli of blends as well as the Poisson's ratio. These equations are based on Goodier's analysis of the elastic properties of material containing a spherical inclusion5•
37 0
08 06 04 02 0
Figure 4.2. Poisson's ratio of blends, predicted by the Kerner equa-tions.
This analysis is extended to the elastic properties of a multicomponent blend by means of an averaging procedure. The packed grains equations were obtained by taking the volume fraction of the matrix material to be zero.
Application of these equations to a blend means that no a priori assumptions about the matrix material can be made. However, as the volume of the blend is
statisti-'
cally filled with the components, an excess of one of the components must result in a 'continuous' phase consisting of grains of this material. Thus i t can be expected that the packed grains equations can be'applied to systems that undergo phase inversion in a symmetrical fashion around the 50/50 composition. Sinte phase inversion of the PS/ldPE
Figure 4.3.
Figure 4.4.
Figure 4.5.
Figures 4.3, 4.4 and 4.5. Scanning electron micrographs of homopoly-mer blends showing phase inversion. Composition 35/65,
50/50 and 65/35 wt.% ldPE/PS, respectively.
blends occurs at least approximately around this composi-tion (figures 4.3, 4.4 and 4.5), i t seemed profitable to compare the outcome of these equations with the experi-mental values for shear modulus and Poisson's ratio.
4. 2. EXPERIMENTAL
The polymers used in the blends were polystyrene - "v - - "v
Styron 664 from Dow Chemical Co. (Mn
=
lOO 000, Mw/Mn=
2.5), and low density polyethylene Stamylan 1500 from DSM, - "v - - "v
Holland (Mn
=
30 000-40 000, Mw/Mn=
30). A partial poly-styrene-polyethylene diblock copolymer was obtained byhydrogenating a partial polystyrene-polybutadiene diblock copolymer (Solprene 410 from Phillips Petroleum Co.) that consists of sequences with the following molecular weights:
[PS-(PS/PB)random-PB]
=
[22000-22000-25000]The blends were prepared on a Schwabenthan laboratory mill
at 190°C. Test specimens were machined from compression
moulded sheets, and had dimensions as indicated by ASTM 0638 type i i i .
The Poisson's ratios of the blends were measured using a dilatometer system on an Instron tensile testing machine 3 . The strain rate was 0.4 min- 1 . Volume changes
of the tensile specimen during a tensile test result in a
liquid displacement in the capillary attached to the
di-latometer. This liquid displacement can be recorded con-tinuously and with high accuracy using a conductivity meter. The Poisson's ratio is calculated from the initial
slope of the sample volume versus elongation curve. For
samples containing less than 25% dispersed polyethylene and copolymer this initial slope corresponds to the linear elastic part of the stress-strain curve and time-dependent behaviour can be ignored. Samples containing higher con-centrations of low density polyethylene and blockcopolymer will show time-dependent behaviour, but the initial slope
corresponding to the Poisson's ratio could be measured accurately at quite small strains (< 0.5%}. The Poisson's ratio of these samples, however, will certainly be some-what strain-rate dependent.
The modulus of the blends was measured on a torsion pendulum (Nonius Instrumentan Fabriek, Delft, The Netherlands). The test specimens had dimensions 120 x 5.7 x 2.7 mm.
4.3. RESULTS AND DISCUSSION
The experimentally obtained values for the shear modulus and the Poisson's ratio of the homopolymers and polystyrene-polyethylene diblock copolymer are listed in tabZe 4.1. These values for the polystyrene-polyethylene diblock copolymer containing blends are listed in tabZe 4.2. As the shear modulus and the Poisson's ratio of ldPE and the partial diblock polystyrene-polyethylene copolymer are approximately the same, i t is possible to consider the combination of both materials as a single phase that
ad-2 heres to polystyrene due to the presence of the copolymer . Doing this, the experimentally obtained values for the modulus and the Poisson's ratio of the blends have been plotted in figures 4.6 and 4.7.
Table 4.1. Mechanical properties of the blend components.
Shear modulus 8 Poisson's ratio polystyrene l.d. polyethylene polystyrene-polyethylene diblock copolymer (X 10 Pa) 12.2 0.87 0.95 0.33 0.48 0.47 41
