Microscopic in situ observation of the plastic deformation of polybutene-1 films under simple shear

Polymer Testing3 (1982) 3-24

MICROSCOPIC IN SITU OBSERVATION OF THE PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR S. BONI, C. G'SELL

Laboratoire de Physique du Solide, L.A. au CNRS No. 155, Ecole Nationale Supdrieure de la Mdtallurgie et de l'Industrie des Mines, Parc de Saurupt, 54042 Nancy Cedex, France and E. WEYNANT and J. M. HAUDIN

Centre de Mise en Forme des Mat~riaux, E.R.A au CNRS No. 837, Ecole Nationale Sup~rieure des Mines de Paris, Sophia Antipolis, 06560 Valbonne, France

SUMMARY

Optical micrographs were obtained in situ during the course of simple shear tests operated on thin films of isotactic polybutene-1 (modification I) and the stressstrain curves were recorded simultaneously. A detailed observation of individual spherulites showed that the radial crystallites perpendicular to the major principal tensile axis of stress are separated by bending and that those inclined on this axis participate in the plastic deformation. It is demonstrated that the simple shear test cannot be performed on polymer films without being perturbated by plastic buckling and by a deformation of the material in the grips. These artefacts do not seriously affect the results concerning the microstructure dependence of the yield stress but make questionable the quantitative interpretation of the plastic regime. A geometric criterion is proposed for the design of shear samples which could undergo the plastic shear strain without side effects.

INTRODUCTION

Although the tensile test has been the most widely used for determining the plastic behaviour of solid polymers, it was shown that shear testing methods are of equal interest when dealing with anisotropic materials (e.g. oriented polymers) or when the influence of a complex state of stress is investigated. Several authors ~ applied the torsion test to plain or hollow specimens. Despite the advantages of this technique, it suffers from the intrinsic problem of the inhomogeneity of stresses and strains along the radius of the twisted cylinder. This difficulty is reduced by using tube-like specimens but then plastic buckling 3 Polymer Testing 0142-9418/82/0003-0003/$2.75 © A p p l i e d Science Publishers Ltd, England, 1982 Printed in Northern Ireland

4

S. BONI, C. G'SELL, E. WEYNANT, J. M. HAUDIN

may occur. Bowden and Jukes 5 developed a plane strain compression test whose resulting state of stress is quite similar to pure shearing if a transversal tensile force is applied. Thanks to this procedure, the authors could determine the yield criterion of several polymers but it was not quite suitable to study the large deformation post-yield regime. It appeared to several authors 6-1° that a plane simple shear test could give the shear stress-shear strain behaviour of polymers. They applied the technique to various amorphous and semicrystalline thin films (isotropic or oriented). It was thus possible to obtain the variation of the critical shear yield stress as a function of the angle between the shearing direction and the orientation axis. However, it can be wondered if the results displayed in these papers can be considered as quantitatively correct, particularly in the plastic region, since the thin film geometry of the specimens might introduce deviations from the bulk geometry. In the present study, the microscopic evolution of isotactic polybutene-1 films will be investigated in the course of a simple shear test. Geometrical and microstructural transformations of individual spherulites will be analyzed and interpreted in terms of the shear straining of the material at a local scale. From the investigation of the local distribution of strain within the samples, we will determine the capabilities and limitations of the simple shear test when it is operated with thin films. We will try at last to derive the optimized geometry of the specimens in order to avoid unwanted plastic instability effects and so to have correct access to the shear stress versus shear strain behaviour of the material.

EXPERIMENTAL TECHNIQUES

Shear-testing apparatus A miniaturized machine was designed and experimented in this work with the capability of applying a shearing deformation to a polymer film at a constant strain rate. Both shear stress and strain were recorded during the test and the microstructural evolution of the material was followed in situ by a continuous optical microscopic observation. Figure 1 shows the main mechanical features of the shearing stage. The film specimen (S) is tightened by pressing screws in two parallel grips G1 and Gz. The gap between the grips can be adjusted to the desired width owing to the transversal fitting of the grip G2. Both grips are held on high precision ball sliders which ensure their parallel shearing movement. Only the displacement of the grip G1 is extensive--it is actuated by the micrometric screw (MS) with an amplitude of 25 mm. The freedom of the grip G2 is just necessary to transmit the shearing force without friction to the force transducer (FT) through the lever (L). The constant shear strain rate is achieved by the

PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR

Fig. 1.

Miniaturized shearing stage adaptable on a transmission polarizing microscope.

synchronous motor (M) whose reduction gear is such that the velocity of the mobile grip G1 is equal to 0.5 mm min -1. The metallic plate which holds the various elements of the machine has overall dimensions equal to 140 x 90 mm 2. It has an elongated window 50 × 20 mm 2 milled under the location of the specimen, so that the apparatus can be mounted on the stage of an optical microscope for in situ observations during the course of a shear test, as shown in Fig. 2. Owing to the particular design of the grips, the specimen is placed at the top level of the apparatus and the correct focusing of the microscope can be obtained even with high magnification objectives. The recording of the shear force versus shear displacement curves was obtained by a X - Y recorder. The Y channel was connected to the conditioner of the force transducer while the X channel was driven by a time base triggered by the switching on of the motor, and so could be scaled directly in millimeters; the accuracy of this recording was controlled by a careful calibration using marked weights for the force and the vernier of the micrometric screw for the shear displacement.

Sample preparation and microstructure As presented in a previous paper la devoted to the tensile properties of polybutene-1, the material used for this work was a commercial polymer (Hiils Vestolen BT 8000, grade 0-1, Mw = 1 225 000, density 0.914). With respect to other polyolefins, polybutene-1 exhibits an original polymorphic behaviour.

6

s. BONI, C. G'SELL, E. WEYNANT, J. M. HAUDIN

Fig. 2.

General view of the shear testing apparatus on the stage of the transmission optical microscope.

Several crystalline modifications were reported in the literature. 12-15 The most important ones are called I and II respectively. The tetragonal modification II, obtained by crystallization from the melt, is unstable and transforms into the stable modification I, which is described as hexagonal or rhombohedral. The transformation occurs spontaneously within a few days 16'17 and can be considerably accelerated by pressure or stress, t2As-21 In this paper, only the deformation of polybutene films in which the crystalline phase is completely transformed into modification I will be considered. The shear samples were cut out of films about 100/~m thick obtained by pressing the molten polymer between two glass slides at 170 °C and then crystallizing it. Two types of microstructure were obtained: 1.

Specimens with an homogeneous spherulitic microstructure (Fig. 3a). These specimens were prepared either by isothermal crystallization in an oven in the temperature range 70 to 100 °C, or by quenching at various temperatures (60 °C in an oven, 22 °C in air, 22 °C in water, -196 °C in liquid nitrogen). Isothermal crystallization from the melt could not be obtained for holding temperatures lower than about 60 °C, because

PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR

i

Fig. 3.

0.5 mm

7

!

Typical spherulite configurations in polybutene-1 specimens: (a) isothermally crystallized at 70 °C, (b) partially crystallized at 100 °C and then quenched in water.

crystal nucleation began during cooling. Therefore such preparation conditions must be considered as quenching procedures. All the film specimens were aged more than 7 days at room temperature prior to being shear tested, so that their crystalline structure was fully transformed into stable hexagonal modification I. The main morphological parameters concerning these specimens are given in Table 1. The mean size of the spherulites was determined by means of direct quantitative microscopy or from the analysis of small angle light scattering patterns. 22 The melting point and the degree of crystallinity of the samples were measured by differential scanning calorimetry (Perkin Elmer DSC 2 calorimeter). It can be seen that the different crystallization procedures led to spherulite diameters varying over a very large range. A simple representation of the evolution of the crystalline morphology as a function of the crystallization conditions can be obtained by plotting the variation of the degree of crystallinity versus the logarithm of the

8

S. BONI, C. G'SELL, E. WEYNANT, J. M. HAUDIN

TABLE 1 CHARACTERIZATION OF THE SPECIMENS TESTED IN PLANE SHEAR. EIGHT TYPES OF CRYSTALLIZATION PROCEDURE WERE USED. FOR EACH PROCEDURE, THE SPHERULITE DIAMETER WAS MEASURED BY OPTICAL MICROSCOPY AND/OR BY SMALL ANGLE LIGHT SCATTERING. THE MELTING TEMPERATURE Tin, THE ENTHALPY OF FUSION AHf AND THE WEIGHT PERCENT CRYSTALLINITY WERE DETERMINED BY DIFFERENTIAL SCANNING CALORIMETRY.

Spherulite diameter (t~m)

Determination method

Weight percent

Conditions

Treatment

1

isothermally at 100 °C

900

optical microscopy

132

20.2

67.3

2

isothermally at 90 °C

500

optical microscopy

130

19.2

64.1

3

isothermally at 80 °C

300

optical microscopy

128.1

17.3

57.7

4

isothermally at 70 °C

220

optical

128

17.2

57.4

5

quenching in air at 60 °C

110

optical microscopy

125

16.2

54.0

6

quenching in air at 22 °C

90

optical microscopy

124.3

15.3

50.9

7

quenching in water at 22 °C

8

quenching in liq. nitrog. at - 196 °C

microscopy

Tm(°C)

AHf

cal/g

crystallinity

+S.A.L.S,

2.

7

S.A.L.S.

115

14.1

47

1.7

S.A.L.S.

108

13

43

spherulite diameter. It appears (Fig. 4) that the degree of crystallinity is roughly a linear function of the logarithm of the spherulite size. Specimens with a few large spherulites embedded in a matrix of very small spherulites. Such specimens were prepared by incomplete high temperature crystallization (e.g. Tc = 100°C), followed by rapid quenching in water at 22 °C. When observed by optical microscopy (Fig. 3b), their microstructure is characterized by isolated round spherulites in a microspherulitic matrix with a lower degree of crystallinity. These particular specimens were also left to transform completely to modification I.

The overall dimensions of the shear specimens (Fig. 5) are 10 mm by 5 mm. The width h of the calibrated shear zone between the gripped edges was chosen to equal about 1-3 ram; the specimen length L was equal to 5 mm and their thickness t was of the order of 0.1 mm. The conventional shear strain is expressed by y = A x / h (where Ax is the relative shearing displacement of the grip) and the shear strain rate by ~. The shear stress is simply given by r = F / ( L t ) (where F is the applied shearing force).

PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR 1

70

9

I

B

I o

-7,

60

o=

so ,,=, Q.

40

I I0

I I00

SPHERULITE

DIAMETER

I000 (~m)

Fig. 4. Experimental relationship between spherulite diameter and crystallinity (weight %) in polybutene-1 samples prepared according to different procedures and fully transformed into modification I. (The procedure references refer to conditions described in Table 1.)

I

' i1

~

t

grip

I I

I

1.3 mm

'1 Ii

L=5rnm

I, I -

ZFig. 5.

Geometry of the sheared polymer films.

10

S. BONI, C. G'SELL, E. WEYNANT, J. M. HAUDIN

Experimental operation After a careful geometrical and microstructural characterization, each specimen was gripped into the shearing stage. In order to avoid any curvature of the film between the grips, a weak tensile stress (about 10 MPa) was applied along the y direction to the specimen while it was gripped, so that the whole surface of the sheared area could be observed by optical microscopy with correct focusing. The driving motor was then switched on and the shear force versus time curve was recorded, while microscopic pictures of the spherulite evolution were taken at given intervals of time. The shear tests were interrupted when fracture occurred. Shear stress versus shear strain curves were computed from the experimental chart.

EXPERIMENTAL RESULTS

Macroscopic plastic behaviour as a function of the crystalline morphology Film specimens with the various spherulite morphologies described above were tested at the same shear strain rate ~ = 6.4 x 10 - 3 s -1. The shear stress versus shear strain curves, displayed in Fig. 6, are characterized by two main stages: (1) A viscoelastic stage with an apparent modulus dr/dy decreasing from 62 to 26.5 MPa as the size of the spherulites and the degree of crystallinity decrease. Unloading sequences showed that this stage is connected to essentially reversible deformation; (2) A plastic stage starting at y -~ 0.5 and characterized by a very small and nearly constant slope dr/dy -- 2.5 MPa. The plastic flow stress is higher as the spherulites are larger. The yielding of the material is gradual and the curves do not exhibit any yield drop, as observed during shear tests in the case of glassy polymers under Tg.3 The determination of the yield stress had then to be done by a conventional procedure--it was chosen to measure the elastic limit at the intersection of lines extrapolated from the viscoelastic and the plastic stages. The plots of Fig. 7 show the variation of the yield stress (and also of the rupture strain) as a function of the microstructural parameters. The yield stress has roughly a logarithmic dependence with the spherulitic size and thus a linear dependence with the degree of crystallinity of the material. The rupture strain seems to obey a more complex dependence since it stays constant for spherulite diameters lower than 100/~m and drops rapidly for larger spherulites. In situ fine scale observation of spherulite deformation (specimens with completed spherulitic microstructure) The in situ microscopic observation of the spherulite evolution during a shear test could be done only on specimens with large enough spherulites. Figure 8 illustrates this evolution in the middle of a sample crystallized completely at

11

PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR

.---3O

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Stress-strain curves obtained with specimens of the different microstructures described in Table 1.

80 °C (with spherulite diameter equal to 0.3 mm). The observation was done between crossed polarizers and the initial configuration at ~ = 0 shows equiaxial spherulites with the usual Maltese cross due to birefringence by the radial crystalline lamellae. As a result of the slow isothermal crystallization, the lamellae are regular without periodic twisting, as assessed by the absence of concentric rings. While the shear test is proceeding, all the spherulites are seen to deform together. Apart from this overall geometrical deformation, each spherulite exhibits a gradual darkening. This phenomenon, which was also noticed in tensile tests, 11 begins here for shear strains of the order of 0-2. It is initially concentrated near the centre of the spherulites, and then spreads gradually over a diameter inclined at about 45 ° with respect to the shearing direction, thus bisecting the ~ and ~ axis (Fig. 5). Within the viscoelastic stage, the darkening is completely reversible (it disappears if the strain is turned to zero). It becomes more and more permanent as the plastic strain increases. Just before rupture, the dark bands have nearly spread over the whole surface of the spherulites, so that the film has completely lost its initial translucence.

12

S. BONI, C. G'SELL, E. WEYNANT, J, M. HAUDIN

40 I ~"

PERCENT 45 50 I I

CRYSTALLINITY 55 60 I I

13-

•

°

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-e

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SPHERULITE Fig. 7.

I

°

DIAMETER

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I000 (ym)

Experimental dependence of the shear yield stress and the rupture shear strain upon the microstructural characteristics.

Evolution under shearing of an isolated spherulite Although the above experiments make it possible to study the effective influence of microstructural parameters upon the mechanical shear behaviour of polybutene-1 specimens, the complex geometry of spherulite boundaries makes it difficult to characterize with precision the local evolution within a single spherulite. Special experiments were thus devoted to the in situ observation of samples containing individual spherulites embedded in a microspherulitic matrix. In these experiments, only the geometrical features will be taken into account; the recording of the shear stress would make no sense since the microstructure is not homogeneous. Photographs in Fig. 9 show typical steps in the evolution of a single spherulite during a shear test at constant shear strain rate 1>= 4.2 × 10-3 s -a. The observations were performed with unpolarized light. In the first picture obtained at X = 0 (Fig. 9a), the centre of the spherulite already presents a small dark spot which is due to the weak preliminary tension which was applied

PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR

13

0

b

C

0 . 5 mm !

I

Fig. 8. General evolution of the spherulites during a shear test in a specimen completely crystallized at 80 °C: (a) y = 0, (b) y = 0.2, (c) ~ = 0-4, (d) ~ = 0-6, (e) ~/= 0.8, (f) ~/= 1 (polarized light).

14

S. BONI, C. G'SELL, E. WEYNANT, J. M. HAUDIN

0

h iiiii i!iiiii!

i i i l ¸'

d

J I

0.5 mm

I

Fig. 9. E v o l u t i o n of an isolated spherulite during a s h e a r test: (a) y = 0, (b) y = 0-25, (c) y = 0.5, (d) y = 0.75, (e) y = 1, (f) y = 2, (g) y = 4, ( h ) ) , = 6, (i) ~, = 7 just before r u p t u r e , (j) after r u p t u r e (unpolarized light).

to the film in the transversal ~ direction. While the shearing proceeds (Fig. 9b to e), the darkening increases and leads again to the formation of a well defined dark band which bisects the ~ and ~ axis and tends to rotate anticlockwise, as the spherulite takes an ellipsoidal shape. When y = 2 (Fig. 9f), nearly all the surface of the spherulite is affected by the darkening, except in the end areas of the ellipse major axis. The shear test could be driven up to a maximum

PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR

15

shear strain y = 7 (Fig. 9i), when fracture occurred in a region far from the observed spherulite. The last photograph obtained after fracture (Fig. 9j) shows the large plastic proportion in the total strain and the persistence of the darkening effect. Thanks to the nearly perfect circular shape of the original spherulite, the evolution of its contour under straining gives direct access to the real local strain distribution, usually described by the 'strain ellipse'. 1.

2.

In the first step, we determined the local true shear strain undergone by the spherulite on the successive photographs. It can be noticed that the total height of tti'e spherulite decreases gradually during the test, due to a small general anticlockwise rotation of the observed zone of the film. The local true shear strain must then be measured as illustrated in Fig. 10 by the ratio )%c = u/R (where R is the radius of the circular spherulite and u is the shearing movement of the upper and lower points C and C' of the undeformed spherulite which are moved to positions T and T' during the shearing and rotating process). From this geometrical analysis it was found that the local film rotation was less than 5 ° in the course of the test. On the other hand, the plot of the local true shear strain Ylocversus the conventional shear strain Y (Fig. 11) shows that ~'1oc is markedly lower (by a factor of about 0.5) than y. This deviation is observed from the beginning of the test and tends to increase some more at the end. Although some error can affect the determination of Yloc (about 10%), it is more likely that the discrepancy arises from the overestimation of the nominal shear strain ~,-- Ax/h, due to the deformation of the film over an actual width larger than the nominal value h. In the second step, we analyzed quantitatively the shape of the deformed ellipse itself. It is known 23 that the simple shearing of a circle of radius R transforms it into an ellipse whose half major and minor axes a and b are

ii l C

undeforrned spherulite Fig. 10.

C

.....

i ~-

deformed spheralite

D e t e r m i n a t i o n o f the local true strain Yloc = u/R o f an individual spherulite.

16

S. BONI, C. G'SELL, E. WEYNANT, J. M. HAUDIN z

I

I

I

I

I

I

/ /

_

-J

,,"

-

_

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0

-

~'~ 0

I

I

I

I

I

I

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2

5

4.

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6

N O M I N A L SHEAR STRAIN Fig. 11.

Local true shear strain Ylo¢ =

u / R versus nominal shear strain spherulite in Fig. 9.

y = Ax/h

for the deformed

given by: a = R / 2 . [(yl2oc+ 4) 1/2 + )'lot] b

=

R/2

.

[(Y{oc+ 4) 1/2 - ) ' l o c ]

The area A = ¢rab of the ellipse should then stay equal to the initial area Ao = arR2 of the circle. From the photographs of the isolated spherulite in Fig. 9, we measured the major and minor axes of the elongated spherulite. We also determined its actual area during the test both by weighing the photograph cut out along the spherulite contour and alternatively by means of a computerized graphic tablet. In the range of experimental errors, it appears that the direct measurement of the area gives data which coincide with the relation A = ~r ab, so that the actual contour of the spherulite is correctly approximated by an ellipse. We displayed in Fig. 12 the variation of the spherulite area versus the relative elongation of its major axis (a - R ) / R . It is evident that the area does not keep constant during the test, as it should do in the ideal simple shear. Instead, we can note that the experimental points are not far from the theoretical variation of area corresponding to uniaxial tension of the film along the direction of the major axis of the ellipse A / A o = [(a - R / R ) + 1] 1/2. Consequently, the actual deformation mode is accompanied by a reduction of the film thickness, instead of keeping constant as predicted by simple shear.

PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR

I

I

I

I

17

I

A/Ao 2

-

1.5-

1~,~, ~

•

I 0

0.5

ideol simple shear

I 1.0

I 1.5

I 2.0

I 2.5

(a-R)/R Fig. 12.

Evolution of the area of the deforming spherulite in Fig. 9.

Identification of the side-effects perturbating the distribution of strains in thin film shearing experiments As we saw in the preceding section, the observed deformation geometry deviates seriously from ideal simple shear. We will analyze now two side-effects which are observed during the tests and which can be responsible for this deviation--straining of the specimen in the gripped region and formation of folds within the calibrated zone. The first unwanted effect is illustrated in Fig. 13 which shows the aspect before and after shearing (y -~ 0.5) of a polybutene-1 specimen initially marked with a square grid of small black dots. The picture after unloading thus gives a description of the plastic strain distribution. The width of the calibrated part in this experiment (h = 2.6 mm) was twice the usual one (h = 1-3 ram) in order to get a sufficient number of deformed grid meshes. This experiment shows clearly the unwanted rotation of the film in the calibrated part. One also notes that the local shear strain in the centre of the specimen is smaller than the overall strain, since the portions of film lying at the limit of the grips experienced an extensive local deformation (both in shear and in inhomogeneous oblique stretching). We can then easily realize that the default error in the true shear strain depicted by the plot of Fig. 11 is due to the

18

S. BONI, C. G'SELL, E. WEYNANT, J. M. HAUDIN

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Fig. 13. Photographsdemonstratingthe inhomogeneityof the deformationin a thin film subjected to a simple shear test. The local distortion of the array of dots shows the unwanted deformationwithinthe grip. imprecise definition of the width of the actually deforming zone and to the divergence of the strain distribution with the ideal one. This problem could not be solved, whatever the tightening force exerted while gripping the specimens. The second difficulty is the development of folds in the calibrated part of the specimen. The photographs in Fig. 14 are overall views of a polybutene specimen 100/zm thick subjected to a shear test. Figure 14b shows, for y = 0.2, the apparition of an oblique fold, inclined about 35° on the shearing direction, which crosses the calibrated part of the specimen. While the strain increases, other folds are formed parallel to the first one (Fig. 14c at y = 0.7). The direction of the folds tends gradually to turn anticlockwise as the shear strain increases (Fig. 14d). Complementary tests showed that the development of folds during the shearing of films can be minimized by increasing the film thickness t or reducing the width h of the calibrated part. Unfortunately, if the dimensions are modified in this way, unwanted deformation tends to increase within the grips and, therefore, the determination of the shear strain tends to be less accurate. Furthermore, it appears that the folding phenomenon is a general feature of film shearing experiments on polymers--this side effect was observed also by Brown et al.8 while deforming in simple shear film specimens of polyethylene terephthalate 250/xm thick and 1.5 mm wide. Robertson and Joynson,6"9 shear-

PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR

19

0

b

C

I Fig. 14.

2 mm

'!

Development of oblique folds during the simple shearing of a polybutene film (observed by polarizing microscopy): (a) y = 0, ( b ) ) , = 0-2, (c) y = 0.7, (d) y = 1.1.

ing oriented polymer films of 100-200/~m thick, chose to reduce their calibrated width h to 0.075 mm only. They apparently succeeded in avoiding the folding process, but admit in one of their papers 6 that their measurement of y had only a qualitative validity due to the intensive deformation in the grips.

DISCUSSION

Deformation mechanisms of the spherulitic microstructure As assessed in previous papers and by the present work, the simple shear testing of polymer films is likely to bring interesting information on the

20

s. BONI, C. G'SELL, E. WEYNANT, J. M. HAUDIN

microstructural evolution during straining. In the case of polybutene-1, it completes the results obtained with tensile tests in a previous paper. 11 In particular, the development of a dark band in unpolarized light was already observed during uniaxial drawing of individual spherulites. In such tensile experiments, the dark band appeared first in the equatorial region perpendicular to the principal axis of stress. In agreement with previous observations, 24 it was correlated to the separation and bending of crystalline lamellae lying along the spherulite radii nearly perpendicular to the tensile axis. This mechanism induces density lowering or void formation in the amorphous interlamellar region. Thus the density fluctuation between amorphous and crystalline layers is considerably increased and, according to the analysis of Debye and Bueche, 25 a noticeable light scattering phenomenon arises from this fluctuation. This scattering phenomenon is responsible for the local darkening observed within the spherulites. The dark band observed during shear tests has the same morphological features as the one observed in tensile tests. However, it appears at about 45 ° to the direction of the applied shear stress l:a. This location of the dark band can be correctly interpreted using a simple mechanical analysis---in the case of simple shear at small strains, the maximum principal axis of stress, which corresponds to tension, is bisecting the - 2 and ~ axis (Fig. 15a). So, it can be easily understood that this tensile stress will promote separation and bending of crystalline lamellae according to the same mechanisms as in uniaxial drawing (Fig. 16). For increasing values of y, the band tends to turn towards the ~ axis. This rotation can also be explained by means of a mechanical analysis of the shear test--it is known that in simple shear the principal axes of strain tend to rotate towards the shearing direction as deformation proceeds. 23 Such a rotation is revealed in Fig. 9, in which we observed that the major axis of the deformed ellipse was turning towards the shearing direction. For a rigid perfectly plastic body, the position of the principal axes of stress remains fixed despite the rotation of the principal axes of strain. Conversely, in a perfectly elastic material the stress axes are subjectedto the same rotation as the strain a x e s . 26 In a polymer the total strain is the sum of an elastic and a plastic strain. In polybutene-1 specimens crystallized in modification I, the elastic component is particularly large and can be related to the mechanism of separation and bending of crystalline lamellae. This mechanism has been described in the literature as responsible for the so-called 'hard elastic' properties, z7'28 As a result of this large elastic strain contribution, the principal directions of stress rotate a certain amount; consequently the dark band is also rotated since it was shown to be perpendicular to the maximum principal axis of stress. The irreversible plastic deformation is mainly due, for its part, to chain tilt and slip, which occur in radial crystallites inclined with respect to the principal

PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR

21

shear stresses

__

t" X

~normal stresses

ra

~'a

a)

b)

Fig. 15. (a) Orientation of maximum shear stresses and principal stresses in ideal simple shear at small strains. (b) Mohr's representation of the stresses. The point representing the sheared plane turns anticlockwise at large strains.

directions of stress. 29'3° In the case of shear tests, the crystallites which are initially parallel and perpendicular to the shear direction are the most active ones. The effect of such a deformation is to align the chains more nearly parallel to the tensile principal axis of stress.

Validity of shear testing of thin films Unfortunately, the homogeneity of shear deformation in thin polymer films was seen to be altered by unwanted side-effects such as development of folds and deformation in the gripped portion of the samples. We will now explain their origin and see how they can be avoided. The formation of unwanted folds during the plastic stage can be interpreted in terms of buckling of the specimen under the effect of the oblique compression stress which is developed in the shearing geometry. As we noticed before, the couple of shearing forces induces in the material a stress field which is characterized (Fig. 15) by one tensile principal stress trr and one compression principal stress tTc whose amplitude is equal to the shear stress. In the case of

/

of crystalline lamellae

~.~.~ Fig. 16.

~ "Ca

Interpretation of the inclined dark band by the bending and separation of crystalline lamellae (schematic diagram).

22

s. BONI, C. G'SELL, E. WEYNANT, J. M. H A U D I N

infinitesimal strains, these principal directions of stress are inclined 45 ° on the shearing direction. It has been shown 31 that the situation is not so different for large strains, except that the principal directions of stress are slightly rotated towards the shearing direction (Fig. 15b). Due to the existence of the compressive component of stress, it can be easily derived that buckling of the specimen can occur if the film thickness is lower than a critical value. A mechanical analysis by Duthei132 has shown, in the case of beams or plates of relatively small length, that the buckling critical stress as is given by the following relation: as = 0.5(oc + 1.3try) - [0.25(0c + 1.3ay) 2 -

crc . Oy] 1/2

where Cry is the tensile yield stress of the material and ac is the classical Euler critical stress, i.e. trc = 7r2EI/12S

where E is the apparent viscoelastic modulus, I is the momentum of inertia of the section with respect to the buckling axis (I ~-he3/6X/-2 in the case of a sheared film), I is the fictitious length of the bent film (l = hX/2/2 for buckling at 45 ° with a doubly embedded solid) and S is the cross section of the bent film (S ~- Lt). As we saw that in a specimen tested in simple shear the maximum compression stress is nearly equal to the shear stress r, the nonbuckling condition can be expressed simply by ~ < as, and then by the following dimensional criterion t2

3x/-2r(1.3oy - r)

hL

1r 2E(try- r)

-->

With the experimental values Cry = 16 MPa, E = 600 MPa, 11 it is found that a specimen thickness of 0.3 mm is necessary to avoid buckling for a shear stress r of 10 MPa (corresponding roughly to the shear yield stress). Because the thickness of tested films was only of the order of 100/~m, the preceding calculation proves that the sample buckling cannot be avoided by any means as long as thin films are used for preparing the samples. A thickness of at least 1 mm is necessary to ensure the stability of the compressive stress. Once buckling occurs, the compressive stress is no longer fully experienced by the material since it is relaxed through the bending of the film. Consequently, it can be stated that the tensile stress originally associated with it in the shearing stress system remains after buckling the major component. This situation can then explain that the shape and the area of the strain ellipse tend to correspond to those in uniaxial tension (Fig. 12). It also explains the severity of the deformation within the grips; because of the unbalanced stress tensor with a lowered compressive contribution, the film is pulled strongly out of the

PLASTIC DEFORMATION OF POLYBUTENE-1 FILMS UNDER SIMPLE SHEAR

23

grips. One also sees that operating the test with a very narrow gap h between the grips would lead to a drastic increase in the relative amount of deformation in the grip region. Nevertheless, the shear testing of thin films is quite valid for the determination of the elastic limit. As we saw in Fig. 7, the shear yield stress could be correctly measured and a quantitative relationship could be derived between this material property and microstructural parameters. Similar tests were operated with other polymers in order to study their shear yield behaviour. In the case of high density polyethylene, for example, it was confirmed that, unlike in uniaxial tensile tests, 33 no geometrical softening due to necking occurred in plane simple shear. From this critical discussion, it can be deduced that the difficulties encountered in the tests at large strains are solely associated with the inability of film specimens to undergo a plastic shearing without buckling or deforming in the grips. The plane shear test can be applicable in the plastic regime provided specimens are used with a sufficient thickness and an adequate geometry. Two of the authors (C. G'Sell and S. Boni) have developed a new shear testing technique based on the design of massive samples which fulfill the nonbuckling criterion, and a special shearing machine able to apply large shear strains with a rigorous precision. This technique is in the course of experimentation and will be the subject of a forthcoming paper.

CONCLUSIONS

Film samples of isotactic polybutene-1 (modification I) were tested in simple shear with a miniaturized shearing stage specially designed to observe the spherulite evolution in situ by optical microscopy. The stress-strain curves obtained with different types of microstructure emphasized the increase of the shear yield stress with the spherulite size and with the degree of crystallinity. The detailed observation of individual spherulites under stress brought a significant confirmation to the previous conclusion that the radial crystallites perpendicular to the major principal axis of stress are separated by bending, while the ones inclined on this principal axis are subjected to glide deformation. The experimental difficulties encountered by previous authors as well as in this work (namely folding and deformation in the grips) were critically analyzed in terms of buckling and deviation from the ideal shear strain geometry. It was concluded that these artefacts did not seriously affect the validity of the yield stress values but made doubtful the validity of the stress-strain curves in the plastic range. It appears that these problems can be avoided by using specimens with a thickness of several millimeters, which are able to experience the

24

s. BONI, C. G'SELL,E. WEYNANT,J. M. HAUDIN

compressive component of stress without buckling. Additionally, the gripped portions of the specimens should be reinforced to avoid unwanted deformation in the grips.

ACKNOWLEDGEMENT The authors are grateful to Mr J. M. Escleine (CEMEF, Sophia Antipolis, France), for his valuable assistance in DSC experiments.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

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