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Volume strain measurements by optical extensometry:
application to the tensile behaviour of RT-PMMA
P. François, J. Gloaguen, B. Hue, J. Lefebvre
To cite this version:
P. François, J. Gloaguen, B. Hue, J. Lefebvre. Volume strain measurements by optical extensometry:
application to the tensile behaviour of RT-PMMA. Journal de Physique III, EDP Sciences, 1994, 4 (2), pp.321-329. �10.1051/jp3:1994132�. �jpa-00249105�
Classification
Physic-s Ahstracts
81.205 81.40L
Volume strain measurements by optical extensometry : application to the tensile behaviour of RT-PMMA
P. Franpois, J. M. Gloaguen, B. Hue and J. M. Lefebvre
Laboratoire de Structure et Propridtds de l'Etat Solide, URA CNRS ?34, U-S-T- Lille.
59655 Villeneuve d'Ascq Cedex, France
(Receii'ed J5 March J993, revised 27 October J993, accepted 3 Noi'ember J993)
Rdsumk. Un systbme d'extensomdtrie optique inforrnatisd a dtd mis au point pour mesurer les variations de volume dans des matdriaux polymbres au cours d~essais de traction. Cette technique
foumii des informations prdcieuses sur l'enchainement des dvdnements dldmentaires de ddforma- tion non dlastique de polymkres ductiles. Elle s'avdre particulibrement intdressante pour les mdlanges renforcds par des dlastombres dans lesquels des modes de ddformation cavitationnels
(crazing~ cavitation des particules d~dlastombre) ou non (bandes de cisaillement) peuvent contribuer h des degrds divers h la ddforrnation totale. Les possibilitds et limitations de la technique
sont illustrdes par des rdsultats prdliminaires obtenus dans le cas du #MMA renforcd
au choc pour
des teneurs variables en particules d'dlastombre.
Abstract. A computer assisted optical extensometer has been set-up in order to record volume strain evolution during the tensile testing of polymer materials. Such a technique provides fruitful information on the sequences of events contributing to the non elastic deformation of ductile polymers. It is of special interest in the case of rubber-toughened systems in which cavitational
modes (crazing, rubber cavitation) as well as fairly constant volume modes (shear banding) may contribute in various amounts to the overall deforrnation. Illustration of the capabilities and limitations of the technique are given with preliminary results obtained on Rubber-Toughened
Poly(methylmethacrylate) (RT-PMMA) at various particle volume fractions.
Introduction.
Since the pioneering work of Bucknall and co-workers [1, 2], a large amount of literature has
been devoted to the quantification of the deformation mechanisms operative in rubber-
toughened plastics. Dilatometric studies during tensile creep or tests at constant strain-rate have been aimed at identifying the nature of the deformation process as a function of tensile strain prior to fracture. Shear deformation is known to occur at constant volume (or may be with a slight densification) whereas crazing and cavitation of the rubber particles result in a
volume increase. The problem is further complicated due to the fact that both types of
mechanisms may occur simultaneously and that the sequences of deformation events may
depend on various morphological parameters. It is thus of great importance to obtain the
JOUR~AL DE PHYSIQUE III T 4 WI FEBRU~RY 19u4 l~
322 JOURNAL DE PHYSIQUE III N° 2
clearest picture of the volume change as a function of longitudinal strain. The experimental set- up proposed below has thus been designed with the aim to offer the most versatile capabilities regarding temperature and strain ranges, and also to avoid the drawbacks of mechanical
extensometers which include range limitations, gauge slippage and potential damage initiation
on the sample surface at the points of gauge clamping in some cases. This optical system is based on the computer-aided video-controlled tensile testing equipment developed by G'sell
and coworkers [3].
Experimental.
SAMPLE PREPARATION. Samples are deformed in tension at constant cross-head speed in an
Instron testing machine. Temperature in the oven chamber is carefully monitored within
±1° in the range 120~ T<470K. Sample strains are measured in the three principal
directions by means of the optical extensometry system described below.
The shape of the specimens is schematically presented in figure I. They are machined out of
parallelepipedic plates with thickness ranging between 2 and 4 mm. Instead of using a standard tensile specimen with constant cross-section, we have adopted this flat hour-glass profile in the central part in order to ensure strain localization while the fairly large radius of curvature
minimizes stress heterogeneities. In such a way, stress is maximum in the central part of the sample and deformation always initiates in this area.
Two adjacent sides of the sample receive a special treatment in order to make it suitable for
optical extensometry. Both surfaces are covered/ with a white paint film capable of
withstanding the imposed sample deformation without breaking. An optical target is then
18
4
R=5
(g ~ ~~~~~~
~
Fig. I. Sample shape and dimensions for optical extensometry.
drawn on the sample. It consists of two vertical black lines aligned along the sample elongation
axis of the front surface and of a black dot slightly spread on both surfaces.
OPTICAL EXTENSOMETRY. The experimental set-up for the determination of sample strains
comprises the following elements, as sketched in figure 2.
Two CCD video cameras (reference IVC 800 from I2S) equipped with zoom lenses
(reference Vivitar 70-200 mm) mounted on bellows (reference Nikon PB6) in order to ensure
lmC
_o
© E b
djjBci'°~~
~ , l
camel
~~meta
2
fi
camera I ontrol screen
camera 2
~ fivideocard
videocard
Fig. 2. -Diagram of the video and data processing set-up.
324 JOURNAL DE PHYSIQUE III N° 2
proper focus on the sample surfaces in all experimental configurations. The first camera points
at the front surface (along direction 2 in Fig. 2) while the second one records sample thickness
(along direction I).
A digitizing and image processing unit which includes :
a microcomputer (reference Compaq 386-25)
a video interface board (reference Matrox MVP-AT) installed in the central unit of the computer
three video monitors, of which two are devoted to the display of analogic images and the third to the processed ones.
The picture of the target area formed on the photosensitive CCD element is digitized in
262144 pixels, that is 512 x 512. The current limitation on the number of pixels to be
processed is due to the digitizing interface since the capability of the CCD camera goes beyond
that value.
EXPERIMENTAL PROCEDURE. When the picture is digitized, a number taken between 0 and
255 is attributed to each pixel. It corresponds to a particular grey level on a grey scale ranging
from 0 for a black element of the picture to 255 for a white one. A picture is then represented by
an array of 512 x 512 integers ranging between those two bounds.
The following step consists in the definition of a threshold value. The picture is then
processed in the following way any pixel for which the initial grey level is below the threshold will be assigned to level 0 and in the same way a pixel with a grey level above the threshold is brought up to level 255, which means that the processed pictures visualized on the monitor are of the binary type, each pixel appearing black or white.
The sample appears as a white shape on a black background, and the drawings of the target
are clearly localized as illustrated in figure 3. The pictures are transmitted to the computer central unit in the form of arrays. The routine has been designed in order to be able to find the location of the lines and columns which contain the minimum number of pixels of a given type
and also to count that number of pixels. In the case illustrated in figure 3, the number of white
pixels of those lines and columns which obey the above requirement are recorded. At any time
during the experiment, these numbers represent the width, thickness and longitudinal distance between the two black lines of the target.
As the tensile test proceeds, the ratio of these data at time t to the initial set of measurements at the beginning of experiment yields the deformations as
~' ~ (~l,1 ~l,oY~(.o where e, is the deformation along direction I at time t and
n~_~, n~ o are the number of pixels
measured along direction at time t and t
=
0 respectively.
Camera I picture Camera 2 picture
Fig. 3. Schematic presentation of a processed picture of sample target and thickness.
Once the deformations are known in the three principal directions, it is straightforward to compute the local volume variation, that is
AVIV
= (I + ei )(I + s~)(I + e~) -1
In the mean time, the computer program records the applied load F on the sample and by combining the load and strains data we have access to the true stress as follows :
~r~ = F/jso(I + s~)(I + e~)j
where So is the initial section of the sample.
DATA AccuRAcY. The digitized pictures cover an area of 8 x 8 mm and both height and
width comprise 512 pixels. The optical resolution is thus limited to 16 ~Lm. Owing to the
O.08 60
50 O.06
( d* 40 ~
b
d q
O.04 ~&°
30 )
q~°~
2011
~ O.02 /
o o.oo
-io
o.oo o.05 o.io o.15
a) E
O.06 o.05
O.04 .'
O.03
0.02 ~
/
O.Ol _.
O.OO
O.OO O.05 o-lo O,15
b) E
Fig. 4. a) Stress (full line) and volume strain (hollow circles) behaviour for 20 % particle volume fraction. b) Separation of elastic (full line), crazing (dashed line) and shearing (dotted line) contributions to the overall elongational strain.
326 JOURNAL DE PHYSIQUE III N° 2
respective dimensions of the target and specimen thickness, resolutions on the deformations
are roughly as follows :
&si
= 3 x10~~
&s~ = 2 x10~~
&s~ = 5.5 x 10~~
Numerical smoothing of the s~(t) curves may improve final precision, to reach 5 x
10~~ whenever data dispersion remains limited. For instance variations in the lighting
conditions may induce a scatter of one pixel. The relative uncertainty on the stress is of the order of 7 x 10~ ~
Results.
Preliminary results will be presented below which deal with the tensile behaviour of Rubber-
Toughened PMMA as a function of particle volume fraction. Reports in the literature
o.io 50
40
j o
« %
# & 30 d
°' O.05 ~$ fl
~ q~ ~s
~ g 20 fi
g ~j/ °
lo
O.00 0.05 o-lo O.15 O.20 O.25
a) E
o. i o
/~~
/
~
o.05 ~/
/ / / O.OO
O.OO O.05 o-lo O.15 O.20 O.25
b) E
Fig. 5. a) Stress and volume strain behaviour for 25 % particle volume fraction. b) Separation of elastic, crazing and shearing contributions to the overall elongational strain (symbols same as in 4).
conceming these materials have mainly considered high volume fractions of reinforcing phase.
Volume strain data have been obtained during creep [4] or constant strain-rate testing [5,6].
They consistently establish that deformation occurs with no or little volume change and it is thus concluded that shear yielding is the dominant process in RT-PMMA.
In a recent study of the ability of these materials to nucleate plasticity, we have investigated
the influence of volume fraction and particle size. Plasticity nucleation is probed by work-
hardening rate K' measurements in the early stages of the non elastic deformation behaviour [7]. It was shown that K' exhibits a striking behaviour, I-e- as the volume fraction of rubber
particles is increased for a given particle diameter K' remains fairly constant at an upper
plateau value and then exhibits a sudden drop for a critical volume fraction which depends on
particle diameter. A drop in K' means an improvement in plasticity nucleation. All results with
particle diameters ranging from 80 to 300nm rationalize to a unique critical interparticle
distance r~ of the order of 60 nm [8]. Moreover critical parameters for crack initiation show the
same kind of peculiar behaviour, with little or no variation on both sides of the same critical volume fraction observed for plasticity. The drop in K' is associated with a sudden increase in
toughness as measured by Kic or Jic 19]. The improvement in toughness is directly related to the
O.O15 35
30
c
~'~~~
° 25~
&o ° 4
G o 6~~ ° 20 #
~ O.005
~
°o $ ~
o ( 15 E
z o ° 2
~
O.COO o~ ~~
5 -O.005
O.00 0.Ol O.02 O.03 O.04
a) E
O.03
O.02
o.oi
o-Do ----
D-DO O.01 O.02 0.03 O.04
b)
Fig. 6. a) Stress and volume strain behaviour for 40 % particle volume fraction, b) Separation of elastic, crazing and shearing contributions to the overall elongational strain (symbols same as in 4).
328 JOURNAL DE PHYSIQUE III N° 2
better ability of the material to nucleate plasticity even though the stress fields differ markedly between the compressive testing for K' and the three point bending of the fracture mechanics.
Based on these findings, it is of great matter to seek whether differences are revealed by
volume strain measurements in the tensile mode.
EXPERIMENTAL RESULTS. The materials used here have been described previously [8). It is
worth mentioning that the particles are of the soft rubber core-hard grafted PMMA shell type with inner and outer diameters of 183 and 207 nm respectively. They have been blended with
the PMMA matrix in a twin screw extruder and the 4 mm thick specimens have been
compression moulded and machined to the final dimensions indicated in figure I.
The volume strains (hollow circles) are presented as a function of tensile elongation for
particle volume fractions of 20 ilb, 25 ilb, and 40 ill in figures 4a, 5a and 6a respectively. Raw data are shown on purpose. Also shown on the same figures are the corresponding stress-strain
curves. As a first comment, it is important to note that in the present configuration the
resolution of the technique does not allow for the determination of the Poisson's ratio. On the contrary, it enables to follow very large deformation, as illustrated in the case of the blend with a 25 ilb particle volume fraction. Regarding the strain to fracture, the latter composition
displays a singular behaviour, since it reaches in a reproducible manner e~
= 0.2-0.25, that is
more than twice the deformation to fracture encountered for the other compositions with higher
or lower volume fractions. The occurrence of a maximum in s~ has already been mentioned [6].
More striking in our case is the fact that the 25 ilb volume fraction corresponds to the
composition for which the critical behaviour in plasticity nucleation is observed [8].
Our preliminary findings regarding the volume strains do not clarify the problem. At least, they clearly show that below 25 ill a cavitational behaviour predominates and is even enhanced for the latter volume fraction. On the other hand beyond 25 ill deformation takes place at
constant volume as illustrated in figure 6 for 40 ill volume fraction, a feature also confirmed for the 45 ill systems not shown here.
A further step consists in separating the various contributions to the observed volume changes as already proposed by various authors [1, 10]. This analysis assumes additivity of both volume and elongational strain components due to elasticity (el), crazing (cr) and shear
banding (sh). It also postulates that shear occurs at constant volume and that the non elastic volume increase is entirely due to the longitudinal crazing strain. Thus considering the
expressions for each volume strain component, I-e- (AVIV )~j
= (1-2 v) s~~, where v is Poisson's ratio
(AVIV )~~
= E~~
(AVIV )~~
=
0
each strain component may be derived [10], namely
s~j = rrIE e~~ =
AVIV (1-2 v
e~~
s~~ = s e~~ + (1-2 v) e~j AVIV
The results are presented in figures 4b, 5b and 6b. Owing to the simple assumptions of the model and the uncertainty in the elastic range, the exact magnitudes are to be considered
cautiously. Nevertheless, the plots obtained for these blends exhibit strongly distinct profiles.
It already establishes that the deformation behaviour is mostly shear banding only beyond the critical volume fraction. The observed volume strains for particle volume fractions of 25 ill and below are clearly indicative of an appreciable contribution from crazing.
Conclusion.
From an experimental point of view, the videometric device offers a versatile technique for volume strain measurements and~ has a great potential for improved resolution.
These results although qualitative provide consistent information on the deformation modes
operative in the tensile behaviour of Rubber-Toughened PMMA. The various sets of mechanical data mentioned in the discussion all point at the same critical transition related to blend morphology [8]. Volume strain data suggest that crazing contributes noticeably to the total deformation up to that same critical volume fraction. Further work is in progress to understand how the corresponding critical interparticle distance influences the deformation behaviour.
References
[I j Bucknall C. B., Clayton D., Dilatometric studies of crazing in rubber-toughened plastics, Nature 231 (1971) lo?.
[2) Bucknall C. B.. Toughened Plastics (Applied Sci. Publ.~ London, 1977).
[3) G'sell C., Hiver J. M., Dahoun A.~ Souahi A., Video-controlled tensile testing of polymers and metals, J. Mater. St-I. 27 (1992) 1.
[4) Bucknall C. B., Partridge I. K., Ward M. V., Kinetics and mechanisms of deformation in RT- PMMA, J. Mater. Sci, 19 (1984) 2064.
[5) Hooley C. J.~ Moore D. R., Whale M., Williams M. J.~ Fracture toughness of rubber-modified PMMA, Plast. Rubb. Process. Appl. 1(1981) 345.
[6] Lovell P. A.~ McDonald J., Saunders D. E. J., Sherratt M. N., Young R. J., Mechanical properties of RT-PMMA, Plast. Rubb. Compos. Process. Appl. 16 (1991) 37.
[7) Franpois Ph., Melot D., Lefebvre J. M.~ Escaig B., New method for measuring the non-elastic work-hardening rate of solid polymers, J. Mater. Sci. 27 (1992) ?173.
[8) Gloaguen J. M., Heim P., Gaillard P., Lefebvre J. M., Plasticity of RT-PMMA effect of rubber particle size, Polymer 33 (1992) 4741.
[9) Gloaguen J. M.~ Steer P.~ Gaillard P.~ Wrotecki C.~ Lefebvre J. M., Plasticity and fracture initiation in RT-PMMA, Polym. Eng. and Sci. 33 (1993) 748.
[10) Heikens D., Sjoerdsma S. D., Coumans W. J., A mathematical relation between volume strain, elongational strain and stress in homogeneous deformation~ J. Mater. Sri. 16 (1981) 429.
