cavitating and non-cavitating semicrystalline polymers
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A Study of the Deformation-Induced Whitening Phenomenon for
Cavitating and Non-cavitating Semicrystalline Polymers
Laurent Farge,1 Stephane Andre,1 Andrzej Pawlak,2 Christophe Baravian,1
Sarah C. Irvine,3,4 Adrian-Marie Philippe1
1LEMTA-CNRS 7563-Universite d e L o r ra i n e, 2 a v e nu e d e l a f o r et d e H a y e, 5 4 5 04 V a n do e uv r e - les - N an c y , F r a nc e
2D e p ar t m en t o f P o l ym e r P h y si c s , C e n te r o f M o le c u la r a n d M a c ro m ol e c ul a r S t u di e s, P o l is h A c a de m y o f S c i en c es , S i e nk i e wi c z a
1 1 2 , 9 0 - 3 6 3 L o d z, P o l an d
3P a ul S c h er r e r I n s ti t u t e, S L S , P S I , 5 2 3 2 V i l li g e n, S w i tz e r la n d
4S c ho o l o f B i o lo g y a n d M e d ic i n e, U n i ve r s it y o f L a u sa n ne , 1 0 1 5 L a u sa n n e, S w i tz e r la n d
Correspondence to: L. Farge (E-mail: Laurent.Farge@ univ-lorraine.fr)
R e c ei v e d 1 4 N o v em b er 2 0 1 2; r e v is e d 1 0 J a n ua r y 2 0 1 3; a c c ep t e d 1 1 J a n ua r y 2 0 1 3; p u bl i s he d o n li n e
DOI: 10.1002/polb.23267
ABSTRACT: I n t h is w o rk , w e u s ed t wo t e ch ni q ue s t o s t u d y t h e d e -
formation-induced whitening phenomenon that occurs when cer-
t a in s e mi c ry s ta l li n e p o ly me r s ( S CP s ) a r e s u bj e ct e d t o t e ns i le
drawing: (1) IPLST (Incoherent Polarized Steady Light Transport)
w a s u s ed f o r c h ar a ct e ri z in g t h e l i gh t s c at t er e rs a n d i n p a rt i cu l ar
f o r d e te r mi n in g t h ei r s i ze . ( 2 ) S R XT M ( S yn ch r ot r on R a di a ti o n
X-Ray Tomographic Microscopy) was used to visualize the inter-
n a l s t ru c tu r e o f t h e d e fo r me d S C Ps . I n p a rt i cu l ar , w i th t h is t e ch -
n iq ue t he p os si bl e p re se nc e o f m ic ro me tr ic c av it ie s c an b e
detected. In the early whitening stage of a cavitating polypropyl-
e n e ( P P ) , t h e I P LS T t e c h ni q ue w a s f o u nd t o s h ow t h at t h e s i z e o f
t he l ig ht s ca tt er er s i s l ar ge r t ha n 1 lm . A t t he s am e t i me , t he
S R XT M m e as u re m en ts s h ow e d t h at n o v o id l a rg e r t h an 1 lm
w a s p r es e nt i n t h e m a te r ia l . T h e m i cr o me t ri c l i gh t s c at te r er s
responsible for the whitening phenomenon may thus not be sim-
p l e c a vi t ie s . I n f a ct , t h is e x pe r im e nt a l s t ud y s u gg e st s t h at t h ey
correspond to areas where smaller objects (possibly nanovoids)
a r e h i gh l y c o nf i ne d . A t t h e s c al e o f v i si b le w a ve l en g th s , t h es e
regions could scatter visible light like individual entities of micro-
m et ri c s iz e. T he s tu dy a ls o s ho we d t ha t t he s iz e o f c av it ie s
observable using SRXTM for a very deformed PP is dependent on
t h e i n it i al d i me n si o ns o f t h e s p he r ul i te s . R e su l ts p r ev i ou s ly
obtained for a non-cavitating high density polyethylene are also
b r ie f ly p r es e nt e d i n t h is a r ti c le t o c o nf i rm t h e t h eo r y t h at d e fo r -
mation-induced-whitening phenomenon may have various ori-
gins for such complex microstructuring.VC 2013 Wiley Periodicals,
I n c . J P o l y m S c i P a r t B : P o l y m P h y s 0 0 0 : 0 0 0 – 0 0 0 , 2 0 1 3
KEYWORDS: l ig h t s c a tt e r in g ; m i c ro s t ru c tu r e ; s t r uc t u ra l c h a ra c -
terization; transparency; voids
INTRODUCTION The main purpose of this paper is to analyze
deformation-induced whitening phenomenon (or more simply
whitening phenomenon) in relation to the evolution of the
microstructure of semicrystalline polymers (SCPs) subjected to
uniaxial drawing. New microstructural objects are created in
the material during the deformation process. If these objects
have a refractive index which differs from that of the surround-
ing matrix, they can scatter visible light. Moreover, if these
objects have a micrometric size (order of magnitude of the visi-
ble wavelengths), they scatter approximately the same amount
of light for all the wavelengths of the visible spectrum (Miescattering) and this results in the whitening phenomenon.1
In this work, we used IPSLT (Incoherent Polarized Steady
Light Transport), an original technique with which we can:
• quantify the whitening phenomenon,2–4
• define the size and morphology of the light scattering
objects,2,5
This therefore makes IPSLT a unique tool for studying the
whitening phenomenon.
Another of our objectives was to analyze the evolution of the
microstructure associated to the whitening phenomenon so, in
addition to IPSLT, we also used Synchrotron Radiation X-Ray
Tomographic Microscopy6 (SRXTM) to visualize the internal
structure of the SCPs for different deformation states.
Undeformed SCPs are generally not completely transparent
for light. Light scattering does not come from the periodic
amorphous-crystalline layer structure where the thickness of the lamellae and amorphous layer is in the range of a few
nanometers. Usually, for non-deformed polypropylene (PP)
or polyethylene, light is scattered by different parts of spher-
ulites or more precisely by bulk micrometric domains with
more or less the same lamellae orientation.7,8
In the case of deformed specimens, the cavitation phenom-
enon is cited in almost all published works to explain the
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deformation-induced whitening phenomenon.9–14 The cavita-
tion phenomenon has mainly been detected using the small
angle X-ray scattering (SAXS) technique which allows the
detection of objects of size in the range 2–100 nm, examples
of such objects being voids of nanometric size (nanovoids).
The correlation between the SAXS detection of nanovoids and
the whitening phenomenon has clearly been established.
SAXS measurements have often shown that nanocavitiesappear in the material at precisely the same strain level at
which the whitening phenomenon begins to be observ-
able.9,15–17 For a PP material for example, it was observed
that the deformation-induced whitening phenomenon was
much more pronounced in the specimen core than in its skin.
Using SAXS measurements, the presence of nanocavities was
revealed in the specimen central regions (i.e., in the regions
that whitened) but no cavity was detected near the specimen
skin15. By infusing low molecular weight penetrants which fill
the free volume of the amorphous phase of SC polymers,
Rozanski and Galeski managed to suppress the deformation-
induced whitening phenomenon.18 Also, nanocavities were
not detected by SAXS for deformed specimens that have not whitened. Lee et al. found that the deformation-induced whit-
ening phenomenon in tensile deformed polymers may be
reduced by the application of external hydrostatic pressure.19
The correlation between nanovoiding and the whitening phe-
nomenon appears obvious although the size of the nanovoids
is still much smaller than the visible wavelengths. In the
light of the Mie theory, it is easy to show that the light scat-
tering phenomenon is still very dependent on the wave-
length1 for such small objects (2–100 nm). Consequently, to
explain the whitening phenomenon, it is sometimes assumed
that, in parallel with the SAXS detected nanovoids, a few
micrometric holes are present in the material.15,20 These
micrometric holes are thus considered responsible for most of the light scattering but this hypothesis is based upon an
assumption that may be questionable: the simultaneous crea-
tion of two void populations with respective micrometric
and nanometric sizes.
We consider that the hypothesis of a simple and straightfor-
ward relationship between cavitation and whitening has yet
to have been clearly demonstrated and few studies exist
which suggest that alternative mechanisms may explain
whitening in polymers.21,22 Our recent works on the subject
have confirmed this possibility: quantitative characterizations
of the microstructure of a high density polyethylene (HDPE)
have been achieved at the micrometric level using both
SRXTM23 and IPSLT2 for different states of deformation. Inshort, the results gave the following findings:
• SRXTM measurements, with a spatial resolution of around
1 lm, were unable to detect any voids for HDPE samples
(R €ochling manufacturer), even for very high strain levels
though the polymer whitens intensively,
• IPSLT measurements led to the conclusion that the scatter-
ers developing in the microstructure initially have a
micrometric size but diminish in size in correlation with
the strain level,
• Tomographic image treatments and IPSLT measurements
gave very comparable results for characterizing the mate-
rial turbidity and anisotropy,
• Material anisotropy first develops in the transverse direc-
tion (perpendicular to the tensile axis) and then reverses,
crossing a new isotropic state before following the obvious
stretching of the specimen.
These studies show that the micrometric objects responsible
for the whitening phenomenon in the studied HDPE are not
cavities. In this work, new SRXTM and IPSLT measurements
are presented for another SC polymers that proved to be
highly cavitating (in particular using volume strain measure-
ments).24 The SRXTM measurement confirmed that this
polymer cavitates at the microscopic level thus providing an
interesting comparison with the non-cavitating HDPE, in par-
ticular by means of the IPSLT measurements. Our first objec-
tive was to determine whether the whitening phenomenon
had similar characteristics at the microscopic level for cavi-
tating or non-cavitating SCPs. Moreover, additional X-ray
experiments [SAXS-wide angle X-ray scattering (WAXS)] were
carried out to analyze the microstructural evolution of the
PP material at a smaller scale. In particular, we tried to
clarify the apparent link between the nanocavitation phe-
nomenon detected by SAXS and the whitening phenomenon.
EXPERIMENTAL
Materials: Properties and Initial Characterizations
In this work, two different SCPs were studied: a HDPE and a
PP, respectively denoted HDPE and PP. The majority of the
experimental results are given for the PP material. The
HDPE material had previously been experimentally analyzed
with the techniques used in this work and the results have
already been published.2,23
However, a few experimentalresults on HDPE are briefly given with the aim of facilitating
the comparison between the two materials.
PP
The PP used in our studies was Malen P, F401: M w ¼ 297,200
g/mol, M n ¼ 56400 g/mol, MFR 3 g/10 min (at 190 C, 2.16
kg). It is produced by Basell Orlen Polyolefins. The samples for
mechanical testing were prepared by injection molding, using a
Battenfeld injection molder. The temperature of the mold was
20 C. The injected samples had a gauge length of 100 mm, a
width of 10 mm and thickness of 4 mm. As usual, the condi-
tions for crystallization were different in the layer contacting
with mold and in the volume (center) of specimens. Thisresulted in skin-core morphology, observed in many injected
specimens.
Thin 20 lm slices made by microtoming were observed in
transmission by polarizing microscopy. Figure 1(a) shows the
evolution of the microstructure of PP from the specimen skin
(left side) to the specimen core (on right). A tiny crystalline
structure was present in the specimen skin. The spherulite
size increased moving toward the specimen center and Figure
1(b) shows the spherulitic structure in the material core. In
this region, the spherulite sizes roughly range from 15 and 60
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lm. The spherulites of crystallographic a form dominated in
PP samples although some spherulites of b form were visible.
Specimens were specifically prepared to study the behavior
of the homogeneous region corresponding to the material
core. For that purpose, a 1-mm thickness was removed near
the specimen skin. These specimens are denoted PPc in the
following. Specimens on which the skin was not removed are
denoted PPs.
The differential scanning calorimetry technique was used to
determine the melting temperature and crystallinity of PP.
The measurements were taken when the samples were beingheated at a rate of 10 K/min. To calculate the degree of crys-
tallinity, it was assumed that the melting heat was 165 J/g
for PP.25 The temperature of the peak maximum was the
same for the skin and volume of sample: 167.5 C. Crystal-
linity was 59% in the skin layer and 61% in the center of
the non-deformed sample. The crystallinity degree was found
to remain constant if the measurement is made on deformed
specimens that have whitened.
The mechanical properties of our PP were studied in detail
previously.15 Yield strain was around 0.09 (true strain) and
yield stress was 37 MPa. The whitening phenomenon started
to become observable at a true strain value of about 0.07–
0.09. The small size of the skin layer makes it difficult to see
with the naked eye whether this region whitens in the same
way as the specimen core or whether it remains transparent.
An increase of the material volume, or ‘‘volume strain’’
(results are not given herein), was observed in the deformed
part of the sample starting from the yield point which showsthat this polymer is potentially highly cavitating.
HDPE
HDPE (grade ‘‘500 Natural,’’ molecular weight 500 000 g/mol,
density 0.95 g/cm3) is produced by R €ochling Engineering
Plastics KG.
This material has been presented in detail elsewhere,2,23 but
for the purposes of this article, it is important to note that:
• polarizing microscopy has yet to enable the observation of
any spherulitic organization,23
• the crystallinity index is 68% and remains unchanged if
the measurement is made on deformed specimens that
have whitened,• the yield stress was 33 MPa and the yield strain was 0.1
(true strain).
Experimental Techniques
All the specimens were deformed in tension. The mecha-
nisms which induce whitening depend only on the sole
deformation state,2 which was characterized using the local
longitudinal true strain e ¼ ln l
l 0, measured in the center of
the necking region. This true strain was determined by
measurements of the distance l between black markers
placed on the specimen surface at the undeformed state
(video-extensometry). At the undeformed state, the initial
distance between the markers was l 0 1 mm. It should be
noted that it is basically a measurement of the applied longi-
tudinal (along the tensile direction) displacement between
two markers placed on the specimen surface. Because of the
curvature of the necked region, e may not exactely corre-
spond to the true strain measurement (Hencky strain) on
the specimen surface. Measurements obtained using 3D
image correlation technique (AramisVR
) have shown that the
resulting error can be of the order of 5%. Moreover, due to
the skin-core morphology and to the complex stress state
resulting from the necking phenomenon, the strain may not
be homogeneous through the specimen thickness.
IPSLT technique operates very quickly which means meas-
urements can be performed dynamically and in situ
duringthe tensile test. This is not the case for SRXTM however and
only post-mortem experiments could be carried out. In that
case, the strain level indicated in this work is the maximum
applied strain measured just before removing the specimen
from the tensile machine.
IPSLT Principle and Experimental Setup
The experimental device used to carry out the IPSLT meas-
urements2 is shown in Figure 2. The input selection of polar-
ized light was obtained with a linear polarizer placed in
front of two liquid crystals retarders. Applying the
FIGURE 1 ( a ) E v ol ut i on o f t he P P m ic r os t ru c tu r e f r om s k in t o
c o r e. ( b ) S p h e r ul i t ic s t r uc t u re p r e se n t i n t h e c o r e o f P P .
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appropriate voltages to the liquid crystal retarders made it
possible to rapidly select four different polarization states
for the laser beam which illuminates the specimen. An iden-
tical setup was used to select four different polarization
states for the backscattered light before it was recorded by
the camera. This all made it possible to obtain 4 4 ¼ 16
intensity images corresponding to every possible polariza-
tion configuration. The 16 M
ij elements of the so-calledMueller matrix could be calculated by performing linear
combinations of these 16 intensity images. The Mueller ma-
trix fully characterizes the optical response of the medium.
In the present case, it should be noted that only M 11, M 22
and the two symmetrical elements M 12 and M 21 had non-
zero values which is a consequence of light transport
through very birefringent medium.26 Moreover the M 22 ele-
ment does not contain any additional information compared
to M 12 or M 21.5 Figure 3 shows the three elements of the
Mueller matrix that we used in this work (M 11, M 12, M 21).
The impact point of the laser is located in a narrow zone in
the middle of the images.
Three quantitative parameters can be extracted from the
M 11, M 12, and M 21 elements by using a procedure based on
the theory of polarized light transport:
• the transport length,
• the anisotropy index, and
• the polarization amplitude.
Transport length lTR . The M 11 element is the backscattered
intensity figure for the natural (non-polarized) light. In other
words, M 11 simply corresponds to the image of the material
surface as it can be observed by the naked eye when the
surface is illuminated by a laser pencil. The upper part of Figure 4(a) shows images corresponding to the backscat-
tered intensity figures at different strain levels for a PPcspecimen illuminated in the center of the necking region by
a non-polarized incident laser. It should be noted that the
incident laser pencil is observable in the center of the
images (center of the necking region) and has a diameter of
roughly 52 lm. On the lower part of Figure 4(a), the M 11
elements are represented using grey levels.
FIGURE 2 E x p e r i me n t al d e v ic e u s e d f o r I P S LT .
FIGURE 3 M 11, M 12, a n d M 21 M u e l l er m a t ri c e s ( P P s s a m pl e , e ¼ 1.7).
FIGURE 4 ( a ) B a c ks c at t e r ed i n t en s i ty (M 11 e l e m en t ) f i g ur e s f o r
f o u r d i f f e re n t s t r a i n l e v e l s f o r P P c . ( b ) P r i nc i p le o f t h e m e a s u re -
m e nt o f l TR f o r P P c (e ¼ 0.17).
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For a non-absorbing medium (which only scatters light), the
transport length corresponds to the average travelling
distance of light in the medium after which the propagation
direction of a photon becomes completely random (i.e., com-
pletely independent of the incident direction).
The transport length variable (l TR ) was obtained from the
M 11 element by considering the evolution of I (q) that is the
angularly averaged intensity as a function of radial distance.
For q > l TR , using the radiative transfer model in the frame-
work of the diffusion approximation, it is possible to find an
analytical solution for I (q) with l TR the only unknown param-
eter. It made it possible to determine the transport length by
fitting the experimental curve [Fig. 4(b)].27
The l TR variable is an indirect quantification of the material
whitening phenomenon.3,4 The turbidity of non-deformed
and as-produced common SCPs corresponds to l TR ¼ 1–2
mm. On the corresponding backscattered intensity figure
[Fig. 4(a) for e ¼ 0], the intensity was small but remained
nearly constant far from the incident laser pencil. During the
deformation process, the diminution of the transport lengthwas caused by the development within the material of
microstructural entities with a different refractive index from
that of the surrounding matrix. If these microstructural
objects had a size comparable or larger than the wavelength,
they were found to scatter approximately the same amount
of light for all the wavelengths of the visible spectrum and
the material became white (Mie scattering).1 The diminution
of transport length therefore corresponds to an enhancement
of the whitening phenomenon. For l TR 0.3 mm, the
deformed material is clearly already deep white: smaller
values of l TR result in changes to the white color which are
hardly discernable to the naked eye. In the following, the
‘‘whitening’’ term therefore refers to the capacity of the
medium to scatter visible light beyond the visual impression.
From a general standpoint view, a scattering event depends
on two parameters: m and x , characterizing the light
scatterer. m is the ratio of the optical indexes between the
scattering objects (nP) and the surrounding medium (nM): m
¼ nP/nM. x is the size parameter : x ¼ 2p nM a/k, k
being the laser wavelength in vacuum (k ¼ 635 nm for the
IPSLT experiments) and a the average (equivalent) radius of
the scattering objects. l TR depends also on the volume frac-
tion f of the scatterers. Using the Mie theory to describe the
scattering event makes it is possible to find the dependence
of l TR on x , m and f. For example, measuring the transport
length can allow for the determination of one of these pa-
rameters if the other two are already known.
Anisotropy Index A. Figure 4(a) shows that the backscat-
tered intensity figure (M 11 element) was geometrically
altered with deformation. The shape of the M 11 element
reflects the anisotropy of the scattering medium. Two phe-
nomena can be responsible for this anisotropy:
• scattering objects becoming themselves anisotropic,
• collective orientation of anisotropic objects, which were
initially randomly oriented in the medium.
To quantify the anisotropy developed within the material, an
anisotropy index ( A) can be defined from the image
intensities taken in two perpendicular directions at q ¼ 2l TR :
A ¼I V I H
I HþI V I H is taken for y ¼ 0 6 5 (or 180 6 5). I V is
taken for y ¼ 90 6 5 (or 270 6 5) .
The anisotropy index can be interpreted as follows: if A >
0, the scattering objects are elongated along the drawingdirection. If A < 0, they are transversally oriented. The ani-
sotropy index definition comes from the theory of light
transport in scattering media (see section ‘‘Image Anisot-
ropy Analysis’’ in the paper of Blaise et al.23). At the scat-
terer level, A depends on the quantity S V /S H. S V is the aver-
age projected surface of the scatterers on a plane parallel
to the tensile axis.27 S H is the average projected surface of
the scatterers on a plane perpendicular to the tensile axis.
A increases when S V /S H increases. However, because the
scattering cross-section is different from the geometrical
cross section of a particle,1 there is no closed-form relation
between A and S V /S H.
Polarization Amplitude P . The two symmetrical M 12 and
M 21 elements can be used to quantify how the medium
affects the polarization state of light.5 If the material shows
strong polarization effects, these elements have a character-
istic pattern with two positive and two negative lobes,
respectively in the perpendicular and horizontal directions
[see Fig. 5(a) down]. For example, for the M 12 element, this
pattern can be interpreted in the following ways. For a non-
polarized incident beam, the backscattered radiation may
still present a certain degree of polarization and in the posi-
tive lobes, the linear vertical polarization state is predomi-
nant compared to the linear horizontal polarization state. In
the same way, in the negative lobes, the linear horizontalpolarization state is predominant compared to the linear ver-
tical polarization state.
If the medium does not show any polarization effects, the
M 12 element does not have this characteristic aspect [see
Fig. 5(a) up left]. Due to the polarization effects, the angular
variation of the M 12 intensity (for example at q l TR )
presents two equivalent positive maxima and two equivalent
negative minima on the 360 angular range. It was chosen to
quantify the polarization effects using the maxima magnitude
(denoted P ) of this curve [Fig. 5(b)]. It was shown that P
only depends on the individual scatterer properties charac-
terized by the optical parameter m and the size parameter
x .3
Monte-Carlo simulations can be used to construct abacuscurves summarizing the dependency of P on the size param-
eter x for given values of the optical parameter m (Fig. 6).5
The different m values used in the simulations approximately
correspond to the possible cases for a SC polymer: amor-
phous objects in a crystalline matrix (m ¼ 0.9), crystalline
objects in an amorphous matrix (m ¼ 1.1) and cavities in an
amorphous matrix (m ¼ 0.75).
Figure 6 clearly shows that the dependence of P on the opti-
cal parameter m is limited. The following remarks are there-
fore valid for all the m values.
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• The polarization amplitude P decreases when the size
parameter increases.• The polarization amplitude becomes significant when the
size parameter x is approximately smaller than 10 or 15.
It corresponds to scattering objects that have a size
smaller than 2 lm.
• In the case of non-spherical objects, the polarization
effects mainly result from the smallest dimension of the
scatterers.
Finally, we should stress at this point that IPLST is a volume
measurement. The size of the probed volume is roughly
equal to (3l TR )3. In this work, the IPLST measurement was
carried out in the center of the necking region where the
strain measurement was obtained.
Tomography Principle
SRXTM experiments were performed on the TOMCAT beam-
line at the Swiss Light Source (Paul Scherrer Institute). 3Dvolume reconstructions were obtained following the map-
ping of a series of X-ray projections acquired over 180 of
sample rotation. At the maximum allowable optical magnifi-
cation, a voxel size of 0.37 lm in each dimension was
achieved (with a corresponding spatial resolution of approxi-
mately 1 lm). The total volumes were of 20483 voxels
representing cubes of edge length equal to 760 lm. The
measurement was performed in the phase contrast mode.
The X-ray energy was adjusted to 10 keV by means of a dou-
ble crystal multilayer monochromator located at approxi-
mately 7 m from the X-rays Source. In the case of materials
made up of light elements like HDPE or PP, the major part of
the contrast is therefore not due to the absorption phenom-
enon but instead results from interference between parts of
wave at either side of an interface.6
SAXS-WAXS
The nanocavities were detected by using SAXS technique. A
0.5 m long Kiessig-type camera was equipped with a pin-
hole collimator and a Kodak imaging plate as a recording
medium. The camera was coupled to a Philips PW 1830
X-ray generator (Cu Ka, operating at 50 kV and 35 mA) con-
sisting of a capillary collimator, allowing for resolution of
scattering objects up to 40 nm. Exposed imaging plates
were scanned by PhosphorImager SI system (Molecular
Dynamics). The objects of the SAXS studies were deformedsamples after mechanical testing. In the following, the
‘‘nanovoid’’ term is specifically used to refer to the nano-
metric cavities that can be detected by means of the SAXS
technique.
The WAXS photo camera was used for observations of lamel-
lae orientation. A source of CuKa
radiation, operating at
50 kV and 35 mA, was used. Two-dimensional scattering
images were recorded by a camera equipped with a Kodak
imaging plate. The distance between a sample and the
recording plate was 5 cm.
FIGURE 6 D e pe n de nc y o f t h e p o la r iz a ti on a mp l it u de o n t he
size parameter.
FIGURE 5 ( a ) P o l ar i z at i o n e f f e ct s : M 12 (or M 21) e l em en t s. ( b )
Quantification of the polarization effect.
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RESULTS AND OBSERVATIONS
IPSLT
Experimental Results
Figure 7 shows the dependency of the transport length on the
true strain for PPc, PPs, and HDPE. The measurement was
obtained in the center of the necking region during a tensile
test. For PPc (and for PPs) the undeformed specimen was
nearly transparent and the transport length therefore had too
high a value to be measurable. The evolution of l TR was very
similar for HDPE, PPs and PPc: l TR decreased when the strain
level increases which complies with the observable intensifica-
tion of the whitening phenomenon. However for strains above
0.6, the constant value reached by l TR was significantly
smaller for PPc (l TR ¼ 0.05 mm) than for HDPE (l TR ¼ 0.15
mm). This whitening level difference cannot be seen with the
naked eye. In the case of PPc, for the very deformed state (e >
1.7), a slight but still significant increase of l TR was observed.
l TR is significantly higher for PPc than for PPs for all the
deformation states. It clearly proves that the whitening
phenomenon is much less pronounced in the region of thematerial skin.
Figure 8 shows the anisotropy index ( A) for HDPE and PPc.
Globally, the same trends were also observed for the two
materials. Firstly, for low deformation states, the anisotropy
index was found to have a negative value. The scattering
objects were then elongated perpendicularly with respect to
the drawing direction. For these low strain levels, this trans-
verse anisotropy was still much more pronounced for PPcthan for HDPE: the quantity S V /S H is then larger for PPc than
for HDPE. Next, for strains of about e ¼ 0.65 for PPc and e ¼
0.55 for HDPE, the index recovered a zero value correspond-
ing to isotropic states. Further deformation induced the well-
known fibrillar configuration28
corresponding to an elonga-tion of the material along the drawing direction and the ani-
sotropy index became positive. This positive anisotropy
increased until e 1.5 for the two polymers being studied.
Figure 9 shows the polarization amplitude plots for HDPE,
PPc and PPs which were found to behave in a very similar
fashion. Roughly, for strains smaller than e 0.3, P was
close to zero and the smallest size of the scatterers was then
larger than 1 lm (Fig. 6). Next, the polarization amplitude
increased with deformation and finally saturated for a strain
value close to e 1. Taking into account the dependence of
the polarization amplitude (P ) on the size parameter ( x )
shown in Figure 6, this evolution of P corresponds to a
diminution of the scatterers size.
At high strain levels the polarization amplitudes were larger
for PPs than for PPc or HDPE. This shows that small light scatterers develop near the material skin.
Concluding Remarks for the IPSLT Measurements
The two studied SCPs have very comparable IPSLT
responses. Three different stages characterizing the evolution
of the microstructure were brought to light:
• Stage 1 (roughly between e ¼ 0 and e ¼ 0.5): During this
stage, transversally oriented micrometric objects are
created. These objects scatter the visible light and are
thereby responsible for the material whitening.
• Stage 2 (between e ¼ 0.5 and e ¼ 1.2): The size of the
scatterers decreases but the white color of the material
does not change. The anisotropy of the scatterers progres-
sively changes from transversally elongated to longitudi-
nally elongated with respect to the drawing direction.
• Stage 3 (starting from e ¼ 1.2): The transport length
remains nearly constant until the end of the tensile test.
The scattering objects are then definitely oriented along
the tensile direction. This behavior can certainly be linked
to the fibrillar microstructure28 of the SCPs.
FIGURE 7 E v o l ut i o n o f t h e t r a n s p or t l e n g t h f o r H D P E a n d P P .
FIGURE 8 A n i s ot r o py f o r H D P E a n d P P c .
FIGURE 9 P o l a r iz a t io n a m p li t u de s f o r H D P E, P P c , a n d P P s .
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SRXTM Results
Tomographic experiments on HDPE have been thoroughly
detailed elsewhere23 and therefore we shall mostly provide
the results obtained for PP herein (except when direct
comparison is desirable for clarity).
PP Material
In addition to the undeformed case (e ¼ 0), three different
pre-deformed samples were studied: e ¼ 0.3, e ¼ 0.7, and e¼ 1.7. As previously mentioned, these values correspond to
the end-strains (and not to the values measured after relaxa-
tion) applied in a tensile test (engineering strain rate at 1.5
103s 1). It should also be noted that these strain values (e
¼ 0.3, e ¼ 0.7, and e ¼ 1.7) were approximately chosen in
the middle of the three stages of the microstructure evolu-
tion as highlighted by IPSLT (see the preceding section).
Tomographic Views for PP. The tomographic views
obtained for the four considered strain levels are given in Fig-
ure 10. The side views (sections parallel to the tensile axis)
are on the left part of Figure 10 with the upper views (sec-
tion normal to the tensile axis) on the right part. These views
were obtained in the material core where the microstructure
is homogeneous [Fig. 1(b)]. These images correspond to 5002
pixels and square of edge length equal to 180 lm.
The darkest regions in the image come from the phase contrast
fringe minima which occur at the interface from lower to higher
density material. The higher the difference in density, the darker
the pixels situated on the side corresponding to the object of
lower density. If this object is small, the dark fringes resulting
from two interfaces situated on two opposite sides of the objects
are superposed and the whole object appears dark on the tomo-
graphic view. The brightest regions are situated on the side of
the interface corresponding to the regions of higher density6.
The following observations can be made:
• In the undeformed state [Fig. 10(a)]: the aspect of the
microstructure is apparently homogeneous at the micro-
metric scale. No difference can be found between the
FIGURE 10 Tomographic views.
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directions of observations. The spherulitic structure, pres-
ent in the core of PPc [Fig. 1(b)], is not visible despite the
density difference between crystallized and amorphous
region. The long period of the polymer (15 nm) is much
smaller than the pixel size (0.37 lm), which makes it
impossible to discern the different parts of a spherulite
corresponding to the areas where the lamellae have more
or less the same orientation. It is thus impossible to visu-
alize a spherulite.
• For a 0.3 applied strain [Fig. 10(b)]: horizontal slightly
dark strips are observable on the side views. These dark
areas correspond to objects of less density. On the upper
view, these regions have roughly a disk shape. Conse-
quently, in 3D, the objects corresponding to these dark
regions look more or less like flat cylinders. Please note
that the term ‘‘dark disks’’ will be used hereinafter to refer
to the objects observable on the tomographic view corre-
sponding to this strain level. Along the tensile axis, the
distances between the ‘‘dark disks’’ range from 15 to
60 lm [see Fig. 10(b) left]. It should be noted that it is
not possible to see cavities at the micrometric level.
• For a 0.7 applied strain [Fig. 10(c)]: the previously
observed ‘‘dark disks’’ have smaller transverse sizes. They
tend to agglomerate to form a kind of ‘‘zebra pattern’’(term used in the following) observable from side views.
No cavities can be seen at the micrometric level.
• For a 1.7 applied strain [Fig. 10(d)]: cavities are perfectly
visible. On the side view, these voids are more or less
agglomerated to form ‘‘cigar shape’’ objects (term used from
now on). Within these ‘‘cigar shape’’ objects, the individual
voids are separated by bridges (sometimes labeled tufts).
Similar ‘‘cigar shape’’ arrays of cavities were also observed
using X-ray microtomography for deformed polyamide 6
specimens.29 Using scanning electronic microscopy (SEM)
observations for PP, these ‘‘cigar shape’’ arrays of cavities
were shown to result from the specific evolution of the ‘‘po-
lar fans’’ of the spherulites.15,30 A marked overall orientation
along the tensile direction is easily visible. It is interesting to
note that the dark areas of the ‘‘cigar shape’’ regions are not
all the same dark color. Some lighter regions can be seen,
especially at the extremity of the cigar tips which indicates
the presence of zones which may still include some matter.
These ‘‘cigar shape’’ objects may be the result of the evolu-
tion of the ‘‘zebra patterns’’ observed for the precedent strain
level. To support this idea, we have included an enlarged
field of view (350 350 lm2) obtained for e ¼ 0.7 (Fig. 11)
in which several ‘‘zebra patterns’’ are visible (indicated by
the arrows). They are organized in a way which suggests
that the ‘‘zebra patterns’’ are the precursors of the ‘‘cigar
shape’’ array of voids observable for e ¼ 1.7.
For PP, Figure 12 shows the largest possible upper field of
view (2048 2048 pixels2) for the strain level e ¼ 1.7. For
this high deformation level, the specimen transverse dimen-
sions have been significantly reduced and it is possible to
see the specimen edge on the tomographic view. In the edge
region, the interface separates two regions with nearly infi-
nite dimensions compared to the voxel size (0.37 lm). The
dark fringe (air side situated) and the bright fringe (material
side situated) are clearly observable here. Figure 12 shows
that the size of the holes varies gradually from the core to
the edge of the specimen. In the central region, where the
largest voids can be observed, the void transverse size is
roughly 8–10 lm. Very close to the specimen edge, no holes
are discernable. The right side of the tomographic view
shows an enlarged part of the picture ( 5) taken at a 150
lm distance from the specimen edge which corresponds to
the region where the smallest observable holes are situated.
Voids of roughly 1 lm (approximately three times the pixelsize) are easily discernable. The presence of smaller voids
cannot be excluded in particular close to the specimen edge.
It should also be noted that the preceding views [from Fig.
10(a–d)] were taken in the region inside the square of
Figure 12, where the holes had the largest size.
FIGURE 11 E nl a rg e d s i de v i ew (350 lm) of PPc a t e ¼ 0.17,
s e v er a l ‘‘ z e br a p a t te r n s’’ a r e i n d ic a t ed b y a r r o ws .
FIGURE 12 E nl a rg ed u pp e r v i ew (750 lm) of PP at e ¼ 1.7
[ t h e s q u a r e i n d i c a te s t h e v o l um e e x t ra c t ed f o r F i g . 1 0 ( d) ] .
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The orientation of the objects visible on the tomographicviews can be linked to the anisotropy characteristics of the
light scatterers shown in Figure 8.
• For the small strains (e ¼ 0.3), the light scatterers are ori-
ented perpendicularly to the drawing direction like the
‘‘dark disks’’ corresponding to Figure 10(b).
• For intermediate strains (e ¼ 0.7), the IPSLT intensity
figures show two approximately equivalent anisotropies in
the longitudinal and transverse directions. This complies
well with the tomographic view in Figure 10(c): The ‘‘ze-
bra pattern’’ objects are oriented both in the transverse
and in the longitudinal directions.
• For large strains (e 0.8), the light scatterers are oriented
along the longitudinal direction. Figure 10(d) shows thesame global orientation.
Grey Level Analysis. Figure 13 shows the histograms con-
structed from the gray-level intensity map corresponding to
the upper views (perpendicular to the drawing direction).
These histograms are normalized with respect to the maximum
peak value obtained in the undeformed state. In the case of the
highly deformed state (e ¼ 1.7), two histograms were obtained:
• the first was calculated with pixels taken in the specimen
core,
• the second was calculated with pixels taken near the
specimen skin.
For the first three strain levels (e ¼ 0, e ¼ 0.3, and e ¼ 0.7),the histograms behave in a rather similar manner as for
HDPE23: they remain Gaussian, and centered on the same
value, which suggest that any evolution of the microstructure
is made without changing the density of the material. But for
the last strain level (e ¼ 1.7), the histogram obtained in the
core shows a peak at 0-level corresponding to very dark
fringes induced by air–material interface at the micrometric
level. Micrometric cavities are present in the material [black
holes on Fig. 9(d)]. This characteristic was never observable
for HDPE even at very high strain levels.
The presence of large zones having 0 density shifts the histo-
gram towards higher levels.
Finally, let us note that the histogram obtained in the speci-
men skin region at the last strain level (e ¼ 1.7) is nearly
identical to that obtained at the undeformed state.
HDPE Material Figure 14 shows a side tomographic view (parallel to the
drawing direction) obtained for HDPE for e ¼ 0.3, that is,
during the whitening stage for this material. Unlike with PP,
it is not easy for the naked eye to distinguish any character-
istic shape on the tomographic view which may correspond
to a local organization of the matter at the micrometric scale.
Further analysis can be performed by calculating the image
2D FFT transform.23 This analysis revealed the presence of
objects that are perpendicularly oriented with respect to the
tensile axis. These objects are certainly associated to very
small changes of matter density compared to the surround-
ing medium and are thereby hardly discernable directly on
the tomographic view.Following on from the work of Blaise et al.,23 starting from
the 2D-FFT transforms of the images, it is possible to
calculate an anisotropy index similar to that used for ana-
lyzing the backscattered intensity figure (M 11 element).
Figure 15 gives a plot of the anisotropy indexes corre-
sponding to the IPSLT and to the SRXTM measurement.
These two techniques probe the matter at the micrometric
scale. The two curves show very comparable trends.
Objects which are transversally oriented with respect to the
drawing direction first appear in the material and then
reorient toward the drawing direction. The behavior simili-
tude of the curves shown in Figure 15 indicates that the
objects revealed by SRXTM certainly play a major role inthe whitening phenomenon.
FIGURE 13 H i s t og r a ms o f G r e y L e v e l X - r a y t o m o g ra p hi c i n t en -
sities (section perpendicular to tensile direction)—PP specimen:
N o t e t h e p e a k a t 0 f o r e ¼ 1 . 7 ( c o re ) .
FIGURE 14 HDPE l- To mo g ra p hi c v i ew f o r H DP E d u ri n g t he
w h i te n i ng s t a ge ( s i de v i e w, (e ¼ 0.3).
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Concluding Remarks for the Tomographic Measurement
Cavities with a size as small as 1 lm are clearly observable
by SRXTM for PP at very high strain levels. No such resolved
holes are visible for the tomographic views corresponding toHDPE or during the whitening stage for PP. For all stages of
the deformation process, the orientation of the micrometric
objects revealed by SRXTM is very similar to that of the light
scatterers. This clearly suggests that these objects (which
cannot be considered as ‘‘voids’’ or ‘‘holes’’) are responsible
for the whitening phenomenon.
SAXS-WAXS
Figures 16 and 17 show the WAXS and SAXS patterns for PP
for different true strain values in particular for the deforma-
tion states for which the tomographic measurement was
obtained. The beam crossed the whole specimen of 4 mm
thickness. If we take into account the small size of the skin
zone [200 lm, see Fig. 1(a)], it can be considered that X-ray
scattering resulted nearly exclusively from the core region.
For small strain levels (e 0.3), concentric rings are
observed on the WAXS patterns (Fig. 16). The orientation of
crystallographic planes is not observed. Spherulites are
known to become elongated along the drawing direction at
this deformation level. Intensive lamellar slip processes
occurs with rotation of some lamellae although this is not
followed by rotation of crystalline planes (see Fig. 9 in Paw-
lak and Galeski30). For higher strain levels, between e ¼ 0.3
and e ¼ 0.7, the orientation of the crystallographic planes,
that is, orientation of structure occurs. For e 0.7, the
fibrillar structure is clearly observable.
The SAXS patterns (Fig. 17) show that the nanocavitation
phenomenon begins for true strain values smaller than e ¼
0.1. The nanovoids are originally elongated perpendicularly
to the drawing direction. For the same strain level for which
a change of the WAXS shape patterns can be observed
(between e ¼ 0.3 and e ¼ 0.7), the SAXS patterns are also
modified. Such evolutions of the SAXS and WAXS patterns
have already often been observed.9,11,13,15–17,18,20,24 Two pos-sible interpretations are possible: reorientation of existing
cavities or formation of a new void population oriented
along the drawing direction. The increase of the total inten-
sity associated to this reorientation of the SAXS patterns
(between e ¼ 0.3 and e ¼ 0.7) is rather small, suggesting
that the first possibility is more probable. Also the volume
strain measurements done for this type of material did not
show any rapid increase, which should be the case if numer-
ous new voids were formed.
DISCUSSION
This discussion section includes three parts addressing three
different issues:
1. clarifying the origin of the deformation-induced whitening
phenomenon,
2. describing some aspects of the microstructural evolution
of the SCPs subjected to tensile loading,
3. highlighting and illustrating the relation between the
initial microstructure and the cavitation phenomenon.
This analysis is based upon the following experimental data:
• at the micrometric level, the quantitative results obtained
by IPSLT and SRXTM,
• at the nanometric and crystallographic levels, the qualita-
tive analysis of the SAXS/WAXS patterns.
Whitening Stage (e 0.3)
The objective of this part is to give more information about
the precise nature of the microstructural objects that scatter
the visible light and are thereby responsible for the whiten-
ing phenomenon. First, we summarize the experimental
observations that were obtained for the strain range during
which the whitening phenomenon takes place. Next we inter-
pret this experimental data.
Observations
For the two materials, the crystallinity index remains con-
stant during the deformation process: whitening caused by
additional crystallization phenomena is therefore precluded.
FIGURE 15 X - r a y S R X TM a n d I P S LT a n i so t r op y i n d ex e s .
FIGURE 16 W A X S m e a su r e me n t s f o r P P c o r re s p on d in g t o d i f fe r e nt t r u e s t r ai n l e v el s ( t h e a r r ow i n d ic a t es d e f or m a ti o n d i r e c t i on ) .
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IPSLT
First, let us remember that the SCPs are not completely
transparent at the undeformed state: the light scatterers are
then the different domains (roughly of micrometric size) of
the spherulites7,8 where the lamellae (at the nanometric
level) have approximately the same orientation. It shows
that the presence of micrometric light scatterers can result
from the local organization of the matter at a smaller scale.
For the two materials studied in this work, the whitening
stage mainly takes place in the strain range 0.08–0.3; the
asymptotic value for l TR being reached roughly for e ¼ 0.5
(Fig. 7). During the whitening stage, the IPSLT technique has
also shown that, either for HDPE or for PP, the light scatter-
ers have a size larger than 1 lm and are anisotropic:
elongated perpendicularly to the drawing direction.
SRXTM
For PP, the tomographic views obtained during the whitening
stage have revealed objects that have a grey level slightly
inferior (darker: less dense regions) than the surroundingmedium, indicating a lower density. In the space, these
objects look like flat cylinders (‘‘dark disks’’), elongated in
the transverse direction [Fig. 10(b)]. The diameter of these
‘‘dark disks’’ is roughly a few tens of micrometers and their
height is approximately comprised between 5 and 10 lm. As
previously mentioned, let us note that the characteristics of
these objects could correspond to the light scatterers high-
lighted by IPSLT: their smaller size is larger than 1 lm and
they have a transverse orientation with respect to the draw-
ing direction. In the case of HDPE, it is not possible to see
by naked eye comparable objects on the tomographic view
(Fig. 14). As previously mentioned, objects that are transver-
sally oriented with respect to the drawing direction can behighlighted by calculating the Fourier transform of the
images. The necessity of using this reciprocal space based
analysis for extracting this information from the tomographic
views shows that the corresponding objects are associated
to very low changes of the matter density. The link between
these objects and the whitening phenomenon was clearly
shown in a previous paper.23
It is important to note that, for the two studied SCPs, the to-
mographic measurement has shown that no hole larger than
1 lm is present in the material during the whitening stage.
SAXS/WAXS (for PP only)
SAXS : A huge increase of the intensity of the SAXS signal was
observed when the material starts to whiten (e ¼ 0.1,
Fig. 17). This observation is generally associated to the de-
velopment of nanovoids in the material: only nanoobjects
presenting a strong density difference with the surrounding
matrix are likely to scatter a significant X-ray amount. As
mentioned in the introduction section, the concomitance
between the increase of the SAXS signal and the whitening
phenomenon was often reported.15–18 The global intensity of
the SAXS pattern increases significantly during the whitening
stage (strain level , e ¼ 0, e ¼ 0.1, and e ¼ 0.3 in Fig. 17)
but remains roughly constant when l TR has reached its final
value (strain level: e ¼ 0.7, and e ¼ 1.7 in Fig. 17). Moreover,
light scatterers and SAXS detected nanovoids are both elon-
gated, perpendicularly to the drawing direction. To summa-
rize, the characteristics of the SAXS detected nanovoids and
the light scatterers are apparently very similar: they both
appear for the same strain level (e 0.1), they develop in
the same strain range e 0.1–0.3 and they have the same
initial orientation. One must keep in mind that the light scat-terers are necessarily much larger than the SAXS detected
nanovoids.
WAXS : WAXS results show that the spherulitic structure glob-
ally still exists during the whitening stage (perfectly resolved
rings remain observable for e ¼ 0.3 see Fig. 16).
Interpretation
In the case of SCPs, the nanovoiding phenomenon does not
occur in a homogeneous way within the material, depending
in fact on the local orientation of the lamellae.10,16 Galeski
et al .31 have outlined the mechanisms describing the
nanovoiding phenomenon under imposed uniaxial tension at
the spherulite scale for small strain levels. According to thisscenario, the equatorial planes are subjected to both a radial
compression and to an accentuated tensile stress. The com-
pression of the stacks of lamellae and amorphous regions
gives rise to unstable kinking of the lamellae. The accentuated
tensile stress acting on the equatorial disks expands amor-
phous material within lamellae kinks into pores. The final
result should be an array of aligned cavities in the equatorial
disks of spherulites (i.e., in the regions where the large dimen-
sion of lamellae is transversally oriented). The average
distance between the centers of the nanocavities can be of the
FIGURE 17 S A X S m e a su r e me n t s f o r P P c o r re s p on d in g t o d i f fe r e nt t r u e s t r ai n l e v e ls ( t h e a r r o w i n d ic a t es d e f or m a ti o n d i r ec t i on ) .
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order of a few tens of nanometers.24,32 This distance is much
smaller than either the visible wavelengths or the pixel size
used for the X-ray tomographic measurements. It is then
possible to envisage that groups of nanovoids, which are very
close together, scatter the visible light like a single micrometer
size object. Such objects (cluster of nanovoids), occupying the
regions where the lamellae are transversally oriented, would
also be transversally oriented with respect to the drawingdirection. In the case of solid materials, it was already
observed that objects corresponding to groups of close nano-
voids can be responsible for light scattering: for example, for
alumina materials containing nanopores, it was shown that
the major scattering contribution results from collective
effects rather from the individual 18 nm pores present in the
medium.33 There exists numerous ‘‘mixing rules’’ (also named
Effective Medium Approximations or simply EMA) that allow
for assigning an equivalent refractive index to heterogeneous
particles.34 Several works have been made to determine if
light scattering by inhomogeneous particles could be modeled
by applying Mie theory to an equivalent homogeneous particle
having a unique refractive index calculated by EMAapproximations. It was shown that, in the case of small inclu-
sions (size < k/10), the Mie theory is still applicable for
modeling the scattering event.35–37 In the Mie theory frame-
work, it could therefore be legitimate to replace the specific
regions of the spherulites in which the nanovoids concentra-
tion is elevated by individual micrometric objects to which
can be assigned a distinct refractive index, differing from that
of the surrounding matrix. In a similar experimental investiga-
tion for HDPE, resolved micrometric holes were never
observed as well as areas of smaller density possibly
corresponding to a collective similar clustering of nanovoids.
Histograms of SRXTM intensities are perfectly Gaussian and
centered on the same grey level as for undeformed samples(see Fig. 13 in Blaise et al.23), which precludes to favor this
hypothesis rather than the opposite (more dense micrometric
objects constitution formed by a concentration of crystallized
areas). As a result, the light scattering micrometric objects
correspond to regions having a density that is very close to
that of the surrounding medium. Another mechanism should
then be envisaged to explain the refractive index differentia-
tion of these regions. One possibility lies in the well-known
martensitic transformation that was often observed for
polyethylene materials. This phenomenon starts at the same
time as the nanocavitation (and whitening) phenomenon.9,38
The martensitic transformation may occur first for the
crystals located close to the equatorial regions of spherulites(region I in the paper of Allan and Bevis39), which would
agree with the observed orientation of the scatterers.
Assuming that the transformation from the orthorhombic
phase to the monoclinic phase is associated to significant
changes of the anisotropic crystals refractive indexes, it may
also contribute to enhance light scattering by these regions.
The creation of micrometric scatterers in the material could
then result from very localized transformations at the nano-
level (nanovoiding in the case of PP and possibly phase
transformation in the HDPE crystals). As previously
mentioned, for PP, the nanocavities are first located in the
spherulite equatorial disks.31 These nanocavities are signifi-
cantly smaller than the pixel size. Consequently, the zones
containing these nanocavities would certainly appear on the
tomographic views as regions having a slightly inferior grey
level. (Gray levels values taken on tomographic images have
been used already for evaluating some porosity due to unre-
solved voids in a SC polymer).40 We can then assume that the ‘‘dark disks’’ observable on the tomographic view for this
low load level [Fig. 10(b)] could be associated to the regions
of lower density (because of the presence of nanovoids) cor-
responding to the equatorial disks of the spherulites. The
shape of these objects (flat cylinders) agrees well with this
assumption. Moreover, in Figure 10(b) (left), the distance
between the objects in the longitudinal direction is also in
good agreement with the spherulite sizes: roughly between
15 and 60 lm. Another possibility is the development of
voids in the amorphous regions between the spherulites. The
spacing would also correspond to the spherulite diameters.
However, the objects revealed by SRXTM appear as flat cylin-
ders with diameters comparable to the spherulite size[Fig. 10(b)]. Such a geometrical shape cannot correspond to
the regions situated between the spherulites. Moreover, if
the voids were not confined within the spherulitic structure,
their size would certainly increase when the specimen is
tensily deformed. It does not correspond to the IPSLT
response for the polarization effects.
In summary, two different processes may be responsible
for whitening in HDPE and PP in this first stage of defor-
mation. For PP, we are led to the conclusion by both IPSLT
and SRXTM that micrometric objects correspond to some
expansion of amorphous regions due to the creation of
numerous nanopores in well-defined areas: the equatorial
disks of spherulites. These nanovoids are transversally ori-ented and the average distance between their centers is
small compared to the visible wavelengths. For HDPE, and
in view of the results presented by Blaise et al.23 at the
micrometric scale, local changes of the refractive index
could also result from the martensitic transformation of the
crystalline phase.
Evolution Toward the High Strain Levels e > 0.3
As previously mentioned, for e ¼ 0.3, l TR has nearly reached
its final value and the two materials studied in this work
almost have their definitive white color. When the strain
level increases, a common tendency was observed for all the
different length scales at which the microstructural evolutionwas experimentally analyzed: a global orientation of the
microstructure toward the drawing direction. For example,
for PP:
• At the crystallographic level (WAXS see Fig. 16): the transi-
tion between the spherulitic structure and the final fibril-
lar structure takes place between e ¼ 0.3 and e ¼ 0.7.
• At the nanometric level: the SAXS measurements (Fig. 17)
show the reorientation of the nanocavities toward the
drawing direction for a strain level comprised between e
¼ 0.3 and e ¼ 0.7.
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• At the microscopic level (IPSLT see Fig. 8): the micrometric
light scatterers are first transversally oriented. Starting
from a strain value comprised in the range e ¼ 0.2…0.3, a
reorientation of the scatterers toward the drawing direc-
tion can be observed. For e > 1.2, the IPSLT anisotropy
index reaches its maximum value.
• At the microscopic level (SRXTM see Fig. 10): For small
strain levels [e ¼ 0.3, Fig. 10(b)], objects presenting a
transverse orientation with respect to the drawing direc-
tion are clearly observable. For intermediate strain levels
[e ¼ 0.7, Fig. 10(c) or 11], it is not easy to discern any
clear orientation on the tomographic views. For high strain
levels, the microstructure is clearly elongated along the
tensile direction [e ¼ 1.7, Fig. 10(d)].
In Figure 11 [or Fig. 10(c)], it is possible to see regions that
are much darker (dark part of the ‘‘zebra patterns’’) than the
‘‘dark disks’’ observable on the previous strain level [Fig.
10(b)]. These very dark regions could correspond to areas
where unresolved voids tend to concentrate.
The tomographic views can be related to observations made
by SEM. For example, in the case of PP, Figure 18(a) shows a
cigar shape arrays of holes imaged by SEM for a strain level
of 1.2. Holes that have a size significantly larger than one mi-
crometer are clearly observable. These holes could then be
resolved using SRXTM and it is clearly the same objects (‘‘ci-
gar shape’’ array of holes) that are imaged by SRXTM [Fig.
10(d]) or by SEM [Fig. 18(a)] for the high strain levels. The
longitudinal size of the ‘‘cigar shape’’ array of holes is
roughly the same in Figure 18(a) (SEM) and in Figure 10(d)
(SRXTM): about 60 lm.
Figure 18(b) shows a SEM picture corresponding to a
smaller strain level of about 0.8. The resolution of the SEM
images is finer than that of SRXTM. Consequently, in Figure18(b), micrometric clusters of intertwined voids and matter
are clearly discernable. Because of the coarser resolution of
the tomographic measurement, these regions could simply
appear on the tomographic view as the dark areas
corresponding to the ‘‘zebra patterns’’ that can be seen in
Figure 10(c) or 11.
Thanks to the fine resolution of the SEM measurement, it
makes no doubt that it is the same microstructural objects
that are imaged in Figure 18(a) and (b) for different strain
levels. The large voids observable in Figure 18(b) could then
not result from the expansion of a unique void but from the
agglomeration of voids of smaller size as the ones that can
be seen in Figure 18(b). Similarly, for the SRXTM measure-ment, it can be envisaged that the ‘‘zebra-patterns’’ observ-
able in Figure 10(c) or Figure 11 evolve towards the ‘‘cigar
shape’’ arrays of holes that can be seen in Figure 10(d). This
evolution could be due to a progressive coalescence of
initially unresolved voids.
Other observations can contribute to strengthen this idea:
On the tomographic view corresponding to Figure 10(d), it
is possible to discern regions (in particular near the cigar
tips) where fragments of matter and cavities are still
combined.
FIGURE 18 ( a ) ‘ ‘ C i ga r s h a pe ’’ a r r a y o f h o l es ( s e e F i g u r e 1 0 d ) i m a g e d b y S E M f o r P P ( s t r a i n l e v e l 1 . 2 ) . ( b ) P o s s i bl y a ‘‘ z e br a p a t te r n ’’
[ s e e F i g . 1 0 ( c ) o r 1 1 ] i m a g ed f o r P P w i t h t h e f i n e S E M r e s ol u t io n ( s t r a i n l e v e l 0 . 8 ) .
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Regarding IPSLT, the polarization effects show that the size
of the scatterers (or more precisely the smallest dimension
of the light scatterers) diminishes. This diminution can be
due to different phenomena:
• Fragmentation of initial scatterers (equatorial regions of
spherulites containing an important concentration of nano-
voids) associated to the destruction of the spherulitic
structure.
• The cavities progressively coalesce leading to the presence
of regions of decreasing size and density
Influence of the Initial Microstructure on the Whitening
and Voiding Phenomena
For PP, at the strain level corresponding to e ¼ 1.7, the spec-
imen width decreased considerably: the skin and core
regions were both visible on an enlarged tomographic view
(Fig. 12). It can be seen that the cavity size increased from
the skin to the core of the specimen. Two different interpre-
tations are possible:
• Porosity gradients can be induced by variations of the
local stress state along the specimen thickness.41 In the
present case, stress inhomogeneities could be caused by
the curvature due to the necking phenomenon.
• The porosity gradient could be associated to the initial
skin-core morphology [Fig. 1(a)], in particular to the
spherulite size.15
Laiarinandrasana et al.41 have observed comparable porosity
gradients for notched specimens extracted exclusively in the
core region: It shows that porosity gradients can result only
from the variations of the local stress state within the mate-
rial. However, in our case, the IPSLT response is clearly dif-
ferent for PPs and PPc. The whitening phenomenon is much
more pronounced for PPc than for PPs (Fig. 7). The study of the polarization effects shows that the light scatterers are
smaller for PPs than for PPc (Fig. 9), which complies with
the tomographic view corresponding to Figure 12. It proves
that the skin-core morphology has a significant effect on the
microstuctural state of the deformed specimens. Conse-
quently, according to us, the porosity gradient observable in
Figure 12 did not only result from the mechanical stress
state within the material. The cavitation phenomenon is also
connected to the initial spherulitic structure and especially
its size distribution, which in turn depends on the manufac-
turing process.
In the case of HDPE, the R €oechling process for producing 1
2 m2
plates preserves the material structure from the de-velopment of any observable spherulitic structure. No cavita-
tion is observed in the deformed states at the microscopic
level which is the same for PP near the skin,.
CONCLUSIONS
The general mechanisms governing deformation-induced
whitening phenomenon for SCP polymers were highlighted
through two similar studies carried out on two different
SCPs: a HDPE, and a PP. At low strain levels, micrometric
objects transversally elongated with respect to the drawing
direction were found to develop in both materials. These
objects scatter the visible light and are thereby responsible
for the whitening phenomenon. For higher strain levels,
these objects become longitudinally oriented while their size
decreases.
For the two studied SCPs and using two independent techni-
ques (Synchrotron Radiation X-Ray Tomographic Microscopy
and Incoherent Polarized Steady Light Transport), it was
shown that no micrometric holes were present in the mate-
rial during the whitening stage.
In the case of PP, the whitening phenomenon could possi-
bly be due to confined groups of nanovoids which initially
develop in regions where the lamellae are transversally
elongated with respect to the drawing direction whereas
another mechanism needs to be invoked for HDPE. Seen as
independent scattering entities, the nanocavities cannot be
considered as responsible for the whitening phenomenon.
But as the spacing between these nanocavities is signifi-
cantly smaller than visible light wavelength, a group of
nanocavities could possibly be considered as a uniquemicrometric scattering object. Regions with size, morphol-
ogy and spacing corresponding to the areas where the
nanovoids are initially confined were identified on the
images obtained using Synchrotron Radiation X-Ray Tomo-
graphic Microscopy.
A high level of correlation was found between the initial size
of the spherulites present in the undeformed state and the
micrometric voids observable at very high strain levels
(when the material already has its final white color) by
means of Synchrotron Radiation X-Ray Tomographic Micros-
copy. This latter observation proves, if proof is necessary,
that careful attention must be paid to published results
regarding microstructural evolution of SCPs under deforma-tion as this depends tremendously on the condition of elabo-
ration (initial microstructure).
ACKNOWLEDGMENTS
St ephane Andre, Laurent Farge and Adrian-Marie Philippe wish
to dedicate this work to the memory of one of the coauthor: Pr.
Christophe Baravian. Christophe died on December 8, 2012.
The present study would not have been possible without his
contribution. He has worked several years in the field of
rheology for developping the innovative light scattering
technique that is used in this work for analysing the SCPs
microstructure evolution.
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