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

VC 2 0 1 3 W i l e y P e r io d i ca l s, I n c .

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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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