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Int J Fract (2019)
219:187–201https://doi.org/10.1007/s10704-019-00389-3
ORIGINAL PAPER
Trouser tear testing of thin anisotropic polymer films
andlaminates
Md Shafiqul Islam · Eskil Andreasson ·Sharon Kao-Walter
Received: 7 January 2019 / Accepted: 6 September 2019 /
Published online: 17 September 2019© The Author(s) 2019
Abstract This research has investigated the essen-tial work of
fracture (EWF) from trouser tear test ofpolyethylene terephthalate
(PET), low-density polyethy-lene (LDPE) films and their
corresponding laminateusing a convenient cyclic tear test method.
Propaga-tion of tear crack in these thermoplastics deflects fromthe
initial crack path due to the material anisotropy. Animprovement to
a two-zone tear model for determin-ing tear EWF was proposed for
LDPE-like materials.Energy dissipation due to non-uniform bending
of thetrouser-legs was determined to be significant in
EWFcalculation of tearing and this was therefore consideredin this
study. To measure the tear EWF in laminates,contribution from
delamination energy dissipation wasaccounted for.
Keywords Trouser tear test · Essential work offracture ·
Flexible laminate · Crack path deviation ·Delamination
M. S. Islam (B) · E. Andreasson · S. Kao-WalterDept. of Mech.
Eng., Blekinge Institute of Technology,371 79 Karlskrona,
Swedene-mail: [email protected]
E. AndreassonTetra Pak, 223 55 Lund, Swedene-mail:
[email protected]
S. Kao-WalterFac. of Mech. & El. Eng., Shanghai Polytechnic
Univ.,Shanghai 201209, Chinae-mail: [email protected]
1 Introduction
Polymers films of low-density polyethylene (LDPE)and
polyethylene terephthalate (PET) are widely usedin packaging
industries, and tearing is a commonmethod of package-opening.
Although there are manyexisting in-plane mode I studies on single
layer as wellas laminates of these thin polymer films
(Kao-Walter2004; Kao-Walter et al. 2006; Andreasson et al.
2014;Zhang et al. 2016), not many out-of-plane investiga-tions
could be found in the literature (Kim and Karger-Kocsis 2004;
Bjerkén et al. 2006; Kao-Walter et al.2009, 2011; Martínez et al.
2010; Andreasson et al.2013).
The essential work of fracture (EWF) of tear in thinpolymer
films has increased popularity to character-ize out-of-plane shear
fracture toughness (Wong et al.2003). The two-leg trouser tear test
which was firstused by Rivlin and Thomas (1953) with rubber,
rapidlybecame a preferred test method for tear testing of
thinsheets and films. ‘Trouser tear test’will be referred sim-ply
as ‘tear test’ later in this article. One of the chal-lenges is
that, when highly extensible materials experi-ence tearing, it is
hard to separate the plastic work donein the legs from the plastic
work done at the vicinity ofthe crack. The total fracture energy
from a tear test canbe separated into geometry dependent
(non-essentialwork) and geometry independent (essential work)
con-tributions to characterize EWF. For energy separationin a tear
test, a two-zone model was proposed byWong et al. (2003). The
authors showed that the plastic
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188 M. S. Islam et al.
zone width increases with progress of tearing up to acertain
length (zone one) from the initial crack tip; andfor any further
tearing, the plastic zone width remainsconstant (zone two). This
research was extended byKim and Karger-Kocsis (2004), who included
a thirdzone that divides ‘zone one’ proposed by Wong et al.(2003)
into two separate zones, wherein the new ‘zoneone’ considers the
crack tip deformation prior to anycrack propagation during a tear
test. A two-zone modelwas selected as the foundation of the current
study,and additional observations were incorporated, as dis-cussed
in Sect. 4. All the earlier studies used multipletear tests for
tear EWF calculation, whereas, the cur-rent study showed that a
single cyclic tear test can besufficient.
During a tear test, the specimen legs bends plasti-cally close
to the crack tip and along the leg width insome cases. Dissipation
of energy from the work doneby plastic bending and straightening of
trouser-legsduring tearing is non-essential work of fracture. It
wasconsidered for EWF calculation by Mai and Cotterell(1984)
formetalwith constant curvature of leg bending.Kim andKarger-Kocsis
(2004) later reported that dissi-pation of energy due to plastic
bending and straighten-ing is negligible for polymers; they did not
report anymeasurement on this. However, for PET, LDPE, andtheir
laminate, the bending was observed to vary alongthewidth of the
specimen leg. Thework of plastic dissi-pation from this non-uniform
bending was consideredas presented in Sect. 3, and its magnitude
was deter-mined to be significant to EWF as shown in Sect. 4.
Studying the tearing of thin polymer laminatesbecome involved as
the films in the laminate responddifferently under load compared to
individual layer;this has been investigated by several authors
(Bjerkénet al. 2006; Andreasson et al. 2014; Zhang et al.
2016;Kao-Walter et al. 2006, 2009, 2011; Islam et al.
2016).Kao-Walter et al. (2011) investigated the LDPE–PETlaminate
under tearing and observed delamination inthe interface which
increased along with tear crackpropagation. This study has also
investigated the signif-icance of delamination in a laminate while
calculatinglaminate EWF.
Further, both LDPE and PET are anisotropic whichresulted in
deviation of the tearing crack from its initialpath as it
propagates. Mode mixing is another chal-lenge. Wong et al. (2003)
described mode III tearingEWF to be very similar to that of mode I
and attributedthis to the fact that mode III tearing at the crack
tip
becomes a mixture of mode I and mode III due tohigh local
deformation (Kim and Karger-Kocsis 2004;Mai and Cotterell 1984).
Bárány studied EWF of PETfor mode I and mode III and found similar
correlationbetween them (Bárány et al. 2005).
This article presents a new cyclic tear test method,proposes
tear EWF calculation method for laminatesand considers non-uniform
bending and delaminationin the trouser-legs as non-essential work
of fracture.The effect of material anisotropy was also checked.The
article is organized as follows: Experiments onstandard tear test
and its extension to cyclic tear teatis presented in Sect. 2.
Section 3 describes the appli-cation of a existing plastic energy
dissipation (non-essential work of fracture) theory to non-uniform
bend-ing of trouser-legs. EWF of tearing was calculated forthin
LDPE, PET films and their laminate in Sect. 4.Section 5 presents
some scanning electron microscope(SEM) observations of fracture
surface and delamina-tion of the tested materials. Results are
discussed inSect. 6 and the paper ends with some conclusions.
2 Experiments
A laminate of LDPE–PET film was examined in thisstudy.
Thematerial was supplied by a packaging indus-try and is a
constituent of liquid food packaging. TheLDPE layerwas separated
from thePETfilm in the lam-inate manually in the laboratory to
perform single layertests. Specimens were cut from a roll of film
as shownin Fig. 1a. A sharp surgical blade was used to cut
thespecimens and the pre-cracks. All tests were performedusing an
MTS Qtest universal tensile testing machine.The films to be tested
were kept at a controlled labora-tory environment with a
temperature of 23 ◦C and 50% humidity for at least 24 h before
specimen prepara-tion. The tests were displacement-controlled. For
anyexperimental results presented, at least three tests
wereperformed.
Cyclic trouser tear tests were utilized to determinetear EWF in
single layers and in the laminate. To com-plement the calculation
of tear EWF and to find a rela-tion between tear andmode I
fracture, additional tensiletestswere performedon the continuumand
center crackspecimens of the same materials.
LDPE,PETandLDPE–PET laminate are anisotropic.Tear and tensile
tests were performed in five differentmaterial orientations as
depicted in Fig. 1a for check-
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Trouser tear testing of thin anisotropic polymer films and
laminates 189
Fig. 1 a Materialorientation for test samplesof the anisotropic
films andb studied specimengeometry
Table 1 Comparison ofmechanical and geometricproperties of the
testedmaterials in MD
E(MPa) σy (MPa) σb (MPa) ν (–) α (–) t (µm)
LDPE 172 5 12.2 0.45 0.0058 25
PET 1550 32.8 72 0.40 0.0364 50
Laminate 1090 – – – – 75
ing material anisotropy . Angles of orientation weremeasured
from MD; the direction 90◦ from the MD isreferred to as cross
direction (CD). From the tensiletest results shown in Appendix A,
the elastic modulusand yield stress of LDPE and PET were observed
to beisotropic. Anisotropy of ultimate stress was significantin PET
but not substantial in LDPE. The Young’s mod-ulus (E), Poisson’s
ratio (ν), initial yield stress (σb),work-hardening parameter (α)
and film thickness forLDPE and PET in MD are presented in Table
1.
2.1 Standard trouser tear test
A standard two-leg trouser tear test method (Standard1993) was
adopted to check anisotropy in the studiedpolymers under tearing.
The dimensions for the tearspecimen is shown in Fig. 1b. The test
was performeduntil the crosshead moved 20 mm to produce a 10
mmcrackpropagation. Influenceofmaterial anisotropywasobserved on
the tear peak load response, the devia-tion of the tear propagation
path, and delamination dueto tear. Tear crack deviation and
delamination can beobserved in the post-test LDPE–PET laminate in
MD(Fig. 2b). Figure 3 shows tear force response at dif-ferent
orientations. The Laminate tear force exhibited
Fig. 2 Tearing of films: a a laminate under trouser tear test
andb a post-test laminate specimen
larger anisotropy compared to the individual layers. Alatter
portion of this article explains the result throughthe crack
deviation and delamination in the laminate.
Tear crack propagation deviated significantly fromthe initial
direction for both laminate and PET (Figs. 4aand 5) but was within
1◦ to 2◦ for LDPE. These devi-ations were measured and presented in
Table 2 alongwith the delamination area in the laminate caused
dur-
123
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190 M. S. Islam et al.
Fig. 3 Force displacementresponse of tearing a PET, bLDPE and c
laminate. (Forexplanations of the coloursin these figure
legends,please refer to the webversion of this article)
Fig. 4 a Crack deviationduring tearing of laminate;b
delamination duringtearing of laminate
ing the tearing. The area of delamination wasmeasuredbased on
the photographs (Fig. 4b) using a desktopapplication
‘plotdigitizer’ (JA 2010).
2.2 Cyclic trouser tear test
For EWF calculation, the specimens were torn only inMD to a
larger extent through five incremental loadingand unloading cycles.
Figure 6 illustrates this incre-mental tearing through loading and
unloading. Notice-ably, the crack propagation can be expected to be
nearly
Fig. 5 Crack deviation during tearing of PET
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Trouser tear testing of thin anisotropic polymer films and
laminates 191
Table 2 Crack deviation inPET and laminate togetherwith
delamination due totearing in degrees (smallcrack deviation of
LDPEwas disregarded)
MD 22.5◦ 45◦ 67.5◦ CD
Crack angle-PET 12 2–4 1 − (3–4) −6Crack angle-laminate 7–8 6–7
1 − (1–1) − (4–6)Delaminated area (mm2) 6.30 5.32 3.30 5.572
7.66
Fig. 6 Cyclic test method for incremental tearing
half of the leg separation. However, this is not practi-cally
the case because the bending of the legs increasesas load
increases, and also there is invariably somedevi-ation to the crack
due to anisotropy. Specifically, at theend of the first cycle,
crack propagation length is signif-icantly smaller than expected as
the specimen needs tobend before the crack can begin to move.
Therefore, toassess the exact length of the propagated crack, it
wasnecessary to record the crack length after each cycle
byinspecting the markings on the specimen. The speci-mens were
marked along the expected crack propaga-tion path (Fig. 2). This
helped to record the propagatedcrack length at any point during a
test. At the end ofloading in each cycle, a pause of 30 sec in test
machinecross headmovement was programmed; this pause wasused to
photograph test specimens to measure the cur-rent curvature of
bending (Fig. 7). Since the tear loadresponse is very small (Fig.
3) when compared to thetensile test response shown in Appendix A,
the elon-gation of the trouser-legs can be reasonably neglectedfor
PET and laminate. It was also not considered forLDPE in this
study.
Fig. 7 Side view of trouser tear specimen, measuring the
innerand outer tear bending curvature from images
3 Bending dissipation of tear
During tearing, the specimen legs endured beam-likebending and
straightening, which may result in plas-tic energy dissipation.
With the advance of tear pre-crack, the maximum bending of a
trouser-leg changesposition. At steady-state tearing, this change
in posi-tion of the maximum curvature is equal to the growthin
pre-crack (da). For energy dissipation during bend-ing (dUdb) at
maximum curvature, the bending energyrelease rate can be written
as,
Gdb = dUdbda
(1)
Kinloch et al. (1994) presented mathematical expres-sions for
this bending dissipation for a bi-linearisotropic hardening
material as a function of normal-ized curvature (k0) of bending
(Kinloch et al. 1994).Depending on the maximum k0 of the beam in a
load-ing history, three probable cases may arise (Kinlochet al.
1994),
Case 1: For 0 < k0 < 1, bending involves elasticloading
and elastic unloading with no plasticity.
123
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192 M. S. Islam et al.
Fig. 8 Dividing the trouser-leg’s width (b) based on level
ofplastic loading
Case 2: For 1 < k0 < 2, bending involves elastic–plastic
loading and elastic unloading, but no reverseplasticity.
Case 3: For k0 > 2, elastic–plastic loading andreverse
plastic deformation are involved.
Tensile responses of thematerials shown inAppendixA indicated
that the hardening could be assumed bi-linear for both materials in
MD orientation. Further-more, if isotropic hardening is assumed,
then expres-sions byKinloch et al. (1994) could be directly
adoptedto measure dissipation of plastic bending and unbend-ing in
the trouser test if bending of the legswas uniform.Instead, bending
is non-uniform (Fig. 7), and it is highlyprobable that along the
width (b) of the trouser-legsbending, the material will experience
all three possiblecases of plastic energy dissipationwith gradual
changesin curvature, from inner to outer curvature (Fig. 8).
According to Fig. 7, the inner curvature kmax andouter curvature
kmin were measured from the tear testimage using the application
plotdigitizer. It was fur-ther assumed that for a small increase in
torn ligamentlength (la), the curvatures remain same at steady
state.The inner and the outer curvatures were then normal-ized
using the equation below:
k0 max = kmaxk1
; k0 min = kmink1
(2)
k1 = 2εyt
(3)
Here, εy is the initial yield strain and t is
trouser-leg’sthickness. Assuming a linear change of curvature
alongthe width of the legs, the normalized curvature can
beexpressed as a function of width, b (Eq. 4). The legwidth can be
divided into three zones as illustrated inFig. 8.
k0(b) = k0 max − bbmax
(k0 max − k0 min) (4)
Analytical beam model for plastic energy dissipationdue to
bending used by citekinloch1994 takes the fol-lowing form for
non-uniform bending:Case 1: For b < bmax (k0 max−1)k0 max−k0 min
; no plastic dissipation.
Gdb1 = 0 (5)
Case 2: For bmax (k0 max−1)k0 max−k0 min < b <bmax
[k0 max− 2(1−α)(1−2α)
]
k0 max−k0 min
Gdb2 = Gemax[(1 − α) k0(b)
2
3+ 2 (1 − α)
2
3k0(b)− 1
]
(6)
Case 3: For b >bmax
[k0 max− 2(1−α)(1−2α)
]
k0 max−k0 min
Gdb3 = Gemax[4
3α (1 − α)2 k0 (b)2
+2 (1 − α)2 (1 − 2α) k0 (b)]
+ Gemax[4 (1 − α) [1 + 4 (1 − α)3]
3 (1 − α) k0 (b)−2 (1 − α)
[1 + 4 (1 − α)2
]]
(7)
Here, Gemax is the maximum elastic energy in thespecimen leg
(for unit width, per unit crack propaga-tion).
Gemax =1
2Eε2yt (8)
Finally, bending dissipation per unit ligament length(la),
Wdbla
=∫ b2 maxb2 min
Gdb2db +∫ bmaxb3 min
Gdb3db (9)
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Trouser tear testing of thin anisotropic polymer films and
laminates 193
Here, la is equivalent to tear crack length. This dis-sipation
is non-essential work of fracture.
4 Essential work of fracture
Asdiscussed previously, a two-zonemodel (Wong et al.2003) was
adopted for tear EWF calculation. In thismodel, total work of
fracture for tear is calculated asfollows (Wong et al. 2003):
WT F = WT E + WT P = wTelat + wT P Spat (10)
WT F is total work , WT E is total essential work andWT P is
total plastic work of tear fracture. Further, wT eis specific
essential work and wT P is specific plas-tic work of tear fracture.
Here, tear crack propagationlength is referred to as ligament
length (la). Plasticizedarea (Spa) is the area of plastic zone near
the crackpropagation path (Fig. 9a, b). Some additional
obser-vations and considerations were incorporated into thismodel
and are presented next.
4.1 Separation of plastic dissipation from bending
Plastic dissipation due to bending Wdb (Eq. 9) in
thetrouser-legs was demonstrated to be significant in thecurrent
case. When Wdb is accounted for, the expres-sion in Eq. 10 takes
the form as follows:
WT F − Wdb = WT E + WT P= wT elat + wT P Spat (11)
Wdb can be calculated from experimental observationsbased on Eq.
9 as described in Sect. 3.
4.2 Evaluation of EWF from only Zone I
During a tear test, a plastic zone is developed closeto the
propagated crack. The width (h) of the plas-tic zone (also called
ligament width) increases as thecrack tip progresses in a certain
manner depending onthe mechanical and geometric properties of the
mate-rial. This is illustrated in the schematic of Fig. 9a.
Thisplastic zone is visible in a teared LDPE specimen aswrinkles of
increasing width (Fig. 9b) and as a thinwhite zone close to
fracture surface for PET teared
Fig. 9 Zones in a tear test. a Schematic for post-tear LDPEwhere
la = l1 + l2, b post-tear LDPE, c post-tear PET
specimen (Fig. 9c). Zone I of a post-tear specimen isthe small
zone ahead of initial crack tip where plasticzone width (h)
increases more rapidly. Observation ofpost-test tear specimens
(Fig. 9c) indicates that the plas-tic zone area (Spa) for PET (for
the tested thickness)was small and barely spread from the fracture
surface.The subsequent SEM study made similar observations.However,
LDPE plastic zone width increased faster inzone I (Fig. 9b). In
zone II (Fig. 9b), the plastic zonewidth increased slowly and
steadily with the increasingligament length. The triangularly
shaped plastic area inzone I (Fig. 9b) can be calculated as Spa =
α′la2. Theplastic area multiplier, α′, as presented by Wong et
al.(2003) is the slope of the ligament width outer bound-ary with
respect to pre-crack path in zone I (Fig. 9a).Therefore, Eq. 11 can
be written as follows:
WT F − Wdblat
= wT e + wT Pα′la (12)
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194 M. S. Islam et al.
The left side of Eq. 12 can be calculated based on exper-imental
measurements. If several experiments can beperformedwithin the zone
I ligament length (la), Eq. 12can effectively be used to
extrapolate the expression forzero ligament length and quantify the
specific essentialwork of fracture (wTe).
4.3 Evaluation of EWF from only zone II
For PET, if contribution from the very small zone I isignored,
the model in Eq. 12 could be directly used forevaluation of EWF
using zone II (zone II is treated aszone I). However, in a
post-tear LDPE specimen, la inzone I is small but significant and
zone II is present.As illustrated in Fig. 9a, b, LDPE had a zone I
(lengthl1) with a sharp increase in ligament width (h) (slopeα′),
followed by zone II (length l2), in which width ofthe ligament (h)
increases comparatively slower (slopeα′′). As in Fig. 9a, it is
possible to extend zone IIbackwards to achieve zero ligament width
at a dis-tance of l ′2 from the beginning of zone II. Further,total
work of fracture can be partitioned as zone I andzone II work of
fracture. The total work of fracture inzone I (WT F−I ) can be
experimentally quantified usingEq. 12. It is then possible to plot
a relation betweenWT F−I I = WT F − Wdb − WT F−I and l2 = la −
l1.Figure 9a implies that specific plastic work of fracture(wT P )
is zero at l2 = −l ′2. Hence according to Eq.14, extrapolating this
curve to l2 = −l ′2 (la = l1−l ′2)provides the specific essential
work of fracture.
WT F−I I − Wdb = WT E + WT P= wT el2t + wT P Spat (13)
WT F−I I − Wdbl2t
= wT e + wT P (h + 2α′′l2) (14)
The length of l ′2 can be calculated by measuring thezone II
slope (α′′) and maximum zone I width (h),
l ′2 =h
2α′′(15)
At l2 = −l ′2, the contribution fromnon-essential
plasticdissipation wT P becomes zero.
Fig. 10 Cyclic loading-unloading test response for tear;
Lam-inate consists of LDPE and PET layers. (For explanations ofthe
colours in this figure, please refer to the web version of
thisarticle)
4.4 EWF in laminates
In the laminate, as in Fig. 2b, PET layer crack
deviates;however, it does so less than as a single layer (Table2).
The LDPE layer in the laminate follows a commondeflected crack path
with PET as long as the delami-nation is small near to initial
crack tip (Fig. 2b). Sincethe PET layer is significantly stiffer
and thicker thanLDPE, it controls the laminate crack deviation. At
thesame time, since LDPE is more isotropic, this restrainsthe
deviation of the laminate crack and results in lessPET crack
deviation in laminate than stand-alone tearat the beginning for
tear. With increasing crack prop-agation, delamination increases,
and the LDPE crackpath deviates from that of PET. Importantly, the
LDPEcrack eventually deviates at least as much as PET ormore
because of the constraint that the stiffer PET layerplaces in
softer LDPE in a laminate. This behaviourincreases the amount of
delaminationwith crack propa-gation and results in smaller
crackpropagation inLDPEthan PET (Fig. 2b). For convenience of
laminate EWFcalculation, the propagated crack length up to the
com-mon crack path of LDPE and PET was assumed. Thenon-essential
energy dissipation due to delamination(Wdel ) must also be
considered in the calculation andincluded in Eq. 16.
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Trouser tear testing of thin anisotropic polymer films and
laminates 195
Table 3 Specific work of PET fracture calculation for different
cycles using Eq. 12
PET (MD) Ligament length (la) [mm] Total work of fracture(WT F )
[N-mm]
Bending dissipation (Wdb)[N-mm]
Specific total work of frac-turewT e+wT Pα′la [N/mm]
Cycle-1 6.80 2.04 0.28 5.20
Cycle-2 11.30 3.66 0.28 5.49
Cycle-3 15.40 5.24 0.29 5.71
Cycle-4 20.00 6.84 0.28 5.72
Cycle-5 24.40 8.41 0.29 5.75
Table 4 Specific work of LDPE fracture calculation for different
cycles using Eq. 14
LDPE (MD) Ligament length in zone II(l2)[mm]
Total work of fracture inzone II ((WT F − WT F−I ))[N-mm]
Bending dissipation (Wdb)[N-mm]
Specific total work of frac-ture in zone II wT e +wT P (h +
α′′l2) [N/mm]
Cycle-1 4.80 2.51 0.10 20.11
Cycle-2 9.50 5.78 0.10 23.51
Cycle-3 14.00 9.36 0.10 25.88
Cycle-4 18.50 12.99 0.12 27.22
Cycle-5 22.90 16.78 0.13 28.44
WT F−I = 0.3144 [N-mm]; h=0.7 mm α′′ = 0.034 and l ′2 = 10.3
Table 5 Specific work of laminate fracture calculation for
different cycles
Laminate (MD) Ligament length(la) [mm]
Total work offracture (WT F )[N-mm]
Bending dissipa-tion (Wdb) [N-mm]
DelaminationdissipationWdel = wdel Sdel[N-mm]
Specific totalwork of fracturewT e + wT Pα′la[N/mm]
Cycle-1 6.60 4.32 0.97 0.0179 6.63
Cycle-2 11.5 9.05 1.06 0.04 8.07
Cycle-3 15.50 14.52 1.18 0.06 9.62
Cycle-4 20.20 20.41 1.15 0.08 10.45
Cycle-5 24.80 26.64 1.21 0.15 11.13
WT F − Wdb − Wdel = WT E + WT P= wT elat + wT P Spat (16)
Wdel = wdel Sdel (17)The area of delamination (Sdel ) can be
measured fromthe post-tear specimen image, and wdel can be
calcu-lated from peel tests as in Appendix C.
4.5 Calculation of EWF from cyclic tear test
Total work of fracture for different ligament lengths(crack
propagation) can be quantified through a sin-gle cyclic tear test
with loading to a certain ligament
length of tearing and unloading to zero reaction force.Then
subsequently re-load for tearing to a new ligamentlength greater
than the first cycle and unload again. Thiscyclic loading and
unloading described in Sect. 2 canbe performed an arbitrary number
of times. Figure 6describes the test method. For any arbitrary
length oftearing, the area under the load-unload curve providesthe
total work of fracture due to tear; additionally, ifthe tearing
length is known, this can be used to calcu-late the specific total
work of fracture using Eq. 12 orEq. 14 for a single layer and Eq.
16 for laminate. Thearea under the curve for loading in cycle 1 is
regardedas AL−c1 and as AU−c1 for unloading after crack prop-
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196 M. S. Islam et al.
agation of length la1. Specific total work of fracture forthe
tear in first cycle is as follows:
wT F1 = WT F1la1t
= AL−c1 − AU−c1la1t
(18)
The loading for the second cycle can be considered tofollow the
same load–displacement path, initially, asfor first cycle (Fig. 10)
and eventually tear to a newligament length la2. Specific total
work of fracture forthe tear from this cycle wT F2 is as
follows:
wT F2 = WT F1 + WT F2la2t
= WT F1 + AL−c2 − AU−c2la2t
(19)
Specific totalworkof fracture (according to the descrip-tion in
Tables 3, 4, 5) can be calculated for a numberof ligament lengths
conveniently from a single cyclictest. Necessary calculations for
specific work of frac-ture are shown in Tables 3, 4, 5 as an
example. ForLDPE, the total work of tear fracture in zone I (WT F−I
)was needed to be measured additionally from a sepa-rate tear test
(Table 4). Noticeably, bending dissipation(Wdb) accumulates in
subsequent cycles. Extrapolationof specific total work of fracture
along ligament lengthwill result in specific essential work of tear
fracture.
Specific essential work of fracture (SEWF) (wTe)for PET tear
using zone I model and with no consid-eration of bending
dissipation was calculated as 5.44N/mm; when considering bending,
it was calculated as4.80 N/mm; having a difference of 11.6 %. For
LDPEtear fracture with and without consideration of
bendingdissipation and using zone II model, SEWFwere 11.84N/mm and
11.1 N/mm respectively; this correspondswith a difference of
6.25%.However, specific essentialwork of laminate tear fracture was
4.524 N/mm, whichis strikingly low (Fig. 11). In the current case,
SEWFforlaminate appeared to not represent the laminate prop-erty
correctly. A zone I model was used for this calcu-lation. Further
investigations could address this issue.
5 Scanning electron microscopy
In the post-test tearing specimens (in MD) three sec-tionswere
cut perpendicularly to the initial crack at 1, 7,and 13mm away from
the initial crack tip, as illustratedin Fig. 12b. The aim was to
study the fracture surface,
Fig. 11 Tearing specific work of fracture for different
materials
Fig. 12 Schematic of a Post-test trouser tear specimen of
thelaminate b section for crack tip SEM observation and c
delami-nation and substrates’ deformations
thinning of thematerials prior to the failure and delami-nation
in the laminate. The cross sections were cut withsharp scissors
andwere gold-coated in aHitachiE-1030Ion Sputter Coater. A Field
Emission (SEM)Hitachi S-4800 electron microscope was utilized for
imaging.
The SEM image of a section (Sect. 1 according toFig. 12b) near
crack tip in Fig. 13a shows significantdelamination due to tearing.
Observations of PET frac-ture surface in Fig. 13b demonstrated that
the natureof PET fracture is less ductile and that the plastic
zonespreads less from the fracture surface. The thinning ofPET
prior to failure is also local to the fracture surface.
LDPE crack surface fracture appeared highly duc-tile (Fig. 13c);
more importantly, there was a signifi-cant reduction in thickness
which indicates damage onLDPE in the laminate is due to
thinning.
Further observation on all three sections accordingto Fig. 12b
agreed that the spread of this thicknessreduction increases with
tear crack propagation. Anincrease in the area that experiences
reduction in thick-
123
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Trouser tear testing of thin anisotropic polymer films and
laminates 197
Fig. 13 SEM-micrographs of a crack tip and b, c fracture
sur-face of LDPE–PET laminate in machine direction
ness with crack propagation is equivalent to an increasein
ligament length width (h) (Fig. 9a).
Figure 12c schematically and Fig. 13a in SEM cracktip section
view of a torn laminate illustrates signifi-cant local strain with
thickness reduction in the LDPElayer, relatively smaller thickness
reduction, and strainof the PET layer and delamination of the
interface.Withincreasingly torn ligament, more area is
delaminated,and width of delamination is increased. As a
result,more LDPE is unconstrained and therefore availablefor
thinning (Fig. 2b).
6 Results and discussion
LDPE layer in the laminate is more ductile than PETlayer. As a
result, the spread of the plastic zone (Fig. 9b)is significantly
larger than that of PET. In a laminate, theLDPE film is constrained
by the interface, and the plas-tic zone cannot spread as in a
stand-alone layer. Thiscauses the laminate total work of fracture
to be lowerthan that of individual layers combined (LDPE+PETin Fig.
14) for lower ligament length. However, asthe crack propagates,
delamination was observed to
Fig. 14 Tearing total work of fracture for various materials
increase along the trouser-legs widths (Fig. 2b). Thisincreases
the volume of unconstrained LDPE that canundergo plastic
deformation (thinning). Also, there isadditional energy dissipation
from delamination. Asa result, the TWF of laminate is higher than
PETand LDPE TWF combined at a larger ligament length(Fig. 14). So,
material anisotropy causes tear crackdeviation anisotropy
(different tear deviation at differ-ent material orientation) which
results in delaminationanisotropy. This explains the reason for
laminate beingmore anisotropic in tear compared to its
constituents.
Plastic dissipations in the trouser-legs during tear areregarded
as non-essential work of fracture. Measuringthe dissipation from
the leg bending curvature rendersthe calculated SEWF more
independent of leg width.This method of measurement can be
beneficial when itis practical to minimize the number of tests by
not test-ing for multiple leg width to omit any width effect.
Theformulation provided in this study can be applied toboth uniform
and non-uniform curvature distribution.
SEWFof PETmeasured by the proposed cyclic tear-ing was
comparable with results found in the literature.The calculated SEWF
for 50µm PET was 4.80 N/mmin this study and 6.35 N/mm for 250µm PET
in theliterature (Kim and Karger-Kocsis 2004). The currentvalue was
smaller because the dissipation of bendingwas regarded as
non-essential work of fracture. The lit-erature reports that
smaller tear SEWF for thinner PETis expected (Kim and Karger-Kocsis
2004). LDPE wasdivided into two zones based on visual inspection,
andthe proposed zone II method bypasses any necessarycalculation
for near crack tip plastic dissipation. Thismethod is applicable to
materials that develop long lig-
123
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198 M. S. Islam et al.
aments with steadily increasing plastic zone width dur-ing tear.
The authors did not find SEWF for LDPE tearreported in the
literature. However, the specific essen-tial work of fracture for
blown LDPE film in mode Iwas reported to be approximately 16N/mm
for 150µmthick LDPE film. The SEWF is more anisotropic forthinner
LDPE, and it ranges between 9 and 43 N/mmfor 15µm thick LDPE
(Rennert et al. 2013). Macro-scopic crack tip observation of a tear
test suggests thatsince LDPE ismore ductile and flexible, it tends
to shiftmode, and loadmore inmode I; therefore, a relation canbe
expectedwithmode I SEWF. In this study, the calcu-lated SEWF of
tear for 25µm LDPE was 11.1 N/mm,which is comparable with the
results reported earlierin the literature. The calculated SEWF of
the laminateof LDPE–PET was significantly low and
necessitatesfurther investigation. Moreover, although the
thicknesscan also exert a significant effect on SEWF value (Kimand
Karger-Kocsis 2004), merely one particular thick-ness for each film
was tested.
Material anisotropy of PET and LDPE affectstrouser tear load
response; therefore, this also affectsEWF. The deviation in tear
crack propagation is alsorelated to the anisotropy. The tear crack
deviationappears to correlate well with the weakest mode I
frac-ture toughness direction of the material (Figs. 15a and16).
Details of the center crack panel test for modeI fracture toughness
determination can be found inAppendix B. Constrained by LDPE, PET
tear crackdeflected less in laminate than as a single layer.
Themore the PET orientation aligns with 45◦, the weakerthe material
becomes for cracking in mode I accordingto Fig. 16a and tear crack
deviation reduces accordingto Fig. 15a. The tear crack tends to
remain straighterclose to 45◦ orientation. For a tear orientation
that dif-fers from 45◦, the crack changes direction toward theleft
or right (approaching from MD or CD) to a cer-tain degree until a
saturation is reached. This relationbetweenmode I and tearingwas
expected; aswith crackpropagation, tear becomes a mixture of mode I
andmode III fracture. Noticeably, in a MD tear specimen,the mode I
loading is in CD; this 90◦ shift holds for allother directions. The
amount of delamination is pos-itively correlated with the deviation
of the crack in alaminate (Fig. 15a, b) meaning smaller
delamination inthe laminate for smaller crack deviation.
The tear tests were performed such that trouser-legswere
separated vertically, which caused the tail of thetear specimen to
hang and bend down due to gravity
Fig. 15 Anisotropy during tearing a crack deviation in PET
andlaminate and b delamination in laminate. (For explanations ofthe
colours in these figures, please refer to the web version ofthis
article)
Fig. 16 Mode I fracture toughness of the tested materials
atdifferent orientations a PET, b LDPE and c laminate. (For
expla-nations of the colours in these figures, please refer to the
webversion of this article)
(Fig. 2a). This can cause the bending curvature at thebottom leg
to be larger than the top one and contributeto additional tear
crack deviation. Particularly in thelaminate, if the more compliant
LDPE side is facingupwards, delaminationwidth increases faster with
tear-ing relative to when the PET side faces upwards. Thiscan
affect the SEWF and worth further investigation.This effect can be
negated by pulling the tear specimensidewise such that the tail
hangs vertically.
7 Conclusions
Trouser tear test of PET, LDPE films, and the corre-sponding
laminate have been examined in this study
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Trouser tear testing of thin anisotropic polymer films and
laminates 199
in five different material orientations. Propagation oftearing
in these thermoplastics demonstrated deviationfrom the initial and
parallel crack path with a mixedmode I and mode III. This was
determined to be causedby the material anisotropy, and the
deviation can berelated to the difference in mode I fracture
toughnessat different material orientations. The crack tends
todeflect toward the weakest material orientation. Theamount of
delaminationwas also discovered to be influ-enced by the material
orientation.
The proposed cyclic tear testmethod for SEWFmea-surement could
produce results comparable to thosereported in the literature.
Energy dissipation due tonon-uniform bending of the trouser-legs
was demon-strated to be significant in the tearing
SEWFcalculationand was therefore considered in this study.
Analyticalexpressions for the calculation of non-uniform
bendingenergy dissipation for a bi-linear isotropic
hardeningmaterial model were presented. A variation of a two-zone
tearmodel was proposed to bypass any plastic dis-sipation
calculation for SEWF calculation in LDPE. Tomeasure the SEWF of
laminates, delamination energydissipation was accounted for.
However, delaminationappeared to expose more unconstrained LDPE
thateffects the laminate behaviourmore than that caused byenergy
dissipation due to delamination. Further study isnecessary to use
EWF for characterization of laminatetear fracture. Also, this study
particularly focused onthin LDPE, PET and their laminate.
Additional studiesare necessary to check the applicability of the
presentedmethods and formulations for other polymers.
Acknowledgements Openaccess fundingprovidedbyBlekingeInstitute
ofTechnology.Thiswork is a part of the research activityof the
Model Driven Development and Decision Support project(MD3S) at
Blekinge Institute of Technology, which is funded bythe Swedish
Knowledge and Competence Development Foun-dation (KKS). Special
thanks to SEM laboratory at ShanghaiPolytechnic University, China
for allowing us to use their facil-ity, and to Dr. Lun Zhao from
Kunming University of Scienceand Technology in China for helping us
with the SEM study.
Open Access This article is distributed under the terms ofthe
Creative Commons Attribution 4.0 International
License(http://creativecommons.org/licenses/by/4.0/), which
permitsunrestricted use, distribution, and reproduction in any
medium,provided you give appropriate credit to the original
author(s)and the source, provide a link to the Creative Commons
license,and indicate if changes were made.
Fig. 17 Mechanical tensile test of a PET film and b LDPE
film.(For explanations of the meanings of the colours in these
figurelegends, please refer to the web version of this article)
Appendix A: Tensile test results
The tensile tests were performed according to the stan-dard ISO
527-3 (Standard 2018). Specimen lengthbetween the tensile grips was
100 mm, width was 25mm (Fig. 1b) and test speed was 20 mm/min.
Repre-sentative force vs. displacement results, presented inFig.
17a, indicate significant anisotropy both in maxi-mum displacement
and peak force for PET. The devia-tion in peak force for LDPE
tensile test responses wasrelatively small, but material oriented
close to MDwasdetermined to withstand higher strain (Fig. 17b).
123
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200 M. S. Islam et al.
Fig. 18 Center crack test results at different material
orienta-tions. a PET F–D response, b LDPE F–D response and c
lam-inate F–D response. (For explanations of the colours in
thesefigure legends, please refer to the web version of this
article)
Table 6 Peak force at different material orientation of the
testedmaterials
MD 22.5◦ 45◦ 67.5◦ CD
Peak load-LDPE (N) 4.72 4.70 4.47 4.77 4.38
Peak load-PET (N) 53.60 47.49 47.15 52.10 54.98
Peak load-Laminate (N) 60.16 51.08 50.30 55.32 57.23
Appendix B: Center crack (CC) panel test
The center crack specimen dimension used in an earlystudy was
adopted as a reference (Kao-Walter 2004).However, because of the
dimension of the producedLDPE–PET laminate, the CC specimens were
down-scaled by a factor of 2.3 to fit the material width in
thisspecific case. Finally, 100 mm-long and 41 mm-wideCC specimens
of LDPE, PET, and their laminate weretestedwith a center crack of
20mm (Fig. 1b). The crackpreparation technique affects the fracture
property sig-nificantly (Martínez et al. 2010); since this effect
wasinevitable, it was ensured that the specimens prepara-tion
conditions were repeatable. Figure 18 presents theforce
displacement (F–D) responses of these tests, andTable 6 displays
the peak forces.
Appendix C: Peel test
TheadhesionbetweenPETandLDPEcanbequantifiedbased on a peel test.
Fracture energy of delaminationwas determined using Kinloch’s
theoretical model ofpeel (Kinloch et al. 1994). 50mm-wide peel
specimenswere used, and LDPE film was peeled off at 90◦ and180◦
until a steady force response had been achieved.Steady force of
peelingwas the only quantity used fromthe peel tests. Necessary
tensile properties of LDPEwere also calculated based on the tensile
test performedin this study. Fracture energy of delamination from
peelwas calculated to be 33 J/m2.
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Trouser tear testing of thin anisotropic polymer films and
laminatesAbstract1 Introduction2 Experiments2.1 Standard trouser
tear test2.2 Cyclic trouser tear test
3 Bending dissipation of tear4 Essential work of fracture4.1
Separation of plastic dissipation from bending4.2 Evaluation of EWF
from only Zone I4.3 Evaluation of EWF from only zone II4.4 EWF in
laminates4.5 Calculation of EWF from cyclic tear test
5 Scanning electron microscopy6 Results and discussion7
ConclusionsAcknowledgementsAppendix A: Tensile test resultsAppendix
B: Center crack (CC) panel testAppendix C: Peel testReferences