Trouser tear testing of thin anisotropic polymer films and ......Trouser tear testing of thin...

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-

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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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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.

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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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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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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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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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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-

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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-

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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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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).

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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

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