OUTSIDE vs. INSIDE CREASING

Transcription

1 Divisin f Packaging Lgistics Divisin f Slid Mechanics ISRN LUTMDN/TMFL-09/5064 OUTSIDE vs. INSIDE CREASING - A PARAMETER STUDY Master s Thesis by Jennie Lillienberg and Emma Lörd Supervisrs Magnus Just, Tetra Pak Annika Olssn, Div. f Packaging Lgistics Matti Ristinmaa, Div. f Slid Mechanics Cpyright 2009 by Div. f Packaging Lgistics, Div. f Slid Mechanics, Tetra Pak, Jennie Lillienberg and Emma Lörd Printed by MEDIA-TRYCK, Lund, Sweden Fr infrmatin, address: Divisin f Packaging Lgistics, Lund University, Bx 118, SE Lund, Sweden Hmepage: Divisin f Slid Mechanics, Lund University, Bx 118, SE Lund, Sweden Hmepage:

2 Abstract Creasing f paperbard is an essential peratin t btain a well defined shape and strength f a package. The creasing tl cnsists f ne male and ne female creasing plate. The male plate presses the paperbard int the female plate and intrduces damage in the creasing zne. Tday the standard creasing peratin at Tetra Pak is that the male creasing plate presses the tp ply (print side) f the paperbard, and female is pressed against bttm ply (back side). This is called utside creasing, and the ppsite is called inside creasing. This master s thesis has the purpse f studying the differences between inside and utside creasing with respect t hw the paperbard behaves during bending and creasing. Since this area is hardly explred the purpse is t make a brad study abut the differences f inside versus utside creasing. Many parameters will be measured and cmputer simulatins will be used t get a better understanding f the parameters invlved. The experimental tests are divided int three different parts: 1) Straight creases are made using a flat bed labratry creasing tl, 2) A bttm crease pattern is made using a flat bed labratry creasing tl, 3) The pattern f a Tetra Brik 250ml Base package is made in pilt plant and tested n paperbard and packaging material. MODDE, sftware using the methd Design f Experiments, is used during tw f the experimental parts in rder t reduce the number f experiments. Straight creases are simulated using Abaqus built in material mdels fr the cntinuum mdel and chesive interface mdel fr delaminatin. The creasing peratin is simulated with rigid creasing plates while the flding peratin is simulated using cnstraints and bundary cnditins. In the experimental part, fr straight creases, there is a significant difference between inside and utside creasing n a few f the respnses investigated, but all tests shw that change f paperbard, crease tl and crease depth have a bigger impact n the respnses than the crease side. Hwever cracks ccur n inside creasing at a lwer crease depth than utside creasing. Frm the ther tw experimental parts, n significant difference between inside and utside creasing culd be fund, and als here change f paperbard, crease tl and crease depth have a bigger influence n the respnses and crack prpagatin. The simulatins d nt give a univcal result since they are all t similar independent f crease depth and web tensin smething that d nt crrespnd with the experimental results. Hwever the delaminatin behavir in the simulatins and the experimental tests are similar, the delaminatin behavir is very different in the inside and utside creasing but this fact is nt shwn in the investigated respnses. I

3 Preface This is a master s thesis made in cperatin between Material Treatment at Tetra Pak and the divisins f Packaging Lgistics and Slid Mechanics at Lund University in the fall f First f all we wuld like t thank ur supervisrs; Magnus Just at Tetra Pak fr his never ending patience with ur questins, Jhan Tryding ur unfficial supervisr at Tetra Pak fr his enthusiasm abut ur wrk, Annika Olssn at the divisin f Packaging Lgistics and Matti Ristinmaa at the divisin f Slid Mechanics fr supprt and knwledge in theretical questins. We als like t thank Jhan Nilssn fr intrducing us t Design f Experiment and MODDE, Mikael Nygårds fr giving us a simulatin mdel and help us in the start up with simulatins, Per-Göran Heide fr helping us with setting up and using the high speed camera, Tmas Linné fr ding all the hard wrk in the lab and last but nt least we wuld like t thank Vladimir Pnjavic and the rest f the department f Material Treatment fr helping and supprting us. Especially thanks t all the peple whse desks we used in their absence. Lund in December 2008 Jennie Lillienberg and Emma Lörd II

4 Table f Cntents 1 Intrductin Backgrund Objective Fcus and delimitatins Methd Methdlgy Wrk prcedure Design f Experiments - DOE Thery Paperbard Finite Element Methd Equatins f mtin Weak frmulatin - Principle f virtual pwer Nnlinear Finite Element Methd Slutin f Nnlinear Equilibrium Equatins - Newtn-Raphsn Methd Material mdel f paperbard Cntinuum mdel Chesive mdel Experimental wrk Experimental tls and parameters Labratry creasing tl Creasability tester Tpgraphy Phtgraphy setup Lab evaluatin f the paperbard s prperties First experimental part: straight creases In parameters Prcedure Secnd experimental part: bttm crease pattern In parameters Prcedure Third experimental part: 250 Base crease pattern...37 III

5 4.4.1 In parameters Prcedure Cmputer simulatin Abaqus Mdel Creasing Flding Prcedure Creasing Flding Results Experimental Straight creases Bttm crease pattern Base crease pattern Cmputer simulatin Discussin Experimental Straight creases Bttm crease pattern Base crease pattern Cmputer simulatin Cnclusins Recmmendatins f further investigatin References...61 List f Appendices...63 IV

6 1 Intrductin 1.1 Backgrund In the 1940 s a develpment prcess, with the purpse f creating a package fr milk that required a minimum f material and maximum f hygiene, started. The result was the tetrahedrn-shaped cartn. This lead t the fundatin f Tetra Pak in the early 1950 s by Ruben Rausing as a subsidiary f Åkerlund & Rausing. Over the next decades the cmpany grew t an internatinal cmpany with filling machines and packaging material factries all ver the wrld, with an ever expanding packaging prtfli with prducts such as Tetra Brik and Tetra Rex. In 1993 the Tetra Laval grup was created and tday, 2008, cnsists f three industrial grups: Tetra Pak, DeLaval and Sidel. Tday Tetra Pak ffers a cmplete prcessing and packaging system fr their custmers. Still the mst imprtant prduct in a Tetra Pak package is milk and cream but a wide range f ther prducts are prcess treated and aseptically packed, fr example juices, tea drinks, sy drinks, tmat prducts and wine [1]. This master s thesis is perfrmed at the department Material Treatment at Tetra Pak that develp and maintain the cnverting prcess f the packaging material such as cnverting penings, creasing and cutting. T assure a high quality package with a defined shape every time, a crease pattern (Figure 1.1) is imprtant when flding a package at high speed. Creasing f paperbard is an essential peratin t btain a well defined shape and strength f a package. The creasing tl cnsists f ne male creasing plate and ne female. The male plate presses the paperbard int the female plate and intrduces damage in the creasing zne. Tday the standard creasing peratin at Tetra Pak is that the male creasing plate presses the tp ply (print side) f the paperbard, and female is pressed against the bttm ply (back side). This is called utside creasing, and the ppsite is called inside creasing (Figure 1.2). 1

7 Figure 1.1. A schematic drawing f the Tetra Brik creasing pattern [8] Since utside creasing is the standard creasing methd at Tetra Pak many studies have been perfrmed within this area. Out f all Tetra Pak factries nly tw factries, Mnte Mr and Pnta Grssa in Brazil, use inside creasing t an almst full extent and inside creasing is there part f the cncept. Figure 1.2. Illustratin f utside and inside creasing (white is the bleached print side f the paperbard) 2

8 Only a certain amunt f tests have been perfrmed within the area f inside creasing and they haven't really given a clear picture f what happens with the paperbard and what the difference is cmpared t utside creasing. Panel tests have shwed that custmers find packages with inside creasing mre attractive because they are perceived as having a mre defined shape and t be easier t grip [3, 6, 7]. 1.2 Objective This master s thesis has the purpse f studying the differences between inside and utside creasing with respect t hw the paperbard behaves during bending and creasing. Since this area is hardly explred the purpse is t make a brad study abut the differences f inside verses utside creasing. Many parameters will be measured such as maximum frces, energy, remaining defrmatin and angles. The surface f the paperbard will be examined clsely t see fr example the height and depth f the creases and cracks in the material. Als cmputer simulatins will be used t get a better understanding f the parameters invlved. 1.3 Fcus and delimitatins The number f experiments required in the experimental part is defined by the number f parameters evaluated, and require that all parameters are cmbined t each ther; this rapidly expand the number f experiments. T btain a manageable number f test cmbinatins and parameters, sme restrictins and delimitatins are made in this master s thesis. During the first experimental tests the fllwing restrictins are made: Paperbard frm three paperbard suppliers Tw paperbard qualities: thin paperbard, used fr prtin packages, and thick paperbard, used fr family packages, frm all paperbard suppliers. Tw crease sides, inside and utside Three web tensins (the frce used t pull the paperbard web) Three crease depths Three straight crease tl gemetries each fr thin and thick paperbard Restrictins fr the secnd experimental part: Paperbard frm tw paperbard suppliers One paperbard quality: thin paperbard 3

9 Tw crease sides, inside and utside One web tensin Tw crease depths fr each paperbard and each crease side Tw tl gemetries, bttm crease pattern Restrictins fr the third experimental part: Paperbard frm tw paperbard suppliers One paperbard quality: thin paperbard Tw crease sides, inside and utside One web tensin Tw crease depths fr each paperbard and each crease side One tl gemetry, Tetra Brik 250ml Base crease pattern (will hencefrth be called 250 Base crease pattern) Als in the simulatins there are sme restrictins due t the mdel used. Restrictins fr the simulatin: One material mdel fr the paperbard Tw crease sides, inside and utside Three web tensins Three crease depths One straight crease tl 4

10 2 Methd 2.1 Methdlgy The methdlgy sets the frames f hw a study shuld be carried ut and is chsen in the beginning f the wrk. Which methd t chse, depends n the gals and character f the study. There are many different kinds f studies and mst f them can be classified depending n hw much ne knws abut a certain area, befre the study [13]. Explratry studies have a main purpse f finding as much infrmatin as pssible abut a pre-decided prblem area that ne lacks infrmatin abut. Since this type f study ften has the gal t get mre knwledge within the prblem area, many different techniques are used t cllect infrmatin. Smetimes knwledge already exists within the prblem area. A descriptive study is limited t examine sme aspects f the phenmenn ne is interested in. The descriptins f these aspects are detailed and thrugh. Often nly ne technique is used t cllect infrmatin. When the knwledge within a prblem area is extensive and theries are already develped, the methd t use is a study f setting and testing hypthesis. This means that ne can assume that smething is true and then test if it s accurate. There s a risk that ther factrs, ther than the factrs in the hypthesis, will affect the result f the test. Because f this it is very imprtant hw the study is built up. The technique fr cllecting infrmatin shuld be as precise as pssible. The three types f studies abve are mstly perfrmed as separate studies but within large prjects tw r all three types can exist [12]. The purpse f this master s thesis is t explre hw inside and utside creasing behaves. Nt many studies have been perfrmed within this area and this wrk has the purpse f expanding the knwledge; this is why the study used is explratry. Research can be quantitative and qualitative and can be seen as hw ne chses t analyze the cllected infrmatin. Qualitative research uses verbal analyzing methds like wrds and detailed descriptins, while quantitative analyzing methds use data that ne can cunt r measure. This master s thesis mstly analyzes quantitative data like frce, displacements etc. but sme data are qualitative like describing hw the material lks like thrugh a micrscpe [13]. 5

11 2.2 Wrk prcedure Based n the bjective and delimitatins f the master s thesis the prject plan is established. In the very beginning f the master s thesis a literature study is carried ut. Develpment reprts, bks and articles cncerning creasing and paperbard are studied and read thrugh in rder t get a theretical input f the area, these will then serve as reference material. Further, cmputer simulatins in cmbinatin with experimental tests are cnducted in rder t evaluate inside and utside creasing frm bth an analytical and experimental perspective. Hence simulatins are carried ut by use f the finiteelement sftware Abaqus. The experimental tests are divided int three different parts: 1) A labratrial part, where straight creases, bth the inside and the utside, are made n paperbard using a flat bed labratry creasing tl. 2) A labratrial part, where a bttm crease pattern (similar t the creases n the bttm f a package) is used t make creases with the labratry creasing tl. These tests are perfrmed in rder t study if there is a difference between creases in the machine directin (MD) and the crss machine directin (CD). Figure 2.1. Illustrating the different directins in the paperbard [18]. 3) A part where the paperbard is creased with the pattern f a Tetra Brik 250ml Base package in the Tetra Pak pilt plant. The paperbard is then laminated with the laminatin specificatin f an aseptic juice package, see Figure

12 Figure 2.2. Package material f a Tetra Brik Aseptic juice package Creases frm all f the experimental parts are flded using a Lrentzen & Wettre creasability tester and studied clsely using different methds: a. Tpgraphy fr measuring surface defrmatin f a crease b. Labratrial tests t find prperties f the paperbard such as z- strength, bending stiffness and thickness f the paperbard. c. Phts f the creasing and flding prcess in the first labratrial part in rder t study delaminatin f the paperbard. T btain a manageable number f test cmbinatins, sme restrictins and delimitatins are made, as stated earlier. Even thugh these restrictins are made, there are still t many cmbinatins f tests t be able t perfrm them all. Since all f the factrs and cmbinatins are desirable, a sftware MODDE, using a technique called Design f Experiments, is used t select a diverse and representative set f experiments in which all factrs are independent f each ther despite being varied simultaneusly. The result is a causal predictive mdel shwing the imprtance f all factrs and their interactins. The mdel can be summarized as infrmative cntur plts highlighting the ptimum cmbinatin f factr settings. Design f Experiments is used in the first and last experimental part when straight creases are made and when a 250 Base crease pattern is used in the pilt plant. Design f Experiments is described in the fllwing subchapter Frm the first analysis f MODDE a certain number f factrs are chsen t be further investigated during the secnd labratrial part, where bttm creases are made using the flatbed creasing tl. 7

13 The experimental results are cmpared t each ther and t the cmputer simulatins. The results are illustrated in tables, plts and figures Design f Experiments - DOE Design f Experiments, DOE, is used t ensure that the selected experiments prduce the maximum amunt f relevant infrmatin. It is imprtant t recgnize that a mdel is an apprximatin, which simplifies the study f the reality. A mdel will never be 100% perfect, but can still be very useful. A cmmn apprach in DOE is t define an interesting standard reference experiment and then perfrm new, representative experiments arund it (see Figure 2.3). These new experiments are laid ut in a symmetrical fashin arund the standard reference experiment. Hence, the standard reference pint is called the center-pint. Figure 2.3. Distributin f a full factrial design with tw factrs In Figure 2.3 the experiments f a full factrial design can be seen with tw factrs, x 1 and x 2. Each dt represents an experiment and the three center-pints are representative middle values f each factr. There are basically three types f prblems t which DOE is applicable. 1. Screening - is used t btain the mst influential factrs, and t determine the ranges in which these shuld be investigated. This is a fairly straightfrward aim, s screening requires few experiments in relatin t the number f factrs. 8

14 2. Optimizatin - is abut defining which cmbinatin f the imprtant factrs will result in ptimal perating cnditins. Since ptimizatin is mre cmplex than screening, ptimizatin designs require mre experiments per factr. 3. Rbustness testing - is used t determine the sensitivity f a prduct r prductin prcedure t small changes in the factr settings. Such small changes usually crrespnd t fluctuatins in the factrs ccurring during a bad day fr prductin, r the custmer nt fllwing prduct usage instructins. The screening methd is the ne used in this master s thesis and is the nly ne f the three methds that is described further. A prblem frmulatin is very imprtant and is carried ut t make the intentins f an underlying experimental investigatin cmpletely clear, fr all invlved parties. There are a number f things t discuss and agree abut, and it is necessary t cnsider six pints. 1) The experimental bjective defines what kind f investigatin is required. One shuld ask: why is an experiment dne, fr what purpse and what is the desired result? This master s thesis uses screening as the experimental bjective since the interest is t find ut which factrs are the dminating nes, and what their ptimal ranges are. T screening the Paret principle applies well, which means that 80% f the effects n the respnses are caused by 20% f the investigated factrs. 2) Definitin f factrs is abut defining the variables which exert an influence n the system r the prcess, due t changes in their levels. The factrs can be divided int cntrllable/ uncntrllable factrs and quantitative/qualitative factrs. A quantitative factr is a factr which may change accrding t a cntinuus scale and a qualitative factr can nly assume certain discrete values. This pint als invlves setting the range f the quantitative factrs and the exact value f the qualitative. 3) Specificatin f respnses is a prcess where ne select respnses that are relevant accrding t the prblem frmulatin. It is ften necessary t have many respnses t well describe the prperties f a prduct r the perfrmance characteristics f a prcess. Respnses can be quantitative r qualitative. A quantitative respnse is a metric with a distinct value, where as a qualitative respnse is abut describing hw well the respnse is perceived n a scale f 1-5, where 1 culd be wrthless and 5 culd be 9

15 excellent. The respnses in this master s thesis that are applied n Design f Experiments nly have quantitative respnses. 4) Selectin f mdel is an integral part f the prblem frmulatin and abut selecting an apprpriate regressin mdel. There are three main types f plynmial mdels: Linear Interactin Quadratic y = b 0 y = b y = b b x 1 + b x 1 + b x b 2 + b + b 2 2 x x x e + b + b 12 x x 1 x b e x b 12 x 1 x e The variable b is a regressin cefficient, x is a factr defined earlier in the prblem frmulatin and e is the residual. The linear mdel can algebraically be seen asy = Xb + e. Since the quadratic plynmial mdel is the mst cmplex it requires mre experiments than the thers. An interactin mdel requires fewer experiments and a linear mdel even less. If the experimental bjective is screening either a linear r an interactin mdel is pertinent. An interactin mdel is recmmended if the number f experiments is easy t handle, but the experiments f this master s thesis have many factrs which makes the linear mdel apprpriate. 5) Generatin f design is the next step f the prblem frmulatin and is intimately linked t the chsen mdel. The MODDE sftware will cnsider the number f factrs, their levels and nature (quantitative, qualitative ) and the selected experimental bjective, and prpse a recmmended design, which will well suit the given prblem [9]. The design chsen by MODDE fr the experimental wrk in the first experimental part is a design called D-Optimal. D-Optimal means that the design maximizes the infrmatin in the selected set f experimental runs with respect t a stated mdel. Given a mdel, the D-Optimal algrithm selects N experimental runs frm the candidate set, which is the set f all ptentially gd runs, as t maximize the infrmatin in the matrix X. The extended design matrix X is created frm the N experimental runs expanded with clumns fr the cnstant and crss terms accrding t the mdel [21], see Figure 2.4. During the third experimental part a full factrial design is used. 10

16 Figure 2.4. The extended matrix X 6) Creatin f wrksheet is the last stage f the prblem frmulatin. The wrksheet is, in principle, very similar t a table cntaining the selected experimental design. It shws which experiments t perfrm and in which rder [9]. In rder t handle the nise f the experiments sme center pints are chsen, which ften are three experiments with the same middle value settings. When the wrksheet is created is it pssible t evaluate the perfrmance f the experimental design prir t its executin by lking at the cnditin number. The cnditin number is the rati f the largest and the smallest singular values f the X- matrix (eigenvalues f X T X) and represents a measure f the rthgnality f the design. The ptimal value f the cnditin number is 1 but a number < 3 is cnsidered t be a gd design. There are several plts and lists available t evaluate the mdel and ne f these is the histgram plt. The Histgram plt is useful fr studying the distributinal shape f a respnse variable. If the respnses are nt apprximately nrmally distributed like the Histgram f Screwness in Figure 2.5 it culd indicate that ne measurement is nt like the thers. It is nt recmmended t apply regressin analysis t a respnse with this kind f distributin and the prblem can be slved by a lgarithmic transfrmatin f the respnse. 11

17 Figure 2.5. Example f a histgram plt The next step f the analysis is t fit the mdel. When the mdel is fitted there are several plts and lists available t evaluate the result. One f the mst imprtant nes is the Summary f Fit plt seen in Figure 2.6 and thrugh this plt the imprtant parameters R 2 and Q 2 can be analyzed. Figure 2.6. Example f a Summary f Fit plt R 2 represents the green bars in Figure 2.6, is called the gdness f fit and is a measure f hw well the regressin mdel can be made t fit the raw data. R 2 varies between 0 and 1, where 1 indicates a perfect mdel and 0 n mdel at all. Q 2 represents the blue bars and is called the gdness f predictin which means that it estimates the predictive pwer f the mdel. This is a mre realistic and useful perfrmance indicatr as it reflects the final gal f mdeling predictins f new 12

18 experiments. Q 2 has the upper bund 1 and lwer limit minus infinity. Fr the mdel t pass this diagnstic test, bth R 2 and Q 2 shuld be high and preferably nt separated by mre than Generally speaking, Q 2 >0.5 shuld be regarded as a gd mdel, and Q 2 >0.9 as excellent. The yellw bar in the summary f fit plt is called mdel validity and reflects whether the right type f mdel was chsen frm the beginning in the prblem frmulatin. The higher the numerical value the mre valid the mdel is, and a value abve 0.25 suggests a valid mdel. Finally, the turquise bar in the summary f fit plt is called the reprducibility. The higher the numerical value the smaller the replicate errr is in relatin t the variability seen acrss the entire design. If the value f the reprducibility bar is small, belw 0.5, it indicates a large pure errr and pr cntrl f the experimental prcedure. Figure 2.7. Example f a regressin cefficient plt T detect strng interactins between different respnses and factrs nrmally a Regressin cefficient plt Figure 2.7 is used. The green bars reveal the real effects f the factrs n each respnse. As can be seen in Figure 2.7 the factr Sp (Speed) has the strngest impact n all three respnses, and it is interpreted as t when the speed is increased all three respnses Breakage, Width and Screwness will decrease. The uncertainty f the cefficients is given by the cnfidence intervals and the size f these depends n the size f the nise. 13

19 3 Thery 3.1 Paperbard Paperbard is made up f fibers that are mechanically defrmed and bnd t each ther withut help frm ther substances. Depending n hw the fibers are defrmed and riented the paperbard gets a variety f prperties. Paperbard is made up f several plies. The surface part is build up with chemical pulp and the middle part is build up with mechanical pulp. Smetimes the paperbard can als be several layers f chemical r mechanical pulp. The surface is ften cated with clay t give a mre even surface, better glss and better printing qualities. Mechanical pulp is wd that have been mechanically reslved. Different pulp qualities are prduced by using different temperature and mechanical prcess. A big advantage with mechanical pulp is that mre than 90 percent f the wd is used, this makes it cheap. But since the fibers get damaged the mechanical pulp results in a weak paperbard. Chemical pulp is prduced by biling wd with water and chemical cmpunds s it can be reslved withut frce. Here nly abut percent f the wd is used. But since the fibers are nt damaged during the prcess they make a strng paperbard [15]. Figure 3.1. Paperbard shwing different plies [16] 3.2 Finite Element Methd In the simulatins the finite element methd can be used t slve the prblem numerically in an apprximate manner [10]. The fllwing text cntains the thery f the finite element methd and defines the material mdel used fr paperbard. There exists a material mdel prpsed by Xia using a cntinuum mdel and an interface mdel, where the cntinuum mdel describes the behavir within the ply, 14

20 and the interface mdel describes the delaminatin between the plies [19]. Hwever, here Abaqus built in material mdels are used fr the cntinuum mdel and chesive interface mdel fr delaminatin, since in this mdel have prven t give gd and realistic curves and describes the delaminatin well [17] Equatins f mtin Figure 3.2. A bdy with vlume V, surface S and nrmal vectr n. An arbitrary bdy has the vlume V, the surface S and the uter nrmal unit vectr n. The frces acting n the bdy are the tractin vectr t alng the surface S and the bdy frce b per unit vlume in the regin V. The displacements are dented by u with the acceleratin vectr ü. T get the equatins f mtin Newtn s secnd law is used: t ds + bdv = S V V ρ u& dv (1) where ρ is the mass density. T refrmulate Eq. (1), recall the divergence therem f Gauss that says that fr an arbitrary vectr and per definitin that V T divq dv = q nds (2) S q q q div, T q = + + = q i i; n =qini x1 x2 q3 Hence the divergence therem can be written [11]: q (3) 15

21 V q, dv = q nds (4) i i Making use f the Cauchy stress, T, defined as [14]: S i i t = Tn (5) Eq. (1) can nw be refrmulated using the divergence therem and the Cauchy stress V ( divt + b ρ u& ) dv = 0 (6) This equatin hlds fr an arbitrary bdy and can be written as: div T + b = ρ& u& (7) These are the equatins f mtin f the bdy; Eq. (7) is ften called the strng frmulatin since this equatin cntains the derivatives f the stress tensr [11] Weak frmulatin - Principle f virtual pwer T get the weak frmulatin ne multiplies the equatins f mtin Eq. (7) with an arbitrary velcity (weight vectr) w and integrates ver the vlume t btain: V T w divtdv T + w bdv = V V w u& dv T ρ (8) Using the Green-Gauss therem, divergence therem and the Cauchy therem the first part f equatin can be written as: Inserting int Eq. (8) renders: Intrducing a symmetric tensr: V T T w divtdv = w tds w: TdV (9) S T T w tds w TdV + w bdv = S V V T : ρw udv (10) V ˆ 1 T D = ( w + ( w) ) (11) 2 V & gives the principle f virtual pwer als knwn as the weak frm. 16

22 V T + ˆ T : T ρ w u& dv D TdV w tds w bdv = 0 (12) V The weak frm is ne f the mst imprtant principles within slid mechanics, since it des nt nly frm the basis fr the finite element methd but als fr several ther numerical methds and is als central fr a number f therems in slid mechanics [11, 14]. This frmulatin is based n the current cnfiguratin smething that is nt knwn and therefre it is better t write it in the reference cnfiguratin. All quantities that are described in the reference cnfiguratin will be dented with a subscript о. Start with cnverting the bdy frces: V S T T w bdv = w b dv (13) V Changing the tractin frces will need t mre wrk using Cauchy s therem, Nansn s frmula: nds d T = JF n s (14) Where ds is the incremental area vectr, J is the Jacbian that can be written as dv J =, F is the defrmatin tensr defined by F = x. Finally intrducing the dv definitin f the first Pila-Kirchhff stress tensr, P as gives: T P =JTF (15) T T T T T tds = w TndS = w JTF n ds = w Pn ds = T w w t ds (16) S S S S S The first term in the weak frm can be rewritten as: V T T ρ w u& dv = ρ w u& dv (17) V The remaining term need a little mre wrk t be transfrmed. Hence we nte that ˆ 1 w = FF (18) V 17

23 where Hence Eq. (11) can be written as: Fˆ = w (19) ˆ 1 1 T (ˆ ˆT T D = FF + F F ) = F Eˆ F 2 1 (20) where Ê is a square matrix: ˆ 1 T ( ˆ ˆT E = F F + F F) (21) 2 Nw the secnd term in the weak frm can be rewritten: D: ˆ T TdV = F Eˆ 1 ( F V V ): TdV = V Eˆ :( F 1 TF T ) dv = V Eˆ : S dv (22) where the secnd Pila-Kirchff stress tensr is defined as: S 1 1 T = F P = JF TF (23) The weak frm is nw cnverted t the reference cnfiguratin [14]: V T + ˆ T T ρ w u&& dv E : S dv w t ds w b dv =0 (24) V S Nnlinear Finite Element Methd Since paperbard is a nnlinear anistrpic material ne has t use the nnlinear finite element methd. Here the equatins in the finite element methd are frmulated. They are based n the weak frm in Eq. (12) and Eq. (24). Here the variables are defined in matrix frm: V Exx E yy Ezz E = ; 2Exy 2E xz 2Eyz Sxx S yy Szz S = ; Sxy S xz Syz u&& x &u & = u&& y ; u&& z wx w = wy ; w z tx t = ty ; tz b b = b b x y z 18

24 19 Green-Lagrange s strain may be written as: = ) 2( ) 2( ) 2( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( z u x u z u x u z u x u z u y u z u y u z u y u y u x u y u x u y u x u z u z u z u y u y u y u x u x u x u x u z u y u z u x u y u z u y u x u z z y y x x z z y y x x z z y y x x z y x z y x z y x z x z y y x z y x E (25) r shrter as: u Au u E u l + = ) ( 2 1 (26) and the weak frm may be rewritten: ˆ =0 + && V T S T V T V T dv ds dv dv b w t w S E u w ρ (27) Using Eq. (26) [14]: u Au u E u l + = ) ( ˆ (28) The bundary cnditins f the bdy are expressed in the displacement vectr u alng the bundary surface S u and the tractin vectr t alng the bundary surface S t. As can be seen in Figure 3.3. Figure 3.3. Bundary cnditins S t and S u

25 The basis f the finite element methd is t express the displacement vectr u with the apprximatin: u = Na (29) where N is the glbal shape functins and a is the ndal displacements f the bdy. The displacement vectr u depends n bth psitin and time while the glbal shape functins nly depend n psitin: This gives the acceleratin u=u(x i,t); N=N(x i ); a=a(t) (30) ü = Nä (31) The arbitrary weight vectr w is chsen with Galerkin s methd in the same way as the displacement u. w = Nc (32) Here c is an arbitrary vectr that is independent f psitin since w is arbitrary and N is defined abve [11]. Frm Eq. (28) and using the matrices frm Eq. (25), ne can get: where E ˆ = ( B0 + Bu ) c = Bc (33) B0 = ln, B = u A( u) H and H = N u (34) Inserting Eq. (32) and Eq. (33) in the weak frm Eq. (27) [14]: T T T T T c ( ρ N NdV ) a& + B SdV N t ds N b dv = 0 (35) V V S V Since this hlds fr arbitrary c matrices, it can be written: T M a&& + B SdV = f (36) V where M is the mass matrix. 20

26 T M = ρ N NdV (38) V and f is the external frces. T T f = N t ds + N b dv (39) S V Eq. (36) is derived straight frm the equatins f mtin withut knwing the particular prblem hence it hlds fr any prblem. When the acceleratins ä are zer Eq. (36) is reduced t the equilibrium equatins: where ψ ( a) = 0 (40) = ψ( a) B SdV f (41) v T These equatins frm the base in the Newtn-Raphsn methd [11] Slutin f Nnlinear Equilibrium Equatins - Newtn-Raphsn Methd T slve a nnlinear prblem the Newtn-Raphsn methd uses the linearizatin f a functin abut a pint. This is dne by guessing a starting value x 0, at the crrespnding pint A n the curve the tangent is determined and this tangent is extraplated t get a new estimate x 1 that is used t find the pint B n the curve that prvides the next estimate x 2 and s n. Figure 3.4. Newtn-Raphsn methd fr a ne dimensinal prblem. 21

27 Assuming that the apprximatin a i-1 t the slutin a have been determined. A Taylr series expansin f ψ abut a i using nly the linear part is: i i 1 ψ i 1 i i 1 ψ ( a ) = ψ( a ) + ( ) ( a a ) (42) a This represents the tangent t the curve at pint a i-1. Since ψ ( a i ) = 0 Eq. (42) becmes: i 1 ψ i 1 i i 1 0 = ψ( a ) + ( ) ( a a ) (43) a T cntinue, we need the derivate ψ/ a als knwn as the Jacbian, having fixed external frces the equatin becmes: Hence it can be shwn that: ψ T ds = B dv + a da V V T db da SdV (44) d S = DtB (45) da Inserting Eq. (44) int Eq. (45) gives ψ = a K t where T T K t = B DtBdV + H RHdV (46) V V S 0 where R = and K t is the tangent stiffness matrix f the bdy. Hence Eq. 0 S (43) takes the frm f: i 1 i i 1 i 1 ( K ) ( a a ) = ψ( a ) (47) t In a Newtn-Raphsn apprach ne start frm a state n where equilibrium is fulfilled and all stresses, strains, displacements and ladings are knwn. The external ladings are then changed t f n+1 and the gal is t find the equivalent stresses, strains and displacements. T get the starting cnditins we knw the ut f balance i 1 frces ψ ( a ) 22

28 ψ a = n i 1 T i 1 ( ) B S dv f + 1 V (48) and taking the mst recent knwn values as starting pint. a 0 = a n ; 0 S =Sn; (K t ) 0 = (K t ) n (49) This gives the first iteratin 1 T ( Kt) n( a an) = fn+1 B SndV (50) V i 1 When the ut f balance frces ψ ( a ) apprach zer the finite element sftware stp the iteratins at a certain value specified in the sftware since the balance i 1 frces will nt reach exactly zer. At this small value f ψ ( a ) ne accept the slutin a i-1. a n+1 = a i-1 ; ε ε ; = i n S ε (51) = i n Every Newtn-Raphsn iteratin is cstly, since the K t -matrix needs t be established in every step. This means that the mdified Newtn-Raphsn ften is used instead. Here the K t -matrix is nly recalculated nce every lad step. The abve equatins are used in Abaqus in an updated frmat, i.e. an updated Lagrange frmulatin. The updated frmulatin takes advantage f the fact that if the reference cnfiguratin is updated cntinuusly in every iteratin t becme equal t the current cnfiguratin the equatin system can be simplified [11]. 3.3 Material mdel f paperbard Figure 3.5. Material directins shwn in the paperbard. 23

29 The material directins in the paperbard are defined as machine directin (MD), crss machine directin (CD) and ut-f-plane directin (ZD) as can be seen in Figure Cntinuum mdel An anistrpic material has different prperties in MD, CD and ZD. Here the material is apprximated with an rthtrpic mdel, hence there are nine elastic cnstants, Yung s mduli: E x, E y, E z, shear mduli: G xy, G xz, G yz and Pissn s ratis: ν ν ν. xy, xz, yz Abaqus uses a rtated Jaumann rate f Cauchy stress ( σ ) t define the cnstitutive law. T btain this stress rate a rtatinal stress rate is first intrduced: R T σ& = ( Q σq) (52) where Q is the rtatin, letting the Jaumann stress rate t be related t the rtatinal stress rate: Qσ& R Q T = σ = σ& wσ σw T (53) allws the evlutin law fr Q t be defined as: Q & =wq (54) Abve the spin tensr w, was intrduced and is defined as 1 T w = ( v v ) (55) 2 where v is the velcity vectr. T define plasticity it is assumed that the rate f defrmatin d can be decmpsed int an elastic part d e and a plastic part d p. 1 2 T e d = ( v + v ) = d + d p (56) A rtated frmat can then be identified as d R T e R p R = Q dq = ( d ) + ( d ) (57) With the abve quantities the relatin fr the elastic prblem is given as 24

30 25 R e R R ) (d σ L = & (58) where the cnstitutive matrix takes the frm = yz xz xy y x yx xy y x yx xz yz y x yz xy xz x z xy zx zy x z xz zx x z zy xz xy z y zy yx zx z y yz zx yx z y zy yz R G G G E E E E E E E E E E E E E E E E E E ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν L (59) with z y x zx yz xy xz zx zy yz yx xy E E E ν ν ν ν ν ν ν ν ν 2 1 = (60) The plastic behavir is described with an rthtrpic mdel. The evlutin law fr the plastic strains is [25]: R R p f σ λ d = & ) ( (61) where f is the yield functin and 0, 0 λ & f and 0 = λ & f shuld be fulfilled [25]. The particular yield functin used in the simulatins is given by the Hill s stress ptential: ) ( ) ( ) ( ) ( σ τ τ τ σ σ σ σ σ σ σ = R xy R zx R yz R y R x R x R z R z R y N M L H G F f (62) Where ) ( x z y F σ σ σ σ + =

31 2 σ 0 1 G = ( 2 2 σ 2 σ 0 1 H = ( 2 2 σ 3 τ L = ( 2 τ z x 0 ) 2 yz 3 τ M = ( 2 τ 3 τ N = ( 2 τ 0 ) 2 xz 0 ) 2 xy σ x σ y 1 ) 2 σ y 1 ) 2 σ z Here σ 0, σ x, σ y, z σ, τ xy, τ yz, τ xz is specified by the user as ptentials [11] Chesive mdel The chesive material used in the interfaces is the chesive material defined in Abaqus. The elastic behavir is defined by tractins (t). Fr uncupled behavir the tractins depend nly n the nminal strains defined as t t t x y z K = xx K yy K zz ε x εy ε z (63) δi Where ε i = ; i = x,y,z, T 0 is the riginal thickness f the chesive element and T i δ are the separatins. The stability criterin requires this K xx > 0, K yy > 0 and K zz > 0. The damage is initiated when the maximum nminal stresses reaches a value f ne. This can be written as: t x ty tz max,, 0 0 tx ty tz 0 = 1 (64) The tractins are then given via the relatin t i = ( 1 d) t 0 d 1, i = x,y,z (65) 0 26

32 Where d dentes the damage evlutin describing the material stiffness degradatin. When d=1 the material have lst it s carrying capacity. The damage evlutin is expnential: 0 δm d = 1 δ max m 1 e (1 1 e max 0 δm δm α( ) f 0 δm δm α ) (66) max Where α is the expnential law parameter, δ m is the maximum value f the effective displacement during lad histry, the effective displacement ( δ m) is define f belw and the effective displacement at cmplete failure ( δ ) and the effective displacement at the initiatin f damage ( δ ) can be seen in Figure 3.6 [20]. 0 m m m x 2 δ = δ + δ + δ (67) 2 y 2 z Figure 3.6. Damage evlutin 27

33 4 Experimental wrk As stated earlier the experimental tests are divided int three different parts: Labratrial tests when making straight creases by using a flat bed creasing machine. Labratrial tests when making creases with the pattern f bttm creases by using a flat bed creasing machine. Tests in the pilt plant when making creases with the full scale pattern f a Tetra Brik Base, 250ml package using a rtatinal crease tl. 4.1 Experimental tls and parameters Labratry creasing tl The labratry creasing tl is munted int a MTS 858 Table Tp System. The male die hlder is restricted t nly mve in the z-directin by rails munted n the U- blt and the female die is munted n a 15kN lad cell (Figure 4.1). Figure 4.1. The labratry creasing tl setup unit. Left: 3D-CAD [2], Right: Phtgraphy [5] A schematic sketch f the creasing tl in the xz-plane during creasing f the paperbard is shwn in Figure 4.2. The male die has a rule sticking ut frm the base and can be chsen t have different heights and widths. The female die has a grve where the paperbard is pressed dwn by the rule during creasing. The grve can als have different depths and widths. The machine directin (MD) f the paperbard is parallel t the x-directin in Figure 4.1. The paperbard is given a prescribed displacement and a lad cell, munted n the creasing tl, displays the web tensin. The speed f the rule is set t be 1mm/s. 28

34 During the peratin ne lad cell measures the ut f plane crease frce in the z- directin (ZD) and ne lad cell measures the in-plane frce in the x-directin (MD). The relative distance between the male and the female die is dented crease depth. The tests were made at a relative humidity f 50±2% and at a temperature f 23±1degree Celsius. Figure 4.2. A principle 2D-sketch f the creasing tl [5] The MTS-creaser makes it pssible t cntrl the web tensin, creasing depth and the creasing speed, and t mnitr web tensin as functin f time, creasing depth as functin f time and creasing lad as functin f time [2]. By use f Matlab the crease frce is pltted as a functin f crease depth (Figure 4.3). The fllwing parameters are established: Maximum frce Energy: area belw the curve Remaining defrmatin f the crease with applied web tensin 29

35 Figure 4.3. Creasing parameters Creasability tester T fld the creased paperbard a Lrentzen & Wettre creasability tester (L&W) is used (Figure 4.4). A clamp n the L&W fastens the specimen and when the clamp rtates frm 0 t 120 degrees a lad cell measures the bending frce (Figure 4.5). Figure 4.4. L&W Creasability tester [2] Figure 4.5. Principle sketch f the L&W creasability tester 30

36 Bth creased and uncreased paperbard f each specimen are flded and by use f Matlab the relatin between the bending frce and the bending angle is pltted (Figure 4.6). The fllwing parameters are established: Maximum frce at r befre 30 degrees f the creased sample Energy, area belw the curve f the creased sample Initial inclinatin f the creased sample (same as initial stiffness f the crease) Final angle after released bending frce f the creased sample Relative Crease Strength RCS The RCS value is the relatin between the maximum frce at r befre 30 degrees f the creased sample divided by the maximum frce at r befre 30 degrees f the uncreased sample. It is desirable with a RCS value as lw as pssible. Figure 4.6. Flding parameters Tpgraphy T study the surface f the creased paperbard an ptical 3D measuring system called MikrCAD, GFM is used. This machine is a cmputer-assisted ptical surface measuring system and is used fr 2D and 3D prfile measurements, as well as rughness measurements f small and micrscpic parts. The functinal structure f the ptical 3D sensr is shwn in the principle picture Figure

37 Figure 4.7. Principle sketch f ptical 3D sensr [22] Stripes with sinusidal intensity f brightness are prjected nt the surface f the paperbard and the prjectin is recrded with a well defined triangulatin angle by a CCD camera. The tpgraphy f the crease is calculated frm the stripes psitin and the values f all registered individual image pints. T analyze the tpgraphy it is split in 30 lines and can then be pltted, see Figure 4.8. The MikrCAD can als be used as a micrscpe and it is pssible t detect if there are cracks alng the crease. Figure 4.8. Tpgraphy split in 30 lines (left), plt f the crss sectin with all 30 lines (right) Matlab is used t plt an average curve f the 30 lines, see Figure 4.9. The tpgraphy is perfrmed n bth sides f the creased paperbard which gives ne plt f a bump and ne f a dip (Figure 4.10). The remaining defrmatin f bth sides f the crease can be established frm the Matlab plts. 32

38 Figure 4.9. Tpgraphy parameters Figure Visual illustratin f dip and bump Phtgraphy setup T film the prcess f creasing and flding a high speed camera is rigged clse t the paperbard. The filming makes it pssible t evaluate the whle prcess when creasing and flding bth frm the inside and the utside and t see if the behavir differs between the tw Lab evaluatin f the paperbard s prperties The paperbards are sent t the lab fr material analysis fr evaluatin f the paperbard prperties. The tests perfrmed n the paperbards are: GRAMMAGE: Grammage (g/m²) THICKNESS: Thickness (µm) TENSILE PROPERTIES: Tensile strength MD and CD (kn/m) Tensile strength rati (%) Tensile stretch MD and CD (%) Tensile stiffness MD and CD (kn/m) E-Mdulus MD and CD (MPa) Tensile Energy Absrptin MD and CD (J/ m²) BENDING FORCE: Bending frce MD and CD (mn) 33

39 Bending frce GM (mn) Bending frce index Bending frce rati DENSITY: Density (kg/m³) SCOTT BOND: Sctt Bnd (J/m²) Z-TENSILE STRENGTH: Z-tensile strength (kpa) 4.2 First experimental part: straight creases In parameters Crease depth: Web tensin: Crease side: Paperbard: 0.1mm, 0.2mm, 0.3mm 1kN/m, 1.5kN/m, 2kN/m Inside, Outside A, B, C (thin paperbards) D, E, F (thick paperbards) Crease gemetry: Straight1, Straight2, Straight3 (t use with thin paperbard) Straight4, Straight5, Straight6 (t use with thick paperbard) Prcedure The samples fr the tests with straight creases have a width f 38mm and a length f 110mm (Figure 4.11). In the MTS creasing tl the distance between the clamps are 80mm. Each test in the MTS creasing tl cnsists f 15 samples and ut f the 15 samples, five samples are flded using the L&W creasability tester and ten samples are measured in the MikrCAD. The number f samples is chsen t get reliable results. Figure Sample fr straight crease test 34

40 Even thugh the number f parameters have been reduced it is nt pssible t perfrm all cmbinatins f tests within this master s thesis. MODDE is a sftware using Design f Experiments explained earlier and by the use f this sftware the number f tests will be cnsiderably less. The MODDE evaluatin is split in tw parts, ne fr the thinner paperbards A-C and ne fr the thicker paperbards D-F. Fr each part there are five factrs: Tw quantitative: crease depth and web tensin Three qualitative: crease side, paperbard and crease gemetry. The respnses chsen t evaluate the first experimental part are frm the creasing prcess: maximum frce, the remaining defrmatin f the paperbard ( dip ) with applied web tensin and the energy (Figure 4.3). Frm the flding prcess the respnses chsen are: maximum frce at r befre 30 degrees, initial stiffness f the creased paperbard, RCS and final angle after released bending frce (Figure 4.6). The evaluatin frm the tpgraphy gives the remaining defrmatin f the crease with n web tensin, bth the dip and the bump (Figure 4.9). By the use f the MikrCAD it is als pssible t see if there are any cracks in the crease area f the paperbard. The final MODDE wrksheets with all experiments fr bth the thinner paperbard setup and the thicker paperbard setup are fund in Appendix A.1 and Appendix A.3. The cnditin number fr these setups is in bth cases equal t 2.11 which is less than 3 and can be cnsidered as a gd mdel. A Matlab sftware gives six plts: crease frce as a functin f crease depth (ne plt with all tests and ne average plt), bending frce as a functin f bending angle (ne plt with all tests and ne average plt) and als plts f the average crss sectin f the crease, bth the dip and bump frm the MikrCAD. The sftware als states the numerical values f the wanted respnses, based n calculatins frm the average plts. The numerical values f the respnses are put int the MODDE wrksheet and the results can be evaluated by use f the histgram plt, the summary f fit plt and cefficient plt. The creasing prcess and the flding prcess are als filmed in purpse t examine if inside creasing behaves different frm utside creasing. 35

41 4.3 Secnd experimental part: bttm crease pattern In parameters Crease depth: Web tensin: Crease side: Paperbard: Vary crease depth until crack limit f the paperbard is reached. Start with crease depth 0.2mm. 1kN/m Inside, Outside A, B Crease gemetry: Bttm1, Bttm Prcedure The samples fr the crease tests with bttm crease pattern have a width f 100mm and a length f 180mm (Figure 4.12). In the MTS creasing tl the distance between the clamps are 160mm. The crease pattern shwn in Figure 4.12 has creases in bth machine directin (MD), crss machine directin (CD) and diagnal directin (DD). In the L&W creasability tester samples fr tests in MD has a width f 15mm and samples fr tests in CD has a width f 25mm. These samples are cut ut frm the 100 by 180 sample, their lcatins are shwn in Figure Figure Sample fr tests with bttm crease pattern Frm the results f the first experimental part a decisin was taken t investigate at which crease depth cracks appear in the paperbard and what the RCS value is, in 36

42 bth MD and CD, fr thse samples. Each test in the MTS creasing tl cnsists f ten samples and f these five are flded using the L&W creasability tester. The prcedure f the secnd experimental part is t start creasing t the depth f 0.2mm and then study if there are any cracks develped in the ten samples. If the crack limit is nt reached a new test is prefrmed with the crease depth increased by 0.05mm. This is repeated until the crack limit is reached. If the crack limit is reached in the first test, the test is repeated with the crease depth decreased by 0.05mm. This is repeated until cracks n lnger are visible. The samples are t be flded by the L&W creasability tester in bth MD and CD. The RCS value is calculated and the result is displayed in a table. 4.4 Third experimental part: 250 Base crease pattern In parameters Crease depth: Web tensin: Crease side: Paperbard: Crease gemetry: Perfrm the test at crease depth 0.05mm and 0.1mm belw the crack limit 1.3kN/m Inside, Outside A, B Crease pattern f a Tetra Brik 250ml Base Laminatin specificatin: Aseptic juice package Prcedure During this last experimental part the paperbard is cnverted in the Tetra Pak pilt plant. MODDE and Design f Experiments is used thrughut this last experimental part and the wrksheet can be seen in Appendix F.1 fr paperbard and Appendix F.3 fr packaging material. The MODDE evaluatin is split in tw parts, ne fr paperbards and ne fr packaging material. Fr each part there are three factrs: One uncntrllable quantitative: crease depth Tw qualitative: crease side and paperbard 37

43 The respnses chsen t evaluate the third experimental part are frm the flding prcess: maximum frce at r befre 30 degrees, initial stiffness f the creased paperbard, RCS and final angle after released bending frce. The cnditin number fr these setups is in bth cases equal t which is cnsidered t be a gd mdel. The creasing prcess is perfrmed at the printing press Briggen where the paperbard is creased when ging thrugh a rtatinal creasing tl, see Figure On the rllers f the rtatinal creasing tl, male and female crease plates are assembled t represent the creasing tl. Tw paperbards are tested, A and B, and tw rlls are used fr each f the paperbards. The rlls have the width 430mm. Figure Briggen (left), rtatinal creasing tl (right) The creasing prcedure starts by trying t find at which crease depth the paperbard cracks fr an utside creasing fr bth paperbard A and B. The crease depth is then decreased until n cracks appear, i.e. 0.05mm frm the crack limit. Half f the paperbard rll is creased at this crease depth and the rest f the rll is creased with a crease depth 0.10mm frm the crack limit. When bth paperbard A and B have been creased with utside creasing the crease plates are switched t inside creasing mde. The prcess perfrmed f utside creasing is then repeated with inside fr paperbard A and B. Samples f paperbard are cllected f the creased paperbard befre the paperbard is sent t be laminated with the specificatin f an aseptic juice package. Samples are then cllected frm the packaging material. The samples f the paperbard and packaging material can be seen in Figure

44 Figure Samples fr 250 Base crease pattern Five samples f each setting fr bth paperbard and packaging material are flded using the L&W creasability tester. The bending frce is pltted as a functin f bending angle and the average curves f inside and utside creasing are pltted in the same plt s they can be cmpared t each ther. 39

45 5 Cmputer simulatin 5.1 Abaqus Abaqus is a finite element analysis sftware used t slve a variety f prblems bth nnlinear and linear. The analysis has three different stages. In the preprcessing the mdel and the physical prblem are defined using Abaqus/CAE, parts can als be imprted frm ther CAD sftware. This file is sent t the simulatin step t be prcessed with Abaqus/Standard r Abaqus /Explicit. Here the numerical prblem is slved and the results are stred in files ready t be pst-prcessed. Abaqus/standard is an implicit slver while Abaqus/Explicit slves the prblem explicit. The pst-prcessing is dne in Abaqus/CAE and is visualized by clr cntur plts, animatins and X-Y plts. [20] 5.2 Mdel The paperbard mdel is a three dimensinal mdel with an ffset f 0.1mm t save cmputer pwer and time during simulatin. The paperbard is lcked in the ffset directin hence it can be resembled with a tw dimensinal mdel. The height is 390μm cntaining three plies divided by tw interfaces; the mdel is expected t delaminate in the interfaces. The tp and bttm ply are mechanical ply and the middle ply is chemical ply. The exact material parameters can be seen in Appendix J. The interfaces are made up by chesive elements and bth the chemical and mechanical plies are cntinuum elements described in Material mdel f paperbard, chapter 3.3. There are nly interface elements in the creasing area since the paperbard is expected t delaminate in this regin. The length f the paperbard is 80mm since this is the length between the clamps in the experimental setup. Figure 5.1: Paperbard with tw interfaces marked red, shwing the different plies. The cntinuum element mesh is made up by C3D8R elements; this means an 8-nde linear brick element with reduced integratin and hurglass cntrl. The chesive elements are COH3D8; 8-nde three dimensinal chesive elements. The mesh is denser in the crease regin t better capture the defrmatin while it is carser in the regins where the clamp shuld be since smaller defrmatins are expected here. 40

46 5.2.1 Creasing The crease setup is the same fr bth inside and utside creasing since the bttm and tp ply have the same material prperties and it is easier t change the fld directin than changing the crease tls. The simulated crease tl has the same dimensins as Straight4 in the first experimental setup. Bth the male and female dies are made up by rigid bdies. In the tangential directin a frictin cefficient f 0.5 is used n the female die, the male die has n tangential behavir hence n frictin. In the nrmal directin bth the male and the female die have a pressureverclsure that is expnential with a pressure f 0.5MPa and clearance f mm fr the female die and 0.001mm fr the male die Flding The best crrelatin with the experimental behavir is fund, accrding t Appendix K, when the flding mdel is made up by cnstraints and bundary cnditins instead f a real clamp and lad cell. The nde sets marked in red in Figure 5.2 are encastred s they cannt mve in any directin as if there was a clamp. 10mm frm the center f rtatin (purple reference pint) a set f ndes labeled lad cell (yellw in Figure 5.2) is tied t the reference pint in the center f rtatin with a cnstraint. Hence if the reference pint in the center f rtatin mves s des the lad cell ndes, this is hw the paperbard is flded. Figure 5.2. Illustratin f the bundary cnditins 41

47 5.3 Prcedure The creasing and flding prcedure cntains five steps: 1. Apply web tensin 2. Male die punch 3. Male die remve 4. Remve web tensin 5. Fld Creasing Figure 5.3. Simulating the creasing The first fur steps are the creasing prcedure. In the first step the web tensin is applied. This is dne by bundary cnditins displacing the yellw end ndes in Figure 5.2, in the lengthwise directin f the paperbard t stretch it. The secnd step is when the male die creases the paperbard by being displaced in the y- directin (Figure 5.3) and in step three the male die is mved back up. In step fur the yellw end ndes are mved back t their riginal psitin. T cmpare the simulatin with the experimental values the reactin frce in the male die is used and recalculated, this is dne by multiplying the frce frm the simulatin with 380, since the width f the simulated paperbard is 0.1mm and the experimental paperbard is 38mm. 42

48 5.3.2 Flding Figure 5.4. Flding after utside creasing Figure 5.5. Flding after inside creasing The last step is the fld prcedure; if the mdel was able t unfld there wuld be ne mre step, but the mdel des nt cnverge. In the fld step the fld reference pint is rtated 120 deg in either psitive r negative directin t give an utside (Figure 5.4) r an inside (Figure 5.5) flding. The value that is cmpared t the experimental value is the mment in the center f rtatin, this need t be recalculated t get the frce using: Mw F = exp lw sim Where M is the bending mment frm the simulatins in Nmm per 0.1mm width, w exp =38mm is the width f the experimental paperbard, w sim =0.1mm is the width f the simulated paperbard and l=10mm is the lever. Due t sme prblem either with calculatins r the values received frm Abaqus the bending frce is scaled dwn with 1/10 t fit the plt, therwise the values are nt reasnable. 43

49 6 Results 6.1 Experimental Straight creases The lab evaluatin f the paperbards prperties shwed that the values lie within the specificatin. The MODDE wrksheet cnsists f 26 tests and can be seen in Appendix A.1 fr the thinner paperbards A-C and Appendix A.3 fr thicker paperbards D-F. The numerical values put int MODDE wrksheet can be seen in Appendix A.2 fr thin paperbard and Appendix A.4 fr thick paperbard. When the MODDE wrksheet, with all the numerical values, is fitted the summary f fit plt can be used t analyze hw well the mdel fits the results. The summary f fit plt fr thin paperbard can be seen in Figure 6.1. The bars in the summary f fit plt; gdness f fit (R 2 ), gdness f predictin (Q 2 ) as well as reprducibility are all excellent accrding the theretical limits, stated in subchapter Design f Experiments - DOE. The bars R 2 and Q 2 are all very high and the difference between them is less than as recmmended. Figure 6.1. Summary f Fit plt fr tests perfrmed with thin paperbard, straight creases The summary f fit plt fr thick paperbard can be seen in Figure 6.2. The R 2, Q 2 and the reprducibility bars are just as fr thin paperbard excellent accrding the theretical limits. 44

50 Figure 6.2. Summary f Fit plt fr tests perfrmed with thick paperbard, straight creases Lking at the cefficient plts in Appendix B fr the thin paperbards nly three respnses shw a significant difference at 95% cnfidence level between utside and inside creasing. These are maximum frce and energy as well as the remaining defrmatin ( dip ) with applied web tensin, all three frm the creasing prcess. Nne f these respnses are measurable in the real prductin line. The respnses with n significant difference between inside and utside creasing fr thin paperbard are: the remaining defrmatin with n applied web tensin, bth dip and bump, frm the tpgraphy, initial stiffness, maximum frce at r befre 30 degrees, energy and final angle frm the flding prcess as well as RCS. The results in Appendix C fr the thicker paperbards D-F are quite different frm the thinner paperbards. Here mre factrs appear t shw significant difference at 95% cnfidence level between inside and utside creasing. These factrs are maximum frce and energy frm the creasing prcess, maximum frce at r befre 30 degrees, energy and the initial stiffness frm the flding prcess as well as the RCS. The respnses with n significant difference between inside and utside creasing are: final angle frm the flding prcess and the remaining defrmatin with n applied web tensin, bth dip and bump frm the tpgraphy. Representative cefficient plts fr thin and thick paperbard are displayed in Figure 6.3 with the respnse being RCS. 45

51 Figure 6.3. Cefficient plt fr the respnse RCS, straight creases: thin paperbard (left), thick paperbard (right) The cefficient plt fr thin paperbard in Figure 6.3 shws that the RCS value is nt significantly depending n the crease side. There is a tendency fr inside creasing t increase the RCS value cmpared t utside creasing but the factrs paperbard, crease tl and crease depth have a greater impact n the respnse. The cefficient plt fr thick paperbard in Figure 6.3 shws that the RCS value is significantly depending n the crease side. As with thin paperbard there is a tendency fr inside creasing t increase the RCS value cmpared t utside creasing and here t the factrs paperbard, crease tl and crease depth have a greater impact n the respnse. Sequences f phts were extracted frm the filming f the creasing and flding prcess. All creasing phts are displayed in Appendix D and all flding phts in Appendix E. Representative phts can be seen in Figure 6.4 and Figure

52 Figure 6.4. Phts f the creasing prcess with straight creases, paperbard D: utside creasing (left), inside creasing (right) It is difficult t see if the paperbard behaves differently when cmparing utside and inside creasing and when studying the phts in Figure 6.4; their behavir lk similar. Delaminatin zne Delaminatin znes Figure 6.5. Phts f the flding prcess with straight creases, paperbard D: utside creasing (left), inside creasing (right) When lking at the phts f the flding prcess in Figure 6.5 it is apparent that inside crease paperbard flds and delaminates very differently frm utside creased paperbard. All phts in Appendix E shw the same behavir. During the first experimental part cracks were discvered in sme specimens. The cracks nly ccur n sme tests and nly n inside creasing. Fr all paperbards except A there are cracks n inside creasing at the crease depth f 0.30 mm, independent f crease tl and ther factrs. Cracks are nt acceptable and are therefre investigated further when lking at bttm creases. 47

53 6.1.2 Bttm crease pattern The lab evaluatin f the paperbards prperties shwed that the values lie within the specificatin. The results frm the tests f bttm creases can be seen in Table 6.1. The table displays the RCS value in the machine directin (MD) and the crss machine directin (CD) and if any cracks are visible. The gemetrical mean RCS value is defined as: RCS = RCS RCS. GM Table 6.1. Results f tests n Bttm crease pattern MD CD Crease tl Crease side Crease depth PAPERBOARD A PAPERBOARD B Bttm1 Bttm2 Outside Inside Outside Inside [mm] RCS MD RCS CD RCS GM Crack RCS MD RCS CD RCS GM Crack N N Yes Yes Yes N Yes N Yes Yes N Yes N Yes N N Yes Yes Yes The red numbers mean that cracks were fund n the samples. After clser examining and flding the specimens there were tw samples that initially seemed t nt have any cracks but when flded and examined clsely, cracks were fund. These tw samples are marked with a red N in Table 6.1. Table 6.1 shws that fr paperbard B utside creasing gives a slightly lwer RCS than with inside creasing independent if crease tl Bttm1 r Bttm2 is used. When using paperbard A it is a bit mre cmplicated. Crease tl Bttm1 in cmbinatin with paperbard A shws that the RCS value is lwer when using 48

54 utside creasing than it is with inside creasing. Bttm2 in cmbinatin with paperbard A shws that inside creasing gives a lwer RCS than with utside creasing Base crease pattern The lab evaluatin f the paperbards prperties shwed that the values lie within the specificatin. The MODDE wrksheet cnsists f ten tests and can be seen in Appendix F.1 fr paperbard samples and Appendix F.3 fr samples f packaging material. The numerical values put int MODDE wrksheet can be seen in Appendix F.2 fr paperbard and Appendix F.4 fr packaging material. The summary f fit plt fr paperbard and packaging material can be seen in Figure 6.6 and Figure 6.7. Mst f the respnses shw a gd and valid mdel with a gd reprducibility. The bars R 2 and Q 2 are high and the difference between them is less than as recmmended. Exceptins are the final angle in MD and the RCS value in bth CD and MD. These three respnses indicate a pr gdness f predictin, but the yellw bars are high which indicate a valid mdel. Figure 6.6. Summary f Fit plt fr tests perfrmed n paperbard, 250 Base crease pattern 49

55 Figure 6.7. Summary f Fit plt fr tests perfrmed n packaging material, 250 Base crease pattern The cefficient plts fr paperbard and packaging material are all displayed in Appendix G and Appendix H shwing that fr all respnses utside and inside creasing alne d nt shw significant difference at 95% cnfidence level. All respnses fr bth paperbard and packaging material indicate that when paperbard B is used the values f all respnses are increased cmpared t paperbard A. Representative cefficient plts fr paperbard and packaging material in Figure 6.8 fr the respnse Energy CD. Figure 6.8. Cefficient plt fr the respnse Energy CD fr 250 Base crease pattern: paperbard (left), packaging material (right) 50

56 As can be seen in Figure 6.8 the crease side des nt make a significant difference at 95 % cnfidence level and at the same time paperbard des make a significant difference. Bth these bservatins are cnsistent with all ther respnses fr bth paperbard and packaging material. Paperbard B seems t increase the energy cmpared t when using paperbard A just as inside creasing indicate an increasing energy cmpared t utside creasing. Paperbard influences the energy and all ther respnses much mre in than the crease side. It is als interesting t see that when paperbard and crease side are cmbined, paperbard B cmbined with utside creasing and paperbard A cmbined with inside creasing indicate a lwer energy while paperbard B cmbined with inside creasing and paperbard A cmbined with utside creasing indicate an increased energy. A graphic cmparisn between utside and inside creasing fr paperbard A with the crease depth 0.23mm and paperbard B with the crease depth 0.13mm f bth paperbard and packaging material in CD and MD can be seen in Appendix I. The plts shw the average bending frce pltted as a functin f bending angle and t see the variatin f the average plts the standard deviatin is included. A representative plt can be seen in Figure 6.9. PAPERBOARD Paperbard B, crease depth 0.13mm, CD Bending frce (mn) Inside, creased Inside, uncreased Outside, creased Outside, uncreased Bending angle (deg) Figure 6.9. Representative plt f bending frce as a functin f bending angle, cmparing inside and utside creased paperbard 6.2 Cmputer simulatin The results frm the simulatins cmpared t the experimental results can be seen in Appendix L where the simulatin is pltted against the experimental result fr the same setup. There are nly five plts but there are six experiments made n this 51

57 crease tl. The sixth simulatin using web tensin 2kN/m and crease depth 0.3mm failed. The tw plts fund belw in Figure 6.10 are the plts shwing the best resemblance between simulatin and experimental values. Figure Cmparing the simulatin with experimental test, creasing (left), flding (right). Appendix M shws a cmparisn between inside and utside creasing during flding fr the cmputer simulatins with the same crease settings. The creasing is nt shwn since the results are exactly the same fr bth cases. As can be seen in Figure 6.11 the inside and utside flding plts fllw each ther very well, inside creasing have a slightly higher bending frce than utside creasing. This is cnclusive fr all three graphs. FOLDING: Inside vs. Outside fr Straight4, Web tensin 1.5kN/m, Crease depth 0.2mm Bending frce (mn) Outside Inside Angle (deg) Figure Cmparing inside creasing with utside creasing in flding 52

58 The delaminatin and flding f the paperbard in simulatin is very different fr inside and utside creased paperbard as can be seen in Figure Figure The delaminatin in the simulatin during flding, utside creasing (left), inside creasing (right). 53

59 7 Discussin 7.1 Experimental Straight creases The results f the summary f fit plts fr bth thin and thick paperbard are very gd which means that the mdel and the results are reliable. The mdel validity may seem lw n sme respnses and is negative fr the respnse remaining defrmatin with applied web tensin (Dip Web Tensin), but accrding t Design f Experiments Principles and Applicatins [9] this is nthing t wrry abut when R 2, Q 2 and the reprducibility bars are as high as they are. The cefficient plts fr thin paperbard shw that nly the maximum frce, energy and remaining defrmatin with applied web tensin frm the creasing prcess are significantly affected by the crease side. Nne f these are measurable in the real prductin line. The RCS value is an imprtant measurement cnsidering hw well the creases are cnverted and when the paperbard is creased in the real prductin line. RCS is ften the nly factr used t study the creases. Neither utside nr inside creasing d significantly affect the RCS value accrding t the cefficient plts fr thin paperbard. A interesting nte is that even thught there in mst cases are n significant difference between inside and utside creasing n the respnses there is a tendency fr the respnses t increase with inside creasing. The cefficient plts fr thick paperbard shw that nly the maximum frce and energy frm the creasing prcess, maximum frce at r befre 30 degrees, energy and the initial stiffness frm the flding prcess as well as the RCS are significantly affected by the crease side. The tests perfrmed n thick paperbard imply an increasing RCS with inside creasing cmpared t utside creasing. This crrespnds with results received frm earlier tests dne n the RCS value while investigating the difference between inside and utside creasing when evaluating the grip stiffness f packages [6]. All respnses seem t increase with inside creasing cmpared t utside creasing. The phts f the flding prcess f thick paperbard shw that utside and inside creasing delaminate very differently. Even thugh the delaminatins are very different they bth seem t delaminate well and cntribute t defined package crners. The crners f inside creasing might be perceived as a bit mre defined than fr utside creasing. Outside creasing gives rise t ne large delaminatin zne while inside creasing has tw smaller delaminatin znes. The fact that fr example the energy and the maximum frce at r befre 30 degrees are higher fr inside 54

60 creasing than fr utside creasing might be explained by that it takes mre energy t create a crack than fr an existing crack t grw. Since the maximum frce when flding is larger fr inside creasing than fr utside creasing this als means that the RCS value fr inside creasing is higher than fr utside creasing. That the RCS value fr utside creased paperbard is lwer than the inside creased paperbard des nt necessary mean that its perfrmance is wrse. Maybe the RCS f an inside creased paperbard cannt be cmpared t the RCS f an utside creased paperbard? Maybe it is like cmparing apples and ranges? There might be a need fr ne specificatin fr utside RCS and n fr inside RCS Bttm crease pattern As have been stated in the results fr bttm crease pattern the crack limit n the different paperbards A and B are very different. Paperbard B has a lwer crack limit fr inside creasing than fr utside creasing. While fr paperbard A the influence f the crease gemetry have t be taken int accunt since the crack limit is ppsite fr Bttm1 and Bttm2. Hence the cnclusin wuld be that there is mre f a difference between the paperbards and crease gemetries than between inside and utside creasing smething that was shwn in the experimental part with straight creases. Investigating the RCS value that is preferred as lw as pssible ne bserves that the lwest RCS value ver all is fr paperbard A in cmbinatin with: crease gemetry Bttm1, utside creasing n the crease depth 0.2mm. The secnd best setting verall and the best setting fr paperbard B is als Bttm1 and utside creasing but with a decreased crease depth f 0.1mm. Fr crease gemetry Bttm2 the best setting is using paperbard A with inside creasing n the crease depth f 0.2mm, this is als the best setting fr inside creasing ver all Base crease pattern The summary f fit plt fr tests perfrmed n paperbard (Figure 6.6) shw a pr mdel fr the respnses RCS CD, RCS MD and final angle MD. It is difficult t say why the gdness f predictin bar (Q 2 ) fr RCS CD and MD is lw but the pr Q 2 fr the respnse final angle MD might depend n the scatter f the numerical values f the center pints, see the numerical values f test 3, 6 and 8 fr the final angle MD in Appendix F.2. The summary f fit plt fr test perfrmed n packaging material (Figure 6.7) als shw a pr mdel fr the respnses RCS CD, RCS MD and final angle MD, just as fr the tests perfrmed n pure paperbard. The respnse final angle MD s pr Q 2 cannt depend n the scatter f the numerical values f the center pints since the 55

61 reprducibility bar is pretty high. It s difficult t say why the respnses RCS CD, RCS MD and final angle MD shw a pr mdel. We have nticed in Figure 6.9 and Appendix I that all tests have the same unflding curve starting at 120deg and ending at 70deg independent f paperbard, packaging material, crease depth and crease directin. What this might depend n is hard t say but it culd be smething with the behavir f the L&W. Nne f the cefficient plts fr paperbard (Appendix G) r packaging material (Appendix H) are significantly affected by the crease side, but are significantly affected by the chice f paperbard. The cefficient plts shw fr bth paperbard and packaging material that all respnses are increased when paperbard B is used cmpared t paperbard A. Even thugh the crease side is insignificant there is an indicatin that the respnses are increased with inside creasing cmpared t utside creasing. The cefficient plts fr bth paperbard and packaging material shw that the chice f paperbard has a greater impact n the respnses than the chice f crease side. The representative plt in Figure 6.9 shws that the curves f the inside and utside creased samples are very similar. The difference between the uncreased samples is larger than between the creased samples, which is quite surprising. The fact that there is a larger difference between the uncreased samples than there is fr the creased samples can cnclude that there is n apparent difference between inside creasing and utside creasing n the measured parameters. When studying the rest f the plts in Appendix I they indicate the same result. 7.2 Cmputer simulatin The cnverting f the mment, btained in the simulatins f flding, t bending frce that can be cmpared t the experimental values shwed that ur values f bending frce are ten times bigger than the experimental values. Hence the simulated bending frce was scaled dwn with 1/10. The reasn fr ur values being s much bigger was nt fund but culd be due t human errr r have smething t d with the values received frm Abaqus. Several attempts were made t find a slutin t the prblem with several different persns ding the calculatins and lking int the values attained. In Figure 6.10 and Appendix L the simulatins are cmpared with experimental results. In creasing the simulatin mst resemblance paperbard D as can be seen in Figure 6.10, unfrtunately nly ne f the simulatins can be cmpared with paperbard D since the ther simulatin that was cmparable with paperbard D 56

62 failed. The failure was prbably due t the fact that the settings where a cmbinatin f web tensin 2kN/m and crease depth f 0.3mm, these are the highest settings s the simulatin did nt cnverge. The simulatin fllws the curve quite well in the beginning f the creasing but cannt capture the maximum frce. This prblem has als been nticed by Nygårds [4]. In the unlading f the creasing the simulatin has the same behavir as the experimental, the curves seem t be parallel. In the flding the simulatin curve des nt fllw the experimental curve as well as in the creasing. Neither des it shw the maximum frce, this crrespnds with results retrieved by Hui [17]. The simulatin curves are very even in their behavir when yield stress is reached this is nt the case fr the experimental curves that have a wavy curve abve yield, this is likely dependent n the fact that ur simulatins are run in Abaqus/Standard, Abaqus/Explicit wuld prbably shw the waves. Cmparing the simulatin and experimental plts in bth creasing and flding it is pssible t see that there is a big difference between the simulatins and experiments. This makes it hard t actually tell if the data we btain frm the simulatin are useful. A better material mdel and setup have t be develped fr the simulatins t better capture the maximum frces. When cmparing the flding f inside and utside creased paperbard in Figure 6.11, the simulatin fr the flding f inside creased paperbard fllws the flding f utside creased paperbard very clsely, this is the same fr all the graphs shwn in Appendix M. Using crease tl Straight4 there is nly a small increase in frce needed t fld a inside crease cmpared t utside crease in all the different settings, the same tendency is fund with the experimental tests. Hence there is n difference between inside and utside creasing in the simulatins fr the mdel used. A prblem with the simulatins is that they all lk very much the same independent f different settings. The maximum frce seems t be the same independent f web tensin and crease depth, the maximum frce in creasing is arund 250N and the maximum bending frce is arund 1200mN, this is nt the case fr the experimental values where bth the maximum crease and flding frce change depending n web tensin and crease depth. Therefre it is nt alarming that the flding curves cmparing inside and utside lk the same. Cmparing the simulated delaminatin in Figure 6.12 with the phts in Figure 6.5 and Appendix E, f the delaminatin in the experimental setup, ne can see that the delaminatin f the flding in the simulatins lk very much like the delaminatin 57

63 f the experimental tests. Hence the delaminatin is well simulated and the tw interfaces seem t capture the behavir well. There were several prblems encuntered during the simulatin except fr the nes already mentined. Such as the unfld step did nt wrk fr mst f the different flding mdels as can be seen in Appendix K, this culd be due t the fact that there seemed t be damping in the material that was nt expected, this was als a prblem since the paperbard started t fld befre there was a resistance t hld the paperbard dwn in the flding using a rtating clamp. This unaccunted damping might als be the reasn the mving clamp curve lk s different frm the ther curves in Figure K.7. Anther prblem in the simulatin f the mving clamp is that the lad cell ges int the material when flding t mre than 90 deg. 58

64 8 Cnclusins Fr the thin paperbards A-C cnsidering the straight crease tl and the creasing prcess there is a significant difference between utside and inside creasing cnsidering the respnses: maximum frce, energy and remaining defrmatin. Paperbard, crease tl and crease depth have a mre significant influence n all the investigated respnses than crease side. Cnsidering straight creases with thick paperbard D-F the crease side has a significant impact n the respnses maximum frce and energy frm the creasing prcess and maximum frce, energy and initial stiffness and RCS frm the flding prcess. As fr thin paperbard the chice f crease tl, crease depth and paperbard have a greater impact n the respnses than crease side. When investigating straight creases bth thin and thick paperbard shw a tendency t crack at a lwer crease depth fr inside creasing cmpared t utside creasing. This als applies fr thin paperbard cmbined with 250 Base crease pattern. Phts f the creasing prcess when using thick paperbard shw that inside and utside creasing behave very similarly. Studying the phts f the flding prcess shw a big difference in delaminatin fr inside and utside creasing. Test perfrmed n thin paperbard when using a bttm crease pattern shw that the paperbard and crease tl have a greater influence n the RCS value than the crease side. Nne f the respnses are significantly affected by the crease side fr thin paperbards and packaging material using 250 Base crease pattern. The chice f paperbard has a greater impact n all investigated respnses cmpared t the crease side. The results frm the simulatin shw that the delaminatin f inside and utside creased paperbard is very different which is cnsistent with the experimental delaminatin. Bth crease and bending frce f the simulatin seem independent f crease depth and web tensin which is nt cnsistent with the experiments. 59

65 9 Recmmendatins f further investigatin In this master s thesis interesting parameters were selected t be investigated after discussin with ur supervisrs, ther parameters might be f interest and give a different answer and might therefre be interesting t examine in the future. Earlier investigatins have shwn that there is a difference between inside and utside creasing cnsidering the perceptin f grip stiffness, which may indicate that there exist sme undiscvered parameters shwing a difference in the shape f the package. The RCS value as stated earlier is an imprtant measure f hw well the crease is cnverted. In this study RCS have nt shwn any univcal difference n inside and utside creasing, but delaminatin differences have been detected between the tw which might indicate that the RCS value needs a cmplement fr evaluating creases. The simulatin mdel needs a clser examinatin since it is unable t capture the behavir f the paperbard. There are several ways t fld the paperbard in the simulatins, in this study nly three were tried and ther pssibilities exist. The best wuld prbably be if a simulatin with a rtating clamp and statinary lad cell wrked since this is clser t the real experimental setup and might give a better crrelatin t the experimental values. 60

66 10 References Tetra Pak internal: 1 Infrmatin brchure frm Tetra Pak, (2005), Tetra Pak develpment in brief, Cde 9704en 2 Just, M. & Tryding, J., (2008), Labratry study f creased bard, Pwer Pint Presentatin Tetra Pak Karlssn, C., Gustafssn, A., Ljung, A., Anderssn, M., Olevall, L. & Strandberg, E., (2008), Prductin Reprt CR TBA Mnte Mr 2007 w 38, Develpment Reprt Tetra Pak nr DR Nygårds, M. (2008) Creasing f paperbard, STFI-Packfrsk Reprt N.:395 5 Nygårds, M., Just, M. & Tryding, J., (2008), Experimental and numerical studies f creasing f paperbard, Preprint submitted t Elsevier 6 Olevall, L. & Tryding, J., (2007), Reduced bard stiffness by use f inside creasing inhuse verificatin, Develpment Reprt Tetra Pak nr DR Rsander, J., (2006), Creasing Develpment TAA, Develpment Reprt Tetra Pak nr DR Tryding, J. & Just, M., (2008), Mem, Tetra Pak Packaging Slutins Base Materials External literature: 9 Erikssn, L., Jhanssn, E., Kettaneh-Wld, N., Wikström, C. & Wld, S., (2008), Design f Experiments Principles and Applicatins, 3rd ed., Umetrics 10 Ottsen, N. & Peterssn, H., (1992), Intrductin t the finite element methd, Prentice Hall 11 Ottsen, N. S. & Ristinmaa, M., (2005), The Mechanics f Cnstitutive Mdeling, Elsevier Ltd 12 Patel, R. & Davidsn, B., (1994), Frskningsmetdikens grunder: Att planera, genmföra ch rapprtera en undersökning, 2nd ed., Studentlitteratur 61

67 13 Regnell, B. & Runesn, P., (2006), Att genmföra examensarbete, Studentlitteratur 14 Ristinmaa, M. & Ljung, C., (2002) An intrductin t stability analysis, Department f Slid Mechanics, Lund University Master s thesis: 15 Bristw, J. A., Fellers, C., Mhlin, U., Nrman, B., Rigdahl, M. & Ödberg, L., (1991), Pappersteknik, Institutinen för Pappersteknik, Kungliga Tekniska Högsklan 16 Eliasn, O. & Hanssn, L., (2005) Evaluating the 3dm Mdel An Experimental and Finite Element Study, Master s Thesis at Lund University 17 Huang, H., (2008), Flding f Paperbard, Master s Thesis at Ryal Institute f Technlgy 18 Just, M. & Pålssn, M., (2003), Rller nip influence n crease gemetry and bending stiffness, Master s Thesis at Lund University 19 Xia, Q. S. (2002) Mechanics f inelastic defrmatin and delaminatin in paperbard, Master s thesis at Massachusetts Institute f Technlgy Manuals: 20 Abaqus v 6.8, (2008), Dcumentatin, Dassault Systèmes 21 MODDE v 8.0, (2006), User Guide and Tutrial fr MODDE, Umetrics 22 OSCAD 4.0, Manual Optical 3D Measuring Device MikrCAD cmpact, GFMesstechnik GmbH Interviews : 23 Nilssn, Jhan. Develpment Engineer, Tetra Pak Laminatin Technlgy, September 11 th, 12 th and 18 th, and Octber 21 st Nygårds, Mikael. Senir Research Assciate, STFI Packfrsk, Octber 9 th and 10 th, Ristinmaa, Matti. Prfessr, Head f Divisin f Slid Mechanics, Lund University, Nvember 20 th,

68 List f Appendices Appendix A Straight creases: MODDE Wrksheet 64 Appendix B Straight creases: MODDE Cefficient plts, thin paperbard 68 Appendix C Straight creases: MODDE Cefficient plts, thick paperbard 73 Appendix D Straight creases: Phts f creasing prcess 78 Appendix E Straight creases: Phts f flding prcess 84 Appendix F 250 Base crease pattern: MODDE Wrksheet 90 Appendix G 250 Base crease pattern: MODDE Cefficient plts, paperbard 92 Appendix H 250 Base crease pattern: MODDE Cefficient plts, packaging material 97 Appendix I 250 Base crease pattern: Cmparing inside and utside creasing 102 Appendix J Cmputer simulatin: Material Parameters 106 Appendix K Cmputer simulatin: Cmparing simulatin mdels 107 Appendix L Cmputer simulatin: Cmparing simulatin results with experimental results 112 Appendix M Cmputer simulatin: Cmparing Inside vs. Outside creasing

69 Appendix A Straight creases: MODDE Wrksheet A.1 Wrksheet, thin paperbard Test Number Web tensin Crease Depth [kn/m] [mm] Crease Tl Paperbard Crease Side Straight3 B Inside Straight3 C Inside Straight3 A Outside Straight3 C Inside Straight3 B Outside Straight3 A Outside Straight1 A Inside Straight1 B Outside Straight1 C Outside Straight1 A Inside Straight1 C Inside Straight1 B Outside Straight2 B Inside Straight2 A Outside Straight2 C Outside 16 1,5 0.2 Straight2 A Outside 17 1,5 0.2 Straight2 A Inside 18 1,5 0.2 Straight2 B Outside 19 1,5 0.2 Straight2 B Inside 20 1,5 0.2 Straight2 B Outside 21 1,5 0.2 Straight2 B Inside Straight2 B Inside Straight2 A Inside Straight2 C Outside 25 1,5 0.2 Straight2 A Outside 26 1,5 0.2 Straight2 A Outside 64

70 A.2 Numerical values f MODDE wrksheet, thin paperbard CREASING FOLDING TOPOGRAPHY Test Number Max. Frce Energy Def. "dip" [N] [J] [mm] Initial Stiffness [mn/ deg] RCS Max. Frce [N] Energy Final angle Def. "bump" Def. "dip" [kj] [deg] [mm] [mm] Cracks N N N Yes N N N N N N Yes N N N N N N N N N N Yes N N N N 65

71 A.3 Wrksheet MODDE, thick paperbard Test Number Web tensin Crease Depth Crease Tl Paperbard Crease Side [kn/m] [mm] Straight4 D Inside Straight4 E Outside Straight4 F Outside Straight4 D Inside Straight4 F Inside Straight4 E Outside Straight5 D Outside Straight5 E Inside Straight5 F Outside Straight5 D Outside Straight5 D Inside Straight5 E Outside Straight5 E Inside Straight5 F Outside Straight5 F Inside Straight5 E Inside Straight5 D Inside Straight5 F Outside Straight6 E Inside Straight6 F Inside Straight6 D Outside Straight6 F Inside Straight6 E Outside Straight6 D Outside Straight5 D Outside Straight5 D Outside 66

72 A.4 Numerical values f MODDE wrksheet, thick paperbard CREASING FOLDING TOPOGRAPHY Test Number Max. Frce Energy Def. "dip" [N] [J] [mm] Initial Stiffness [mn/ deg] RCS Max. Frce Energy Final angle Def. "bump" Def. "dip" [N] [kj] [deg] [mm] [mm] Cracks N N N Yes Yes N N N N N N N N N N Yes N N N N N Yes N N N N 67

73 Appendix B Straight creases: MODDE Cefficient plts, thin paperbard 68

74 69

75 70

76 71

77 72

78 Appendix C Straight creases: MODDE Cefficient plts, thick paperbard 73

79 74

80 75

81 76

82 77

83 Appendix D Straight creases: Phts f creasing prcess D.1 Paperbard D, utside

84 D.2 Paperbard D, inside

85 D.3 Paperbard E, utside

86 D.4 Paperbard E, inside

87 D.5 Paperbard F, utside

88 D.6 Paperbard F, inside

89 Appendix E Straight creases: Phts f flding prcess E.1 Paperbard D, utside

90 E.2 Paperbard D, inside

91 E.3 Paperbard E, utside

92 E.4 Paperbard E, inside

93 E.5 Paperbard F, utside

94 E.6 Paperbard F, inside

95 Appendix F 250 Base crease pattern: MODDE Wrksheet F.1 Wrksheet, paperbard Test Number Crease Depth [mm] Paperbard Crease Side A Inside A Outside B Outside B Outside A Outside B Outside A Inside B Outside B Inside B Inside F.2 Numerical values f MODDE wrksheet, paperbard CD MD Test Number Initial Stiffness [mn/ deg] RCS Max. Frce [N] Energy Final angle Initial Stiffness [kj] [deg] [mn/ deg] RCS Max. Frce [N] Energy Final angle [J] [deg] RCS GM

96 F.3 Wrksheet, packaging material Test Number Crease Depth [mm] Paperbard Crease Side A Inside B Outside A Inside A Outside B Outside B Outside B Outside B Inside B Inside A Outside F.4 Numerical values f MODDE wrksheet, packaging material CD MD Test Number Initial Stiffness [mn/ deg] RCS Max. Frce [N] Energy Final angle Initial Stiffness [kj] [deg] [mn/ deg] RCS Max. Frce Energy Final angle [N] [J] [deg] RCS GM

97 Appendix G 250 Base crease pattern: MODDE Cefficient plts, paperbard 92

98 93

99 94

100 95

101 96

102 Appendix H 250 Base crease pattern: MODDE Cefficient plts, packaging material 97

103 98

104 99

105 100

106 101

107 Appendix I 250 Base crease pattern: Cmparing inside and utside creasing I.1 Paperbard A, paperbard PAPERBOARD Paperbard A, crease depth 0.23mm, CD Bending frce (mn) Bending angle (deg) Inside, creased Inside, uncreased Outside, creased Outside, uncreased PAPERBOARD Paperbard A, crease depth 0.23mm, MD Bending frce (mn) Inside, creased Inside, uncreased Outside, creased Outside, uncreased Bending angle (deg) 102

108 I.2 Paperbard B, paperbard PAPERBOARD Paperbard B, crease depth 0.13mm, CD Bending frce (mn) Inside, creased Inside, uncreased Outside, creased Outside, uncreased Bending angle (deg) PAPERBOARD Paperbard B, crease depth 0.13mm, MD Bending frce (mn) Inside, creased Inside, uncreased Outside, creased Outside, uncreased Bending angle (deg) 103

109 I.3 Paperbard A, packaging material PACKAGING MATERIAL Paperbard A, crease depth 0.23mm, CD Bending frce (mn) Inside, creased Inside, uncreased Outside, creased Outside, uncreased Bending angle (deg) PACKAGING MATERIAL Paperbard A, crease depth 0.23mm, MD 2500 Bending frce (mn) Inside, creased Inside, uncreased Outside, creased Outside, uncreased Bending angle (deg) 104

110 I.4 Paperbard B, packaging material PACKAGING MATERIAL Paperbard B, crease depth 0.13mm, CD Bending frce (mn) Inside, creased Inside, uncreased Outside, creased Outside, uncreased Bending angle (deg) PACKAGING MATERIAL Paperbard B, crease depth 0.13mm, MD 2500 Bending frce (mn) Inside, creased Inside, uncreased Outside, creased Outside, uncreased Bending angle (deg) 105

111 Appendix J Cmputer simulatin: Material Parameters J.1 Cntinuum mdel Table J.1. Elastic parameters fr anistrpic material Ply E 1 E 2 E 3 G 1 G 2 G 3 v 12 v 13 v 23 Tp Middle Bttm Table J.2. Plastic parameters fr istrpic material in 45 directin Ply σ 0 σ f ε f Tp Middle Bttm Table J.3. Ptential fr Hills s yield surface Ply P 11 P 22 P 33 P 12 P 13 P 23 Tp Middle Bttm J.2 Chesive mdel Table J.4. Interface prperties Ntatin Interface K md 1000 K cd 1000 K zd 400 S md 0.35 S cd 1.2 S zd 1.2 δ f 10 α

112 Appendix K Cmputer simulatin: Cmparing simulatin mdels T get a gd simulatin mdel several mdels are tried t see which resembles the experimental values best. The riginal crease mdel is made by Mikael Nygårds [24] and is used with sme smaller changes. Unfrtunately due t the fact that MODDE was used when making the experiments the crease depth 0.2mm and the web tensin 1.5kN/m with the crease gemetry Straight4 are nt available frm all paperbards. Therefre the simulatins are cmpared with experimental values frm the crease gemetry f Straight5 but with the crease depth f 0.2mm and web tensin 1.5kN/m. K.1 Creasing The same crease mdel is the starting pint fr all flding mdels. The male and female dies are bth made f rigid bdies. A clser descriptin f the mdel can be seen under Simulatin mdel in in the main reprt. Figure K.1. Creasing f paperbard The crease curve fr all the flding mdels shuld hence lk as the ne belw. Figure K.2. Creasing f paperbard 107

113 K.2 Flding There are several flding mdels described belw. K.2.1 Cnstraints This is a mdel where the lad cell and the clamp are made with cnstraints and bundary cnditins. The ndes n the right side where the clamp f the L&W are lcated, are nt allwed t mve, this is enfrced by bundary cnditins in any directin r angle. The ndes 10 mm n the left side f the crease where the lad cell shuld be in an L&W are tied t the center f rtatin by a cnstraint. The center f rtatin is then the pint that rtates and the lad cell ndes fllw. This mdel can be flded t 120 deg but will nt unfld after the fld. Figure K. 03. Flding using cnstraints and bundary cnditins K.2.2 Mving lad cell In this mdel the clamp and the lad cell are made up f rigid surfaces t lk mre as the experimental set up. But ppsite t the real experimental set up the lad cell is here rtating arund the center f rtatin. The reference pint f the lad cell is in the center f rtatin. This mdel can nly rtate 58 degrees befre crashing if ne uses full integratin n the cntinuum elements, when using reduced integratin the paperbard will fld arund the lad cell as well as the center f rtatin. 108

114 Figure K.4. Flding with a rtating lad cell K.2.3 Mving clamp This is a similar mdel t the ne abve; the clamp and the lad cell are bth made f rigid bdies. But here the clamp is rtating arund the center f rtatin. The reference pint f the clamp is in the center f rtatin. This is the mdel that lks mst like the experimental set up. Here full integratin f the element are used, this influences the crease as well as the fld s the bttm right elements have a lt f plastic defrmatin and wuld prbably crack in real life, this might als be the reasn that it has a higher male reactin frce in the last part f the crease peratin. In this flding mdel the frce in the reference pint n the lad cell is used instead f the mment in the center f rtatin. Figure K.5. Flding with a rtating clamp 109