hui huang and mikael nygårds - innventia.com report 441.pdf · fo material for packaging. ... 6.1...

According to Innventia Confidentiality Policy this Report is confidential until 2013-09-15 Package performance - BCT and point loading of paperboard packages

Innventia Report No.: 441

Package performance

BCT and point loading of paperboard packages

Carl-Magnus Everitt, Gustav Marin, Philip Ekfeldt, Hui Huang and Mikael Nygårds


September 2013

Public report



Acknowledgements

This project has been run as a cooperation between Innventia and BiMaC Innovation at

KTH. Innventia had the objective to utilize knowledge and the numerical finite element

models that had been developed within BiMaC Innovation to study a neighbouring but

still different problem than what had been studied at KTH. As a part of Innventia’s in-

kind contribution we wanted to develop a deeper understanding of package

performance, which included making and testing of packages. Thereafter the testing was

evaluated by analytical models, and finally simulated by the finite element method. In

order to establish the cooperation and exchange of ideas and knowledge Innvenita

performed the making, testing and analysis of packages, while KTH at the same time

performed the finite element analysis.

At Innventia this has been run within two SK-founded projects, Power of Packaging and

FO Material for packaging. The financial support from these projects is gratefully

acknowledged.

For BiMaC Innovation this project has shown that the knowledge generated within the

centre can be transferred to the partner companies, and it has also verified that the

models and experimental techniques developed are stable and can be used for other

purposed than they were originally made for. This contributes greatly to the impact

BiMaC Innovation can have in product development within the paper based industry.


Innventia Report No.: 441 1

Table of contents

Page

1 Summary ............................................................................................................... 3

2 Introduction ............................................................................................................ 4

3 Materials ................................................................................................................ 5

4 Experimental characterization ................................................................................ 6

4.1 Tensile Test .................................................................................................................. 6

4.2 SCT – Short Span Compression Test ......................................................................... 7

4.3 Bending Test ................................................................................................................ 8

4.3.1 Bending stiffness .......................................................................................... 8

4.3.2 Bending resistance ...................................................................................... 10

4.4 Shear tests ................................................................................................................. 13

5 Experimental setup .............................................................................................. 14

5.1 BCT ............................................................................................................................ 15

5.2 Point loading .............................................................................................................. 17

6 Theoretical models .............................................................................................. 19

6.1 McKee’s equation....................................................................................................... 19

6.1.1 Cigarette package ....................................................................................... 19

6.1.2 Milk package .............................................................................................. 19

6.2 Grangård’s equation .................................................................................................. 20


6.2.2 Milk package .............................................................................................. 20

6.3 Ristinmaa’s equation .................................................................................................. 21


6.3.2 Milk package .............................................................................................. 22

6.4 Kirchhoff’s plate theory .............................................................................................. 23

7 Results ................................................................................................................ 27

7.1 Box compression testing ............................................................................................ 27

7.1.1 Cigarette packages ...................................................................................... 27

7.1.2 Milk packages ............................................................................................. 41

7.2 Point loading .............................................................................................................. 53

7.2.1 Cigarette packages ...................................................................................... 53

7.2.2 Milk packages ............................................................................................. 60

7.3 Analytical results ........................................................................................................ 64



7.3.1 McKee’s equation ....................................................................................... 64

7.3.2 Grangård’s formula..................................................................................... 67

7.3.3 Ristinmaa’s equation .................................................................................. 69

7.3.4 Kirchhoff’s plate theory.............................................................................. 72

8 Finite element model ........................................................................................... 76

9 Discussion ........................................................................................................... 84

9.1 BCT ............................................................................................................................ 84

9.2 Point loads ................................................................................................................. 84

10 Conclusions ......................................................................................................... 86

11 References .......................................................................................................... 87

Appendix A – Tensile test plots ................................................................................... 88

Appendix B – Results from folding using the L&W creasability tester .......................... 90

Appendix C – Data from shear tests. ........................................................................ 102

Appendix D – Drawings of cigarette package ............................................................ 112

Appendix E – Drawings of milk package ................................................................... 114

Appendix F – Coordinate systems for the point loads ............................................... 116

Innventia Database information ................................................................................ 117



1 Summary In this report different means of estimating the quality of packages from some basic

material tests have been investigated. By looking at data from tensile tests, short span

compression tests and bending tests, the quality of milk and cigarette packages has been

estimated with McKee’s, Grangård’s and Ristinmaa’s equation and with Kirchhoff’s

plate theory.

It was found that Ristinmaa’s equation gave a rough estimation of the BCT strength of

the packages. However, the quality can be better estimated with McKee’s equation after

adjusting the geometric constants of the equations to the measured data. The conclusion

was drawn that if the goal is to estimate the quality of previously not built packages,

Ristinmaa’s equation gives a good idea of the BCT strength. The estimation will be

better for simpler designs of packages. By testing the package design with other

materials a better estimation can be achieved with McKee’s equation.

To test the handle ability, the packages were subjected to point loads. Here it was found

that a simple approximation with a Kirchhoff plate was not enough. A finite element

was therefore made in order to simulate point loads of the package. It was shown that

realistic deformations could be captured by the model when continuum elements were

used to represent the paperboard.



2 Introduction There are many ways to evaluate package performance. There are situation where

package performance relates the load that packages need to withstand during

transportation or order to accurately protect the goods. It can also relate to the behaviour

during consumer contact. The term package performance is therefore very wide, and

relates to the fact that the package should be design such that it performs well.

The objective in this study is to test two different packages, one potential milk package

and one cigarette package, as seen in Figure 1. Both packages will be produced and

tested by the Box Compression Test (BCT) and a point load test. The BCT test is

adequate when the package strength is considered, e.g. during storage or transportation.

The point load test should simulation consumer contact since it can mimic a finger that

is pushed into the package.

Figure 1. The milk and cigarette packages used in this study.

To get increase the understanding of how different paperboard properties contribute to

the package performance, then several different paperboards has been used to make the

packages. In addition, the mechanical properties of the paperboards have been evaluated

using in-plane tensile tests, short compression test (SCT) and bending tests.



3 Materials The packages were built from several different paperboards with different properties.

The cigarette packages were made by using 7 different paperboards, as listed in Table 1.

As seen in the table these paperboard had fairly similar grammages, ranging from 211 to

248 g/m2. Paperboard Ac was a duplex board, while Paperboards Bc-Gc were solid

bleached boards. It should be mentioned that Gc is the same paperboard as Fc, but to

form the package it was folded with the bottom surface facing outside.

Table 1. Material properties for the cigarette paperboards.

Cardboard

Grammage [g/m2]

Measured grammage [g/m2]

Thickness [µm]

AC 240 248 316

BC 240 244 305

CC 220 224 276

DC 220 222 320

EC 215 213 334

FC 205 211 320

GC 205 211 320

To make the milk packages 5 different paperboards were used, as listed in Table 2.

Among these paperboards the grammage differed more, ranging from 200 to 300 g/m2.

Table 2. Material properties for the milk paperboards.

Cardboard

Grammage [g/m2]

Measured grammage [g/m2]

Thickness [µm]

AM 200 200 272

BM 220 218 302

CM 300 293 449

DM 315 301 465

EM 275 277 437



4 Experimental characterization To evaluate the properties of the paperboards, three kinds of tests were used: Tensile

test in MD and CD, short span compression test (SCT) and bending test. These test

results were then used to predict the results of the BCT and point load tests. All the

collected data is also presented in Table 3 at the end of this chapter.

4.1 Tensile Test

To evaluate the tensile strengths of the different paperboards specimens with a width of

15 mm was used. They were fixed with clamps with a testing length of 100 mm. The

sample was then subjected to an increasing elongation of 100%/min, while the

elongation of the sample and the applied force were recorded, until the sample broke.

The Young’s modulus for the paperboards was obtained from the results by a linear fit

to the slope of the stress-strain plot calculated from the test; see an example in Figure 2.

A linear fit was made between 0.05% and 0.2% strain where the slope coefficient equals

the Young’s modulus. The evaluated Young’s moduli in MD and CD for the different

paperboards are plotted in Figure 3 and 4. The tensile test data is the average of at least

10 tests. Stress-strain plots for all paperboards can be found in Appendix A.

Figure 2. Example of stress-strain curves in MD (green) and CD (red) from the tensile testing.



Figure 3. Young’s modulus obtained from tensile testing for the cigarette package boards.

Figure 4. Young’s modulus obtained from tensile testing for the milk package boards.

4.2 SCT – Short Span Compression Test

Short span compression testing evaluates the short span compression properties of the

paperboard. A 15 mm wide sample is compressed in the length direction, by two clamps

0.7 mm apart, until it breaks. The maximum force is then recorded and divided by the

width of the sample. The testing results can be found in Figure 5 and 6. The SCT test

data is the average of 10 tests in both MD and CD.



Figure 5. SCT results for the cigarette package paperboards.

Figure 6. SCT results for the milk package paperboards.

4.3 Bending Test

Another characteristic property of paperboards is how easily it’s bending. Two different

tests were performed to measure this for all paperboards in the report. Both tests use

samples with a width w= 38 mm. These samples were, at one end, fixed in a rotating

fixture and on the other side the displacement was prohibited and the force required to

do so, recorded. The bending tests data is the average of five tests. All the data can be

found in Appendix B but the most important are displayed in graphs below and in Table

3.

4.3.1 Bending stiffness

First the bending stiffness, Sb, was measured. Here the distance, l, between the rotating

fixture and the load cell was positioned 10 mm from the center of rotataion. The

rotation angel, ϴ, of the fixture was gradually increased from 0 to 90 degrees with the



speed 90 degrees/s. From the test data, the slope of the linear part for each paperboard

was extracted; see Figure 7-9 for data from the tests. To convert the data to SI units,

2

3 tan

P lSb

w

(1)

which is based on elementary beam theory.

Figure 7. Example of bending test results.

Figure 8. Bending stiffness of cigarette package paperboards.



Figure 9. Bending stiffness of milk package paperboards.

4.3.2 Bending resistance

In the second test the distance l was increased to 50 mm and the maximum angle of

bending was decreased to 15° to adjust the test to the standardized test of [SS-ISO 2493-

1:2010]. Here the maximum value of the force was extracted. These values are referred

to as the bending resistance, BR, of the paper and are visualized in Figure 10-12.

Figure 10. Example of bending resistance test results.



Figure 11. The bending resistance, BR, of the cigarette paperboards.

Figure 12. The bending resistance, BR, of the milk paperboards.



Paperboard Young’s modulus

/ MPa

SCT / N/m

Bending stiffness

/ Nm

Bending resistance

(15°) / mN

Ac 6031/2539 6988/4730 0.068/0.033 191.8/83.0

Bc 5281/2596 5862/4085 0.065/0.035 175.8/83.8

Cc 4858/2472 4923/3726 0.046/0.026 118.6/60.6

Dc 4828/1756 5343/3031 0.072/0.030 183.8/73.2

Ec 4374/1754 5091/3208 0.074/0.029 184.2/78.8

Fc 5055/1999 5690/3517 0.083/0.039 187.2/79.6

Gc 5055/1999 5690/3517 0.089/0.038 184.4/89.8

Am 4714/2007 4128/2628 0.045/0.024 111.6/63.4

Bm 4816/1809 4659/2741 0.059/0,030 165.0/64.6

Cm 5112/1914 6806/4328 0.179/0.086 498.4/194.2

Dm 4812/1709 6027/3770 0.181/0.089 540.0/193.6

Em 5771/1882 6673/4291 0.178/0.077 456.4/145.6

Table 3. Values from the plots above. Results are in MD/CD format.



4.4 Shear tests

The ability to resist shear stresses was evaluated for the cigarette paperboards at 13

different depths by using the Notched Shear Test. To perform this test, test pieces with a

width of just above 200 mm in CD was cut out from the paperboards. On these, two cuts

were made from opposite sides on the paperboard with varying depth parallel to CD.

The cuts were made with a short distance (5 mm) between them and so that on one side,

this first cut was shallow and the other one deep. The cut had a slope so that on the

other side, the first cut was deep and the second one shallow. The paperboards were

reinforced with plastic laminate to secure the deformation pattern. After the lamination,

the ends of the test pieces were cut off and then they were cut into 13 specimens, each

with a width of 15 mm. Finally they were all tested in the same machine with the same

setup as for the tensile tests. These tests give the shear strength profiles of the

paperboard in the out-of-plane direction; see Figure 13 for an example of the results and

Appendix C for all collected data.

Figure 13 Shear strength profile and all rawdata from shear testing for Paperboard Ac



5 Experimental setup Two types of packages were tested. One classical cigarette package and one design of a

milk package. The cigarette package was manufactured using the rotary die cutter at

Innventia. In this case all blanks had the same direction, where MD is defined in Figure

12. The milk packages were manufactured by the flat bed die cutter at Innventia. Then

sheets could be rotated in two different directions, 1 and 2; see Figure 15 and 16 for

definitions. The package in Figure 15 has direction 1.

Figure 14. The fiber direction for the cigarette packages.

Figure 15. The milk packages with direction 1.



Figure 16. The milk packages with direction 2.

5.1 BCT

When stacking the products for transport or storage, they get subjected to compression

loads. To evaluate how much load the different packages can carry, BCT tests were

performed, using a loading rate of 1 mm/s and a prescribed loading of 15 mm. The load

cases for the BCT are defined in Figure 17 - 21. After the tests were performed they

were analyzed in Matlab to extract the BCT load. The load was defined as the maximum

load before a great enough dip in the curve. This, since the dip was thought to indicate

damages of the structure. To avoid noise and dips due to imperfections the peak force

was defined as the force for which the force of the next deformation step and the force

at 0.3 mm more deformation both were lower.

Figure 17. BCT for load case 1 for the cigarette package.





Figure 20. BCT for load case 1 for the milk package.



Figure 21. BCT for load case 2 for the milk package.

5.2 Point loading

When a customer picks up a product, it is important that it feels robust enough. To test

this stiffness, a point load was used instead of a plate as in the BCT to simulate the

thumb of a hand lifting up the package. The point load was applied at several different

locations according to Figure 22-23. Except from the plate being switched out for a

point load everything else was setup as for the BCT tests, i.e. the loading rate was 1

mm/s and the prescribed deformation was 15 mm.

Figure 22. The loading points for the cigarette package.



Figure 23. The loading points for the milk package.

From the measured force-displacement curves the initial elastic part of the curves was

used to calculate the stiffness. This was done using a linear fitting between two points in

Matlab. The value of this slope [N/mm] was then compared to the calculated values

from analytical models.



6 Theoretical models To estimate the strength of the packages four theoretical models were used to compare

their predictions with the experimental studies of the deformation of the packages in the

different load cases. Three analytical models were evaluated by comparison to the

critical loading during BCT, and one theory was evaluated by comparison to the point

loading tests.

6.1 McKee’s equation

McKee’s equation (McKee et al. 1963) if often used to predict the critical load during a

BCT test for corrugated boxed. The critical loading, P, is formulated as,

C

10.5 2 1

MD CD

bb bP C F Sb Sb Z

, (2)

where Fc depends on SCT values for both MD and CD and the load direction. The

constant Fc will be calculated for each box design. Z is the circumference of the

package. C and b are constants which normally are about 375 and 0.75 respectively. Fc

should be expressed in kN/m, and Sb in Nm and Z in m. The constants have been

estimated through optimization of different boxes since they are geometry dependent.

6.1.1 Cigarette package

The expressions for Fc and Z of the package for each load case can be found in Table 4.

Table 4. Expression for Fc and the value of Z, for cigarette package.

Load case Expression for FC Z [m]

1 C

MD CD8.8 5.5

14.3

SCT SCTF

0.286

2 C MDF SCT 0.22

3 C CDF SCT 0.154

6.1.2 Milk package

For the milk package, CD and MD were changed in both load cases, which gave four

different values of Fc, see Table 5.

Table 5. Expression for Fc and the value of Z, for milk package.


1.1 C

MD CD7 28

35

SCT SCTF

0.35

1.2 C

CD MD7 28

35

SCT SCTF

0.35

2.1 C CDF SCT 0.27

2.2 C MDF SCT 0.27



6.2 Grangård’s equation

Grangård’s (Grangård, 1972, Grangård and Kubat, 1973) equation is often used to

predict the BCT strength of paperboards boxes. It is similar to McKee’s formula. The

critical loading is defined as

0.5

CP k F Sb , (3)

where Fc depends on SCT values for both MD and CD depending on which direction

the fibres are oriented in the load carrying walls and k is a constant which depends on

the geometry. The idea is that each package has its own constant k to account for the

stability of the geometry.


The expressions for Fc for each load case for the cigarette packages can be seen in Table

6.

Table 6. Expression for Fc for the cigarette package.


1 C

MD CD8.8 5.5

14.3

SCT SCTF

0.286

2 C MDF SCT 0.22

3 C CDF SCT 0.154

6.2.2 Milk package

The milk packages have panels in both CD and MD, which gave two expressions for Fc

for each package. Hence, four different values of Fc can be found in Table 7.

Table 7. Expression for FC and the value of Z, c and k, for milk package.


1.1 C

MD CD7 28

35

SCT SCTF

0.35

1.2 C

CD MD7 28

35

SCT SCTF

0.35

2.1 C CDF SCT 0.27

2.2 C MDF SCT 0.27



6.3 Ristinmaa’s equation

Ristinmaa et al. (2012) have derived an expression for BCT testing of panels, which

also can be used to predict the behaviour of flatter boxes. In this method, the packages

are divided into different panels and flaps. Each panel will contribute to the critical

compression force

P C FP P P P (4)

where , Pp is the critical load for a regular panel. The expression for the critical force in

a regular panel is given by

P 12

2

W t BRP a

BRa t H

SCT

(5)

where a1 and a2 are dimensionless parameters which value depends on if the panel is

loaded in MD or CD. BR is the force that is required for bending the sample 15°, W is

the width and H is the height of the package. The thickness, t, vary with respect to

which cardboard that is analysed.

PC is the critical load for a corner panel. The expression for this load is defined as

CP CP,P CP,CP P P , (6)

where the extra index P is for panel region and C is for corner region.

PCP,C is calculated as

4

CP,C 3 1B b

atP a SCT t e

, (7)

where a3 and a4 are constants which values depends on which sides that is carrying

loads and B and b are parameters defined in (Ristinmaa et al., 2012).

PCP,P is calculated according to

CP,P 52

6

B t BRP a

BRa t H

SCT

, (8)

where, a5 and a5 also are dimensionless parameters.

PF is the critical load for flaps. This is calculated in the same way as Eq. (6), but is

multiplied with a dimensionless Flap factor which is set to 0.3. All the dimensionless

parameters are defined in Table8.

Table 8. Values of the dimensionless constants.

Constants a1 a2 a3 a4 a5 a6

MD 1792 13870 8,865 0,0921 2506 57820

CD 1397 10920 10,44 0,0753 2453 85180




Values of the parameters that are used in the different load cases can be found in Table

9-11. The different lengths are defined in Appendix D, where also the numerical values

of the parameters can be observed. For each load case, different sides are carrying load,

and the side numbers are defined in Appendix D.

Table 9. The parameters for load case 1.

Side H [m] Width [m] b [m] Load direction

3 0.023 W3 - CD

1 0.023 B1 0.0382 MD

2 0.023 B2 0.00975 MD

4 0.023 F4 0.011 MD



3 0.054 B3 0.00575 MD

5 0.054 B5 0.013 MD

6 0.054 B6 0.027281 MD

7 0.054 B7 0.02175 MD



2 0.026 B2 0.0055 CD

5 0.026 B5 0.013325 MD

8 0.026 B8 0.013325 MD

6.3.2 Milk package

Values of the parameters that were used in the different load cases can be found in

Table 12-13. The different lengths and numerical values are found in Appendix E. Since

the milk packages were cut out in both directions of the paper, all sides in the tables was

carrying load in both MD and CD separately, which can be found in Appendix E.


Side H [m] Width [m] b [m]

1 0.071 B1 0.025

2 0.071 B2 0.00975

5 0.071 B5 0.008

3 0.071 F4 0.018




Side H [m] Width [m] b [m]

4 0.071 B4 0.025

5 0.071 B5 0.018

6.4 Kirchhoff’s plate theory

To predict the packages stiffness’s with respect to point loads 1 – 3, Kirchhoff’s pate

theory was used. This theory makes, among others, the assumptions that the

deformation of the plate can be described with only the displacement of the plate’s

middle plane, which is the plane in the middle of the plate’s two surfaces. It also

assumes that all shearing forces and membrane forces are too small to affect the

deformation of the plate.

The deformations of the plates where calculated through the potential energy, U, of the

system

( ) ( ) ( ) (9)

where, W is the elastic energy of the deformed plate, P is the applied force, w is the

shape of the deformation and xi and yi are the coordinates of the applied load. The shape

of w was chosen to fulfil the kinematic boundary conditions according to Table 14-16.

The definition of the coordinate systems can be seen in Appendix F. To keep the

calculations on a reasonable level, the boundary conditions used corresponds to either a

freely supported plate or a fixed supported plate. The real case would be somewhere in

between. This since the corners of the packages should give more support than none, as

in the freely supported case, but not as much as a fixed support. The coordinates for the

point loads can be found in Table 17. The shape of the deflection w was assumed to

follow the expressions in Tables 18-20.

Table 14. Boundary conditions for point load 1 and 2 on the cigarette packages.

Assumption Boundary

condition

At

1 w = 0 y=0 x=0.062 y=0.055

w’= 0 x=0

2 w = 0 y=0 x=0.062 y=0.055

w’’= 0 x=0

3 w = 0 y=0 x=0.062 y=0.055

w’’= 0 x=0 y=0 x=0.062 y=0.055

Table 15. Boundary conditions for point load 3 on the cigarette packages.

Assumption Boundary

condition

At



1 w = 0 x=0 y=0 x=0.023 y=0.055

3 w = 0 x=0 y=0 x=0.023 y=0.055

w’’= 0 x=0 y=0 x=0.023 y=0.055

Table 16. Boundary conditions for point load 1 and 2 on the milk packages.

Assumption Boundary

condition

At

1 w = 0 x=0 y=0 x=0.10 y=0.071

2 w = 0 x=0 y=0 x=0.10 y=0.071

3 w = 0 x=0 y=0 x=0.10 y=0.071

w’’= 0 x=0 y=0 x=0.10 y=0.071

Table 17. Coordinates for the point loads.

Point load x y

Cigarette point 1 0.031 0.028

Cigarette point 2 0.01 0.028

Cigarette point 3 0.012 0..028

Milk point 1 0.05 0.036

Milk point 2 0.05 0.036

Table 18. The assumed shape of w for point load 1 and 2 on the cigarette packages.

w1 = 0.055 0.124y xC sin cos

w2 = 0.0620.055

yC sin cos x

w3 = 2 2

0.055 0.124y xC sin cos

Table 19. The assumed shape of w for point load 3 on the cigarette packages.

w1 sin0.055 0.023

y xC sin

w3 2 2sin0.055 0.023

y xC sin

Table 20. The assumed shape of w for point load 1 and 2 on the milk packages.



w1 sin0.071 0.10

y xC sin

w2 0.036 0.10y y x xC

w3 2 2sin0.071 0.10

y xC sin

When the assumptions have been made, the elastic energy of the plates are calculated as

( )

∬ [( ) ( ) [

(

)

]]

(10)

where D is the bending resistance of the plate, which was calculated as

( ) (11)

where an assumption of isotropic homogenous material was used, and t is the thickness

of the paper and v is Poisons ration, which was set to 0,293 since the calculations where

done for isotropic materials.

To calculate the constant C in the assumptions for w, the expression in Eq (10) was

derived with respect to C to find the minimum potential energy of the system with

respect to C. This yielded the results of Table 21-23. With these constants and with P

set to unity load, the deflections were calculated. The calculated values where then

inverted to achieve the stiffness of the whole plate as the force required [N] per

deflection [mm].

Table 21. The constant C for point load 1 and 2 on the cigarette packages.

Assumption C =

1

10 13

0.124

1.42829 10 2 4.54982 10

ixP cos

D v

2

0.062

5,56287 2 3,09029

iP x

D v

3 2

0.124

15924.6 2

ixP cos

D

Table 22. The constant C for point load 3 on the cigarette packages.

Assumpti

on

C =



1

75975 4 2

P

D

3

9 133 08013 10 2 6.14989 10

P

D v

Table 23. The constant C for point load 1 and 2 on the Milk packages.

Assumption C=

1

10 132.18354 10 2 3.52474 10

P

D v

2

2 2

20 12

0.036 0.05

1.6 10 2 6.19559 10

P

D v

3

10 135.48784 10 2 2,95734 10

P

D v



7 Results After the empirical tests were performed, the constants referring to the geometry in

McKee’s equation and Grangård’s equation were adjusted. In this chapter, the analytical

results are plotted against the empirical test results. Since the geometry constants are

adjusted the part of interest is how similar the shapes are since that’s what the paper

quality affects.

7.1 Box compression testing

Both the cigarette and milk packages where tested by the BCT, deformed packages at

peak load can be seen in Figure 24 and 25.

Figure 24. BCT load of the cigarette packages in load case 4 at fully deformed state.

Figure 25. BCT load of the milk packages in load case 1 at fully deformed state.

7.1.1 Cigarette packages

The force-displacement curves from the BCT testing for load cases 1-3 can be found in

the Figures 26-50. A detailed description of what can be found in each figure can be



found in the table below. In addition, the maximum BCT forces and the stiffnesses for

all packages have been evaluated.

Load case Number of

packages

Rawdata plots for

Paperboards Ac-Gc

Evaluated BCT strength

and stiffneses

1 6 Figures 26-32 Figures 33-34



Figure 24. The BCT results for cigarette package A, load case 1.



Figure 27 The BCT results for cigarette package B, load case 1.

Figure 25. The BCT results for cigarette package C, load case 1.



Figure 26. The BCT results for cigarette package D, load case 1.

Figure 30. The BCT results for cigarette package E, load case 1



Figure 31. The BCT results for cigarette package F, load case 1.

Figure 27. The BCT results for cigarette package G, load case 1.



Figure 28. Measured BCT forces and BCT stiffness for all cigarette package tests from load case 1.The BCT stiffness recorded for each test on load case 1.




Figure 30. The BCT results for cigarette package B, load case 2.





Figure 33. The BCT results for cigarette package E, load case 2.



Figure 35. Measured BCT forces and BCT stiffness for all tests from load case 2.The BCT stiffness recorded for each test on load case 1.




Figure 37. The BCT results for cigarette package B, load case 3.





Figure 40. The BCT results for cigarette package E, load case 3.



Figure 43. The BCT force recorded for each test on load case 3, in N.

Figure 44. The BCT stiffness recorded for each test on load case 3, in N/mm.



7.1.2 Milk packages

The force-displacement curves from the BCT testing for load cases 1-3 can be found in

the Figures 26-50. A detailed description of what can be found in each figure can be

found in the table below. In addition, the maximum BCT forces and the stiffnesses for

all packages have been evaluated.

Load case Number of

packages

Rawdata plots for

Paperboards Am-

Gm

Evaluated BCT strength

and stiffneses


2 2 or 6 Figures 63-72 Figures 73-74

Figure 45. The BCT results for milk package A1, load case 1.




Figure 47. The BCT results for milk package B1, load case 1.




Figure 49. The BCT results for milk package C1, load case 1.




Figure 51. The BCT results for milk package D1, load case 1.




Figure 53. The BCT results for milk package E1, load case 1.



Figure 56. The BCT stiffness recorded for each test on load case 1, in N.




Figur2 66. The BCT results for milk package E2, load case 2.




Figure 68. The BCT stiffness recorded for each test on load case 2, in N.

7.2 Point loading

7.2.1 Cigarette packages

Both the cigarette and milk packages where tested by point loading according to load

cases 1, 3 and 4.

The force-displacement curves from the point loading for load cases 1, 3 and 4 can be

found in the Figures 78-84. During testing some loading-unloading cycles were tested,

which can be seen in the figures. A detailed description of what can be found in each

figure can be found in the table below.

Load case Number of

packages

Rawdata plots for

Paperboards Ac-Gc

1 1 Figures 78-81

2 4 Figures 82-88

3 1 Figures 89-95



Figure 75. Load case 1 in fully deformed state and after unloading.





Figure 69. The recorded force and displacement for point load 01 on cigarette packages A and B.

Figure 70. The recorded force and displacement for point load 01 on cigarette package C and D.

Figure 80. The recorded force and displacement for point load 01 on cigarette package E and F.



Figure 71. The recorded force and displacement for point load 01 on cigarette package G.

Figure 72. The recorded force and displacement for point load 02 on cigarette package A and B.

Figure 83. The recorded force and displacement for point load 02 on cigarette package C and D.



Figure 87. The recorded force and displacement for point load 03 on cigarette package C abd D.






Figure 73 The recorded force and displacement for point load 04 on cigarette package C and D.




Figure 93 The recorded force and displacement for point load 04 on cigarette package G.

7.2.2 Milk packages

The force-displacement curves from the point loading for load cases 1, 3 and 4 can be

found in the Figures 78-84. During testing some loading-unloading cycles were tested,

which can be seen in the figures. A detailed description of what can be found in each

figure can be found in the table below.

Load case Number of

packages

Rawdata plots for

Paperboards Ac-Gc

1 1 Figures 94-98

2 1 Figures 99-103

Figure 74. The recorded force and displacement for point load 01 on milk package A1 and A2.



Figure 95. The recorded force and displacement for point load 01 on milk package B1 and B2.

Figure 75. The recorded force and displacement for point load 01 on milk package C1 and C2.

Figure 97. The recorded force and displacement for point load 01 on milk package D1 and D2.



Figure 76. The recorded force and displacement for point load 01 on milk package E1 and E3.

Figure 77. The recorded force and displacement for point load 02 on milk package A1 and A2.

Figure 100. The recorded force and displacement for point load 02 on milk package B1 and B2.



Figure 101. The recorded force and displacement for point load 02 on milk package C1 and C3.

Figure 102. The recorded force and displacement for point load 02 on milk package D1 and D2.

Figure 78. The recorded force and displacement for point load 02 on milk package E1 and E2.



7.3 Analytical results

7.3.1 McKee’s equation

The results here display the correctness of the estimations for BCT results made by

McKee’s formula. The constants C and b have been optimized compared to the

measured results, with the mean square errors minimized.

7.3.1.1 Cigarette package

Due to limitations in the amount of packages available only five tests were performed

for load case 1. For load case 2 four tests were made while only one test was made for

load case 3. The average values are plotted in Figure 104-106 with error bars which

display the maximum and minimum recorded value.

Figure 79. McKee estimation of load case 1, C = 155.57, b = 1.014.





7.3.1.2 Milk package

Three tests were performed for each of the packages Cm,2, Dm,2, Em,2, while only one test

each were performed for the rest of the packages. See Figure 107-110 for the average

values, with error bars indication the maximum and minimum recorded value, for each

test.




7.3.2 Grangård’s formula

The results in this chapter display the correctness of the prediction of BCT results made

by Grangård’s formula. The constant k has been optimized compared to the measured

results.


For the cigarette packages the results of Figure 111-113 was obtained.

Figure 82. Grangård estimation of load case 1, k = 14.60.






For the milk packages the results of Figure 114-117 was obtained.





Figure116. Grangård estimation of load case 2, k = 8.40.


7.3.3 Ristinmaa’s equation

With help of Ristinmaa’s equation, the following predictions were made.


Se Figure 118-120 for the predictions of the BCT strength of cigarette packages.

Figure 85. Ristinmaa prediction for load case 1.






In Figure 121-124, the results of Ristinmaa’s predictions are displayed.




7.3.4 Kirchhoff’s plate theory

The results from the plate theory calculations can be viewed in Figure 125-132.

Figure 125 The results of point load 1 on cigarette packages with E = Eaverage.

Figure 126. Optimized results for point load 1 on cigarette packages.



Figure127. The results of point load 2 on cigarette packages with E = Eaverage.

Figure 128. Optimized results for point load 2 on cigarette packages.



Figure 129. The results of point load 3 on cigarette packages with E = Eaverage.

Figure130. Optimized results for point load 3 on cigarette packages.



Figure 131. The results of point loads on milk packages, with E = Eaverage.

Figure 132. Optimized results for point loads on milk packages.



8 Finite element model A finite element model of the cigarette package was created and simulated using

Abaqus/Standard. The model was used to simulate three loading cases, as seen in Figure

133. In order to build the package in the Abaqus a creased and cut blank was

considered. The blank was considered to consist of a number of panels, as illustrated in

Figure 153. Each of these panels were then positioned into the folded package, as also

seen in Figure 134. Each panel was in the model considered to have a thickness of 0.3

mm, and only one element was used to represent the paperboard in the thickness

direction. Two simulation approaches were used to create models:

Continuum model, where C3D3 elements were used

Shell model, where SC8R elements were used.

Hence, no delamination was accounted for in the models. In order to form the package

the panels were attached to each other. This was done with a row of elements in the 45

degree direction compared to the two panels, see Figure 135. This element row would

represent the creases in the package. Since the creases have had a damage evolution

during the creasing and folding history, then the in-plane material parameters were

assumed to be 50% of material parameters used for the panels, and the out-of-plane

parameters were assumed to be 10% of material parameters used for the panel.

Load case 1 Load case 4

Figure 133. Load cases 1 and 4 tested in the finite element model.



Figure 134. The panels from the blank were used to form the package.



Figurinsättning (enkelt radavstånd, centrerad)

Figure 135. The corners in the package was represented by elements in the 45 degrees direction in relation to the two panels it connected.

An anistropic elastic model, with Hill’s yield criteria and isotropic hardening was used

to represent the paperboard material in the package. This model has previously been

used by Huang (2013). When the continuum elements were used, then the full 3D

behaviour was considered. However, when the shell elements were used, then only the

in-plane components were considered. The material constants can be found in Table 24.

Table 24. Material constant used to represent the paperboard material.

Parameter Value

Exx / MPa 5281

Eyy / MPa 2596

E45 / MPa 3529.4

Ezz / MPa 100

Gxz / MPa 72.1

xy 0.418

𝝈 / MPa 30.33

𝝈 / MPa 13.1

𝝈 / MPa 13.1

𝝈 / MPa 0.68

𝝈 / MPa 13.92

𝝈 / MPa 0.68

H 1387



Simulation was performed by a constrained displacement of the rigid surface that

represented the point load. For load cases 1, 2 and 3, both the continuum and shell

elements were used in the simulations. In Figure 135-138 the deformed packages at

peak load can be seen.

Figure 136. Simulations of load case 1 using continuum and shell models.



Figure 137. Simulations of load case 4 using continuum models.

Figure 138. Simulations of load case 4 using shell models.



Figure 139. Deformed packages at peak load for load case 1 and 4.

In the contour plots it can be observed that load cases 1 and 2 for the continuum and

shell response look quite similar. This is since it is mainly deflections of the panels that

dominate the behaviour. However, for load case 3 the deformed contour plots look

different. When the continuum elements were used the simulations managed to capture

localized damage as the panels formed local folding damages. When the shell elements

were use the deformation of the panels was only due to panel deflection. Therefore, the

continuum elements were able to capture a more realistic deformation pattern. This can

be verified by studies of the deformed packages at peak load in Figure 140. The use of

continuum elements were also judge to be much better when the force-displacements

curves from the simulations using continuum and shell elements were compared to

experimental curves. The shell elements gave a stiffer response than the continuum

elements, as seen in Figures 140 and 141. This was because the continuum element

could deform in out-of-plane shear, which is weak. Since the continuum elements

would deform plastically in the out of plane directions, the deformed packages from the

simulations and testing had similar shape after unloading, as seen in Figure 142.



Figure 140. Verification of force-displacement curves for load case 1.

Figure 141. Verification of force-displacement curves for load case 4.



Figure 142. Comparison of the simulation and tested packages after unloading from load case 4.



9 Discussion The quality of different estimation methods was evaluated. However, no effort was put

to quantify the uncertainties of the results. All packages test were performed for rather

small series which makes the empirical results uncertain. Larger amounts of package

tests would ensure more reliable results. Also, no estimations of the uncertainties in the

calculated estimations were performed. This could prove to be valuable information to

see if the difference between the estimated values and the measured ones are within the

range of uncertainty.

9.1 BCT

The optimization of the geometry constants was based on minimizing the mean square

errors between the estimations and the measured loads (McKee et al. 1963). This

procedure worked better for McKee’s equation than for Grangård’s which shows that

adjustments of the power constant b improve the results. Grangård’s equation is similar

to McKee’s with b kept constant at 0.5.

Regarding Ristinmaa’s equation, it did not yield as good results in this test series as it

did in the original paper where the maximum deviation was +/- 20%. This probably

depends on how the panels were defined. In Ristinmaa’s equation, all load carrying

panels have to be a corner panel, a panel or a flap. For the packages in this report that

had and opening in the cigarette package and gable top in the milk package, perhaps

new expression have to be defined to account for other panel deformation patterns to

improve the results.

The constants used in the Ristinmaa method were calculated using different materials

by the authors of the report (Ristinmaa et al. 2012). This could have impacted the test

results since they were not derived from the materials used in this project.

Also the BCT values can be defined in different ways. Here, the maximum value before

a big enough dip in the graph was used since it was assumed that these dips indicated

that the packages were damaged. The question here is how big the dip should be to not

count as noise but instead as damage of the package. Another approach would be to take

the total maximum value of each test, since this is the maximum load the package can

carry before being too deformed.

9.2 Point loads

Regarding the assumptions made in Kirchhoff’s plate theory. This won’t be the case for

the experiments performed for this report since here; the deformations are much greater

than the thickness of the plate. Already after the deformation reaches half the height of

the plate, the membrane forces starts to contribute to the stiffening of the plate. This is

probably the reason to why the calculated stiffness for the milk packages is much lower

than the measured one. But since the deformation has a linear part, calculations which

includes membrane forces should yield better results.

For the cigarette packages on the other hand the results are better. For point load 1 and

2, the results are close, which might be due to that the surface has one free boundary

which lowers the membrane forces. Another explanation is that the vertical walls of the



cigarette packages deform more than the walls of the milk packages, making the upper

surface look softer.

For point load 3, the deformation was much smaller than for the other test results which

should give rise to lesser membrane forces and therefore more accurate results.

However, the structure for this test is less stable which makes the results less reliable.

The boundary conditions can also be improved by taking into account the stiffness of

the creases instead of viewing them as infinitely soft or stiff.

To better capture the deformation mechanisms activated during point loading a FEM

model was developed and simulations were performed. By using the FEM model more

realistic boundary conditions of the panels could be accounted for, since each panel then

is connected to the corners. However, in the model one needs to define the properties of

the corners that has been deformed and damaged during the creasing and folding

operation. Here, we assumed that the properties could be reduced by 50% or 10%.

When the continuum model was used this gave good simulation data compared to the

experimental data. However, the properties of the corners are still large unknown, and

much more attention can be put on characterizing the properties better. Our

approximations were based on reductions during folding for creases, which are about

50%. While we assumed that the out-of-plane properties would be reduced even more.

When the shell model the global response could not be captured as well as with the

continuum model. This is because out-of-plane properties have not been accounted for.

In the experiments we could see that the out-of-plane deformations are activated, since

local damage normally occurs during folding. Therefore, continuum elements should be

used to better capture the observed and known deformation and damage mechanisms. If

even a more accurate model should be used, then also delamination can be accounted

for. However, here it was judged to cost more in computations efficiency, compared to

what it would give in identifying important paperboard behaviours.



10 Conclusions The strength of packages is affected by many factors, such as the geometry, paperboard

properties and imperfect. However, the BCT strength could be well predicted by the

McKee and Grangård formulas. But, McKee’s and Grangård’s equations require

adaptation of the geometrical constants. When this fitting had been done the predictions

fitted the experiments well. Further on it would be interesting to see how good the

predictions would be for new packages.

Regarding Ristinmaa’s equation, no adaptation should be needed. However, the results

were not as accurate as with the McKee and Grangård formulas. The conclusion was

that even Ristinmaa’s equation requires some mapping to test results of the package, at

least for the more complex packages when it is not clear how to classify the panels. On

the other hand, Ristinmaa’s equation offers much better estimations of previously

untested geometries since it’s built on deformation patterns.

During point loading of the packages the membrane forces and boundary conditions

affected the results to much, therefore Kirchoff’s plate theory could not predict the

results very well.

However, FEM simulations using continuum elements could capture the deformations

well. It was also concluded that continuum elements was better to use than shell

elements. This was since the out-of-plane behaviour contributes to the deformation

activated during point loading of the packages. This is not accounted for by shell

elements.



11 References Grangård H (1972)

Some aspects of the compressive strength of cartons

Svensk Papperstidning,

Grangård H and Kubat J (1973)

Compression of board cartons

Svensk Papperstidning,

McKee, R.C., Gander, J.W. and Wachuta, J.R. (1963).

Compression strength formula for corrugated boxes,

Paperboard Packaging, (48), 149-159.

Ristinmaa M, Saabye Ottosen N, Korin C (2012)

Analytical Prediction of Package Collapse Loads – Basic considerations

Nordic Pulp and Paper Research Journal Vol no.4/2012



Appendix A – Tensile test plots

Figure A1. Stress-strain curves for Paperboard Ac-Fc that was used to make cigarette packages.



Figure A2. Stress-strain curves for Paperboard Am-Em that was used to make milk packages.



Appendix B – Results from folding using the L&W creasability

tester

Figure B1. Moment-angle plots in MD and CD for creased samples of Paperboard Am.

Figure B2. Moment-angle plots in MD and CD for creased samples of Paperboard Bm.



Figure B3. Moment-angle plots in MD and CD for creased samples of Paperboard Cm.

Figure B4. Moment-angle plots in MD and CD for creased samples of Paperboard Cm.



Figure B5. Moment-angle plots in MD and CD for creased samples of Paperboard Em.

Figure B6. Moment-angle plots in MD and CD for creased samples of Paperboard Cc.



Figure B7. Moment-angle plots in MD and CD for creased samples of Paperboard Bc.

Figure B8. Moment-angle plots in MD and CD for creased samples of Paperboard Cc.



Figure B9. Moment-angle plots in MD and CD for creased samples of Paperboard Dc.

Figure B10. Moment-angle plots in MD and CD for creased samples of Paperboard Ec.



Figure B11. Moment-angle plots in MD and CD for creased samples of Paperboard Fc.

Figure B12. Moment-angle plots in MD and CD for creased samples of Paperboard Gc.



Figure B13. Bending resistance calculation in MD and CD for Paperboard Am.

Figure B14. Bending resistance calculation in MD and CD for Paperboard Bm.



Figure B15. Bending resistance calculation in MD and CD for Paperboard Cm.

Figure B16. Bending resistance calculation in MD and CD for Paperboard Dm.



Figure B17. Bending resistance calculation in MD and CD for Paperboard Em.

Figure B18. Bending resistance calculation in MD and CD for Paperboard Ac.



Figure B19. Bending resistance calculation in MD and CD for Paperboard Bc.

Figure B20. Bending resistance calculation in MD and CD for Paperboard Cc.



Figure B21. Bending resistance calculation in MD and CD for Paperboard Dc.

Figure B22. Bending resistance calculation in MD and CD for Paperboard Ec.



Figure B23. Bending resistance calculation in MD and CD for Paperboard Fc.

Figure B24. Bending resistance calculation in MD and CD for Paperboard Gc.



Appendix C – Data from shear tests.

Figure C1. Rawdata from shear testing in MD of Paperbaord Ac using the DNS test.



For paperboard B

Figure C2. Rawdata from shear testing in MD of Paperbaord Bc using the DNS test.



Figure C3. Rawdata from shear testing in MD of Paperbaord Cc using the DNS test.



Figure C4. Rawdata from shear testing in MD of Paperbaord Dc using DNS test.



Figure C1. Rawdata from shear testing in MD of Paperbaord Ec using DNS test.



Figure C6. Rawdata from shear testing in MD of Paperbaord Fc using DNS test.



All this data put together

Figure C7. Shear strength profile of Paperboard Ac.

Figure C8. Shear strength profile of Paperboard Bc.



Figure C9. Shear strength profile of Paperboard Cc.

Figure C10. Shear strength profile of Paperboard Dc.



Figure C11. Shear strength profile of Paperboard Ec.

Figure C12. Shear strength profile of Paperboard Fc.



Figure C12. Shear strength profile of Paperboard Ac-Fc.



Appendix D – Drawings of cigarette package

Figure D1. Side numbers for BCT 1 on cigarette packages.





Figure D4. The dimensions of the cigarette package.

Figure D5. The names of the cigarette packages sides for BCT.



Appendix E – Drawings of milk package

Figure E1. Side numbers for BCT 1 on cigarette packages.

Figure E2. Side numbers for BCT 2 on cigarette packages.



Figure E4. The dimensions of the cigarette package.

Figure E5. The names of the cigarette packages sides for BCT.



Appendix F – Coordinate systems for the point loads

Figure F1. Coordinate system, for pint load 1 and 2 on cigarette packages.

Figure F2. Coordinate system, for pint load 3 on cigarette packages.

Figure F3. Coordinate system, for pint load 1(left) and 2 (right) on milk packages.



Innventia Database information

Title

Package performance - BCT and point loading of paperboard packages

Author

Carl-Magnus Everitt, Gustav Marin, Philip Ekfeldt, Hui Huang, Mikael Nygårds

Abstract

In this report different means of estimating the quality of packages from some basic

material tests have been investigated. By looking at data from tensile tests, short span

compression tests and bending tests, the quality of milk and cigarette packages has been

estimated with McKee’s, Grangård’s and Ristinmaa’s equation and with Kirchhoff’s

plate theory.It was found that Ristinmaa’s equation gave a rough estimation of the BCT

strength of the packages. However, the quality can be better estimated with McKee’s

equation after adjusting the geometric constants of the equations to the measured data.

The conclusion was drawn that if the goal is to estimate the quality of previously not

built packages, Ristinmaa’s equation gives a good idea of the BCT strength. The

estimation will be better for simpler designs of packages. By testing the package design

with other materials a better estimation can be achieved with McKee’s equation.To test

the handle ability, the packages were subjected to point loads. Here it was found that a

simple approximation with a Kirchhoff plate was not enough. A finite element was

therefore made in order to simulate point loads of the package. It was shown that

realistic deformations could be captured by the model when continuum elements were

used to represent the paperboard.

Keywords

Mechanical properties, BCT, cigarette, packaging, point load, FEM

Classification

1240

Type of publication

Public report

Report number

441

Publication year

September 2013

Language

English

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