Mark J. Kirwan Paper and Paperboard Packaging Technology
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Blanks for RSCs from the corrugating machine are further converted on flexo
folder gluers. Special design profiles are cut and scored on a die-cutter/scorer.
Machines are also available which incorporate many typical features of
corrugated box printing and conversion in one in-line machine, Figure 11.28.
The following features are indicated in Figure 11.28:
A is the feeder which can handle a wide range of board thickness, from thin
microflute to double-wall corrugated board
B is a 4-colour flexographic printing unit
C is a rotary diecutter. A diecutter is necessary for the production of sophisticated
box designs, i.e. boxes with features other than simple scores and slots
D is a slotting unit with waste removal
E is a folder-gluer unit where the side seam is completed
F indicates two-process touch-control screens which are used to set up and
operate the machine
G stacks the boxes in bundles and ejects them from the machine in a controlled way.
Features of such a machine are the automation of the adjustments, i.e. the set-up,
required when changing from one box design to another, attention to the removal
of board dust generated during cutting and noise reduction.
11.3 Corrugated fibreboard – functions
11.3.1 Box stackability
The main function of a corrugated paperboard box is to contain and protect packed
goods during distribution. The growing use of palletization in warehousing and
transportation requires that corrugated boxes have good stackability.
11.3.1.1 Pallet arrangements
Specific commercial software is available to design the best position of the
corrugated boxes on the pallet with respect to utilization of the volume and overall
stability. The structure, as shown in Figure 11.29, is calculated using a software,
such as the CAPE system or other expert systems.
11.3.1.2 Intrinsic compression
Corrugated board is the most appropriate material to achieve high stackability,
forming a lightweight rigid structure composed of liners separated by corrugated
fluting papers.
Stackability is best measured using the box compression test (BCT) expressed
in DaN or kg. BCT is the top-to-bottom compression strength. Several standards
have been published, for example FEFCO, ISO, AFNOR, etc. In the FEFCO
method, the measurement is made on an empty box. The application of a method
for measuring BCT, mean and standard deviation is defined in FEFCO Testing
Method No. 50. In ISO 12048, BCT measurement is made on filled boxes.
Figure 11.28 Martin combined in-line rotary diecutter, slotter, flexo folder gluer. (Reproduced, with permission, from Bobst SA.)
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Empirical approach to compression strength: McKee formula
The most widely known formula which links the box compression strength with
the mechanical properties of its components is the one devised by McKee (McKee
et al., 1963):
Box compression strength = K × ECT
a
× FS
b
× D
c
where D is the dimension of the box (perimeter); FS is the flexural stiffness of
the board; ECT is the edge crush test of the board; and K, a, b and c are empirical
constants.
Box dimensions have an important role in determining stackability, and designers
take this into account, using a chart based on the perimeter and height of the box
together with the basis weight or grammage of the corrugated board. Figure 11.30
illustrates the relationships involved.
For given box dimensions, the BCT (measured in DaN) of the corrugated
board package depends both on the ECT and the flexural stiffness of the combined
board.
The original McKee equation (statistically derived from a relatively small
number of experiments run in the early 1960s) overestimates the effect of the ECT
and underestimates the effect of the flexural stiffness.
To improve on this, more extensive laboratory tests have been run. It has been
seen that the BCT is mainly a function of the box dimensions, the combined board
thickness (calliper), the grammage and the flexural stiffness of the combined
board.
Figure 11.31 shows the variation of BCT for rectangular cases 40 cm×
30cm × 30cm, with the board grammage for two different stiffnesses.
The first one given is for C flute (4.2mm calliper), the second for B flute
(2.8mm calliper).
In addition to the factors already discussed, it is very important to take into
account the flute size and hardness of the corrugated board as well. The thickness
of the combined board is an important element in determining the vertical
Figure 11.29 Structure of the pallet.
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compression performance. Multi-wall combinations like B+C=BC or B +E=BE
combine to increase the board thickness and thus the weight and stiffness of the
structure.
The flexural stiffness term (FS) in the McKee formula is obtained from classical
thin plate theory (Pommier & Poustis, 1989). (Thin plate theory is the classic
0
0
100
200
300
400
500
20 40 60 80 100
Height (cm)
BCT (Da N)
P = 2.0 m – BW = 560 g/m
2
P = 1.4 m – BW = 425 g/m
2
C flute
Figure 11.30 Effect of box dimensions and grammage (basis weight) on stacking strength BCT.
(Height of box in cm.)
P = perimeter of the box, BW = basis weight or grammage of the corrugated board.
350 400 450 500 550
Corrugated board grammage (g/m
2
)
160
200
240
280
BCT (Da N)
B flute
C flute
Figure 11.31 Effect of flute size, i.e. C and B flute with different stiffnesses, on BCT.
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approach for evaluating raw material performance in mechanics in order to predict
the bending stiffness of composite materials, i.e. sandwiches.) This stiffness is
created by the moment of inertia of the material.
The thickness of the board and the quality of the fluting (or its hardness,
defined later) both play important roles in determining the moment of inertia. In
order to get the ultimate box compressive strength, fluting with perfect waveform
is also needed.
A second factor used in calculating flexural stiffness is the modulus of elasticity
(Young’s Modulus, or MOE) of the liners. This is currently measured using an
ultrasonic test, the tensile stiffness index. Figure 11.32 compares two liners of
equal thickness (calliper). Liner 1 has a high MOE compared to Liner 2. The
flexural stiffness of the combined board is strongly differentiated by the difference
in MOE, especially as liner basis weight increases.
In practice, flexural stiffness is difficult to measure and is not used as a regu-
lar test.
The ECT test is better known, and is commonly used to estimate the potential
strength of the board. As shown in Figure 11.33, this element is not dependent on
the thickness of the board; but depends mostly on the grammage of the board.
A combination of paper strength parameters can be made and used to predict
ECT with more precision, as indicated in the following formula for a single wall
corrugated board.
Flexural stiffness machine direction
Flexural stiffness (N cm)
1600
1200
800
400
0
0 50 100 150 200 250
Liner 1
Liner 2
C flute
Liner
g
ramma
g
e (
g
/m
2
)
Figure 11.32 Effect of liner MOE on combined board flexural stiffness.
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ECT = 0.585 (SCT
CD1
+ SCT
CD2
) + 1.203 CCT
CD
r
2
= 0.944
SCT
CD
is the short compression crush test strength in the CD of the liners
(1 and 2) and CCT
CD
is the compression crush test strength in the CD of the
fluting. (Note: CCT is not Concora Compression Test – a similar shaped sample is
used as for Concora Medium Test, CMT, but the load is applied totally differently.
The load is applied at the edge of the paper. The test is not used very often, but it is
similar to the ECT test.)
Semi-empirical prediction of compression strength
In order to expand beyond the classical box theories, new methods of measuring
stackability are always being considered.
The following diagram is based on a photograph, Figure 11.34, which shows
the stress distribution in a boxboard panel under compression. The influences of
the bi-directional distribution (MD and CD) of the material can be seen. This
buckling phenomena, not accounted for in classical theory, is characteristic of
corrugated board material behaviour under load, and has been the basis of R&D
investigations (Gunderson, 1981; Pijselman & Poustis, 1982; Thielert, 1984; Springer
et al., 1985; Pommier & Poustis, 1986a; Thielert, 1986; Pommier et al., 1988).
14
12
10
8
6
4
2
0
0 200 400 600 800 1000 1200 1400
Corrugated board grammage (g/m
2
)
ECT (kN/m)
B flute C flute BC flutes
Figure 11.33 Effect of grammage and flute size on ECT.
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Mathematical models of prediction
The application of finite element analysis has been developed to predict the
behaviour of corrugated board panels and structures.
A developed linear elastic analysis code, referred to as SYSTUS, is able to
evaluate the bending stiffness of corrugated board.
The corrugated medium defined in the calculation code incorporated trapezoidal
mesh structure and the models assumed perfect bonding between fluting and the
liners. By applying the technical theories of corrugated performance and with good
control of calliper (thickness) and board hardness in the box plant, it is possible to
predict, accurately, how a corrugated box will perform under a stacking load.
Figure 11.35 is a prediction of corrugated board shape produced using ANSYS
software.
Finite element software to predict package performance under load can be
applied for test cases, predicting the effect of complex design features such as
access (hand) holes.
Figure 11.34 Based on a photograph of stress distribution in a board panel under vertical compression.
Figure 11.35 Corrugated board shape predicted by ANSYS (software).
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11.3.1.3 Lifetime and safety factors
To define box compression (BCT) in the environment means that one takes the life
cycle of the box into account together with the duration of the stacking mode and
safety coefficients (factors).
As creep material behaviour is concerned, i.e. slow deformation over time under
load, the box performance has been simulated using the following experimental
protocol, named fatigue, resistance of the corrugated boxes.
Whereas the life of a box begins while the corrugated board is being produced,
the whole set of constraints which are mostly determining its enduring appearance
become manifest when the box is used in the course of distribution. The box is
subjected to many different kinds of stresses: vibrations, shocks, falls, ageing, and
sometimes cycles of moisture and temperature variations.
In the laboratory, it is possible to quantify these stresses in order to describe the
evolution, or variation, in the course of time of the performance of a box when it is
subjected to compression and when it passes through moist environments.
The box resistance to vertical compression (BCT) is the parameter that gives
the best account of the effects of transport and storage conditions, and of the
stackability of the boxes. The user is thus interested in obtaining the best possible
resistance of the box to vertical compression, not only at the time of purchasing
a box, but also throughout the life cycle of the box. This can be translated in terms
of a search for the maximum lifetime of the box, which can be expressed as the
time at the end of which the box will collapse under a calculated compression
load (BCT
0
).
This describes the standard course of creep tests which we have followed for
obtaining a representation of the box behaviour. For simulating the dynamic and
climatic stresses, we have subjected the box to a system of vibrations and we
have placed it in atmospheres with variable temperatures and humidities. In the
laboratory, it is possible to accelerate the time required for the box to collapse
under a given load – by selecting the load BCT
0
. According to the stress conditions
or the environment conditions, the time for the box to collapse depends on the
value of the load being applied versus the value of the compression strength of the
box (BCT
0
/BCT). For instance, if the box is stored at 23 °C and 50% RH, the load
required to cause the box to collapse between 5 and 15min is approximately 90%
of the box compression strength.
In the following example, RSCs, C flute, size 400mm ×300 mm ×300mm, made
with Kraft liners from 150 to 225 g/m
2
and various fluting mediums (recovered
papers and semi-chemical, from 110 to 180g/m
2
), have been tested in two different
environments.
The BCT values of the various cases have been measured under static conditions.
They fall within a range of 350 ± 50 kg at 23 °C and 50% RH, and within
130 ± 15 kg after having saturated them with moisture during 72h at 20 °C and
90% RH.
The lifetime versus the percentage of load being applied is plotted in the graph
shown in Figure 11.36. Each dot represents the average value of 10 measurements
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made on each composition. This average time is significant, since we have
verified, as Thielert (1984, 1986) also did that this time followed a normal law of
statistical distribution.
It has been observed that:
•
As expected, the passage through a moist environment significantly reduced
the compression strength compared with that which was obtained on the
same box specification stored in a dry environment. A box composition which
has withstood 310 kg average in a dry surrounding had the same lifetime as
the one which could withstand only 120kg in a damp surrounding.
•
Vibrations disturb the system’s stability: for a same lifetime, another box
composition which has withstood 300kg had its potential decreased by 40%,
meaning that it will only withstand a 170-kg load.
It is interesting to apprise the behaviour of each one of the box components.
A classification of papers is possible using the creep rate parameter.
From the creep rate of the paper, i.e. a test developed by Smurfit which is similar
to the short span compression of the paper components, it is possible to measure,
as a function of time, the dissipation energies involved during the deformation
under the stress being applied. It is logical to consider that the resistance to this
stress varies in an inverse relation versus the value of the energy being released.
Level of applied load (%)
80
60
40
20
51015200
100
0
Lifetime (min)
20 °C and 90% RH 23 °C and 50% RH + Vibrations 23 °C and 50% RH
Figure 11.36 Corrugated board lifetime versus compressive load applied.
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Thus, the more resistant the material will be, the smaller will be its deformation;
the amount of released energy will therefore be smaller.
Under fixed operating conditions as to stresses and time, working within the
elastic range of the material, it is possible to compare the papers together and to
define a fatigue resistance (FR) index.
This FR index is given by the relation:
(%)
in which W
ref
is a reference energy value selected arbitrarily as the lower limit for
the observed values, and W is the energy released through creeping. In order to
illustrate this proposition, we have opted to present the following results obtained
from a comprehensive sampling of many industrial papers available on the market,
and these results are expressed as the mean geometric values for the MD and CD.
If we bring together the set of creep rate measurements and the traditional
classification of papers according to their bursting index, it is found that the two
parameters vary inversely with each other; equally, from its very definition, the fatigue
resistance index is proportional to the bursting index, Table 11.8. Thus Figure 11.37
FR=
W
ref
W
----------
Table 11.8 Results illustrating creep rate, energy release and fatigue resistance (geometric mean values)
Notes: Experimental conditions: σ
0 MD
=18 MPa, σ
0 CD
=8MPa → σ
0
12MPa; creep time=15 min. Reference
energy: W
ref
= 60 kPa.
Nature of paper Burst index
Creep rate
(Pa
−1
s
−1
)
Energy release
(kPa)
Fatigue resistance
(%)
Test liner 180 g/m
2
2.5 5.7 130 46
Kraft liner 150 g/m
2
3.5 1.6 86 70
Kraft liner 150 g/m
2
4.5 1.2 76 80
8
6
4
2
0
123456
Creep rate (Pa
–1
s
–1
)
Burst index
Well
Test
liners
Kraft
Figure 11.37 Creep rate classes of packaging papers (Well = Wellendorf, fluting paper).