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INFLUENCE OF VARIOUS FACTORS 0N CUSHiON
LOADING RATE

Thesis for the Degree of M. S.
MlCHlGAN STATE UNIVERSWY
EN - LAANG KARL SHEU
1975

uIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII m z/

1293 10569 7191

 

 

 

 

 

 

 

This is to certify that the

thesis entitled

INFLUENCE OF VARIOUS FACTORS ON
CUSHION LOADING RATE

presented by

ln-Laang Karl Sheu

has been accepted towardsg'fulfillment
of the requirements for

MS degree in Packaging

J. W. Goff

 

Major professor

Date 2-27-76

 

0-7639

 

 

 

I I .

ABSTRACT

INFLUENCE OF VARIOUS FACTORS ON
CUSHION LOADING RATE

BY

Karl Sheu

The physical properties of many plastic cushion foams
vary with the rate of load applied. This means that the
loading rate will affect its performance. Thus, loading rate
should be considered as one of the design criteria for
package-cushion design. This study was intended to evaluate
some factors which would influence the loading rate of

cushions under test condition and in practice.

INFLUENCE OF VARIOUS FACTORS ON
CUSHION LOADING RATE
BY

In-Laang Karl Sheu

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
School of Packaging

1975

ACKNOWLEDGMENTS

I am greatly indebted to Dr. James W. Goff, whose

advice and timely assistance made it possible to finish

this thesis.

ii

TABLE

LIST OF TABLES . . . . . .
LIST OF FIGURES . . . . .
INTRODUCTION . . . . . I .
TESTING PROCEDURE . . . .
Selection of Sample . .
Sample Conditioning . .
Dynamic Loading Test .
Test Calculation . . .

DATA PRESENTATION . . . .

Effect of Drop Height .

OF CONTENTS

Effect of Cushion Thickness . . . .

Effect of Cushion Shape
Effect of Container . .

DISCUSSION . . . . . . . .

CONCLUSION . . . . . . . .

APPENDICES
I Calculation of Loading Rate from Shock
Pulses . . . . . . . . . . . . . . .
II Influence of Thickness of Corrugated

Pads on Loading Rate . . . .

III Loading Rates of Selected Creased

Corrugated Pads . . . . . . . . . .

REFERENCES . . . . . . .

iii

Page
iii

iv

Ch muww La)

H\D\l0\

21

23

25

27

3O

LIS T OF TABLES

Table Page
1 Loading Rates for Various Drop Heights . . . 7
2 Loading Rates for Various Thickness of

Foams . . . . . . . . . . . . . . . . . . . 8
3 Loading Rates for Various Thickness of

Firm Reclaimed Polyurethane . . . . . . . . 10
4 Loading Rates for Various Shapes of

Urethane Foam . . . . . . . . . . . . . . . ll,
5 Loading Rates for Urethane Foam Using Two

Different Containers . . . . . . . . . . . . 12
6 Influence of Compression History on

Loading Rate . . . . . . . . . . . . . . . . 17

11.1 Loading Rates for Corrugated Boxes with
Various Thickness . . . . . . . . . . . . . 26
III.2 Loading Rates for 200 Pound Test Pads with
Various Styles . . . . . . . . . . . . . . . 29
111.3 Loading Rates for 275 Pound Test Pads with
Various Styles . . . . . . . . . . . . . . . 29

iv

LIST OF FIGURES

Page
Typical package flat drop test shock
pulses . . . . . . . . . . . . . . . . . . . 19
Sine wave . . . . . . . . . . . . . . . . . 23

Styles of corrugated pads . . . . . . . . . 28

INTRODUCTION

Foamed polymeric materials possess properties which make
them applicable as impact absorbers. They can undergo large
compressive deformation and absorb relatively large amounts of
energy during deformation. However, the mechanical properties
of many cushioning foams vary with the rate of loading applied;
i.e., they exhibit rate-dependent behavior. The rate-depen-
dence can be due to various factors, such as the structure
of foams, compression of gas in closed cells as well as the
rupture of closed-cell walls.

The generally accepted dynamic testing methods of
cushioning materials, for example ASTM Test Method D1596,
more or less ignore the cushioning quality of the container
itself and some other factors which could cause the change of
loading rate. A series of analyses was proposed for studying
loading rate and investigating those variables which could
affect loading rate. Among them are:

1. Effect of drop height on loading rate.

2. Effect of variation of cushion thickness on loading

rate.

3. Effect of container variation on loading rate.

4. Effect of temperature variation on loading rate.

5. Effect of shape variation of cushioning materials

on loading rate.

No consideration was given to humidity, difference in manu-
facturing process, or other possible variables.

In this study, emphasis would be placed on the inter-
relation of loading rate in different types of tests rather
than on the correlation of mechanical behavior of foams with
their material properties. Besides, this study was not in-
tended to be a thorough evaluation of shock response or
loading rate of the package tested, but only comparison
which would indicate those factors that could contribute the
change of loading rate. Nor was it intended to make a

quantitative study of the effect of those factors.

TESTING PROCEDURE

Selection of Sample

 

Almost all the package-cushion foams available are
rate-dependent and are in many different densities, shapes,
thickness, etc., and can be in the form of molded, die-cut
or extruded pads. In this test, Dow Ethafoam 220(2.2 PCF),

an extruded material, was used.

 

Sample Conditioning
For each single loading test in the series, a new sample
must be used. After cutting the samples were exposed at
least for seven days in a humidity room (70t2°F, 50:2 per-
cent R.H. and good air circulation). This program makes‘
sure that the cushioning materials would approach equilibrium

moisture content from the previous condition.

Dynamic Loading Test

 

The basic equipment required consists of a shock machine,
a dummy load, and acceleration measuring and recording equip-
ment. The procedure followed is to construct a dummy load,
instrument this load and package it in a variety of ways
depending on the factors to be observed. It was intended
only to observe the effect of drop height on loading rate in
this test. No container was used here.

The dummy load used by School of Packaging is an 8 x 8

3

inch wooden block. With the cushion size set at 8 x 8 inches
the cushion loadings are accompanied by use of metal plates
resting on the cushions. Discrete weights of metal plates
were used to encompass the useful cushion-loading range. The
determination of optimum stress loading in the block was
purely empirical. The weight of test block and metal plates
was 39.25 pounds.

A fixture was secured over the block and made immovable
by setting a nut above the bar and one below it. This
restrained the block from moving upward away from the table
and restrained the bar from moving towards the table, which
would increase the stress on the block during shock. An
accelerometer was mounted in the block so that transient
acceleration pulse applied to the block in a vertical direc-
tion could be monitored. The impact in the test was measured
by using a coupler in conjunction with the accelerometer.

The output from the accelerometer was fed into a storage
oscilloscope. The peak "G" level and the duration of the
impact pulse were recorded.

In the drop test, the beginning drop height was 4 inches
and was increased by 4 inches on each successive drop until
24 inches was reached. After each drOp, each cushioning
material was replaced by a new one before making the next
drOp. This was felt to be more realistic, since it eliminated
the possible cumulative effect of repeated impacts on the

same cushion.

Test Calculation

 

The peak acceleration and the duration time received by
the oscilloscope were recorded. The method of calculation
of loading rate is shown in Appendix I. A loading rate list

was thus obtained and made the comparison readily available.

DATA PRESENTATION

A literature review showed that no data have been avail-
able to evaluate the effect of drop height on loading rate.

Actual laboratory work was done to calculate the loading rate.

Effect of Dr p Height

 

The test method was described in the previous part.
The peak acceleration and duration time are presented in

Table 1, along with the values of loading rate.

Table 1. Loading Rates for Various Drop Heights

 

 

 

Drop Height Shock Duration Loading Rate
in Inches in g's in msec in 106 lbs/min
4 21 20 ' 4.94

27 22 5.78
12 35 22 7.50
16 43 22 9.20
20 61 20 14.36
24 78 18 20.40

 

The following analyses of the other influencing factors
were derived from the existing data. The most common type of
data is the "cushion curve." The cushion curve shows what
peak acceleration will be transmitted by various thickness
of cushion for different values of Static stress. A consid-
erable number of cushion curves have been generated. The

solution for cushion loading rate, however, requires the

6

values of peak acceleration and duration time for each
drop.

The school of Packaging has run extensive drop tests for
cushioning materials in the past several years. Some data
are in the form ready for use. Cushion curves with accelera-
tion-time records of the shock prepared by Forest Products
Laboratory (FPL) can be also used for the analysis. The FPL
employed different measuring systems from that used by the
School of Packaging. It is not intended here to evaluate
the variation of test measuring devices. However, comparison
of the results for the purpose of evaluating each influencing
factor must be based on the same measuring instruments to

eliminate instrument variation.

Effect of Cushion Thickness

 

An arm type package drop tester was used to conduct the
drop tests (8). A drop height of 30 inches was set for all
cushioning materials. Both A-flute and B-flute boxes were
used. The weight of the dummy load was 11.5 pounds. The
test data and loading rates are shown in Table 2. Although
the concentration was on plastic foams in this study, there
are many cushioning applications for corrugated board loaded
as a cushioning pad. Corresponding test results for curru-
gated pads are presented in Appendix II.

Other test data developed at MSU (7) were expressed in
peak acceleration and velocity. The conversion of these

data into the form of peak acceleration and duration time

Table 2. Loading Rates for Various Thickness of Foams

 

 

 

Cushioning Thickness Box Shock Duration Loading Rate
Material in Inches Used* in 9's in msec in 10'7 lbs/min
Dow Ethafoam 1 A 89.7 6.0 2.06
Dow Ethafoam 2 67.8 7.0 1.37
Delvatex l A 81.2 6.0 1.87
max

Delvatex 2 A 55.4 7.5 1.02
Type K

Swedish Crucible 2 B 90.5 6.0 2.08
Expanded PS

Swedish Crucible 3 B 75.2 6.0 1.73
Expanded PS

Swedish Crucible 4 B 70.4 7.5 1.29
Expanded PS

Leewood 2 B 83.3 6.0 1.92
PE 13

Leewood 3 B 76.5 6.0 1.76
PE 13 .

Leewood 7B 2 B 61.0 8.0 1.05
Polyurethane

Leewood 7B 3 B 51.5 9.0 0.79
Polyurethane

Tbyad NF 2 A 49.1 11.0 0.62
Chemfoam

Toyad NF 3 A 32.0 13.0 0.34
Chemfoam

 

*Box used: A

B

A-flute box
B-flute box

is required. A means of doing this is described in reference
12. If it is supposed that the rebound velocity was 20 per-
cent of the impact velocity, then the velocity change would
be 120 percent of the impact velocity. The duration time
which corresponds to a specific drop can be computed from
these equations:

Am x 386.4 x T x 10‘3 = AV

AV = 1.2 x V

where:
Am = peak acceleration,
T = duration time, msec,
V = impact velocity, inches/sec, and

AV = velocity change, inches/sec.

Therefore, T can be obtained through the equation:

1.2 x v x 103
386.4 x Am

 

T:

The thickness of cushioning material, container used, shock,
duration time, and the corresponding loading rate are shown

in Table 3 for those cushions examined in reference 7.

Effect of Cushion Shape

 

The only available information about the effect of
cushion shape on loading rate was derived from references 13
and 14. The tests were conducted on urethane foams and
expressed as curves of accelerationetime records. Single-wall
200 pound test B-flute corrugated boxes were used. Each
package was dropped 24 inches to land flatwise on the bottom

of the box. The relevant figures are summarized in Table 4.

10

Table 3. Loading Rates for Various Thickness of Firm Reclaimed.

 

 

 

Polyurethane
Thickness Plate Weight V in Shock Duration Loading Rate
in Inches in lbs. inches/sec in 9's in msec in 106 lbs/min
1.983 4.0 152.7 54.3 7.3 4.29
1.983 4.5 150.8 54.5 7.2 4.89
1.983 5.0 152.7 54.9‘ 7.2 5.49
1.983 5.5 152.8 56.1 7.0 6.33
1.983 6.0 152.7 59.7 6.6 7.83
1.983 6.5 153.3 61.5 6.5 8.85
1.983 7.0 151.5 61.8 6.3 9.86
1.983 7.5 152.0 61.4 6.4 10.40
1.983 10.0 152.7 72.9 5.4 19.44
1.983 15.0. 151.6 90.4 4.3 45.41
2.041 4.0 152.2 51.9 7.6 3.93
2.041 4.5 151.9 54.3 7.2 4.86
2.041 5.0 153.5 53.0 7.5 5.09
2.041 5.5 152.8 54.8 7.2 6.03
2.041 6.0 153.5 59.0 6.7 7.61
2.041 6.5 152.6 60.7 6.5 8.73
2.041 7.0 152.4 60.6 6.5 9.41
2.041 7.5 151.8 61.8 6.4 10.41
2.041 10.0 152.8 67.7 5.8 16.80

2.041 15.0 153.0 84.8 4.7 34.46

 

11

The corresponding figures for corrugated board are presented

in Appendix III.

Table 4. Loading Rates for Various Shapes of Urethane Foam

 

 

 

Shape of Dummy Load Shock Time in Loading Rate
Foam in lbs in g's msec in 105 lbs/min
Side Pads 4.0 32.9 24.0 6.58

" " 7.8 21.4 30.8 6.50

" " 20.6 22.9 36.0 15.72

" " 34.0 32.9 36.0 37.28

" " 43.5 43.1 31.1 72.34
Corner Pads 4.0 22.5 31.0 3.48

" " 7.8 14.3 42.3 3.18

" " 13.7 19.3 42.9 7.40

" " 20.6 35.0 39.0 22.18

" " 39.2 56.3 35.0 75.66

 

Effect of Container

 

The container effect is observed to be an important
factor in the performance of cushioned packages utilizing
the side pads and corner pads for cushion application (13,
14). Either single-wall 200 pound test B-flute boxes or
cleated plywood boxes were used. Each package was dropped
flatwise from a height of 24 inches. The relevant data are

shown in Table 5.

12

Table 5. Loading Rates for Urethane Foam Using Two Different Containers

 

 

 

 

Cushion Container Dummy Load Shock Time in Loading Rate
Shape Used* in lbs. in g's msec in 105 lbs/min
Side Pads C 4.0 32.9 24.0 6.58
" " P 4.0 37.9 33.0 8.10
" " C 7.8 21.4 30.8 6.50
" " P 7.8 21.0 32.0 6.14
" " C 20.6 22.9 36.0 15.72
" " P 20.6 16.4 42.0 9.66
" " C 34.0 32.9 36.0 37.28
" " P 34.0 18.6 49.1 15.46
" " C 43.5 43.1 31.1 72.34
" " P 43.5 23.6 44.0 28.00
Corner Pads C 4.0 22.5 31.0 3.48
" " P 4.0 23.8 32.0 3.58
" " c 7.8 14.3 42.3 3.18
" " P 7.8 15.0 38.0 3.72
" " C 13.7 19.3 42.9 7.40
" " P 13.7 17.9 42.3 6.96
" " C 20.6 35.0 39.0 22.18
" " P 20.6 20.0 39.0 12.68
" " C 39.2 56.3 35.0 75.66
" " P 39.2 43.8 36.0 57.24
*Container Used: C = Corrugated Box
P = Plywood Box

 

I'll II II .l'IIII'q lllllllll'

DISCUSSION

Although so far the factors which affect the loading
rate are not completely known, it is evident that drop height,
cushion thickness, container type, and cushion shape do influ-
ence the loading rate. The effect of temperature will be
discussed later on.

Close examination of the drop testing data revealed
that loading rate varies with drop height. The higher the
drOp height is, the higher loading rate the cushion will
experience. This is due to the high peak acceleration and
short duration time the cushion is subjected to when dropped
from a considerable height. For one case, the loading rate
at 24-inches drop is almostiknn:times as large as the one at
4-inches drop. For this reason, adequate consideration of
the drop height is necessary.

Another influencing factor is the cushion thickness.
The shock level and duration time experienced at various
thickness indicates that loading rate decreases with the
increase of cushion thickness. This can be related to the
general idea that thick cushioning material tends to give
more protection on product than thin cushioning material;
i.e., it can decrease the loading rate on the cushion and
eliminate the product damage. While overpackaging or under-
packaging are equally undesirable, a further investigation

of the influence of cushion thickness is essential.

13

14

The third factor arises from the consideration of cushion

shape. It is obvious from the test data that corner pads
experienced substantial lower loading rates than side pads.
In drop testing, some kinds of cushion shape may prove to be
more protective than other shapes of the same material. The
reason is that some configurations tend to distribute the
force (or energY) received throughout the whole cushion and
hence decrease the loading rate. Every change in dimension
and geometric configuration should be thoroughly examined for
possible loading rate change.

The fourth factor involved the consideration of the
effect of the type of container. The container effect was
found to be an important factor in determining the severity
and the duration of shock experienced by the contents of a
cushioned package during rough handling. As shown in Table
5, the advantage of heavily loaded cleated plywood boxes
is evident. However, plywood boxes have somewhat less shock
protection for the light loads than did the single-wall fiber-
board boxes. This result would lead to an assumption of
possible differences in shock level and duration time and in
the resistance to downward movement of the dummy load pro-
vided by friction between the cushion and the vertical side
panels of the container. The difference at high static stress
for packages involving fiberboard boxes and plywood boxes
could be attributed to the energy absorption by the con-

tainers themselves. This example reveals the complexity

of container problem.

15

Unfortunately, it is not possible to obtain the informa-
tion regarding the temperature effect on loading rate. How-
ever, temperature does have some influence on loading rate.
Some work has been done on determining the effect of tempera-
ture extremes on the properties of package-cushioning materials.
Most of the programs devoted to such research involved static
testing, while others included dynamic loading on the materials.
The results of these tests performed on various samples of PE
foam, vinyl foam, and latex foam are mostly in the forms as
load versus deflection at room temperature, low temperature,
and elevated temperature.

Dynamic testing data in reference 5 revealed that for a
given static stress on a specific thickness of a typical
flexible polyurethane cushioning material, higher peak
acceleration and shorter duration time would be obtained for
a drop test at -65°F than for one at room temperature (70°F).
Some plastic foams, such as flexible polyurethane and poly-
vinyl chloride foams, appear to increase in stiffness continu-
ously from 60°F to -50°F, becoming almost rigid at 30°F. Also
rubber and rubber-bonded materials in general appear to
increase peak acceleration with a decrease in temperature.
However, the effect of temperature on the package, the foam and
container, is quite another story. It is to be noted that
the change of loading rate is not simply the combination of
the changes on the cushion and container. All presentations
to define loading rate change at temperature extremes must

be examined carefully.

16

No attempt is made here to evaluate the cumulative degra-
dation of the package protection caused by repeated package
impact, as would be experienced in service. Neither is there
any attempt to evaluate creep effect that might alter the
cushion loading rate after extended storage periods during
which the cushions support the dead weight of the content.

It must be borne in mind, however, that the load-compression
curve and dynamic response of some cushioning foams are sensi-
tive to previous compression history of the foams, exhibiting
a decreasing stiffness and load-bearing capacity with an
increasing number of compression cycles. Not all cushion

foams exhibit such a property. Some foams are almost com-
pletely free from the effect of a previous compression history.
Two examples (8) are shown in Table 6.

One interesting result has been pointed out by Wilson
(15) that both static and dynamic tests have established that
there is a significant increase in the effective stiffness of
a cushion when it is enclosed. This increase must be con-
sidered when designing protective packaging. The energy
absorbed by a cushion increases when the lateral expansion of
the cushion is restrained. This measure must be adopted in
cushion testing because the generally accepted testing methods
deal with the materials only rather than considering the
whole package as a complete system.

So far, no direct evidence supports the assumption for
the calculation of loading rate made in Appendix I. One

recent report by Notle (16) indicated that the approximation

l7

 

 

 

Table 6. Influence of Compression History on Loading Rate
Cushioning Drop Shock Time Loading Rate
Material No. in g's in msec in 106 lbs/min
Leewood 7B 2"
Polyurethane 1 61.1 1.05

" 2 61.1 . 1.05

" 3 61.1 1.05

" 4 61.1 1.05

" 5 61.1 . 1.05

" 10 61.1 . 1.05

" 15 61.1 1.05

" 20 61.1 1.05

" 25 61.1 . 1.05
Toyad NF 2"
Chemfoam 1 49.1 11.0 0.62

" 2 50.9 11.0 0.64

" 3 55.9 11.0 0.70

" 4 57.2 11.0 0.72

” 5 57.2 11.0 0.72

" 10 58.4 11.0 0.73

" 15 59.7 11.0 0.75

" 20 60.9 11.0 0.76

" 25 60.9 10.5 0.80

 

of irregular loading by intervals of constant stress rate to
predict creep and relaxation of polyurethane. Stressing which
varies with time in an irregular manner can be approximated
by intervals of constant rate. -This gives some implication
that the approximation of irregular loading by constant
loading rate as used in Appendix I could be a reasonable one

because dynamic testing is a fast procedure, in which the

duration time is expressed in milliseconds.

18

Obviously, each cushioning material exhibits a charac-
teristic shape of the shock pulse. The shock shape is
essentially the way in which the amplitude changes with time.
The shape of the shock pulse is dependent on the energy
dissipated during the impact, which in turn depends on the
package, the contents, as well as the surface the package
strikes. Figure l (8) illustrates the shock pulses received
by the dummy load during flat drop tests. These pictures were
hand duplicates of polaroid photograph of oscilloscope traces.
For certain shapes the shock pulse, especially those centrally
symmetric pulses, the calculation of loading rate may be
closer to the approximation used in Appendix I than those
with irregular shapes.

The interpretation of data calls for an exercise of
judgment, and differences of opinion would arise even if all
of the figures were available. For one thing, it is important
to note the damping effect of cushioning material. This
phenomenon may cause the complex shapes of the shock pulse
and result in change of the loading rate. The determination
of the values of peak acceleration and duration time requires
careful consideration.

In conducting a test to determine the loading rate, the
package is subjected to an impact on a rigid surface. Ideally,
surfaces on which packages might be dropped range from con-
crete floors, truck beds, to identical packages. Each of
these surfaces will result in a different shock. Thus, each

will impose a different loading rate. In actual distribution,

 

 

 

 

I\
/\
A

 

Figure l.

19

3.0 ms risetime
l pad "A" flute
corrugated board

3.0 ms risetime
3 pads "A" flute
corrugated board

6.0 ms risetime
1" Dow Polyethylene
Foam

13 ms risetime
4" Toyad type NF
Neoprene

7.5 ms risetime

2" Delvatex Type K

Reclaimed polyure-
ane

Redrawn from reference 8, p.

Typical package flat drop test

 

 

 

> > > >= >—

 

3.0 ms risetime
2 pads "A" flute
corrugated board

3.5 ms risetime
4 pads "A" flute
corrugated board

6.0 ms risetime
3" Leewood type
PE-13 Reclaimed
Polyurethane

9.0 ms risetime
3" Leewood type
78 Reclaimed
polyurethane

5.0 ms risetime
2" Toyad type
KR—l Expanded
polystyrene

shock pulses.

20

containers usually rebound to some extent immediately after

a flat drOp. This phenomenon causes the increase of peak
acceleration experienced by the item. No attempt has been
made in this study to investigate the loading rate under such

conditions.

CONCLUSIONS

In review, the loading rate under dynamic test is in
the range of 105 to 107 pounds per minute. This is a tre-
mendously high value. Some cushions either broke down or
bottomed out under high loading rates. Not only did the
physical properties of cushioning materials have significant
changes, but also the shock responses of the packages exhibit
extraordinary behavior under such conditions. However, little
work has been done in this area. This probably goes unnoticed
in many cases because conventional methods do not stress
either the importance of loading rate or the factors which
affect loading rate.

Generally, the conventional testing methods, those
employing the dynamic testing principal, seek to:

1. simulate as nearly as possible, with a compact and
simple device, the effects of rough handling and drOp on a
cushioned product;

2. record as accurately as possible the results of
the tests;

3. determine to varying degrees of accuracy the
possible effects of complex dynamic responses and their use-
fulness as design criteria.

Further study is recommended to investigate the pos-
sible quantitative relationships between loading rate and

those influencing factors. It would be possible to obtain

21

It i If I ‘1'!!! II III’II' II. I J‘Il‘lllll II I

22

more accurate results using electronic differentiator and
automatic recording instruments in future cushion evaluations.
The differentiator would automatically determine the slope

of each point along the curve and locate the maximum slope
which is the loading rate. It is believed that more accurate
and applicable information can be obtained through this

approach.

(I II ‘ I'll I III! II II. ‘(II

APPENDICES

ll- I

APPENDIX I

CALCULATION OF LOADING RATE FROM SHOCK PULSES

APPENDIX I

CALCULATION OF LOADING RATE FROM SHOCK PULSES

The shock pulse generated in a drop is generally an
approximate half-sine wave (Figure 1.1). The amplitude of a
shock is commonly measured in "g's" (acceleration of gravity).
The horizontal axis represents the length of time or duration
of shock. By definition, loading rate is the force applied
over certain periods; i.e., pounds per minute in this study.
For dynamic testing, loading rate can be best represented

by the maximum slope of the shock pulse.

  

a
le—-——-‘c-——-’|

Figure 1.1. Sine wave.

The slopes of the curve at point a and point b are
approximately equal to zero. The slope reaches maximum at
point c. Thus, the slope at c can be used to represent the
loading rate. Since slope varies along the curve, an approx-
imation for the loading rate can be reached by plotting a
straight line between point a and point b. The slope of

the straight line could be regarded as the slope of the curve

23

24

at point c; i.e., the approximate value of the loading rate.

Therefore, the loading rate is equal to

A x W
R = .3L—~——— x 60 x 103
t1
where:
R = loading rate, in lbs/min.,
t1 = duration time between a and b, in msec.,
= weight on the cushion, in lbs., and

Am = peak acceleration divided by acceleration of gravity.

Generally, shock data are reported in the form of peak
acceleration and total duration time rather in partial dura-
tion time as t1 in the curve. Therefore, a second approxi-
mation is required. A simple solution could be obtained

by assuming the partial duration time t1 equal to one half

of the total duration time; i.e.,

where T is the total duration time in msec.
Accordingly, loading rate from dynamic testing could
be computed from the equation:

W x Am 3
R = —————— x 10 x 60
t
1
W x Am
= -————— x 1.2 x 10

APPENDIX II

INFLUENCE OF THICKNESS OF CORRUGATED

PADS ON LOADING RATE

APPENDIX II
INFLUENCE OF THICKNESS OF CORRUGATED PADS

ON LOADING RATE

The four groups of data presented here (8) were derived
by utilizing instrumented dummy loads cushioned with A-flute
200 pound test corrugated pads. A—flute containers were used.
Each package was dropped 25 times. Only drop 1 was recorded
here.

Group 1 used one corrugated pad placed so that the
flutes ran at right angles to the flutes directly beneath.
This meant that the dummy load was cushioned by three layers
of corrugated board (two flap layers and one pad). Each
layer of board had the flutes running at right angles to the
layers adjacent to it.

Group 2, 3, and 4 used two, three, and four pads,
respectively. In each case, the flutes were placed at right
angles to those in the adjacent layers.

The weight of the dummy load was 11.5 pounds. Table
11.1 shows that loading rate decreases as the thickness

increases (or the number of pads used increases).

25

Il‘lll'

26

Table II.l. Loading Rates for Corrugated Boxes with Various

 

 

 

Thickness
Group Shock in g's Duration Loading Rate
in msec in 106 lbs/min
1 123 3.0 5.64
2 141 3.0 6.49
3 103 3.0 4.74
4 85 3.0 3.36

 

Group 2 is exceptional, possibly due to experimental error.

APPENDIX III
LOADING RATES OF SELECTED

CREASED CORRUGATED PADS

l . I|q l I II [I]. I‘ll ‘l' I I ll.‘ ‘1' {I III

APPENDIX III
LOADING RATES OF SELECTED
CREASED CORRUGATED PADS

The data were based on reference 10. The corrugated
boards used in the construction of the test pads were 200
pound test or 275 pound test C—flute board. The three pad
styles chosen are presented in Figure III.2. Finished pad
dimensions for all pad style were 8" x 8" x 2". Each package
was dropped from a height of 30 inches. The package drop
tester employed was an L.A.B. spring loaded tester. The test
data are shown in Table III.2 and Table III.3.

It is interesting to note the loading rate variation
under different static stresses. For pad style A, it exhibits
considerably high loading rate under low static stress. While
under high static stress, 0.304psi or higher, pad style A
appears to have lower loading rate as compared with the other
two pad styles, especially in the use of 275 pound test board.
Apparently, loading rate depends on the stress applied, pad

material, and pad style.

27

Ill

28

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

STYLE A PAD

STYLE B PAD

 

 

 

 

 

 

 

 

 

 

 

STYLE C PAD

Source: Redrawn from reference 10, p. 3.

Figure III.2. Styles of corrugated pads.

 

29

Table III.2. Loading Rates for 200 Pound Test Pads with
Various Styles

 

 

 

Pad Stress Dummy Load Shock Duration Loading Rate
Style in psi in lbs in g's in msec in 106 lbs/min
A 0.192 12.3 37 10.0 5.46

B 0.192 12.3 28 18.2 2.28

C 0.192 12.3 28 16.4 2.52

A 0.304 19.5 11 13.6 1.90

B 0.304 19.5 16 11.8 3.18

C 0.304 19.5 11 12.7 2.02

A 0.417 26.7 11 17.3 2.04

B 0.417 26.7 12 14.5 2.66

C 0.417 26.7 11 25.0 1.40

 

Table III.3. Loading Rates for 275 Pound Test Pads with
Various Styles

 

 

 

Pad Stress Dummy Load Shock Duration Loading Rate
Style in psi in lbs in g's in msec in 106 lbs/min
A 0.192 12.3 31 10.0 4.20

B 0.192 12.3 30 12.7 3.48

C 0.192 12.3 30 14.5 3.06

A 0.304 19.5 16 10.9 3.44

B 0.304 19.5 11 10.9 2.36

C 0.304 19.5 5 20.0 0.58

A 0.417 26.7 11 12.7 2.78

B 0.417 26.7 11 4.5 7.84

C 0.417 26.7 7 5.5 4.08

 

REFERENCES

10.

REFERENCES

Mustin, G. S. "Theory and Practice of Cushion Design,"
SVM-Z, The Shock and Vibration Center, 1968.

U.S. Department of Defense Military Standardization Hand-
book, Package Cushion Design, Military Handbook 304,
par. 3.2.1.2.5.1. U.S. Naval Supply Depot, Philadelphia,
Pa., Nov. 1964.

Stern, R. K. "Design Criteria for Wood and Fiber Pack-
aging and Package Cushion Design," Amer. Management
Asso. Packaging Series, No. 52, 1957.

Mustin, G. S. "A New Approach to Package Cushioning
Design," Shock and Vibration Bulletin, No. 35, pt.
5, pp. 193-202, Feb. 1966.

Gigliotti, M. E. "Design Criteria for Plastic Package-
Cushioning Materials," Plastec Report 4, Plastics
Technical Evaluation Center, Picatinny Arsenal, Dover,
N.J., 1961. i

Gigliotti, M. E. "Investigation of Cushioning Materials,"
Modern Packaging, Vol. 34, No. 1, pp. 148-52, 262,
Sept. 1960.

Goff, J. W. and Blake, H. C. "Acceleration-Stress Pro-
perties of Additional Selected Cushioning Materials,"
MSU School of Packaging, Supplement to Technical
Report No. 1, Apr. 1962.

Goff, J. W. and Blake, H. C. "Response of Some Shock
Measuring Devices to Package Drop Test Shocks," MSU
School of Packaging, Technical Report No. 3, June 1964.

Goff, J. W., Blake, H. C., and McGinnis, M. A. "The
Degradation of Corrugated Board Utilized in Package
Drop Tests," MSU School of Packaging,Technical Report
No. 10, Sept. 1965.

Goff, J. W. and Blake, H. C. "The Energy Absorbing Pro-

perties of Selected Creased Corrugated Pads," MSU
School of Packaging, Technical Report No. 11, Apr. 1966.

30

I; III... III-I. II .I. I I I .I II

ll.

12.

13.

14.

15.

16.

31

Goff, J. W., Pierce, 8. R., and McCall, D. G. "The
Application of the Shock Spectrum Derived Damage
Boundary Theory to the Evaluation of the Shock Trans-
missibility of Corrugated Board," MSU School of
Packaging, Technical Report No. 16, Apr. 1969.

U.S. Department of Commerce Project No. 4-35711, Sub-
mitted by MSU School of Packaging, Feb. 1974.

Jordan, C. A. "Container Effects in Cushioned Packages:
Urethane Foam Side Pads," U.S. Forest Ser. Res. Pap.
FPL 91 Forest Products Lab., Madison, Wis. 1968.

Jordan, C. A. "Container Effects in Cushioned Packages:
Urethane Foam Corner Pads," U.S. Forest Serv. Res.
Pap. FPL 109 Forest Products Lab., Madison, Wis., 1969.

Wilson, K. S. "Relative Energy Absorption Properties of
Free and Enclosed Cushions," MSU Department of Forest
Products, Master thesis, 1958.

Notle, K. G. and Findley, W. N. "Approximation of
Irregular Loading by Intervals of Constant Stress
Rate to Predict Creep and Relaxation of Polyurethane
by Three Integral Representation," Transaction of
the Society of Rheology, Vol. 18, No. 1, pp. 123-143,
1974.

 

"IIIIIILIIIIIIIIIIIII‘5