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ON THE EEFECT OF MOISTURE CONTENT ON THE
SHOCK TRANSMISSION PROPERTIES OF
HONEYCONI CUSHIONINC

By

Punnepe Aevenit

A THESIS

Submitted to
Hichigen Stete university
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

School of Peckeging

1988

ABSTRACT

ON THE EFFECT OF MOISTURE CONTENT ON THE
SHOCK TRANSMISSION PROPERTIES OP
HONEYCOMB CUSHIONING

37

Punnape Asvanit

The effect of moisture content on the cushion curves for Honeycomb was
investigated and a mathematical approach aimed at the development of a
model to predict the peak acceleration was attempted. Two different cell
sizes of Honeycomb having various moisture contents were used to
determine static crushing strengths and dynamic shock transmission
values for three different drop heights at seven different static
stresses. The two mathematical models attempted were the adiabatic air
compression model and an energy approach based on a dynamic extension of
the static stress strain curve. Because of the complicated structure of
Honeycomb, neither model provided accurate results and it was therefore
concluded that modelling was impractical. A curve fitting approach which
resulted in a high degree of correlation with the experimental data was

used instead.

Dedicated to my parents, Sermsuph and Sutham Asvanit

iii

ACKNOWLEDGMENTS

I would like to express my sincere thanks to Dr. Gary J. Burgess as my
advisor for his understanding, guidance, and time. There are no words

that can express my appreciation.

I would also like to thank Dr. Paul S. Singh for his thoughtfulness,

support, and advice as a member of my committee.

I would also thank to Dr. George E. Mase for his time and support as a

committee member.
Also, special thanks to Mr. Mark Jacobson, Director of Marketing for

International Honeycomb Corporation, for providing the materials and

funds for this research.

iv

TABLE OF CONTENTS

LIST OF TABLES eeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
LIST op FIGURES ................................................
LIST OF SYMBOLS eeeeeeeeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
CHAPTER 1 eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
INTRODUCTION AND LITERATURE REVIEW eeeeeeeeeeeeeeeeeeeeeee
CHAPTER 2 ......................................................
MATERIALS AND TEST METHODS ..............................

1 Materials and Storage Conditions ..................

2.
2.2 Determination of the Moisture Content .............
2.3 Static compression Test eeeeeeeeeeeeeeeeeeeeeeeeeee
2.

4 Drop Test eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

CHAPTERB OOOOOOOOOOOOOOOOOOOO...0.0.0.0...OOOOOOOOOOOOOOOOOOOOO
RESULTS OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO0.00000000000000.
CMPTERA 0.0.0.0000...OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

ANALYSIS OF DATA eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

4.1 Adiabatie Model eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
4.2 Static Stress Strain Curve Model ..................
4.3 Curve Fitting Approach eeeeeeeeeeeeeeeeeeeeeeeeeeee

CHAPTER 5 eeeeeoeeeeeeeeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

DISCUSSION AND CONCLUSIONS eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
APPENDICES

APPENDIX A : DATA TABLES eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

APPENDIX B 2 THE CORRELATION COEFFICIENTS 0000000000000...

APPENDIX C 2 THE COMPUTER PROGRAM FOR THE CURVE FIT .000000
' COEFFICIENTS

APPENDIX D 1 METHODS OF MANUFACTURING MONEYCOMB MATERIALS 0

REFERENCES COO...COOO0.0...OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.

V

vi

vii

viii

10
10
10
11
12
13
16
16
19
19
19
23
26
39

39

43
53
57
59

61

TABLE

LIST OF TABLES

Equilibrium moisture content for the 1/2 inch and
3/4 inch cell sizes at the 4 moisture conditions
after 14 days of storage

The initial peak stress and strain for the 1/2 inch

and 3/4 inch cell sizes at the 4 moisture conditions

Data for
1/2 inch

Data for
3/4 inch

Data for
1/2 inch

Shock
for a

Shock
for a

Shock
for a

Shock
for a

Shock
for a

Shock
for a

Comparison between

the moisture content for the 3/4 inch and
cell sizes at the 4 moisture conditions

the initial peak stress and strain for the
cell size at the 4 moisture conditions

the initial peak stress and strain for the
at the 4 moisture conditions

cell size

transmission
24 inch drop height for 4

transmission
30 inch drop height for 4

transmission
36 inch drop height for 4

transmission
24 inch drop height for 4

transmission
30 inch drop height for 4

transmission
36 inch drop height for 4

data for the

data for the

data for the

data for the

data for the

data for the

experimental

and the correlation coefficient

Comparison between experimental
and the correlation coefficient

vi

3/4 inch
moisture

3/4 inch
moisture

3/4 inch
moisture

1/2 inch
moisture

1/2 inch
moisture

l/2 inch
moisture

cell size
conditions

cell size
conditions

cell size
conditions

cell size
conditions

cell size
conditions

cell size
conditions

and calculated data .........
for the 3/4 inch cell size

and calculated data .........
for the l/2 inch cell size

PAGE

l7

17

43

43

44

45

46

47

49

50

51

53

SS

LIST OF FIGURES

FIGURES
l. Crossection of a Honeycomb cushion ooooooooooo-ooocoo-cocoo-
2. A typical stress strain curve for Honeycomb ................
3. A typical shock pulse recorded on the oscilloscope .........
a. Free body diagram of a Honeycomb cushion at .................
maximum compression in a drop
5. Comparison between the curve fit and experimental ..........

10.

11.

results for the 1/2 inch cell size for a 24 inch
drop height at 3 moisture conditions

. Comparison between the curve fit and experimental ..........

results for the 1/2 inch cell size for a 30 inch
drop height at 3 moisture conditions

. Comparison between the curve fit and experimental ..........

results for the 1/2 inch cell size for a 36 inch
drop height at 3 moisture conditions

. Comparison between the curve fit and experimental ..........

results for the 3/4 inch cell size for a 24 inch
drop height at 3 moisture conditions

. Comparison between the curve fit and experimental ..........

results for the 3/4 inch cell size for a 30 inch
drop height at 3 moisture conditions

Comparison between the curve fit and experimental ..........
results for the 3/4 inch cell size for a 36 inch
drop height at 3 moisture conditions

Methods of manufacturing Honeycomb material ...............

vii

PAGE

15

22

33

34

35

36

37

38

60

N

LIST OF SYMBOLS

initial pressure before compression, (14.7 psi.)

final pressure at any instant during compression, (psi.)
initial volume before compression, (inch3)

final volume at any instant during compression, (inch3)
ratio of specific heats, (1.4 for air)

drop weight, (lb)

drop height, (inches)

deflection, (inches)

load bearing area, (inchz)

cushion thickness, (inches)

buckling stress, (psi.)

maximum strain, (inches/inch)

static stress, (psi.)

peak acceleration, (g's)

calculated peak acceleration, (g's)

experimental peak acceleration, (g's)

variance

sum

number of data

a,b,c,d,e,f,g,p,q,r coefficients

viii

m4
INTRODUCTION m 1.1th mm

During the period from 1953 to 1959, the Structural Mechanical Research
Laboratories at the University of Texas in Austin,Texas, under contract
with the Delivery Quartermaster Research and Development command [1,2],
had investigated many kinds of cushion materials to determine the best
available material suitable for single drop aerial delivery.
Specifically, the dynamic stress strain curves were investigated to
provide information about the energy absorption characteristics of the
material from which the cushion properties of the material could be
determined. Honeycomb cushioning was determined to be the cushion most
suited for this particular use. The structure of Honeycomb is a core
consisting of oval cells bounded on both sides by curved panels as shown
in Figure l. The entire structure is made from unbleached Kraft
linerboard paper. The oval core structure is constructed from Kraft
paper with a 33 pound basis weight and the face panel from 69 pound
basis weight linerboard. Following the selection of Honeycomb as the
most practical cushioning material for aerial drops, the many factors
which affect the dynamic stress strain curve such as density, moisture
content, impact velocity, and temperature were investigated. Hopf [3]
studied the effect of moisture content on the static stress strain curve
of Honeycomb cushion and found that the stresses and consequently the
energy absorption capabilities decrease as the moisture content

increases. Later, Ripperger [4] published a paper on the energy
1

 

 

-face

My ocore

- face

 

 

 

 

 

 

 

 

 

W
1————w—-+

Figure l : Crosaection of a Honeycomb cushion

3

absorption characteristics of paper Honeycomb based on research
conducted at the University of Texas in Austin. In 1983, cushion curves
for Honeycomb were experimentally developed by Singh [5] under standard
lab conditions of 72'F & 50$ RH. To date, this body of knowledge
constitutes virtually all that is known about the cushioning properties
of honeycomb. Still, some very important behavioral characteristics of
Honeycomb came out of these analyses. The most important of these are

brought out in the static stress strain curve.

A typical static stress strain curve for a Honeycomb cushion is shown in
Figure 2. The various parts of the curve correspond to three distinct
types of behavior during compression. During the first stages of
compression, the stress builds up very rapidly in a nearly linear
fashion. The material compresses elastically with no visible change in
shape until a point is reached where the Honeycomb core starts to
buckle. Buckling continues under a nearly constant reduced stress until
the cushion reaches a strain of about 65$. At this point, all of the
the Honeycomb cells have completely collapsed and the Honeycomb cushion
acts like a solid block of paper under compaction. Therefore, the stress
builds up rapidly again and exceeds the initial peak stress as the

applied load increases.

The energy absorbed per unit volume of cushion during compression is
just the area under the stress strain curve up to the point of
compression. This includes energy which is dissipated and stored energy
which is recoverable. The amount of recoverable elastic energy is

typically very small compared to the total energy absorbed during impact

/

 

 

 

 

5
since buckling of the Honeycomb cell walls is irreversible. The stress

strain curve during unloading from the compaction stage is also shown in
Figure 2. The area under this curve is the elastic energy recovered
during the rebound stage of an impact and corresponds to the rebound
energy per unit volume of cushion given back to the impacting object.
The ratio of this rebound energy to the energy dissipated is called the
‘ Resilience ' [4] which is considered to be a fundamental dynamic
material property related shock absorption ability. Since an excessive
amount of rebound energy given back to an impacting object is
potentially damaging to this object simply because this subjects the
object to repeated impacts, a cushion with a high resilience is not
considered to provide adequate protection. Honeycomb cushions typically
have very low resilience values which are essentially constant up to
compaction and therefore are considered to be very good dissipaters of
impact energy. Consequently, Honeycomb is an excellent cushion material
for single drop use. The resilience however rises when the cushion is
compressed to a strain of around 70‘ to 75‘ [2] since this is the point
at which compaction dominates. After this point, the stress increases
rapidly which results in large decelerations. Ideally, the cushion
designer would like to operate in the low stress region (flat part) of
the static stress strain curve since this results in the smallest
deceleration. For this reason, Hitting [6] recommends a precompression
of 0.2 inches before using it as a cushion in order to overcome the
initial peak (bulking) stress. However, if complete crushing of the pad
is expected, precompression is not nesessary. In general, the larger
cell size cushion is less resilient than the smaller cell size cushion.

Also, resilience tends to decrease when the impact velocity increases.

The dynamic stress strain curves obtained from five grades of Honeycomb
material produced results which were similar in shape to the static
curves except that the dynamic stresses were higher [2]. The grade of
Honeycomb cushion is simply a measure of its overall density due to cell
size, different combinations of paper basis weights and percent resin
impregnation. The percent difference between the static and dynamic
stress for a given strain depends on the cell size ,the cushion density,
and processing. Karnes et al [2] tested five untreated Honeycomb grades
and showed that for a core density range of 1.0 lb/ft3 to 2.6 lb/ft3,
the average dynamic energy absorption is about 44$ higher than the
static value. The maximum strain under dynamic test conditions at the
point of bottoming out (compaction) was about 2 to 5 percent higher than

the static maximum strain value.

The effect of density on peak stress was also studied [2]. Cushions with
densities ranging from 1.0 lb/ft3 to 3.0 lb/ft3 were used and the peak
(buckling) stresses were found to range from 1400 lb/ft2 to
10,000 lb/ftz. The effect of cushion density on dynamic energy
absorption by changing the strain from 70‘ to 80‘ was also studied. It
was found that the increase in energy absorption of the 1.0 lb/ft3
density cushion was 15‘ and for the 3 lb/ft3 density cushion, 22‘. But
the variation in density among two hundred 3/4 inch cell size Honeycomb
samples made from paper with a basis weight of 99 lb. was found to be
35‘ and the variation in maximum crushing stress was 25‘ [2]. Therefore,
even though density seems to influence the energy absorption ability

of Honeycomb material, variations in density among samples from the same

7

lot obscure the relationship between the two. Other factors however also
effect the crushing strength. Among these are cell size, the thickness

of glue line, processing, moisture and temperature.

When Honeycomb is subjected to different relative humidity environments,
it normally takes about 14 days for it to reach equilibrium although 90‘
of the equilibrium moisture content is absorbed or desorbed within the
first 48 hours [3]. The size of the specimen is of course the major
factor that determines the time it takes for the sample to reach its
equilibrium moisture content. For Honeycomb with a low moisture content,
the static stress strain curve shows a dramatic reduction in stress
after the initial peak stress is reached because of the brittle nature
of the structure. For Honeycomb with a high moisture content, resistance
to buckling is diminished so this reduction is not as pronouced.
Moisture content nevertheless affects the static stress strain curve
significantly and the effects are different depending on ‘ moisture
content and cell size. 0n the average, Honeycomb shows a decrease in
energy absorption of around 60‘ when the moisture content is increased
from 6‘ (dry) to 20‘ (wet). In the dynamic stress strain curve case, for
the 3/4 inch cell size, an increase in moisture content did not effect
the initial peak stress until the moisture content was more than 12‘ and
the decrease in average stress was found to be around 45 percent when a
moisture of 17‘ was reached [1]. For the 1/2 inch cell size, the average
stress decreased gradually to about 25‘ when the moisture content was
increased from 10‘ to 24‘. For light grade Honeycomb with a 1 inch cell
size, there is no significant difference in stress due to moisture

content. It was very interesting to find that after exposing Honeycomb

8
to the weather for 30 days during which 4.5 inches of rain fell and then

drying the sample in sunlight for 3 days, no change in the crushing

strength was detected over unweathered samples.

Impact velocity and temperature are two additional factors which were
studied. The effect of impact velocity on energy absorption
characteristics of Honeycomb was found to be insignificant for impact
velocities up to 90 fps [2]. Temperature seems to be a factor that
affects the crushing strengh of Honeycomb only through its effect on
moisture content. There is only a slight difference in average crushing
strength between O'F and 85'F for low moisture contents [4]. An increase
in the moisture content at O'F has the net effect of raising the

crushing strength due to freezing.

The final factor which affects Honeycomb cushion performance is the
perimeter to load bearing area ratio.. A high perimeter to area ratio
causes ‘ blowout ' of the cell walls along the edges which then reduces
its resistance to compression. This blow out occurs as a result of an
unbalanced pressure from the air trapped in cell during compression.
Lighter density Honeycomb is more vulnerable to blow out. By keeping
this ratio small and the impact velocity less than 60 fps, this factor

is not a serious problem.

The research performed by Singh et al [5] on standard Honeycomb was
aimed at evaluating the effects of cell size, cushion thickness and drop
height on the shock transmitted. All of the samples used in this study

were stored at standard conditions of 72'F and 50‘ RH and the drop

9

testing was done under the same conditions. Honeycomb was found to yield
the typical concave cushion curves except at the bottoming out point
where the peak acceleration increased rapidly. The purpose of this study

is to extend this work to include the effects of moisture content.

m1

MATERIALS AND TEST METHODS

2W

The Kraft Honeycomb cushions used in this research were manufactured by
International Honeycomb at University Park Illinois. In this study, two
different cell configurations, l/2 and 3/4 inch, were tested. Samples
measuring 8'x8” were carefully cut from 3' thick Honeycomb stock and
separated into l/2' and 3/4' cell groups. The specimens were further
divided into four groups and placed in four different temperature and
humidity conditions for at least 2 weeks in order to achieve equilibrium
with the ambient atmosphere. The four conditions were :

a) lOOiZ'F & 3213 ‘ R.H.

b) 99il'F & 83i3‘R.H.

c) 4112'F & 8813 ‘ R.H.

d) Freezer @ S'F
which represent various combinations of equilibrium moisture contents
within the samples. To achieve these conditions, humidity chambers were
used. The temperature and humidity of the chambers containing the
samples stored in conditions (b) and (c) were automatically controlled.
For the others, only the temperature was automatically controlled and
the relative humidity was left dependent on the temperature. The
humidity chambers remained closed except for opening and closing so that

the variation in relative humidity was taken to be that characteristic
10

11

for this equipment, 13‘. A psychrometer was periodically used to verify
the temperatures and humidities for the first three conditions. Since no
reliable estimates of relative humidity could be made inside the
freezer, the moisture content for the last case was left undetermined

but is expected to be low.

MW

Method: The ASTM D644-55 method [7] which is the standard for
determining moisture content of paper material by oven drying was
followed with the exception than an airtight weighing container was not
used to transfer the specimen from the vacuum oven to the balance.
Instead, some of the specimens were transfered from the conditioning
chamber to the balance by wrapping them in a polyethylene bag to prevent
moisture loss to the atmosphere during transfer. The remaining samples
were left in the chambers for drop testing later. The specimens were
weighed as quickly as possible after removal from the bag. The initial
weight was recorded and the specimens were placed in a vacuum oven for 6
hours at 90'F. The oven used was a Vacuum Oven Model No. 5831
manufactured by National Appliance Company and the scale was an
Analytical Balance Hodel AB 160 manufactured by Mettler Company. After 6
hours, the vacuum oven was flushed with nitrogen and the specimens were
immediately transfered to a glass desiccator filled with anhydrous CaSO4
and allowed to cool to room temperature for at least 45 minutes. They
were then weighed to determine the dry weight. Each weighing was done in
duplicate. The moisture content on a percent dry basis was then

determined by

12

Percent Moisture - [ (W1 - w2)/w2 ] x 100
where WI - original weight of the moist specimen and

"2 - weight of specimen after vacuum oven drying
The percent moisture contents of the specimens were determined after

seven and fourteen days of storage.

WW

Haterials: The two different cell sizes of Kraft Honeycomb cushions
measuring 8'x8' were conditioned at the 4 different conditions for two
weeks.

Apparatus: A Lansmont Model 76-5K compression tester with a capacity of
6000 pounds was then used to perform the compression test. The output of
the load cell was coupled to an Allen Datagraph Incorporated series 715
plotter which recorded the entire force versus deflection curve during
compression with the tolerance of $0.3‘ on force.

Method: Each specimen was enclosed in a polyethylene bag to prevent any
change in moisture content during the test. A 50 pound preload was
applied and the force was increased until the strain reached 90‘. Using
the force versus deflection curves obtained from the plotter, the peak
compression force and corresponding deflection were recorded for five
identical specimens at each moisture condition and cell size. The stress
versus strain curve was obtained by dividing the force by the load

bearing area and the deflection by the cushion thickness respectively.

13
WE

Materials: Specimen sizes varied depending on the desired static stress
(pounds per square inch) because of practical load limitations imposed
by the drop tester:

a. A specimen size of 8"x8' was used for static stresses ranging
from 0.3 to 2.3 psi.

b. A specimen size of 6'x6' was used for static stresses ranging
from 2.49 to 4.09 psi.

c. A specimen size of 4”x4" was used for static stresses ranging
from 4.4 to 5 psi.

Some of specimens were cut to the required size using a bandsaw before
placing them in the controlled condition chambers.
Apparatus: The equipment used for the drop test consisted of:

l. A Lansmont Corporation Model 23 cushion tester with a flat
dropping head onto which ballast weights could be loaded, a lifting
mechanism, and rebound break trigger switch.

2. A Dytran Model 3030A piezoeletric accelerometer with a output
characteristic of 10 mV/g's and a tolerance of 12‘ was mounted on the
droping head of the drop tester.

3. A Kistler Model 5116 AC piezotron coupler with a tolerance of
15‘ was used to amplify the output of the accelerometer.

4. A Kikusui 20 MHz series 5020-ST storage ocilloscope with a
tolerance of i3‘ received the signal from the coupler and displayed the
shock pulse from the accelerometer. The accelerometer mounted on the
free falling dropping head responds to the shock incurred by the
dropping head contacting the cushion and sends a signal though the

coupler for amplification. The enhanced signal is then sent to the

14
oscilloscope where the shock pulse is displayed and stored on the

screen. A typical shock pulse recorded on the oscilloscope is shown in
Figure 3. The peak acceleration and the shock duration was determined
using the oscilloscope settings and the accelerometer output
characteristic. For example, in Figure 3, the height of the shock pulse
on the oscilloscope screen is 3.2 div. Therefore, the output of the
accelerometer is 3.2 div x 100 mV/div - 320 av and the peak acceleration
is 320 mV/lOmV/g - 32 g's. The width of the shock pulse is 4 div and
therefore the shock duration is 4 div x 5 ms/div or 20 ms. In reading
the peak acceleration on the oscilloscope, an error can occur due to the
thickness of the trace which is typically 0.1 division. The percent
error depends on the vertical sensitivity and the peak acceleration
values. Since in this research 3 different vertical sensitivities were
used, the percent error is based on the maximum value which is 6.25‘.
For example, using a vertical sensitivity of 100 mV/div to record a 16 g
peak acceleration, the error can be 0.1 div/1.6 div. or 6.25‘.

Hethod: The ASTM 1596-78a method [8] for determining the Shock
Absorption Characteristics of Package Cushioning Materials was followed
with the exception that only one drop was performed since Honeycomb does
not recover after the first impact. Duplicate samples were used for each
static stress. Each specimen was wrapped in a polyethylene bag while
tranfering from the conditioning chamber to the testing lab since the
testing lab is kept at standard conditions of 7313.5'F and 50i2‘RH.
Three different drop heights (24,30,and 36 inches) and seven different
static stresses for each drop height were used for each storage

condition and cell size. Only the peak acceleration was recorded.

15

 

 

 

 

 

 

 

 

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Vertical Sensitivity - 100 mV/div.
Sweep Rate - 5 ms/div.

Figure 3 ° A typical shock pulse recorded on the oscilloscope

RESULTS

The equilibrium moisture contents for both cell sizes after 14 days of
storage are shown in Table 1. Note that the percent moisture contents
for the 1/2" and 3/4' cell sizes differ by only 1‘. Since the moisture
content for the freezer condition turned out to be as high as that for
the 99°F & 83‘RH environment, only the first three moisture content
conditions will be used in the remainder of this analysis. Specifically,
the three different moisture contents for the 1/2 inch cell size were
taken as 5.56‘, 14.65‘, and 18.28‘. and for the 3/4 inch cell size, as
5.26%, 14.34, and 19.23‘ The raw data from which these values were

determined are presented in Appendix A.

The static compression test results for the different cell sizes and
moisture conditions are shown in Table 2. The initial peak stress for
the 1/2 inch cell size was about twice as much as that for the 3/4 inch
cell size for each moisture condition. The strains corresponding to
these initial peaks ranged from 2.8‘ to 4.75‘. Note that the initial
peak stress decreases as the moisture content increases. At 19‘ moisture
content, this stress is half that for a moisture content of 5‘, which

agrees with Hopf [3]. Details are presented in Appendix A.

16

17

I§h1g_1 Equilibrium moisture content for the 1/2 inch and 3/4 inch cell
sizes at the 4 moisture conditions after 14 days of storage.

Condition ‘MC for 1/2 in. i s.d. ‘HC for 3/4 in. i s.d.
cell size cell size
100'F & 32‘RH 5.56 i 0.092 5.26 t 0.158
99'F & 83‘RH. 14.65 i 0.003 14.34 i 0.100
41’F & 88‘RH. 18.28 i 0.013 g 19.23 i 0.134
Freezer(5'F) 15.86 i 0.099 15.64 i 0.465

I§h1§_2 The initial peak stress and strain for the 1/2 inch and 3/4 inch
cell sizes at the 4 moisture conditions

Cell size Condition Stress i s.d. Strain t s.d.

(inch) (psi.) (in./in.)

1/2 100'F&32‘RH. 51.93 t 1.410 0.048 1 0.0053

99'F&83‘RH. 32.29 i 1.190 0.038 i 0.0030

41’F&88‘RH. 24.65 i 0.954 0.034 t 0.0017

Freezer(5'F) 29.73 i 1.320 0.039 t 0.0050

3/4 100'F832‘RH. 24.44 t 0.522 0.045 t 0.0032

99'F&83‘RH. 14.33 i 0.500 0.028 1 0.0018

41°F&88‘RH. 13.20 1 0.513 0.029 1 0.0028

Freezer(5'F) 14.02 i 0.734 0.039 t 0.0797

18

The experimental data for the shock transmission values G for the 1/2'
and 3/4' cell size specimens at the four moisture conditions are shown
in Tables 5.A through 6.C in Appendix A. When plotted against static
stress to obtain the cushion curves, the result was not a smooth curve.
This can be explained in part by the small number of repetitions used
during testing and by inherent errors associated with measuring G. Note
that in general, the peak accelerations are higher for lower moisture
contents than for high moisture contents. This result was expected since
for both cell sizes, the low moisture content samples could withstand
more static stress than high moisture content samples. The lowest peak
acceleration values on the cushion curves are in the range of 20 to
30 g's depending on cell size, drop height, and moisture content. For
the both the 1/2 inch and 3/4 inch cell size, the bottoming out point
for high moisture contents occured at lower static stresses than for low

moisture contents.

SEWER—4.
ANALYSIS or nan

In this analysis, the development of a mathematical model to predict
the shock transmission characteristics of honeycomb during the contact
phase is considered, the purpose of which is to eliminate the need for
cushion curves. But the model must be able to predict the shock
transmission values using only basic information with good accuracy and

must also be practical for use.

W

Starting with a model for a semi-rigid paper structure enclosing trapped
air in the form of a rectangular cushion, two resisting forces must be
considered. The first is the paper structure itself. The stress required
to buckle the honeycomb columns depends on the stiffness of the paper,
the cell size, the thickness of the sample and the moisture content in
the paper. The buckling stress may be determined from theoretical
considerations but is better obtained from the static stress strain
curve as the initial peak stress. The second force comes from the
compressed air trapped in the cells. If compression is assumed to be

adiabatic then

19

20
ka - povok (1)

where k is the ratio of specific heats for air, taken to be 1.4.
P and V are the pressure and the volume of specimen at
any instant during compression.
Po and V are the initial pressure (14.7 psi.) and volume
of specimen.

The mechanical work required to compress the air from volume V0 to V is

Povok 1 1
Work - - PdV - -——— - -——- (2)
v0 k-1 k-l v k-l

V
o

 

The final compressed volume of the cushion may be obtained from an
energy balance in which the potential energy of the falling weight goes
into compressing the trapped air and buckling the paper structure. The
potential energy is the weight multiplied by the drop height and the
work done by the outside atmosphere is just the atmospheric pressure
multiplied by the change in volume. The work required to buckle the
paper is the buckling stress multiplied by the change in volume and the
work to compress the trapped air inside is given in equation (2). The
energy balance from release of the weight to maximum cushion compression

then is

 

povok 1 1
W(h+x) + PoAx - + o Ax (3)
v

k-l k-l V k-l b
o
where x is the maximum compression, 0 is the buckling stress, h is the
drop height, H is the weight, and A 12 the loading bearing area.

Setting x/t - c (maximum strain), (4)

where t is the cushion thickness, the initial and deformed cushion
volumes become,

Vo - At and V - Vo(1-¢) (5)

21

and the energy balance in equation (3) is

 

 

povo“ 1 1
W(h+¢t)+PV£- - -—-.--1 +0V6 (6)
o o k-l vok 1 (1_e)k 1 b 0
Setting W/A - a - static loading, (7)
a h ab 1 1
——- - + e + 1 - - e - k-l - 1 (8)
Po t Po k-l (l-e)

From equation (8) the maximum strain e may be determined for each static
loading a and drop height h once the buckling stress ab is known from
the static compression test. This value may then be used to find the
peak acceleration using Newton's Law. Equating the unbalanced force from

Figure 4 to mass times acceleration gives

(P + a A - POA - W - mass x acceleration - WC

1))

Where G is the peak acceleration in g’s. Using equations (1),(5),and (7)
gives

 

P 1 ob
c-—° k-1 +—-1 (9)
o (1-¢)

where e is the solution to equation (8).

Unfortunately, the cushion curves generated by equations (8) and (9) by
using various drop heights, static loadings and thicknesses do not fit
the experiment data. This suggests that the model is inadequate and must
be elaborated on. The sources of error in the model are most likely due
to the fact that the air inside the cells is not truly trapped during

compression since the buckling of the Honeycomb cells causes the paper

22

 

 

 

 

I, "<I})

Figure 4 : Free body diagram of a Honeycomb cushion
at maximum compression in a drop

23

to tear allowing air to flow thoughout the Honeycomb network, similar to
what happens in an open cell foam. Since the original model already
produces equations which are difficult to use, it is expected that a
more elaborate model will produce even more complicated results and so
the modelling approach will be abandoned in favor of a more practical
approach. This approach uses the static compression stress strain curve
to predict shock transmission values in the belief that all of the
relevant resisting forces left out in the previous model are accounted
for in the stress strain curve. The only obvious force which will not
show up in the static compression test results is the viscoelastic or

strain rate dependent term. This approach will be discussed next.

W

The research conducted at The University of Texas [1,2] was aimed at
using the dynamic stress strain curve to predict the peak acceleration
in a drop. An example of the calculation of peak acceleration was given
but no verification that the calculated results agreed with the
experimental ones was demonstrated. Since the dynamic stress-strain
curve is very difficult to obtain experimentally due to the need for a
high strain rate compression tester, the approach which uses the dynamic
stress strain curve to predict shock level will be carried out by
assuming that the dynamic stress is a constant multiple of the static
stress for each value of strain. This multiple will then be determined
by requiring that the predicted shock levels match the experimental ones
as closely as possible in an overall sense. The expected size of this

value is 1.4 corresponding to earlier research [2] which found that the

24
dynamic energy absorption is about 1.4 times the static energy

absorption.

An energy balance requires that the potential energy of the impacting
mass in the drop is absorbed by the cushion material in the form of
stored and dissipated energy. Since the sum of these energies is just
the area under the dynamic stress stain curve multipled by the volume of

cushion and the potential energy is just weight times drop height,

e
At I m ode - WH
0

which leads to

‘m 0H
ode - - (10)
0 t

Equation (10) gives the maximum cushion strain ‘m for a given drop
height H and cushion thickness t in terms of the static loading 0.

Starting with Newton's law,

F - W - WC
where F is the peak cushion force exerted on the object and rearranging,
F on
G - - - l - -— - 1 (11)
W a
where an - F/A
and a - W/A - static loading.
The general procedure then is to calculate the maximum strain ‘m 'from

equation (10) for a given drop height, static loading, and thickness

using the dynamic stress strain curve. The peak stress on corresponding

25

to this value of ‘m is also found from the assumed dynamic stress strain
curve and this result is then substituted into equation (11) to get the
peak acceleration. Starting with the experimentally determined static
stress-strain curve shown in Figure 2, the assumed dynamic stress strain
curve was taken to be :
dynamic a - C x static a (12)

where C is a constant. Investigating various values for C ranging from
1.1 to 3 in steps of 0.1, the above procedure to determine G was carried
out and compared to experimental values for G. The correct value for C
was taken to be the constant which gave the least variance between the

calculated and experimental data.

Unfortunately, no single constant factor was found which gave acceptable
results. Therefore, the static stress strain curve cannot be used as
such to predict the peak acceleration. This is a result which is
specific to Honeycomb since for most plastic foam cushions such as
Ethafoam 220‘, the static stress strain curve can be used to predict the
peak acceleration with good accuracy [9]. The main reason for the
failure of this approach is that there are many factors involved in the
dynamic compression of honeycomb which must be considered. Some of these
are the buckling of the paper cells, the post-buckling compaction of the
paper which may lead to tearing and rupture and the resultant flow and
compression of air thoughout the cell network. All these factors are
influenced by the strain rate and therefore do not show up in the static
stress strain curve used as the basis for this model. Having attemped
several models with limited success, it was determined that the most

practical approach was to fit the data base to a descriptive equation

26

which takes into account all of the Honeycomb cushion parameters such as
cell size, thickness, and moisture content as well as drop parameters

such as drop height and static loading.

W

This approach begins with the assumption that there exists some function
which relates peak acceleration G to the static stress a for a given
cell size, moisture content and drop height, in the form,
C - f(o)
which presumably has a Maclaurin series expansion [10],
f(a) - a + be + caz + da3 + ea“ + £05 + ... (13)

Since the function f(o) is not known beforehand, the usual approach
cannot be used to find the coefficients ,a,b,c,d,.... The series will
therefore be truncated and fitted to the experimental data. The choice
of the degree of the polynomial left after truncation must be based on
the fact that it should be able to produce a curve with a variable
curvature and yet be able to smooth out any fluctuations in experimental
data that would lead to oscillatory behavior. For these reasons, a cubic

polynomial was chosen since this allows the curvature to change linearly

with the static stress,

Gc-a+ba+c02+da3 (14)

The first derivitive of this is the slope and the second derivitive is
the rate of change of slope or the curvature : f" - 2c + 6do. At this
point, there are four unknown coefficients (a,b,c,d) which must be

determined for each data set (drop height, moisture content and cell

27

size). Since there are seven data points for each data set, the cubic
equation will obviously not fit the experimental data exactly. The
procedure for fitting the cubic to the experimental data will therefore
be based on a least squares approach which involves minimizing the
variance between the predicted (cubic) and the actual (experimental)
data. The variance is defined as the sum of the squares of the
differences between the experimental data the cubic predictions,

N

2
Var - 2 ( Cci - Gexp1 ) (15)
i-l

where Var variance

N - number of data - 7
Gc1 - cubic prediction values from i - l to N
Gexp1 - experimental data from i - l to H

Substituting Cc from eqution (14) into equation (15) gives

N 2 3 2
Var - X (a + bo1 + co + do - Cexp1 ) (l6)

1_1 i i
The coefficients a, b, c, and d are determined by requiring the variance
to be a minimum. This in turn requires that the partial derivitives of
the variance with respect to each unknown coefficient a, b, c, and d be
equal to zero which leads to the system of linear equations shown below

in matrix form,

 

 

 

 

 

' u {o 202 203' 'a‘ ' )gmmp1

)3. 202 2,3 )3.“ b 20cm,

2.2 2.3 2a“ 205 c ' 20%.”, (17)
.2? 2a“ za” 2a“. .a. [23%po

 

The sums in the 4x4 matrix on the left are pure numbers related only to

28

the static loadings used and the sums in the 4x1 vector on the right are
pure numbers related to both static loading and the shock levels
obtained experimentally. The coefficients a, b, c, and d obtained from
the solution to the system of linear equations in equation (17) are then
substituted back into equation (14) to predict the peak acceleration as
a function of static stress. At this point, the cubic obtained applies
only to the data set corresponding to the N data (o1,Gexp1) used in
equation (17) and this data set is for a particular drop height, cell

size, and moisture condition.

Having obtained the cubics for the three different drop heights with the
same cell size and moisture content, the next step is to combine the
three different cubic equations for these drop heights into one equation
which will be valid for a given cell size and moisture content. To do
this, the coefficients a, b, c, and d for the three different drop
heights of 24, 30, 36 inches, will be replaced by functions a(h), b(h),
c(h), and d(h). Again, using the fact that every function has a
polynomial series representation, the new coefficient a(h) will be taken
as a quadratic in h,

a(h) - e + fh + 5112 (18)
with similar expressions for b(h), c(h), and d(h). The three new
sub-coefficients, e, f, and g are chosen so that equation (18) produces
the correct value for ‘a' in the cubic equation (14) when the associated
drop height is used. More specifically, starting with the cubic fit

equations for the three drop heights h h2,and h

1' 3’

+ b o + c o2 + d o3

h ; G - a1 1 1 1 (19)

l

29

. 2 3
2 , G - a2 + bzo + c2o + dzo (20)

. 2 3

3 , G - a3 + baa + C30 + d3o (21)
with all a's, b's, c's, and d's known, the coefficients e,f and g in
equation (18) must satisfy

h

h

a1 - e + £111 + ghl2 (22)
a2 - e + fhz + ghz2 (23)
a3 - e + fh3 + gh32 (24)
Equations (22), (23), and (24) can be written in matrix form as
1 h1 h12 e a1
1 1.2 1122 f - a2 (25)
1 h3 h32 g a3

The solution to this equation will reproduce the original coefficients
in the cubics exactly since there are precicely three conditions for
three unknowns. Similar procedures hold for b(h), c(h) and d(h). Now the
new equation for the peak acceleration G as a function of static stress
and drop height is

G - ( e1 + f

h + glh2 ) + ( e2 + f h + gzh2 )o

l
+ ( e3 + f

2
h + g3h2 )a2 + ( ea + f h + gahz )a3 (26)

3 4

Equation (26) represents the cushion curves for a given cell size and
moisture condition. The next and final step is to modify this equation
to account for moisture content. Since there were only three moisture
contents studied in this research, the procedure used to incorporate
moisture content into equation (26) is the same as that used for the
three different drop heights. Each of the coefficients e,f,and g in

equation (26) is represented by a quadratic equation in the moisture

30

content. For example,
e(mc) - p + q(mc) + r(mc2) (27)

For each of the three different moisture contents, the coefficients p,
q, and r are chosen so that the appropriate values of e are obtained.
Having done this, a total of 36 coefficients per cell size are needed to
generate the Honeycomb cushion curves for the peak acceleration G versus
static stress o as a function of drop height and moisture content. Since
these 36 coefficients were determined from 63 total data points, it may
be argued that a significant reduction in data set to a simpler form has
not been achieved. The true advantage in going to a polynomial fit such
as this however is that the resulting equation can be used to

interpolate and hopefully extrapolate the original data.

Therefore equation (26) with the e's, f's, and g's replaced by the
approprite quadratics in moisture content can be said to represent the
cushion curves for each cell size in the range of drop heights from 24
to 36 inches and moisture contents from 5‘ to 20‘. The results of the
curve fitting procedure for the 36 coefficients for the 1/2' and 3/4'

cell are shown below.

1/2” cell size :
c - [ ( 2141.7 - 586.6335mc + 28.23396mc2 )
+ ( -131.os19 + 40.1117mc - 1.955971»:2 )h
+ ( 2.187297 - 0.67702mc + 0.033222»2 )1:2 1
+ [ ( .5921.151 + 1592.872mc - 74.80475»2 )
+ ( 403.0712 - 111.7416mc + 5.2735mc2)h

+ ( -6.738682 + 1.887945mc - 0.089581mc2)h2 ]o + ...

3/4" cell size :

The predictions
experimental data

be very good.

31

4278.041 - 1102.514mc + 50.797021».2 )

-295.5754 + 77.602l3mc - 3.587287uc2 )h

4.973702 - 1.314057mc + 0.0610037mc2 )h2 152
-869.4235 + 217.7587mc - 9.8951114:2 )

50.77529 - 15.36812mc - 0.699846mc2 )h

-1.02519 + 0.261585mc - 0.0119425»2 )h2 153 (28)
3595.99 - 784.0774mc + 37.35841»2 )

-235.5423 - 49.6109lmc - 2.393295lc2)h

3.84757 - 0.77626mc + 0.375613mc2 )h2 1

-12775.91 + 2769.62mc - 132.8082mc2 )

848.1788 - 179.4374mc + 8.65857mc2 )h

-13.97149 + 2.85055mc - 0.1374lmc2 )h2 ]o

12907.01 - 2889.705mc + 141.7144nc2 )

.858.3288 + 189.815mc - 9.344711»2 )h

14.31955 - 3.04068mc + 0.14913»2 )h2 152

-4055.452 + 943.0456mc - 47.34888mc2 )

273.5282 - 62.48795mc + 3.14258»2 )h

-4.474995 + 1.00335mc - 0.0501251“:2 )h2 1a3 (29)

of equations (28) and (29) are compared to the
in Figures 5 through 10. Visually, the fit appears to

A quantitative measure of fit is provided by the

correlation coefficient [11],

32

 

Else-612
R - _ 2 (30)
ZIGexp-G]

 

Z Gexp

N

 

with E - (31)

where N is the total number of data (N - 63 for each cell size), Gexp
are the experimentally determined shock levels and Gc are the predicted
values from the fitted curves. Using the data in Appendix B, the
correlation coefficient for the 1/2' cell size was found to be

R - 0.9670 and for the 3/4' cell size, R - 0.9927, both of which are

considered to be very good [11].

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DISCUSSION AND CONCLUSIONS

Honeycomb cushioning is a unique structure considering the effects of
the cell on overall cushion strength. It is because of this structure
that certain errors associated with the measurement of shock
transmission values are unavoidable. The first of these errors is
related to the strength of a normal cell compared to that of a partial
cell. If the cells of a specimen are cut during cushion fabrication, the
strength of sample will significantly decrease as compared to a foam
cushion composed of much smaller cell sizes. The reason for this is the
effective bearing area. A partial cell has virtually no strength
whatsoever and since the crossectional area of a single cell makes up a
significant portion of the actual load bearing area, the overall effect
of an edge of severed cells considerably reduces the true bearing area.
For example, for an 8'x8' sample with 1/2' cells where all four edges
have been cut, the apparent bearing area is 64 inch2 and the true
bearing area is 55.2044 1 16‘ inchz. For the 3/4' cell size, the true
bearing area is 51.1426 1 25‘ inchz. These areas were determined by
subtracting the area associated with the row of cut cells along the
perimeter from the apparent bearing area. The shape of the cell used in
this calculation was taken from actual measurements. For the l/2' cell,
an ellipse with diameters 0.5' and 0.6875" was used and for 3/4' cell,

an ellipse with diameters 0.75” and 1.0625". Evidently, the smaller the
39

40

sample size, the more effect the loss of the partial borderline cells

has on bearing area.

Another source of error is the compound instrument error associated with
the signal sent from the accelerometer to the oscilloscope. From
section 2.4 under apparatus used in the Drop Test, the errors associated
with the accelerometer, coupler, oscilloscope and the width of the trace
are 12‘, 15‘, 13‘, and 16.25, respectively. The compound signal error is
therefore 116.25. The errors associated with the cushion curves
themselves may therefore be split into two parts : the error on G is
116.25‘ and the error on static loading is 116‘ for the 1/2” cell size

and 125‘ for the 3/4' cell size.

The effect of moisture is evident on both the crushing strength and on
the cushion curves. Since moisture weakens the fibers in paper, both the
crushing strength and the shock transmission properties tend to
decrease. In general, the effect of moisture content can be assessed by
examining the rate of change of G with respect to me in the fitted
curve. For example, for the 1/2" cell size, from equation (28)
ac
-—- - [ ( -586.6335 + 56.46792mc ) + ( 40.1117 - 3.91194mc)h
amc + ( -0.57702 + 0.066444mc )h2 1
+ [ ( 1592.872 - 149.6095mc ) + ( -111.7416 + 10.547mc)h
+ ( 1.887945 - 0.179162mc )h2 ]o
+ [ ( -1102.514 + 101.59404mc) + ( 77.60213 - 7.174574mc )h

+ ( -1.314057 + 0.1220074mc )h2 1a2 + ...

41

+ [ ( 217.7587 - 19.7922mc ) + ( -15.36812 - 1.399692mc )h

+ ( 0.261585 - 0.023885mc )h2 153 (32)

Using values for me in the range studied (5.56‘ to 18.28‘) and drop
heights h in the range 24' to 36', the value for aG/amc is always
negative which shows that the peak acceleration decreases when the

moisture content increases in agreement with the experimental results.

The average percent difference between the curve fit and experimental
results for the 1/2' cell size is 15.189‘ and for the 3/4' cell size is
9.253‘. The maximum percent difference for the 1/2' cell size is
107.492‘ and for the 3/4' cell size is 31.306‘. Most of the high percent
difference points occurred at the low points of the curves where the
values of peak acceleration were low. Even though the maximum percent
difference for the 1/2' cell size was very high, there were only two
results that exceeded 50 percent difference which was most likely the
result of an error in collecting the experimental data. All of these
percentages were based directly on the experimental results without
considering experimental errors which can be as much as 116.25‘ for C.
By varying each experimental G up to 116.25‘ to obtain the best and
worst agreement with the fitted curve, the average minimum and maximum
percent differences were recalculated. The average minimum difference
was 4.523‘ for the 1/2' cell size and 0.821‘ for the 3/4' cell size and
the average maximum difference was 32.396‘ for 1/2' cell size and

26.735‘ for 3/4' cell size. Both are still acceptable.

42

The curve fitting method is not a mathematical model which means that
its validity is limited to the range of experimental data collected.
Equations (28) and (29) can be used to predict the peak acceleration
within the range of experimental drop heights and moisture contents
studied. It is hoped that these equations can also be used to
extrapolate the data for moisture contents below 5‘ and above 20‘ and
for drop heights less than 24" and above 36". Equation (28) was used to
predict the shock transmission value for the 1/2” cell size with an 8‘
moisture content in an 18" drop with a static loading of 2 psi. The
predicted result of 50 g’s was lower than the experimental result of 62
g's with a percent difference of 24.792‘ which is within the limits of

accuracy for the cushion curve equations.

APPENDICES

APPENDIX A

DATA TABLES

I§b1g_3 Data for the moisture content for the 3/4 inch and 1/2 inch
cell sizes at the 4 moisture conditions

Condition Cell Size Sample No. ‘mc 7days ‘mc l4days

(inch)

100°F&32‘RH. 3/4 1 5.64 5.37

2 5.396 5.15

1/2 1 5.80 5.62

2 5.83 5.49

99°F&83‘RH. 3/4 1 14.19 14.41

2 14.27 14.27

1/2 1 13.91 14.65

2 13.77 14.65

41°F&88‘RH. 3/4 1 17.94 19.13

2 17.95 19.32

l/2 l 18.05 18.29

2 17.71 18.27

Freezer(5°F) 3/4 1 14.51 15.31

2 14.87 15.97

1/2 1 15.66 15.79

2 15.43 15.93

Table 4.5 Data for the initial peak stress and strain for the 3/4 inch

cell size at 4 moisture conditions

Condition Sample No. Stress(psi.) strain(‘)
100°F&32‘RH. l 24.33 0.050
2 24.67 0.043
3 23.61 0.047
4 24.59 0.043
5 25.00 0.043

43

Ighlg 4,5 (continued)

99°F&83RH.

4l°&88‘RH.

FREEZER(5°F)

Uprl-I' UwaH

m9wNH

44

13.73
13.91
14.36
14.77
14.86

13.42
13.92
12.59
13.20
12.86

12.81
14.69
14.02
14.08
14.52

00°00

60°00 00°00

Igblg_4‘fi Data for the initial peak stress and strain for

cell size at 4 moisture conditions

Condition

100°F&32‘RH.

99°F&83‘RH.

41’F&88‘RH.

FREEZER(5°F)

Sample No.

U14§wNH “#UNH UfiwNH

UI§UNH

Stress(psi.)

52.75
53.14
52.38
51.83
49.56

33.75
33.08
32.34
31.47
30.80

23.91
23.81
25.09
25.78

28.91
30.38
31.17
27.89
30.33

.030
.027
.030
.027
.027

.030
.027
.033
.030
.027

.040
.030
.043
.033
.050

the 1/2 inch

strain(‘)

0000 OOOOO OOOOO

OOOOO

.057
.047
.047
.043
.043

.033
.040
.040
.040
.037

.033
.033
.033
.037

.047
.037
.040
.037
.033

45

I§b1g_§‘5 Shock transmission data for the 3/4 inch cell size for
a 24 inch drop height for 4 moisture conditions

Condition Static Stress Sample No. C
(psi.)

100°F&32‘RH. 0.5 l 68

2 68

0.75 l 42

2 44

1.0 1 44

2 38

1.5 1 3O

2 28

1.75 l 20

2 22

2.0 l 36

2 40

2.3 1 74

2 68

99°F&83‘RH. 0.5 l 42

2 46

0.75 l 40

2 40

1.0 l 30

2 31

1.2 1 27

2 25

1.4 l 20

2 19

1.6 1 l7

2 15

1.75 1 31

2 30

41°F&88‘RH. 0.5 1 50

2 46

0.75 l 34

2 34

1.0 1 24

2 23

1.2 l 28

2 26

1.4 l 20

2 20

1.6 1 30

2 31

1.75 l 47

2 50

46

Ishle.§1A (continued)

FREZZER(5°F) 0.5 l 58
2 52

0.75 l 54
2 54

1.0 l 30
2 30

1.25 1 40
2 42

1.5 l 28
2 28

1.75 l 30
2 30

2.0 l 60
2 50

Ighlg_§‘fi Shock transmission data for the 3/4 inch cell size for
a 30 inch drop height for 4 moisture conditions

Condition Static Stress Sample No. C
(psi.)
100°F&32‘RH. 0.5 1 68
2 70
0.75 l 48
2 44
1.0 l 50
2 44
1.25 l 38
2 42
1.5 1 30
2 36
1.75 1 68
2 64
2.0 l 90
2 88
99°F&83‘RH. 0.5 1 46
2 48
0.75 l 40
2 38
0.9 l 25
2 26
1.0 1 28
2 25
1.2 1 28
2 29
1.4 l 33
2 36

47

Igb1g_§‘fi (continued)

1.6 l 65
2 58

41°F&88‘RH. 0.5 l 48
2 46

0.75 l 32
2 30

0.9 l 34
2 31

l 0 1 24
2 22

1.1 l 20
2 22

1.2 1 26
2 23

1.4 l 54
2 58

FREEZER(5°F) 0.3 1 90
2 92

0.5 l 56
2 60

0.75 1 56
2 58

1.0 l 28
2 26

1.25 1 42
2 42

1.5 1 3O
2 28

1.75 1 88
2 82

Igblg_5Ԥ Shock transmission data for the 3/4 inch cell size for
a 36 inch drop height for 4 moisture conditions

Condition Static Stress Sample No. C
(psi.)

100'F&32‘RH. 0.5 l 64

2 66

0.75 1 44

2 44

1.0 l 44

2 42

1.25 1 40

2 42

1.5 1 68

2 68

Table 5,9 (continued)

99’F&83‘RH.

41°F&88‘RH.

FREEZER(5'F)

48

.75

.75

.25

.75

NHNH

hbh‘hih‘EDP‘NDF‘BJPJhDPJNJF‘ NJF‘NDF‘hahihih‘hih*h3h‘h>h‘

NDFJNDF‘NJF*NJP‘NDP‘NJF‘NDP‘

130
125
170
160

80
85
50
48
4O
42
24
25
27
32
32
34
72
64

72
76
48

36
34
35
32
28
26
42
46
100
110

88
9O
54
56
56
54
26
28
4O

84
80
160
150

49

Igblg_§‘5 Shock transmission data for the 1/2 inch cell size for
a 24 inch drop height for 4 moisture conditions

Condition Static Stress Sample No. C
(psi.)

100°F632‘RH. 0.5 1 140
2 145

1.0 1 78
2 74

2.0 l 50
2 54

3 02 1 32
2 30
4.09 l 30
2 35

4.4 1 26
2 32
5.0 1 40
2 40

99°F&83‘RH. 0.5 l 98
2 97

1.0 l 52
2 48
2.0 l 30
2 24
2.49 l 20
2 23

3.02 l 18
2 20
3.56 1 24
2 22

4.0 1 42
2 40

41°F&88‘RH. 0.5 1 105
2 100

1.0 l 58
2 58

2.0 l 32
2 32
2.49 1 20
2 24

3.02 l 15
2 18
3.56 1 24
2 20

4.0 l 38
2 34

50

I§h1§_§*5 (continued)
FREEZER(S°F) 0.5 1 130
2 125
1.0 1 80
2 76
2.0 l 36
2 38
3.02 1 34
2 32
4.0 1 20
2 18
4.4 1 45
2 40
5.0 1 72
2 75
Igblg_§‘fi Shock transmission data for the 1/2 inch cell size for

a 30 inch drop height for 4 moisture conditions

Condition Static Stress Sample No. C
(psi.)

100'F&32‘RH. 0.5 1 150

2 145

1.0 1 76

2 76

2.0 1 44

2 50

3.02 1 38

2 36

3.56 l 30

2 27

4.09 l 65

2 62

4.4 l 84

2 80

99'F&83‘RH. 0.5 l 100

2 97

1.0 1 46

2 48

1.5 l 32

2 28

2 0 l 32

2 ‘ 28

2.49 l 28

2 25

3.02 l 31

2 32

51

I§h1g_§‘fi (continued)

3.56 1 42
2 38

41°F&88‘RH. 0.5 1 105
2 100

1.0 1 60
2 58

1.5 1 34
2 36

2 0 l 35
2 36

2.4 1 34
2 34

3.02 l 20
2 17

3.56 1 88
2 80

FREEZER(5°F) 0.5 1 138
2 135

1.0 l 78
2 74

2.0 1 44
2 44

2.49 l 30
2 30

3.02 1 30
2 36

3.56 l 34
2 32

4.0 l 74
2 78

I§h1g_§‘§ Shock transmission data for the 1/2 inch cell size for
a 36 inch drop height for 4 moisture conditions

Condition Static Stress Sample No. C
(psi.)

100°F&32‘RH. 0.5 1 150

2 135

1.0 1 80

2 80

1.5 1 60

2 58

2.3 l 52

2 50

3.02 1 36

I§h1e_§‘§ (continued)

99'F&83‘RH.

41°F&88‘RH.

FREEZER(5°F)

.56

.09

.703

.02

.49
.02

.56

52

NHNHN

NHNHNHNHNHNHNH

NHNHNHMHNHNHNH

NHNHNHNHNHNHNH

40
35
29
115
110

100
100
52
48
40
34
26
26
38
37
44
40
82
88

105
110
56
54
34
36
34
34
28
28
58
54
66
64

130
130
72
76
42
42
36
40
36
34
40
40
90
80

THE CORRELATION COEFFICIENTS

APPENDIX B

The correlation coefficients for the 1/2" and 3/4' cell size between the

experiment data and calculated data using equations (28)

determined as shown below

where

Gexp - experimental peak acceleration (g's)
Gc - calculated peak acceleration (g's)
N - number of total data (63 for each cell size)

 

 

 

R - correlation coefficient

and (29) are

(B-l)

(3-2)

Igh1g_1 Comparison between experimental and calculated data and the
correlation coefficient for the 3/4 inch cell size

2
O

VOQNO‘U‘L‘U’NH

Gexp

64.
50.
37.
23.
.721
39.
70.
67.
52.
41.
37.
43.
60.
91.
66.
42.

26

841
713
697
561

555
736
443
048
307
553
120
343
556
731
717

Ge

68.
43.
41.
29.
21.
38.
71.
69.
46.
47.
40.
33.
66.
89.
65.
44.

53

OOOOOOOOOOOOOOOO

‘ Difference

4.
l7.
8.
18.
27.
4.
0.
2.
13.
12.
.117
.667
.571
.872
.663
.916

u
NNNNOO‘

646
937
065
755
243
092
372
257
148
113

I§b1§_1 (continued)

17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63

37
48
75
116
170
43

41.
31.
23.
18.

21

29.
47.
36.
29.
26.
26.
36.
62.
80.
55.
33.
27.

27

38.

67

47.
35.
25.
21.
23.
33.

48
46

35.
27.

23

22.
27.
56.
71.
53.
32.
27.

29

51.

104

.133
.565
.595
.810
.794
.453
270
810
673
886
.009
276
500
200
820
848
386
798
362
059
930
874
691
.452
340
.412
283
799
737
696
680
963
.490
.283
952
201
.404
973
395
750
163
185
511
582
.675
656
.606

54

43.
41.
68.
127.
165.
44.
40.
30.
26.
19.
16.
30.
47.
39.
25.
26.
28.
34.
61.
82.
49.
41.
24.
29.
33.
68.
48.
34.
23.
27.
20.
30.
48.
47.
31.
32.
23.
21.
24.
56.
74.
46.
35.
33.
27.
44.
105.

OOOUIOOOOMOOUIOOU!MOOUIOOOOUIUIOOU‘UIUIUIUIUOOUOUIOUIOOOU‘COO

The average percent difference is

The maximum percent difference is 31.306‘.

9.253‘

The correlation coefficient is - 0.9927

P‘P‘F‘
rioaoa

w
NHO‘NHO‘NHJ-‘HwGFwO-‘WQ

H

rdr‘ra
meow»

.644
.451
.169
.384
.512
.243
.175
.295
.950
.149
.306
.013
.064
.179
.941
.313
.418
.661
.402
.959
.143
.380
.024
.942
16.
.865
.494
.291
.519
.644
.400
.354
.021
.526
.974
.305
.757
.395
.816
.339
.834
.620
.111
.666
.907
.400
.375

182

55

I§§1g_§ Comparison between experimental and calculated data and the
correlation coefficient for the 1/2 inch cell size

No. Gexp Cc ‘ Difference
1 134.268 142.5 5.777
2 91.648 76.0 20.589
3 43.200 52.0 16.923
4 29.345 31.0 5.339
5 33.474 32.5 2.997
6 35.279 29.0 21.652
7 ' 36.430 40.0 8.925
8 139.588 147.5 5.364
9 91.708 76.0 20.668

10 37.245 47.0 20.755

11 29.870 37.0 19.270

12 42.111 28.5 47.756

13 63.042 63.5 0.721

14 78.787 82.0 3.918

15 133.420 142.5 6.372

16 95.549 80.0 19.436

17 63.455 59.0 7.551

18 31.445 51.0 38.343

19 31.640 35.0 9.600

20 55.303 32.0 72.822

21 102.101 112.5 9.244

22 93.623 97.5 3.976

23 58.010 50.0 16.020

24 22.336 27.0 17.274

25 18.335 21.5 14.721

26 21.114 19.0 11.126

27 29.168 23.0 26.817

28 37.914 41.0 7.527

29 96.389 98.5 2.143

30 51.977 47.0 10.589

31 30.097 30.0 0.323

32 24.306 30.0 18.980

33 28.028 26.5 5.766

34 35.467 31.5 12.594

35 38.950 40.0 2.625

36 97.738 100.0 2.262

37 56.902 50.0 13.804

38 32.322 37.0 12.643

39 26.255 26.0 0.981

40 32.440 37.5 13.493

41 53.159 42.0 26.569

42 80.705 85.0 5.053

43 99.071 102.5 3.345

44 65.291 58.0 12.571

45 26.891 32.0 15.966

Ighlg_§ (continued)

46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63

20.
19.
25.
34.
97.
66.
41.
25.
22.
38.
.740
106.
57.
33.
29.
38.
50.
66.

77

018
739
705
224
957
800
536
797
503
386

727
870
565
594
222
164
931

56

22.
16.
22.
36.
102.
59.
35.
35.
34.
18.
84.
107.
55.
35.
34.
28.
56.
65.

OOOOOOU‘OWOUIOOUIOOUIO

The average percent difference is
The maximum percent difference is 107.4928
The correlation coefficient is - 0.9672

15.1898

.009
.630
.841
.933
.432
.220
.674
.332
.815
.492
.452
.719
.218
.100
.959
.507
.421
.971

10

20
3O
4O
50

60

7O

80

90

100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
500
510
520
530
540
550
560
570
580

APPENDIX C

THE COMPUTER PROGRAM FOR THE CURVE FIT COEFFICIENTS

REM . PROGRAM FOR PREDICTING SHOCK TRANSMISSION VALUES FOR HONEYCOME
CUSHION -
DIM 8(10)
PRINT * INPUT CELL SIZE OF THE HONETCOMD IN INCH (0.5 OR 0.75)
INPUT Z
IF Z - 0.5 OR 0.75 THEN GOTO 60 ELSE PRINT - YOUR SELECTED CELL SIZE
IS NOT AVAILABLE ,TRY AGAIN !! - ; GOTO 30
PRINT " INPUT MOISTURE CONTENT IN PERCENT AND DROP HEIGHT IN INCHES“
INPUT MC,H
PRINT - How MANY STATIC STRESS POINTS DO YOU NANT 7 '
INPUT N
PRINT - INPUT THE STATIC STRESSES -
FOR I - To N
INPUT S(I)
NEXT I
IF Z - 0.5 THEN GOSUD 500
IF 2 - 0.75 THEN GOSUB 800
A - E1 + P1*H + G1*H‘2
B - E2 + F2*H + G2*H‘2
C - E3 + F3*H + G3*H‘2
D - E4 + F4*H + G4*H*2
LPRINT
LPRINT
LPRINT ~ HONEYCOME CUSHION CELL SIZE --;z - INCH-
LPRINT MOISTURE CONTENT -';MG '1 AT DROP HEIGHT -“;H "INCHES“
LPRINT
LPRINT STATIC STRESS (psi.) G (g's)-
FOR I 1 TO N
C - A + B*S(I) + C*S(I)‘2 + D*S(I)‘3
LPRINT USING - ##.## ';S(I);
LPRINT USING ' ####.###';G
NEXT I
END
E1 - 2141.7 - 586.6335*(MC) + 28.23396*(Hc‘2)

F1 - -131.05190 + 40.1117*(MC) - 1.95597*(HC“2)
Gl - 2.187297 - 0.67702*(MC) + 0.033222*(MC)

E2 - -5921.151 + 1592.872*(MC) - 74.80475*(MC“2)
F2 - 403.0712 - 111.7416*(HC) + 5.2735*(MC‘2)

G2 - -6.738682 + l.887945*(HC) - 0.089581*(HC“2)
E3 - 4278.041 - 1102.514*(HC) + 50.79702*(HC“2)
F3 - -296.6764 + 77.60213*(HC) - 3.587287*(HC“2)
G3 - 4.973702 - l.314057*(HC) + 0.0610037*(HC‘2)

57

58

AREEnéix_§ (continued)

E4 - -869.4235 + 217.7587*(MC) - 9.8961*(MC“2)
F4 - 60.77629 - 15.36812*(MC) + 0.699846*(HC“2)

590
600
610
620
800
810
820
830
840
850
860
870
880
890
900
910
920

G4 - -1.02519 + 0.261585*(MC) - 0.0119425*(Mc‘2)
RETURN

E1 - 3696.99 - 784.0774*(MC) + 37.36841*(Mc‘2)
P1 - -235.6423 - 49.61091*(HC) - 2.393295*(Mc*2)
G1 - 3.84767 - 0.77626*(HG) + 0.375613*(MC“2)

E2 - -12776.91 + 2769.62*(MC) - 132.8082*(Mc‘2)
P2 - 848.1788 - 179.4374*(MC) + 8.65857*(Mc‘2)
G2 - -13.97149 + 2.85055*(MC) - o.13741*(MC‘2)
E3 - 12907.01 - 2889.705*(MC) + 141.7144*(Mc‘2)
P3 - -868.3288 + 189.815*(MC) - 9.344711*(Mc‘2)
G3 - 14.31966 - 3.04068*(MC) + o.14913*(Mc‘2)

E4 - -4056.462 + 943.0456*(MC) - 47.34888*(Mc‘2)
P4 - 273.6282 - 62.48795*(MC) + 3.14268*(Mc‘2)
G4 - -4.474995 + 1.00335*(MC) - 0.050125*(Mc‘2)
RETURN

APPENDIX D

METHODS OF MANUFACTURING HONEYCOMB MATERIALS

There are two main methods that are used to manufacture Honeycomb
materials, the expansion process and the corrugation process. The
expansion process is the most commonly used. All of the samples used in
this research were made by this process. The corrugation process is
mainly used for higher density honeycomb materials. Both of these

processes are briefly described below in reference to Figure 11.

Expan§19n_flxggggg : Fabrication starts with paper sheeting cut from web
stock on which adhesive node lines have already been placed. Layers of
these sheets are stacked on top of each other with alternating glue
lines and cured to form the block. The block is then cut to the required
dimensions and the stack is expanded by pulling it apart. The cell size
of the Honeycomb is controlled by the distance between the glue lines

and by the amount of expansion.

Qg::uga§ign_£xgggss : Here the web is first passed through corrugating

rolls to form the corrugated sheet and then the corrugated sheets are
stacked, glued, and cured. The core thickness, width, and length are

then cut directly from the Honeycomb block.

Illustrations for both processes are shown in Figure 11.

59

60

 

Expansion process

 

 

 

 

Figure 11 : Methods of manufacturing Honeycomb materials [12]

LIST OF REFERENCES

10.

LIST OF REFERENCES

Karnes, C.H., J.W. Turnbow, E.A. Ripperger, and J.N. Thompson,
'High- Velocity Impact Cushioning, Part IV, The Effect of Moisture
Content and Impact Velocity on Energy-Absorption Characteristics of
Paper Honeycomb“, Structural Mechanics Research Laboratory, The ‘
University of Texas, Austin, May 1, 1959.

Karnes, C.H., J.V. Turnbow, E.A. Ripperger, J.N. Thompson, ' High
Velocity Impact Cushioning, Part V, Energy Absorption
Characteristics of Paper Honeycomb”, Structural Mechanics Research
Laboratory, The University of Texas, Austin, May 1959.

Hopf, J.P., ”Equilibrium Moisture Content of Paper Honeycomb and Its
Effect on Energy Absorbtion', Forest Products Laboratory, Project
No. 7-87-03-0048, Report No.1, December 1955.

Ripperger, E.A., “Energy Absorption Characteristics of Paper
Honeycomb”, Engineering Mechanics Research Laboratory, The
University of Texas, Austin, May 18, 1967.

Singh, S.P., M. Graham, J. Cornell, “Cushion Testing of Kraft Paper

Honeycomb", School of Packaging, Michigan State University, April
1986.

Hitting, R.H., ”Investigation of Paperboard Honeycomb Material for
Use as Cushioning in Aerial Delivery of Supplies And Equipment“,
Quatermaster Food and Container Institute for the Armed Forces,
Project No. 7-87-03-002, March 9, 1954.

ASTM D 644-55, “Determining Moisture Content of Paper Material by
Oven Drying", American Society for Testing and Materials, 1982.

ASTM D 1596-78a, ”Test Method for Shock Absorbing Characteristics of
Package Cushion Materials”, American Society for Testing and
Materials, 1983.

Taw, R.H., “Developing a Mathematical Model For a 45 Degree Edge
Drop to Predict the Dynamic Behavior of a Low Density Closed-Cell
Foam", Master's Thesis, School of Packaging, Michigan State
University, 1988.

Spiegel, R.H., "Theory and Problems of Advance Calculus”, Schaum
Publishing Company, New YOrk, 1963.

61

62

11. Freund, E.J., "Modern Elementary Statistics", Sixth Edition,
Prentice-Hall, Inc., New Jersey, 1984.

12. English, K.L., "Honeycomb : Million-Year 01d Material of the
Future", Materials Engineering, January 1985, P.29-33.