THE APPLEMWGN' G? 7.1% SHOCK
EPECEEUM DEEEVED EAMAGE .SOUNDARY
THEGRY EC} T’HE EVAL£ch'§’§ Q‘bé CE E‘HE

SHQCEC ERANEMESSEMLEW Q?
CQmfiUGAEEQ EGAED!

“tests 500 We Dugout (2’5 M. S.
MECHEGAN STATE {ENIVERSZTY
Douglas Gregory McCaH

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University

 

 

ABSTRACT

This study demonstrates the use of a new theory in
shock analysis. This theory was derived from the concept
of shook spectrum by Robert E. Newton at Monterey Research
Laboratories, Inc.

The author treats corrugated board as a damageable
item and locates damage boundaries for A-, 3-, and C-flute
corrugated board at various static stress levels. These
boundaries show the dividing line between shocks uhich alter
and eventually crush the flutes and those shocks which have
no effect on the flute structure. Various damaging shocks
were applied to the corrugated board samples. The effects
of these shocks on the item on the apposite side of the
corrugated board were found to be greatly amplified in

most cases.

THE APPLICATION OF THE SHOCK SPECTRUM DERIVED
DAMAGE BOUNDARY THEORY TO THE EVALUATION OF
THE SHOCK TRANSMISSIBILITY OF CORRUGATED BOARD

By

Douglas Gregory thall

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of
MASTER OF SCIENCE

School of Packaging

DEDICATION.

To my loving wife, Pat, for her patient understanding

and her undying.ccnfidence.

11

ACKNOWLEDGEMENT

The author wishes to thank Dr. James w. Goff for

his helpful consultation.

111

TABLE

Table of Contents. . .
List of Tables . . . .
List of Figures. . . .
Introduction . . . . .
Equipment. . . . . . .
Procedure. . . . . . .
Data . . . . . . . . .
Analysis . . . . . . .
Conclusions. . . . . .
Appendix I . . . . . .
Appendix II. . . . . .
Appendix III . . .,. .

Bibliography 0 o a a 0

OF CONTENTS

iv

iv

vi

15
42
45
u?
49
51

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

LIST OF TABLES

1 Heeponse on A-flute Board to Shocks with High
Acceleration to Velocity Change Ratios

2 Response on B-flute Board to Shocks with High
Acceleration to Velocity Change Rgtios

3 Reaponse on C-flute Board to Shocks with High
Acceleration to Velocity Change Ratios

a Response on A-flute Board to Shocks with Low
Acceleration to Velocity Change Ratios

5 Reaponse on B-flute Board to Shocks with Low
Acceleration to Velocity Change Ratios

6 Response on C-flute Board to Shocks with Low
Acceleration to Velocity Change Ratios

7 Response on A-flute Board to Large
Magnitude Shocks

8 Reaponse on B-flute Board to Large
Magnitude Shocks

9 Reaponse on C-flute Board to Large
Magnitude Shocks

10 Largest Shocks Whose ReSponse Varied
Less than 10 Percent

11 Points Used to Define Damage Boundaries

10

11

12

13

1h

18
19

Figure
Figure

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure

Figure

Figure

13

1n

15

LIST OF FIGURES

Schematic Diagram of Testing Apparatus

Schematic Diagram of Three-dimensional
Damage Boundary
A-flute Front View

Damage Boundary,

A-flute Damage Boundary, Tap View

A-flute Damage Boundary, Side View

B-flute Damage Boundary, Front View

B—flute Damage Boundary, Top View

B-flute Damage Boundary, Side View

C-flute Damage Boundary, Front View

C-flute Damage Boundary, TOp View

C-flute Damage Boundary, Side View
Selected Input Shocks Within the A-flute
Damage Boundary at a Static Stress of

0.13 psi, Showing ReSponse Acceleration

for Repeated Inputs

Selected Input Shocks Within the A—flute
Damage Boundary at a Static Stress of
0.28 psi, Showing Reaponse Acceleration
for Repeated Inputs

Selected Input Shocks Within the A-flute
Damage Boundary at a Static Stress of
0.38 psi, Showing ReSponse Acceleration
for Repeated Inputs

Selected Input Shocks Within the A-flute
Damage Boundary at a Static Stress of
0.52 psi, Showing Reaponse Acceleration
for Repeated Inputs

vi

20
21
22
23
2a
25
26
27
28
29

30

31

32

33

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

16

17

18

19

20

21

22

23

Selected Input Shocks Within the B-flute
Damage Boundary at a Static Stress of
0.13 psi, Showing ReSponse Acceleration
for Repeated Inputs

Selected Input Shocks Within the B-flute
Damage Boundary at a Static Stress of
0.28 psi, Showing Reaponse Acceleration
for Repeated Inputs

Selected Input Shocks Within the B-flute
Damage Boundary at a Static Stress of
0.38 psi, Showing Response Acceleration
for Repeated Inputs

Selected Input Shocks Within the B-flute
Damage Boundary at a Static Stress of
0.52 psi, Showing Response Acceleration
for Repeated Inputs

Selected Input Shocks Within the C-flute
Damage Boundary at a Static Stress of
0.13 psi, Showing Reaponse Acceleration
for Repeated Inputs

Selected Input Shocks Within the C-flute
Damage Boundary at a Static Stress of
0,28 psi, Showing Reaponse Acceleration
for Repeated Inputs

Selected Input Shocks Within the C-flute
Damage Boundary at a Static Stress of
0.38 psi, Showing ReSponse Acceleration
for Repeated Inputs

Selected Input Shocks Within the C-flute
Damage Boundary at a Static Stress of
0.52 psi, Showing ReSponse Acceleration
for Repeated Inputs

vii

3a

35

36

37

38

39

no

#1

INTRODUCTION

The analysis of transient acceleration pulses has been
an important area of study in packaging for many years.

When an item is dropped or receives a shock in some manner,
it may break or become damaged. It has been known that a
soft material placed around an item can reduce the magni-
tude of the acceleration felt by the item. The ratio of
the applied acceleration to the acceleration felt by the
item is referred to as the transmissibility of the material.
The transmissibility of a material is not always less than
one, i.e., the acceleration experienced by the item is not
always reduced by the material used as a cushion. In some
cases the acceleration experienced by the article is many
times the applied acceleration. For this reason, it is
important to understand the relationship between the shock
and the transmissibility of a material.

The newly expounded Damage Boundary Theory, which is
based on a concept of shock spectrum, greatly simplifies
the analysis method of measuring the amount of acceleration
which an article experiences from various input accelerations.
The theory is primarily used to define the input shocks
applied directly to an article which will cause a predetermined

amount of damage or acceleration to an element of that article.

In this paper the theory is used to define the shocks which
will alter, i.e., crush, the flute structure of corrugated
board.

Corrugated fibreboard has been growing in use since
1912 and is widely accepted for use as a shipping container
for a myriad of products. Investigations have been made of
the effect on products shipped in corrugated containers due
to various environments. It is the intent of this study to
investigate the shocks which cause the board itself to
become damaged. The transmissibility of the board changes

once it has been damaged. This result is also examined.

EQUIPMENT

The following equipment and apparatus were used to

gather the data presented in this document.

1.

7.
8.

9.

10.

Shock Machine - Monterey Research Laboratories
Model MRL 3636

Universal Programmer - Monterey Research
Laboratories Model MRL 2680 - Adjusted for
square wave pulses

Gas Regulator --Monterey Research Laboratories

Felt Ralf Sine Programmer - Monterey Research
Laboratories

High Strength Plastic Half Sine Programmers -
Monterey Research Laboratories

Piezoelectric Accelerometers - (2) Kistler
Model 808A

Charge Amplifiers - (2) Kistler Model 503
Band Pass Filer - Krohn-Hite Model 330M

Storage OscilloscOpe - Tektronix Model 564
with Model 3B3 Time Base and Model 3A72 Dual
Amplifier Plug-in Units

Laminated Maple Plywood Block - 8—inch cube with
provisions for mounting an accelerometer at its
geometrical center and for attaching various
amounts of weight - Michigan State University
Packaging Laboratories

PROCEDURE

An accelerometer was mounted in the plywood block so
that transient acceleration pulses applied to the block in
a vertical direction could be monitored. Ass illustrated in
Figure l, the block, with an 8" x 8" sample of corrugated
board under it, was placed on the shock table of the shock
machine so that shocks could be applied to the lower surface
of the board. A metal bar was secured over the block and
made immovable by securing a nut above the bar and then one
below it. This restrained the block from moving upward
away from the table or the corrugated board and restrained
the bar from moving toward the table, which would have
increased the effective weight of the block during the
shock. Another accelerometer was attached directly_to the
shock table and was used to monitor the shocks which the
table received. The shocks which the table received were
the shocks which were applied to the bottom surface of the
corrugated board. A series of five identical shocks were
applied to a given sample of corrugated board. Initially
shocks with high ratios of acceleration to velocity change
were applied using a single felt programmer. A new sample
of corrugated board was inserted for each series of five
drOps. The velocity change of the shock was increased for

each successive series of five drops by incrementing the

u

Ha
drop height 1/8 inch until the magnitude of the reaponse
acceleration monitored in the block On the corrugated sample
varied by more than 10 percent of its value on the first
drOp. It was assumed that if this variation occurred, the
flute structure was permanently altered. This procedure
was followed at static stresses of 0.13, 0.28, 0.38, and
0.52 psi on A-, B-, and C-flute ZOO-pound test corrugated
board. The velocity change was determined from the drOp
height and the coefficient of restitution for each
programmer.

Using rectangular pulses with low ratios of acceleration
to velocity change generated with a square wave programmer,
the acceleration was incremented by increasing the pressure
in the programmer by l00 psi after each series of five
successive drOps on the same sample until the reaponse
varied more than 10 percent. This procedure was followed
using the static stresses and board sizes stated in the
previous paragraph from a drop height of 25 inches.

The high strength plastic programmers were used to
generate shocks which caused a definite variation in the
reSponse shock. The shocks were applied as before to the
four static stresses on each board size in series of five
identical inputs. DrOp heights of 3, 6, 9, and 12 inches

were used.

SCHEMATIC DIAGRAM OF TESTING APPARATUS

 
 
 
 
 
  
 
 
 
    
  

Metal Bar

Test Block

Accelerometers Detachable

Weights

Corrugated
Sample

 

Shock Table

Shock Programmer

Figure 1

Table 1

Response on A-flute Board to Shocks with
High Acceleration to Velocity Change Ratios

 

- Input ReSponse Acceleration (g)
Flute Static Drop P -‘Icc. ‘VéI.
Size Stress Ht. gram- (8) Change 1 2 3 h 5
(psi) (in) mer (ips)

 

A 0.52 3/8 Felt 33 27.5 33 3“ 33 33 33

" ' 1/2 " 36 31.8 36 3n 3h 32 32
" 0.38 1/2 " 36 31.8 36 36 36 36 36
* ~ 5/8 ' A? 35.6 #7 A6 A5 A6 A5
" " 5/8 * 4U 35.6 an #5 #5 #5 an
” " 3/“ ' 53 39.0 53 50 #8 A6 u6
" “ 7/8 * 56 uz.1 56 52 so #8 #7
" 0.28 5/8 ” 55 35.6 55 55 55 55 55
~ ~ 3/u w 60 39.0 60 6o 60 58 57
' " 7/8 " 63 “2.1 63 62 62 62 62
" " l ' 64 #5.0 64 63 62 62 62
" ' 1-1/8 “ 7h 47.8 7h 68 60 60 58
" 0.13 l ' 76 45.0 76 76 76 76 76
". ” 1-1/8 ” 88 #7.8 88 88 88 88 88
' " l-l/fl ” 95 50.4 93 95 95 95 95
" ' 1-3/8 w 100 52.8 100 98 100 100 102
” ' 1-1/2 " 106 55.1 106 110 109 112 110
n " 1-1/2 . 116 55.1 116 118 122 127 126
” ” 1-3/4 " 120 59.6 120 122 122 137 lAO

' ' 2 " 128 63.7 128 132 138 140 1&2

 

Table 2

Response on B-flute Board to Shocks with
High Acceleration to Velocity Change Ratios

 

Input Response Acceleration (g1
Flute Static DrOp 'Pro- Ace. VéI. _
Size Stress Ht. gram- (g) Chan e 1 2 3 h 5
(P81) (1n.) mer (1p8§

 

B 0.52 1 Felt 82 45.0 82 82 82 82 82

w " 1-1/u v 88 50.0 88 87 88 88 8a
. " 1-3/8 - 87 52.8 87 92 99 102 1ou
« ~ 1-1/2 - 100 55.1 100 11A 120 118 128
” 0.38 1 ” 72 “5.0 72 72 72 72 72
4 ~ 1-1/2 . 112 55.1 112 112 111 111 112
~ ~ 1-5/8 ~ 118 57.3 118 118 118 120 120
~ - 1-3/u ~ 120 59.6 120 120 120 122 120
~ - 1-7/8 ~ 120 61.7 120 122 120 132 190
” 0.28 2 ” 155 63.7 155 155 155 155 155
. . 2A1/8 w 118 65.6 118 115 111 111 111
~ ~ 2-1/u ~ 160 76.6 160 155 158 155 168
~ 0.13 2-1/2 ~ 185 71.1 185 185 185 185 185
" " 3 " 220 77.9 220 210 220 215 220
w v 3-1/2 . zuo 8u.2 zuo 235 2uo 2uo 2ao
~ ~ 3-3/4 n zuo 87.1 zuo 235 232 228 220

. a u w 260 90.0 260 260 250 235 220

 

Response on C-flute Board to Shocks with

Table 3

High Acceleration to Velocity Change Ratios

 

 

 

__: Input Response Acceleration(g)
£1220 32:66: D82? g:::: 12?. Chgn'e 1 2 3 a 5

(psi) (in.) mer (ips?

0.52 1/2 Felt #3 31.8 #3 #3 #3 #3 #3
” 5/8 ' 52 35.6 52 #8 #81 #8 #8
' 5/8 ” 50 35.6 50 52 50 50 50
” 3/4 " 52 39.0 52 53 56 58 60
' 3/4 ” 54 39.0 5“ 56 56 55 56

0.38 5/8 " #2 35.6 #2 #2 #2 #2 #2
w 1 n 66 u5.o 66 65 66 67 66
" l ” 68 #5.0 68 68 68 68 68
” l " 68 #5.0 68 67 66 66 67
" 1-1/8 " 72 47,8 72 72 70 67 64
” 1-1/4 " 74 50.# 7# 69 68 67 65

0.28 1-1/8 " 78 #7.8 78 8# 82 82 82
' l-l/# " 9# 50.# 9# 92 92 88 87
' 1-3/8 “ 96 52.8 96 93 91 89 86
" 2 ' 97 63.7 . 97 93 90 89 87

0.13 1-1/# " 96 50.# 96 96 96 96 96
” 1-1/2 ” 116 55.1 116 120 119 118 120
” 1-3/# ' 128 59.6 128 130 130 128 128
" 2 " 135 63.7 135 138 138 137 136
" 2-1/# ” 147 67.6 147 145 155 162 163

 

Table #

Response on A—flute Board to Shocks with
Low Acceleration to Velocity Change Ratios

 

Input Response Acceleration (g)

Flute Static DrOp Pro- Acc. VEIT'

Size Stress Rt. gram- (g) Change 1 2 3 # 5
(psi) (in) mer (ips)

 

A 0.52 25 Square 27 220 27 27 27 27 27

" " ” ” 30 ” 30 80 - - -
' 0.38 ” ” 36 ” 36 36 36 36 36
” ” ” “ 38 ' 38 38 38 38 130
w w w w 52 w 110 _ _ _ -
' 0.28 ” ” #6 " #6 #6 #6 #6 #6
w w w a 43 w 55 6o 65 68 70
. . ~ ~ 50 ~ 60 63 7o 80 -

” 0.13 " ” 78 ” 78 78 78 78 78

 

10

Table 5

Response on B-flute Board to Shocks with
Low Acceleration to Velocity Change Ratios

 

Input Response Acceleration (g)
Flute Static DrOp ‘Pro- 500. VeI.
Size Stress Ht. gram- (g) Change 1 2 3 # 5
(P81) (in.) mer (1P8)

 

B 0.52 25 Square 60 220 60 60 60 60 60

. w ~ ~ 6# n 6# 6# 6# 124 -

~ ~ w n 68 ~ 68 68 68 68 130
~ 0.38 - ~ 56 n 56 56 56 56 56
" " ' " 72 " 72 72 72 72 72
~ 0.28 s ' 75 " 75 75 75 75 75
' 0.13 ” ” “5 " 45 45 45 “5 “5
. n w - 6# « 6# 6# 6# 6# 6#

" " " " 76 1' 76 76 76 76 76

 

11

Table 6

Response on C-flute Board to Shocks with
Low Acceleration to Velocity Change Ratios

 

Input ReSponse Accelerationg(g)
Flute Static DrOp 'Pro- Acc. ‘VeI.
Size Stress Ht. gram- (2) Change 1 2 3 # 5
(P81) (in.) mer (ips)

 

C 0.52 25 Square 36 220 36 36 36 36 36

n . w w #o w #0 #o #o #0 #o
w . n n 5# w 5# 80 100 - -
~ 0.38 c n #6 n #6 #6 #6 #6 #8
. . w u #8 . #8 #8 #8 #8 112
. . . . 56 . 56 56 85 96 110
. w w . 60 . 76 80 88 9# -
n w n w. 72 w 72 114 - - -
- 0.28 . ~ 75 ~ 75 75 75 75 75

" 0.13 " " 76 " 76 76 76 76 76

 

12

Table 7
Reaponse on A-flute Board to Large Magnitude Shocks

 

Input Reaponse Acceleration (g)
Flute Static Drop “Pro- A66. ‘ve1.
Size Stress Ht. gram- (3) Change 1 2 3 # 5

 

(p81) (1n.) mer (1p8)
A ' 0.52 9 380 112 1000 - - § - -
n u 6 250 91.8 150 1700 3000 2600 3100
~ ~ 3 130 6#.9 80 100 700 1000 1000
~ 0.38 12 500 130 1300 - - - -
~ 7 9 380 112 #50 3800 - - -
n n 6 250 91.8 135 1900 2#00 - 2500
n " 3 130 6#.9 80 120 2#o 800
~ 0.28 12 500 130 700 #500 - - -
" ~ 9 380 112 250 2300 - - -
w w 6 . 250 91.8 150 320 1#00 2000 2300
~ ~ 3 120 6#.9 90 135 170 170 5#o
~ 0.13 12 #20 130 1100 2000 3000 5000 8000
~ ~ 9 360 112 3#0 350 550 500 1500
n w 6 250 91.8 220 300 300 #20 #20

” " 3 140 64.9 1#O 135 1#0 1#O 1#O

 

13

Table 8
Reaponse on B-flute Board to Large Magnitude Shocks

 

- Input Response Acceleration (g)
Flute Static Drop ro- K60. VeI.
Size Stress Ht. gram- (g) Change 1 2 3 # 5

 

(P81) (in.) mer (ips)
B 0.52 9 380 112 1000 - - é - -
. ~ 6 250 91.8 180 1500 2800 3000 3500
". ' 3 130 6#.9 130 160 330 700 1000
~ 0.38 12 500 130 1300 - - - -
~ " 9 380 112 #00 2000 - - -
n 5 ~ 6 250 91.8 220 600 1800 2500 2600
" ” 3 130 6#.9 120 180 180 170 #00
~ 0.28 12 500 130 700 #500 - - -
* n 9 380 112 370 800 - - -
. . 6 250 91.8 250 #00 800 1900 2000
~ ~ 3 120 6#.9 150 150 160 180 195
- 0.13 12 #20 130 1900 #000 2600 3100 3000
" " 9 370 112 #50 500 600 500 630
~ ~ 6 250 91.8 280 2#0 270 320 380

” " 3 1&0 64.9 1&5 150 155 155 155

 

1“

Table 9

Response on C-flute Board to Large Magnitude Shocks

 

 

In ut ReSponse Acceleration $52
Flute Static DrOp Fro- Icc. VeI. "*

Size Stress Ht. gram- (g) Change 1 2 3 h 5

 

(P61) (in.) mer (1P8)
C 0.52 9 380 112 1000 - - - -
. w 6 250 91.8 1#0 1#00 2200 2#00 2#00
" " 3 130 6#.9 80 1#0 #00 800 900
" 0.38 12 500 130 1500 - - - -
" " 9 380 112 280 2700 - - -
n " 6 250 91.8 260 900 1900 2100 2700
" " 3 130 6#.9 100 150 300 750 1000
n 0.28 12 500 130 #00 3600 - - -
” ” _ 9 380 112 300 1800 - - -
~ 0 6 250 91.8 200 550 1600 2800 2800
" " 3 120 6#.9 105 1#0 150 155 160
n 0.13 12 #20 130 700 1600 #000 5000 3800
" " 9 370 112 320 ##0 580 #50 720
w u 6 250 91.8 320 3#0 360 390 #00

" " 3 140 64.9 140 1#0 140 1&0 140

 

ANALYSIS

On the basis of the largest shocks whose reaponse
varied less than 10 percent, damage boundaries were drawn
which showed the dividing line between shocks which did
not cause the flute structure to be altered and those which
did (Figures 3, 6, 9). The horizontal portion of the damage

1 referred to by the author as the acceleration

boundary,
boundary, was determined directly from the data where pulses
with low acceleration velocity change ratios were used. The
curved portion of the damage boundary, referred to by the
author as the transition boundary, connects the horizontal
and vertical portions of the damage boundary and is theoreti-
cally a % sine wave. The vertical portion of the damage
boundary, referred to as the velocity change boundary, was
determined from points which were actually on the transition
boundary by applying a correction factor derived in Appendix I.
The information necessary to determine the damage
boundaries for some combinations of static stress and flute
size was unobtainable from the equipment used. However,
utilizing a three-dimensional concept of damage shown in

Figure 2 for each flute size, a reasonable prediction was

made of the unobtainable damage boundaries in the following

 

1Robert E. Newton, Fra ilit AsseSsment Theoryfiand Test
Procedure (Monterey, 153%), p. II.

15

16

manner. From the obtainable damage boundaries for A-flute
board plotted in three dimensions it was assumed that,
without any shock being applied, a specific level of stress
for each type of board would alter the flute structure.
Hence, for any given amount of static stress less than this
specific level, the amount of acceleration which must be
experienced by the block to produce the level of stress
necessary to alter the flutes can be calculated. From this
assumption a relationship between the acceleration boundary
and static stress was determined for each board size
(Appendix II) and plotted on the side view of the damage
boundaries (Figures 5, 8, 11).

It was also assumed that before any crushing or
alteration of the flutes take place that a high Spring
rate exists for a sample of corrugated board.1 Using a Spring
rate for each board size as determined from the obtainable
damage boundaries, a relationship between the velocity change
boundary and static stress was determined for each board size
(Appendix III) and plotted on the tOp view of the damage
boundaries (Figures 4, 7, 10). Using these relationships
determined, damage boundaries were predicted for the combi-
nations of static stress and flute size where these damage
boundaries were unobtainable from the data.

Having thus obtained damage boundaries for all

combinations of static stress and flute size, the effect

 

lThis Spring rate is high enough so that a corrugated board
sample is effectively solid, and any shocks applied are
transmitted through the board without alteration.

17

of the various input shocks which caused wide variations

in the reaponse shocks was examined. To do this, the input
shocks for a given static stress and flute size were plotted
with the damage boundary correSponding to that static stress
and flute size (Figurale-23). Values of response
acceleration which were less than the applied acceleration.

were underlined.

18

Table 10

Largest Shocks Whose Beeponse varied Less than 10 Percent

 

 

 

 

Flute Static Low Accézel Ratio High Accégel Ratio
Size Stress cc. e . ange cc. A . A
(p81) (5) (ips) (s) (1p8) (198)
0.52 27 220 33 27.5 23.9
0.38 36 “ #7 35.6 27.8
A 0.28 46 ” 6H “5.0 36.3
0.13 76+ ” 116 55.1 -
0.52 60 220 88 50.# #1.8
0.38 72+ * 120 59.6 -
B 0.28 76+ " 118 65.6 -
0.13 76+ " 2#0 8h.2 -
0.52 #0 220 50 35.6 28.7
0.38 #6 ” 68 45.0 37.5
C 0.28 76+ " 9h 50.# -
0.13 76+ " 135 63.7 -

 

19

Table 11‘
Points Used to Define Damage Boundaries

 

Point on Transition- Point on Transition-
Flute Static Acceleration Acc.Boundary Transition Vel.Boundary
Size Stress W W
Acc. AV Acc. AV Acc. AV Acc. .AV

(8) (ips) (s) (1p3) (s) (ips) (s) (ips)

 

 

0.52 27 220 27 37.6 33 27.5 5“ 23.9
A 0.38 36 220 36 #3.? #7 35.6 72 27.8
0.28 #6 220 #6 57.0 6# #5.0 92 36.#

 

B 0.52 60 220 60 65.7 88 50.“ 120 ”1.8

 

0.52 36 220 36 #5.1 50 35.6 72 28.7
0.38 #6 220 #6 58.9 68 #5.0 92 37.5

 

20

SCHEMATIC DIAGRAM OF THREE DIMENSIONAL DAMAGE BOUNDARY

 

 

 

 

 

 

 

 

 

Top View
/] .
_ .1.11 __ -_.---,-,)T,/”’/E
__ 1 g _ 1-7/ a
I
P:
l:: <I-—-——--
II
\
T “3‘ Side View
A -__ 2
Acceleration ‘t::-::: --- 3
i 38
‘ //4°
: s”
10
Stat

 

 

 

———-—->
//////)7 Velocity Change

Front View

Figure 2

1
2

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and m~.o

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63,, a... 68 at a:

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CONCLUSIONS

Any shocks applied to corrugated board which were
outside of its damage-boundary did not affect the flutes
and had the same effect on the article on the Opposite side
of the corrugated board as if the corrugated board were
solid. It was evident that shocks applied to corrugated
board which were within the damage area had a devastating
effect on the object on the Opposite side of the board,
eSpecially if the shocks were repeated. The farther away
from the damage boundary these input shocks were, the fewer
shockawere necessary to completely crush the flutes.

Shocks applied to corrugated board when a container is
drapped have a high acceleration-velocity change ratio. In
order for these shocks to crush the flutes of the container
they would have to cross the damage boundary in the velocity-
sensitive range. The range of drOp heights which would
generate shocks with sufficient velocity change to cross the
damage boundaries investigated here would be from 0.8 inches
for A-flute at a static stress of 0.52 psi to 9.1 inches for
B-flute at a static stress of 0.13 psi. These values are for
articles which eXperience no rebound. Any rebound eXperienced
by an article will cause these drop heights to be less. DrOpS
which are not flat will also cause these heights to be less

because the weight of the article must be supported by a

#2

“3

smaller area of board which effectively increases the static
stress. It was shown that less velocity change was required
to alter the flutes if the static stress was increased. From
these observations it is eXpected that a great majority of
package drOps will result in alteration of the flute structure,
and subsequent shocks will be amplified when eXperienced by
the Object on the Opposite side of the corrugated board.

Since drOps occur with random orientation, it is possible
that a package would not receive more than one impact at the
same part Of its container. This would warrant a further
consideration of first impacts. For input shocks in a small
range close to the damage boundary there is some cushioning
effect from the corrugated board on the first impact. This
is due to the flutes being crushed by the shock,which causes
the shock to be lengthened in time and reduced in magnitude.
Repeated shocks or shocks which are outside of this range are
sufficient to crush all of the flutes, allowing the objects
on both sides of the board to collide.

According to Rule #1 of the Uniform Freight Classifica-
tion, the maximum weight allowable in a box constructed of
ZOO-pound test singlewall board is 65 pounds. The sum of
the dimensions cannot exceed 75 inches. Assuming a minimum
of three inches for any one dimension, the maximum static
stress in a ZOO-pound test singlewall container would be
0.723 psi, and the minimum static stress would be 0.050 psi.

Based on this and the predicted relationships derived in

nu

Appendix III, the range of drop heights which will cause

enough velocity change to allow damage of the board is from
0.571 to 23.6 inches. In actual practice, this range will
be much lower since this range is also based on no rebound

and perfectly flat drOps.

APPENDIX I

DERIVATION OF A FORMULA WHICH GIVES THE VELOCITY
CHANGE PORTION OF A DAMAGE BOUNDARY WHEN ONLY A POINT
ON THE TRANSITION AND A POINT ON THE ACCELERATION PORTION
' OF THE DAMAGE BOUNDARY ARE KNOWN

Given a damage boundary with the following points

and line segments:

VW - Velocity Change Boundary
WY ~ Transition

YZ - Acceleration Boundary

w - De'sired'Boi'nt (Aw.-..Vw)

 

 

 

X - Known Point (Ax, Vx)

 

Y - Desired Point (Ay, V?)
2 -Known Point (AZ, v2)
The arc WXY is a isine wave with its origin at W and

its peak at Y, therefOre

 

A -A

Sin-1 " x

Vx-Vw ‘ I:IAy

- -
y w Sin'l(l)
From damage boundary theory:
17
Ay = A2, A.w = 2A2, V3, 3 5- VW

“5

#6

Substituting into Eq. (1) and solving for VW:

Vx

V ..
w 2A -A
Sin-ll z at]
A2

 

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77
( __.- 1 )
2 Sin"I (l)

Allowing that the angles will be Specified in degrees,

Eq. (2) becomes:

Vx

Vw 3 - .
ZAZ-Ax

(0.006342) Sin-1
AZ

SAMPLE CALCULATION

For A-flute board at a static stress Of 0.28 (Fig. 3,

Table 10)

2-6
Sin'l‘Z-EEE = Sin‘l (0.61) - 37.6

VW ‘ 45,0
(0.006342) (37.6) + 1

VW '3 3603

Since vy =.%§ vw and AW = 2A2, all values for

points W, X, Y, and Z are defined.

APPENDIX II

RELATIONSHIP BETWEEN
THE ACCELERATION PORTION OF THE DAMAGE BOUNDARY
AND STATIC STRESS

The amount of stress which would alter the flutes with
no shock is the product of the static stress and the shock
in g's experienced by the weight which caused the static
stress. Since the acceleration which the weight experienced
is twice the input acceleration for shocks along the
acceleration boundary, this critical stress, 80, for A-flute
board is: I
s 2 (SS)(2Ap/s)

c
28.0 psi for shocks applied at 0.52 psi

3 27.# psi for shocks applied at 0.38 psi
3 25.8 psi for shocks applied at 0.28 psi
Since this critical stress should be a constant for a
given board size, the best estimate of that constant would
be the average of the three values.
'S0 = 27.1 psi
The relationship between the acceleration boundary
and static stress for A-flute board becomes:
(SS)(2Ap/s) = 27.1
and the value of the accleration boundary is given by:

Ap/g = 13.55/38

a?

U8

The value of the acceleration boundary is then:
Ap/g = 13.55/38
Similarly, equations can be found for the other two
board sizes:
Ap/s
Ap/a

31.2/SS for B-flute
18.1/SS for C-flute

These relationships are plotted on the side View Of their

reapective damage boundaries (Fig. 5, 3, and 11).

APPENDIX III

RELATIONSHIP BETWEEN
THE VELOCITY CHANGE PORTION OF THE DAMAGE BOUNDARY
AND STATIC STRESS

From damage boundary theory it is know that

1 A
‘1 2w fo ( )

g-
0
H
(D
E:
H
II

limiting velocity change for the
velocity change boundary, in./sec.
A a response acceleration which begins

to cause flute alteration, in./sec.2
fo = frequency of test block on corrugated

sample when flutes are unaltered

1 k
Substituting fc 3.5%; E ,
Ac = ZAP ,
and SS 3 mg/64 = static stress, psi

into EQ. (1) and solving for k,
k a 98800 (AP/g)2 ss/(xsv1)2. (2)

For A-flute board Ap/g = 13.5/SS from Appendix III and
k a 1.82X107/AVi ss (3)

49

50

Solving EQ. (3) at the various statis stresses,
k a 61300 lb./in. at 0.52 psi
k . 62000 1b./in. at 0.38 psi
k = #9000 1b./in. at 0.28 psi
For purposes of extrapolation, it is assumed that k is a
constant over the range of static stress in consideration
and the best estimate of its value is the average of these
three values.
5': 57n00 1b./in. for A-flute board.
Substituting this value back into equation (3) and
solving for NI , .
svl . 17.8/ ss‘é
Similar equations for the other two board sizes can
be obtained:
B-flute 4V1 a 30.2/ss*§
C-flute Avl a 21.9/ss*%
These equations are plotted on the tOp view of their

reSpective damage boundaries (Figures 4, 7, and 10).

BIBLIOGRAPHY

Newton Robert E. Fra ility Assessment Theory and
Test Procedure. ficnterey: Monterey Research
ra or es, Inc., 1968.

Harris, Cyril M., Crede, Charles E. Shock and Vibration
Handbook. New York: McGrawaHilI BOOK Company, Inc.,

9 .
Mindlin, Raymond 0., "Dynamics of Package Cushioning,"

Bell 8 stem Technical Journal, V01. 2h (July-Oct.,
I553, 535-331
g o

 

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