MECHAMCAL ANQ RHEOLOGECAL PROPERTIES
OF GRAEN

Thais for 9h: Down :29 9h. 9.
MECRIGAN STA?! RiNWERSéTY
Garaid Charis: Zoarb
1958

T _ u 131: um; winging"); [in y}: (Q My! {11! {me um '

35

This is to certify that the

thesis entitled

l‘lECfiAl‘JICAL AND RHSOLOGICAL PROPJE’EL‘JS OF GRAIN

presented by

Gerald C. Zoerb

has been accepted towards fulfillment
of the requirements for

PhoD. degree in AgriCUltural
Engineering

 

flmm/ Q44

Maior rolessor

Carl l?“ o 11

 

Date Parch 1;, 19:8

 

0-169

 

 

 

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)VlESl_J RETURNING MATERIALS:
Place in book drop to
LIBRARIES remove this checkout from
“ your record. FINES will

be charged if book is
returned after the date
stamped below.

 

 

 

 

 

 

 

 

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OF GRAIL

by

r‘! - s n a ‘ _‘ P7
uerala bAaPleb goers

AN ABSTRACT

a an - u H 7‘ u o -, n. ’1.-fi,.»L~ "4- ~: n.

u witL3d to toe ocuool Lor advdnced orddndoe o-‘liou db
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.lCth n o dte UHLV2L3;tZ of Agricultuie o

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ea science ;4 ‘erolgl tuisillment of
rV ‘ . ‘~‘i'v ' V' J- I l' ‘— ’ ‘ 3" , i

r dlrnndeiu, f:u one tv;brmxz of

DOC'i' OR OF E IEIL 05 OF] LY

Approved W ¢t' W

A35 RACT

Little information has been found describing physical bro—
perties of individual grain kernels. a library search revealed
no information pertaining to mechanical prOperties, such as com-
pressive strength, modulus of elasticity, etc. Problems such
as kernel crackage during threshing and handling may be analyzed
more readily when basic information concerning mechanical pro-
perties of grain is made available. Ihe objective of this
study was to determine some basic mechanical and rheological
properties of individual bean, corn and wheat kernels.

A SR§4 strain gage transducer Was designed and built to
measure load and deformation for the individual kernel under
test. by means of electronic equipment, load, deformation, and
time relationships were recorded simultaneously. a pendulum
impact tester was constructed and used to measure the energy
re.uired for impact shear.

The desired relative humidity was obtained with various
saturated salt solutions in a dynamic equilibrium noisture

um much faster than in a

L—‘o

chamber. The grain reached equilitr

static Chamber, thus preventing exceSsive mold formation at the
higher moisture levels.
The effect of moisture content on kernel preperties was

the chief parameter studied. Uther parameters investigated
were the effect of rate of deformation, and the relation of

kernel yosition, edge or flat, to strength characteristics.

Gerald C. Zoerb

iii

The following mechanical prOperties were investigated:
yield strength and maximum compressive strength of the kernel
in the edge and flat positions, average shear stress, modulus
of elasticity in compression, modulus of resilience and modulus
of toughness. Comparison was made of the energy required to
rupture the grain kernel by impact shear and by static shear.

a preliminary study of kernel hysteresis loss, obtained from
loading and unloading cycles, was carried out.

hoisture content had the greatest influence on the
strength properties of grain. The compressive strength, modu-
lus of elasticity, maximum compressive stress and shear stress
generally decreased in magnitude with an increase in.moisture
content. energy requirement for impact shear was higher than
static shear at high moisture; the reverse was true at low
moisture. iodulus of resilience and modulus of toughness did
not vary greatly with moisture change.

Some rheological properties of pea beans were examined.
The effect of rate of deformation on the resulting force was
qualitatively examined for pea beans. Stress relaxation with
time was studied for three moisture levels and three deforma-
tion rates. .Initial rate of deformation had more effect on
the rate of stress relaxation than moisture content or the
initial amount of deformation. Relaxation time was constant
with various deformation amounts. n two-term eXponential equa-
tion was obtained graphically to express the stress relaxation-

time relationship.

Gerald C. Zoerb

RECHANICAL AND RHEOLOGICaL PROPERTIES
OF GRAIN

by
Gerald Charles Zoerb

A T131138 IS

Submitted to the School for advanced Graduate Studies
at hichigan State University of Agriculture
and Applied Science in partial fulfillment
of the requirement for the degree of

DOCTOR OF PHILOSOPHY

Department of agricultural Engineering

1958

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101" ‘UlSQI‘JS SO 8X11"

Dr. Carl ..'. hall, .’u*‘=‘-ic7.tll ui al 2321:“i1'1e:31°i.';,3 Depa1t:..ent, under

L)‘ 7..)
whos e continual inSpiration and guidance this iizestigation

w as und 3 r t al: e n .
Grat efil acknowledgement is also extended to Professor

7"

Eaul DeKoning, applied he hanics Department, Dr. .sesley r.

1-J

suczele and hr. dichard C. Lic olas, n ViiCAltural angintaeri ng

Department, an"; Dr. Donald 0. 1.0117: ery, Ih;;sics i297“; rent,

to Dr. a. u. Farrell, Head,

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encouragement throughout 13:13 work.

vi

Gerald C. Zoerb'
Candidate for the Degree of
Doctor of Philosophy

Final Examination:
December 30, 1957, 10 A.H.

Dissertation:
mechanical and Rheological Properties of Grain

Outline of Studies:
Major subject: Agricultural Engineering
Minor subject: Physics ~

Biographical Items:
Born November 22, 1926, Delisle, Saskatchewan, Canada.

Undergraduate studies, University of Saskatchewan,
1944-1948. ‘

Graduate studies, University of Minnesota, 1948—1950;
Michigan State university, 1955-1958.

Experience:
Massey Harris 00., summer 1947; Canadian Co-op Implements
Ltd., summer 1948; Graduate Teaching Assistant, University ,
' of Minnesota, 1948-1950; Instructor and Assistant Professor
South Dakota State College, 1950, 1952-1955; United States
Air Force, 1951-1952; Graduate Assistant, Michigan State
University, 1955-1957. '

Honorary Societies: -
Sigma Pi Sigma, Sigma Xi.

Professional Societies:

American Society of Agricultural Engineers
American Society for Engineering Education

TABLE OF CONTENTS

ADSTIRI‘XCT 000000000000000000000000000000‘0000000000000000

ACKKOIJLJSDGL‘JLLII‘ITS 000.0000000000000000.0000000000000000.

VITA ...o..Io0..0.00000000000.00000000000.000000000000.

LIST OF TABLES 0000000000000000.0000000000000000000000.
LIST OF FIGURES .C.....0......O...........O...........

INTRODUCTION .0000000000000000000000000000000000000000.

Definition Of The PrOblem 0000000000000000e00000000

Statement Of The TheSiS'PrOblem 0000000000000000000

Objective .‘............OOCOOOCO.C...’...'.........

REVIEW OF LITER$TURE o0o0000000000000000000000000000000

APPARATUS 000000000000000000000000000000000000000000000

RCQUirementS 00000000000000000000000000000000000000

DeSign ......._-‘.....0......C......................‘

Load Transducer ...............................

Design calculations .......................

LaXImum-Stress i2_beams 0000000000000000000

haximum deflection gt.middle‘2£ beam ......

Deformation Transducer - Cantilever Beam ......

Design_calculation ........................

Strain Gage Configuration .....................

Load cell traDSduceng 000000000000000000000

Cantilever beam deformation ...............

calibration 000000000000000000000000000000000000000

Load Cell 000000000000000000000000000000000000.

Cantilever Beam Calibration ...................

Other Features of Apparatus .......................

CrOSShead SpGGdS 0000000000o0000000000000000000
Relationship Between Chart Speed and Crosshead

Travel 000000000000000000000000000000000000

Pendulum Impact Tester ............................

DCSiEH Calculations 000000000000000000000000000

finergy Relations 000000000000000000000000000000

Correction for Losses .........................

LIETliODOLOGY 0000000000000000000000000000000000000000.00

CompPeSSive TeStS 00000000000000000000000000000000-

Shear TCStS 00000m000000000000000000000000000000000

fieasurement Of Energy 0000000000000000000000000a000

ImpaCt TeStS 0000000000000000000000000000000000

finergy Of Deformation 0000000000000000000000000

HyStereSiS LOSS 0000000000000000000000000000000

Total dnergy versus Surface area ..............

Calculation or surface Area 0000000000000000000

RheOlogical PrOpertieS 000000000000000000000000000o

dates Of Deformation 00000000000000000000000000

Stress Ralaxation 00000.00000000000000000000000

 

 

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3105*93 JED DldCUJJlUK

Comyressive Tests
Comlres ive
Con :preSsive
UOEH*»195-1VG
Core Comgres
3118111“ 183358 0000000000000
Punch Shear Tests ...
Leasurement Of dnergy ...
Impact Tests ........
flysteresis Loss
lodulus of HeSili

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for
for
for
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A Practical application From The Res
Shilsnl‘ll 00000000000000.000.000.000.000.
mechanical Properties .............
AhGOlOSiCJl Properties 000000000000
other Observatixnrs ................
CUMCLkQIOuO .................I.........
QLJZJSTILIQ FOR FURTHER 3?UDY .........
dPPEnDIX 000000000.00000000000000000000
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Crngurison of Compressive Force at Ieditn Speed
Re1uired to Defori Yellow Dent Corn to the Yiel‘
Eo int and to lax 'wxm Strength at Four Ioisaure Levels

1 >0 1-_‘ ___ I“ fly) - "T f 4" —-|1 L‘

J1 1111118 Kmnel 1131.10 11.1t ......I................. 129

ssive Force Requ e

Pea Jeans to the Yield Po
A '1 Q

"d at hedi 11m Speed to Deform
”..lt 10. (3/0 (1.1). 111 :3 L19 DC;

1t BIYQI-QYlFRU' Strerqfifll

and 11st Eosi,lons ...... 150

Force ;equi1 d to Deform So t Red Jinter Wheat to
the Preportioual Limit, Yie 1 Point and Kaximum
Strength at 13.0% d.b. in the Flat Position at

":0 .1 fl r-
1171788 Speed: 0000000000000000000000000000000000000 1'51

38. Comparison of CJVCJ seivc Farce at Kediux Speel
iEe quired to De1m1r1 deft Rea flinter wheat to iEe
310151 fault 11111.1 1:) Leg-:ilnxu'n Strength at “Rio Dis Jure
Le ve els 31th the Ke1nel in the uljt losi tion ....... 152

A9. 1ner3y for Failure of Yellow Dent Corn by Imgact
Shear at Four Loisture Levels, inch-younds per

S~1Ll§ire 11.10::- OOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO lrI-v

A10. xfimnégy for Faillufie of Soft Itwl.tu1t13r wheat by
Impact Shear at :Fnucl o eture Le vels, inch-p unds
(””31 SC‘lLl-ure iI-lcll ......OOOOOOOOOOOOOOOO......COOOOO 154

All. £ner3y for Failure of Pea ZEEeans by Impact Shear at
Four Koisture Levels, inca-pounde per square inch . 38

~ ‘* 1 “\ 0 J- ~ *5 . ‘."\ A, _ 5

115. energy nequired to Rupture Pea oecns, -wp.op d. b. Dy
Impact Shear at T”o Velocities, incEl Iounls p r
sq‘dell’je iI-iCl-l .........OOOOOOOOOOOOOO0.000.000.0000. 156

15.
15.
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18.
19.
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LIST OF FIGURES

General View Of apparatus 0o...0..0.00000.0.0....0
UndeTSide 0: load Cell unit 00000.00.0.0000.00000.
Load cell unit ready for compressive test ........

ue&m dCUign or load Cell 000.0000.00.0000....0...0

Physical and electrical locations of 83-4 strain

gages 0.000.0....000.....0..0.....00.00.00.......0
dheatstone bridge circuit .........................

Schematic setup for calibration of load cell unit .

Calibration Of 103d Cell unit 0....00000000000......

Schematic setuv for calilration of deformation unit.

‘1 s

c ematic diagram of drive mechanism .............

Another use for load cell unit -- testing plastic

beam SpeCimCiS 0.000000000000000.000000000000.....
PelldUlUIn iNlPZlCt toe-Star 0.00.000000.00.00.000000000
SthCh Of imp&Ct teSter 00.00000000000000000000...

Schematic of impact tester for determining energy

relationships 0.00.00...0.0.00.000000000000000.000
Dynamic equilibrium moisture chamber .............
Drawing of dynamic equilibrium moisture chamber ..
Linature Tyler sieves and core specimens .........
upgaratus for punch shear tests ..................
fiepresentative oscillograph charts ...............
apparatus for static shear test ..................

Lumbering syStem for Tyler Sieves 0000......00000.

Lechanical models used to represent rheological

1 ~ .
DeflaVlOI’ O000.000..00000000000000.00000.00.0000...

15
16
17
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Load-deformation curves for yellow dent corn ......

Load-deformation curves for yea beans at two

NIOiStWJI.e levels ...........0......OOOOOOOOOOOOOO...

Load-deformation for pea beans at three moisture

levels 00............OOOOOOCOOOOOOOOO.......0......
Load-deformation curves for soft red winter wheat ..

Relation between modulus of elasticity, maximum
stress and moisture content for yellow dent corn

in COfipPeSSlOn 0...000.00.000.00...00.00.000.000...

Relation between modulus of elasticity in compression

and moisture content for soft red winter wheat ....

Relation between maximum stress in compression and
moisture content for soft red winter wheat ........

1

Relation set C
stress for pea

L

n “lab thickness and calculated shear
be ns using punch test .............

co

Relation between shear stress and moisture content
for soft red Winter wheat and yellow dent corn ....

Relation between shear stre<s and moisture content

fox-1138a ‘L/eans .0.................OOOOOOOOOOOOOOOOOC

energy requir ments for rupture of soft red winter
Wheat RCTDSlS by inpaCt Shear ..000000.....0000....

nts for rupture of yellow dent corn
t

'r '3 4., -~ ’ t~"«r.
allCL SUdLlC 0116;qu 0000000000000...

dnergy requirements for rupture of pea beans by

static shear and impact shear ............,,,.,,,.,
Representative oscillograyh charts for wheat cores .

Hysteresis lOOpS for soft red winter wheat cores ...

O

Hysteresis loops f r yellow dent corn kernels .....

Hysteresis loops for pea beans ....................
energy to deform pea beans to yield yoint and soft
red winter>rdunm:'to the yield.;tfixu::nri1naximum

z. 4.3, t a- H-) 5 .2. “‘ . ,.
Shrenguu do MVU1dm Speed 00.00.00.00.0.0.0...0.....

uncrgy to deform yellow dent corn to the yield point
in edge and flat FOSitionS 0.00.00.00.00000000000..

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finer 3y to deform yellow cent corn to the maximum
strength in the flat position .................... 95

Load-deformation curves for pea bean rt 52.8
percent moisture (d.b.) for three 3 s ......... 99
effect of rate of deformation on the resulting
compressive force for pea beans at 32.8 percent
mOiSture (dObO) ......OOOOOOOOOOOOOO0.00.00.00.00. 100

Rate of shear strain as a function of stress for
four t‘rpe 38 Of .LlLLiU. .0...0000000.000.000.000...... 10]-

Stress relaxation for pea I‘eans at various moisture
levels and amounts of deformation ................ 102

GraphiCal determination of stress elaxatio n equa-
tion for pea beans at 18.5 percent moisture and
4505 percent dolor -ati 0.0.00000.00.00.00000000. 104

r'.’\

3 a ‘s rel ¢"ation curves for pea beans at os.8
3 nt moisture, d.o., in fl't position ......... 106

cal lfie Iresentation of pea beans by two
units in 3911903 0.0.0.000000000000.....000 108

pa
>4
5'~
F1
ede-

Jorce required for deformation of pea beans a

medium Speed 00.00....000000.....00.0000.00.000.0. 109

Graphical picture of sensitivity of mechanical
mOiSture meter for Ped beans 00.00......0..0.0.000

INTRODUCTION

Definition Of The Problem

Grain farming represents one of the largest segments of
the agricultural industry, particularly in central United
States and in western Canada. Both the farmer and the indus-
trial food processor handle grain in a variety of operations
from planting through harvesting to processing. Many problems
are encountered in the various Operations. A good example is
the problem of pea bean crackage during handling in elevators.
Grain cracking during the threshing operation is always a po-
tential hazard affecting the quality of the final product.
Also, relatively high power requirements are needed in the
grain size reduction process. In Spite of the tremendous ex-
penditure of time and labor in the various operations associ-
ated with grain, very little is known about the basic mechan-
ical properties of the individual kernel.’

Certain basic data, such as Specific heat, dielectric con-
stant, thermal coefficient of expansion, coefficient of fric—
tion, equilibrium moisture content, etc., have been obtained
to a small extent in the last 10 years. These data are still
scattered and often not available for more than one grain.

No information has beerxuncwvered to this date on the mech—
anical or rheological properties of grain. Basic data, such

as compressive strength, impact shear resistance, modulus of

resilience, are important and in some cases necessary engin-
eering data in studying size reduction as well as seed resis-
tance to cracking under harvesting, handling and drying con-
ditions. From an energy standpoint, this information can be
used to determine the best method (shear, impact or static
crushinfi: etc.) to break-up or grind grain. Data for other
properties will have singular or multiple us 3. Furthermore,
and perhaps much more important, when basic data are uncover-
ed, ew uses for the product and new ideas for further re-
search.will become available.

It is essential that the civil and the mechanical engin-
eer know the mechanical or engineering properties of steel,
wood, coal, stone, plastic or other materials with which he is
dealing. Similarly, the agricultural engineer must have basic
information about grain, one of our chief agricultural

products.

Statement Of The Thesis Problem

The four parts of the thesis problem are:

l. The design and construction of an apparatus suitable
for measuring the mechanical and rheological preper-
ties of individual grain kernels.

2. The determination of compressive and shear strength

characteristics of corn, wheat, and beans at various

moisture levels and rates of deformation.

0. The determination of energy relationsnips in seed de-

.L

formation, failure by impact, and surface area

produced.
4. A qualitative study of some rheological preperties

of one grain (pea beans).

Objective

(f)
3

The broad objective of thi

,3

tiesis study i» to obtain

L

some basic knowledge of the nechanical preperties of grain.
The ultimate goal through_increased Knowledre of grain proper-
tiesis greater efficiency of operation and the UNVgllinf of

new methods and perhaps new uses for grains.

 

 

E§§—#

Hn’ J1... " W 01" IlTahA‘v’R ‘

There has been no Ivor}: refereed on ta) uubul‘llifl-filtjflll of
the :1; herdwmil pqvnwartiln: of gpmiin; ijrpextixmrtei 151 this
study. Nowever, certain physical properties of jndiv1dual
kernels, such as specific gravity, coefficient of fliction,

J- 1"

ceefficieru,<m. Hiermml.cnqanr;ion and e u 'li.ud1cnr~oisture
ccnitern; ?u1ve1 eern1 1w31cn3tcml bjr Vancigmy' izvvcsgtigyatcnfis. 3118
avaijiflale waxic dai¢:;and lixrieruiCTt.for fail: Cfi151n €1u91 as
tKerwal 00nd ctivitv and RFTlC of reyose iave te:n um1111/0d
10y i C.L1] (Inf-'7).

The only lata available related to the mechanical pro—
Pe143°es (if irmzividtmtl serwhs are swmne *ue ler21“PU Vthi L?

‘)

cnieilgr inte1<rsted 311 the

L~o n (12:5) on pea beans. he

relation: 1ip between Lean crack re and moisture content. he

‘

measured tne load requilc ed b0 crack the bean 333$ coat ant
1" ~ .-‘- 1 arr-f7. '7‘. ‘°~- 4' -'~ ' Y‘ ° 4-} a 7‘ -.-, . ,7 72. v? o 7 '° a w.” ° Hf ‘3')
J. '~)Un‘-t L,» nil LJKJ \v uridbioii 1n Lu1‘4 .1.‘>l (,C a. 2(1C.;I‘u‘ Q " ls‘ -1“) L“ 11.1 C
.- '— , ~~ h. ,1 vn'.~ r. (‘Y‘ r‘ y 3, \-, .‘ , ’ r, a: _ i ‘ -’ ,, --1
content rafge "as small, flan C.Cp t.b. to 9-3” L.b. ror
‘gecz:s aan.!;er1:seexus 131 tlx3 flilt 1;osilzicn1, idle :f01mn3 rchiuiiuad

4‘ i . .‘ 1- pa
JKI'. ullll.‘ ..iii-

0
:1:

ts crack the bean soed ceat ULl ind a static l

C?

chine viried from ll '0 45 pounds. The aveiage moisture con-
tent Wes 8.3» W.b. and the aVe‘ege force has 21.7 rain
impact tests were conducted.

although no measurements of energy of deformation for in-

 

mcisture weight
nmfibwemfigmqrmfivmjmfi'xbfl

gr
- -
l\

w.b.: wet basis:

ciividual grain kernels have been reported, extensive experi-
rnents on feed grinding with commercial burr and hammer mills
iiave been carried out. These studies have shown the relation-
Slllp uhen grinding between power requirements, grain moisture,
17ineness, speed and rate of feeding. Krueger (1927) found that
tjde capvcity for corn, lh/hp-Hr, increased as the speed decrees-

rrl, though not in direct proportion. Tn addition, the product

go

-weeomes coarser with decreased Speed, Although less horsepower
1&5 required per pound of material as the speed decreases,
rusthing is known of the relation between input energy and the
Silrface area produced. Silver (1931) demonstrated that at a
gyiven rate of grinding, the power increased With increased
Ifiineness and with higher moisture content.

In the grinding process most of the mechanical energy is
ciissipated in the form of heat. This raises the tmeperature
01‘ the product and the surrounding air. The actual tempera-
tixre rise of the grain will depend on its specific heat, its
ttuermal conductivity and the distribution of heat losse. from
time grain by conduction, radiation and convection. Silver
fwnxnd.temperature rises of up to 500 F for fibrous material
beirrg finely ground.

When a solid is deformed by application of a load and
the Iload is then released, a hysteresis loop is formed. Thus
the (energy required.to deform it will be greater than +‘he

U

exhxrgy given Up when the load is released (except for perfect-

ly elastic solids). The energy retained in the material ap-

pears as heat. In the grinding process, the rise in temper-

ature is said to be due to "friction" created between the
tyurrs or hammers and the grain. As a kernel of grain or
ifiragment of a kernel is encountered by successive ribs on the
gyrinding plate, it is no doubt deformed several times before
igt fractures or is reduced in size by the rubbing action.
ifliis repeated deformation plus the rubbing action raises the
ggzrain temperature. Since the efficiency of grinding is con-
:SLidered to be higher with less temperature rise, a prelim-
;113ary investigation of elastic hysteresis of grain kernels is
<221rried out in this study. This information should be useful
:11: future studies in size reduction of grain.
The relationship between energy of crushing and new sur-
;feice produced in the crushing of rock, has been studied by
nralqy investigators. In most instances the uncertainties in
nueeasurement of surface area made the results questionable.
Kdvcyng gt a; (1949) have worked with quartz, glass, halite,
allfii fluroite, and have used water and air permeability methods
t4) determine the surface area. For material larger than 65
Inesih, water permeability was used, and between 65 and 200
nussli, air permeability was used. Energy was applied by im-
Pamrt. These researchers found a linear relation between the
net, input work to crushing and the new surface area produced,
except for halite. "hen the energy was applied by slow com-
prefssion, a slightly curved relation was observed showing de-
creasing surface produced per unit of energy with increased
Crushing.

In grinding of agricultural grain, tests have been

basis oi energy .er gound of ground feed,
Lyn-nr/lb, at a given ”fineness modulus . since a certain fine-
IleéLS modulus figure Can be obtained by an iniinite combination

0; fl’ei ght retained on the various creens, it does not give a

(I)

"O

'traie picture 01 the surface area produced. Licholas and hall
(1E357) have deve leped a mathematicalnethod for expressing the av-
eiuige particle size in a ground grain. an eXL1ession is deveIOp-

cxi ;in Jiis s adv for the total surface area in a sample of ground

h 4- ‘fi 9 " l 1 (N ‘ ,x‘z- -“ . ‘ ’ r" '2‘ A, F 1 ' ‘
oteenoerg (leeg) Jab Ou aimed stress-st ain (a ctaall load-

elxangption) erv s for paper. when CAO load was applied, and

tlieqi released, a definite hysteresis loop Was ottaincl. ihe
...“ ‘ f. 4‘ I l Nfr, 01 7‘ ~‘. . 7 C C'L’Nj‘: ( Va ”V \’ (N) r
U; Opt, 0.. LIL" O V OA‘c “VuLQll C1£I VG ' “U 5.) UK!» ‘1 VJ- OLI UlAe UDCJLIQ

.0 1 , '- 0 7 _ 1 - ‘ _‘ fl‘ r ‘ _u H
lxaaxiing 1 n on td‘ iirst. ”tecnbc1g called

sic arable permanent set was observed. Aurth>rmore, on the sec-
ond. loading the paper showed a llanounc ed yield point at the max-
imm Jil stress of the first process. inis is caused by the first

n

es 0; t11e :3a1;el .

stregining process changing the11r0pe1

She influence of the rat: of straining of mat;:ials on
sarerngth properties Eur; 1een inves;igate£i2r;znany norkerS.

‘Ahmilcfil (lQéC) states that the speed of load aprlication in

- .L: ‘ ‘ _ .‘ ....r, 0 fl _-:_o g ‘V‘ .. -,13 - 7 ~-.-». .

L35v411g RUJUGP makes little a1f1erence in ordinary ranges of
I ‘1‘ . I, O 0 - a

1/8 cc) 2 ia/min. In tension tests on la metals, Jones and

Ioore (1910) concluded that, except fa” stsialc1s steel, the

er; ha‘ ‘ 4.. 4. , , . ..v- ,1 I. . ;.‘..,...'. . -° - °
8 ‘e+cxl statement could be made that a zariatizn in rate of

A

stra

Ho

1‘31 . - - v 1 . 1‘ x y, M : q - 9.- "? ‘1' 5~ -. -‘\ -- ‘ . '. -
Ii 11cm h pelcent pe1 Linute to uh percent ier n1nute

‘70 .3 ,0 , p o _ J o 1. ~ ~ - o
“14. introduce a variation not [greater than one Lercent in

the value of yield strength or tensile strength. Davis at a;
(1941) state that the effect of speed variations within the
range of normal rates of loading on the strength of brittle
Inaterials such as cast iron appears to be small.

The rate of straining has more effect in the case of a
"plastic" or "visco-elastic" material. hith.impact tests for
Iaewsprint where the time of straining was of the order of one-
tflaousandth of a second, Steenberg found that an increase in
tile rate of straining of one million times (over static tests)
ixicreased the breaking load ten times. However, for ragbond

pnaper, the corresponding increase in breaking load was only

60%.
Dachinger et al (1957) have measured the work required to
sfliear aSparagus at various speeds. Work was determined by

nusasuring the area under the force-displacement curve. A high
ccnmrelation was obtained for both work and maximum force with
fiJorousness of asparagus.

Physical properties of single wool fibers have been in-
veustigated by hontgomery and Evans (1955). During the force-
axtension.curve, they found a definite elastic or hookean
Pegicmxfrom which.an elastic modulus was computed. other
parameters obtainted were stress at 20 percent extension, rel-
ative work at 20 percent extension, and stress at the breaking
Point. 4 rate of extension of 0.5 in/min was used. These in-
vestigations were carried out on wool from various sheep and
their properties compared at various_stages of the manufactur-

1n8‘process.

(O

Rheological properties of many materials have been inves-
tigated. dheology is defined as the deformation ani flow of
matter. Its goal is to describe the mechaniCal behavior of a
material in terms of the three variatles, stress, strain, and

time. as stated by Lason (1948), when a body is subjected to

L

a loading, the strain consists essentially of two components:

1. an instantaneous deformation associated
with an idea elastic body. This is
assumed to be completely recoverable.

. a time-dependent portion, repr senting
"flow" characteri~tics of a viscous
liquid.

Of the time-dependent strain, part is recover-
able. This is known as "primary creep”. fhe non-
recoverable or irreversible creep is called ”second-
ary creep”.“

( Q

1

The above quote indicates that tne stress-strain rela-

. " yw d ‘ '~ " . 4.‘ D
for a visco-elastic material d pend on the rate 01

CT
L10
A
U
:3
U)
v-IJ
EJ-
j
(.1

sixressing or straining. Lason obtained curves ior raps" which

3 iotea hi'hor stress ”or a given strain wi“h increased strain-
ing; rates. Lis rates of straining were 0.043, 0.11 and 0.22
:‘fL’CG;H3 pe*°‘*“rn1:e.

The elastic defOPfiatiONS in cheese are1not large.

‘ ‘ ' a . , l ‘ ‘ {r7
“ff (:1 If”: {1,} J” 1;}, 1, (100‘, L‘ flat, Sf OW [-11:31 (313m ‘0 1.3 .Ltlr . DEV 4.3 (l 9'1 )

.
1"

I. ' -— - 4- . - , -. -. "— — ‘fi‘Afif‘ "A v“ 7“ ( 1 l \(V

“‘“ des 1ai“rd '“ o “inn“:ic IIWT'EPblffl3 11. 1e1111 01 .i1101a La) 01

."._~u .. VI.)

1 " .. ,. I”
2 _ . ‘ J ,1 fl, ‘
w o -flfi ’ J o A .. ,3 3 J W ‘ ,1
41 k: : A. 4" f .2 C ‘ " '7.“ "1-» 1'3_1._‘Il .L L» w v ~— -A u D < J-
k x __ .'
.. : | . ‘ I /*.~‘ ‘1 ‘ —‘,—~ r a vv
' r I- . ... 1 - . 1 l‘ ,— ' (“.3 ‘ Af j
.2 a 7 1. . | ,\~pnvv } V\ ] ' p ,L ...- Kl I_L .1- 1, g L
"“ k. .LC (-..E)‘ ‘. .‘..‘.. . 1.4 v1 H
; . . a - o 7‘ :- o 1“ 1-- -1, ‘ “'1. A 1.. 4.“?
-4- . \ ‘ z | W V k V ‘L‘ 'ul.as:) Ml .l A (\J .1 V J V 4 v
‘ I l ' _, ...I -
1 '1
CC
... " O
.3 ' L.‘
W 0 F “ r)
O \ . _ 1‘s . | 6
1 1 ,. J_ O . . . l. a .1 ‘ .. ‘ I) 3 b) A. K \ _‘ ‘
“L ) k>1 41(- pb‘lj- ‘,,l‘~ Lo .1. on ..‘Q .A J L )A- --- ‘~- J L J J L 4-; A J-

‘fikason, S. G.;
3 49, NO 5 - 207.

"Rheology of Paper”; Pulp Paper (hag.)

Can.

stealing“ proeosgt of bread as 111213.111th by Scott-'Tlair (1155-).
txiny devices have been orploygi for “emfrrlflf tge cyangos in
'“”M3 force defomnation rclationski s of the crumb. (Tecanic-
ally "crumb” refers to "crumb—structure”, 1.8., the texture
of"the material not necessarily following crumbling.) decent-
ly' attention has been drawn to the measurement of crumb ”firm-
Iie:us” (load required to produce constant deformation). Bice
aril weddes (1049) in their experiments on bread state that
lJOEfli elastic and plastic preperties are present.
tinat plastic flow is an appreciable factor in the compression
kauen,fresh bread is subjected to stress, but that t:
'bijlities for plastic flow decrease when the crumb becomes
Incnse rigid. The elastic properties then predominate and the
loeliavior of the crumb closely approaches that of a pure elas-
ti.c Inaterial.

Plysical tes s are made on bread dough to determine the
”dcnigh” and baking properties of wheat flours. Various in-
strLunents -- the Farinograph, fixtensograph, Fermentograph and
Amylxograph -- measure the rheological properties of the dough.
The ciata obtained from these tests allow prediction of the
typfii and quality of proiuct to be expected.

’Fhen a plastic body is strsined it cannot preserve its elastic
Potential energy indefinitely. Thermodynamically, the poten-

I

tial energy may be gradually converted into heat, leaking out,
so to Speak, by relaxation of the stresses. The time in which
1‘ 0 ° 4., 1

tnC stress is reduced to its eUh part is called toe thus of

relaxation, tr- For a ”true” liquid tr:; 0 and for an ideal

the practical importance of stress relaxation in paper

hens been pointed out by Steenberg. If for example, a sack of

Genrent is dropped or a sudden jerk is applied to newsprint on

must be released rapidly

V
o .

a Isotary printer the resultant QCPGSS

or"brittle fracture occurs. The rate of stress relaxation

vaasies with different kinds of papers. Steenberg noted that

hue stress decay did not fit into a simple logarithmic formula,

arxi advanced the possibility that the relaxation process after

ruapmid straining: in contrast to the slow relaxation process,

.is a function of the preceding rate of straining.

Lason obtained relaxation curves for paper at various

:nncnants of strain. The 105 of stress plotted against time pro—

flIIQel parallel straight lines on semi-log paper, except for the

first part of the stress decay vhich was Very rapid. Fe 9130

fcnlnd that increasing humidity (moisture content of paper) re-

31flted in a substantial increase in the rate of relaxation.-
Hlynka (1957) in working with structural relaxation of

breeui dough found that the relaxation curve closely approximat-

ed tdie equation of a hyperbole of the form (L-LA)t = C, where

IJif3 the extensogram load at constant s rple extension at rest

period t, LA is the theoretical load which the relaxation

curve approaches asymptotically at long rest periods, and C is

a constant. The constant C describes the curvature of the

hyperbola and is inversely related to the rate of relaxation
(called relaxation constant). LA describes the upward dis-

placement of the hyperbola or the asymptote that it approaches

12

at infinite time. Hlyn.-a used those constants from the relax-

ation curve in studying the visco-elastio behavior of dough as

modified, for- example, by the addition of improving agents.

APPARATUS
Requirements

To determine experimentally the mechanical and rheological
‘prnoperties of grain it is necessary to have some means of meas-
‘uifiing the applied load or force and the amount of seed defor-
rnaision as a function of time. It is also highly desirable to
hsrve a recording unit to provide a continuous and permanent
iceczord of the existing relatiozships. To satisfy these re-

qiuirermnts a load cell testing unit was built with SR-4 strain

3. es as the sensing means. squipment was available for ampli-

02
(a

re

{yiJag and recording the output signal from a strain gage trans-
ducer.
It is necessary for the strain cage load cell to meet the

s
folLlowing requirements;
1. Reasure the total f rce applied to the seeds.
2. Reasure the deformation of the seed.
3. Record the above parameters simultaneously in relation
to time.
4. Be capable of applying a load or force at various
rates.
5. Have a relatively high capacity (250 pounds) but with
good sensitivity (measure to one ounce of force).
6. Have very small or negligible deflection as the load

is applied so that the observed deformation is that

due to the seed and not the deflection of the

l4

transducer supporting the seed.

7. Sufficient flexibility to allow interchange of the
various testing heads (shear, compression) to be
mounted on the same unit.

Figs. 1, 2, and 5 show the load cell and component units.

Design

Igoad.fransducer

The maximum force encountered in testing the three grains
Vlould occur in a compressive test on corn at low moisture
lxavel with the seed in the flat position. This force was
nmeasured to be approximately 200 pounds. To allow for some
'Wfactor of safety" the load cell was designed for a maximum
capacity of .2350 pounds.

The most difficult requirement to meet is the small de-
fTLection of the transducer as in part 6. It was for this
Insason that a preliminary setup based on a cantilever bean
wars dismissed. To mirimize deflection of the load transducer
Witfia applied load, a pair of intersecting mutually perpendic-
'ulaiwbeams were used. These "fixed” beams were formed by cut-
ting;slots in a 6" X 2” channel. See Fig. 2.

For a beam fixed at both ends with a concentrated load at
the center, the maximum bending moment is at the center and
ends, In this case it was desirable to have a built up or
raised seed platform at the center of the beams. Consequently
the ends of the beams were selected as locations for the

strain gages.

 

15

 

Fig. 1. General view of apparatus.

1.
2.
3.

5.
6.

Electric motor and speed reducer (1725 to

9.6 RPM).

Sprockets for upper end of vertical shaft to
give various speeds to the crosshead.
Forward-off-reverse switch.

Load cell testing unit with compressive "head"
in place.

Brush amplifier BL-320 used in the cantilever
beam deformation circuit.

Brush amplifier BL-52O used in load measuring
circuit.

Brush oscillogrsph, BL-202, used to record out-
put from lead and deformation circuits.

Plug to connect load bridge to BL—52O amplifier.

Fig. 2.

 

 

The under-side of the load cell unit showing
location of strain gages and the crosshead
drive mechanism.

16

17

 

 

Fig. 3. Load cell unit ready for a compressive test on
a kernel of corn in the “flat" position.

SR-4 strain gages under a wax covering.
Seed platform.

Cantilever beam

Zero clearance adjustment screw between
crosshead and cantilever beam.
Crosshead.

Vertical crosshead shaft.

BL-202 oscillograph.

Compressive "head'.

CD~30\U1 J-‘uMH
O

18

Design calculations.

 

 

 

§§
X“
“R
\ \\\*\f
R
i.
$3
t
i
§>‘

   
  

5/0/ 661/ If) C/i’flrJflF/
5,8— 4- s/ra/n ‘7an

Feam design of load cell

Kaximum stress in beams. For a 250 pound load, each beam will

 

essentially carry 125 pounds.

For beams, 0.20" X 0.75" X 5":

fl :_ PI 3 M :' 78.2. //.7"/5
max 75-?- 8
cM’- 4x253 -—/6jé20/pud

4” 5:6?" 070(2)
This value is well below the elastic limit for steel.

maximum deflection at middle of beams.

, «3 /2___5'x 3' 3x /Z
A7I/5‘X 2.- P’z ::’ -.Sww—J—tmsfl'ys Wm)3
59251 /92 x oxxo

//
=<200544

it is apparent that the beams in this situation are not
perfectly fixed at each end, with the result that the actual
deflection for a load of 125 pounds (250 pounds total) may be

somewhat different from the calculated value above. The

grezatest accuracy in deformati

lxaetis, that is, While

lorf it: elasti

0

f0 1";nations, tne imports

ma t ion is (3 ac recs

1nued.vas found totw!1inear mwi

A (corwection for this

lDej?ormation Transducer -

a cantilever beam arrangement,
Laseri to measure the vertical travel
tli compression head Was lowered to

éuljlasting screw mounted

the

Wcmlld.deflect the cantilever

strain gages

tfle
limi
nee of

‘tlst‘; 3'

cantilever beam.

11th lar;

(inflection

Cantilever

on the crosshead

any a di'i

1’1

C)

fcvrnte orl

onal travel of
beam .

near the cantile ever 5

hence,

LO'rb’

J.

by ‘bending would indicate seed deformation.

A BPUSh BL“202 ,

corwi the crosshead movement.

Wlli l e

SfiKnlld be noted

4“ a a o -
“inks, prequelng a Str

the other recorded

One cha

vertical travel or

eight line

01’].

J— ‘ .-
e L10

...I‘
No.8

1_ r J.
Cudl'w

Gefwlndent u; on chart Speed and the crosshea

IV: .for given chart

and or

or Eseed deformation could be rel

wt

to

F“ ‘ wfi , J—‘-,
ssncad speeds tn

the product

..J

g .

8

Mn . "V - “ 'L- r‘
4.13 40111" 6111611 U .2:

is

set

V’-

b
”'1

two-channel oscillograyh

that the crossicad movement is

{V
0

she crosss

8" ,‘1

.1.

L18

L-Jo

iroiwl'. 1.375:
the gtuain kcnvual is 5 ,ill lie-
er' loaxhs arr} COIYM:S;!H%117A"lc-
great rccnrecy in measuring Cef'r-
steel defiection of the beans a» a
C. 01. inch 7391" (-1.0 timinriq “ “ j_l:(‘.~
. .
rill r111? Jeri“ ’foe eats
Beam.
as seen in Fig. 3, was
of the crosshead. when
contact the seed, the

to touch

mounting

C‘
.b‘L/LU

9""
\

nnel recorded

head

83-4

the strain pros uced

used to re-

def orm Lt i

vertical

SCEUIt and a horizontal dis placement on the ch;rt.

(33°

\utormat ion chait line m=y

anpear to be redunlart.

, --» - - «l-
mQVGILCL-lu

A f.
01 a
-r, r
i ”lg ,
.,

C 73:1"

‘

the vertical movement could be detsmunec from the chart witn-
out the cantilever when analyzing, da«a, i;— would be xractically
impossible to know the magnitude of the deformation a‘luring; a

test. The deformation line ms a constant ‘1

l

" o lion": mu oh.

(I)

lie :1

C
i

to

movement had taken place at any time. It we also extremely
useful where it was desired to stop the crosshead at a reins

.l—

corresyonding to a fredetsrmin d dgforrtiation.
Des iffn calculations. The only regyzgirement for the can i- eve ‘
beszn was that it be capable of a =:lejlec“ion at the free and

he largest desired deformation without exceeding tfie

ci-

equal to

elastic strength of the steel in the bear... ‘i'his deflection

‘ +‘3m1 ‘I\"\¢\‘u1fi -' I' X 071‘ X f] ’7 n ~~'. .4 n‘ f‘.‘~ ‘3-
[L S ..va U'QLLM. .L g k) .~IU hiss; v-._\JDL...-.

(14‘ J'Q'I’X ‘fil’infJ G‘WK‘?

I7 . e -- ' "r . “n 5-7/1». 7 - n ‘— ~‘ ‘-
l'Or a. CdfltlleCI been, L‘--L/ [.L'J.~1{JC‘.J.L‘~)1‘1 gu but; )- Q‘..

i

i
I"
e)

 

3
fly,“ w/Ht/x .Pz': 04’ X3K 3OX/06X/Xf[03‘§
(732593X /2,
= 0.953 /./D

5.— Me = 0.?83X725'A 0-5‘112 :- /7,/00fl54'.
T ”we?

[—10
O
:5

<3
9 nnf‘ V‘fl‘n —~
otrain cage Coniigurat

L . . "a " ‘1 . . o
E cel__l‘ transdu ers. ine locat; on Oi one opt—«i Strain :s

 

for the load cell is shofin in Fig. 5. Type 55 be of

()1
5:1

 

 

 

 

 

 

Can ”1% er beam

gages

Load Ce// gages

 

 

09%?» 6Q
‘55 e Q9
Qc?

 

 

 

 

 

 

 

 

 

 

 

 

 

V - f Bras/7
6/u5/7

 

 

 

 

 

t'——"+ bras/i
. " . r' [9,7710] fer OSC/V/Oan/vé
“7:35"? 1 mo

 

 

 

A770AAS‘
Pl/J’J/CA z. & [256776/6/4 1. [ac
F76. 5. F 59—4 SEGA/N GAGES

o

‘94
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-... . ‘1. .. l. ’-‘ ,r - ‘ l1 I I. ‘ .1.“ ,. I -. A w a q,"
I“‘;_)"‘ JlLV lLJ L.) J L 18 SILL (.DA. ‘IJ"‘.3 {-e 1:. , t Lu - ‘68 .. \Afy; to L/V )LI], 1-
,3(: 3'3]?+ in ‘32.. ’1‘, 2. ,\1 U“ ‘ 3 7 r1 #10 “OC ‘3‘]. I '3 r rv‘c. '7 Camp
va u v» ~...\~L ,_ . l .L. it, ._ MUL1\’ U - “I . l I
. 1 \ v4—
sirrein .oula te Tresent.
fin ‘ “a . n a w- z : ~ -- , - .
lfie use oi foul active area \eignt gages) ingtani or
“er‘ oxin'ix‘rxlee" lee e “ i "Vl;t‘7 c)“ ‘7“> r1“"t "“~' ~ 1 “r c..
”J ‘ ‘I ’ '5 ' ‘ «L ‘ D lJ..-v LC: 1 'u-‘l 9' ..L b.1(4 .L $J_ . &‘Ll~_) 1 1C* u "H“ V

’ - ’wrortent since the deflection or strain for a give n 10

- .0 ha , (“I‘ H .II .t i ,. .2 .2 .
l as po ointed out eoowe. lee A gegzs ere in tension

U VII? '3 7') 0-) J C.I1d 'L‘fle ”h H fir!) 'rw‘ r' '3 . n ')1'r1v\'.‘1 ‘3 r‘ .1: '9 1 7" I. ~ a," -. ‘9'. / -~. ‘7-

-L.K ”Ci an. t» L-;.'_ D bewleo “Pb l c\-4.l.l./.L QUQLO-.. dCCOl \4..L-L;,.'.d
'v- H * H .3 11"” .. .— '- fl - .1 ' . V‘. :. A v.1. . 4.‘

tile 11 aha L» ‘Ldges Linyt Le jfileced 31; Hflqu t,n, arms (1. pJe

'2... : ‘ -' A- - °-.-. °-— . 1 ..__ .—.-'~ 44. .- ,
brl;_l_i-‘e C_LI10L,1.LL. AX ifir]--Cl‘ ELL Li-Kszlekl Cage ‘«-‘-L \I .20 -eran::e)fl - en

- «V -. k “ /~ 0 N ‘ ... s“ A '1 _. _l‘ 3 ‘ ‘ L _o 0-. / I ‘ _.
tire strain gwges lo belt tie electrieel output is inde,en ,nc

7

.n 97‘ _,‘° _ f“ e, “‘3'" . J.., ,. -13.. -.. 2 “5.“ - ‘mT.
.L \J’.v'e Z'Jllllx.’ OJ. lOps'sl -t '1' 1103. U .1- all tjn Lei-U S .4.~-4‘(L Lei-Lk‘.tf 04.4 - .

 

 

 

 

 

 

 

Pa
/ /
_.. /
\\
\
‘—-. . ‘
‘Bruéye
Chafipuf‘
Wheats tone bridge circ nit
Fig. 6
In eel or;Jion, the strain gege resisten e in one leg of

k w _ n .~ g - . , ., .
tale ufiflutSthO LPnge cirCUit, Re: 13 seunted 3v an oyenCir-

(“lited resistor of considerably higher value, RP' when RP

18 she nted ecross Ra, the bridge is unle elenced. This unbalance

can be con idered as a1 artificial strain {(7.1le1 can Le cali-
br-ated on t

In the above figure:
_ i .. 2
g): £3 FE and (if; _-:: Fa ‘ E —.-. I; _ .fi—L’af’ :- $5",
.8. + E. (”a + 75}: a. + E:

A [3/61. s A lei/Ea
A 4/4 8

7777* ‘

9
‘—

 

‘¢.,/3 fete/or /'5 Je‘levc’./ A] .' 6/:
Ali/e .. 61‘ ... __,::~__._..,....
‘9 ’ a; ‘ (E‘Ififmyw) 6r (cur £7»)

For the Brush BL-SBO emolifier, R = 390,000 ohms. with

the bridge circuit of Lie. 5, the total resistanc in each

(I)

arm is 2 X 120.4 = 240.8 ohms. rBhe simulated strain. when HP

is shunted across it.

|

 

240.8 3/3 -4 . .
e = " X/o 102‘)
597/370, 000+24o.5> /4’7

1 \

311-ce there are four active Triage art-is, tne indicated strain
during, operation will ee four times the actual strain as given
by the above calibration. lience, to estimate the sensitivity
during ope ation, the simulated strain is:

-4
—e

e: 3/3K/0 =75.3x/a My”,

4 O

In calibration, a total of 750 attenuator lines was used
"‘ a gen deflection of 15 lines with the attenuator set on 50.
-'~lls set—tint“. is euriva ent to 78.5/750= 0.104/4 in/in per
E’Ctenuator lire on the chart.

1

4 Q a 1 1
nor a 2-poune load on each oeam (g pouna load on the

(D

seed), the bending monent under the cent r of the strain gage,

“L . .

at a distance x = 1: inch, frozz the end is.
gflazL— —/Z)= 0.:x> .ex'fi; .-5> r-._0MA?5'//%r/é
Then
L t
5.1 7 :62)

This stress corresponds to a strain of

 

 

o. ... " -6 o
(f __= 43.(7fl_‘ = 0.5733X/0 H)
sox/Ob

for 8 ounces of load or 9.61 ounces per/a inch. Thus a l..en

2h

cieflection of one line is equivalent to 0.10i/a in/line X
29.61 ozé¢(inflz:l.0 ounces of f rce. nettidiigly, to measure
21 force of 200 rounds, the oscillograph would reguire 300 A
1&3:= 320C attenuator lines. lnis could be obtained by an at-
teenuator setting of 100 with 5‘
tCDtal of 40 lines.)
(Sssntilevgr deformation beam. The arrangement of the strain
ggerges and th. bridge circuit is also JLOWE i Fig. 5. For
Iaiurposes of estimating the sensitivity in a; vaice, the EL-320
eunqjlifier used in this circuit has about 1/10 the amplification
Of'. the BL-520. One line on the chart would be equivalent to
atnout oneflinch. From the calculations above, a deflection of
0.41 inch produces a stress of 17,100 psi. This is equivalent

to 21 deflection of .0007 inch per/44in. of strain or per atten-

uator chart line.
Calitration

Load Cell

in tne calibration of the load cell unit it was consid-

e . "N .1. _ " ‘ . o q n, .
red 1rr<antant to note tne numter oi lines oi dcilecti;wx

on the oscillograph for a given load on the
crosshead moving down as it would be during

accordingly a channel- -iron support member u-»

a

crosshead and the load was applied through s first class

T4!

lever system as illustrated schematically in ig. 7. For each

loading, W1, the value from the chart was taken when the bar

was in a horizontal position.

r770 ma 5/: Cross/Dec (2’.

CD

 

 

 

 

 

 

57er
a b——->-"-«————C 2%sz"
« 6/6. M(b%c)
r(f:;L*‘ifiZ‘—_5::2:ffbrn7. M6
TE?

bCilEfiHLP.’-€in’3 Sutlp f‘OP calibration of load cell ”pit

Fig. 7 i“

The calibration curve is given in Fig

. 8. As expected
lie relationship is linear. Some points are off the line

Sigightly due probably to the difficulty of estimating the

exxict number of lines of chart deflection. Of course this

eruéor is exaggerated at the higher attenuator settings.

Ihis calibration curve shows a sensitivity of 2.11 ounces

PBI’ attenuator line. This is about twice as high as the cal-

culated value or one half the calculated 8 nsitivity. The

Principal reason for this discr repancy is proeablgr due to the

fact that the load is not truly a concentrated one, since it

ICED dud 96w Kc .EQRVNQQG

Ahka \0\ m3 wax %\ mmkxv. \ GXQR

00V\ 003‘ OOQ\

Q

9N“,

QQN

 

\

Q

\a

 

 

 

\\

 

\

\

 

\

\

 

\

 

 

 

 

n

 

h

_

boas b\ when «0.0 $in
\mRQKEY “We - VQ

 

 

 

 

 

i

a

i

 

 

 

 

 

.mo 6Q

i; M . MNSm. rm.
rm. W
a/
\ (/7 . ohms /w
a m
n p
BQM .. Mhfim m)
a
3
08m, -09an
Q l muwnx
Rs». . and“?
i

.‘r/
is spread over the width of th seed platform. Eurt‘ermore:

in the calculation of the strain it was assumed that the beams
were ideally 11k ed. The beam widt1s Were M011 cut sereuhat
wider on the mlil i machine than the calculated three-0*
o ‘ 7711 O _0 \ ... 5 1 N --‘| , " 'V , ‘ ._ V V , .0 A
incn. these conditions, uOUlQ CuUSU the calculated stress to

be higher th:.1n the actual str ss.

Cantilever—beam Calibration
Fig. 9 shows schematically the setup used for calibration
(Jf the deformation unit. This calibration showed that one chart

lhine represented a vertical deflection of 0.0012 inch.

   

Cross/76461 .
Can 7‘1/8t/e/ beam

/%n1€5i QWZZ/

 

 

 

(ng4L——€§secfpflbf/brnv

F—fi

////////////r’ ///7

Sche.:natic se trp for calibration of deformation ugit

 

 

 

 

 

1":

rig. 9

Otlusr Features of the Apparatus

EESMsshead speeds. Fig. 10 is a schematic diagram showing the
driwre mechanism. Table 1 gives rat as of deformation avail-
ablEB. 111e load cell unit its elf was cla1ped between two
larggs angle irons on a track, so when the speeds "an“ changed,

\IDJ. O

the Ixnit was sim1p1y moved along the track until the new ch:

11

P-

center distance was reached. Mlis feature may be see“ i‘

ll 1

Crossbead’

  
   
 
   
 

7/7/88 Sprocke/‘s used:
/-— w¢7
z —- 4a 7
1—847

-———-—c—-.—-—-
—

 

._ /. é EP/W

Fig. 10 Schematic diagram of drive mechanism

TABLE 1

CROSSHEAD SPEEDS

 

 

 

Sprocket Speed of Vertical Speed
on Crosshead Shafts of Crosshead,
Shaft A RPM in/min
14T 0.93 .0777
48T 3-20 .2666

84T 5.60 .4667

 

Relationship between chart seeed and crosshcad travel. For

‘

the purposesof expediting he removal of information ”rem th

..LJ. v-..
oscillbgraph chart, the relationship between head Speed and

‘ O

chart Speed is summarized in Table 2. his relationship made

it possible to get the total deformation by simply finding the
product of the appropriate constant and the number of 5 mm

chart diVisions.

TABLE 2

VERTICAL DEF caution,
INCHES/5m 0F came TRthIL

 

 

 

Chart Slow Medium. Fast
Speed Crosshead Crosshead Crosshead
.0777 in/min .2666 in/min .4667 in/min
Slow, 5mm/sec .001295 .00444 .00778
Fast, 25mm/sec .000259 .oooess .00155

 

Use in testing other materials. Fig. ll shows how the appara-
tus was used in another research project to measure and record
the load—deformation relationship for epoxy resin-glass cloth

laminated beam Specimens.

Pendulum Impact Tester

The simple pendulum shown in Fig. 12 was constructed to
measure the impact strength of grains at the various moisture

leVGIS. Jith this unit the impact load was applied in shear.

 

Fig.11. Load cell unit employed (in another
research project) to measure and record
the load-deformation relationships for
epoxy resin—glass cloth laminated beam
specimens. '

Fig. 12.

 

Pendulum Impact Tester.

The kernel was held in the Jews of
the small vise shown in the center
of the figure.

(,1
(\3

Due to the extremely small size of the grain kernels, it
was impossible to apply an impact load in flexure as is
most commonly done for steel. The seed specimens were
held by means of a vise mounted on the pendulum frame.
The pendulum leading edge swings by the face of the vise
with as little clearance as possible. The seed is

thus broken off by a combination of a shearing and a

bending action.

Design Calculations

Some preliminary trials were conducted to determine
what initial potential energy would be needed to break the
tougher high moisture grains. It was found that about
5 inch-pounds of energy was sufficient. According y, a
bar i” X l" X 5" was chosen as the hammer and a 1/8 inch
section as the double arm.

.1

It was necessary to choose a pendulum such that the

center of percussion would be located in the hammer rather

ffie

than up on the arm. ins radius of gyration is given as:

1:: W ________ (x)

the moment of inertia of the pendulum shown below in

w o 0

fig. 15 about the axis of rotation s elven by:

U

1.. = z/é/w’)+ M.("/73z+12+51) —--*-'(z5 I

’7

v1 _ o 1_ . ‘ .
Jnere n1 is tn mass 01 the arms and L2 is the hammer mass.

53

x %_ __ _ _L For a density of 0.285 lb per
cu in, m1 =..00555 lb-secz/ft

.79 x 7a and Mg = .01105 lb-secz/ft.
Upon substituting in equa-

tion (2), the moment of in-

e
S

ertia is 0.04927 lb-secz-ft,

 

from which k = 20.7 in.
This value means that the

H " center of percussion of 0.7
in below the top of the

5—5; Sketch of
' ‘ L" impact tester hammer.
4.

 

Fig. 13

Energv nelations

  

9.: 44° 50' for low velocity
impact tests

9,: 70° 42' for high velocity
impact tests

w = 0.4.298 /b.

  

I
I
l
I
\ ' //
\\h'__—a’
Schematic of impact tester for determining energy relationships
Fig. 14
By the use of a knife edge, the center of mass of the
pendulum was found to be 17.813 inches from the axis of rota-
tion. The total weight was 0.3??0 pounds. a fixed initial
37313 9. (angle of fall) of 44° 30' was used for the loser

velocity imfact tests

1
.sa :31": N"- 7‘
.1‘ .. :.L' .

E= W1. (:05 9; - [4/st 9/

- I I 'N '» ~ ‘
0 Lil") I; L L“.

.fi. ,.,\ .:.
utl4 .1

..

//oZZ 60$ 69‘ (£475) ) /.,1- /A.

For t‘: “3 ”“velocit* tests, "iffi EL‘= 77.70,
5: ma C295 19: - 20/, m- a;

Ir1 or’34ir111 3ges'ns, ;fl:e tritirusw '. e]. oi‘ t7u1 ficw1lulinn,
lS reasured by 6; Was indicated by a frictitn printer. To
3* :3"\ Lh» accuracy , :n electrieal in‘i01ting means 723 de-
vise}. as s‘a n in Fig. 13, a tractor -a"u¢to driven by an
electric motor suppliefl the nece sear" vol,a o to are the $3?
oetaean a -ointer on the ondJl. 1n1 'n& a s‘ationtey ~~onnd-
ed wire ”oun‘ed in the graduated quadrant. a sheet of tlin
Sager was flacti bet' on,the 3313;;p;1 Yire and the ehdulum
poixieer (Dince 1: ye 1111r":t0ff».1 for {as irtvtant 5d: its
maximum travel, sGVeral c*“cn"rert holes hose wurned in the
paper. It mas then ~1sy to see the s acuated seals penind the

,.~ .-~ .. 9

piper and thus read z
Correction £01 Losses

Jith 72s electrical indicator, there were no losses from

he indicator arm, but there were losses due to bearing fric-

tion in the pe iulum and ti? dncg 01 the pan slum. The follow-
i13 procedure as given ty Davis 21 g_ (1041) was used to de-

111 ne

(1'
1 t-
i
3

these losses

without any seed in the vise, t”

1-1

in w‘1e normal manner Angle 9:, was record-:11

‘ ‘ 0‘ .- ~.‘ -. -v ,- .1 ‘ “1 ‘ t ' 0' .1 q ' J" “V““'
aulua 1a a ain reieasea and allowed to make
3 4‘ ‘ Q T “.‘§ ". m a -A_- an A fi'rq‘ ‘fi."\"

Nal‘u ant. Q DaCl‘.) . i118 I:.cubnct0 w :13 lluu C 3n3160

C‘
L.)

released

11'“

‘x

no

'1

"1“.“
- 1’ LC

(

331 . pen-

3.11 183

A

o for-

SI

ted to the frame

A-
, 0‘
.u
..I-‘
4 .

 

.... ‘

 

 

until the last swi g. This ”nnle 1:3 calls? En.
. C;
The energy lost in air drag ani beacin~ friction of the
pendulum was assumed to be aistributed uniformly over their

ranges of action. as an example, 31 was found to be 44.3 0

0 ”he average angle of rise betw en readings

O
Q)
0

and B2 was 59
B1 and 32 is %(Bl+ 32); hence, a complete average swing, down
and up, is approximately %(Bl+’32) X 2== 85.90. The energy
lost in air drag and pendulum friction during one average
forward sning is represented by an angle,

53—52 = 443-3% 2 0.4270
// //

 

' 1

The energy lost in tnis manner during either a downward or
upward swing of 44.50 is represented by an an;le,

J 44.3;{2 x 0.427) .-.— 0.2260

z 83.?
Thus the effective angle of fall 91 , was 4-2.5 + .2250 =

1‘

44.520”. The corrected angle of rise after rupture 01 the

observed anrle 4- 0.226 X observed angle
0 44.3

The small amount of energy lost in imparting motion to

the txroken kernel is negligible.

, .)

hETHODOLOGY
Three grains, corn, wheat, and beans, were used in this
Stflde. The three principal parameters in the determination
of? compressive strength were moisture content, rate of load—
irng and the seed position (either flat or on edge). In the
sluear tests, a constant speed was used, and the kernel wa
Eueld in the "flat” position. Thus the moisture content was

A

tile only parameter. In practically all series 01 tests 0

.
H

resplications were run. To reduce the large number of tests,
tlie effect of temperature on the mechanical prOperties was
nxjt studied. a total of 755 tests on individual kernels was
ccnnducted.

‘, . . -: 2 t ' ,. . ,,, ' ‘ .0 V . . 3
Lie size (ewiie, flat,rnrlfilenwtn u.t¢nmsion\ of‘emmjh ~sa‘
. u l I \ I ~ I

- 4.
Afr—s measure. with a tfi‘icr'wmeter and ares recorded before each
iuesf;, Gr91312xaeis of (HM!!IQPieLJ'8YK1IJNfl st

Inge of :1pt1rit¢r

'.’ ) . ; r. ' I . . PA‘ ,g ,‘ . .... '. .
.'n 0 uses in all tests. inc cord used was a hybrid Varietv
U

-A

cwvu"unlj gratn in Ventral Michigan. Selkirk soft rel winter
“'":7’?é;l, anti L'EC‘.‘“;-"-.K.ii.‘, pea bean Vf-.1"ieti»‘3:3 ‘.’A "31"9’3 113m} in t‘n’i‘g

“' s ‘. ‘

»,t.J, go attcnpt ygs made in this study to measure

meclnanical properties of different varieties of each grain.
It was necessary to have a means of regulating the grain
m01813ure level for each of the tests. Since grain is hygro-
scopic, its moisture content will depend upon the relative
humixiity and temperature of the surrounding air. A moisture

equildibrium box was.designed and constructed to produce four

37

different relative humidities at a constant temperature.

Since the air in these chambers is kept in motion by means of
a fan, the unit was called a "dynamic equilibrium moisture
chamber". This unit is shown in Fig. 15 and 16. Static equi-
librium chambers could be used for grain at the lower moisture
levels. However, for higher moisture contents the grain.may
mold (after a period of about three to six days) before the
equilibrium moisture content is reached. With the dynamic
equilibrium chamber, equilibrium is reached in one day.

The expected grain moisture content was calculated from

the empirical equation: *

/-EH= e
in which RH, the relative humidity, is represented as a deci-

n
_c7WWQ

mal; T, the absolute temperature, deg R; Mo’ the equilibrium
moisture content, percent, d.b.; and c and n are constants

varing with the materials.

Compressive Tests

The load cell unit with a compressive head mounted in
place is shown in Fig. 5. dach grain was tested in the flat
position and on its edge. (The design of the load cell allow-
ed the kernel to be located at any place on the seed platform
without affecting the magnitude of the indicated force.) To

determine if thenawas any speed effect each grain was tested

 

*Hall, C. W.; Dr in Farm Cro s; bdwards Bros. Inc., Ann
Arbor, hichigan, 195g, éh.2, p. .

 
   

NOTICE
STOP MOTOR BEFORE OPENING DOORS.
FOR SPACE. CONTACT DR. HALL.
a ': fag-.jiegx

 

Fig. 15 Dynamic Equilibrium Moisture Chamber, showing
thermostat and heating element (light bulb).

DWWI W/C [(7U/L/BP/UM

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

H :4 *‘ ,— ’- r— " ,,
. x Mama/RE CHAMBCR * 1
some: "=/' n "' ’
0 fl - t Cf" “~75
\J
4 .
3t” ‘ ".../.1
o I :3 J." V "“‘-""”
I l r small
. sit‘ “
v :w/ ‘
C ‘ I “I 1 b
' .‘ K4 \ 'j A
5 ‘ 1% ‘ *-~»v
o ‘ -. V \ X / Infant/d '
i ‘ t _ Celia/UM
: a L
,, -1 1 . mi
‘

554701! 4’
56415”?- e"

  

 

 

 

I// dma'fls 9‘5 -" ku/v:
‘ ‘ ." i .1 f" J’L,w;.‘/ 'lstf‘f

d ‘4 ‘-e, ..A.‘ Jr: /-f/fl‘,

 

 

 

DITA/L OF DPAWEPS

 

  

u I}: ah: screen Inert

ELCQ ea -...

 

 

 

 

 

 

 

 

 

 

Fig. 16

 

 

40

at the three head speeds of 0.0777 in/min, 0.2666 in/min, and
0.4667 in/min given in Table 1. In the following pages, these
speeds Will be referred to as slow, medium and fast. From '
the oscillograph chart, values for proportional limit, (yield
point and maximum strength were recorded in pounds.

In the compressive tests the strength is expressed in
terms of pounds per kernel rather than in pounds per square
inch of cross section perpendicular to the direction of load
application. In determination of strength properties of near-
ly all materials, the various parameters (yield point, maximum
strength, etc.) are expressed (in terms of force per unit area.
IWith a grain kernel, its irregular shape makes this impossible.
The force could be divided by an estimated average cross-sec-
ti on area of the kernel, but this would only give a superfi-
cial or apparent stress value. Furthermore, the actual
strength of the kernel in pounds may be more valuable informa-
tion in design of equipment.

Since a value for compressive stress could not be obtain-
ed using the entire kernel, it was decided to cut a "core"
from the kernel to obtain a specimen of known deminsions. For
each grain these cores were made by cutting each end off the
kernel, leaving a middle section of approximately three-fifths
the original length. With corn, a rectangular parallelepiped
was formed, while wheat and beans became barrel—shaped pieces.
The faces were out with e razor blade and_the dimensions
measured to the nearest thOusandth inch vith a micrameter.

See Fig. 17, parts (4),,(5). (6).

41

 

Fig. 17

m
e

(D QQW": U
o

(I t '.’

. .; ‘ ‘ *h/ 'e 332,4 I’
h 'i' ‘ A" ‘

‘. .‘ J): 1.3 I '4": [ x, ’3‘), W. I (T)
A? ' x u 2 . .h .. 7’ ‘.
‘f- ’ t 4 A
{A "0 1:! {(-9 17‘ ‘
"3
")3 J -.‘.::1 j
'/ L!
J L) “7 (3

Minature Tyler sieve series, six sieves and pan.
Corn which has been fractured from the edge pos-
ition by compressive tests. At left and right
is the material retained on the top and second
sieve respectively.

Same as 2, except corn was tested from the flat
position.

Corn "core" specimens, before test.

Wheat "core" specimens, after test.

Bean "core" specimens, after test.

Bean slabs, showing the hole made by the punch
shear test.

Pea Beans after the punch shear test.

42

The load was applied parallel to the original length of
the kernel, or perpendicular to the cut faces. For wheat and
beans, the cross sectional area was calculated by taking the
area of a circle whose diameter was equal to the average of
the.major and the minor diameters of the kernel. For 20 wheat
kernels, the average major diameter ("edge" dimension) was .
0.154 inch; the average minor diameter (”flat" dimension) was
0.114 inch. With corn, the sides were shaved with the razor
blade, giving a rectangular parallelepiped whose dimensions
cauli easily be taken. .

These cores were used in tests to determine the follow—
ing parameters at four moisture levels:

1. maximum stress, psi.

2. Slope of stress-strain curve in the elastic range,

k, lb/in of deformation.

3. The percent deformation at maximum strength (ASL/L).

4. The modulus of elasticity, psi.

TheSe cores are not considered to be perfect specimens as
far as uniformity of dimension is concerned, since in the case
of wheat and beans they are slightly barrel-shaped rather than
cylindrical. .However, the calculated values of stress should
be:much.closer to the actual average stress than by using the

entire kernel and trying to estimate the cross-sectional area.

Shear Tests

TWO types of "static" shear tests were used; a punch test

“i 3

in which 5‘ COP”! “’3“ 1‘1“? 7’5'8 I‘va‘vclil frfm the. kernel; and n.
s ingle shearing—action test in which the complete ‘arerqel ms

sheared 1‘71 half.

The load cell unit with the hep/(i us ad for the. punch tests
iv- shown in Fig. 18. The platfors‘n (2) has holes clri'L‘ei in it
Corresponding in size to the pznch above. Tvo punch sires were
tried. The larger one, l/B incn in diameter, prove-:1 unsucessfnl,
s ince for corn it caused a crack to O("(tll]" during the test be.
tween the punch hole and the edge or pericarp. rEhis cracking;
resulted in a sudden decrease in sppliel force and was not a
13,-793117‘8 of the sicarim force, so tlet rather than sE'irwring
out, a core, the kernel merely cracked or broke, apart. .. he
smaller punch, l/l‘fS inch in diameter, was also not suitable
for testing ("":eat or corn, For vheat, even a punch of this
size, tended. to crush the entire kernel rather torn to shear
out a core. "'ith corn, the kernel cross section is extremely
inhomogeneous. Thus the shear stress would depend entirely on
whether the embryo or starchy.r endosperm was chosen for tie.
test. rThe kernel is very hart txroughout the outer flinty an-
Gospexnn section, and quite soft in the, central embryo section.
It was decided to use time ism3 s near test in V." ic‘n the, entire
kernel. was s'xeared off. This test veg-ind give an "average"

\

value for true shear stress.

1

The puncu test was used for a series of tests on beans at.
the higher moisture levels. Tielow about 15"} d.b.”“ (lL’aj'S w.b.),

'7‘ ¥ ‘ O 0
tr, Jean is so crittle it merely fractures and no core can be

m _--—

,. moisture Wcitht
(i.h. dry basis: dry‘ficight x 100

 

44

 

Fig. 18 Apparatus for punch shear tests.

2. Base plate containing holes to match the
punches used. The interior of this base plate
was machined to provide space for the plugs
sheared from the kernels.

8. Punch shear "head".

Other parts are identified in Fig. 3.

45

sheared from the bean.

Originally the punch test was considered to be a suitable
means of measuring shear strength because the shear area would
be known fairly accurately. However, in an actual test, the
bean deforms slightly under the punch until a force is reached
which shears the plug out. This means that the shear area
should include the "effective" thickness, that is, the thick-
ness under the punch at the point when the maximum.force is
observed on the oscillograph chart. If the product of the
original bean thickness and the punch circumference is used
for the area, this phenomenon of initial compression (plus
shear) will give a different calculated shear stress for dif-
ferent thicknesses of the same homogeneous material. This
effect was observed more closely by taking shear plug tests
on bean slabs of various thicknesses. (Except for the seed
coat, pea beans may be considered homogeneous.) Oscillograph
charts for two punch tests on bean slabs of different thick-
ness, but the same moisture content, are shown in Fig. 19,
charts 2 and 5. Charts 1, 4 and 5 are examples of compressive
tests on corn and beans, which will be discussed later.

Static tests in single shear were conducted with the ap-
paratus shown in Fig. 20. A rigid plate, Fig. 20, (9) is
bolted to the seed platform (2). This plate contacts the ker-
nel which is held by the vise (8). Thus parallel forces are
applied through the plate and the vise to the kernel. The
average unit shearing stress was calculated by dividing the

total force by the cross sectional area of the kernel parallel

   
 

i; "Fllgj‘xaffi '.

fifl'fls?

u“ : ~-
'-- 1"," — .Ri} ,."‘.i|{ 'I‘f :In I

Ef'toWlm-o :3, mi.
0.4-.22. n ma»:
e.‘ - ,m” : J21-
' 8.! ..Je .
I511? 0.. “alum: 3-0
931' End’s“! .1}?! «w

a 0.. ..v MR'

._ ‘ ' .' . 430
.’.:" Q.
C"
.1

Fig. 19

46

 

Representative Oscillograph Charts.

1. Compressive test on corn at 15.8% d.b. and at
medium speed with the kernel in the edge posi-
tion. Area "a" represents the modu1us of resil-
ience while area "a" plus area "b" represents
the modulus of toughness.

2 & 3. Punch shear tests on pea beans at two slab
thicknesses

4. Compressive test on pea beans at 22.8 % d.b.

5. Compressive test on pea beans at 10.6 % d.b.

 

— 24.... .

amnireufixsf'_'

 

Fig. 20 Apparatus for the static shear test.

2. Support base for shear bar.

8. Vise which held the grain kernel in the
flat position.

9. Shear bar or plate.

Other parts are identified in Fig. 3.

 

48

to the applied force. It should be noted that this arrange-
ment does not produce a shearing stress entirely free from
bending or compressiye stresses. Even if double shear could
have been used, there would be shear combined with bending.
Pure shear, free from bending and compression, could be secur-
ed by torsion, but of course this is physically im§OSSible

with grain kernels.

heasurement of energy

Impact Tests

The measurement of energy required to break the kernel
by impact shear was obtained by use of the impact tester shown‘
in Fig. 12. The same vise as used in the static shear tests

rm

(Fig. 20) was employed to hold the seed. lne energy required
to rupture the grain kernel is equal to the difference in po-
tential energy of the pendulum between its initial and final

position. This was given earlier by equation (3) as:
E= WA Cos 92-? W1. cos 9,

where N is the weight of the pendulum, 1b, L is the length

of the arm to the center of mass, inches, and 9/ and 9.2. are
initial and final angles reSpective y. For a given initial
point, the second term in the above equation becomes a con-
stant. host of the tests were conducted with an initial
angle of 44° 50'. This produced a theoretical velocity of

impact of 5.24 ft/sec. with the pendulum arm length used,

it was impossible to increase this velocity to any great ex-
tent by using larger initial angles. with the speed range
available, one would not expect a noticeable velocity effect.
however, one series of tests was carried out on beans at

a. _ . . _ o . ... , ,
e2.8% d.b. With 63.- 79 42'. fnis greater angle proouced

a theoretical velocity at impact of 8.87 ft/sec.

Energy of Deformation

One of the chief objectives of this study was the deter-
mination of the energy required to deform kernels of grain
under various conditions. Specifically, it was esired to
measure the resilience and toughness of the kernel.

The resilience is evaluated by the area under the elastic
portion of the stress-strain curve. This area represents the
work required to deform the material to its elastic limit,
i.e., the energy that the kernel can absorb without undergoing
permanent deformation. Schmidt and harlies (1948) define the

modulus of resilience or resilient energy, of a material as

 

 

the energy required per unit volume to deform the material to
its elastic limit. In this study the modulus of resilience

is exp‘essed in terms of energy per kernel. This energy we
obtained directly from the oscillograph chart by measuring the
area under the force-deformation curve with a plenimeter.

For each test the apprOpriate constant was calculated, with
account taken of crosshead speed, chart Speed, amplifier
attenuator setting: and planimeter constant for the test con-

ditions. To obtain the energy value, then it was necessary

50

merely to take the product of the planimeter reading and its
constant.

"Toughness" involves the idea of energy required to rup-
ture a material. The modulus of toughness is given by Davis
_t,§1 (1941) as the amount of work per unit volume of a
material required to carry it to failure under static loading.
For brain the energy was measured on the oscillograph chart,
up to the point of maximum strength. Toughness is an impor-
tant property of a material from the standpoint of its ability
to withstand impact loads which cause stresses above the

yield point. Eig. 19, chart 1, shows the area representing

the modulus of resilience and of toughness for corn at 15.8%

d.b. Crosshatched area a represents the modulus of resil-

ience. The modulus of toughness or the energy up to the

-"
maximum strength, Em, is given by area "a"

plus area ”b”.
In this particular test, the elastic limit was reached at a
deformation of 2.0 percent and the maximum strength at 5.6

percent deformation;

Hysteresis Loss

By loading and unloading the grain kernel hysteresis
loops were obtained. The difference between the work of
compression and the work of retraction represents the hyster-
esis loss. This energy is dissipated as heat. The hysteresis
loops were obtained by plotting load versus deformation up

1

to a given load. From tni

U)

point the unloading curve was

plotted back towards the origin.

51

Total Energy VerSus Surface Area

During compression tests on corn, the kernel fractured
into many small peices. The amount of ”grinding" or pulver-
izing action produced depended upon the grain moisture con-
tent and whether the kernel was loaded in the edge or flat
position.. In each case the loading was continued until the
kernel was deformed to one half of its original dimension.
after each test the crushed kernel and small fragments were
scooped into a metal container. The contents of the can,
containing all the material from ten tests, was oven dried to
constant weight at 212° F. It was then put through a minature
Tyler sieve series by shaking the unit in a Ro-Tap machine
for 5 minutes. The minature sieves are shown in Fig. 17, (1).

The minature Tyler sieves were constructed to facilitate
accurate weighing of the fractions retained on each sieve.
The sieves were soldered to sections of 1% inch thin walled
pipe which were machined at the top and bottom to allow the
sections to fit tightly together. each sieve section was
light enough that it could be weighed on an analytical bal-
ance. mach fraction of material retained on the various
sieves was weighed to the nearest tenth millogram.

Fig. 17 also shows the different type of crushing action
obtained by the static compression tests. In Fig. 17, (2),
the corn has been under compression from an edge position.
Thernaterial at the left was retained on the tOp screen, and

that at the right remained on the second sieve. In Fig. 17,

(3), the corn has been crushed from a flat position. Again

52

the left and right pictures represent the material remaining
on the first and second sieve respectively. These pictures
show the tendency for the corn to Split down the center to
form relatively large fragments or ”slabs” when compressed
from the edge position. In the flat position, the kernel
cracks on the outer edges and forms many very small particles.

The material retained on the other four sieves and on the pan

is not shown.

Calculation of Surface area

To compare energy input and surface area produced, it
is necessary to have a suitable means of expressing the total
surface area as a function of the weights of material re-
tained on the individual sieves. The chief difficulty en-
countered in studies of rock crushing by various investiga-
tors has been the problem of surface area determination.
From the derivation of average surface area by Nicholas
and Hall (1957) we have:

<i'= EEJVzcfifl'an EE:é$Z&'€cz

2 275 2 >7;

where Ni is the number of particles on sieve i, ei is par-

 

ticle edge dimension, and a1 is the surface area of a par-
ticle. The particles are assumed to be cubes. The total
area can be found by adding the particle area on each sieve.
The derivation of the expression for the total surface area
for the minature sieve series used is given as follows:

The number of particles, N, contained in a weight N of

particles of edge, e, is:

 

 

 

 

 

 

 

 

 

 

7
/V: 1!...
5 (assuming cubes) where ‘9 is the den-
4 sity. For the Tyler sieves each sieve
5 has an Opening twice as large as the
2 one below it. Hence
. A .1.“ '1 C'. . ~. r~ Q .
IP143. 21 Numbering The particles on sieve sl ale assumed
system for _ .
Tyler sieves to be half way between Si and si+-l.
{Plierl . .
e. = 5.4- 54+/ = S; + 25..- = 3/2, 5,;

 

Z - 2.

 

/-7 - 2 x7; -.- é éef/w =— 2 germ- .... a (gag

(....z 6:?- d.- z P 6‘. 3

zéau/a _é7_£!_’éa

. .r 5
4*; 6.3/25“ ‘2 8

 

Wkuxre A1 is the total surface area on any sieve 1 between 2
and '7. Since the pan has zero opening, the surface area of

the 1oarticles remaining on the pan is

g, t éG‘M: ée/‘M :— GM -_-.- 6W! : /ZW

...."

6 63,3 (a e, C” 5% C s;

 

 

 

rt , J. _.
+39 tCfinal surface area is the sum of one aoove expressions:

7."
fit: ____/2//V, + fE-Wc',

63 5: ("L (J 5" ---------- (4)

 

with the nwnbering according to Fig. 21.

To use the above equation, it was necessary to determine
the grain density. The corn kernels were placed in a mixture
of chloroform (Sp. gr. 1.475 @ 25° C) and acetone (Sp. gr.
0.7880 @ 25° C). The ratio of the mixture was varied until
five out of 13 kernels floated and five sank. The kernel
specific gravity was obtained by weighing a known volume
(50 cc) of this solution. For corn this value was found to
be 1.175. by combining this value with the other constants
in the equation, the total surface area (in2) on each sieve
was the product of the fraction weight in grams and a

constant.

Rheological Preperties

As mentioned earlier, rheology may be defined as the
study of deformation and flow of matter. It attempts to
describe the mechanical behavior of a material in terms of
three variables, stress, strain and time.

When a perfectly elastic body is deformed, it takes its
final shape immediately without any time lapse. In other
words, the deformation is time independent and a function of
the applied load (or stress) only. For a perfectly elastic

body Hooke's law applies:

8: Z. ''''' 7"" (5)

where e is strain, in/in; 9f is the applied stress, force

per unit area; and a is Young's modulus of elasticity in

55

tension or compression. In shear, this equation is:
Xr— 52 --------- <6)

where X is the shear strain, s is shear stress and G is the
modulus of shear or rigidity.

When a very small force is applied to a liquid it will
deform since it has a zero elastic limit or zero elasticity.
The force required to move a plate of area A,separated from
another plate by a distance d, is directly proportional to
tile area and the velocity, and inversely proportional to the

s eparating distance.

F: 7 (225.) --------- - m

where 77 is the coefficient of viscosity.
From the above, F/A =shear stress, 3, and v = dx/dt,

so that Szlgljé.
400‘-

Integrated, this equation may be written

r:§ :: §—+ ---------- (8)

where X is the shear strain. For an ideal liquid (Newtonian)
the rate of flow is 3/7 . The above type of flow is called
viscous flow.

Between. the extremes of elastic deformation and viscous

flow, is a type of flow called plastic f'low. When a solid

 

lS deiormed beyond its yield point, it will flow and exper-
ience a permanent deformation. This phenomenon is called

Plastic flow. Beyond the elastic limit the flow may be

56

:Lilnear as in the case of viscous flow, or it may be non line
esxr. for the ideal linear we get an equation similar to
ecyuation (8) above,

3/: s—s’ 2‘ “"""""" (9)
7?’ I

.Scrhmidt and Larlies (1948) call 7’ the pseudoviscosity or
plastic viscosity.

Kookean ideal elastic deformation in a solid
and Newtonian flow in a liquid may be considered
as the two “xtremes of rheological behavior. It
may be said that there are three basic types of
deformation, elastic deformation, plastic flow
and viscous flow. Lany products such as rubber
and plastiCs may be considered as combinations
and modifications of the three behaviors. The
action of these complex materials under load is
often represented by mechanical models composed
of elastic and viscous elements acting in series,
in parallel or both.*

Nhen a body possesses both elastic and viscous character-
ijstics it is sometimes called "visco elastic". To help visu-
lxize the relationship between deformation, load, and time, a

Inecfiianical model is often used as shown in Fig. 22.

 

1,
LT)

w

 

(a) (b) (0)
F143. 22 mechanical models used to represent rheological
behavior; (a) a Maxwell unit, (b) a Voigt unit
(c) a Maxwell and a voigt unit in series.

Q'a

'-
e

bChmidt and harlies; Principles of high-Polymer Theory
a

329 §£_£Z§igg; LcGraw Kill, 1948. Excerpts from Chapter 7.

57

In the case of the Maxwell unit a given stress will
cause an instant elongation (or compression) of the elastic
spring plus a deformation due to movement of the piston in
the dashpot. If a certain model represents the behavior of
a particular material, rheological equations may be written.
For example Steenberg (1949) considered that rheological
characteristics of paper could be represented by a model as
in Fig. 22 (0), except that a spring would be added in series
with the dashpot in the parallel unit.

For a Maxwell unit the strain at any time will be the
Sum of the elastic and viscous elements. From equations (6)

and (8) above:

a’= 5/4 ““1 X319

Xiafil :"58 4' 59f ----------- (10)
4x: 1.. 2’3 + 3
2? a (It 77 ---------- (11)
€_(_5 :: éfl’és
60 4t 7

0" d5 -_- 65$!— .52. ----------
dr dz‘ 7' (l2)

Wher: 7’: 7/3 is a constant called relaxation time or the

time constant. The analogous equation for tensile or com-

pressive stress (assuming Ec = Et) is

41 : fa’c _. 3:. ————————— (13)
at at 7’
DJ and G are related in the elastic range by
E: Z¢//*/“) ---------- (14)

Wnere/a is Poisson's ratio.

58

Rate of Deformation

From Fig. 22 above, it is apparent that the rate of de-
formation will be important in determining the resultant
force (or stress) on the unit at any time. If the load is
applied very quickly, the dashpot will not have time to op-
erate. It will act as if "frozen". The Maxwell unit will
behave almost like the elastic portion alone. On the other
hand a slow deformation will cause the dashpot to have much
more influence. From equation (13) it can be seen that the
magnitude of the time constant,7’ , is very important. If
the rate of deformation is low, i.e., the time of deformation
is long, with respect to ’7’ , the viscous element will domin-
ate the action. Similarly a short time of deformation With
respect to 7’ , means that the Spring or elastic segment will
be most important.

The effect of rate of deformation was examined for pea
beans at the higher moisture levels. Data were also plotted
for wheat at slow and fast speeds but at a lower moisture

level.

Stress Relaxation ‘

As mentioned, one rheological distinction between a
liquid and a perfectly elastic solid is the relaxation time;
for an ideal liquid it is zero, and for a perfectly elastic
Solid it is infinite. It is obvious that for a visco-elastic
bOdy such as grain, the relaxation time will have some value

betueen these extremes. Relaxation time is a measure of how

fast the grain can dissipate stress after receiving a sudden
deformation. It is therefore considered an important rheolog-
ical prOperty of grain.

In the tests on pea beans, the kernel was given a cer-
tain percent deformation, at a given crosshead Speed. after
the crosshead was stopped, the relaxation of stress appeared
on the oscillograph, since the chart continued to travel.
From this record, the logarithm of force was plotted against
time on semi-log paper. The instant at which the crosshead
Stepped was taken as zero time. This relationship of stress
Pelaxation was measured for three deformation speeds and for
various amounts of deformation.

The basic equation (15) above which assumes a Laxwell

unit representation, is restated:

3‘}; = Eda —-.§: {aw

Q‘ince the deformation rate is zero when the crosshead is
S”SOpped, the term Ede/dt is zero. By integration, we obtain

Q's qzéj-% --------- (15)

Where q; is the initial stress when t = 0. This equation
Shows that one expects a straight line relation between stress
and time on semi-log paper. In such a case, the time con-
Stant 7’, is the time for the original stress to relax to
OHS eth its original value. This time, as previously stated,

is the relaxation time.

It should be noted that for pea beans, force rather than

stress was plotted against time, since the cross sectional
area of the bean is not knox‘fn. Since stress is merely force
divided by a constant (area) the s}.1ape and the time constant
of the curves is unaltered by plotting force instead of

Stress. v

RESULTS hLD DlSCUoSlON

Compressive Tests

Compressive Tests for Corn
Considerable variation was obtained in the results of

compression tests on individual kernels. Two reasons for the
high variance are the inhomogeneous nature of the corn seed
and. the stress concentration set up by its irregular shape
or irregular bearing; surface. That the irregular bearing
surface was a big factor is apparent upon comyaring the

esults of corn tested on the edge and the flat position.
Since the edge surface of most kernels is quite smooth and

relatively straig'zfiit, the point loads are minimized n the

Po

edge test. when loaded in the flat position, many kernels
are slightly dome shaped, which caused early failure and. a
10W apparent maximum strength. Kernels having straight, flat
sides are able to take higher loads than domed shaped kernels
before failure.

Results from these original tests are given in Tables Al,
52: AS, All and A5. In each case the average value, the

standard deviation, (T , and the coefficient of variation'x‘,

C, are given. Since the absolute value of the standard de-

viation may be quite different in two sets of data,

use of

 

a; C = <r/ave x 100

the coefficient of variation allows direct comparison of the
two groups. It will be referred to henceforth as the C value.

In tests at three Speeds on corn, at one moisture level,
(14.375 d.b.), C was around 20 percent for the edge tests and
averaged about 55 percent for the flat tests. (Tables Al
and .12) Approximately the same range of C values is given
in Tables he”: and 12.5 where the forces at the yield point and
maxim a point are given for four moisture levels.

It should he noted that the yield yoint is not too def-
inite in tests at higl‘ier moisture contents. The indefinite
location of yield point is particularly noticeable for the
flat tests. The force-deformation curves are often curved
to the maximum strength. For consistency in tabulating
the data, the yield point was taken as the point Where an
increase in deformation occurs without increase in force.
with high moisture kernels, a definite maximum point is not
alxu’ays indicated. In most cases a maximum point is reached,
followed by a drop in the force on the chart. l“urther
deformation causes the force to ll’lCI"‘fse again. This in-

crease should not be considered as repressntinc exern>l

V

0+-

strength, but rather as the force resulting from the crush-
ing action. Ely the time the maximum point was reached, the
kernel had failed, i.e., its original dimensions ~were de-
SUI‘OYed. dith high moisture, the force simply increased
with deformation, and no maximum was shown on the chart.

L . o 0
in this case the ;;ernel was ”plastic" in nature.

"1‘ g n
Hie force-deformation curve varied irom one kernel to

C)
(a

m‘

aIZOthCT, and the curves in rig. 23 represent an average for
1() tests. Thus, each point on the curve is the average force
iTCu? 10 tests at that yarticulur deformation. Beyond the
maximum strength, the lines are dotted as the force Varia-
izixon beyond tais joint is quite irregular. The curves in
r9143. 23 Show a definite maximum goint. as would be expected
Elt inigher moisture levels, the maximum force was reached
\Vitfll greater deformation. fne yield point is not indicated
iri these curves beCause of the averaging process. field

arni muximum force values for edge and flat tests are given

ir1 Tables 44 'n; A5.

Congoressive Tests for tea Beans

< V .
.L

3. 24 illustrates the result of compressive test

on

U)

A ’ a V
peex beuns at two moisture levels. nt 10.0” d.U., tne beans

sruynee elastic properties, for both the edge uni ilat rosi-

1V

ticnus. In the flat no

A

I

:ition, a yield point was reached at

$1)
or
O

(.4

P

Ct
(I!
*U

k I

"3’

O

(5‘

H

F,

cf

deformation. 1n the edge test, no yield

L‘. -. ~ ~ . 1 5 ~

the snuali Space oeteeen the two cotyledons. (it snoule

C \"1‘7‘ :3 3 1.“, ‘ ., 131 w‘) 3 .399". L 1"“ . r \o C . (5 1 r t‘ . O G“, ‘1 . ed
VJ- JMLI] J f1»sve A40; Li VJ. J. VCU o-Liorl 8. cornprbuu le Odd ls) 0:.1’ l

. ‘. _o O 4_ ‘_. > o _ A _ v _g _ o "‘1‘,‘ _“\

in thB flat peeitlon than in the edge posit on.) inus, the

apparenit‘yield point in the flat test was most likely the

A A)“ 7‘ v {a o _ 1‘ .. _0' . u_ .. ~ . "1“ n .u ~ A! \. ,
vvupresnsite failure point Oi one or oOLn oi the teen nuchs.

)

.0 .
-3. 7,, it- x o a o f“ r ".-v o a _ ~ ._ _v_ 3 j _ r. ‘3‘,“ l- 0 ~“_ Q" __ 3.. , .
*v0~ tulle slifiht Jldld or relative detainuti,t UGUM on

 

 

\ . {list I, i J ‘1... I II.
. v ) 4 ¢ .OF“.I‘?§.|‘ ‘
F , \ I Itll WWII! «5.x \

64

 

 

14.6 %
.35 - s -
q
\
\
\\
A5870 0—~~
30 r- . --0” \
\
\
\ \
\ \
\ \
\ \
25 " \\ \\
Q \
\\ \
/ .2 ‘
8 73 \D Q\
20 - \\
\
\
\
s
Q /5 t
0‘
‘8 26.0 %
o
\1 /o ..
5' -
[ac/2 Poi/77‘ average
Va/ue far /0 Ass/s.
__l l l I J j L 1 l
c / 2, 5 4 5 6 7 8 9
Der’Ormf/on, percenfi
Haze AOAD— DEFOE’MAT/OA/ CUE v55 Foe

JELAOW DEA/7’ coew AT FOUE
MO/STUBE AEVELS (36 db) wave!
THE kEEA/EL PLACED 0/v EDGE.
MED/UM SPEED.

 

65

Eat/7 pol/77‘ average a ‘o
5‘0- Va me for /0 /es%5

  
    
 

40 L/0-6% [/af

 
 
  

 

 

 

E)
- 50 ..
S
‘8 /o.6% on edge.
3 0
2 b o
49.5% a
or? 9490
/0 +- 3
a - “/ /8-5% f/azl
o/S/
40/ 1 J_ A 1 4 L 1 1 1
O / Z 3 4- 5 6 7 <3 ? /O

Deforma/z’on, pgrcerfi‘.

£7624.- LOAD-DEFOEMAT/O/V (URL/ES FOE :05»:

BEA/vs A7' MED/UM 5/0550 (azwmflfi
AND ’47 TWO MOISTUEE [El/[1.5610(6)

‘rv (~
In LL

more 5 available

space

drop-off of force Was the maximum

bean. Che above explanation uccat

straight-line portions or the cuer for who
10.6 percent moisture.
The first portion of tile curve for the

1.0 8;.-

expla'n qualitstivcly this paard

OJ. tho our 8 is lincar gluost to tho
nith higg moisture, lo 3 fl’ffcrc

cdvo .35 flat .ositiins. lt spgoirs

.. 9-. -, .-' ‘,,. 4..
ov;::‘visc::is gm.ogo1 LL38 32w; o._nn-tc
71- J. "‘ i“, .‘. 4- i L. V, _ .‘ \ .F-
“t, o;s .Lfiu'lhois Atrc, eh“, (J Obc'nJ.C.

A .- - ‘ _ V" : . 'V ‘ ~ - ’fi -
Cl ct: 1' t w vagiii.01‘-1-, is i)

.1. , , -, ,- 9. ° . p ‘ P R .q J-
so ual CPOSS'muCJLOMJ ir,; is not
° ‘ ° . . .~ It v-1 _ n J-
is oov1ousl; greater tor not ilst L

o .0 .
WulStUPC in

curvature

for further deformation.

7 '1-
"\
LILLI

gr

next

edge tests is

lanation HUS been LQLLlLL.

not occur“ bet cc
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It is of interest to note the relationship obtained for
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F17. 95, portions of the deformstisn range epycsr us a

‘ W . --1~ -. ‘ . -0 \’~ . -- ’ T ' r n \’~ "1'. ,“fi - r» n r
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moisture beans, the volume under the loading head remains

I

almost constant, end is equal to A x h, where h is the bean
height uni A is the average cross—sectional area. at u deforma-
tion of 50 percent h is equal to one-half its original value.
Then A must be vc’y nearly twice -s large to keep V constant.

The curves shown in tin insert on rectilinear scale were

3;; reduction oi‘ the force

rt"

obtained from the semi-log curves

or load to u load *er unit area.

(n

('11 f‘ t‘) . , '7 r') C‘ \ , ° , ,_‘ , ... ... r "I .-.
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Compressive Tests for Wheat
Preliminary tests showed that there was no significant
difference in the force required to dciorm wheat from ei
3flu3.flut or cd;x33wm3itiun. Ccummruunitly, all Iluuflicr tests
Jere made wi th the i';e1_"r1el in the flat yositi an.
Loud-deformation curves for wheat up to 10 yorcont do-

I

ormution are given in #13

. Be. A definite olestic r nge
is shown for the two lower moisture levels. The yield and

maximum points were quite indefinite for the 20.5 percent

 

  
     
  

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SOFT EEO W/A/7'EE W’HEAT A7
THEE/E MOISTUEE LEVELS.

‘w . . r . ' J V' t r-“ W" ‘ D ’. “N ‘ '— r‘ 'x
curve, walls no maximum Jas swann lor tne L7.u perCent test.

r-«J

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J

semi-log 3 er, essentially a straight line relationslir

6.5

T5
t

aas obtained, esntcially between 20 and 55 percent deforma-

L

tion.

Original data are tabulated in Tables a7 and n8.

Core Compressive Tests
As mentioned earlier, cores were cut from tie grain

kernels and used as compressive test specimens- fhe use of

n 3- "

these cores allowed the data to be expressed in terms of

4"

average stress, since the cross-sectional area oi the core

could be determinel. Those cores are shown in Fig. 17.

The most important proterties studied with the cores

'3

' ~v. "7- ‘ ~ n A - ' 4 . J"? . v‘ x "a u o - in r s" 1. --‘-~ v .~
ve_e 9J9 modulus o: UldSBlClUJ in comyless1on and tnc max-

\

imum compressive stress. These prorerties are shown graph—

4.

ically for corn in iig. 27 ans for wheat in Fig. 2

\)

(

8 and 29.

1

L -‘ - n ‘ ' ' . ,- ‘ ' H . a -_ - (‘ a -, r- . .. ~.
}ropsrtios tha were investigated are summarized in

Table 3.

Lodulus of elasticity and maximum Stress versus moisture

‘

are plotter in rig. 27. a linear relation holds in both

cases between 15.e and 18.8 percent moisture. Inere agpcars
to be a transition between the 18.8 and 23.0 percent levels.
lhis effect is later shown in impact tests. The corn is
quite elastic below 18.1 percent butmore plastic towarls the
l

Or" ‘ ‘ ‘ V . n ‘ "1 (w r‘ "N ‘1 “‘ ‘\ . m, ’1 ”V a” o“ " fl
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TABLE 3

SUMMARY OF PROPERTIES OF GRAINS
AT FOUR MOISTURE LEVELS

 

 

 

Tests Slope Of
Percent To Stress-Strain zip/L At Max. Modulus
Grain Moisture Compute Curve In Maximum Stress Of
d.b. These Elastic Region Strength psi Elasticity
Average k, lb/in % psi
Values
Corn 15.4 5 li,0.‘?0 14 .2 4811 55? , GOO
1*,0 5 1;,2to 15.7 4145 53,?00
18.8 5 9,650 15.1 5335 49,900
23.0 5 5,790 19.7 2892 51,740
Beans-fr 6.4 5 1?. 560 3. 6 4370 M ,soo
Wheat 15.7 5 0,168 11.1”} 3259 46 .040
17,9 5 5,14% 8.9 3094 55,600
21.0 5 4- o 14“ B Q .1 2458 351,':4 :30
24.8 5 3.556 33.7 2574 54,700
17.0 10 6,540 10.0 5161 66,190
18.4 10 3,085 11.3 2627 43,340
20.7 10 4.503 11.5 2391 4R,e60
24.2 10 1,920 20.3 1741 19,210

‘*No elastic properties for higher moisture levels.

 

 

 

rsheat. Ten extra tests at each moisture level tore run in
an effort to explain the apparent peak obtained at 17.3 per-
cent moisture during the first series of tests. The dashed
Zlines represent a variation of one standard deviation on

p

teach side oi the re ression line.

equations are given to represent the relationships in

F; l
Ho
0"}
U}
Q

27, 28, and 29 between the moisture limits specified.

U)
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Phinch Shear Tests

The punch shear tests were used only for pea beans and
pmea.bean slabs. The effect of initial compression on the
exileulated shear stress is shown in Fig. 30. Since the
sliear slabs are homogeneous, the calculated shear stress
skujuld be constant regardless of the thickness. The values
plxattcd in Fig. 50 are calculated on the basis of the orig-
inaLL 31$) thickness. Typical oscillograph curves obtained
for"these tests are shown in Fig. 19, with sample calcula-
tierns on the chart. Actually, the shear stress should be
exfunsssed in terms of an ”effective thickness”. This thich-

’3 ‘ 'v", r' ‘ - H" \ (\‘Vfi‘ r “ '3 - '\ “ I“".‘M “ . "
nVSs Laould oe that Jrcsent at tie time the maiinum iorce is

reaahetl on the oscillogrash chart. By using an eifective
0P equifivalent thickness, calculated stress would be constant

Witn 3141b thickness. The thinner the slab, the more nearly

correct ‘the calcula ed stress should be, i.e., the closer

 

 

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:required to shear the seed is divided by the cross-sectional
zarea parallel to the amplied force, s==F/A. There Was some
compression and bending before failure by shear took place.
Fe Ls the calculated shear stress should be termed "break-

” stress. Failure by bending (tensile failure) instead

iJag
(sf shear was more conzmon at the low moisture levels.

Fig. 51 summarizes the relation between maximum shear
srtress (or breaking stress) and moisture content for wheat
earrd corn. The bending strength of corn decreased more than
“Ileat with increasing moisture content. In compression tests,
a. greater variation in compreSsive strength was found for

Ctzrn than for wheat with changes in moisture content.

nst moisture content for

7
Ho

Shear stress is plotted

9.3
'7‘

,3

f

13621 beans in Fig. 32, over a wide moisture range. Relatively
Iii':n snear stress Was found around 18 percent moisture con-
‘terit. This increase in strength.may be explained as follows.
At 'the low moisture level (6.4% d.b.) the bean kernel is

brijstle, and failure by bending occurs (tension in the lower

edgua). In the intermediate range, the bean is rc‘ lativ 1y
tougfii, rais in 18 the shear Stress. at ry 1i::h me is Mu e

J . , . ‘

levelxs (37.6p d.b.) tne oean becomes very soft, and thus

requiexes much less force to shear it in half.
Leasurement 01 energy

Impact {Pests

RBSHJltS from the impact tests for wheat using the impact

 

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80

tester (Fig. 12) are shown graphically in fig. 35. The
emery is expressed in terms of the kernel cross-sectional
area in order to reduce the Variance, and also to serve as

a better means of Comparison with the other grains. The graph
shows a linear relation between 13.9 and 21.7 p‘rcent moisture.
The relatively sharp increase at the high moisture level is
accounted for by the soft or spongy nature of the kernel.

at lower levels a more brittle material explains the lower

\A

impact ene 33.? required.

1'18 311 shows impact energy required to rupture corn.

were similar to wheat. It was decided to make a cam-
par—ison of the energy required to rupture the kernel by static
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"3

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means of a planimeter. The total energy under the curve up

to the noint of rupture was divided by the seed cross section
to {get a value in terms of in-lb/ix . In each type of test,
.1 (by the Same vise) in the flat position.

n imp a ct and

Po

ixle effect of :1 er'ttle --Vnd a ‘l;:3u;_;11:':za't.;rial
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1.1.,"11 I-i-J1ouLlI't: 'c; ’13. 1:01;"..05111 law) \-.L). vul- ‘-“~ /" “OL'O L“"re

.. ...,L‘, "1*- p. ,. x.-. J
(.0 li;Uu-JOLLS. 1110 «PU--..;VLII’ L416

moisture variation in either direction from this central

0
(D
Cr
C:
O
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"\
V
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C}
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energy re-

1 1-

quirements are about the same tetween 15.Pp d.b. and l€.5p C.’.

[)

Original data ior impact Sled” tests on the three (rains

O (s

are tabulite d in uplrendix A, Tables n9, n10, All, and A n.

hysteresis LOSS
7" . «_ \r‘. .» .0 l n ,3 .1 -° 71 7-11“. ‘.':C‘Q‘. q 4-; N .f ”“73. Lin/.211
'6'1C1C1- alt-[(q‘L i»; 1L) OJQCK .LA- COIILJI lec'—.).LL11’ L-i¢ Q'LJ. v a. \‘K/
' .- -- -- ,. ..-”- --‘A J- ~‘__ ... ,.‘ ,nfi- 0
the force-deformation curve :c‘ruounts the work ehfeddzd in
- -..- - -...- r1 .. ..- . .. . .71.]. :w ...w . .0 .
loadinr: the s-.>ec_u:--:n. ..‘ne aktd unaei tne tan-loading

lwqusesents the ene‘Hy returned to the machine by the s:eeimen.

Fwd
l

. L‘ -3 -. J-
!

etly e astie materials, e1e area under the

(D

"31f

F

I"!
O
(D
1
rx
0
"5

‘ V ’n {I

loadiruétmm unloading curves will not be equal. Lhe eiiier-

"5

. ,;-‘|. .H. 71.. ..Y .' _., -- ..- , ' .
ur e 01 the macarial to leeover its

- a

ence is due to C.13 f.i

I...»

‘1‘ “.‘ “ ‘3‘ \“-. [v . 4‘ ‘- 7 ‘. '5. "' 4‘“ ’fi 7"‘15‘.’ ‘-.
04 ice-111.41 (1111.41.51 Oil-o 111.3 v.11 lbl *. an ine a3 tic “()1 ul’. -c. (,1 011
V‘

. "\ _fi 1 1 . 1 a ’ .._
L_ Vxl / . ,_‘ r g-n ' ~ ‘-_ -‘ 4_ . “ ‘ . . .'-‘ r. -.. ,_,' t ‘. , w. r, _‘ x ‘
1» :PCMAucwa.~uiien may'Lmz em forary cu':,WM¢anent. ..n. enclos-

04'
LAD

p‘.‘

ed hysimaresis loo; rep1esents energy dissipated as

U"

1 o

.-J

I‘ :3 :-: ,-. ,9 ,- 5* 1-1 .. w , ,..z_. -. 9 .. .0 - ,. - t- _
“1 rel-MuiVe SJZU 01 1.11:; masters-‘51:; 101)}- i“ .1 I:‘.Oe.‘.ui’t;

C”.
O
()

 

 

 

 

of how much the techrature rf a material will increase when

Yerzley (1939) dealinc with rubber, eXpresscs the per

C)

flvstc resis loss x 100

HVsteresis 1083‘6=:
J” ” snergy expended in loading

This is sometimes also called the "specific damping capacity”.

Yerzlev refers to the enercv returned to a test machine bv
J ()9 o
the syQCi in; n on unloading as the resilience of the test

Specimen. He expresses resilience also as a percent:

(1

“esil‘ Ice , __ enelr3 returnei in unloadingr X 100
_L LIV 1‘; v _ '\ O ... O
’ ’ energy expended in loading

(This meaning is different from that used in "medu us of
resilience” in the next section.) It follows from the def-
inition that,
A hysteresis-+ fl resilience == 100
Hysteresis leaps were obtain3d by loading and unloading

grain kernels with the load cell testin ng unit. big. 03

J n

snows examples of oscillograph charts lrom whic] loops were

1

plotted. lhe loops were obtained by plotting the loading

4.

curve up to a given load; from tlla. foiz

..J
C!"

, the unloauin

(-)

in. It sloulj be

03

‘7 " ' a ~‘ ‘ . 1' ~"“ 3 ‘ PI "' ' ‘47"
CHI V'L' JILLS £21013th bucix tO'ualflu tilt} Oil.

charts 2 and 5, that the initial loading

’3
F;;
H.
03
‘0

i,
line izas a lower slope than the succeeding loading lines.
nts is due to a mechaniCal conditioning action that taxes

)

place <iuriru~

C.)

the maiden loading. mach loading line alter

1m irrit.ial loadinr_, nas almost exactl" the same slope.

 

 

86

 

 

 

/'/ i/ W. Il- ’
_‘“—T ., h‘ —_" " _*"" "
'¢ LL
2 I T) I“: z
_ fun
3" r], . i) u; M, («r-s, SAu
.— . / ‘ "\ (1.;

Fig. 36 Representative oscillograph charts for wheat core
tests, with increasing deformation (and time) from
right to left, and force on vertical axis.

1. Compressive core test.

2. Loading-unloading cycles from which hysteresis
loops were obtained.

3. Loading-unloading cycles and compression to
failure.

' .r‘ -L‘

ine effect Ol this mechanical condition n3 is lurtwer shown

H-

in th hysteresis looss drawn in Fig. .37.

s the maiden loading—unloading cycle

. [—4
O
C

"C5
8
w

H

U
m
f—Jo

0‘?
O
()1
\1

‘0
'u-Jo

for wheat cores at 17.0 percent moisture. It is obtained
from Hig. 33, chart 2. This loop shows a larger hysteresis
loss than loop A2 which was obtained from the second loading-
unloading cycle. Also, as shown in the oscillograph charts,
line slepe is greater for A2 than for Al. Loop

the loadins

8
Bl is the result of an initial loading-unloading cycle at

...

20.7 percent moisture. The magnitude of the Lystorcsis

9n,

ine percent “esil-

losses (percent) is given in Fig. 57.
ience is simply lOO minus these values.
Similar hysteresis loops are plotted for corn at two

moisture levels in Fig. 38. as in Fig. 37, a greater hys-
teresis lo"s is shown at higher moisture levels as well as
on the initial loading—unloading cycle. In each figure, the

point where the unloading line meets the x-axis s a measure
of the inelastic deformation of the kernel. This deformation
nun; be reCOVerable with time.

fig. 39, for pea beans, shows that moisture Content has

ziggreat influence on the hysteresis loss and on the degree

of set.

-v'

kOdUIJJS of Resilience and Lodulus of Toughness
This energy to deform grain kernels to the elastic limit
is tht:1nodulus of resilience. The ODGPSY to deform grain

1.; -, , - "x _ o _ o . a -. n
2.8111815 to the mmumum strength is tne modulus oi tongjincss.

 

25" Hys/eres/s /osses: q
4 = 46-5 %
_ H2 :5 26-4- 70
20 I— : 5/ =4Q5 70 d
I
I
/70%a’b :
I I
I5 I. : -I
\Q' I
\ I /70 %0.’b.
" l
‘0 I
G I
Q /o .. .1
I
I
I ' 20.7%016.
I
5f" E : ..I
: I
I I
. I I
/ 1' i L
0 / z 3 4- ? 6
Deformaf/orz, in X /0‘3
£76. :57 HYSTEEES‘IS maps Foe SOFT

   

88

 

 

BED W/IVTEE WHEAT COEES.
Loops A,4'>5u MA/DE/V LOADING
Cycz ES , LOOP A, , saw/v0
LOAD/N6 CYCLE.

70

50

load, /6.
8

‘8

l0

4 = 453%
r- fiz=/5Té% d
5,: 68.2%

   
  
    

Ays/eres/‘s /osses;

/5'-8 % db.

 

__.—_.—————_.____..___—._--————-——

A578 7. all).

Q

 

   

     

 

r—o ———~————--—
‘Ot_o\‘________________

 

“Mk

L I

1
2 3 4' 5 6 7
D eforma #00, [771 /0 '3

SP9

FIG. 38 HYSrEEES/s LOOPS Foe YELLOW

D£NT COB/V KEENELS. LOOPS
A,&5, MAIDEN LOAD/N0 CYCIES,
100/3 A2, SECO/VD AOAD/IVG CYCLE.

39

mt

 

/8.5’%O(b

    

Hy s/er esis bars:
A7 = 57- 6 7. _

 

 

 

 

 

 

6r
a: 76.5%
4-}- ~
‘3
.. 5.
‘0
U
3 ._ -
3282:0415.
o 7 é 3 3f 5 — '3' 3 9 I10
Oeformah’on, lf7X/0 '3
_1 l _L J
w / 2 3 $- é'

FIG. :59

D e form a/ion , parcel: f.

HySTEEES xs LOOPS FOE PEA
BEA/V5 AT 7'qu Iva/57085
LEI/£7.6- AOOP ,4, SECOND
LOAD/N6 CZYCZE} LOOP 5
FDUETH 40A D/Né' (ya E.

91

The energy required to de i'orm pea beans to the elastic
limit and wheat to tie elastic limit and maximum strength
is shown graphically in Fig. 40. although the ultimate
strength for beans ta 3 SWIoIn to be greate1 (Fig. 24) in the

flat position, the modulus of resilie ence is hi3: her in the

edge FO‘itien. Fig. 40 shows the greater variation between
individual tests (ten tests conducted for each rosition) in

A

the edge position.
is

m

. 41 gives energy to deform corn to the elastic limit
in the edge and flat positions. A greater variation in en-
ergy is noted in the flat pos i'ion. This was a so true
for the force required to reach the elastic limit. (Tables
A4 and 115)

unergy requi ired to deform corn to the maxinum strength

lat positions is presented graphically in

H)

in the edge and

Fig. 42 and 45, respectively. A direct comparison of energy

"D ."‘I

igures is diificult owing to the diiierent scales

"2\

in the

(0

e

tests.

CI-

used. a greater energy variation occurred in the fla

‘

n study of Figs. 40, 41, 42, and 13 shows that the range
Of energy values for any given grain and type of test is
appro mzim ately the same for each It Mi tux 6 level. On the otaer
hand, when force alone is considered in these centressive
tests, the variation with moisture content is considerable.
The decrease in tiength (or elastic greperty ) with increased
moisture is offset by the increased deformation required to
reach the elastic limit or maximum strength point. Lhus the

0

energy Values in contrast to the force values, remain

(O
E Q

 

 

 

 

 

 

 

 

 

 

 

O
'700‘L’ o q
o O - Beans
o-Wfieaf
.600 _ _
O
[ac/7 poi/7f represen/s
one 4:952?
0500b X .1
‘k ‘k
‘k
\ * “I ‘3 s t a s g
g S: I? Q x Q “k a .
X ‘ \J n d» n, g ' “E
Q) ”i a Q) Q) Q)
smote; 53> u. If “I ”s d L“ .
i I.
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33 ° ‘
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LL} ‘ o . . .
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g . g . ‘ ,
E . I - z
i ' 3 . °
Ohm ”a. E==d
M. 6 /é-0 /6./ 20. 5

Ma's/are A eye/5) percen/ d- b.
F15. 4O Ext/5865’ 7'0 DEFOEM PEA BEA IVS 7'0
.Y/ELD POI NT A/VO 501-7 850 W/zvfff
WHEA7 7'0 77/13" .Y/[AD PO //v7 A/VD
MAX/MUM $7E£IV6779 AT Mia/UM
SPEED. ’

 

 

 

 

 

 

 

 

 

0.6I-
X -I
. edge pas/flan
x f/a/ Pas/{ion
0.7 I.
Eacfi pO/‘nf re resen
one {es/z F k
X
0.6 ..
x W ‘1
fi
X
X
\ 0'5 " x“
0
§ x ’1
X x x
E .
k 0.4-. EL“ x: fig
9‘ x '-
‘s X
| XX .
R
\
.03 . ' . '
33 “ x 4
0% c: Q l K o
. x
0.2 - g. :1 x .
if ' ‘
x " ’
i.: ”X i x z x :. °
0., b ::o X : 4
:- x : ; 3:5 1‘
-6 #—
/5'5 /5-2 26.0

MO/sfare [eye/5, farce/71‘ d.b.

FIG. 4/ ENEEGJ/ 7'0 DEFOE’M YELLOW DEA/7' COEN
729 THE Y/ELD F70/N7' //V EDGE AND F£A7
POSITIONS.

 

 

 

 

 

 

 

0.7 _ $43 _
m E b
a I
E
as _. . _
0'5 .. : O —I
O 0
V ' 0 . . O
m , .
E ° : .
Q’ 0
V 0'4 - . I x , _
\ O . ' 3 g z
1 , . . . .
s: . . .
§ 03 .. .
.\ . :
‘\ o o . .
>3 0 o t o
0-2 .. .
00/ I- -I
. Each ’90th represen/S
one fesf.
O l + I I
/4-6 /5.8 Iaz 26.0

MOI 5 fan? (eye/s, perm/7 f db.

FIG. 42 ENEEGY 7‘0 DEFOEM YELLOW
‘ DENT COB/V 7U MAX/MUM
STBEN67H //V THE EDGE P05777044

 

95

 

3.5 g l
‘4»;
V)
g u
I I O
5.0 A
2.5 o _1
\.
0.) ' 0
Q 20, ° ..
t ' .
V
t I . . ‘
“vs . ' q
Q
é : ‘ t . '
S; ' . . '
We . .
i) : 3 ’
Q
Lu , .
O O
0-5 . . 3 _
z 526/; loo/07‘ repreSen/s
one fesf.
J.—_-_.l l L L
/4.6 /58 43.2, 25.0

MO/‘s/ure [eye/5‘, perc 9777‘ db.

F/G. 4-5 ENEE’GV 7'0 OEFOEM YELLOW

DEA/7‘ COP/V 7‘0 THE MAX/MUM
STEENGTH x/v THE FLAT POS/r/ON

 

relatively constant.

Total energy Versus Surface area

The total energy to deform corn to one-ha'f its oriqinal
dimension from the edge or flat position, was obtained from
the oscillograph by means of a planimeter. ne crushed
material fr m 10 tests was oven dried and a sieve analysis
was made with the minature Tyler sieves (Fig. 17). Tne

'0

surface area w 3 calculated from these weight fractions by

 

7
fl: = /2 VV/ + E 4%
e S; "a e 5,;

This equation was derived assuming the particles to be cubes,
but the same result is obtained if Spheres are assumed.

The results are summarized in Table 4. This phase of
the energy study was quite unsuccessful owing to the unsat-

”2‘

isfactory measurement of the surface area. she a

r?”

Iove equa-

tion is believed to represent the total surface area 11 a

ng action occurs as with commercial grinders,

F"

nd

[—1.

reasonable .r
In or shing the corn kernels by compression, insu
break up of the kernel'occurred (Fig. 17). as a result the
tOp sieve retained too much material which amount accounted
for 50 percent of the calculated surface area in most cases.

1 in the tOp sieve has made

F’-
9:.

It is apparent that the mater

C)
F'}

up chi-fly 0 original surface area (surface coating), rather

'71‘,.

than new area produced by fracture. ine total energy index

ELLATIOUSIIE Blfflnlh ENERGY AND SURFACE AREA
mr\ 3" ‘7

11:. Chi v L111» 1‘4

EDGE AND FLAT POSITIONS

 

‘T'xznv-L' _'

 

11. V

 

Grain . Total Energy
Position in-lb/kernel Total
anl Loisture applied to Kernel Surface Tctp_
Head p d.b. to Crush to area our“
steed One-half Initial in5
Edmension
V Gd
Slow 14.3 15.06 5.01 2.2
Led 14.6 12.77 5.51 2.4
fast 14.3 10.92 5.25 2.1
Led 15.8 9.45 4.65 2.0
Led 10.2 15.51 4.67 2.8
Slow 25.0 10.90 3.56 5.2
Led 25.0 8.72 5.29 2.3
Fast 26.0 15.94 5.50 4.2
FLaT
Slow lé.6 00.95 4.57
Le . 14.6 62.2- 7.79
fast 14.6 62.12 5.06
Ied 15.8 00.52 5.00
Led 18.2 30.55 5.65
led 26.0 64.45 5.59

 

(a
Q)

vidin? the total energy by the calculated
1 a

‘1
g)

H-

was obtainea by d
surface area as shown in Table 4. 4his index figure is
merely a relative figure for comparison. he weight should

be put on it in an absolute sense. The index value shots

)

he edge peeition

CT’

an adVantage for crushing the kern-l in

rather than in the flat position.

Rheological Iroperties i

For a perfectly elastic material the resultant stress is
independent of the rate of loading. for a viscous material

the rate of straining is very importart. From equation (5),

w ' a

where X is tne shear strain, 3 is snear 0trees and n.is the
coefficient of viscosity. If t is large, i.e., .4376”- is

small, the tress will be low and vice versa. Fig. 44 shows

U)

a slight but not intertant difference in the resultant load
(stress) for three rates of deiormation.
stress would probably be greater if larger variations in
deformation rates coulr be used, and if the beans were tested
at a susewhat lower moisture content. at 52.8 percent they
‘Pe extremely soft. A check on the speed effect for wheat
at 14.6 percent moisture showed no noticeable difference
between slow and fast speed. at this moisture, the wheat

is more elast 0.

Ho

 

 

 

30.. .1
I/
’e
I/’
,/
.20... l/ ’ ..
~Q // /
\ , /
/
b‘ I f , 95/
g as .2 /,
0 ////
\J ’ /
/
’0- // ,7177780’ .1
// .
/;”/ {(265 pal/77‘
/
I e value
g,l¢1 S/ow arerag
Cf’ ¥br A0 fcsfis
0' 1 1 1
/o 20 30 4-0
Deforma/xon, percenf
F g. 44 Loa d-d eiorn1ation curves for pe ca beans
at 52. 8 percent roisture (r1 .b.) for
three speeds.

The velocity effect is {resented in a dif f3rent way in
Fig. 45, with rate of deformatior1 plotted agai1st corpresa
force. 718. 46 i iven below as 1 reans of cualita.tiv flf
explaininr 110 curvt of ‘ig. 45.

11t tae 20 and C20 p-rce:1t deformati-m points, '; 1e pea

be,n1 (--.afl moistu1e, d., ) lot as an ideal ;1astic sali
53J~. (c) , };ogev 1, 1 ’e per Ee‘CVYirtions of $5 an
40 ' rcent t? -:H;s shay as a -u1si-pla:tic miterial
ill 1'15. 4-3 (d).

9

 

lat

 

 

 

 

m t
o e 1W s
. _ a . ._
C . s . .
e a a . .
S _ .2 . ..
7 a 1 __ 11 __ 1 -
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m a a a a
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In ‘ s \ \
a ‘ . ‘ \
~ s \x
m ._ a x \
O . . \ x
r? a 2 x xx
e ‘ ~ \ \
D N T a x xx \\
l a c x
.a a a a a
1w. New... $5.133“? as N can uMR can .8 R sex.
E P p u p r p u
0 “ \0 \M‘ 8 N0: («0 U“

fi0§\6\mmm\sm Node» \mv.

‘30. Au. WNNMQ. 0h MSVM 9n bfimdfiiluxok ck Vim
mmMQFuI\>\Q fiOkhMMMM\—\m amnm $18
that mm... {M 3% (Hem \ummqmsxu. ioxhutmmfiauv

101

fibfito/SAawdeb?

 

 

 

 

 

 

 

Sires: F“

-1 '1 17' IX! '

(a) (b) (C) (61)

E13. 40 Rate of shear 3“rain as a fw1ction of stress f
for f;nua ty es <1? fluin:1: (a) lraxconl U1 or g
viscous liquid; (b) non-1eut011an or suasi— f
viscous liquid; (0) ileali7 56d plastic solid, 1
I? .0 _ , o o o | O '0 ‘
Ulngham solid; (d) quasi-plastic material. 1"

Stress Relaxation
Stress relaxation o1 pea beans ea: tudied at several

moisture contents, at Various amounts of deformation and

at three initial deformation rates. The beans were deformed

to a cert-in fraction of their original 1i ensign, and see

Q.)

crossh ad was stepped. The oscillograyh chart 051tinued to
Inove so that a continous force-time record vas obtained.

an [s o
. it 101“ mlPC‘B D1013-

Relaration urves are snown in :i

(”l

‘ture levels. Curves 5 and 4 are for the same moisture, but
1iifferent amounts of ae1ormation. all of these curves

nearesent relaxation after deformation at a medium steed.
‘Phe speed effect on relaxation is shown later.

‘fhe curves in Fig. 47 are nearly parallel and p1 ot as

 

 

H-

'WAlfrey, Turner, Jr. ; Lechan cal Behavior of mix;

' ‘- W —— “-5-— r.
Polymers); Int-"Isc1e1ce Iu. “1131112316, lnc. 1.e'.: 1' r.-:, 1pm; p 54.

 

I50 l- @_ /8-5% db, 45:] 7° JQIOHWO/I'O”

  
  
  

 

 
  
 

, a—zza‘z db, 44.8% def

—-326 d ,(oHC
® . / 6’ ({{ZSZ?esec)

  

   

29
,5 @—32.az’db, 360% defi
F (7;: /6 68 sec)
£29;
deg
87
96961220427 sec)
5'
+1- o(7;=o.439 sec)

 

J l 1 J

 

 

1 4 L 1 1
o 02 0.4 as 0.8 /-0 /-z /.4 /6 £8 2.0 2-8
Time, sec.

F76. 4 7 $7555 5 EELA XA now roe P£A BEA/V5
AT VAe/oos MO/Sfé/zeé' LEVELS A/VD
AMOU/V 7's 0F DEFOEMA T/0/V.

 

105

straight lines after a time of about 1.4 seconds. It was

(’1‘

decided to try 0 express the Stress relaxation in equation
form which would describe it during the initial second as

well as for greater lengths of time. In addition, descrip-
tion of the early yortion of the curve would aid in describing
the rheological behavior (and/or mechanical model) of beans
under stress relaxation. It has been shown that equation (15)

cr V's;é
" 0

gives the stress relaxation for a material that may be rep-

.L

reseLted as a model, by a Lax ell uni'.
dince the stress relaxation curves are not true exponen-

tial relationsh'ns, i.e., straight lines on semi-10g paper,

A

is desirable to express the variation with time by means

(‘1'

i'
of a small number of eXponential terms. a graphical method*
is used. Fig. 48-illustrates the proceedure. Jhen plotting
force (or stress) against time it was observed that the
relation is linear on semi-log paper at the larger v lues

of time. a straight line through these points projected up
to zero time gives the exponential term with tae largest
time constant, 77 . Fhis is subtracted from the original
force-time curve in the range of small time values, and a
new line of the log of the difference is similarly plotted.
fhis gives tne evponential term with the next largest time

constant, 7; . This could be carried out a tnird time, but

w 0

, Essays in Rheolosv; Pitman 1 Sons Ltd;
0

 

1..)
O
,1.
\1
‘00
(J
..)
9.)
"3
Ct-
L
*3
01

.flua

Pu“

104

 

[yaaf/om' j: a? 8 - Z”

  
 

-t‘

 

 

1 1 1 L l _l ,L - L. J L l

O 0.2. 0.4 0.6 as A0 /.z /.¢ £6 £8 2-0 32
Wine, sec.

£76.48 GPAPHICAL DETERMINATION OF 57,9555
EELAXAWO/V EQUATION FOE PEA BEA/VS
AT /8.5 PERCENT MOISTURE AND
45. 5 PEECENT DEFDEMAT/OIV.

 

 

105

the chance for error becomes greater as the differences be-
come smaller. For pea beans, the relaxation is expressed
very well by two exponential terms. as shown in Jig. 48,

the complete equation is:

31:46 + 5’28 ------ ----- (1'7)

 

r. Am.

The constants a1 and A2 are evaluated by setting t=?O. 1

1‘

Graphically A1 and 52 are simply the y—intercepts of the 1

dashed line and of the log force-time difference line. The
'. -.J. 4- ...1.°~ - 1 . ,0

time constants, ufllCfl also represent tne relaxat1on time are H
a

 

found by taking the slope of two straight lines:

7’:

O ‘ ‘\

Evaluating tne constants for the curve of Lig. 48, the

force-tine relaxation equation is:

..t -t
./(27 11537
F: wage ’4 4- 25183

The relaxation times (time constant) are given in Fig. 47
by curves 3 and 4, for beans at the same moisture (52.8w d.b.),
but at a different amount of deformation. Bho relaxation

times are practically equal. inis was found to be true at
other moisture levels. That is, regardless of he amount
01 deformation, at a given moisture level, the relaxation

times were equal. Of course the greater the deformation,

'

the larger the force value.

Relaxation curves are plotted in Fig. 49 for varying

rates of deformation on rectilinear paper. This allows the

fi.l L.'J‘4J]l.1lJ‘l vllIIvIUEI-JRYFIIIILIY 9..

10:3

: 3.3m Goamxauwwn
e 8.“ \fiuN “why Vmfl O.U\u.0 Man.
#0 no N u Guns hen... Vm I Dike. «an.
o 9 NJ... \m.mm amp... 3.» QKNV .98.
® @V. «Bum .80 fin same man.

 

1w

 

 

 

 

 

 

 

. Am awn
%
on law!
6
W s M\OS\ thQQQw DVm\n~.V@ Knewos<3n~s¢03 II kfi. N No » “\mam. $.30“ “\0 9mm.
F G Renew»! a t ..I am. VN. . «\mm s I No. u use.
\Q 1 G RGQSSS : t . e ..|.. u&. 0 o\o me. \\ n \m & Men.
9 hoax : z : liars u. seen : n \\.m Men.
MISS} honour 333.8va
taxsm \0». u .50.?
p P h P b p [bl
0 9m \.& N.“ ..u..N $0 fiam bum

3.3m» men.
\30. ARV MENNMM QMFLXLVVer DQQVMG WON mung UMXZM
Lu. .uNG them. nmzw. KormflQmm «at» \>\ \Nx. u. touxflxok

stress relaxation rates to be more noticeable. (Curve 2 and
s in is. 49 are curves 3 and 4 plotted in Fig. 47.) 'i5. 49
shows that the initial rate of deformation has a definite
effect on the relaxation rate. Time constants corresponding
8

to tde first and second exronential terns, are summarized

in the figure. Considerinr the aHOint of defor~itlon and

re
the rate of deformation, the ti:e for the Lean t be deform- 5
ed, is also listed. 1
It is ap arent that 'it11 the slower rates of deformation, 3
_-l
time is allowed for th material to creep or to even begin F
1

stress relaxation before the crosshead movement is stopped.
when Hie cros head is stOpped, less relaxation is necessary

than in the case of rapid initial deformation. Thus in
considering the effe ct of rapid deformation upon stress re-
laxation in beans, the rat e of deformation will chiefly de-
termine the relaxation time, while the 222223 of deformation
will determine the ini ial magnitude of the force at the

be ,rinni in; of stress relaxation (or end of deformation)
period.

Since the force at any time during relaxa tiol Can be
ex12ressed by the 22E.Of two exponential terms of the form
/9€1/?J , it is concluded that pea beans can be represented
rheologiCally by two haxwell units in series. As above,
72.7%? , where 7? is the viscosity of ttu: vigcq1
element (dashpot) and E is the medulug of elasticity

of the elastic element. Representing the behavior of beans

in this manner accounts for the distinct actions represented

108

1

by the two exponential terms. El and 32 are different as are
7% and7fi;.

~

enunical represen—
-tivn of pea beans
I

77‘ $ is .. _.

It must be borne in mind that the model suits the ideal case;

actually the Viscous phase of the bean is probably quasi-

I izoz‘ML—‘H 35*" ‘.
.

viscous or quasi-plastic and the elastic segnent ’s certainly

not perfectly elastic.

A Practical Application from the Results

In Comparing the various parameters investigated with
moisture content, it beczme ap‘:_arent that in many cases the
variation of the dependent variable was great enough that
it could be used as a measure of moisture Content in grain.
SpecifiCally, the foice-doformation curves for beans and
the punch shear tests on beans showed promise in this respect.
1"19;. 51 shows the relationship between force and moisture
at various deformations. The greater the slope of the line,
the more desirable the situation for detain hing moisture.

—‘

irst glance it a

O

,1
1'

H)

apears that the éC percent defor-

1.
.1.
v"... ?_ _o 1 ' ..‘ w -_ ~ 1 3‘ 3“ A _ L ’ TT N , g ‘. .

iation curve \L'Jillxl oe this best one to use. i‘O‘HOVCl" ..i one

”tundurd deviation above or below the line is considered,

Force, lb.

 

109

 

 

xzo __ ..
0': 1: I88
K Sfana’ara’ o'er/a f/on, V",
\ for ID {957‘s
/00 L \ -
\ ® 40% defer/77a f/on, [bf

50 _. -

<3: 1' l4.8 \(st: [46
6 \ ® / h \

0 L so °. 2 -
\F F/ar‘ j \
O\\ \ \
\ $1 a z \
40 r- \ \ crst 4.;
\
\ \ \0
01-1: 2.4. \ \\ \
(is) 30 75 def, \ \
20 _ \\ 031,0 edge. \ .4
\o 58
CD Pane/7 s/mar‘ [ac/7 po/n/ arms/a 033.3
7‘9 Sf, {:70 7‘. va/ae for /0 feS/s.
0 L J I L l
/6 ‘ I8 20 22 24

Mois fare, Farce/77" m b.
FIG. 5/ FOECE 8500/1950 Foe
DE F0 EMA T/OIV OF PEA BEA/VS
AT MED/UM SPEED (0.2671'n/min)

-.u
. Q

110

the gunch shear test, curve é, would be chosen. Carsider
the steepest yortion of the £0 yercent deformation curve, i.e.,

.1.

between 15.3p w.b. and 16.5p U.b., and the punch shear DCSt

(curve 4). Bhese two curves are redrawn to a larger scale

in FiA. 52.

C“!

g

In Pie. 52, one staneard deviation is subtracted at the

O

'— 1‘ I "' l '9 f :5 L‘-~ 1- A a a" 3'7“. "W7 O" :‘. " ‘f' r‘fi-P'UI 4'7; 11"? “I“ '. (3V1 is V
lQoJN v.0. yoint o. the top Lulv~ownv Mu ~w-~~»iu wv-‘nux-u .
, ,‘ - ,. J. '-1_ F‘ r: '1 . 1 .- _' '3..- ' A ' ‘Y‘ . ;-‘ .‘, 3‘. . ‘. ‘
(IJJxlel du Mile lb.(-’/U V1.1). ." 04.1th 59‘. JJirllsig) U110 1")-Llltb A dlld
"\ __ o ‘1 J— o_ _g ‘_\0‘ _ "ho‘ oy ‘ _~«A I:
s, a relatively .leb luC .LS ow Aimed. inis line ..as the 2

i

.1 ' 1' v r .‘—‘ v ‘ “ .' - o 1‘! ‘2 v “ ‘
lones.,.mmx31ble slepe t-hn. ca be obtaihfid 113,.een fee 3

 

15.8” w.b. and 8.5” W.b. points without deviatine from either

original point on curve 1 by more than one standard devia-
tion. The steepest gossible slope (naintaining a maximum

variat on of one standard deviation) would be obtained by
adding and subtracting one standard deviation in the reVerse
order from above.

For the moisture range of 2.935 w.b., the line A 3 gives
a value of 2.15 lb/percent moisture. Jaking t
tions for the punch test, line C D, Fig. 52,

Q J 0

cent moisture. .;‘.1is means one-g xrsithin this moisture rang-e

4 a: u~q-.- , . A. L-f.‘l-.‘. ...
(do.urihg a linear relatiansbi
"’ A "x ‘N 1 V? i ‘\ . ‘f. ‘ «'1 A I r“ ‘1 "x L- , " fl ,~ ‘ A. " ‘2 ' . ‘ ’fi "‘

11‘; CCDSQI’J t0 be sole o'D luudozll c oiiu .LQPCE} Tovllll EU. _..0
”TV ' in" l.,;. _ -- ..?;.. ..°. '7 . y. -10 I ,1"? 5-...3‘. 5“ 3” -~\')‘)
‘IUDCH QM u a CQi'e 11"..) .‘a J. _.1 L 1.11 O...) ‘ £31-].r1uik’ t J ‘1055 . 1.1.9.8 - LOAD ‘. LA]. 0
‘4- " "‘ J‘ " " " " \ I‘ J‘ 'o ' "' ' ‘ v 1!! " ‘ ‘ \ 1- ‘>
CGHVleb a; the nearest pol cent . lt ..-« eulu seen that an in-

‘ ’ H. ‘9 H \‘1 4 I ‘ 1‘ "\ '. . 'H‘ . ‘ y" ;- A ~ - ‘ Q '—-. i ~ ‘ ‘ Q

e/(l)ell$ .LVU 1'15: C-.c~u.-. CA1 :uClSLUj"C (15;: 1,; air C0110. ~43 11..-].th t 0 17.533"

Sure tnis range quite Vasilt.

'4— LI. .. . .-t. 4.°_1 m... A -- -- 3,. ...! L‘. 1- . .- " \ -, — n!
AL. one LI‘CSGuo 91.1.8 tilt: lal'lxz" .LD ‘v._L*Jf1011U pill} lT.€AfJb’CQ.LVG

111

£20 ,. q
= 2!: I88
40 % deforma/Ion, f/ar‘
TKJ\ @urve /, 1‘76 5/)
mo _ was -+
\\
3 ~ ~“‘-—X<‘fi-~5 art
50 ‘
P C .6 d '1
S/OPe, Zo/S/b/7’ Nb \\1I4 é
v7." 146
s .0, ‘ "
q
8
t
Lk 40 - -
(312,4 Punch Sfiear fies/3. f/ai‘
(Curve 4, F1657)
20 ,, Ck‘ ““\..\.~ -1
\k‘ D
Z \29 mo
/o,0e, 5.32 /b/% wb.
J ..-

 

 

 

/5 ,2 27 fa ,9
Mo/sfw’e Confem’, percenf w.b.
F/G.5Z éBAF’H/CAL P/ CTUEE OF
SENS/r/V/Ty 0F MECH-
AN/C‘AL Moan/£5 METEE
Foe PEA 854 N6. '

means

cial moisture meters operate on

‘— . ' w-v: L-
abl\)l,l utLl)

,.
$3:
0
t 1'
Ho
<1
[-0
do

LA

r van-

5.?

useful to knot the

ity before harvest.

.,, .‘
out:

. .A .. .1—
L 11318 LAlI‘C

lield roisgur

n -r« ..2 q' . '-.'.. , ...-L... - 1"
Cl deterMJJJJQ31101sture cxmitent o-

nciyle

TN , .'.
i.l .I.

level.

uln. 1'.

1’"

Genes

C

112

ost commer-

lectrical

. :4..,
gtentlr,

lum;—-m. Q»...- —-o _,.= ..‘xlfi
1

l x l xx V 11.!w I 1| 11%.: a ‘
,’ h.“ I! 1.1 .
‘ y l -..; ..3 a -w - w
n ‘ .uL.‘ 1. I.) ,lfl.‘v.4.. -‘

 

 

 

 

1.. o egg-41-- c ul 1' r op .‘L e s

The mechanical prOperties of grain are needed to analyze
problems encountered in grain harvesting, handling, and pro-
cessing. Seed crackage and damage by cr‘shing are enc;untered F‘

during threshing and handling operations. Grinding grain is i

a relatively high energy process accompanied by low efficien-

- -. hh‘.‘_A-'__-_._- . -

cy. To solve these problems or make improvements in existing

(parational techniques, investigation should begin with the

‘M-

determination of basic preperties of the individual grain
kernel.

a strain gage transducer was designed and built to
measure the mechanical and rheological properties of grain.
Electronic equipment was used to amplify and record load-
deformation relationships.

Properties u-re examined for three grains -- corn, wheat,

and pea beans. The effect of moisture content_on the mech-

arameter

'

anical preperties of grain kernels, was the chief p
investig;ted. Four moisture levels, ranging from 10.65 d.b.
to 32.85 d.b., were used. Other paramete=s studied were the
effect of rate of deformation and kernel position (edge or
flat), on strength characteristics. Rates of deformation of
0.0777 in/min, 0.267 in/min, and 0.407 in/min, were used.
Temperature effect was not studied. All data were obtained

at room temperature. Ten replications were made for practically

all tests.
leis inves ig tion consisted of a quantitative study of
the following mechanical properties and/or characteristics

for each grain with the variables indicated:

1. Maximum kernel strength, lb. -- edge and flat posi-

tion, four moisture levels, three deformation rates. r-a

The maximum strength of the kernel depended greatly on

moisture content and seed position for the test. 1'he average 5

_ 9!? L-i .

maximum Compressive force for corn kernels in the edge posi-

3J '1'" ‘
l
l
—.

tion decreased from 45.5 to 17.5 pounds with a moisture in-
crease from 14.6% d.b. to 26.0% d.b. In the flat position
the compressive force decreased from an average of 96.7 to
73.7 pounds for the same moisture range. Variation between
individual tests was much greater in the flat position than
in the edge position. These tests were run at the medium
Speed of 0.257 in/min.

The maximum compressive strength of wheat kernels increas-
ed-sligntly up to 20 percent moisture. Above this level no
elastic preperties and no point of maximum strength were
found.

Pea beans showed Q.ightly higher strength in the flat
Position than in the edge position at low moisture. Seed
POSition made little difference fit higher moisture.

Rate of deformation had no significant effect on the
resulting compressive force at low moisture levels. A sig-

nificant speed effect was noted at the five percent level,

he" ever, for corn in the edge position at 26.0A d.b. The
fast deformation rate produced an average maximum strength
of 22.5 pounds while the medium and slew rates gave strength

averages of 17.5 and 16.1 pounds respectively.

2. Yield Strength, lb. -- edge and flat position, four

moisture levels, three deformation rates.

hoisture, kernel position and rate of de; ormstion had

‘

the same effect on yield strength as on niximum strength.

1. aximum strength values ‘anged from about 50 percent to

30 percent higher tlan t1e vield strength values.

5. laximum Com ressive Stress, psi -- c01e spec: meis,

four moisture levels, one deformation rate. (slow).

a linear relation existed between maximum stress and

,,- ° . .n -. ET ~ ..- 'v -‘ ‘\ - \ T‘.-~- -'-,- - r-L nu
11013 ture lI‘ORL lu.‘i,=o LO lu.u‘,o Cub. fOl’ COPIJ. J-ng{J-1film; eoI’Coo

(I)
C-
C
H.»
(3
<3
9:
"3
P.
S-
do
F o
D

Ian; e7 from 4800 psi to 2900 psi for a moi

‘ V :— I ' ‘ \ r37. 1" 1 1-v rr‘ n . A - ‘
fn“>a: lu.ep d.b. to bQoCfl d.b. lJG Clue 1elat1ve eflect o-
L'T'5lLZtur‘e g'as f ound for uneat, but the Izagniizude of the values
" 3‘ Qbmt to percent lo Pr.

¢ ‘ u 1 r‘ c-‘--. . A V. - ,- -. A r! 1‘
a. nodulas f filasUiCitv, 151. -- core spGCimens, four

 

m01sture levels one deformation rate slow .
9

:J-

Lodulus of elasticity relationship th moisture parallel-
‘ed maximum stress. fhe range for corn was 50,000 psi to

0 ’ O A o c e v— «'7. ’
~9:OOO p81 ior a meisture cnange from lCogfi to sc.0fl d.b.

S LP.M.'~.1 .4

11;

L an

godulus of elasticity of corn decreased as percent rise a

.1

4: percent moisture increase. dimilariy, for wheat a 5; per-

cent decrease in modulus of elasticity was obtained from a
55 percent moisture increase. because of the non-elastic
nature a high moisture, data were obtained for pea beans

at only one moisture level.

 

‘4.
i
5. Shea Stress, psi -- flat position (in vise), four
0 L. o "
meisture levels, slow deformation rate.
Shear stress for corn decreased from about 1250 psi to j
950 psi for a moisture increase from 14.5» to 21.0w d.b. . 1

.Shear stress for wheat stayed relatively constant at about

)81 within the 15.7 to 24.5a d.b. Passe-

0. Static and Impact energy Reguirements for Kernel

 

nupture, in-lb/ins -- flat position (in vise), four
moisture levels, slow speed (0.0777 in/min) and

pendulum impact velocity (5.24 ft/sec).

For corn, impact and static energy valles were about

.1

equal at intermediate moisture content (13.5p to 18.5} d.b.).
At moisture levels below this range, however, inpact energy
was lower than static shear energy, and above this noisture
range impact shear energy was higher than static shear energy.
At 21,25 d.b., impact and static shear energy requirements Jere

about equal; at a moisture f 5Gaid.b., energy required to

O

rupture the kernel was 2.8 times as great by impact shear

‘

as witq static shear.

117

Corn and wheat i ract energies ranged from about 15 to

o ) o . o o ‘ f ( ‘-
25 in-lb/in~ for a meisture variation from 15p to 25p d.b.

‘ C . A n O 9
tea bean impact energies went irom a low of 0.5 in-lb/in“

at 8.7% d.b. to 55 in-lb/in2 at 56.2% d.b.

7. Modulus of Resilience, in-lb/kernel -- edge and flat
positions, four moisture levels, one defo~mation rate

(except at low and high moisture levels).

Phe modulus of resilience showed a relatively large

-_ .._.-. ..--H--.__ .._.

variation between individual kernels at a given moisture

l “a...“

content. The absolute variation was, however, quite constant
from one moisture level to another. A typical value for wheat
was 0.05 in-lb/kernel. For corn 0.12 in—lb/kernel and

0.5 in-lb/kernel were typical values for the edge and flat

positions respectively.

8. Toughness or Lodulus of Toughness, in-lb/kernel --

 

 

 

edge and flat position, four moisture levels, one
deiormation rate (except at low and high moisture

levels).

Larger variation between individual kernels was observed
ftn°rnodulus of toughness than for modulus of resilience.
Lodulus of toughness values averaged from two to five times

greater than the modulus of resilience energies.

9. Hysteresis Loss, percent, -- flat position (corn and
beans), core specimens (wheat), two moisture levels,

two deformation levels.

 

 

I ul!|l.|.l '7

118

HysterCSis losses were greater with higher moisture
content and with the initial loading-unloading cycle. For
wheat, the initial cycle produced a hysteresis loss of 44.5
percent. and the second cycle a loss of 20 percent. For
the same conditions with corn, the losses were 59.5 percent
and lé.9 percent. also with corn, in'tial cycle loss was
59.2% for 15.8% d.b. and 62.6% loss for a moisture content

of 26.03 d.b. Similar losses were obtained for pea beans.

Rheological Properties

1. Rate of Deformation —- pea beans, one moisture level,

three deformation rates.

fhe variation in rates of deformation used in this study
was not great enough to cause an important difference in the
canpressive force on pea beans at a moisture content of
52.83 d.b. Ideal plastic properties seemed to be present
at the lower amounts of deformation (20 percent), and quasi-

plastic effects appeared at greater deformations 35 percent).

2. Stress Relaxation -- pea beans, three moisture levels,

 

three deformation rates for one moisture level.

The rate 01 stress relaxation in pea beans was found to
be a function of the preceding deformation rate. Stress
relaxation rate was somewhat dependent on the ameunt of de-
formation. Stress relaxatien time, however, was found to

be completely independent of amount of deformation. This

 

phenomenon was checked for two moisture levels of 18.55 d.b.
and 52.8% d.b. hoisture content had very little effect on
relaxation time. Pea bean relaxation may be represented
rheologically by a mechanical model consisting of two Maxwell

units in series.

Other Observations 3

The feasibility of indirectly determining grain moisture

content by means of a mechanical test on single grain seeds

 

was considered. The possibilities of such a moisture meter

appear quite good, particularly for pea beans.

 

 

 

 

 

CONCLUSIONS

as a result of this study of mechanical and rheological

preperties of grain, the following conclusions are presented:
1. Of the parameters investigated, moieture on ent has

the greatest influence on the mechanical properties of 1

grain. all strength properties generally decrease in 5

magnitude as moisture increases. Energy required for

seed rupture by impact increases as moisture increases.

‘A >Qc‘rnc‘uz .Afic-J -:

l

Variation in mechanical properties with moiscure change
is greater for beans than for rheat or corn. elastic
properties are present at low moisture; plastic prep-
erties appear at high moisture content.

2. Rates of deformation varying from 0.0777 in/min to
0.478 in/min in compressive tests, have no effect on
kernel strength at low moisture, but show some signifi-
cant difference at high moisture for corn at the five
percent level.

3. Laximum compressive strength of corn at all moisture
levels, depends greatly on whether the kernel is in an
edge or flat position. For wheat, there is no signifi-
cant difference in strength for either position of the
kernel. “ith pea beans, seed position makes a differ-
ence on strength at low moisture, but not at the higher

levelSo

9.

lsl

Punch shear tests are unsatisfactory as a means of de-
termining shear stress of corn and wheat.
Lodulus of elasticity values for wheat and corn are
very similar, ranging from 50,000 psi at around 15.5%
d.b. to approximately 25,000 psi at 23% d.b.. Laximum
ompressive stress for wheat Varied from approximately
3300 psi to 1700 psi for a moisture change from 15.5%
d.b. to 25.0% d.b. This moisture range produced a
compressive stress change for corn from 5000 psi to
2500 psi.
At high moisture more energy is required to rupture
grain kernels by impact shear than by static shear.
The reverse is true at low moisture.
Specific damping capacity and relative elastic preper-
ties can be evaluated in grain by means of hysteresis
loops. Hysteresis loss depends chiefly on strain his-
tory (wheticr the loading-unloading is maiden cycle or
some later one) and on moisture content.
‘he force required to deform grain to the elastic limit
and maximum strength points decreases as the moisture
content increases. The range of modulus of "esilience
and modulus of toughness, however, is quite constant
with the four moisture levels. The decrease in strength
was found to be compensated for by an increase in due-
tility or toughness.
Stress relaxation with time can be represented by two

Kaxwell units as used in rheolOgy studies.

”u‘o‘m‘ «gnu—u 5“":

u
t

10.

duantitatively, stress relaxation with time
given by the sum of two exponential terms.
rate of deformation has more effect on the
stress relaxation than moisture content or
amount of deformation. Relaxation time is

with various deformation amounts.

The use of the strength properties of grain

promising as the basis for the development

rate of
the (initial)

constant

3 appears Fifi

of an

I
inexpensive but accurate mechanical moisture meter. )

 

Aq-fi 1V1,« \rfi*7

~VYT ‘(“."V‘ /“ 1"‘ .fi(‘ ,.‘ "III ‘ ., ‘ ‘t'rj ‘7
[DUCJxJiJJi‘LHMQ 1‘01: Fk .( AJ.“ with}:

It is difficult in one investigation to study in detail
all phases of mechanical and rheological properties of grain,
Certain phases of tne investigation suggested additional pro-
blems for study.

1. The effect of temperature on mechanical an:1 r :eolog ital
properties should be studied.

2. Impact data, obtained by inpinging grain against a
hard surface, would be useful in knalyyi 113 bean crac‘ :rge.

5. szf te‘esi.s losses in srair kernels should he investi-

k.‘

.__.__—.__..1.
‘t ' . --’

gated in more detail. Py a preliminary mechanical condition-
ing, the grain Icern el can be TLEdQ more brittle; this action
may re educe energy re uirements during the griolios process.
4. Rheological properties of grai ns mry he studied more
conveniently if strain is measured as the result of a constant
applied stress. In this study, stress (fore?) vas recorled as
a result of a constant strain rate.
5. The possibilities of a nechanieal moisture meter
should oe investigate d further.
6. Grain hardness should be investigated. Pe erueps herd-
ness can he used as .n indirect measure of moisture content.
7. Determination of the coefficient of thermal eXpansion
of grain kernels by :nears of strain gages stould be invest? at d
8. Proyerties of other grains, and other varieties of corn

,/“”“\
HIEQt and benafs ,/ should be studied.

’ur'

“m

 

"I-..
a

\ 1‘7 q
APPLNDIX i

 

 

 

 

 

185

TABLE A 1

{0333, lb, ssgtlaio To 3810; PROPORTIOLAL 11111.
YIELD P0111 “Lo 11x1111 STRELGTE, 303
YELLOW DENT CORN AT 14.6% d.b. (12-7% “ob-)
I; 188 8008 POSITION AT THREE sesgos

Proportional Limit Yield Point Maximum Strength

 

. u -M ....H
I.

__ -.
.

 

lam -....-

O
‘2 \
“C“!

 

 

 

Slow Med. Fast. Slow Med. Fast Slow Med. Fast

26.2 28.8 26.5 28.2 49.8 59.4 29.2 49.8 59.4

16.1 ' 28.8 54.1 22.9 29.6 55.4 24.9 48.7 55.4

22.5 22.2 18.5 25.6 58.9 20.9 59.5 58.9 28.0

56.7 26.9 21.6 56.7 55.4 57.4 56.7 58.0 40.0

15.1 19.7 25.6 28.8 21.6 54.1 42.7 52.1 57.5

51.5 15.1 22.5 56.7 59.5 41.2 63.0 40.7 41.2

28.8 27.5 21.6 50.8 50.4 55.4 45.2 48.5 48.5

27.5 28.2 51.5 55.0 57.4 46.4 45.8 44.5 49.8

52.8 26.2 50.2 59.5 52.1 2.8 45.9 45.8 46.5

56.7 24.9 24.9 49.8 40.6 52.4 49.8 40.6 52.4
Ave:

27.2 24.6 25.4 55.2 57.5 57.5 42.1 44.8 41.8

$37.6 4.8 4.8 7.7 10.1 8.1 10.1 10.4 7.1
C'N: .

27.9 19.5 18.9 25.2 27.0 21.7 24.0 25.2 17.0

fexp for porgorticnal limit (slow, med, fast =:C.44; f.95::5.55

fexp for yield limit (slow, med, fast)==0.72; f.95= 3.35

fexp for maximum strength (slow. med, fast)=:0.27; f.35==o.5

‘3’: q— .
C : /AVG .X 100

TABL‘

A 0
I'LL:

t‘J

80808, 15, 38131380 TO REACH PROEORTIOKAL LILIT,
11810 POINT AND msxlium STRELGTH,
FOR YELLOW DENT CORN AT 14.6% d.b. (12.7% w.b.)

IN THE FLAT POSITION AT TREES SPEEDS

 

 

Proportional Limit

Yield Point

Maximum Strength

 

 

 

Slow Med. Fast Slow Med. Fast Slow 18d. Fast
41.9 44.5 85.0 59.0 81.5 95.0 59.0 81.5 216.0
40.6 45.9 62.2 44.5 55.0 80.5 205.0 55.0 91.7
88.5 65.5 52.8 88.5 65.5' 52.8 151.0 75.5 91.7
55.4 28.8 29.5 55.4 52.4 45.8 94.2 56.1 105.0
58.0 27.4 72.0 55.0 42.7 78.6 55.0 42.7 115.2
59.5 49.8 41.0 52.4 49.8 50.7 81.2 120.0 50.7
59.5 52.7 40.8 60.2 51.1 40.8 68.0 84.7 245.0
75.5 8.8 89.0 90.4 54.1 91.7 90.4 89.2 144.0
40.6 88.5 56.2 40.6 88.5 65.5 157.0 167.0 65.5
21.0 62.9 95.0 21.0 65.6 151.0 170.5 86.5 151.0
Ave: '
45.8 47.9 58.5 54.7 58.4 71.4 110.9 85.8 125.6
T:
18.7 18.6 24.0 20.7 15.9 28.7 48.8 54.0 59.0
0*:

 

fexp proportional limit (slow, med, fast):
fexp yield point (slow, med, fast) = 1. 9;

fexp maximum strength (slow, med. fast) = 1.56

 

0*:- (r/Ave X 100

 

127

TABLE A 5

FORCE, lb, 85051880 TO REACH
YIELD POINT AND MAXILUT STRENGTH FOR YELLOW DENT CORN
AT 26.0% d.b. (20.65% w.b.) 15 THE EDGE.POSITION .
AT THREE SPEEDS

 

 

Yield Point maximum Strenéth

 

 

 

56.4

.1 Slow: lied Fast Slow lied Fast
9.2 13.1 2209 10.5 17.3 22.9

10.5 15.1 15.8 15.1 16.5 18.5

7.9 15.7 19.7 9.8 22.5 27.5

16.6 8.5 14.4 18.5 15.6 20.8

7.9 8.5 19.7 12.8 14.4 26.2

18.5 14.4 22.5 21.5 17.7 22.5

11.1 9.8 6.6 18.5 15.5 11.8

20.0 16.2 19.7 21.8 25.6 20.0

12.4 15.7 25.6 21.5 17.0 27.1

9.6 15.1 28.0 15.8 19.6 29.5

Ave: 12.1 12.8 19.1 16.1 17.5 22.6
q-; 4.4 2.8 5.7 4.4 5.5 5.0
0*: 21.9 29.8 27.5 18.9 22.1

 

fexp: yield point (slow, med, fast): 6.50; f.95 = 5.55

fexp’ maximum strength (slow, med, fast) = 5.79; f.95 = 5.55

0* = “7.4% X 100

TABLE A 4

COMPARISON OF COKPRESSIVE FORCE (1b)
AT KEDIUM SPEED REQUIRED TO DERORE YELLOW DENT CORN
”TO TRE YIELD POINT AND TO MAXIMUM STRERGTR
AT FOUR MOISTURE LEVELS (% d.b.)
WITH THE KERREL OR EDGE

 

 

Yield Point Maximum Strength

 

 

 

14.8 15.8 518.2 28.0’ 14.8 15.8 . 18.2 26.0
49.8 21.0 19.8 ' 15.1 55.0 26.2 26.7 17.5
29.8 50.1 57.5 15.1 48.7 58.7 49.7 18.5
58.9 45.8 24.9 15.7 58.9 51.7 55.4 22.5
55.4 58.0 59.5 8.5 58.0 45.2 44.5 15.8
21.8 18.5 20.5 8.5 52.1 21.7 24.9 14.4
59.5 24.9 18.5 14.4 40.7 41.9 26.2 17.7
50.4 18.5 51.8 9.8 48.5 21.8 55.4 15.5
57.4 21.9 22.5 18.2 44.5 24.9 27.5 25.6
52.1 25.8 28.8 15.7 ‘45.8 50.8 47.1 17.0
40.8 58.7 52.8 15.1 40.8 58.7 54.9 19.8
Ave: 57.5 27.7 28.5 12.8 45.5 55.5 55.2 17.5
V} 10.2 8.8 7.2 2.8 7.6 9.7 8.7 5.5
c: 27.2 51.0 25.2 21.9 18.8 28.9 24.7 18.4

 

 

129

TABLE A 5

COszRISOH 0F COKPRESSIVE FORCE (1b)
AT LADIUM SPEED REQUIRSD T0 DEFORh YELLON DENT CORN
TO THE YIELD POINT AND TO MAXIKUM STRENGT
AT.FOUR MOISTURE LEVELS (% d.b.)
WITH THE KERNEL LYING FLAT

 

 

Yield Point Maximum Strength

 

 

 

:14.8 15.8 ‘718:2' 28.0 514.8 15.8 18.2 28.0
81.5 59.5 69.5 52.4 81.5 118.0 -- -75.2
55.0 49.2 99.6 --' 111.0 100.0 144.0 -"
85.5 98.1 85.5 75.4 75.5 104.7 . 157.5 86.5
52.4 58.4 80.9 96.9 70.7 124.5 85.5 98.9
42.7 100.0. -- 121.2 81.2 170.5 198.5 --
49.8 59.5 157.0 58.7 120.0 41.9 -- 52.4
51.1 74.4 - 144.0 95.4 84.7 205.0 144.0 95.4
54.1 85.5 '45.9 -54.1 89.2 82.0 45.9 55.8

= 88.5 44.5 58.0 -- 187.0 155.0 - 52.4 --

65.6 55.8 55.0 -- 86.5 _55.8 128.0 --
Ave: .

58.4 82.5 85.7 72.9 98.7 115.5 98.0 75.7
0718.9 21.1 40.2 52.5 27.2 48.4 50.2 22.7
C:

27.2 55.9 '48.0 44.5 28.1 40.9 51.2 50.8

 

C = qf/sve X 100

TABLE A 6

COMPRESSIVE FORCE (1b) REQUIRED
AT MEDIUM SPEED TO DEFORM PEA BEANS
TO THE YIELD POINT AND MAXIMUM STRENGTH

AT 10.6% d.b. IN THE EDGE AND FLAT POSITIONS

 

 

 

 

 

150

 

 

 

Yield Point Maximum Strength

Edge ~ Flat Edge Flat

84.2 44.5 84.2 “68.1

55.7 55.0 55.7 75.4

85.8 55.0 104.8 84.8

85.5 59.5 65.5 82.5

45.2 22.9 45.2 40.9

52.4 19.1 52.4 70.7

80.5 52.4 82.9 75.4

28.8 58.9 45.8 94.5

75.4 16.8 75.4 80.5

55.0 49.8 55.0 98.9

Ave: 58.0 41.4 82.1 74.5
d’. 14.5 15.2 18.8 -15.7‘
c:‘ 25.0 56.7 27.0 21.1

 

c = T/Avex 100

 

l l

()3

TABLE A 7

FORCE, lb, REQUIRED TO DEFORM SOFT RED WINTER WHEAT
TO THE PROPORTIONAL LIMIT, YIELD POINT
AND MAXIMUM STRENGTH AT 16.0% d.b. (15.8% w.b.)
IN THE FLAT POSITION AT THREE SPEEDS

 

 

Yield Point Maximum Strength

Proport i onal Limit

 

 

 

 

Slow Med . Fafi Slow Med . Fiast Slow Med . Fae t
5.6 6.9 7.9 15.1 10.5 12.5 15.9 11.8 25.1
7.2 5.2 7.6 15.1 11.9 14.4 22.2 15.4 15.5 .
7.2 5.6 5.9 9.8 15.1 12.5 9.8 19.0 20.7
9.5 7.2 11.1 21.0 11.8 15.1 21.0 12.1 19.0
6.5 7.9 4.9 8.5 15.1 14.1 17.0 16.1 16.4
6.5 7.5 7.2 10.5 12.5 12.6 11.5 12.5 15.7
6.5 . 7.5 7.5 14.4 15.7 20.5 19.0 14.1 20.5
7.5 6.2 5.6 15.7 8.5 9.5 17.7 8.9 10.9
5.9 8.5 11.5 11.4 12.5 16.4 15.8 18.0 16.4
5.2 7.2 6.5 11.1 11.1 9.8 15.8 11.8 11.5
Ave:

6.8 6.9 7.6 2.9 12.5 15.7 15.9 15.8 16.9
0’:

1.1 .9 2.1 5.4 2.8 5.0 5.9 5.0 5.7
C:

16.2 15.0 27.6 26.4 22.8 21.9 24.6 21.7 21.9
fexp’ proportional limit (slow, med, fast) = 0.74; f.95 = 5.55
fexp: yield paint (810W, med, fast) = 0.515 f.95 z: 3.55
fexp: maximum strength (slow, med, fast) = 1.925 {"95 ~.—.. 5.55

 

15’

TABLE A 8

COMPARISON OF COMPRESSIVE FORCE (1b)
AT MEDIUM SPEED REQUIRED To DEFORM SOFT RED WINTER WHEAT
TO THE YIELD POINT AND TO MAXIMUM STRENGTH
AT TWO MOISTURE LEVELS (% d.b.)
WITH THE KERNEL IN THE PLAT POSITION

 

 

 

 

 

 

Yield Point Maximum Strength
18.0 86.3* 16.0 20.3
10.5 17.7 11.8 19.6
11.9 16.4 13.4 18.4
15.1 13.1 19.0 13.8
11.8 8.8 12.1 12.6
15.1 21.6 16.1 21.6
12.5 18.3 12.5 , 19.0
13.7 17.7 14.1 19.0

8.5 15.7 8.9 15.7
12.5 8.5 18.0 8.5
11.1 9.8 11.8 11.5
12.3 14.8 13.8 15.8

1.9 4.3 2.9 3.9
15.5 29.0 21.0 24.7

 

c = (r/Ave x 100

TABLE A 9

21131201? E03 P11111181; 0. 172.110.; 0.11.? 00R};
81' 11.310? EXILE-.3 ..T 1701’}. £01531???) lzilVLL-S,
' ' . 7

-~vnv- ‘p,’x'-" ,. o— »$" .u-v « ,
luxur}: 0113.; 1111 5.31153... 11.51

 

 

13.4.7: d.b. 18.1% d.b. 19.2% d.b. 211.7% d.b.

13.5
13.6

9.8
16.8
27.5
15.6
15,2
14.9
11.4

9.3

17.9
15.4
17.0
17.6
19.9
14.6
21.1
22.7
19.8
14.2

19.6
19.6
26.0
20.4
21.5
21.4
15.9
21.7
55.2
19.8

24.8
51.9
28.5
26.5
19.5
26.5
44.7
20.4
28.5
51.2

 

14.8

4.8

w
01 F:
O O
m m

(\J
C [Q
o

\1

28.2

 

c = (r/Ave ;< 100

TABLE A 10

.....

ENERGY FOR FaILURE 0F SOFT RAD thTER uhfiaT
BY IRPACT SHEAR AT FOUR LOISTURE LEVELS
IRON-POUNDS FER SQUARE INCH

 

 

16.9% d.b. 18.7% d.b. 21.7% d.b. 24.5% d.b.

 

 

18.3 18.9 19.6 20.6
12.9 20.0 18.0 28.9
19.7 11.5 16.0 37.1
10.4 17.6 15.7 26.6
16.7 11.0 19.8 21.0
17.0 19.3 18.0 26.6
19.4 19.4 20.7 23.7
21.4 17.6 16.5 21.6
25.5 16.4 18.8 17.5
12.7 18.9 19.6 17.5
Ave: 16.1 17.1 18.3 24.1
7’: 3.5 3.1 1.6 5.7
0: 21.8 18.1 8.7 25.3

 

TABLE A 11

EIJEEI‘GY FOR FAILURE OF PEA 813.115
BF.” 11.13.01” 311112.111 AT POUR EALOIJI‘L‘RLJ LEVEJLS
ILGIi-PCUI‘JDS 1.1.11 SQUIIRJZ 1.01:

1

 

 

 

 

8.7% d.b. 18.5% d.b. 22.8% d.b. 36.2% d.b.
3.14 36.8 40.1 72.6
1.54 48.7 55.7 74.5
2.13 30.7 45.0 48.8
3.03 36.9 45.21 69.3
2.81 37.3 44.1 53.3
4.95 34.6 46.4 , 54.3
5.00 40.8 55.2 83.3
2.70 26.1 57.2 59.5
3.40 31.4 62.5 63.2
5.94 22.8 62.6 73.5
3.46 34.6 51.3 65.2
1.32 7.0 7.6 10.3
8.2 20.2 14.8 16.3

 

 

TABLE A 12

ENERGY REQUIRED TO RUPTURE PEA BEANS
22.8% d.b. (18.6% w.b.) BY IMPACT SHEAR
AT TWO VELOCITIES, INCH POUNDS PER SQUARE INCH

 

 

 

 

 

 

8.: 44° 30' 9.: 79° 42'
(Vel.of Impact 5.24 ft/Sec) (Vel.of Impact 8.87 ft/seé7

40.1 2 46.8

55.7 57.2

45.0 49.1

45.2 45.8

44.1 59.4

45.4 44.5

55.2 48.2

57.2 57.2

62.5 51.7

61.6 41.9

Ave: 51.5 48.0
q‘: 702 507
C: 14.0 11.9

 

fexp = .80,

12.95 = 4.41

Alfrey, Turner Jr.
1948. Mechanical Behavior of High Polymers. Interscience
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1955 Strength of Materials. McGraw Hill 00., New York.

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1955 Bean Crackage Studies. Unpublished report.

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1957 The Rheology of Cheese, Butter and Other hilk
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1957. Dryinngarm Crops. Edwards Brothers, Inc. Ann
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1957 Lines of Attack on Dough Chemistry. Jour. of Ag.
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1940. An Investigation of the Effect of Rate of Strain
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1940 Rubber in Compression. ASTM, Bulletin no. 106, 9.

 

1 3

Krueger, N.C.
1927. Basic Principles Involved in the Design of the
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113:2"! F
I‘t."_’ .
I”.- ‘ .’-\ - " . 'l" — '. \, .— 1‘. V 1.- T‘? —-‘ ”gm.— '- -~V
PP‘WX’o InthuCLrwuwaIIUILInqars, Iru>., New Vork.
\ : , - T1 A‘
51.1.1331), f... It.
‘1 13 IV . 1 '. ‘ ‘0’" * 0‘ _ .1 ‘ . ‘f‘ ‘
lawl. re‘xltvrlxmier ITN‘LDtLQ9‘hLWUS NUJHUQBLTI‘440, ,nLo

.
‘15:}..10' E'in‘t’o alt/91410151. 210151.91", Chine

Steawfirer , B.
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1
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- , “
Heiner, A.

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