A11101 31DM5a

NBSIR 82-251 3 (jQ

MBS

PUBLICATIONS

AlllOt 4075E7

Characterizing the Interfiber

Bonding of Currency Paper Pulps

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Materials Science

Polymer Science and Standards Division

Washington, DC 20234

Final Report Covering the Period

October 1, 1980 through September 30, 1981

March 1 982

Prepared for

r “*ureau of Engraving and Printing

.S. Department of Treasury

-00 /ashington, DC 20401

56

;2-2513-R

l982

NATIONAL BUREAU OF STANDARDS

LIBRARY MAR 15 1983

^o^.-C\Cc .

NBSIR 82-2513

CHARACTERIZING THE INTERFIBER

BONDING OF CURRENCY PAPER PULPS

J. C. Smith

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Materials Sciences

Polymer Science and Standards Division

Washington, DC 20234

Final Report Covering the Period

October 1, 1980 through September 30, 1981

March 1 982

Note: This document has been prepared for the use of the

Bureau of Engraving and Printing. Responsibility for its further use rests with that agency.

Prepared for Bureau of Engraving and Printing

U.S. Department of Treasury

Washington, DC 20401

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Table of Contents

Page

Summary and Conclusions i

Review and Discussion of Some Previous Ideas 1 Materials Studied and Experimental Procedure 7

Characterization of the Force-Elongation Curve 8

Results for Woodpulp Specimens 14

Results for Currency Pulp Specimens 17

Force Level Parameters

for Characterizing Interfiber Bonding 21

References 24

i

Summary and Conclusions

The purpose of this project has been to study the nature of interfiber

bonding in paper and to develop parameters that characterize the interfiber bond

strength. Most of the data for these studies were obtained by means of tensile

tests on specimens cut from low-density open-web handsheets made from Kraft

woodpulp or from currency paper pulp. These tests were expected to provide

information of use in attempts to develop a durable currency paper made from

woodpulps.

In a typical test a specimen 1 cm wide by 2 cm long was extended in a sensitive tensile tester. On the resulting chart record the force rises and dips

through a series of peaks, and eventually diminishes to zero. Each force drop,

or jag in the curve, is assumed to indicate the breaking of a bond between fibers.

In previous work on woodpulp specimens three different parameters had been derived

from force-elongation data. For one of these parameters the percent elongation of

the specimen at each bond break was plotted versus the number of bond breaks. The

initial slope giving the average elongation between breaks was used as a parameter

to characterize the amount of bonding per unit area of specimen.

For a second parameter the force drops incurred by the specimen in a series

of breaks were averaged to obtain a quantity characterizing the average interfiber

bond strength. In a third parameter the energy loss incurred by the specimen in

each of a series of breaks was calculated, and these energy losses were averaged

to obtain a quantity characterizing the average interfiber bond strength. During

the past year the rationale for these latter two parameters was reexamined. It

was found that because of the dependence of the force drop and energy loss upon

the size of the hole opened up by the bond break it was necessary to impose

restrictions on the way the averaging process was carried out. It was also

necessary to obtain by an independent measurement a parameter characterizing the

average mesh size (distance between bonds on a fiber segment) of the specimen

network tested.

The first parameter had been evaluated for Northern and Southern Kraft

woodpulps and currency pulps, and results were reported previously. The force

drop and energy loss parameters were not evaluated, as most of the emphasis during

this past year was placed on characterizing the force-elongation curve up to bond

break, and in studying how the characteristic constants of this curve changed as the specimen deteriorated during test.
ii

If during a tensile test the extension is reversed until the force drops to

zero and the specimen is then reextended, a curve up to the first bond break is

obtained for the force-elongation behavior of the specimen at that particular

stage of the test. In order to study how the specimen deteriorates during a test

a series of these curves is obtained as a part of the testing procedure. According

to previous work on woodpulp specimens these curves are well fitted by the

equation

(x-x )/x

F = C

2

[ e

0 c

- 1]

Here F i s the force and x is an elongation variable. x

q

is the value of this

variable when the force is zero, x^ is a characteristic length believed to be

approximately proportional to the average size of the meshes in the specimen.

is a quantity analogous to a "spring constant"; that is, its value is

approximately proportional to the width of the specimen, but it is also sensitive

to the structure and force distribution within the specimen.

In order to understand the force-elongation behavior, it is postulated that

during extension the force sustained by a specimen is channeled through the fiber

segments in a series of interlocking parallel pathways. In addition there are many

other fiber segments available that do not sustain force because they have a curled configuration or are not sufficiently oriented in the direction of stretch.

However, as the elongation of the specimen is increased these fiber segments

successively join with the other segments in the network and add to the force

resisting elongation.

The quantity x

c governs the rate at which additional fiber segments sustain

part of the force. If x^ is small the exponential term in the force-elongation

equation above increases rapidly as x increases. This would be the behavior

expected of a network with a small average mesh size, thus the association of x^

with mesh size. The quantity depends upon the primary structure of the network;

that is, upon the number of pathways able to sustain force at the start of the

elongation process. This primary structure is maintained intact throughout an extension until the first bond break occurs. The primary structure then changes

slightly and the effect of this change is evinced by a change in the value of

Bond breaks also cause changes in the value of x^, but these changes are not so pronounced as the changes in
Ill

As the elongation progresses the unstrained length of the specimen increases.

This increase in length is made manifest by an increase in the value of x^; thus,

for a given reextension curve the unstrained length l is equal to + x

q

- x

g where £ is the original unstrained length of the specimen, and x is the value

o s of x

q

for the initial force -elongation curve. The values of ji for a series of

reextension curves obtained during a test can be used to characterize the

progressive deterioration of the specimen.

As part of the experimental work during this past year, representative values

of the quantities and x^ were obtained for a number of Northern and Southern

Kraft woodpulp handsheets. For each specimen tested successive values of

characteristic strain x were plotted versus the fractional increase in specimen

unstrained length - l« A reference value (x /£")

Q

was then obtained by a linear extrapolation to £/XQ

* 1 = 0. It was found that values decreased very

rapidly as the specimen deteriorated during a test, so in this case values of

log

e ^2 were extrapolated to find a reference value of (in C

2^ 0

* A short series of tests was made to see if the values of an<* x

c depended

upon the shape of the specimen. Specimens of dimensions 1x2, 1x5 and 2x5

cm-width x length were used in these tests. It was found, as expected, that' values

of (x /^)

q

and (in ^2^0 ^°r t*ie I arger area specimens had less scatter. Evidently

textural inhomogeneities in the handsheets had dimensions of the order of 1 cm. In all of the other tests lx2-cm specimens were used, although in the light of

these results a lx5-cm specimen might have been a better choice. A 2x5-cm

specimen provides even less scatter in values of and x

c

^ ^ut at considerable

sacrifice in sensitivity in the measure of force drop or energy loss per break.

According to the previous discussion it is expected that should increase

as the density of the handsheet is increased. In order to test this, values of

(in ^ 2^0 were pl°tted versus area density for a series of Northern woodpulp

handsheets of density values varying between 1.5 and 3.5 g/m^ a It was found that

(in C^) ^ncreasec* In 311 approximately linear fashion with density. Values of

(xco/i> were plotted versus area density for the same series of handsheets.

(x JD o was found to decrease in an approximately linear fashion with density, as was expected. Similar results for C and x were obtained in tests for a series

z c of handsheets of Southern Kraft woodpulp.
iv

The parameters (in C ) and (x /y) were also determined for a series of

2 o c o handsheets of the same density prepared from Northern Kraft woodpulp beaten

various amounts in a laboratory beater. It was expected that increased amounts of

beating might increase the number of bonds per unit area, resulting in an increase

in the value of (in C ) and a decrease in the value of (x /£) . These

L o co

expectations were confirmed. Similar confirmation resulted from tests on Southern

Kraft woodpulp handsheets.

Although these test results were in accordance with expectations, the scatter

in specimen-to specimen values was very large. This scatter may be attributed to

the textural inhomogeneity of the handsheets. Some variation results from

differences in the average density of the test specimen, but serious imprecision

may result from density fluctuations in the test specimen. During a test the

distribution of forces in the specimen may change so that at different times a major

portion of the load is shifted from one portion of the specimen to another, thus

the values of C and x measured from the reextension curves will fluctuate in

L C

accordance with variations in local density of the test specimen. Under these

conditions the extrapolated values of (in C ) q anc* o are n0t ver^ Preci se - Because of the difficulty in obtaining good reference values of and x^

for a handsheet or for a test specimen, it may be prudent to change the method

for calculating bonding parameters. Instead of evaluating a parameter for each

test specimen by using average values of and x^ in the calculation, it may be

more desirable to evaluate subparameters for different stages of a test, using

the changing values of and x^ in the calculation. These subparameters could be

averaged in a suitable fashion to obtain a representative value for the specimen.

According to the results just given the force-elongation behavior of a woodpulp specimen can be satisfactorily represented by a single exponential

equation having as parameters the quantities x

c

anc* x

0

* F °r currency pulp

specimens, however, this equation is found to be inadequate. When a currency pulp

specimen is extended it behaves as though there were two mechanisms operating in

parallel/ a strong spring-like force that dominates the initial stages of the

extension, and a force mechanism similar to that operating in woodpulp specimens

that dominates the later stages of the extension. The strong spring-like force

might simulate the effect required to orient a fibrous network partially

immobilized by numerous adhesions between small fibrils and by the cementing

action of fines. The initial strong spring-like force might also result from
V

an initial maldistribution of forces in which the force resisting extension is

sustained by only a few highly extended fiber pathways. Thus the force-elongation

behavior can be expressed by an equation of the type

(x-x )/x

F = k(x - x ) + C [e ° C

- 1] o L where k is the spring constant of the spring-like force.

The force-elongation behavior of a large number of currency pulp specimens

has been analyzed using the equation just given Q In most instances significant

values of k were required to obtain a good fit to the data. This suggests that

much of the binding in currency pulps is achieved by other means than simple

bonds at fiber junctions 0 Thus in this case the concept of an interfiber bond

strength characterized by force drop or energy loss parameters may not be

appropriate.

Although for currency pulp paper it might be necessary to discard the concept

of average interfiber bond strength, a suitable characterization of the overall

ability to hold together might yet be possible. Force level and elongation

parameters have been tentatively proposed for this purpose. There parameters were

developed for wood pulp papers, but their generalization for. use with currency

pulp papers seems possible. T0 find a force level parameter for a test specimen,

the average force F at which bonds break is measured in the vicinity of each

reextension curve. These values are then reduced to the values F that would be

sbi

obtained if the force-elongation behavior of the specimen were governed by

coefficients having the values C and x . The force level parameter is the

s OS

average value of the F^ . To find an elongation parameter, the specimen strain

6. . at which bonds break is calculated for each F The elongation parameter

br bi

for the specimen is the average of the £ . f°rce level and elongation

parameters have not been adequately evaluated from test data, so their applicability

and usefulness have not been established.

1

Review and Discussion of Some Previous Ideas

In this research tensile tests have been emphasized as a means of

characterizing bonding between paper pulp fibers. The test specimens are cut

from low-density open-web handsheets made from the pulp to be evaluated. The

force-elongation curve for such a web specimen has a jagged appearance similar

to that shown in figure 1. The force is seen to rise and dip through a series

of peaks, and eventually diminish to zero. Each force drop, or jag in the curve,

is assumed to indicate the breaking of a bond between fibers. Thus forceelongation curves should provide information that could be used to characterize

bond strength.

The handsheets tested, however, have a very complex structure. The pulp

fibers have a distribution of lengths and diameters, and may have straight or curled configurations. The interfiber bonds at the fiber crossovers have a broad

distribution in strength. The fibrous network of the specimen consists of meshes

of a large variety of shapes and sizes. The density of the handsheet fluctuates

from spot' to spot along its surface. In this circumstance any generalization

about the texture of the specimen or its tensile behavior is true only to a rough approximation. The validity of any parameter for characterizing average

bond strength therefore must be established empirically.

1. Amount of Bonding per Unit Area

If, in a tensile test, the average elongation between successive jags is

small, the web has a relatively large number of fiber crossovers per unit area,

and most of these crossovers are bonded. On the other hand, if the average

percent elongation per break is large, the web has only a few interfiber bonds

per unit area. This means that there is a low density of crossovers, or that many

of the crossovers are not bonded or both. In order to characterize the number of

bonded crossovers per unit area, the percent elongation of the web at each break

is plotted versus the number of bond breaks, and the initial slope of this curve

is used as the appropriate parameter. This parameter has been evaluated for a number of woodpulp and currency pulp specimens [l - 4]"^. The method has been

discussed in a previous report [5],

1. Figures in brackets indicate references at the end of this report.
2

2. The Force Drop Parameter

Each time a bond breaks as the network is being extended the force drops

abruptly, indicating that some of the fibers are no longer carrying load. It

would seem intuitively that the magnitude of this force drop is related to the

average level of the interfiber bond strength in the network; thus the average

of a series of force drops should provide a parameter for characterizing bond

strength. However, in order to develop this parameter the rationale involved

must be examined in more detail.

Assume that the network is composed of randomly distributed fibers joined

together at the crossovers by bonds, each of which has the same strength. SUch

a network would consist of a variety of meshes of various shapes and sizes. The

fiber segments between bonds would have a distribution of lengths in straight

or curled configurations. When the network is extended the fiber segments between

bonds would tend to orient in the direction of stretch, and some of these segments

would straighten out and sustain force. The force sustained by the entire network

would be channeled along a number of parallel interlocking pathways. The forces

in the fiber segments, however, would vary greatly from segment to segment

because of the different orientations and because' of inhomogeneities in the

network structure. Many fiber segments would not sustain any force at all because

their curled configurations could not be straightened out until bonds are broken

in adjacent load bearing segments. This situation provides a considerable

redundancy in fibers available to bear load, and suggests that the forceelongation behavior of the network might not be noticibly affected after a series

of random bond breaks.

When a bond breaks the force borne by the two segments involved is

redistributed through adjacent segments. The size of the associated force drop

would seem to depend upon the number of load bearing segments in the vicinity of

the break that are appreciably affected. This in turn would depend upon the size

of the hole that is formed, or on the size of the meshes in the vicinity of the

broken bond. Some model studies [5,6] have suggested that the size of the force

drop is directly proportional to the size of the meshes involved in the break.

Assume then that the bond breaks occur at random in the network, and that

the size of each associated force drop D is proportional to a length H

characteristic of the mesh that is open ed up; i.e., is a constant

independent of mesh size. Thus the distribution of a series of force drops would
3

be the same as the distribution of mesh sizes in the network, and the average

of a series of force drops would be proportional to the average mesh length . Consider a network (l) in which all of the bonds are of strength S Consider

also a network (2) composed of fibers arranged exactly the same way as in (l),

but whose bonds have a greater strength S^. Then, if for bond breaks associated

with the same mesh size in each network approximately the same fraction of the

force is lost, the force drop will be greater than D It follows that the

average of a series of force drops ^

in network (2) will be greater than a similar average for network (l). It is in this sense that a force drop average

D can be said to characterize bond strength in a network. If the force drop

corresponding to a given mesh size is a monotonic increasing function of bond

strength, will still be greater than This latter assumption is more

probable as it is in agreement with some model studies [5,6],

In the discussion so far it has been assumed that the average force drop D

for a specimen is obtained by averaging all of the force drops in a suitable

portion of the force-elongation curve. However, in practise very small force drops

cannot be counted because the full-scale setting of the recording instrument may

not provide enough sensitivity to detect them, and very large force drops should

not be used because, although they occur infrequently, they have too great an effect on the average. Force drops should not be counted until the extending

specimen has achieved a reasonably uniform distribution of forces throughout its

area, a situation which usually occurs after the first peak force has been

attained; nor should force drops be counted after damage accumulation in the

specimen has become obvious. Thus the force drops D to be averaged are those

occurring in a certain limited sequence, and which exceed a lower value 5 and are less than an upper value A.

In order to characterize bonding in a given handsheet it is necessary to

average the values of D obtained for each of the test specimens cut from the

handsheet. It will be assumed that bond strength is the same over the entire area

of the handsheet, but it cannot be assumed that the average mesh size is uniform

over this area. Experimental evidence indicates that a characteristic length x , believed proportional to the average mesh size, varies significantly from specimen

to specimen in a given handsheet. Because of this variation in average mesh size

it is necessary to adjust the values of 8 and A from specimen to specimen to

provide appropriate compensation. The method of measuring the characteristic
4

length x^ used in making this adjustment is explained in a later section of this

report.

Suppose that the average mesh size in a given specimen is characterized by

an experimentally determined length x and that an average force drop D is found

by averaging those force drop values D lying between a lower limit S and an upper

limit Z4o Consider then another specimen (A) from the same handsheet, but having an average mesh size characterized by an experimentally determined length x^ This

suggests that in the frequency distributions of mesh lengths for the two specimens,

a mesh length in specimen A corresponds to a mesh length in the other

specimen, but differs from it in length by a factor x

ca/x

c

> i.e., = x

cA^m

/x

c

. As the bond strengths in the two specimens are the same, the force drops must

vary directly as the characteristic lengths; or, = i^pp / = x

ca^/xc

* ^rom

this one can infer that = x^D/x if the force drops to be averaged lie

between the limiting values ~ x

cA^/xc and " XCA^V

In order to obtain a force drop parameter characterizing bond strength in a given

handsheet, it is necessary to choose parameters x , d and A characterizing a comparison state. should then be determined for specimen A by averaging force

drops lying between = x^^/x^ and = x ^>/x . Similar values Dg, etc.

should be determined for other specimens. The quantities ®a^x

cA^

D

B^X

cB*

D

C^X

cC

etc. are comparable determinations and can be averaged. The force drop parameter

D characterizing bond strength in the handsheet is given by

n

It should be kept in mind, however, that this parameter is not unique. Many other

values of D can be obtained depending upon the standard parameters x

c

, o and Z1 chosen to define it.

In the above discussion it was assumed that each bond in the fiber network

had the same strength, but in reality there is a broad distribution of bond

strengths. The effect of this broad distribution is mitigated to some extent

because in a tensile test the weakest bonds are usually the ones broken. This

limits the variation in bond strength affecting the measurement. In developing

the rationale for the force drop parameter D it was necessary to use other

questionable assumptions. The validity of this parameter for characterizing

bonding can only be established empirically. Force drop parameters D have not as yet been evaluated for various materials, as current work has been concerned
5

with methods for evaluating x . c

3. The Energy L0 ss Parameter

Each time a bond breaks some of the strain energy stored in the network is

dissipated. Thus it would seem that the average energy dissipated per bond break

might be used as a parameter to characterize average interfiber bond strength.

There are two methods that might be used to obtain this parameter. In the first

method the work to extend the specimen from break to break is summed up and

plotted against the number of breaks. One then searches for a region of the

force-elongation curve in which a series of force drops of approximately the same magnitude occurs, the force level is approximately constant and the specimen is

not noticibly deteriorated by the series of bond breaks. Under these conditions

it is supposed that there is a one-to-one relationship between force level and

the amount of energy stored in the specimen network. Thus if the energy stored

remains constant, the work done in extending the specimen over the series of

breaks is equal to the energy dissipated by the breaks. The curve of work-to-break

versus number-of -breaks should have a slope in this region equal to the energy

dissipated per break, which is the desired parameter. A detailed discussion is

given elsewhere [l]. Parameters for various woodpulp samples have been evaluated

and given in previous reports [2.3]. Results obtained by this method, however,

are influenced by the judgement of the observer, and thus may be open to question.

The energy loss for an individual bond break can be calculated from the slope

of the force-elongation curve just before a break occurs, and the values of the

force just before and just after break. An energy loss parameter can then be

obtained by averaging the energy losses for a series of individual bond breaks.

Calculation of energy losses for individual bond breaks has been discussed

elsewhere [5]. As in the case of force drops, the energy loss for a bond break

depends in an approximately linear fashion upon the size of the mesh that is

opened up, and nonlinear ly upon the strength of the bond that breaks [5,6],

Therefore this energy loss parameter must be obtained by averaging those energy

losses lying within certain limits, in a manner similar to that just described

for force drops. Energy loss parameters in which those individual energy losses

lying within certain limits are averaged, have not as yet been determined for

various materials.
6

4. Other Bonding Parameters

4 serious shortcoming of the force drop and energy loss parameters is their

dependence on the average mesh size of the specimen networks that are being

tested. However model studies [5,6] have suggested that for an individual bond

break both the force drop D and the associated energy loss U depend linearly

upon the size of the mesh that is opened. D and U also depend upon the bond

strength, but the relationship is supposed to be nonlinear and different for the

two quantities. Thus the relation U/B should be independent of mesh size but have

a nonlinear dependence on the bond strength. It has been shown elsewhere [5] that

the ratio U/D = F^/F^' where F^ and F

1 are the force and slope respectively of

the force-elongation curve evaluated at the middle of the associated force drop.

The quantity F^/F^' ^as t*ie <^^mens ^ons length. It would seem then that if the

ratio U/D (or F /F ' ) were averaged over a number of bond breaks a suitable

b b

parameter for characterizing bond strength would be obtained. This parameter

could be thought of as a length characteristic of the average elongation required

to break a bond.

When attempts were made to evaluate this parameter it was found that the

quantities F /F 1 measured tended to have a constant value independent of the

force level at break F In several experiments to check this a specimen was

elongated, the elongation removed, and the specimen reelongated in order to obtain

a complete force-elongation curve to break. Corresponding values of F and F' were

measured at various points along this curve. For all specimens tested these points

were found to satisfy the linear relationship F' = a + bF^ where a and b are constants. At large values of F the quantity F’/F is essentially constant. Thus it can be inferred that the parameter just proposed is insensitive to bond strength.

However the universal relationship between F' and F is a valuable discovery,

because from it the force-elongation equation for the specimen can be derived, and

the constants in this equation can be used to characterize the network.

In concept, perhaps the simplest and most direct way to characterize

interfiber bond strengths is to measure the force levels at which bonds break,

adjust these force levels to compensate for deterioration in the network, and then

calculate a parameter from these adjusted force levels. This can be done in several

different ways. In order to perform the calculations, however, it is necessary to

know the constants characterizing the force-elongation behavior of the specimen

network. These force level parameters, therefore, will be developed at the end of

this report, after the force-elongation behavior of the network has been discussed.
7

Materials Studied and Experimental Procedures.

During the past several years a number of low-density open-web handsheets

had been prepared from Northern and Southern Kraft woodpulps and from

unfractionated and fractionated currency pulps. A description of these pulps

and the methods used for preparing the handsheets has been given elsewhere [4],

Force-elongation curves were obtained for a series of Northern Kraft handsheets

2 having densities varying from 1.5 to 3.5 g/m , and for a series of Southern

2

Kraft handsheets having densities varying between 1,75 and 3.5 g/m . Forceelongation data were also obtained for handsheets prepared from Northern and

Southern Kraft woodpulps that had been subjected to different amounts of beating.

In addition data were obtained for handsheets made from various currency pulps.

A description of the handsheets tested is given in tables 1 and 2.

Tensile tests were conducted on specimens 2 cm long and 1 cm wide except for one series in which the specimen dimensions were varied to investigate the effect

of specimen shape and size. Crosshead speed of the tensile tester was 0.2 cm/min

except for the specimens of 5-cm length, which were strained at a speed of

0.5 cm/min. During the tests the direction of extension was frequently reversed

to unload the specimen and then resumed to obtain a series of force-elongation

curves. Most of these tests had been performed previously, but during the current

year data from these tests were reworked and reanalyzed. A few tests were also

performed during the current year. In these tests more force-elongation curves

were obtained for a given specimen in order to provide better data on progressive

deterioration in the specimen during a test.

Tests were performed in a laboratory maintained at 20° C, 507= R.H. on specimens stored under these conditions at least 12 hours before testing. The

handsheets from which the specimens were obtained were not always stored under

these controlled conditions, and may have changed somewhat during the time

interval between preparation and testing.
8

Characterization of the Force-Elongation Curve*

In a previous report [4] it was shown that the force-elongation curve of

a test specimen usually can be fit by the equation

x/x

F = C ie

C

- C

2 (1)

where F is the tensile force sustained by the specimen, and x is a distance

variable measured in the direction of the elongation. C^, C^ and x^ are constants

evaluated from the data. In this section the method of fitting force-elongation

data is reviewed, and the ideas involved are further clarified and developed.

Consider the recorder trace, figure 2, obtained by testing a specimen from

2 a 2.5 - g/m handsheet of Northern Kraft woodpulp (29-119-1, specimen 3). The

specimen was 2 cm long by 1 cm wide. 1 cm of chart travel corresponds to a specimen extension of 0.01 cm, and full scale force for the specimen was 98 mN

(10 g) 0 At intervals the test was stopped, the extension was reversed until the

tensile force in the specimen was zero, and the specimen then reextended to

obtain a new force-elongation curve. Recording traces during reversal of the

crosshead travel are not shown.

The general condition of the specimen at various stages is noted on the

figure. For the first five reextensions the specimen did not develop any large

holes or tears, and the state of the specimen at the beginning of the reextension

is described as "intact". At later stages of the test the specimen developed

holes and tore at the edges as it deteriorated.

In figure 3 are shown plots of F', or force per unit elongation, versus

force F for the first eight reextended force-elongation curves of figure 2.

The origin of the F* scale has been shifted vertically for each of these plots,

and arbitrary units have been selected to display the plots to best advantage.

The curve corresponding to each plot is identified by its region of chart travel.

The plots are seen to be linear and to have positive intercepts on the F' axis.

Plots similar to these have resulted from most of the tests on specimens formed

from woodpulps.

It will be noticed that the early points corresponding to small values of F

usually fall below the straight line. At these beginning force values the slope

of the force-elongation curve increases rapidly as the network fibers start to

orient. It is only after the initial orientation that the network behaves so that
9

F* increases linearly with F. Also it has been found in general that F',F data

from the initial force-elongation curve in a test does not fit well to a straight

line. In this instance F' usually rises rapidly, becomes constant until F is

moderately large, and then increases linearly with F. Data from the first two

reextension curves often tend to plot in similar fashion. This behavior is

thought to arise from an initial maldistribution of forces in a network, and

will be discussed more completely later. It is only after the network has been

"broken in" that F' has a good linear correspondence with F. In the plot of

figure 3 data from the initial force-elongation curve therefore has been omitted.

Sometimes when a test specimen is unloaded the recorder trace does not

return to the original zero force level. This behavior is usually an effect of

hysteresis. Its consequences can be minimized by waiting a few minutes before

reextending the specimen, but it is more practical to reextend immediately and

to correct data from the new curve for the change in baseline. Sometimes a shift

of baseline is due to a change in the recorder system, a circumstance especially

likely because of the high sensitivities required by these tests. Thus a correction

for baseline shift should be made in any event.

Force-elongation cqrves of these paper network specimens exhibit viscoelastic,

or hysteretic, behavior. Thus the slopes of the force-elongation curves will

depend upon the rate of extension. The rate of extension therefore must be

maintained at some standard value in all of the tests in order to obtain

comparable results. This precaution should minimize the influence of viscoelasticity,

but the possibility of other hysteretic effects should be kept in mind in the

interpretation of data.

Let the equation of a straight line faired through a plot such as those

shown in figure 3 be

dF

dx *

(C

2

+ F) ( 2 ) c x is the reciprocal of the slope of the straight line, and C„/x is the intercept

c z c on the F' axis. Eq (1), given previously, is the solution of eq (2). In order

to find the constants and x , eq (2) is fit by the least- squares technique

to F*,F data from the force-elongation curve. The constant is then found by

fitting eq (1) (with and x^ already evaluated) to x,F data from the

force-elongation curve.
10

According to eq (1), F becomes zero when

x = x = ln(C /C ) (3)

o Z L Thus eq (1) can be put in the form

(x-x )/x

F = C

2

[e

0 c

- 1] (4)

x is the value of the distance variable at which the force just increases from

zero, so x - x^ is the elongation of the network,, As the specimen fibers become

better alined, and as the specimen deteriorates with increasing stretch, the

unstrained length of the specimen increases. Thus for each successive reextension

curve of figure 2, successively increasing values of x

q

should be expected.

In figure 4 data from the first eight reextension curves of figure 2 have

been corrected for small shifts in the baseline and replotted as solid lines.

The constants C of x and x were then determined for these curves, and values

2

3 c o3 of x and F calculated for the fitting curve from eq (4). The fitting curves,

plotted as dashed lines, are seen to be in good agreement with the original

data in this instance. Only the values of x

q

, calculated from eq (3), differ

slightly from the values might have been determined by inspection of the original

data.

When a fibrous network is stretched segments of the fibers composing the

network tend to orient themselves in the direction of the extension through the

combined action of forces along their lengths. As the extension proceeds more

and more of these segments between bonds become oriented and bear load. As a result of this process the force-elongation curve has a slope that increases

with increasing elongation. Thus the reaction of the network to extension could

be modeled by a system of parallel filaments of unequal length, each filament

adding to the resistive force of the system as the extension is increased. This

model, discussed in a previous report [4], provides an insight into the meaning

of the constants C„ and x 0 2 c From an inspection of eq (4) it is seen that x^ has dimensions of length.

If the magnitude of x^ is small the force-elongation curve will rise rapidly as x - X

q

increases. This is the kind of behavior that might be expected to result

from testing a network composed of many meshes of small average size. The small

mesh size assures that additional parallel pathways that sustain force are rapidly formed during extension of the network. This suggests that x

c is a parameter having a characteristic length that is proportional to the average
11

mesh size of the network,. If this assumption is valid might be of use in

finding values for the force-drop and energy-loss parameters, and might provide

an additional indication of the number of bonded crossovers per unit area in a test specimen.

Eq (4) can be rearranged in the form

r/x

F = C */x + C,[e c

- 1 - f/x ] (5)

C l C

where jf is the elongation x - x

q

. The linear term in eq (5) represents the

contribution of the parallel pathways that sustain force immediately upon

stretching. The nonlinear term represents the contribution of additional pathways

that form as the elongation is increased. The value of each term is proportional

to Ck. Thus C- may be expected to increase as the width of the specimen is

Z Z

2

increased, or as the density in g/m of specimens made from the same pulp furnish

is increased.

During a test the specimen deteriorates, and as a result its unstrained

length increases to a value given by

= ^ + x — x „ (6)

o o s where is the original unstrained length of the specimen, and x

g is the value

of x

q

for the initial force-elongation curve. For figure 2, the test specimen

had an initial unstrained length of 2 cm, and the value of x

g as read from the

recording trace was 0.0 cm. The quantity x has been termed a characteristic

» '* , *

*' ' length, but in actuality this expression is strictly appropriate only when

specimens characterized by this term have the same unstrained length. During a test the unstrained length JL of the specimen increases slightly. Therefore in

comparing results for the different reextension curves values of the

characterisitc strain should be used. The quantity has the dimensions of

force and should not be explicitly dependent on the length /.

Table 3 gives the values of constants characterizing the force-elongation

curves of figure 2. According to this table the constant decreases rapidly in

value as the specimen deteriorates during a test. The nature of this decrease is

demonstrated in figure 5 where C

^ is plotted logarithmically versus the fractional

increase in length ^/ZQ

~ !• The straight line approximating this dependence is

passed through the data points determined from the third, fourth, fifth and

sixth reextension curves. The first two points were too high, indicating that

the specimen probably was not "broken in" by the initial extension. The points
12

corresponding to the seventh and eighth reextension curves are also high.

According to the notes on figure 3 the specimen was visually intact for the

first five reextensions and deterioration was noticible starting with the sixth

reextension. This increase in the value of after deterioration has become

noticible was usually observed in the oth^r specimens tested. A mechanism

accounting for this increase is not known, however it seems reasonable to assume

that deterioration at this stage is so extensive that the shape of the specimen

has become changed. Values of the constants obtained with this reshaped specimen

should no longer be compared with values applicable during the early stages of

deterioration.

A value for In characteristic of the undeteriorated but broken-in

specimen can be obtained by extrapolating along the approximating straight line

to the point where the fractional increase in length 1 - Z/Z is zero. For the

specimen of figure 3 this extrapolated value (In C^) is -2.19. The corresponding

value of (^

2

^ 0

N. As is evident in this example however, considerable

subjective judgement is involved. In many cases the plotted data show more

scatter, possibly due to different kinds and locations of damage incurred by a specimen as the tensile test progresses. In these situations the extrapolated

value of and what this value represents become even more uncertain.

In figure 6 characteristic strain data * /£ obtained from the test of

figure 2 are plotted versus the fractional increase in specimen length 2, 1

1

-1.

The characteristic strain seems to decrease linearly with fractional increase in

specimen length, according to data from the third through sixth reextension curves. Characteristic strains from the first two reextension curves are too high, possibly

indicating that the specimen has not yet been broken in. The decrease of

characteristic strain with increasing deterioration of the test specimen was

usually observed in the other tests but the reason for this decrease is not

understood and requires further study. The points corresponding to the seventh

and eighth reextension curves plot high, possibly indicating that the specimen

by then is so deteriorated that its shape and other characteristics have changed.

A value for x 19 characteristic of the undeteriorated but broken-in

c specimen can be obtained by extrapolating along the approximating straight line

to the point where the fractional increase in length is zero. For the specimen

of figure 3 this extrapolated value (x /Z) is 0.0225. the corresponding value of

a co

(x ) is 4.50 x 10 m.

c o
13

Values of (C.) and (x ) found by extrapolation are parameters characteristic

Z o co

of the force-elongation behaviors of the specimens tested. If these parameters

are evaluated for specimens cut from the same handsheet, scatter in the values

obtained should be indicative of the textural homogeneity of the handsheet. The

quantities (C an<^ ^ X

c^o

ma^ a ^- so be use an reducing bonding parameters

evaluated from various specimens or various handsheets to values corresponding

to standard values of (C.) and (x ) . Standard values of the bonding parameters

l o co

thus obtained then could be intercompared.
14

Results for Woodpulp Specimens.

A short series of tests was made to see if the values of and x^ depended

upon the shape of the specimen,. For these tests specimens of cm-width x length

1 x Z, 1x5 and 2x5 were cut from the same hand sheet. The hand sheet

2

(29-119-1,2,3) was of 2.5 g/m density formed from Northern Kraft woodpulp beaten

5,000 revolutions in a laboratory beater. In the tests crosshead speed was

0.2 cm/min for the specimens of 2-cm length and 0.5 cm/min for the specimens of

5-cm length. Values of (In C 0 ) and (x H ) obtained from these tests are given

Z o c o in tables 4, 5 and 6.

Scatter in the values of (In

Q

and (x /^)

o f°r t^ie ^ x 2-cm specimens,

table 4, was too large for any meaningful comparisons with results for the other

two specimen sizes. Scatter in the values for the 2x5 and 1 x 5-cm specimens,

according to the standard deviations found, was appreciably lower. This agrees

2 2 with expectations, as the areas of these two specimen sizes are 10 cm and 5 cm

2 respectively, but the area of the 1 x 2-cm specimen is only 2 cm . Thus the

effects of textural inhomogeneities in the specimens of larger area evidently are smoothed out.

For the 2 x 5-cm specimens the average value of (In is -2.19

corresponding to a value of 0.1119 N. For the 1 x 5-cm specimens (In is

-2.98 corresponding to a value of 0.0508 N. The value for the 2 x 5-cm

specimens is roughly twice that for the 1x5 cm-specimens, in agreement with

expectations. The values of (x /2) for the 2x5 and 1x5 specimens are

c " o approximately the same, indicating that the value of x is not dependent on the

width of the specimen. This observation is consistent with the idea that x^ is

a length characteristic of the average mesh size of the specimen network.

The tests just described indicate that specimen dimensions of 2 x 5 or

1 x 5 cm yield the most precise results. The 1 x 5-cm specimen size might be

preferable, however, because force drops that occur during a test are more

clearly delineated. In addition the long narrow configuration tends to minimize

edge effects at the clamped ends, which might prevent proper orientation of the

network fibers and an even sharing of the tensile force throughout the width of

the specimen.

It should be noted that these tests, performed on the handsheet designated

as 29-119-1,2,3 were performed in April 1981, and featured more frequent

reextensions of the specimens than had been done in tests performed previously
15

in 1980. This tended to improve the precision. Other results to be presented

will not be as precise as they were mostly obtained from tests on 1 x 2-cm

specimens in which fewer reextensions were performed.

According to previous discussion it is expected that should increase

as the density of the test specimen is increased, because the higher density

specimens have more fibers per unit area and hence more pathways to sustain a tensile force. It is also expected that x^ should decrease as the density of the

test specimen is increased, because the higher density specimens have a smaller

mesh size. In order to verify these expectations values of (In Ch) and (x fi)

Z o co

were obtained for a series of Northern and a series of Southern Kraft woodpulp

handsheets of various densities. The results are given in tables 7 and 8. The

fluctuations in the values (In C„) and (x /j}) as indicated by the standard

2 o co

deviations are large, and it is hard to discover any dependence of these

quantities upon handsheet density. This dependence is more obvious in the plots

of figures 7 through 10, where it is seen that (In C^) increases and (x

tends to decrease with increase in handsheet density, in agreement with

expectations. Linear regression lines have been drawn through the data points

to make this more obvious.

The fibers in the Southern pulp furnish are coarser than the fibers in the

Northern pulp furnish. Thus a handsheet formed from the Southern pulp would have

fewer fibers per unit area than would the Northern pulp handsheet of the same density. There would be fewer oriented fiber pathways in an extended Southern

pulp specimen, hance for the Southern pulp would be less than for a Northern pulp specimen of the same density. Also the mesh size of the Southern

pulp specimen would be larger, hence x^ for the Southern pulp would be larger

than x

c for a Northern pulp specimen of the same density. It is interesting to

note in tables 7 and 8 that for handsheets of Northern and of Southern pulp of

2 densities 1.75, 2.0, 2.5 and 3.5 g/m , for the Southern pulp is less than

C

2

for the Northern pulp (except for Northern pulp handsheet 29-1-4), and x^

for the Southern pulp is larger than x

c for the Northern pulp. The imprecision

of the measurements, however, is so great that this apparent confirmation of

expectations must be regarded as somewhat fortuitous.

The parameters (In C„) and (x //) were determined for a series of

Z o co

handsheets of the same density prepared from Northern Kraft woodpulp beaten

various amounts in a laboratory beater. Parameters were also obtained for a
16

similar series of handsheets prepared from Southern Kraft woodpulp Q The results

are given in tables 9 and 10 o The data from these tables are plotted in figures

11 through 14. The effect of beating should be to increase the number of bonds

per unit area of the handsheet. Thus the number of pathways sustaining tensile

force should increase, and the mesh size should decrease with the degree of

beating. Inspection of table 9 and figures 11 and 12 shows that these expectations

are borne out for the Northern Kraft pulp handsheets. This dependence of (In C 0 ) q

and (x A£)

q

upon beating is not so pronounced for Southern pulp. The linear

regression lines plotted in figures 13 and 14, however, show the expected trend.
17

Results for Currency pulp Specimens

The methods described previously for evaluating the parameters x , x^,

and C

2

have worked well for test specimens made from Northern and Southern Kraft

woodpulps, but when specimens made from currency pulps are tested, a difficulty

arises. To illustrate, consider the graphical data of figures 15 and 16. The

force-elongation curve, figure 15, was obtained by testing a specimen (28-159-1,

2

specimen 12) from a 2.5-g/m handsheet of unfractionated currency pulp. Figure 16

gives plots of slope F' versus force F for the first seven reextended forceelongation curves of figure 15. The origin of the F' scale has been shifted

vertically for each of these plots, and arbitrary units have been selected to

display the plots to best advantage. The curve in figure 15 corresponding to

each plot is identified by its region of chart travels

The F, F' data for the reextension curves can be fit by a straight line,

as required by eq (2), but only for forces exceeding approximately 1.5 units in

the plots of figure 16. In the initial regions the F' data fall above the fitted

straight lines. The intercepts on the F

1 axes, which should be equal to the

values of C /x , are to° low for the first three curves, and are negative for

the later curves.

The example, figures 15 and 16, is typical not only for tests on handsheet

specimens of unfractionated currency pulp but also for the specimens made from

various length fractions and from a pulp from which the fines were removed. The

F, F' behavior just shown can be explained if it is assumed that when a currency

pulp specimen is stretched there are two mechanisms operating in parallel:

a strong spring-like force that dominates the initial stages of the extension, and

a force mechanism described by eqs (1-4) that dominates the later stages of the

extension. The strong spring-like force might simulate the effort required to

orient a fibrous network partially immobilized by numerous adhesions between

small fibrils and by the cementing action of fines. The initial strong spring-like

force might also result from an initial maldistribution of forces in which the

force resisting extension is sustained by only a few highly extended fiber

pathways. The force-elongation behavior of such highly extended pathways might

be nonlinear at very small extensions but rapidly approaches linearity while the

specimen extension is still small.
18

The behavior just described can be approximated by the equation:

x/x

F = k(x - x ) + C e

C oi - C

z (x-x )/x

= k(x - x ) + C [e ° C- 1] o 2

x/x

= kx + C^e C“ C

3 (7)

Here a linear force of spring constant k has been added to eq (1), and it is

assumed that the force in this spring and the forces in the mechanism acting

in parallel are both zero at extension x

q

. The parameter is a constant

defined by

C

3 = C

2 + kx

c ln (C

2

/C

1

) (8)

The parameters k, x^, C^, C

^ and xq

in eq (7) can be evaluated by the

following proceedure : The first order differential equation corresponding to

eq (7) is

F* - k = ~ [C + (F - kx)] (9) X j c If a value is assumed for k, the parameters and x^ can be found by fitting

eq (9) to experimental x, F, F' data. Parameter then can be found by fitting

eq (7) (with k, x^; known) to experimental x, F data. Parameter C

2

is found

from eq (8) by Newton’s method, and parameter x

q

is then found from eq (3).

The values of the parameters just found depend upon the value of k that was

assumed, to find the proper value of k it is necessary that the quantity

n x./x (k) „ X][F^ - kx^ - C^(k)e 10 + C^Ck)] be a minimum,

i=l

This quantity can be minimized with respect to k by a systematic trial and

error process.

Force-elongation curves were obtained on specimens made from handsheets of

currency pulp, of several length fractions of the pulp, and of a pulp from which

the fines had been removed 0 The test procedures have been described previously.

Full-scale forces encountered during the tests were usually 100 mN (lOg) or less.

The parameters characterizing the first few curves for each specimen are given in

tables 11 through 15.

It is seen from these tables that in almost every instance k is greater than

zero; i.e., a springlike force is required to provide a good fit of eq (7) to
19

force-elongation data. Data in table 11 characterize specimens made from

unfractionated pulp (28-159-1). Data in tables 12, 13, 14 and 15 characterize

length fractions (28-159-2,3,4) and a pulp from which the fines were removed

(28-159-5), and yet in these tables the values of k are about the same as those in

in table 11 0 This suggests that if the initial strong springlike force measures

the effort required to orient a partially immobilized network, this immobilization

may be attributed more to numerous adhesions between microfibrils than to the

cementing action of fines. Adhesion between microfibrils could also produce

inhomogeneities in the network and cause an initial maldistribution of tensile

forces resisting extension. The cementing action of fines and the presence of

numerous adhesions involving microfibrils are evident in pictures taken with an scanning electron microscope [4] . The initial strong springlike force is usually

not present when unf ibrillated and fine-free specimens made from Kraft woodpulp

are tested.

The parameter x^, which is related to the average mesh size of the specimen

network, has a smaller value for specimens made from the short-length fraction

of currency pulp, table 14, than for the other specimens, as might be expected.

According to tests on woodpulp specimens, x^ remains constant or decreases

slightly for successive reextension curves. This trend can also be observed in

the currency pulp data. However there is also a tendency, in tests on the same specimen, for low values of x^ to be associated with high values of k, and vice

versa. In tests on woodpulp specimens, where k is usually zero, fluctuations in x

c are not so prevalent. It is likely that in tests on currency pulp specimens

the values of k cannot be determined very accurately, and that the constant

fluctuation of k values produces increased variability in values of x^.

The parameter characterizes the strength of the nonlinear network force

in a fashion analogous to the way k characterizes the strength of the springlike

force. Previous tests on woodpulp specimens indicate that in successive

force-elongation curves for the same specimen decreases rapidly, thus

providing an index sensitive to deterioration of the specimen. This rapid

decrease in for successive force-elongation curves is also apparent in the

tabular data, tables 11 through 15. The values of undergo fluctuations

influenced by variations in values of k, but this probably must be accepted.

It is necessary to determine some approximate value of k in order to determine

a meaningful value of
20

Although the fluctuations observed in k and limit their use in

characterizing currency pulps, the measurements demonstrate the presence of an initial strong springlike force, and suggest that much of the binding between

fibers is achieved through a large number of small bonds to microfibrils. In

such a circumstance it would not be appropriate to attempt a characterization

of interfiber bond strength in currency pulps through the use of force drop or energy loss parameters. These bonding parameters are more applicable to Kraft

woodpulps

.
21

Force Level Parameters for Characterizing Interfiber Ponding

In concept, perhaps the simplest and most direct way to characterize

interfiber bonding is to measure the average force sustained by the specimen

when bond breaks occur, however a crude parameter obtained by averaging the

breaking forces over a specified extension would not provide a very precise

characterization of interfiber bonding. The force sustained by the specimen when

bonds are breaking depends upon the specimen deterioration . The force also

depends upon how the component forces are distributed among the fiber segments.

In the early stages of an extension the force is channeled through only a few

fiber pathways, and bonds along these pathways must be broken in order to obtain

a force distribution sufficiently uniform for characterization purposes. Moreover,

the distribution of fibers in each test specimen is nonuniform, and various flaws

such as small holes are present. Thus at various stages of an extension the fiber

segments sustaining most of the force may be expected to shift from one region of

the specimen to another.

In order to compensate for these effects it is necessary to know the values

of the constants C x and* x that characterize the force-elongation behavior of

2

7 c o the specimen, and to know how these constants change as the tensile test progresses.

A more suitable force level parameter then might be determined as follows : From

the values of C and x characterizing a series of reextension force-elongation

z c curves obtained during a test, select a standard pair of values C and x . — s cs Measure the breaking forces in the vicinity of each reextension curve, and then

calculate what the equivalent breaking force would be for a specimen having a force-elongation behavior governed by the coefficients C and x . Average these

Zs cs equivalent breaking forces to obtain the force level parameter.

A more detailed procedure will now be discussed:

1. Perform a tensile test upon a specimen for which many reextension forceelongation curves are obtained, and evaluate the constants of these curves. For the

i th curve let the constants be designated as C . „ x . and x .. 2. Assume that in a certain region of force drops the force-elongation behavior is

described, by the i th curve; measure the average force level in this region by

integrating under the curve of breaking forces and dividing by the amount of

extension. Designate this average breaking force as F . Substitute F^ into eq (4)
22

(x, ,-x .)/x . F = C [ e bl 01 C1

bi 2i

and solve for S. . ~ bi

" *bi

- x

01

- 1 ]

, obtaining

( 10 )

bi xci

In 1 + Jzl

C

2i/

( 11 )

3. Find the unstrained length Jt. of the specimen from eq (6) and then calculate

5bi £

( 12 )

The quantity Fs the average strain required to produce a bond break in the

region of the i th curve. Ideally the ^ for a given specimen should all have approximately the same value. Some tentative calculations,77however, have shown that the 6, . increase bi

with increasing i and approach a constant value. Thus to find a suitable average

6^ for the specimen the first S^

used in the averaging should not be less than

approximately 5% of the average value. The value of 6^ should be a weighted

average; that is, each 6^ should be multiplied by the range of extension to which

it applies, and the sum of these products should be divided by the sum of the

extension ranges 0 The parameter thus obtained characterizes the average

D breaking strain for a specimen whose force-strain parameters C an<^ He within a certain range of experimental values 0 To obtain a force level parameter for the specimen 1

1. Substitute the F . into eq (4) and solve for bi

(13)

£.16 . F . e bl C1 = 1 +

21 6

bi/eci Calculate only those values of e for which the 6^

. have approximately the same value, as determined in the previous calculation of 6^ . C a i cu late also the

quantities 6 . ~ x . /J?.. ci ci 1

2. Choose a characteristic strain 6 such as , for instance, the value of £ . for

CS

^bi/€ci

C1

which i has the lowest value in the series of e that was just calculated.

Calculate the quantities

6 .16 £.16. . s .le

,

bi cs _ r bi

e - Le

6, .IS

Cl

j Cl cs (14)

The values of e ^

CS should be approximately the same because the values of

6^^ are approximately the same,
( 15 )

3 0 Calculate the quantities

F = C [ e bl CS

- 1] sbi 2 s using for C^ the value of C^ _ corresponding to the chosen for £

2i ci 'cs The

parameter F

, obtained by a weighted average similar to that for gives the

breaking force level for the specimen corresponding to the force-strain

coefficients C and £ . 2 s cs A parameter F * obtained by a simpler calculation could be used alternatively.

This parameter is defined as T/£.

F * = C [ e sb 2s

cs

- 1 ] (16)

The parameter F gives the average force level for bond breaks in a specimen

having a force-strain relationship governed by the constants C and £ . in order

S OS

to find a parameter F^ characterizing a number of specimens from the same handsheet sample, it is necessary to choose arbitrary values of C and £, for

CS

the sample, reduce each F to its equivalent value corresponding to and £

S D 2so iCS'

and then average these values „ When this parameter F^ i s used for specification

purposes The values of C and 6 upon which it depends must also be given.

^ s c s A corresponding parameter 6^ for a handsheet sample might be obtained by

averaging together the £ for a number of specimens. This parameter might be

b

independent of the values of C and 6 for the individual specimens, and of ___ •— S OS

C and £ for the sample, but this concept has not been tested experimentally.

It has been noted previously that the concept of the average bond strength

of an interfiber junction is valid in the case of papers made from woodpulp. For

papers made from currency pulp the fibers are joined together by many bonds

between microfibrils and rigidly held by the gluing action of fines. In this case characterization of an interfiber bond strength by such parameters as average

force drop or energy loss per break is no longer appropriate. For both kinds of

paper, however, it might be suitable to characterize the overall ability to hold

together by means of a force level parameter. In the preceding discussion this

parameter was developed for woodpulp papers, using eq (4). Similar more general

parameters applicable to both currency and woodpulp paper might be developed by

applying the same rationale to eq (7).

As noted above the force level and elongation parameters must be considered

as tentative. There has not been sufficient time during this reporting period to

test their validity and usefulness. The rationale, however, seems plausible and

worthy of application at some future time.
24

References

1. J D C. Smith and E c L, Graminski, Characterizing the Interfiber Bond Strengths

of Paper Pulps in terms of a Breaking Energy, NBSIR 76 - 1148. Available

from National Technical Information Service PB 264,689.

2. J e C. Smith and E. L. Graminski, Characterizing the Interfiber Bond Strength

of Paper Pulps in Terms of a Breaking Energy* Effect of Beating^

NBSIR 77 - 1286. Available from National Technical Information Service

PB 276,473*

3« J a C. Smith and E 0 L 0 Gramiinski, Characterizing the Interfiber Bonding of

Paper Pulps: Effect of Preparation Pressure on Tensile Test Specimens.,

NBSIR 78 - 1459 o Available from National Technical Information Service

PB 280,291o

4 0 J 0 C. Smith and E. E c Toth, Characterizing the Interfiber Bonding of Currency

Paper Pulps, NBSIR 80 - 2190.

5 0 J 0 C. Smith, Characterizing the Interfiber Bonding of Paper Pulps: Rationale

for Bonding Parameters Derived from Tensile Test D a ta, NBSIR 79 - 1722.

Available from National Technical Information Service PB 80 - 150329.

6 . J c C 0 Smith, Tensile Behavior of Some Mathematical Models of Paper Networks,

J. Research NBS, 299 - 318 (1979).
Description

of

Woodpulp

H

a

ndsheets

Tested g

o

4J 0)

cd 5-( CO CO <t" o- CO CO CO <) CO CM

5-4 3 PU LO <1- uo m in m± LO NO

cd w 4*5 CO CO CO CO CO M3

a. cn

a) <u u 5-4 (u a

&oG • o o o o o o o o o o o o

> o o o o o o o o o o o o

JJ <u o o o o o o o o o o o o

CO •n •N ON •k •N •s •s •N ON «> ON a) in m t—4 CM in in m r—

1

CM n o o

fQ t—• T 1

u cm n •H e n n n n n o n n n n n CO o • o • • • • o • • o 9 G 00 CM CM CM CM r—

4

r—

1

CM CM CM CM CM CM va

TJ

OJ

=3g

4-J c

oa

3 G 3 g 3 3 3 3 3 3 3 3

5-4 5* 5-4 u 5-4 5-i r-J 5-4 !-i 5-i a. <y at d> a) 0) dJ 3 a; <u d) d) di T—

l

405 jo 4= 43 40 4= 40 40 40 -3 40 40 3 U 4J 4-1 4J 4J 4-i 4J 4J 4J 4-J 4-J 4-1 PL, 5-4 3 3 3 5-i U s-< 5-1 5-4 5-4 !-i 3

O O O O O O o O O o O O

z CO CO CO z z z z Z Z z CO

G

o

4-1 •r^ t—< CM

d) 4-J NO P*N CO ON t—4 i—4 d) a- 1 1 1 1 1 1 40 •r-J ON ON ON ON O' ON r—4 CM cn <1" n NO W 5-i n n n m m n 1 1 i 1 i ! TO CJ r—

4

r—

4

r—

4

r—4 r—-1 i—4 r—

(

r—

1

t—

4

i—

i

r—

4

3 W 1 1 i 1 1 1 1 i i 1 i 1 cd <u 00 CO 00 O' 00 00 o> ON ON ON ON ON z CM CM CM CM CM CM CM CM CM CM CM CM
Table 1

Continued.

i—1

i—i

r-J 00 CO 00 r-^ JJ 0) '

"

oo

CO JJ r—i

r—

J

r—1 3 CO cn CO CO r—i H 03 cn CO cn 3o

•^i o

4-1 o o o CO 3 CO 00 00 *

\ m 3 CO o> ON r—l a 3 "

01 jj n» u CO

PL. 03 so

•r—l 4J 0) CO Sj co

mm inm

Sj 3 Oj <4 <(

(0 CO CO CO CO CO

CL CO

0) a) Sj Sj

CL.

a

00s • o o o o •r"i > c o o o

4J 0) o o o o

CO

u •V •> "S 0) in m m m

03

jj CM

m

m •r—i ,e CM O m CO • 9 • • 3

0) Q

oo CM cn CO t—1 s 3 3 3

!j !j Sj Sj cl 4) 3 3 3

r—1

jo r" JO JO 3 JJ JJ JJ JJ

CL.

u Sj SJ 3 o O O O 2 2 2 CO 3O

JJ •rJ 3 JJ r—l CO in 3 3 i 1 i i jo 3 00 CO 00 CO

co 00 r-J r—i r—1

1—1

03 rJ P—1

i“1

t—l

r—l 3 CO 1 i 1 i 3 3 a> O' O' <T> 2 03 CM CM CM CM

r—lr-l i—l 1—i

i—I

00 00 CO

00 00 "— \ \ m ON

r—l CM i—l

t—iT—l • • o -— \ g £ £

<r 3 CJ o

r—l 1—1 CM

cl

_

n JO

JJ 4J JJ 03 03

•H •i—l *rj o o M3 M3 M3 s £

co CO n- \ M.

v—s •V •V o o c £ £ £ .—i

r—1

CM CM CM

O o o O O O CM m in

r—it—l

i—l -3 J3 JO

JJ JJ jj oo 00 00 3 3 3 3 3 3

i—i

T—I r—i 3 3 3 3 3 3 £ £ p

m

m CO CO CO •H •^i •H in m in o 3 O

co CO co CO co 3 3 3

CL COa

CO CO CO • IV • IN , n 3 3 3

JJ JJ JJ 3 3 3

03 33 03

JJ JJ JJ o o o o o CO CO CO o o o o o 3 3 3 o o o o o JJ JJ JJ

•s

A. *1 »>

A

in

m

mmm Jj JJ JJ 3 3 3 3 3 3 3 !j Sj 3 3 3

4J UJ cw LJ U-. LJ

•r—l •r—l •r-i 03 03 03 o m in m m • a • a 9 JJ JJ JJ CM CO CM CM CM 3 3 3

J2 JO J2 M3 M3 M3 1 1 1 a> CT\ c\ m m m r-J T—i i—1 3 3 3 3 £ 1 i i 3 3 3 Sj 3 00 CO 00 3 3 3 3 3 CM CM CM

JO ,3 rJ JJ 13 JJ JJ JJ CO CO 3 3 3 U 3 3 3 3 3 O O O O O

CO CO 2 2 2 jj JJ JJ 3 3 3 3 3 3 i—1 j3

cn COX

"O 03 T) c P5 C o CM 1/ cdn 3

J3

d. r* 1—1

1—1 T—I CM CO 1 1 1 1 a; 3 a) 00 CO O'. o^ g £ s

r—l i—l I—l r—i 1—1 53 3 Co

i—l r—i i—li—l1 r—i co cn cn i Cr\ 1 C'N 1 O' • • • CM CM CM CM CM i—i CM cn
Description

of

Currency

Pulp

Handsheets

Tested - ' O o o o o 43

oo 00 co oo 00 4J

44

g 00 T—1

CM

B fa

01 4-1 T—4

l—J CM CM CM o t—< gH G

X>

5-4 44

01 44Gg 3

fa X5G

44g

G 43 • C o 01 G o

fa

X 54 fa

4J

G 3 44

CO Ol

G COO

!-i r>. ON 33 01G

cO

— n.

G 54 fa g o i—,

V. CO • 54 4-4 3 4-1 CO CM CM lh 1—4 01 a. C U CO \ \ V "—

G 3

fa

X 1—i

CM CM CM CM

OG

fa fa 4-4 4J O OG m 44

54 'Cl- 43

1- M-l CO 60

Ml fa fa 54 44 G

CO 3 G !3 a o <£> to o CM 00 O o o CO CM t-H o CM r^. <4-4 T3 ?->

•r-! 0 a • • • • • G 54 4J X rfa X 54 X O fa r—4 G

CO 0)

G a.

5-1 fa •H

G 43

fa >> 54fa

X o G

4J

G X)

54 •iH

XG >

IV

G S fa

/-“M /-I 44 XI s 43 43 G x /i 43 01 01 C G G

-G 01

G

G fa

OGO

01 Q)

BB fa •r*l •H

G

B fa 44 44 6 m o O CM o m X) m G S G

<1- co =S= fa fa

U 54

X 1—4 =3= fa <4-4 60 44 G =s= v-' '—

4-) >—/ w •» 01

m

G

CO fa fa > fa

G • 43 c M fa M m -a 3 CM 44 o 01 G

G 1-1G

GGG

G

G 44

G

O 4-)OOOO

O fa

O 44 •H

fa o •r-1 fa •r-4 fa fa -9 o *r4

4-1 CO 4J 4J 4J 4J 01 4-) §

44 01 fa

O S-l o O o O

G o 01

G r—i

CO 44

GGGG

C

GG

G 3

5-i

G

U 5-i i-i £4 fa S-iG !>>X fa

fa 33 fa1fa fa fa fa fa 54

Oc 4-4 G O 54

54 XI

54

G 3 54 4-4

G

a

G

O

O s

4J fa c 44

0) 4J r-4 CM CO

m

G 01 43

0) CO 1 1 1 1 i 44 fa 60

43

G O'* <y\ CT*

G fa fa

01 60

m LOmmmG 3 G

x fa i--i »—

J

r—ir—1

fa pa fa s c 01 i 1 i i i CO 0) 00 00 00 00 00 • o X X CM CM CM CM CM r—1

CM
m 00 on

m nO nO CO m3

CM mt CO CM CO in CO ON O in CM m CO CO m CO r—

rH on r—1

CM

m CO o CM 3 o CO no CM 00 <3 NO

r

—1 • • • • • • • • CM CM cn m)- m m LO 1 1 i 1 i i i 1

CM o cn <t o ON m3 00

00 CO CM in <1- cn r-»

m

CO in NO cn <f ON O' 00 CO r-- CM o ON CO o CO CM r—1

T—1T—1

T—1 o o o o o O O O o o

CM

<u o t—1

T-“l CM CM CM CM 3

00 & 1 <3 1 ON 1 00 1 CM CM 1 r—1 1 NO

•H CM CM <3 o CO NO ON

pH o a CO Mf ON VsO NO M3 r". r—4 CO m NO T*l m3 NO

<-W r—i

m CM f

r^» <3 Ml- CO 0 • o • O o • • •

co

d> i—i

rd3H

to

0)>

i-l 3 CO CO CO CO CO CO CO CO O i 1 I 1 8 i i 1 CO in CO <3 CO NO o CO 3 O CO CO NO O in 00 Mf o o X E CM nO r->. CO m in o ON

cw r^. in ON

m r—i CM CO r- <)• CO CM CM CM o r—i

O o • • o • • • • X . > T333 m o m o O LO in o O f—1 o o o T“i o r—f m i CO ON I''- v3 CM CO CO _ P T—1 o NO r-« O ON r-~ NO o Mf o r" cn Ml" m o r—1

r—i CM CM cn Ml"

m

u o o o o o o O o o • 9

cn 4J33

•u

cn NO <1- 00 <3 CO <3 NO n- 3 CO i—l CO m o CO Ml- CM O CM o ON r—1

r- ON o o r—i CM CM <3 m nO CO r—i E o O o O o o o r—i m CM CM CM CM CM CM CM CM o O o o o o O O O o • • • 9 • • 9

cn

d>3

r““i 3> CO CO CO CO CO CO CO CM 1 1 1 1 1 1 1 1 CO o «—-l o CM r—i

CO o NO Ml- CO Ml- CO Ml" NO CM

X E CO r—

J

CO in o 00 <3 o

CM o ON Ml- r^. ON r—1

r—1

CM CM <3

m NO CO T—< o o O O 9 9 9 • O NO CM CM • o• vO• NO 9 o o • o CM cn m 3 CM m ON T—1

r—i r—i r—i > i i i 1 | i i i 3O CM o 00 o NO CM CM CM o • o • • • • •

r—i CM CM

m r-* ON T—i
Table 4

Extrapolated Values (In anc^ (x /^)

q

^ or Specimens-'

of 1-cm Width and 2-crn Length.

Specimen (In C

2

) 2/

o Sloped SD-/

29-119-1-3 -2.19 -97.58 .02 4

-4 -3.47 -21.35 .10 6

-5 -2.02 -94.05 .12 5

-6 -2.08 -63.28 .09 4

-12 -2 0 75 -34.55 .13 7

-2.50 ± 0 .61 std. dev.

Specimen (x

c /i> o Slope SD n

29-119-1-3 O 0225 -.3655 .0006 4

-4 .0128 -.0208 .0005 6

-5 O 0260 -.4378 .0009 5

-6 .0248 -.3248 .0012 4

-12 .0217 -.1332 .0009 7

.0216 4- — • 0052 std. dev.

o 1. Cut from Northern pulp handsheet^ 2.5 g/m density.

2. In is logarithm to the base e. is expressed in Newtons.

3. Slope of linear regression line.

4. Standard deviation of fit.

5. Number of data points.
Table 5

Extrapolated Values of (In and (x ID c for

o Specimens'

of 1-cm Width and 5 -cm Length.

Specimen (ln C

2

) oi/ Sloped SD-/ 5/ n

29-119-2-4 -3.09 -29.50 .16 7 -6 -3o 19 -80.60 .10 4

-7 -2.78 -94.63 .15 4

-10 -2.87 -58.21 .02 4

-12 -2.95 -88.54 o 00 o 4

-2.98 ± 0.17 std. dev.

Specimen (x ID c o Slope SD n

29-119-2-4 .0237 -.2300 .0010 7

-6 .0184 -.2726 .0003 4

-7 .0243 -.5521 .0012 4

-10 .0171 -.1807 .0001 4

-12 .0183 -.1750 .0014 4

.0204 — .0034 std. dev.

‘

2

1. Cut from Northern pulp handsheet, 2.5 g/m density.

2. In is logarithm to the base e. C

0 is expressed in Newtons.

3. Slope of linear regression line.

4. Standard deviation of fit.

5. Number of data points.
Table 6

Extrapolated Values of (In C ) and (x I/) for Specimens”/

Z o c o of 2-cm Width and 5 -cm Length.

Specimen (In C ) y

Z o Slope”/ SD-/ 5/ n

29-119-3-4 -2.40 -97.03 .14 5

-6 00

T—

1

• 1 CM -45.08 .23 6

-7 -2.23 -44.18 .08 5

-9 -2.18 -35.49 .19 3

-10 -1.94 -114.35 .26 5

-2.19 ± 0. 17 std, dev.

Specimen Slope SD n

29-119-3-4 .0190 -.2838 .0004 5 -6 .0191 -.1495 .0013 6

-7 .0186 -.1428 .0003 5

-9 .0194 -.2257 .0012 3

-10 .0163 -.3284 .0013 5

.0185 ± .0013 std. dev.

2

1. Cut from Northern pulp handsheet, 2.5 g/m density.

2. In is logarithm to the base e. is expressed in Newtons.

3. Slope of linear regression line.

4. Standard deviation of fit.

5 0 Number of data points.
Table 7.

Extrapolated Values of (In C„) and (x / ?)

2 o c o for Northern Kraft Pulp Hanasheets

of Various Densities.

Hand sheet Density (In C

2. 0

(x

1 0

designation

g/m

2

28-159-11 1.5 -5.75 - 0.34

2/ .0230 — • 2/ 0047-7

28-159-12 1.75 -4.06 ± 0.34 .0217 — • 0068

29-1-1 2.0 -4.53 -L. 0.54 .0167 -f- — • 0024

29-118-1 2.25 -3.53 ± 0.49 .0215 — • 0038

28-159-6 2.5 -3.12 - 0.51 .0185 — • 0050

28-119-1 2 0 5 -2.50 - 0.61 .0216 • 0052

29-1-4 2.5 -3.88 0,74 .0172 4*— 0 0044

29-118-3 3.0 -3.14 ± 0,54 .0198 — • 0033

29-118-5 3,5 -2.27 0.89 .0166 +— • 0029

1, In is logarithm to the base e. is expressed in Newtons.

2. Standard deviation. Values given are the averages of determinations from

5 specimens in most cases
Table 8.

Extrapolated r Values of (In C ) and (x /£,) 2 o c o for Southern Kraft Pulp Handsheets

of Various Densities.

Hand sheet

designation

Density

, 2

g/m

(In C ) 2 o x"

o o

29-118-7 1.75 -5.10 ± 0.24“^ .0273 ± .0018“/

29-118-10 <N . o -4.74 ± 0.55“/ .0241 ± .0066

^

29-159-7 2.5 -3.37 ± 0.76“/ .0290 ± .0064“/

29-118-12 3.5 -2.69 ± 0.72“/ .0198 ± .0046-/

1. In is logarithm to the base e. is expressed in Newtons.

2. Standard deviation. Average of determinations from 2 specimens.

3o Average from 5 specimens.

4. Average from 4 specimens.

5 0 Average from 10 specimens.
Table 9

Extrapolated Values of (In C.) and (x /£)

2 o c " o for Handsheets of Northern Kraft Pulp

Beaten Various Amounts.

Handsheet Beating (In Vo17 >T

o

<k_. o designation

revolutions

29-1-2 1,000 -4.47 ± 0.31-/ .0212 ± .0028~/

29-1-3 2,000 -3.82 ± 0.52^ .0182 ± .0017~/

29-1-4 5,000 -3.88 ± 0.74~/ .0172 ± .0044“^

29-1-5 10,000 -3.15 ± 0 . 64~

//f .0160 ± .0026^

Table 10.

Extrapolated Values of (In C.) and (x /l)

2 o c o for Handsheets of Southern Kraft Pulp

Beaten Various Amounts.

Hand sheet

designation

28-159-8

28-159-9

28-

159-7

29-

1-6

Beating (In C ) ^

2 o uc /v o

revolutions

1,000

2,000

5,000

10,000

-4.14

-4.72

-3.37

-4.21

+

+

-f4-

0.68

0.74

0.76

0.55

5/

3/

6 /

6 /

.0290 ± .0052-^

.0251 ± ,0062-/

.0290 ± ,0064~/

.0218 ± .0060^

1. In is logarithm to the base e. 2. Standard deviation. Average of

3. Average from 7 specimens.

4. Average from 8 specimens.

5. Average from 3 specimens.

6. Average from 4 specimens.

is expressed in Newtons,

determinations from 6 specimens.
Table 11.

Parameters for Handsheet Specimens Made From

Unfractionated Currency Pulp (28-159-1).

Specimen No.

and (Curve)

k X

c ci °2 Xo

N/m m N N m

1(1) 11.0 .17950E-3 .24538E-2 . 71022E-2 . 19077E1(2) 0.0 .20785E-3 . 60210E-3 .52331E-2 .44943E1(3) 13.4 . 12386E-3 . 69801E-6 . 339 19E-3 .76618E7(1) 48.0 . 14955E-3 .79367E-3 . 68461E-2 . 32225E7(2) 17.1 . 15515E-3 . 33037E-4 .20488E-2 . 64036E7(3) 15.1 . 15946E-3 .40923E-5 . 1035 0E -2 . 88232E7(4) 8.0 .17077E-3 .79007E-6 .66103E-3 . 11492E7(5) 3 0 8 o 1884 IE-3 .24228E-6 .57717E-3 . 14650E8(1) 0.0 . 14663E-3 . 10991E-2 .35426E-2 .17161E8(2) 22.7 .12584E-3 .29037E-4 .47293E-3 .35114E8(3) 10.6 . 17516E-3 .39 84 IE -4 .94042E-3 .55376E8(4) 14.0 0 15431E-3 .22499E-5 .37837E-3 . 79082E8(5) 1.3 .22948E-3 • 65904E-5 . 66225E-3 . 10579E10(1) 44.8 . 14360E-3 . 10222E-2 . 37019E-2 . 18480E10(2) 4.7 .17696E-3 .43533E-3 .32734E-2 . 35702E10(3) 10.7 . 14762E-3 .77245E-5 .57998E-3 .63745E11(1) 5.7 .17823E-3 . 85904E-5 . 3442 0E3

. 65777E11(2) 8.4 . 14813E-3 .23560E-6 . 14788E-3 .95426E11(3) 6.8 . 16879E-3 . 13995E-6 . 145 6 IE -3 .11726E11(4) 5.8 . 18279E-3 .70253E-7 . 16734E-3 .14213E11(5) 8.3 . 17539E-3 . 65180E-8 .28822E-3 . 18762E-

'3

•33

•33

3

2

2

3

3

3

3

2

3

3

3

3

3

2

2

2
Table 11. Continued

Specimen No.

and (Curve)

k X

c

c

i °2 X

o

N/m m N N m

12(1) 9.4 . 19211E-3 .24179E-3 . 10984E-2 .29075E-3

12(2) 0.0 .23586E-3 .23618E-3 . 17234E-2 .46876E-3

12(3) 0.1 .24344E-3 .86008E-4 . 12839E-2 . 65807E-3

12(4) 5.8 . 19162E-3 .24834E-5 . 39139E-3 .96962E-3

12(5) 8.3 .17513E-3 . 13945E-6 .23125E-3 . 12984E-2

12(6) 3.4 .22277E-3 .45700E-6 . 37860E-3 . 14969E-2

12(7) 6.5 . 19604E-3 . 20523E-7 . 30738E-3 . 18848E-2

12(8) 3.5 .23027E-3 . 37541E-7 .33589E-3 .20952E-2

12(9) 5.9 . 19481E-3 .59532E-9 . 22025E-3 .24976E-3
Table 12.

Parameters for Handsheet Specimens Made From

Currency Pulp Fraction I (28-159-2).

pecimen No.

.nd (Curve)

k X

c ci

C

2

X

0

N/m m N N m

2(1) 24.2 .20738E-3 .55819E-3 .16934E-2 .23015E-3

2(2) 19.7 o 17192E-3 .35163E-4 .40765E-3 .42126E-3

2(3) 15.1 .20196E-3 . 11039E-4 .32697E-3 . 68435E-3

2(4) 8 o 0 .29771E-3 .34276E-4 .82818E-3 .94815E-3

2(5) 9.1 ,25387E-3 .20517E-5 .33147E-3 .12909E-2

5(1) 24.8 .99183E-4 .98388E-4 .57215E-3 . 17461E-3

5(2) 4.0 .19083E-3 .20132E-3 . 11695E-2 .33574E-3

5(3) 7.8 .10443E-3 . 14636E-7 . 61410E-4 .87111E-3

8(1) 23.9 .13930E-3 .42940E-4 .21509E-3 .22444E-3

8(2) 16.7 .1765 IE-3 .17207E-4 .16572E-3 .39979E-3

8(3) 11.7 .20686E-3 .96346E-5 .23403E-3 .65991E-3

8(4) 4.5 . 32164E-3 . 34382E-4 .55075E-3 . 89216E-3

8(5) 4.7 .29389E-3 .28264E-5 .42231E-3 . 14714E-2

10(1) 14.4 .18855E-3 .20636E-3 .46340E-3 .15253E-3

10(2) 10 o 7 .17719E-3 . 16314E-4 . 14243E-4 . 38394E-3

10(3) 7 a 8 .20794E-3 . 61396E-5 . 12564E-3 .62769E-3

10(4) 7.3 .24032E-3 . 30561E-5 .21510E-5 .10223E-2

10(5) 5.5 .25032E-3 . 63961E-6 . 14121E-3 .13510E-2

10(6) 4.0 .29 168E-3 .59859E-6 0 18892E-3 . 16785E-2

10(7) 5.2 .27454E-3 .53950E-7 . 13301E-3 .21442E-2

14(1) 24.2 .14933E-3 . 12596E-3 .45033E-3 . 19025E-3

14(2) 10ol 0 18557E-3 .35457E-4 .28298E-3 .38545E-3

14(3) 2.6 0 24944E-3 .29515E-4 0 38305E-3 . 63938E-3
Table 13.

Parameters for Handsheet Specimens Made From

Currency Pulp Fraction II (28-159-3).

Specimen No.

and (Curve)

k X

c c

i C2

X

o

N/m m N N m

3(1) 11.2 .21423E-3 .57560E-3 .21276E-2 .28006E-3

3(2) 7 o5 .21601E-3 .73670E-4 .67427E-3 .47825E-3

3(3) 3.7 .24705E-3 .24391E-4 .44923E-3 .71975E-3

7(1) 3.6 .22645E-3 .91134E-3 .17026E-2 .14153E-3

7(2) 0.3 .23933E-3 o 16033E-3 .28889E-3 .14092E-3

7(3) 0 o 6 .31575E-3 .10215E-3 .53825E-3 .82474E-3

7(4) 1»4 .31413E-3 .25804E-4 .71412E-3 .10431E-2

8(1) 13.7 .18549E-3 . 14984E-4 .25620E-2 .95368E-3

8(2) 6.1 .21357E-3 .58117E-5 . 17009E-2 .12129E-2

8(3) 13.2 . 1 642 6E -

3

.17274E-7 .32618E-3 .16173E-2

10(1) 21.6 0 14877E-3 .63033E-3 .34575E-2 .25321E-3

10(2) 6.1 . 14941E-3 .14781E-4 .65930E-3 .56744E-3

10(3) 9.1 . 17371E-3 .44125E-5 .20830E-3 .66958E-3

11(1) 1.6 . 17947E-3 .15483E-2 .53673E-2 .22311E-3

11(2) 0.0 . 19266E-3 .23023E-3 . 11048E-2 .30215E-3

11(3) 8.4 .11531E-3 .26113E-6 . 35571E-4 .56668E-3
Table 14.

Parameters for Handsheet Specimens Made From

Currency Pulp Fraction HI (28-159-4).

Specimen No.

and (Curve)

k X

c c

i °2 X

0

N/m m N N m

2(1) 0.0 .12182E-3 .11679E-2 .35463E-2 .13530E-3

2(2) 0.0 .10063E-3 .40726E-4 .19714E-3 . 15870E-3

2(3) 17.3 .81302E-4 . 82898E-7 . 12003E-3 .59170E-3

2(4) 11.6 .81615E-4 .13341E-8 .29156E-4 .81550E-3

2(5) 5.6 .11950E-3 .10233E-7 .95196E-4 .10920E-2

4(1) 35.0 . 11574E-3 .95250E-3 .44520E-3 . 17848E-3

4(2) 8.4 .11680E-3 .69912E-4 .16140E-2 . 36666E-3

4(3) 1.5 .11133E-3 .11610E-5 .74780E-5 .20737E-3

9(1) 9.3 .11610E-3 .77947E-3 .30958E-2 . 16013E-3

9(2) 20.4 .10429E-3 .17516E-4 5 .42568E-3 .33274E-3

9(3) 14.6 . 11742E-3 .23481E-5 .20245E-3 .52333E-3

11(1) 27.4 .11750E-3 .14906E-2 .51031E-2 . 14460E-3

11(2) 20.4 .10513E-3 . 14101E -4 .28909E-3 .31755E-3

11(3) 9.0 .13211E-3 .34119E-5 . 14798E-3 .49804E-3

13(1) 6.0 .17827E-3 .23326E-3 .11461E-2 .28379E-3

13(2) 5.0 . 19295E-3 .44637E-4 . 10750E-2 . 61386E-3

13(3) 5.5 . 15412E-3 .21375E-6 .13672E-3 .99577E-3
Table 15.

Parameters for Handsheet Specimens Made From

Currency Pulp Less Fines (28-159-5) •

Specimen No.

and (Curve)

k X

c C

1 °2 X

0

N/m m N N m

1(1) 14.2 .15243E-3 .84484E-4 .58113E-3 .29395E-3

1(2) 13.1 .15060E-3 .48763E-5 .22533E-3 .57726E-3

1(3) 11.8 .15495E-3 .26148E-6 .13460E-3 .96744E-3

8(1) 12.4 .20390E-3 .1215 IE-2 .24635E-2 . 14411E-3

8(2) 13.2 .19176E-3 o 10270E-3 .52610E-3 .31327E-3

8(3) 11.6 .18555E-3 .66111E-5 .21302E-3 .64436E-3

10(1) 43.0 .11977E-3 .80178E-4 .54252E-3 .22900E-3

10(2) 9.9 .20492E-3 .16608E-3 .13967E-2 .43591E-3

10(3) 0.0 .22563E-3 .43567E-4 .11195E-2 .73246E-3

11(1) 69.4 .10362E-3 .10610E-2 .21655E-2 .73922E-4

11(2) 4.4 . 17978E-3 .65611E-3 .39485E-2 .32267E-3

11(3) 0.4 .17871E-3 .45919E-4 .13073E-2 .59849E-3

13(1) 0.0 .25165E-3 .6665 IE-2 .10956E-1 .12507E-3

13(2) 9.6 .16088E-3 .17686E-3 .86927E-3 .25617E-3

13(3) 10.5 .14095E-3 .31879E-5 .20464E-3 .58662E-3

13(4) 5.2 .19190E-3 .48777E-5 .28541E-3 .78089E-3
o

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cvl

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Figure

1.

Force-elongation

curve

for

a

handsheet

specimen

of

beaten

2

Southern

kraft

pulp,

2.5

g/m

mass

per

unit

area„
I\jw ‘ jQdOd

CHART

TRAVEL

,

cm
5

4

3

2

I

0

0

0

0

0

0

0

0

FORCE , ARBITRARY UNITS

. Plots of force change per unit extension versus

force for reextension curves, figure 2.
NUJ ‘ 3DiJ0i

Figure

4.

Comparison

of

test

data

with

fitting

curves:

solid

lines,

curves

from

test,

figure

2;

dash

lines,

fitting

curves

from

eq

(4).
FRACTIONAL INCREASE IN LENGTH

F igure 5 a Plot of In vs fractional increase in specimen length,

data of table 3.

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Figure

8.

Plot

of

(x

/JO

as

a

function

of

area

density

for

Northern

Kraft

pulp

handsheets.
o

to

to

o

to

to

s CJ

o

(M

to

o

<

II! a:

Figure

9.

Plot

of

(In C

)

as

a

function

of

area

density

for

Southern

Kraft

pulp

handsheets.

Z

o

2

C

is

expressed

in

Newtons

and

density

in

g/m

.
o«

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PO

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to

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C4

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LlS

Q

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Id

££

<

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J-i 3M•H

Pm

function

of

area

density

for

Southern

Kraft

pulp

handsheets
Figure 11. (In C„) as a function of beating for Northern Kraft pulp handsheets,

° 2 o 2

C is expressed in Newtons. Density of handsheets is 2.5 g/m .

Figure 12. (xco//) as a function of beating for Northern Kraft pulp handsheets.
BEATING , I0

3

REV.

Figure 13. (In C ) as a function of beating for Southern Kraft pulp handsheets.

« o

2

C

2

is expressed in Newtons. Density of handsheets is 2.5 g/m .

BEATING , I0

3

REV.

Figure 14. (x IV) as a function of beating for Southern Kraft pulp handsheets.

c o
o

Nw HOdOJ
FORCE

CHANGE

PER

UNIT

EXTENSION

4

ARBITRARY

UNITS

Figure 16. Flots of force change per unit extension versus

force for reextension curves, figure 15.
NBS-114A (rev. 2 -ec) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

. PUBLICATION OR

REPORT NO.

NBSIR 82-2513

2. Performing Organ. Report No. Nat. B ur . Stds.

NBSIR 82-2513

3. Publication Date

June 1982

4. TITLE AND SUBTITLE

Characterizing the Interfiber Bonding of Currency Paper Pulps

5. AUTHOR(S)

J ack C . Smith

6. PERFORMING ORGANI ZATI ON (If joint or other than N BS, see instruction s) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

* inal

10/1/80 thru 9/30/81

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State. ZIP)

Bureau of Engraving and Printing

Treasury Department

Washington, DC 20401

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Specimens of low-density open-web handsheets made from woodpulp and from a currency paper pulp were tested in a' tensile tester to obtain data for

characterizing interfiber bonding. During the tests the direction of extension

was frequently reversed and the specimen reextended to obtain a series of

force-elongation curves. For woodpulp specimens the force-elongation behavior

was well represented by an exponential equation involving three parameters;

a strength parameter, a parameter proportional to average mesh size of the fiber

network and a parameter characterizing the unstrained length of the specimen. This

force-elongation behavior is consistent with the concept of a network held together

by simple bonds at fiber crossovers.

For currency pulp specimens the equation giving force as a function of

elongation comprised the sum of an exponential term and a linear term. This

behavior is consistent with the presence of an additional binding force, such as that provided by massive glued junctions or numerous bonds between microfibrils.

Therefore the interfiber bonding cannot be well characterized in terms of an average bond strength. A. force level parameter and a related elongation parameter

applicable both to woodpulps and currency pulps are suggested as an alternate

means of characterizing the strength of a test specimen.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Adhesion of paper fibers; bonding of paper fibers; paper fibers, bonding;

paper pulps, characterization; paper, tensile tests.

13. AVAILABILITY 14. NO. OF

_l Uni i mi ted x

For Official Distribution. Do Not Release to NTIS

1 1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

PRINTED PAGES

20402. 15. Price

1 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

USCOMM-DC 6043-P80


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