PEER-REVIEWED FIBER MEASUREMENT

Defects in fibers include curl, kinks,crimps, microcompressions [1], and

various types of folds and twists [2].Defects affect both single fiber and sheetmechanical properties. Despite consider-able effort, defects in fibers remain diffi-cult to measure and their exact effects onsheet mechanical properties are hard toquantify using existing theories of thestrength of paper. Of all the differenttypes of defects in fibers, kinks, twists,and angular folds most strongly affectpaper strength [2]. These are seriousdefects across which a fiber will not beable to bear a load. A fiber with a sharpkink in it will act as two independent seg-ments within the sheet for the purposesof bearing a tensile load, reducing theeffective fiber length and therefore thesheet strength.

Page and Seth [3] examined the reduc-tion in the strength of paper made frompreviously dried fibers compared topaper made from never-dried fibers.Theyconcluded that the strength loss in papermade from previously dried fibers wasdue to a combination of loss of shearbond strength and from defects inducedin fibers during drying. The shear bondstrength loss ranged from 0% to 46%,depending on the nature of the defectsthat were assumed to have occurred inthe drying process [3].The imprecision ofthe estimate arose because the authorscould not quantify the nature and quanti-ty of the defects in the sheet fibers.

where G is the gap between the jaws,BL(G) is the breaking length, FBL is theaverage fiber breaking length, and l is theaverage fiber length. Boucai stated thatthe equation was only valid for G<0.35land gave no derivation of the equation.El-Hosseiny and Bennett [9] provided arelatively complete theory of zero- andshort-span strength that considers theeffects of distributions in the fiber length,elastic modulus, and tensile strength.However, these distribution functionsmust be known to use the theory quanti-tatively.

In the work that follows, I develop thetheory of the zero- and short-span test toallow the average load-bearing elementlength within the sheet to be determinedfrom zero- and short-span data.The term“load-bearing element” is used ratherthan “fiber” because fibers may containkinks or other defects across which loadcannot be transmitted. In such a case, it isthe lengths between these seriousdefects (load-bearing element lengths)that are important in determining themechanical properties of the sheet [1].The theory is used to examine changes inload-bearing element length with dryingtreatment and to examine whether dry-ing the fibers introduces serious defects.

ZERO-/SHORT-SPAN TEST: THEORY

We begin by defining the angle, θ as 0°

along the loading direction. If we consid-er a single, straight load-bearing element

A zero-span tensile test uses no gapbetween the jaws, while short-span ten-sile tests involve testing with a small gap(known as the span) between the jaws.Researchers have long used zero-spantests as a measure of average fiberstrength [4]. Fiber defects can have amajor influence on the zero and short-span strength. Perez and Kallmes [5]defined the probability, f

c, that a fiber

does not contribute to the zero-span testbecause of curl and concluded that, for atypical zero-span test, f

c≈ 0.4. More

recently, Mohlin and Alfredsson meas-ured the change in zero-span strengthwith fiber defects [6].An increase in thenumbers of serious defects (kinks) signif-icantly reduced the measured zero-spanstrength.This suggests that, given an ade-quate theoretical framework, we canpotentially use zero- and short-span test-ing to quantify fiber defects within asheet of paper.

The first theory of the zero-span testwas by Van Den Akker et al [4]. Theyfound that for a randomly oriented fibernetwork, the zero-span breaking length is(3/8)Ib, where I is the number of fibersthat would have spanned between thejaws if all fibers had been aligned in thedirection of the applied stress and b isthe fiber breaking load. A theoreticalexpression for the short-span strength isdue to Michie [7]. Later, Boucai [8]expressed the zero- and short-span break-ing length of an unbonded network offibers as BL(G)=(3/8)FBL(1-1.13G/l )

VOL. 2: NO. 8 TTAAPPPPII JJOOUURRNNAALL 3

Determination of load-bearing element lengthin paper using zero/short span tensile testing

WARREN BATCHELOR

ABSTRACT: This study presents an equation developed to estimate, from zero and short-span tensiletests, the average length of load-bearing elements (the distance between serious defects along a fiber length)within a sheet of paper. The equation was used to examine the effect of drying treatment on the average load-bearing element length in paper made from five furnishes: two radiata pine kraft pulps, a Eucalyptus globu-lus kraft pulp, a eucalypt neutral sulfite semichemical (NSSC) pulp, and a recycled pulp. Of the three sets ofhandsheets for each pulp, the first used never-dried pulps, the second used reslushed handsheets that hadbeen air-dried under restraint, and the third set was made from reslushed handsheets that had been ovendried. For all five furnishes, the average length of load-bearing element was approximately equal to the opti-cally measured arithmetic average fiber length and did not decrease after the fibers were dried. The resultssuggest that the reduction in the strength of paper made from previously dried fibers, compared to never-dried fibers, is not due to the introduction of serious defects during drying.

AApppplliiccaattiioonn:: This study helps explain the loss of sheet strength that occurs after paper is made from recycled fibers.

4 TTAAPPPPII JJOOUURRNNAALL AUGUST 2003

FIBER MEASUREMENT

with length, l, and random orientation, θ,within a sheet of paper, then the proba-bility of the load-bearing element cross-ing a single jaw line of width W

jis

approximately

(1)

where Lsand W

sare the length and width

of the test sheet and it is assumed thatW

j, L

s, W

s>>l. If we consider a second

jaw placed at a span, G, from the first,then if the load-bearing element hasbeen gripped by the first jaw, the proba-bility that both jaws grip the load-bearingelement is P

2=1-(1/cosθ )G/l.

If the separation between the jawshas increased by ∆G during the test, thenthe overall strain on the test section isε =∆G/G, and the strain, ε

f, in a fiber ori-

ented at θ and gripped by both jaws isε

f=εcos2 θ , provided ε is small.Therefore,

the force in this load-bearing element isF

f=ECεcos2θ where E is the fiber wall

Young’s modulus and C is the fiber wallcross-sectional area. The component ofthis force in the test direction is

Ff=ECεcos3θ (2)

If the fibers are randomly oriented,then the fiber-orientation probabilitydensity function is 2/π and the averageforce on a load-bearing element, F

av, can

be determined by multiplying Eq. 2 bythe probability P

1P

2that a fiber will be

gripped by both jaws and averaging overthe range of possible fiber orientations toyield

(3)

where A (=LsW

s) is the area of the sheet

and fcis the fraction of fibers, gripped by

both jaws, that do not bear load due toout-of-plane curl or other defects [5].The upper limit of integration occursbecause for angles beyond this value, theload-bearing element can never bridgethe gap between the jaws. In the deriva-tion of Eq. 3, only the contribution offibers gripped by both jaws are considered. Accordingly, these equationsonly apply to wetted sheets, where there is minimal fiber-fiber bonding.

Therefore, this theory is directly applica-ble to the measurements on the rewettedsheets presented later in this paper.

Integrating Eq. 3 yields

(4)

A first-order Taylor series expansion inpowers of G/l is accurate for G<0.7l andyields

(5)

where the factor 32/9π is numericallyequal to 1.13 and this equation is similarto that given by Boucai [8].

If there are I(G) load-bearing ele-ments that satisfy the condition l>32G/9π, then the total force at a given strain,F (ε, G), is given by

(6)

where the index, k, denotes each of theI(G) distinct load-bearing elements, eachwith different Young’s modulus andlength.This can then be rewritten as

(7)

where EClG

is the average value of EClfor the set of I(G) fibers.We cannot usethis equation to predict the sheetstrength in a zero-/short-span test,because sheet-breaking strain and f

care

unknown. However, as will be shown,we can extract considerable useful information.

If G=0 then I(0) is the total number ofload-bearing elements within the sheet,which is given by

(8)

where B is the sheet grammage, ω is theaverage coarseness of the fibers, and l

0

is the arithmetic average length of load-bearing elements within the sheet.

If, for the individual load-bearing ele-ments, the value of EC is largely inde-pendent of the length of the load-bearingelement, we can make the followingapproximation:

(9)

Substitution of Eqs. 8 and 9 into Eq. 7and setting G=0 yields

(10)

and the derivative of F(ε ,G) with respectto G at G=0 is

(11)

where it has been assumed that EC0and

I(0) are independent of G when G<< l0.

Therefore, the arithmetic averagelength of load-bearing elements in thesheet, l

0is given by

(12)

where εfrac

is the strain at which fractureoccurs.Thus, by measuring the breakingload as a function of the span betweenthe jaws, G, we can determine the aver-age length of the load-bearing elementswithin the sheet of paper.This is an inter-esting result, as no method of doing thishas previously been presented.

EXPERIMENTALFive pulps were tested to evaluate thetheory. Amcor Research and TechnologyCentre supplied four commercial pulpsfrom Amcor mills: two unbleached radia-ta pine softwood kraft pulps (called radi-ata pine kraft No. 1 and No. 2), anunbleached, neutral sulfite semichemical

VOL. 2: NO. 8 TTAAPPPPII JJOOUURRNNAALL 5

(NSSC) eucalypt (mixed species) pulp,and an unbleached recycled pulp. AEucalyptus globulus pulp was also used.This had been pulped in a laboratorydigester and then oxygen bleached to akappa number of 17.9. All pulps exceptradiata pine kraft No. 2 had been storednear 0°C. Radiata pine kraft pulp No. 2was collected directly from a brownstock washer at a kappa number of 45.All handsheets used in subsequent test-ing were then made within a week of collection.

We used a British Handsheet machineto make 60 g/m2 handsheets under stan-dard conditions, except that the sampleswere not refined in a PFI mill. We madethree sets of handsheets for each furnish.The first set of handsheets, was madeand then air-dried under restraint (in theresults, these are called never/air dried).After drying the sheets were used fortesting. The second set of handsheetswas air dried under restraint beforebeing reslushed, formed into handsheetsagain, and air dried under restraint again(called air/air dried).The last set of hand-sheets was allowed to dry unrestrainedin an oven, before being reslushed andformed into handsheets to be air driedunder restraint (called oven/air dried).

Fiber length measurements on thewet starting pulps were made using aKajaani FS 200. For the waste and thepine kraft No. 1 pulps, fiber length meas-urements were also made on samplestaken from the two reslushed pulps. AnInstron Universal Tester was used tomeasure tensile strength. The zero- andshort-span measurements were made onrewetted samples using a Pulmac zero-and short-span tester.The zero- and short-span measurements were generally madeaccording to AS/NZS 1301.459rp:1998,except that the pulps were not refined ina PFI mill before testing.

RESULTS AND DISCUSSIONFFiigguurreess 11--55 show the results of the zero-/short-span measurements for the fivefurnishes. Each figure shows threecurves, one each for the never/air dried,air/air dried, and oven/air dried sets ofhandsheets. Figures 1-5 show little differ-ence between the zero- and short-spanstrengths for the handsheets prepared bythe different methods (never/air dried,air/air dried, and oven/air dried). This isconsistent with literature indicating thatdrying has little effect on the zero-spanstrength [10, 11]. Differences betweenthe three curves are smallest in Fig. 1,

which shows the data for the NSSC euca-lypt pulp. There is also very little differ-ence between the curves for the euca-lypt kraft pulp (Fig. 2). Figure 3 (wastefurnish) shows that the never-/air-driedsheets were weaker than the air-/air-dried sheets at all spans, with the oven-/air-dried sheets generally having inter-mediate strength.The pine results showdifferent trends for the two pulps. Forradiata pine kraft No.1 (Fig.4), the never-/air-dried sheets generally had the lowestzero-/short-span strength. This is also incontrast to the measurements on radiatapine kraft No. 2 (Fig. 5), where very littledifference can be seen in the zero-/short-span strength for the never-/air-dried andthe air-/air-dried sheets,but the oven-/air-dried sheets had uniformly lower zero-/short-span strengths.

A partial explanation for the differ-ences between the two sets of pine kraftdata may be that radiata pine kraft No. 1had deteriorated while in storage.Evidence for this comes from FFiigg.. 66,which shows the sheet tensile strengthfor the five furnishes and the three meth-ods of preparing the handsheets. In Fig.6,all of the furnishes (except radiata pinekraft No. 1) show a common trend withthe never-/air-dried sheets the strongest

TE

NS

ILE

IN

DE

X,

Nm

/g100

908070605040302010

00 0.2 0.4 0.6

SPAN, mm

Never/Air driedAir/Air driedOven/Air Dried

1. Tensile index vs. span for eucalypt

NSSC handsheets prepared from

never-dried, air-dried, and oven-dried

pulps.

TE

NS

ILE

IN

DE

X,

Nm

/g

160

140

120

100

80

60

40

20

00 0.2 0.4 0.6

SPAN, mm

Never/Air driedAir/Air driedOven/Air Dried

2. Tensile index vs. span for

Eucalyptus globulus kraft handsheets

prepared from never-dried, air-dried,

and oven-dried pulps.

TE

NS

ILE

IN

DE

X,

Nm

/g

80

70

60

50

40

30

20

10

00 0.2 0.4 0.6

SPAN, mm

Never/Air driedAir/Air driedOven/Air Dried

3. Tensile index vs. span for waste

paper handsheets prepared from

never-dried, air-dried, and oven-dried

pulps.

TE

NS

ILE

IN

DE

X,

Nm

/g

140

120

100

80

60

40

20

00 0.2 0.4 0.6

SPAN, mm

Never/Air driedAir/Air driedOven/Air Dried

4. Tensile index vs.span for radiata

pine kraft No. 1 handsheets prepared

from never-dried, air-dried, and oven-

dried pulps.

TE

NS

ILE

IN

DE

X,

Nm

/g180

160

140

120

100

80

60

40

20

00 0.2 0.4 0.6

SPAN, mm

Never/Air driedAir/Air driedOven/Air Dried

5. Tensile index vs. span for radiata

pine kraft No. 2 handsheets prepared

from air-dried once, air-dried twice,

and oven-dried pulps.

TE

NS

ILE

IN

DE

X,

Nm

/g

70

60

50

40

30

20

10

0NSSC Waste Eucalypt

kraftPineNo.1

PineNo. 2

Never/Air driedAir/Air driedOven/Air Dried

6. Sheet tensile index measured from

handsheets prepared from never-

dried, air-dried, and oven-dried pulps

for the five different furnishes.

6 TTAAPPPPII JJOOUURRNNAALL AUGUST 2003

FIBER MEASUREMENT

and the oven-/air-dried sheets the weak-est, which is consistent with generalobservations in the literature. In the caseof radiata pine kraft No. 1, both thenever-/air-dried sheets and the air-/air-dried sheets show identical tensilestrengths, possibly indicating that theradiata pine kraft No.1 had hornified dur-ing storage.

To determine the average length ofload-bearing element using Eq. 12, thezero-span strength and the slope of thestrength versus span curve at zero spanmust be determined.This is complicatedby the presence of an unknown residualspan, which must be added to all of thespans.The residual span is the distance infrom the jaw edge required to fully holdthe fiber and will depend on clampingpressure, the paper-jaw coefficient offriction, the sheet density, and the forceat which the sample breaks. In theabsence of an accurate way to measurethe residual span, load-bearing elementlengths were calculated using the resid-ual span of 0.2 mm, as proposed byBoucai [12] and Cowan [13].

If the residual span is 0.2 mm, thenthis must be added to all of the spans,giv-ing a range of spans of 0.2-0.8 mm. It isthen necessary to extrapolate the data toa span of zero, in order to use Eq. 12.TTaabbllee II shows the load-bearing elementlengths determined using three of sever-al methods investigated for fitting thedata. Given the limited number of datapoints, I decided to use only linear orquadratic functions to perform the fits.

The theory developed in this paper sug-gests that the fitting should differ for theshort and long fiber furnishes. For thelong fiber pulps (radiata pine kraft No. 1and No. 2) where l

0>>G, we assume that

ECG, l

G,and I(G) are independent of G.

This implies from Eq. 7 that the zero- andshort-span strength will be linearlydependent on G.Table I shows the datafor two linear fits, one a linear fit of thefull set of data and the other a linear fit toa restricted set of data (spans:0.2-0.4 mmmeasurements at nominal spans from0.0-0.2 mm).This last fit is likely to pro-vide the most accurate fit, as the aboveassumptions are not true at larger spans.For the short fiber pulps, EC

G, l

G, and

I(G) are not independent of G at anyspan, making the dependence of thezero- and short-span strength on G diffi-cult to predict without knowledge of thedistribution of fiber properties.Therefore, a quadratic function was cho-sen for the short fiber pulps, which wasgenerally sufficient to accurately repre-sent the data across its range.

TTaabbllee IIII compares the load-bearingelement lengths from Table I with fiberlengths measured by a Kajaani FS 200.The load-bearing element lengths usedfor comparison with the optical fiberlength data are highlighted with a graybackground in Table I.The correspondingvalues in Table II are similarly highlight-ed. Both the arithmetic fiber length andthe length-weighted fiber length aregiven for comparison.The data in Table IIgenerally show a reasonable match

between the measured arithmetic fiberlength and the average length of load-bearing element. In 11 of the 15 data setsmeasured here, the average load-bearingelement length calculated from fittingthe zero-/short-span data agreed to with-in 0.2 mm with arithmetic fiber lengthmeasured optically. The best matchbetween the measured arithmetic fiberlength and the average load-bearing ele-ment length occurs for the never-/air-dried samples.The worst match was forthe oven-/air-dried pine kraft No.1 sheetswhere the estimated load-bearing ele-ment length was 1.82 mm and the arith-metic average fiber length was 1.18 mm.Furthermore, when the average load-bearing element length is examined fordifferent pulp drying treatments, there isno reduction in load-bearing elementlength with increasing severity of dryingtreatment. Indeed, for all five furnishes,the average load-bearing element lengthcalculated from the fits is somewhathigher for the oven-/air-dried sheets thanfor the never-/air-dried sheets. It is notclear why an increasingly severe dryingtreatment would have caused the load-bearing element length to increase.Remember that these results wereobtained on rewetted papers. Thereremains the question as to the applica-bility of the results to dry paper, as mois-ture often weakens fibers [14]. However,as the load-bearing element length isdetermined from a strength ratio (Eq.12), any change in fiber strength withwetting will have no effect on the

I. Load-bearing element length (mm) determined from different methods of fitting for a residual span of 0.2mm.

NEVER/AIR DRIED AIR/AIR DRIED AIR/OVEN DRIED

LLiinneeaarr,, LLiinneeaarr,, LLiinneeaarr,,QQuuaaddrraattiicc 00--00..44 mmmm LLiinneeaarr QQuuaaddrraattiicc 00..00--00..44 mmmm LLiinneeaarr QQuuaaddrraattiicc 00--00..44 mmmm LLiinneeaarr

Eucalypt NSSC 0.61 0.82 0.97 0.74 0.90 1.02 0.69 0.86 0.99Eucalypt kraft 0.67 0.92 1.04 0.79 1.00 1.02 0.74 0.96 1.02Waste 0.63 0.82 1.26 0.73 0.90 1.26 0.75 0.92 1.23Pine No. 1 1.00 1.19 1.97 1.33 1.32 2.02 1.75 1.82 1.88Pine No. 2 0.89 1.29 1.69 1.26 1.21 1.83 1.24 1.50 1.71

II. Comparison between load-bearing element length and optically measured fiber lengths. Values in italics were not

measured but have been assumed to be identical to those measured optically for the never-dried pulps.

NEVER/AIR DRIED AIR/AIR DRIED OVEN/AIR DRIED

LLooaadd--bbeeaarriinngg LLeennggtthh LLooaadd--bbeeaarriinngg LLeennggtthh LLooaadd--bbeeaarriinngg LLeennggtthhAArriitthhmmeettiicc,, eelleemmeenntt wweeiigghhtteedd,, AArriitthhmmeettiicc,, eelleemmeenntt wweeiigghhtteedd,, AArriitthhmmeettiicc,, eelleemmeenntt wweeiigghhtteedd,,

FFSS 220000 lleennggtthh,, ffiitt FFSS 220000 FFSS 220000 lleennggtthh,, ffiitt FFSS 220000 FFSS 220000 lleennggtthh,, ffiitt FFSS 220000Eucalypt NSSC 0.63 0.61 0.81 0.63 0.74 0.81 0.63 0.69 0.81Eucalypt kraft 0.57 0.67 0.71 0.57 0.79 0.71 0.57 0.74 0.71Waste 0.61 0.63 1.14 0.63 0.73 1.17 0.59 0.75 1.10Pine No. 1 1.23 1.19 2.19 1.27 1.32 2.21 1.18 1.82 2.15Pine No. 2 1.56 1.29 2.43 1.56 1.21 2.43 1.56 1.50 2.43

VOL. 2: NO. 8 TTAAPPPPII JJOOUURRNNAALL 7

FIBER MEASUREMENT

calculated load-bearing element length,because all zero- and short-spanstrengths will be reduced proportionally.

Thus, no reduction is observed inTables I and II in load-bearing elementlength with drying treatment. Thisimplies that the loss of sheet strengthcommonly observed the first time a pulpis dried is not due to serious defects,such as kinks, being set into fibers, there-fore reducing the load-bearing elementlength. This is consistent with results[15] suggesting that the major cause ofthe strength loss in drying is a reductionin the fiber-fiber shear bond strength.Another possible contributor to strengthloss upon drying [3] is the production ofminor defects such as microcompres-sions, which affect the fiber mechanicalproperties without changing the load-bearing element length.

CONCLUSIONSThis study described an equation devel-oped to allow the average length of load-bearing elements within a sheet of paperto be estimated from zero and short-spantensile tests. This was used to examinethe effect of drying treatment on theaverage length of load-bearing elementin five furnishes: two radiata pine kraftpulps, a eucalyptus globulus kraft pulp, aeucalypt NSSC pulp, and a recycled pulp.For all five furnishes, the average lengthof load-bearing element was approxi-mately equal to the measured arithmeticaverage fiber length for the never-/air-dried pulps. The average length of load-bearing elements increased as the harsh-

ness of the drying treatment intensified.The results imply that the reduction ofstrength of sheets made from previouslydried compared to never-dried pulps isnot due to the introduction of seriousdefects, such as kinks, into the fibers dur-ing drying.

ACKNOWLEDGEMENTSI gratefully acknowledge many useful dis-cussions with Daniel Ouellet (Paprican),Russell Allan (Amcor Research andTechnology), and Bo Westerlind (SCAGraphic Research). Some of the pulpswere supplied by and the handsheetsmade at the Amcor Research andTechnology Centre. The experimentalassistance of Glenda Spencer, MichaelBriggs, and Geoff Ennis is gratefullyacknowledged. TJ

LITERATURE CITED1. Page, D. H., Seth, R. S., Jordan, B.

D., and Barbe, M. C., “Curl,Crimps, Kinks andMicrocompressions in Pulp Fibers- Their Origin, Measurement andSignificance,” Papermaking RawMaterials, Punton, V., ed.,Mechanical EngineeringPublications, London, 1985, pp.183-227.

2. Mohlin, U. B., Dahlbom, J., andHornatowska, J., TAPPI J., 79(6):105(1996).

3. Seth, R. S. and Page, D. H., TAPPIJ., 79(9): 206(1996).

4. Van Den Akker, J. A., Lathrop, A.L., Voelker, M. H., and Dearth, L. R.,TAPPI J., 41(8): 416(1958).

5. Perez, M. and Kallmes, O. J., TAPPIJ., 48(10): 601(1965).

6. Mohlin, U.-B. and Alfredsson, C.,Nordic Pulp Paper Res. J., 5(4):172(1990).

7. Michie, R. I. C., Textile Res. J.,33(6): 403(1963).

8. Boucai, E., “The Zero-Span Test: ItsRelation to Fiber Properties,”International Paper PhysicsConference, Mout Gabriel, QC,1971, pp. 3-5.

9. El-Hosseiny, F., and Bennett, K., J.Pulp Paper Sci., 11(4): J121(1985).

10. Gurnagul, N., TAPPI J., 78(12):119(1995).

11. Seth, R. S., “The differencebetween never-dried and driedchemical pulps,” Solutions! forPeople, Processes and Paper, 1(1):95(2001); full text atwww.tappi.org.

12. Boucai, E., Pulp Paper Mag. Can.,72(10): 73(1971).

13. Cowan, W. F. and Cowdrey, E. J. K.,TAPPI J., 57(2): 90(1974).

14. Gurnagul, N. and Page, D. H.,TAPPI J., 72(12): 164(1989).

15. Gurnagul, N., Ju, S., and Page, D.H., J. Pulp Paper Sci., 27(3):88(2001).

Received: July 20, 2000Revised: February 14, 2002Accepted: February 18, 2002

Results of this study were originally pre-sented at the 1999 International PaperPhysics Conference.

This paper is also published on TAPPI’sweb site <www.tappi.org> and summa-

rized in the August Solutions! forPeople, Processes and Paper magazine

(Vol. 86 No. 8)

INSIGHTS FROM THE AUTHORThe idea for this study developed as I was researchingpaper strength and looking at how the changes in fiberproperties caused by refining affect strength. The zero-span strength is used in equations for paper strength. Ibecame interested in how the measured zero-spanstrength relates to the properties of the fibers.

My previous work focused mainly on low-consisten-cy refining. Following this work, the emphasis of myresearch shifted more towards fiber and sheet mechan-ical properties.

One of the most difficult aspects of this work was try-ing to take into consideration distributions in fiberproperties during work on the theory.

I had expected that one of the causes of strength losson drying would be the introduction into the fibers of

large defects such as kinks and twists. The researchpresented here shows that this is not true.

Although mills may not directly benefit from thisresearch at the moment, the information presentedhere is one more step toward understanding the loss ofsheet strength that occurs after paper is made fromrecycled fibers.

As a next step, I worked on a method to measurefiber stress-strain properties usingzero- and short-span tensile tests. — Warren Batchelor

Batchelor is with the Australian Pulp andPaper Institute, Department of ChemicalEngineering, P.O. Box 36, Monash University,3800 Victoria, Australia. Email Batchelor atwarren.batchelor@eng.monash.edu.au. Batchelor