paper physics（下）

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1、Chapter5In-planetensilepropertiesWhentheexternalstressofpaperreturnstozeroafteraloadingcycleintotheplasticregion,bondedfibersegmentsareundercompressivestress,andfreesegmentsundertensilestress.Thisfollowsbecausefreesegmentshavenotelongatedplastically.Therefore,theymustbeundertensilestresswheneverthe

2、externalstrainislargerthanzero.Thisisthecaseafterloadingthepaperintotheplasticregion.Sincethetotalstressofthenetworkiszero,weconcludethatbondedsegmentsareundercompression.Ebeling37confirmedthegenerationoflocalcompressionsandtensionsinhisthermodynamicmeasurementsasFig.24shows.Hefoundthattheinternale

3、nergyofpaperincreasesinaloadingcycleintotheplasticregion.Theincreaseintheinternalenergyinsuchacycleequalsthemechanicalworkminusthenetheatreleasedfrompaper.Internalenergyincreasesbecausethereiselasticenergystoredinthecompressedandstretchedsegmentsalthoughtheaveragestressiszero.Inter-fiberbondsopengr

4、aduallywhenpaperstretches.Theopeningofbondsisnotthecauseforthenonlinearcurveasnotedearlier.Page,Tydeman,andHuntstudiedtheopeningofbondsunderalightmicroscope40.Mostbondsopenedgraduallyanddidnotbreakcompletelyevenwhenpaperwasstrainedtofailure.Completebondfailureswererare.Thegradualopeningofbondscanbe

5、understoodbythedistributionofinternalstresswithintheoftenirregularbondareas41,42.Thereductionofbondingareawithpaperelongationisreflectedintheopticalpropertiesofpaper.Forexample,thelightscatteringcoefficientincreases.Foragivenpaper,theincreaseinlightscatteringcoefficientislinearlyproportionaltothepl

6、asticelongationasFig.25shows43.Figure25.Lightscatteringcoefficientvs.plasticstrainofpaperinaload-elongationtest43.ModelsSincetheload-elongationbehaviorofpaperseemscontrolledbythecorrespondingfiberbehavior,onemighttrytoderiveamodelthatgivesthelinkinaquantitativeform.Forexample,inmicromechanicalmodel

7、soneconsidersatypicalfiberembeddedinahomogeneousbackground44−47.Thepredictivepowerofsuchmodelsislimitedbecauseonecannotmeasureallthedetailedpropertiesoffibersandbondsthatthemodelsrequire.Anothercomplication