水射流加工方式

ORIGINALARTICLE

AbrasivewaterjetmachiningsimulationbySPHmethod

WangJianming&GaoNa&GongWenjun

Received:10September2009/Accepted:4January2010/Publishedonline:29January2010#Springer-VerlagLondonLimited2010

AbstractAbrasivewaterjetmachining(AWJM)isanon-conventionalprocess.Themechanismofmaterialremov-inginAWJMforductilematerialsandexistingerosionmodelsarereviewedinthispaper.Toovercomethedifficultiesoffluid–solidinteractionandextra-largedefor-mationproblemusingfiniteelementmethod(FEM),theSPH-coupledFEMmodelingforabrasivewaterjetmachin-ingsimulationispresented,inwhichtheabrasivewaterjetismodeledbySPHparticlesandthetargetmaterialismodeledbyFE.Thetwopartsinteractthroughcontactalgorithm.Thecreativityofthismodelismulti-materialsSPHparticles,whichcontainabrasiveandwaterandmixtogetheruniformly.Tobuildthemodel,arandomizedalgorithmisproposed.Thematerialmodelfortheabrasiveisfirstpresented.Utilizingthismodel,abrasivewaterjetpenetratingthetargetmaterialswithhighvelocityissimulatedandthemechanismoferosionisdepicted.Therelationshipbetweenthedepthofpenetrationandjetparameters,includingwaterpressureandtraversespeed,etc.,areanalyzedbasedonthesimulation.Theresultsagreewiththeexperimentaldatawell.Itwillbeabenefittounderstandtheabrasivewaterjetcuttingmechanismandoptimizetheoperatingparameters.

KeywordsAbrasivewaterjetmachining(AWJM).Randomizedalgorithm.CouplingSPH/FEM.Abrasivematerialmodels

1Introduction

Abrasivewaterjet(AWJ)cutting,duetoitsvariousdistinctadvantagesoverothercuttingtechnologies,suchasnothermaldistortion,highmachiningversatility,highflexi-bility,andsmallcuttingforces[1],isbeingincreasinglyusedinvariousindustries.

Forabrasivewaterjetcuttingprocessinfluencingbyseveralprocessparameters,suchashydraulic,abrasive,target,andcuttingparameters,etc.,proposingtheappropri-atemodelingforAWJmachiningisaheatstudyfield.Bothanalyticalandempiricalmethodshavebeenused,includingfuzzylogicalgorithms[2]andreactionkinetics[3],toresearchtheAWJmachiningprocess[4].However,bothempiricalmodelsandheuristicapproachesneedextensiveexperimentdata,whichisamajordrawbackduetohighexpenseandlimitedapplicability.Thereareafewliter-atures[5,6]focusedonthenumericalsimulationsoftheimpactprocess,whichoftenusefiniteelementmethod(FEM)withasingleabrasivetocalculatetheerosivewearduringabrasivewaterjetmachining,andtheabrasivewasmodeledasarigidballignoringitsmaterialproperties.Asitisjustamicro-modelingstudywithoutconcludingthefactorsofmachiningprocessorthemechanismoftheAWJmachining.UsingtheFEMmethodtosimulateAWJMprocess,whichisthefluid–solidimpactingproblemsandaccompaniedwithlargedeformation,mayleadtothedistortionofthemeshandwasdiscussedinthearticle[7].Toovercometheabovedifficulties,wedevelopedacoupledmethodofsmoothedparticlehydrodynamic(SPH)

W.Jianming(*):G.Na:G.Wenjun

SchoolofMechanicalEngineering,ShandongUniversity,Jinan250061,China

e-mail:wangjianming@sdu.edu.cnG.Na

e-mail:gaoxiaodou0116@hotmail.com.cnG.Wenjun

e-mail:gwjagassi@yahoo.com.cn

228andFEM.TheappealofSPHforhigh-velocityAWJimpactisthatitisamesh-freemethodandbelongstoLagrangianframe,whichdonotneedmeshconnectivitysoastoallowseveremeshdistortions.BySPHmethod,thecontinuousmaterialisexpressedbyaseriesofparticles,whichcarrysomephysicalquantitiessuchasmassandvelocity.Thischaracterisregularlyadaptedforhydrokineticsproblems.JohnsonandBeisselappliedSPHinhigh-velocityimpact-ingproblemsandgotencouragingresults[8–10].SPHcouldovercomethedefectofFEMandbelongstoLagrangianframedescription,thus,thecomputationwillbemorecompactandautomatic.

SPH-coupledFEmethod-basedmodelingforabrasivewaterjetmachiningsimulationispresentedinthispaper,inwhichtheabrasivewaterjetismodeledbySPHparticlesandthetargetmaterialismodeledbyfiniteelements.Thetwopartsinteractbycontactalgorithmof“nodes-to-surface”inLS-DYNA.Themulti-materialsSPHparticlesmodeling,inwhichtheabrasivesandwatermixtogetheruniformly,isfirstproposed.Therandomizedalgorithmfortheactualmasspercentageoftwomaterialsisused.BasedontheexplicitprogramLS-DYNA,thehybrid-codeofSPHandFEMisconductedtosimulatethemachiningprocess,andthesimulationresultistestedbytheexperimentaldata[11].

2Basictheory2.1BasictheoryofSPH

Insteadofagrid,SPHusesakernelinterpolationto

approximatethefieldvariablesatanypointinadomain.Anestimateofthevalueofafunctionf(x)atthelocationxisgiveninacontinuousformbyanintegraloftheproductofthefunctionandakernel(weighting)functionW(x−x′,h)

Z

hfðxÞi¼

fðx0ÞWðxÀx0;hÞdx0

ð1Þ

Ω

WherehfðxÞiAkernelapproximationhSmoothinglength

x′

Newindependentvariable.

Thekernelfunctionusuallyhasthefollowingproperties:Compactsupport,whichmeansthatitiszeroevery-wherebutonafinitedomaininsidetherangeofthesmoothinglength2h:WðxÀx0;hÞ¼0

for

󰀂󰀂xÀx0󰀂

󰀂!2h

ð2Þ

IntJAdvManufTechnol(2010)50:227–234

Normalized:Z

WðxÀx0;hÞdx0¼1

ð3Þ

TheserequirementsensurethatthekernelfunctionreducestotheDiracdeltafunctionwhenhtendstozero:

hlim!0

WðxÀx0;hÞ¼dðxÀx0;hÞð4Þ

Andtherefore,itfollowsthat:

hlim!0

hfðxÞi¼fðxÞð5Þ

Ifthefunctionf(x)isonlyknownatNdiscretepoints,theintegralofEq.1canbeapproximatedbyasummation:

Z

hfðxÞi¼

fðx0

ÞWðxÀx0

;hÞdx0

%XNmjfÀxÁÀ

0ÁjWxÀxj;hΩ

j¼1ri

j

ð6Þ

Wheremj/ρjisthevolumeassociatedtothepointjor

particlej.

Equation7constitutesthebasisofSPHmethod.Thevalueofavariableataparticle,denotedbysubscripti,iscalculatedbysummingthecontributionsfromasetofneighboringparticles(Fig.1),denotedbysubscriptjandforwhichthekernelfunctionisnotzero:

hfðxXNmiÞi¼

jfÀxÁÀ

Àx0ÁjWxij;hið7Þ

j¼1rj

2.2Variablesmoothinglength

Iflargedeformationsoccur,particlescanlargelyseparatefromeachother.Ifthesmoothinglengthremainsconstant,theparticlespacingcanbecomesolargethatparticleswill

Fig.1Setofneighboringparticles

IntJAdvManufTechnol(2010)50:227–234notinteractanymore.Ontheotherhand,incompression,toomanyparticlesmightenterintheneighboringofeachother,whichcanslowdownthecalculationsignificantly.Therearemanywaysdealingwithhinwhichthenumberoftheneighboringparticlesremainsconstantrelatively.Thesimplestapproachistoupdatethesmoothinglengthaccordingtotheaverageddensity

󰀅󰀆1h¼hr0

0dr

ð8Þ

Whereh0Initialsmoothinglengthρ0InitialdensityρCurrentdensity

d

Thenumberofdimensionsoftheproblem.

Benzsuggestedanothermethodtoevolvethesmoothinglength,whichtakesthetimederivativeofthesmoothingfunctionintermsofcontinuityequationdh1hdrdt¼Àdrdt

ð9Þ

Equation9canbediscretizedusingtheSPHapprox-imationsandcalculatedwiththeotherdifferentialequationsinparticles.

2.3CoupledSPHwithFEA

ThecouplingSPHwithFEAisimplementedbymeansofthecontactalgorithmof“CONTACT_ERODING_NODES_TO_SURFACE”inLS-DYNA.ThecouplingprocessisshowninFig.2:theleftpartrevealsthecomputationprocessofSPHandtherightpartindicatestheFEAprocess[12–14].

3Modelingdescription

AnAWJimpactingaductilemetalplatewillbemodeledandsimulatedtoinvestigatethemachiningmechanismandparametersinfluence,includingjetvelocityandtraversespeedetc.Themodelparameterscomefromtheexperi-mentaldata[11]tobeconvenientforcomparisons.Thetargetwasa3-Dmetallicblock(CarbonsteelAISI1018).TheAWJcuttingconditionislistedinTable1.Inthissection,modelingmethod,materialmodelsandSPHparticlesmodelingfortwokindsofmaterialsarediscussed.3.1Modelingmethod

ThecoupledSPH/FEMmethodisusedforabrasivewaterjetmachiningsimulation.Theabrasivewaterjetis

229

Fig.2CouplingSPHwithFEA

modeledbySPHparticlesandthetargetmaterialismodeledbyfiniteelements.SPHcanbeseenasaspecialelementandisembeddedby“ELEMENT_SPH’’inLS-DYNA,wheretheSPHelementiscontrolledbynode(particle)numberandnode(particle)mass,andthetwopartsareinteractedbycontactalgorithm.Theparticleforceimposesonthesurfaceoffiniteelementbycontacttypeof‘‘CONTACT_ERODING_NODES_TO_SURFACE’’inLS-DYNA,wheretheslavepartisdefinedwithSPHparticlesandthemasterpartisdefinedwithfiniteelements.However,thedifficultyoftheSPHparticlesmodelingisthatitcontainstwokindsofmaterialparticles,abrasiveandwater,andanewalgorithmisproposedtoresolvetheprobleminthefollowingsubsection.3.2Materialmodels3.2.1Watermaterialmodels

ThemodelingforwaterisbasedonanSPHformulationofmovement,thewatermaterialmodelleadstotheselectionoftheNull-MaterialmodelinLS-DYNA,whichallowsequationsofstatetobeconsideredwithoutcomputing

Table1AWJcuttingconditionsNo.Parameter

Value1Waterjetpressure,P(Pa)100–350

2Waterjetnozzle,dn(mm)0.333Traverserate,u(mm/min)234Abrasiveflowrate,ma(g/s)2.565Standoffdistance,S(mm)36AbrasivemeshNo.(garnet)807

Mixingtubediameter,dm(mm)

1.02

230deviatoricstressesandaccordswiththehydrodynamicbehaviorlaw.WeusetheMie–GrueisenequationofstateforthewatermaterialmodelsinEq.10(refertoRef.[15]),anditscoefficientsareshowninTable2(refertoRef.[16].)

rÂÀgÁÃP¼hOC2m1þ1ÀO2mÀa2m21ÀðS1À1ÞmÀS2mm3

i2þðgOþamÞmþ1ÀS2ðmþ1Þ2ð10Þ

3.2.2Abrasivematerialmodels

ThemodelingfortheabrasiveisalsobasedonanSPHformulationofmovement.TheNull-Materialmodelisusedforabrasivematerialtoo.Consideringthematerialbehaviorofabrasive,thelinearpolynomialequationofstateisproposed,whichdefinestherelationshipbetweenpressureanddensity,anditisderivedfromRefs.[17].ThePvs.ρrelationshipisdefinedas

P¼C2

0ðrÀrmixÞ

ð11Þ

WhereC0Speedofsoundofsolidabrasive

ρmixTheinitialincompactabrasivedensitywhichincludessomeair

ρ

Thecurrentabrasivedensitywhichincludessomeair

And

rmix¼ð1Àa0Þraþa0rair

ð12Þ

aV0¼airVð13Þ

WhereρaThedensityofsolidabrasiveρairThedensityofairVairThevolumeoftheairV

The

totalvolume

Table2ValuesofthecoefficientsinMie–GrueisenequationusedforwaterNO.Parameter

Value1Velocityofsound,C(m/s)1,480

2Grueisengamma,y00.49343volumecorrection,a1.3974Coefficient,S12.565Coefficient,S2−1.9866Coefficient,S30.22867

Density,ρ0(kg/m3)

1,000

IntJAdvManufTechnol(2010)50:227–234

TransformtheEq.11totheformofthelinear

polynomialequationofstate,whichisexpressedas

P¼aÀþbÁ

1mþa2m2þa3m3þb1m2m2þb3m3r0eð14ÞWherem¼

rrÀ1

ð15Þ

mix

SubstitutingEq.15intoEq.11,wecangainthefinallinearpolynomialequationofstateoftheabrasive:

P¼C2

0rmixm

ð16Þ

WhereC0isthespeedofsoundofsolidabrasive,itsvalueis9.03km/sandcanbeobtainedfromRef.[18].3.2.3Targetmaterialmodels

Themetallictargetisconsidertobekinematichardeningmodel,whosepropertiesparametersarelistedinTable3.Innumericalsimulation,theremovalofelementmethodisusedtoimitatethecrackgrowthandmaterialfailure,andthecriterionofmaterialfailureisspecifiedinthematerialmodel.Totheplastichardeningmodelfortarget,theplasticfailurestrainissetasacriteriontoexaminetheprobabledamagedzone.ThisstrategywasalsoadoptedinRef.[19].3.3SPHparticlesmodelingfortwokindsofmaterialsusingtherandomizedalgorithm

Tomodelthetwomaterialsofabrasiveandwater,theactualmasspercentageoftwomaterialsintheSPHparticlesmodelingisthekeypoint.Anewwaytoachievetheparticlesmodelingisproposedinthispaper.Firstly,thevolumetricflowratesoftheabrasiveandwateraccordingtotheirmassflowratearecalculated;secondly,basedonthevolumetricflowratesofthetwomaterials,thevolumepercentageofeachmaterialcanbedetermined,thevolumepercentagedeterminestheparticlenumbersoftwomaterialsandthediameterofsingleSPHparticleisdeterminedaccordingtoabrasivesizeintheexperiment.Consequently,thewholenumberofSPHparticlesisgained.Finally,the

Table3MaterialpropertiesfortargetmaterialsNo.Parameter

Value1Materialdensity,ρ3(kg/m3)7,8602Elasticitymodule,E(GPa)2103Poisson'scoefficient,v0.2844Yieldstress,σy(MPa)2605Tensilestrength,σb(MPa)3506

Failurestrain,ε

0.33

IntJAdvManufTechnol(2010)50:227–234Fig.3Flowchartforrandomizedalgorithm

randomizedalgorithmisutilizedtorealizethepercentageoftwokindsofSPHparticlenumbersandtheirdistribution.ThealgorithmflowchartisshowninFig.3.Withtheirparticlenumbersanddensity,theSPHparticlesincludingtwokindsofmaterialspropertiesareestablished,whichcanbeseeninFig.4.Theblueparticlesdenotethematerialsofabrasiveandthegreenonesrepresentthewater.

Fig.4SPHparticlesfordifferentmaterialdeterminedbyrandomizedalgorithm

231

Fig.5SPH/FEAmodelforAWJsimulation.aInitialmodel.b,c,dAWJMsimulationresultsatdifferenttime

4Simulation,numericalresult,anddiscussionsAccordingtotheexperimentalconditions[11],thecarbonsteelAISI1018ischosenastheworkpiecematerialfortheexperiment.Thedimensionofthesampleis:100mminlength,13mminwidth,and65mminheight.TheAWJ

Fig.6RelationshipbetweentheAWJvelocityVeandthepressureP

232

Fig.7Erosionprocessinthecentriccross-sectionoftarget

IntJAdvManufTechnol(2010)50:227–234

conditionsusedinthisstudyarelistedinTable1.Amodelofabrasivewaterjetmachiningmodeliscreatedanditssimulationresultsarecomparedwiththeexperimenttovalidatethecorrectionofthemodeling.ThemodelingmethodisdepictedinSection3,theabrasivewaterjetismodeledbySPHparticleswithabrasiveandwater,thetargetmaterialismodeledbyfiniteelements,whichisshowninFig.5a.Theabrasivewaterjethasthediameterof1.02mmandtheheightof76mm,thestand-offdistanceis3mm.Thereareatotalof2,399SPHparticlesinthemodel.ThediameterofasingleSPHparticleisdeterminedaccordingtoabrasivesizeintheexperiment.TheamountanddistributionofSPHparticlesisdeterminedbytherandomizedalgorithm.Thetargetmodelisinthesizeof100×13×65mm,meshedbyeight-nodesbrickelement,thenumberofelementsis11,960withthenodesof30,184.Thenon-reflectingconditionsareadoptedontheboundaryoftargettoeliminatethereflectionofstresswaves,bywhichtheinfiniteboundaryconditionscanbesatisfied.TheSPHparticlesandtargetelementsareinteractedbycontactalgorithm.TheinitialvelocityofSPHparticles,VeisdeterminedaccordingtothewaterpressureP,varyingfrom100to350MPainTable1,therelationshipbetweenVeandPisshowninFig.6.TheVeisanimportantparameterforthemodelanditcanbeapproximatedbythemomentumtransferequationbe-tweenincomingandexitofabrasivewaterjetnozzle[20,21].ThetraversespeeduisalsogiventotheSPHparticles

Fig.8VariationofcutdepthhwithpressureP

Fig.9Relationshipbetweenjettraverserateandthedepthofpenetration,ma=0.45kg/min

IntJAdvManufTechnol(2010)50:227–234asanotherinitialvelocity.Figure5b,c,darethesimulationresultsatdifferenttimesundera100-MPapressure.

Figure7showsthecentriccross-sectionoftheimpactareaatdifferenttimeunderthepressure100MPa.Theplasticdeformationwasfoundtobelocalizedintheimpactarea.Itshowsthatthedepthofcutincreasesasthetimeincreasing.Asaresult,theplasticdeformation,intheformofacrater,significantlyincreasesuptoitsmaximumdepthatthetimet=255μs.

Figure8showstheeffectofthepressureonthecutdepthinAWJM.Ingeneral,thedepthofpenetrationincreaseswithwaterpressure,asmoreenergywillbeabletoremovemorematerial.Thisincreaseisalmostinalinearformatinitialstage,andasthewaterpressurefurtherincreases,therateofincreasedeclines,whichisduetothefactthatahigherwaterpressuretendstoopenawiderkerfwhichwillhaveanegativeeffectonthedepthofpenetration[22].Comparingthesimulationresultswiththeexperimentdata[11],thesimulationresultsappeartobeabletorepresentthistrendverywellatwaterpressureupto250MPa.Italsoshowsagoodagreementwiththeexperimentatawaterpressure350MPathoughitoverestimatesthedepthofpenetrationinsomecases.Thus,themodelcanbeconsideredtobevalidbyexperimentforwaterpressureupto350MPa.

Inordertostudytheinfluenceofthetraverserate,webuildanothermodelbasedontheexperimentdata[23],whichissimilartotheexperiment[11]excepttheabrasivemassflowrateandjettraversespeed.FromFigs.8and9,wecanseethedifferentcutdepthatthesamepressureintwoexperiments.Figure9alsoshowsthatthedepthofpenetrationdecreaseswiththeincreaseofjettraverserate.Thisisduetoseveralfactors:first,asthetraversespeedincreases,thenumberofparticlesimpingingonagivenexposedtargetareadecreases,whichinturnreducesthematerialremovalrate.Second,Momberetal.[24]havefoundthatthedampingandfrictioneffectinthejetdecreasesasthejetexposuretimedecreases(orthejettraverserateincreases).Thus,theincreaseinthejettraversespeedwillreduceenergylossofparticlesandimprovethematerialremovalrate.Third,ithasbeenreported[22]thatwithafastertravelofthejet,fewerparticleswillbeabletostrikeonthetargetmaterialandopenanarrowerslot.Consequently,asaresultofthereducingenergylossandthenarrowingkerfwidthatahightraversespeed,thedeclinerateofthepenetrationdepthisreducingandthecurvesinFig.9tendtoflattenasthetraversespeedincreases.

5Conclusions

1.ThispaperpresentsacoupledSPH/FEMmethodto

simulatetheabrasivewaterjetmachining.Themodel

233

dealswithfluid–solidinteractionandthematerialmodelofabrasiveisfirstproposed.TheSPHparticlemodelingfortwokindsofmaterialisalsoproposed.Theabrasivewaterjetmachiningissimu-latedsuccessfully.

2.Basedonthetestdata,themodelhasbeenshowntobe

abletoprovideadequateestimationofthecuttingperformanceandmightbeusedforprocesscontrolaswellasoptimizingtheoperatingparameters.

3.Thegoodagreementbetweensimulationresultsandthe

experimentaldatahaveconfirmedthecorrectnessandcredibilityofthemodel.

AcknowledgmentsTheresearchteamwouldliketoacknowledgethefinancialsupportbytheNaturalScienceFoundationofShandongProvince,China(No.Y2007A07).

References

1.JurisevicB,BrissaudD,JunkarM(2004)Monitoringofabrasivewaterjet(AWJ)cuttingusingsounddetection.IntJAdvManufTechnol24:733–737

2.KovacevicR,FangM(1994)Modelingtheinfluenceoftheabrasivewaterjetcuttingparametersonthedepthofcutbasedonfuzzyrules.IntJMachToolsManuf34(1):55–72

3.MomberAW(1995)Ageneralizedabrasivewaterjetcuttingmodel.Proceedingsofthe8thAmericanWaterJetConference8:359–371

4.ParikhPJ,LamSS(2009)Parameterestimationforabrasivewaterjetmachiningprocessusingneuralnetworks.IntJAdvManufTechnol40:497–502

5.EltobgyMS,NgE,ElbestawiMA(2005)Finiteelementmodelingoferosivewear.IntJMachToolsManuf45:1337–13466.ManiadakiK,KestisT,BilalisN,AntoniadisA(2007)Afiniteelement-basedmodelforpurewaterjetprocesssimulation.IntJAdvManufTechnol31:933–940

7.MaL,BaoRH,GuoYM(2008)WaterjetpenetrationsimulationbyhybridcodeofSPHandFEA.IntJImpactEng35:1035–428.JohnsonGR,BsisselSR(1996)NormalizedsmoothingfunctionsforSPHimpactcomputations.IntJNumerMathEng39:2725–2741

9.JohnsonGR,StrykRA,BeisselSR(1996)SPHforhighvelocityimpactcomputations.ComputMethodsApplMechEng139:347–373

10.JohnsonGR,BsisselSR,StrykRAA(2000)Generalizedparticle

algorithmforhighvelocityimpactcomputations.ComputMech25:245–256

11.HassanAI,ChenC,KovacevicR(2004)On-linemonitoringof

depthofcutinAWJcutting.IntJMachToolsManuf44(6):595–605

12.CampbellJ,VignjevicR,LiberskyL(2000)Acontactalgorithm

forsmoothedparticlehydrodynamics.ComputMethodsApplMechEng184(1):49–65

13.JohnsonGR(1994)LinkingofLagrangianparticlemethodsto

standardfiniteelementmethodsforhighvelocityimpactcomputations.NuclearEngDes150:265–274

14.AttawaySW,HeinsteinMW,SwegleJW(1994)Couplingof

smoothparticlehydrodynamicswiththefiniteelementmethod.NuclearEngDes150:199–205

234

15.LS-DYNAKeywordUser’sManual(2005)LivemoreSoftware

TechnologyCorporation

16.SteinbergDJ(1987)Sphericalexplosionsandtheequationofstate

ofwater.LawrenceLivermoreNationalLaboratory,Livermore,CA17.GrujicicM,PanduranganB,QiaoR,CheeSemanBA,RoyWN,

SkaggsRR,GuptaR(2008)Parameterizationoftheporous-materialmodelforsandwithdifferentlevelsofwatersaturation.SoilDynEarthquEng28(1):20–35

18.GwanmesiaGD,ZhangJ,DarlingK,KungJ,LiBS,WangLP,

NeuvilleD,LiebermannRC(2006)Elasticityofpolycrystallinepyrope(Mg3Al2Si3O12)to9GPaand1000°C.PhysEarthPlanetIn155(3-4):179–190

19.BitterJGA(1993)Astudyoferosionphenomena:partI.Wear6:5–21

IntJAdvManufTechnol(2010)50:227–234

20.MEITobgy,EGNg,MA(2007)Modelingofabrasivewaterjet

machining:anewapproach.CIRPAnnals-ManufacturingTechnology21.HashishM(1993)Pressureeffectsinabrasivewaterjet(AWJ)

machining.JEngMaterTechnol11:221–228

22.WangJ(1999)Abrasivewaterjetmachiningofpolymermatrix

composites—cuttingperformance,erosiveprocessandpredictivemodels.IntJAdvManufTechnol15:757–768

23.PaulS,HoogstrateAM,VanL,KalsHJJ(1998)Analyticaland

experimentalmodelingofabrasivewaterjetcuttingofductilematerials.JMaterProcessTechnol73:189–199

24.MomberAW,MohanRS,KovovacevicR(1999)On-lineanalysis

ofhydro-abrasiveerosionofpre-crackedmaterialsbyacousticemission.TheoretApplFractMech31:1–17