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2711200711ACTAOPTICASINICAVol.27,No.11November,2007:025322239(2007)1121980273(,100084):,,,,,;,,,:;;;:TN911.74:A3973(2004CB619304)(10625209,10472050,10121202):(1978-),,,E2mail:panb04@mails.thu.edu.cn:(1965-),,,,,E2mail:xiehm@tsinghua.edu.cn:2006211227;:2007205221Full2FieldStrainMeasurementBasedonLeast2SquareFittingofLocalDisplacementforDigitalImageCorrelationMethodPanBingXieHuimin(DepartmentofEngineeringMechanics,TsinghuaUniversity,Beijing100084)Abstract:Inordertoobtainreliablestrainfield,full2fieldstrainmeasurementbasedonleast2squarefittingoflocaldisplacementfordigitalimagecorrelationmethodisproposed.Theprincipleofdigitalimagecorrelation(DIC)methodisintroduced,andfull2fieldstrainmeasurementbasedonlocalleast2squarefittingisexpatiated,straincalculationneartheborder,holeandcrackarealsodiscussed.Theresultsfromhomogeneousdeformationtestandthetensiletestofthealuminumspecimenwithaholeinthecenterobviouslydemonstratedthevalidityofthistechnique.Largestraincalculatingwindowisrecommendedtouseincaseofhomogeneousdeformation,socalculationresultsapproachtruevalue;Forinhomogeneousdeformation,largecalculatingwindowshouldbeselectedtoaccordingtothenoiselevelofthelocaldisplacementfield,butwhendisplacementfieldhashighaccuracy,smallercalculatingwindowisselected.Keywords:opticalmeasurement;digitalimagecorrelation;least2squarefitting;strain1,I.Yamaguchi[1]W.H.Peters[2](Digitalimagecorrelation,DIC)20,[38],(,)0.020.1pixel,,,(Newton2Raphson,N2R)[8,9](),,[8],1%[1012][10,11,13][12],,,,22.1(Referenceimage),(Deformedimage)(x,y)(2M+1)pixel(2M+1)pixel(M),,()(x,y),u,v,,()210pixel2.21,(x,y)(x,y)(1):x=x0+x+u+5u5xx+5u5yy,y=y0+y+v+5v5xx+5v5yy,(1)u,vx,y,(x,y)(x,y)(x0,y0),ux,uy,vx,vy1Fig.1Schematicdiagramofreferenceandtarget(ordeformed)subsets2.3f(x,y)g(x,y),[14]:Cf,g(p)=Mx=-MMy=-Mf(x,y)-fmMx=-MMy=-M[f(x,y)-fm]2-g(x,y)-gmMx=-MMy=-M[g(x,y)-gm]22,(2)p,fm=1(2M+1)2Mx=-MMy=-M[f(x,y)]2,gm=1(2M+1)2Mx=-MMy=-M[g(x,y)]2,,,189111:,,g(x,y)=ag(x,y)+b,a,b,(2)2.4(2),Cf,g(p)p=(u,ux,uy,v,vx,vy)T6,[0,4],Cf,g(p),Cf,g(p)0,ýCf,g(p)=5C5pii=1,2,,6=-2Mx=-MMy=-Mf(x,y)-fmMx=-MMy=-M[f(x,y)-fm]2-g(x,y)-gmMx=-MMy=-M[g(x,y)-gm]21Mx=-MMy=-M[g(x,y)-gm]25g(x,y)5pii=1,2,,6=0.(3)(3),ýC(p)=ýC(p0)+ýýC(p0)(p-p0)=0,(4)p=p0-ýC(p0)ýýC(p0).(5)p0,ýC(p0),ýýC(p0),(Hessian)G.Vendroux[9],,,ýýCf,g(p)=52C5pi5pji=1,2,,6j=1,2,,62Mx=-MMy=-M[g(x,y)-gm]2Mx=-MMy=-M52g(x,y)5pi5pji=1,2,,6j=1,2,,6.(6)2.5,,[8],,,[15]2.610-4pixel,510-63,,,,()(),,,,0.02pixel,5pixel,=15(0.020.02)=800010-6,=110(0.020.02)=400010-6,,,(),,289127(),[,(2M+1)(2M+1),2],,,,,2(2M+1)(2M+1)Fig.2Schematicdiagramoflocaldisplacementregioncontaining(2M+1)(2M+1)datapoints,,uv,u(x,y)=a0+a1x+a2y,v(x,y)=b0+b1x+b2y,(7)x,y=M,a0,a1,a2,b0,b1,b2,u(x,y),v(x,y)u(x,y)(2M+1)(2M+1),(2M+1)(2M+1)u(x,y)(2)u=[u(0),u(1),,u(n)],n=(2M+1)(2M+1)-1,(7)u(x,y):u=Xa]1-m-m1-m+1-m1001m-1m1mma0a1a2=u(-m,m)u(-m+1,m)u(0,0)u(m-1,m)u(m,m),(8)a0a1a2=(XTX)-1XTu,(9)(XTX)-1XTX,v(x,y)b0b1b2=(XTX)-1XTv,(Cauchy)[16]x=5u/5x=a1,y=5v/5y=b2,xy=5u/5y+5v/5x=a2+b1,(10)(Green)[16]Exx=5u5x+125u5x2+5v5x2=a1+12(a21+b21),Eyy=5v5y+125u5y2+5v5y2=b2+12(a22+b22),Exy=125u5y+5v5x+125u5x5u5y+5v5x5v5y=12(a2+b1)+12(a1a2+b1b2).(11),(2M+1)(2M+1),Xu(x,y)(),311112121,,(9)4,,:41pixel41pixel,5pixel4.1PengZhou[17]389111:3,:576pixel576pixel,4pixel,4000,20x200010-63(a),(b)Fig.3Simulatedspeckleimages.(a)Referenceimage,(b)deformedimage4xu(x),x4(2121)x,5,(200010-6),54xu(x)Fig.4DisplacementfieldinxdirectionobtainedbyNewton2Raphsonmethod65(332121)6,,,,5ux(2121)Fig.5Thedisplacementfieldinxdirectionobtainedbylocalleastsquaresfittingmethodstraincalculationwindowofusing2121points6Fig.6Thecalculatedstrainofhomogeneousdeformationbyvariousstraincalculationwindow7Fig.7Thegeometryofthinaluminumsamplewithacenterhole4.2(LY10),7,1.5mm8(a),,489127()CCD(PanasonicWv2Bp330768pixel576pixel,8bit)(uv)9xyxy10,2121,,98CCD(a),(b)Fig.8ImagecollectedbyCCDcamera.(a)Referenceimage,(b)deformedimage9(a)u(b)vFig.9The(a)uand(b)vdisplacementfieldsobtainedbydigitalimagecorrelationmethod10(a)x,(b)y,(c)xyFig.10The(a)x,(b)yand(c)xystrainfieldsobtainedbylocalleastsquarefittingtechniquefordisplacementfield11(11112121)x,(),,;,589111:11xFig.11Thexstraindistributionalongthelineperpendiculartotensiledirectionusingvariousstraincalculationwindow5,,,,,,,1I.Yamaguchi.Alaser2specklestraingange[J].J.Phys.E,1981,14(5):127012732W.H.Peters,W.F.Ranson.Digitalimagingtechniquesinexperimentalstressanalysis[J].Opt.Engng.,1982,21(3):4274313MichaelA.Sutton,StephenR.McNeill,JeffreyD.Helmetal..AdvancesinTwo2DimensionalandThree2DimensionalComputerVision[C].P.K.Rastogi,ed.TopicsinAppliedPhysics,SpringerVerlag,2000,77:3233724PanBing,XieHuimin,XuBoqinetal..Developmentofsub2pixeldisplacementsregistrationalgorithmsindigitalimagecorrelation[J].AdvancesinMechanics,2005,34(3):345352(inChinese),,.[J].,2005,35(3):3453525PanBing,XieHuimin,DaiFulong.Anevaluationofsub2pixelregistrationalgorithmsindigitalimagecorrelation[J].ActaMechanicaSinca,2007,39(2):245252(inChinese),,.[J].,2007,39(2):2452526HouZhende,QinYuwen.Studyonanewmethodofdisplacementmeasurementbasedonfractalimagecorrelation[J