8 6 03 JOURNAL OFEXPERIMENTAL MECHANICS Vol.8 No.6 Dec.03 00-4888(03)06-076-09 * 0,,,, (., 03004;., 70049) INSTRON5544 0 Mooney-Rivilin Yeoh,,, Mooney-Rivilin Yeoh - - Mooney-Rivilin Yeoh, ABAQUS, Mooney-Rivilin Yeoh 0 ; O34 A DOI0.750/00-4888--88 0 Mitchson Swann(954), [],, 0 5~0mm,,,, 0,, 0, [],, ( ), - [3] [4] Mooney-Rivilin Yeoh Ogden,, [5],. 0, * 0--3; 03-04-08,,, E-mailchenweiyi@tyut.edu.cn
76 (03 ) 8, 0.%, 0.94%, 6 0 4, Ф=0mm, h =30mm 3. INSTRON5544, [6] Mulins,, mm/min, 0mm, Merlin Fig. Thedeviceofcompressiontest 3 - Fig. Nominalstress-strainexperimental forspecimenno.3., σ= F A = F π d = 4F πd ε= Δl l ( σ,f,a,d,ε,l,δl ) -, 3, 3 - ( ). Mooney-Rivilin Yeoh,, I I I 3 Cauchy-Green, W [7] W = W (I,I,I 3 ) () I =λ +λ +λ 3 () I =λ λ +λ λ 3 +λ λ 3 (3) I 3 =λ λ λ 3 (4) λi =+εi (5) [8] ()~(5) [] Mooney-Rivilin W =C 0 (I -3)+C 0 (I -3),C 0 C 0 Mooney-Rivilin ;W Cauchy-Green I
6 0 763 I [9] Yeoh W =C (I -3)+C (I -3) +C 3 (I -3) 3,C C C 3 Yeoh [] W, S ij = W = W I + W I + W I 3 (6) E ij I E ij I E ij I 3 E ij,s ij Piola-Kirchhof ;E ij Cauchy-Green 0, I 3=, λ, ε,, () (3) (7) (8) (6) λ =λ=+ε [] λ =λ 3 = λ = +ε I =λ +λ +λ 3 =λ + λ = (+ε) + +ε (7) I =λ λ +λ λ 3 +λ λ 3 =λ+ λ =(+ε)+ (+ε) (8) ( ) W + ( ) W ( I I +ε ) σ =(λ-λ - ) W + W λ - = (+ε)- I I (+ε) Mooney-Rivilin Yeoh, ( ) ( ) ( ) ( ) ( (+ε) ) +4C (+ε) 3-3(+ε)- (+ε) + 3 3 (+ε) + ( ) (+ε) + 4 (+ε) - 9 3 (+ε) - ( 6 ) σmr =C 0 λ- +C 0-3 =C 0 +ε- λ λ (+ε) +C - 0 (+ε) (0) 3 σy =C +ε- +6C 3 (+ε) 5-6(+ε) 3 +3(+ε) +9(+ε)- 4 (9) () MR Y Mooney-Rivilin Yeoh (0) (), ε<, Mooney-Rivilin, n>3, ε 4, Mooney-Rivilin σmr =C 0 (4ε 3-3ε +3ε)+C 0 (0ε 3-6ε +3ε) () Yeoh, n>5, ε 6, Yeoh.3 σy =C (6ε 5-5ε 4 +4ε 3-3ε +3ε)+C (8ε 5-5ε 4 +3ε 3 )+54C 3 (3ε 5 -ε-) (3) Mooney-Rivilin Yeoh, () (3), Origin, 3 4, 3 Mooney-Rivilin C 0 C 0 C 0 =0.86±0.03, C 0 =-0.777±0.07 Yeoh C C C 3 C =0.63±4.E-04, C =0.±5.38E-04, C 3 =.76E-04±3.96E-06
764 (03 ) 8 3 Mooney-Rivilin Fig.3 Mooney-Rivilinmodelfitingcurve 4 Yeoh Fig.4 Yeohmodelfitingcurve 3 3. 3 4, 5, 0 Fig.5 Thedeviceofmeasuring coeficientoffriction,,,, 5
6 0 765,,,,, ( n, β,m ) Tab. Thedatatableoffriction scoeficient n 3 4 5 6 7 8 9 0 β ( deg) 7 7 7 6.5 7.5 7 7 7.5 6.5 7 m(g) 0 404 606 808 00 44 66 88 00 f=tanβ, f, f = n n i= 3. tanβ i = 0 0 i= tanβ i 0.3, Mooney-Rivilin Yeoh, ABAQUS Tab. Materialparametersofmodel C0/C C0/C C3 D Mooney-Rivilin 0.86-0.777 0 Yeoh 0.63 0..76E-4 0,,, Mooney-Rivilin Yeoh,, 4-node (CAX4HR), ( ), f= 0.3( ), Nlgeom on, x y, 6 Mooney-Rivilin S Fig.6TheMooney-Rivilinmodel ssstresscloudinfrictionless S - (σ-ε) - 6 3, 6 7 Mooney-Rivilin S
766 (03 ) 8 -,S 8 9 Yeoh S - 7,Mooney-Rivilin Fig.7 ThesimulationcurveofMooney-Rivilinmodelwithoutfriction 8 Yeoh S Fig.8 TheYeohmodel ssstresscloudwithoutfriction 9,Yeoh Fig.9 ThesimulationcurveofYeohmodelwithoutfriction
第６期 王丽丽等 １１０ 甲基乙烯基硅橡胶材料参数的确定 ７６７ 图１０ 和图 １１ 分别表示 Ｍｏｏｎｅｙ Ｒ ｎ 模型在摩擦系数 ｆ ０ １２３ 时的 Ｓ２２ 应力云图和模拟所得的 应力 应变曲线与 ３ 号试件的实验数据所得的名义应力 应变曲线的比较图图 １２ 和图 １３ 分别表示 图 １０ Ｍｏｏｎｅｙ Ｒ ｎ 模型在摩擦系数 ｆ ０ １２３ 时的 Ｓ２２ 应力云图 Ｆ １０ Ｔｈｅ Ｍｏｏｎｅｙ Ｒ ｎ ｍｏｄｅ ｓｓ２２ ｓ ｅ ｓ ｓｃ ｏｕｄ ｎ ｈｅｃ ｏｅ ｆ ｆ ｃ ｅｎ ｏ ｆｆ ｃ ｏｎｆ ０ １２３ ｇ 图 １１ Ｍｏｏｎｅｙ Ｒ ｎ 模型的模拟曲线 １２３ ｆ ０ Ｆ １１ Ｔｈｅｓ ｍｕ ａ ｏｎｃｕ ｅｏ ｆ Ｍｏｏｎｅｙ Ｒ ｎ ｍｏｄｅ １２３ ｇ ｆ ０ 图 １２ Ｙｅ ｏｈ 模型在摩擦系数 ｆ ０ １２３ 时的 Ｓ２２ 应力云图 Ｆ １２ ＴｈｅＹｅ ｏｈ ｍｏｄｅ ｓｓ２２ ｓ ｅ ｓ ｓｃ ｏｕｄ ｎ ｈｅｃ ｏｅ ｆ ｆ ｃ ｅｎ ｏ ｆｆ ｃ ｏｎ １２３ ｇ ｆ ０
768 (03 ) 8 Yeoh f=0.3 S - 3-3 Yeoh (f=0.3) Fig.3 Thesimulationcurve ofyeohmodel(f=0.3) 4 4. Rivilin Yeoh, ABAQUS Mooney-Rivilin Yeoh 7, 9 3, 7 9 Mooney-Rivilin Yeoh 0, Mooney-Rivilin Yeoh, Origin Mooney-., Moo- ney-rivilin, 4.,,,,,,,,, Mooney-Rivilin Yeoh, ε= /3<0.35,ε ε 4 ε 6, Mooney-Rivilin ε 4,Yeoh ε 6, Yeoh, ε ε 5 ε 6, Yeoh ε 6, - - []. [D].,995,5()97-08 (FanXuejun.Celularmechanics [D].Advancesin Mechanics,995,5()97-08(inChinese)) [],,. Mooney-Rivilin Yeoh [J]., 008,55(8)467-47 (HuangJianlong,XieGuangjuan,LiuZhengwei.Mooney-Rivilin modelandyeoh model basedonhyperelasticfiniteelementanalysisofrubbermaterials[j].journalofrubberindustry,008,55(8)467-47(inchinese)) [3],. [M].,005 (ZhangShaoshi,ZhuangZhuo. CompositeMaterialandtheViscoelasticMechanics[M].BeijingMechanicalIndustryPress,005(inChinese)) [4],,. [J].,0,39(4)56-6 (LuoHuaan,WangHuaming,YouYoupeng.Theaxistensiletestmethodandsimulationofhyperelasticmembrane [J].JournalofSouthChinaUniversityofTechnology,0,39(4)56-6(inChinese)) [5] Pearson I,Pickering M. The determination of a highly elastic adhesive s material properties and their representationinfiniteelementanalysis[j].finiteelementsinanalysisanddesign,00,37(3)-3.
6 0 769 [6],. [J].,005,5()50-58 (LiXiaofang,YangXiaoxiang. Hyperelasticconstitutivemodelofrubbermaterials[J].JournalofElastomer,005,5()50-58(inChinese)) [7],. [J].,006,53()9-5 (ZhuYanfeng,LiuFeng,etal. Theconstitutivemodelofrubbermaterial[J].JournalofRubberIndustry,006,53()9-5(inChinese)) [8] Mooney M.Atheoryoflargeelasticdeformation[J].JournalofAppliedPhysics,940,(9)58-59. [9] YeohO H.Cterizationofelasticpropertiesofcarbon-blackfiledrubbervulcanizates[J].RubberChemistryand Technology,990,6379-805. OntheMaterialParametersDetermination of0 MethylVinylSiliconeRubber WANGLi-li,WANG Yu-xing,LIYong-sheng,LIU Bao-bao,CHEN Wei-yi (.InstituteofAppliedmechanicsandBiomedicalEngineering,TaiyuanuniversityofTechnology,Taiyuan03004,China;.MechanicsandEngineeringInstituteofEngineering Mechanics,SouthwestJiaotongUniversity,Xi an70049,china) AbstractInordertounderstandingthe mechanicalpropertiesof0 methylvinylsiliconerubber, largedeformationuniaxialcompressiontestwascarriedoutbyusinginstron5544.constitutive relationexpressionsforsmaldeformation wasobtained,basedonexistingconstitutiverelationsof Mooney-Rivilin modeland Yeoh modeland by using Taylor series expansion method. Then, corresponding material parametersin Mooney-Rivlin model and Yeoh model were obtained by nonlinearfitingofexperimentaldataobtainedfrom above-mentionedconstitutiverelation Nominal stress-straincurvefrom fitingisinagreement withthatfrom experimentaldata.using material parametersobtainedfrom nonlinearfitingof Mooney-Rivlin modeland Yeoh modeland ABAQUS software,finiteelementanalysis wasconducted.calculation resultsshow thatthe validity and feasibilityofmaterialparametersofmooney-rivlinmodelandyeohmodelareverified. Keywords0methylvinylsiliconerubber;strainenergydensityfunction;hyperelasticity