2005-2006 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Hu, JL

Shi, FJ

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? 26 ?? 3?2005 ? 6??　?　?　?Journal of Textile ResearchVol.26 , No.3Jun., 2005???????石风俊1 ,胡金莲2(1.????? , ?? ??　450003;2.?????? , ??)?　?　????????????????????????????。?????????????? , ??????? ,?????????????。??????????????????????????。????????????????? ,?????????????????。???????????????????????????? ,???????????。???　????;????;?????;????????:TS 101.4　　　?????:A　　　????:0253-9721(2005)03-0015-04Bending behavior of woven fabricsSHI Feng-jun1 , HU Jin-lian2(1.Zhongyuan Institute of Technology , Zhengzhou , Henan　450003 , China;2.The Hong Kong Polytechnic University , Hong Kong , China)Abstract　The bending behavior of woven fabrics under low curvature conditions was analyzed.The fabricwas assumed to behaveviscoelastically and to be subjected to frictional restraints in bending deformation.The frictional restraint was considered to beproportional to the curvature.A model had been constructed by a standard linear solid element and a paralleled frictional slidingelement.The equations of the model for a cyclic curvature variation were derived.A set of parameters of the equations for eachfabric had been obtained experimentally.Predictions of the bending rigidity and hysteresis for the fabrics were calculated and thetheoretical calculations agree well with the experimental observations.Key words　bending rigidity;bending hysteresis;linear viscoelasticity;woven fabrics????:石风俊(1962-), 男 ,教授 , 博士。主要从事纺织材料方面的研究。　　?????????????? 、????? 、??????????????????[ 1] 。??????????????? 、?????????????????? ,??????????? 。?????????????????????[ 2 ～ 4] 、????[ 5, 6] 、??????[ 7 ～ 9] ? 。Ghosh??[ 10] ?????????????? 。????????? ,??????????????????? ,????????????????????????。?? ,??????????????????????? ,??????????????? 。1　?　?????????????????????????????。????? ,??????????? ,???????????????? 。???????????????????? ,?? ,??????????????????????????????????????? ,?? 1??。?????M(k)=Mv(k)+﹒k |﹒k |×Mf (1)?? ,M(k)????????(cN·cm cm);k ??????(cm-1);Mf ???????(cN·cm cm);?? ﹒k  ﹒k ????????。???????? ,??????????????? 。?????? ,???????????????M0 。??? ,?????????????????[ 1] 。???? ,???????????????????? 2HB ,??????????????????????? 。?? ,??????????????????? ,??2??。?????????????? ρ?? ,???????????Mv(t)=at +b(1-e-t T) (2)DOI :10.13475/j.fzxb.2005.03.005? 1　??????????????????????? 2　???????-??????? ,a = E1E2E1 +E2ρ;b =E21(E1 +E2)2ρη;T =η (E1 +E2)? E1 、E2????????;η????????。?????? k ＊ 、-k＊??????? ,????????? 3??。? 3　?????????????????????? 、?????? ,??????????? 。??????????(2)???。?? Boltzman ???? ,??????????????????????????? ,???????? 3? 1 、2 、3 、4??????? 。????????????? ρ,??????? k ＊ ,k =ρt , t＊=k ＊ ρ,??? t＊ 、2t ＊ 、3t ＊ 、4t ＊?????????Mv1 =Mv(t ＊)=at ＊+b(1-γ)t =t ＊Mv2 =Mv(2t ＊)-2Mv(t＊)=-b(1-γ)2t =2t ＊Mv3 =Mv(3t ＊)-2Mv(2t ＊)=-at＊ -b(1-2γ2 +γ3)=-Mv1 +γMv2t =3t ＊Mv4 =Mv(4t ＊)-2Mv(3t ＊)+2Mv(t ＊)=b(1-γ2)(1-γ)2t =4t ＊(3)?? , γ=e-t＊ T =e-(E1+E2)t＊ η。??3 ,????? k＊ 、-k ＊?????? ,?1 、2 、3 、4????????M1 =Mv1 +μk ＊ =at＊ +b(1-γ)+μk＊t =t ＊M2 =Mv2 =-b(1-γ)2t =2t ＊M3 =Mv3 -μk ＊ =-Mv1 +γMv2 -μk＊t =3t ＊M4 =Mv4 =b(1-γ2)(1-γ)2t =4t ＊(4)?? , μ???????????(cN·cm2 cm)。?? ,??(4)??? 3?????? ,????????? 。?? ,??????????????? ———???? 2HB ????? 。?? 3?? ,???????(4)???:2HB+=M+(k′)-M-(k′)=Mv+(k′)-Mv-(k′)+2Mf(k′)=b(2 -e-k′ρT -2e-k＊-k′ρT +e-2k＊-k′ρk )+2μk′(5a)2HB-=M+(-k′)-M-(-k′)=Mv+(-k′)-Mv-(-k′)+2Mf(-k′)=b(2 -e-4 k＊-k′ρT +2e-3 k＊-k′ρT +e-2 k＊+k′ρT -2e-k＊-k′ρT -2e-k＊+k′ρT )+2μk′ (5b)?? , +???????? , -???????? ,2HB+? 2HB -???????+k ?-k ????????。???????????? 2HB:2HB =(2HB++2HB-) 2 =bQ +2μk′ (6a)Q =0.5(4-e-4k＊-k′ρT +2e-3k＊-k′ρT +e-2k＊+k′ρT -2e-k＊-k′ρT +e-2k＊-k′ρT -2e-k＊+k′ρT -2e-k＊-kρT -e-k′ρT)+2μk′ (6b)????(4)?? M1 、M2 、M3 ???(6)??????? ,????γ=M1 +M3M2T = k ＊ρln M1 +M3M2a =ρk＊M1 + ρk＊ · M22M2 -M1 -M3 -μρb =- M33(M2 -M1 -M3)2(7)16【　】 ???? 2005?　? 3??? ,???????????:E 1 = aT +bTρE2 = a(aT +b)bρη=T(E1 +E2)=(aT +b)2bρμ=2HB -bQ2k(8)?? ,????????????-??????3?????????????。2　??????? 5 ?????? ,?????? 1。??? 20 cm×20 cm???? ,??????????????。???????? KES-FB-2 ?????? 。???????? 0.5 cm-1 s ,???????? 2.5 cm-1 。?????? 5??? ,?????? 、????????。??????? B????? 2HB ???1。????????????。? 1　???????????? ?? ?? ??? (g·m-2)?? cmB (cN·cm2·cm-1)2HB (cN·cm·cm-1)? ? ? ?1 ? ? ?? 161 0.032 9 0.105 9 0.078 9 0.026 0 0.037 62 ? ?? 198 0.036 0 0.055 6 0.149 3 0.073 3 0.047 73 ?? ?? 127 0.032 2 0.027 0 0.075 4 0.035 0 0.103 04 ?? ?? 245 0.062 7 0.162 6 0.132 7 0.082 6 0.062 95 ??? ?? 183 0.044 4 0.121 8 0.078 2 0.053 0 0.044 33　???????3?? ,??????? 1 、2 ? 3???? ,?????(7)?(8)?????????????? 2。? 2　???????????????? ???? (cN·cm2·cm-1) ??????M1 M2 M3 E1 E 2 η μ1?? 0.266 7 -0.015 4 -0.267 8 0.121 11 0.633 38 1.404 15 0.000 45?? 0.198 9 -0.013 4 -0.201 5 0.078 69 0.372 39 1.430 10 0.009 262?? 0.166 1 -0.022 2 -0.168 2 0.076 74 0.147 77 0.470 11 0.007 32?? 0.373 8 -0.025 8 -0.385 1 0.138 95 0.563 73 4.221 67 0.022 463?? 0.204 2 -0.056 2 -0.224 9 0.124 53 0.145 60 1.348 62 -0.020 03?? 0.073 6 -0.027 3 -0.085 4 0.004 56 -0.003 84 0.004 28 0.034 844?? 0.401 6 -0.055 1 -0.447 2 0.162 06 0.020 98 4.846 22 0.014 60?? 0.360 4 -0.055 6 -0.402 7 0.157 86 0.072 85 4.198 21 0.002 815?? 0.327 0 -0.034 8 -0.333 8 0.150 53 0.482 42 1.936 17 0.001 10?? 0.201 0 -0.027 4 -0.219 5 0.081 95 0.079 83 2.055 38 0.007 30　　??????? B(cN·cm2 cm)?????2HB ???????????。???? B ?2??? B+? B -???? , ?? 3 ??。?KES-FB-2???? ,?????? 0.5 cm-1 s?? ,???+2.5 cm-1 、-2.5 cm-1?????。B +??????????? , ???? 0.5 cm-1 ?1.5 cm-1????????????????? 。B -??????????? , ????????-0.5 cm-1?-1.5 cm-1????????????。?(3)?(4),????B+=M+(1.5)-M+(0.5)=Mv+(1.5)-Mv+(0.5)+1.5μ-0.5μ=aρ-be-1.5ρT +be-0.5ρT +μ (9a)B-=M-(-0.5)-M-(-1.5)=Mv-(-0.5)-Mv-(-1.5)-0.5μ+1.5μ=aρ+b(e-6.5ρT -e-5.5ρT -2e-4ρT +2e- 3ρT)+μ(9b)B =aρ+12 b(e-6.5ρT -e-5.5ρT -2e-4ρT +2e-3ρT -e-1.5ρT +e-0.5ρT)+μ (9c)?? ,???(9)?? 2?????? ,???????????? B+ 、B-? B ,?? 3。???? ,???????????。?? ,2HB+? 2HB-???????????±1 cm-1?????? ,? k =1?? 2?????172005?　?3? ???? 【　】　　　 ? 3　?????????????????????? ??? B (cN·cm2·cm-1)B + B - B??? B (cN·cm2·cm-1)?? %??? 2HB (cN·cm·cm-1)2HB + 2HB- 2HB1?? 0.106 9 0.101 0 0.103 9 0.105 9 1.89 0.023 4 0.028 7 0.026 0?? 0.080 0 0.075 4 0.077 7 0.078 9 1.48 0.034 6 0.041 9 0.037 62?? 0.066 9 0.058 5 0.062 7 0.055 6 12.85 0.045 6 0.054 1 0.049 6?? 0.150 6 0.144 5 0.147 5 0.149 3 1.14 0.071 0 0.093 1 0.076 83?? 0.084 1 0.068 9 0.076 5 0.075 4 1.51 0.021 8 0.063 7 0.035 0?? 0.030 6 0.024 0 0.027 3 0.027 0 1.01 0.096 8 0.120 0 0.103 04?? 0.162 9 0.159 1 0.161 0 0.162 6 0.98 0.077 4 0.280 7 0.082 6?? 0.146 5 0.141 0 0.143 8 0.132 7 8.34 0.055 9 0.192 4 0.062 95?? 0.132 1 0.120 1 0.126 1 0.121 8 3.50 0.045 2 0.063 7 0.053 0?? 0.081 6 0.077 9 0.079 7 0.078 2 1.95 0.039 9 0.085 9 0.044 3??????(5)?(6),?????????????????。????????????? 3。??? ,????? 2HB ?????? 2HB(??1)???? 。4　?　?1)?????????????????????????????????????。2)???????????????? 3??????????。3)????????????????????? ,?????????? 2HB +? 2HB -(k =±1 cm-1)????????????????。????:[ 1 ] 　Postle R , Carnaby G A , de Jong S.Mechanics of Wool Structures[M] .London:El li s Harwood Ltd , 1988.[ 2 ] 　Abbott G M , Grosberg P , Leaf G A V.The elastic resistance tobending of plain-woven fabrics [ J] .J Text Inst , 1973 , 64(3):346-362.[ 3 ] 　de Jone S ,Postle R.An energy analysis of woven-fabric mechanics bymeans of optical-control theory ,Part Ⅱ:pure-bending properties[ J] .J Text Inst , 1977, 68(3):362-369.[ 4 ] 　Ghosh T K , Batra S K , Barker R L.The bending behavior of plain-woven fabrics , Part Ⅲ:the case of bilinear thread-bending behaviorand the effect of fabric set[ J] .J Text Inst , 1990 , 81(2):255-271.[ 5 ] 　Konopasek M.Computational aspects of large deflection analysi s ofslender bodies[ A] .In:Hearle J W S , Thwaites J J , Amirbayat eds.Mechanics of Flexible Fiber Assemblies[ C] (NATO ASI Series).Netherlands:Si jthoff &Norrdhoff ,Alphen ann den Rijn , 1980.275-292.[ 6 ] 　Lloyd D W ,Shanahan W J , Konopasek M.The bending of heavy fabricsheets[ J] .Int J Mech Sci , 1978 , 20(5):521-527.[ 7 ] 　Chapman BM.Determination of the rheological parameters of fabric inbending[ J] .Text Res J , 1975 , 45(2):137-144.[ 8 ] 　Shi Feng-jun , Hu Jinlian , Yu Tongxi.Study on bending of wovenfabrics[ J] .Journal of China Textile University , 2000 , 17(1):51-56.[ 9 ] 　Grosberg P.The mechanical propert ies of woven fabrics , Part Ⅱ:thebending of woven fabrics[ J] .Text Res J , 1966 , 36(2):205-211.[ 10] 　Ghosh T K , Batra S K , Barker R L.The bending behavior of plain-woven fabrics, Part Ⅰ :a critical review[ J] .J Text Inst , 1990, 81(3):245-255.(上接第 11页)　　2)???????????????????????????? 。3)???????????????????????????。?????? ,????????????????? ,???????????????????????????????? 。????:[ 1 ] 　Benoit B Mandelbrot.The Fractal Geometry of Nature[ M ] .SanFrancisco:W H Freeman and Co , 1982.[ 2 ] 　??? ,???.?????????????[M] .??:????? ,1998.[ 3 ] 　???.?????????[M] .??:????????? , 2000.18【　】 ???? 2005?　? 3?

Bending behavior of woven fabrics

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