一种新的聚合物基复合材料应力松弛经验模型
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摘要
视黏弹性元件弹簧和粘壶的特性参数为时间的函数,建立双变参Maxwell模型,求解其本构方程及松弛函数,探讨了其松弛函数与经验KWW函数的关系,提出了一种新的应力松弛经验模型。运用最小二乘原理,建立该模型参数的确定方法。开展了玻璃纤维增强聚合物(GFRP)复合材料的长期应力松弛实验,并通过实验数据的分析验证了该模型的正确性。研究表明,新应力松弛经验模型拟合曲线与实测曲线吻合较好,相关系数达到96%以上,说明了该模型适合描述GFRP复合材料的黏弹性松弛特性。
Based on the assumption that the characteristic parameters of spring and dashpot of viscoelastic element are a function of time,double-variable parameter Maxwell models were established.Their relaxation functions were obtained by resolving the variable parameter constitutive relation.The relation between the relaxation function and the empirical KWW function was discussed,and a new empirical model for stress relaxation was proposed.The parameter determination method was established by the principle of the least square.The long term stress relaxation test of glass-fiber reinforced plastic(GFRP)composites was carried out,and the proposed model was verified through the experimental data.The research results show that the proposed model curve and experimental curve approximately coincide with each other,and the correlation coefficient reaches 96% or more.It shows that the model is suitable to describe the viscoelastic relaxation properties of GFRP composites.
Based on the assumption that the characteristic parameters of spring and dashpot of viscoelastic element are a function of time,double-variable parameter Maxwell models were established.Their relaxation functions were obtained by resolving the variable parameter constitutive relation.The relation between the relaxation function and the empirical KWW function was discussed,and a new empirical model for stress relaxation was proposed.The parameter determination method was established by the principle of the least square.The long term stress relaxation test of glass-fiber reinforced plastic(GFRP)composites was carried out,and the proposed model was verified through the experimental data.The research results show that the proposed model curve and experimental curve approximately coincide with each other,and the correlation coefficient reaches 96% or more.It shows that the model is suitable to describe the viscoelastic relaxation properties of GFRP composites.
引文
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[17]SCHIESSEL H,METZLER R,BLUMEN A,et al.Generalized viscoelastic models:Their fractional equations with solutions[J].Journal of Physics A:Mathematical and General,1995,28(23):6567-6584
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[20]朱四荣,梁娜,李悦等.玻璃钢管的长期刚度测量及预测[J].复合材料学报,2016,33(11):2492-2499.ZHU S R,LIANG N,LI Y,CHEN J Z.Measurement and prediction for long-term stiffness of glass fiber reinforced plastic pipes[J].Acta Materiae Compositae Sinica,2016,33(11):2492-2499(in Chinese).
[2]British Standards Institution.Plastics piping systems.Glassreinforced thermosetting plastics(GRP)pipes and fittings.Methods for regression analysis and their use:BS ISO10928—2009[S].British:British Standards Institution,2009.
[3]梁军,杜善义.黏弹性复合材料力学性能的细观研究[J].复合材料学报,2001,18(1):97-100.LIANG J,DU S Y.Study of mechanical properties of viscoelastic matrix composite by micromechanics[J].Acta Materiae Compositae Sinica,2001,18(1):97-100(in Chinese).
[4]舒乐华.聚合物基复合材料黏弹性性能预测[D].湖南:湘潭大学机械工程学院,2010.SHU L H,Study of viscoelastic properties for polymer matrix composites[D].Hu’nan:Xiangtan University School of Mechanical Engineering,2010(in Chinese).
[5]于航,周储伟.纤维复合材料黏弹性动态性能的细观力学分析[J].振动工程学报,2011,24(4):359-362.YU H,ZHOU C W.Micromechanics analysis of viscoelastic dynamic properties of fiber composite materials[J].Journal of Vibration Engineering,2011,24(4):359-362(in Chinese).
[6]RUI M G,MORAIS J L.A simple and effective scheme for data reduction of stress relaxation incorporating physical-aging effects:An analytical and numerical analysis[J].Polymer Testing,2013,32(7):961-971.
[7]MOJTABA H Y,PEARL L S.Stress relaxation of a polycarbonate blend after hygrothermal aging[J].Mechanics of Time-Dependent Materials,2013,17(6):171-193.
[8]QAISER A A,PRICE J,Estimation of long-term creep behavior of polycarbonate by stress-time superposition and effects of physical aging[J].Mechanics of Time-Dependent Materials,2011,15:41-50.
[9]张义同,严宗达.变温黏弹性的一般理论[J].力学学报,1993,25(6):685-696.ZHANG Y T,YAN Z D.The general theory of viscoelasticity under non-constant temperature condition[J].Acta Mechanica Sinica,1993,25(6):685-696(in Chinese).
[10]张义同.变温黏弹性蠕变型本构方程[J].固体力学学报,1995,16(2):152-156.ZHANG Y T.The creep constitutive law under non-constant temperature states[J].Acta Mechanica Solida Sinica,1995,16(2):152-156(in Chinese).
[11]金丰年,浦奎英.关于黏弹性模型的讨论[J].岩石力学与工程学报,1995,14(4):355-361.JIN Fengnian,PU Kuiying.Discussion of viscoelastic model[J].Chinese Journal of Rock Mechanics and Engineering,1995,14(4):355-361(in Chinese).
[12]WILLIAMS G,WATTS D C.Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function[J].Transactions of the Faraday Society,1970,66(14):80-85.
[13]帅词俊,段吉安,王炯.关于黏弹性材料的广义Maxwell模型[J].力学学报,2006,38(4):565-569.SHUAI C J,DUAN J A,WANG J.A method of establishing generalized Maxwell model for viscoelastic materials[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(4):565-569(in Chinese).
[14]张小玉,黄乾钰,陈建中.聚合物基复合材料单向板黏弹性模型[J].华中科技大学学报,2015,43(1):30-33.ZHANG Xiaoyu,HUANG Qianyu,CHEN Jianzhong.The viscoelastic model of PMC unidirectional plates[J].Journal of Huazhong University of Science and Technology,2015,43(1):30-33(in Chinese).
[15]康永刚,张秀娥.非定常微分型黏弹性本构模型[J].力学学报,2012,44(2):456-459.KANG Yonggang,ZHANG Xiu’e.The non-stationary differential constitutive models of viscoelasticity[J].Chinese Journal of Theoretical and Applied Mechanics,2012,44(2):456-459(in Chinese).
[16]康永刚,张秀娥,张华明.聚合物应力松弛的非定常微分型本构模型[J].高分子材料科学与工程,2013,29(4):178-182.KANG Yonggang,ZHANG Xiu’e,ZHANG Huaming.The non-stationary differential constitutive models for stress relaxation of polymer[J].Polymer Materials Science and Engineering,2013,29(4):178-182(in Chinese).
[17]SCHIESSEL H,METZLER R,BLUMEN A,et al.Generalized viscoelastic models:Their fractional equations with solutions[J].Journal of Physics A:Mathematical and General,1995,28(23):6567-6584
[18]孙钧.岩石流变力学及其工程应用研究的若干进展[J].岩石力学与工程学报,2007,26(6):1081-1106.SUN J.Rock rheological mechanics and its advances in engineering application[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(6):1081-1106(in Chinese).
[19]ARAO Y,YUKIE O,KOYANAGI J,et al.Simple method for obtaining viscoelastic parameters of polymeric materials by incorporating physical-aging effects[J].Mechanics of TimeDependent Materials,2012,16(2):169-180.
[20]朱四荣,梁娜,李悦等.玻璃钢管的长期刚度测量及预测[J].复合材料学报,2016,33(11):2492-2499.ZHU S R,LIANG N,LI Y,CHEN J Z.Measurement and prediction for long-term stiffness of glass fiber reinforced plastic pipes[J].Acta Materiae Compositae Sinica,2016,33(11):2492-2499(in Chinese).