基于均匀化理论的混杂纤维混凝土有效弹性模量计算
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摘要
混杂纤维混凝土是典型的多相多层次非均质复合材料,在弹性阶段其宏观尺度力学行为由细观、微观乃至纳观组成与结构决定。为探究材料微细观结构对宏观尺度力学性能的影响,在微细观力学框架下,基于Mori-Tanaka法和三相模型,建立了考虑界面作用的钢-聚丙烯混杂纤维混凝土弹性模量的多尺度均匀化理论模型,在经过试验结果验证的基础上,进行了影响因素拓展分析。结果表明:钢纤维的掺入提高了混凝土弹性模量,其提高幅度随钢纤维体积掺量的增大而增大,而聚丙烯纤维的掺入对弹性模量的影响不大;混杂纤维混凝土弹性模量随纤维界面弹性模量的增大而增大,且纤维掺量越大其增大幅度越大;增大钢纤维和聚丙烯纤维界面厚度均会减小其弹性模量;骨料体积分数是影响整体弹性模量的主要因素,表现在骨料所占体积越大,材料整体弹性模量也越大。
Hybrid fiber reinforced concrete(HFRC) is a typical multi-scale heterogeneous composite material and its macro-scale mechanical behavior at elastic stage is determined by its meso-, micro-and nano-components and structures. In order to explore the influence of microstructure at smaller scales on the macro-scale mechanical properties, a multi-scale homogenization theory model considering the interface effect for predicting the elastic modulus of steel-polypropylene(PP) hybrid fiber reinforced concrete was proposed based on the Mori-Tanaka method and three-phase model. The theoretical data from this model is in reasonable agreement with the experimental results from the reported literatures, thus proving the validity of this model. In the comparative analysis, the addition of steel fiber can enhance the elastic property of concrete slightly and the enhancing effect develops with the increase of fiber dosage, while the effect of PP fiber is negligible. Moreover, the elastic modulus of HFRC improves with the increase of the fiber interface property but reduces slightly with the increase of the fiber interface thickness. In addition, the aggregate volume fraction is another important factor affecting the HFRC elastic property: the larger the aggregate volume, the greater the HFRC modulus.
Hybrid fiber reinforced concrete(HFRC) is a typical multi-scale heterogeneous composite material and its macro-scale mechanical behavior at elastic stage is determined by its meso-, micro-and nano-components and structures. In order to explore the influence of microstructure at smaller scales on the macro-scale mechanical properties, a multi-scale homogenization theory model considering the interface effect for predicting the elastic modulus of steel-polypropylene(PP) hybrid fiber reinforced concrete was proposed based on the Mori-Tanaka method and three-phase model. The theoretical data from this model is in reasonable agreement with the experimental results from the reported literatures, thus proving the validity of this model. In the comparative analysis, the addition of steel fiber can enhance the elastic property of concrete slightly and the enhancing effect develops with the increase of fiber dosage, while the effect of PP fiber is negligible. Moreover, the elastic modulus of HFRC improves with the increase of the fiber interface property but reduces slightly with the increase of the fiber interface thickness. In addition, the aggregate volume fraction is another important factor affecting the HFRC elastic property: the larger the aggregate volume, the greater the HFRC modulus.
引文
[1]黄承逵.纤维混凝土结构[M].北京:机械工业出版社,2004:1-27.
[2]赵国藩,彭少民,黄承逵.钢纤维混凝土结构[M].北京:中国建筑工业出版社,1999:1-47.
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[5]CHI Y,YU M,HUANG L,et al.Finite element modeling of steel-polypropylene hybrid fiber reinforced concrete using modified concrete damaged plasticity[J].Eng Struct,2017,148:23-35.
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[7]BUDIANSKY B.On the elastic moduli of some heterogeneous materials[J].J Mech Phys Solids,1965,13(4):223-227.
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[9]PASA D V F,MAGHOUS S,CAMPOS F A,et al.A micromechanical approach to elastic and viscoelastic properties of fiber reinforced concrete[J].Cem Concr Res,2010,40(3):460-472.
[10]GAL E,KRYVORUK R.Meso-scale analysis of FRC using a two-step homogenization approach[J].Comput Struct,2011,89(11-12SI):921-929.
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[12]XU L H,DENG F Q,CHI Y.Nano-mechanical behavior of the interfacial transition zone between steel-polypropylene fiber and cement paste[J].Constr Build Mater,2017,145:619-638.
[13]胡杰,徐礼华,邓方茜,等.聚丙烯纤维增强水泥基复合材料界面过渡区的纳米力学性能[J].硅酸盐学报,2016,44(2):268-278.HU Jie,XU Lihua,DENG Fangqian,et al.J Chin Ceram Soc,2016,44(2):268-278.
[14]徐礼华,余红芸,池寅,等.钢纤维-水泥基界面过渡区纳米力学性能[J].硅酸盐学报,2016,44(8):1134-1146.XU Lihua,YU Hongyu,CHI Yin,et al.J Chin Ceram Soc,2016,44(8):1134-1146.
[15]ZHAO S J,SUN W.Nano-mechanical behavior of a green ultra-high performance concrete[J].Constr Build Mater,2014,63:150-160.
[16]WANG X H,JACOBSEN S,HE J Y,et al.Application of nanoindentation testing to study of the interfacial transition zone in steel fiber reinforced mortar[J].Cem Concr Res,2009,39(8):701-715.
[17]CONSTANTINIDES G,ULM F J.The effect of two types of C-S-H on the elasticity of cement-based materials:Results from nanoindentation and micromechanical modeling[J].Cem Concr Res,2004,34(1):67-80.
[18]CHRISTENSEN R M,LO K H.Solutions for effective shear properties in three phase sphere and cylinder models[J].J Mech Phys Solids,1979,27(4):315-330.
[19]ESHELBY J D.The determination of the elastic field of an ellipsoidal inclusion,and related problems[J].Proc R Soc London,1957,241(1226):376-396.
[20]LI G Q,ZHAO Y,PANG S S.Four-phase sphere modeling of effective bulk modulus of concrete[J].Cem Conc Res,1999,29(6):839-845.
[21]LUTZ M P,MONTEIRO P J M,ZIMMERMAN R W.Inhomogeneous interfacial transition zone model for the bulk modulus of mortar[J].Cem Concr Res,1997,27(7):1113-1122.
[22]ZANJANI ZADEH V,BOBKO C P.Nanomechanical characteristics of lightweight aggregate concrete containing supplementary cementitious materials exposed to elevated temperature[J].Constr Build Mater,2014,51:198-206.
[23]VANDAMME M,ULM F J,FONOLLOSA P.Nanogranular packing of C-S-H at substochiometric conditions[J].Cem Concr Res,2010,40(1):14-26.
[24]THOMAS J,RAMASWAMY A.Mechanical properties of steel fiber-reinforced concrete[J].J Mater Civ Eng,2007,19(5):385-392.
[25]焦楚杰,张季超,孙伟.钢纤维混凝土单轴受压试验研究[J].建筑科学,2005(5):1-5.JIAO Chujie,ZHANG Jichao,SUN Wei.Build Sci(in Chinese),2005(5):1-5.
[26]焦楚杰,詹镇峰,彭春元,等.混杂纤维混凝土抗压试验研究[J].广州大学学报(自然科学版),2007(4):70-73.JIAO Chujie,Zhan Zhenfeng,PENG Chunyuan,et al.J Guangzhou Univ:Nat Sci Ed(in Chinese),2007(4):70-73.
[27]YAO W,LI J,WU K.Mechanical properties of hybrid fiber-reinforced concrete at low fiber volume fraction[J].Cem Concr Res,2003,33(1):27-30.
[28]HUANG L,XU L H,CHI Y,et al.Experimental investigation on the seismic performance of steel-polypropylene hybrid fiber reinforced concrete columns[J].Constr Build Mater,2015,87(1-2):16-27.
[29]CHI Y,XU L H,ZHANG Y Y.Experimental study on hybrid fiber-reinforced concrete subjected to uniaxial compression[J].J Mater Civ Eng,2014,26(2):211-218.
[2]赵国藩,彭少民,黄承逵.钢纤维混凝土结构[M].北京:中国建筑工业出版社,1999:1-47.
[3]李艺,赵文.混杂纤维混凝土阻裂增韧及耐久性能[M].北京:科学出版社,2012:1-13.
[4]CHI Y,XU L H,YU H S.Constitutive modeling of steel-polypropylene hybrid fiber reinforced concrete using a non-associated plasticity and its numerical implementation[J].Compos Struct,2014,111:497-509.
[5]CHI Y,YU M,HUANG L,et al.Finite element modeling of steel-polypropylene hybrid fiber reinforced concrete using modified concrete damaged plasticity[J].Eng Struct,2017,148:23-35.
[6]MORI T,TANAKA K.Average stress in matrix and average elastic energy of materials with misfitting inclusions[J].Acta Metall,1973,21(5):571-574.
[7]BUDIANSKY B.On the elastic moduli of some heterogeneous materials[J].J Mech Phys Solids,1965,13(4):223-227.
[8]TENG T L,CHU Y A,CHANG F A,et al.Calculating the elastic moduli of steel-fiber reinforced concrete using a dedicated empirical formula[J].Comp Mater Sci,2004,31(3/4):337-346.
[9]PASA D V F,MAGHOUS S,CAMPOS F A,et al.A micromechanical approach to elastic and viscoelastic properties of fiber reinforced concrete[J].Cem Concr Res,2010,40(3):460-472.
[10]GAL E,KRYVORUK R.Meso-scale analysis of FRC using a two-step homogenization approach[J].Comput Struct,2011,89(11-12SI):921-929.
[11]GUAN X F,LIU X,JIA X,et al.A stochastic multiscale model for predicting mechanical properties of fiber reinforced concrete[J].Int JSolids Struct,2015,56/57:280-289.
[12]XU L H,DENG F Q,CHI Y.Nano-mechanical behavior of the interfacial transition zone between steel-polypropylene fiber and cement paste[J].Constr Build Mater,2017,145:619-638.
[13]胡杰,徐礼华,邓方茜,等.聚丙烯纤维增强水泥基复合材料界面过渡区的纳米力学性能[J].硅酸盐学报,2016,44(2):268-278.HU Jie,XU Lihua,DENG Fangqian,et al.J Chin Ceram Soc,2016,44(2):268-278.
[14]徐礼华,余红芸,池寅,等.钢纤维-水泥基界面过渡区纳米力学性能[J].硅酸盐学报,2016,44(8):1134-1146.XU Lihua,YU Hongyu,CHI Yin,et al.J Chin Ceram Soc,2016,44(8):1134-1146.
[15]ZHAO S J,SUN W.Nano-mechanical behavior of a green ultra-high performance concrete[J].Constr Build Mater,2014,63:150-160.
[16]WANG X H,JACOBSEN S,HE J Y,et al.Application of nanoindentation testing to study of the interfacial transition zone in steel fiber reinforced mortar[J].Cem Concr Res,2009,39(8):701-715.
[17]CONSTANTINIDES G,ULM F J.The effect of two types of C-S-H on the elasticity of cement-based materials:Results from nanoindentation and micromechanical modeling[J].Cem Concr Res,2004,34(1):67-80.
[18]CHRISTENSEN R M,LO K H.Solutions for effective shear properties in three phase sphere and cylinder models[J].J Mech Phys Solids,1979,27(4):315-330.
[19]ESHELBY J D.The determination of the elastic field of an ellipsoidal inclusion,and related problems[J].Proc R Soc London,1957,241(1226):376-396.
[20]LI G Q,ZHAO Y,PANG S S.Four-phase sphere modeling of effective bulk modulus of concrete[J].Cem Conc Res,1999,29(6):839-845.
[21]LUTZ M P,MONTEIRO P J M,ZIMMERMAN R W.Inhomogeneous interfacial transition zone model for the bulk modulus of mortar[J].Cem Concr Res,1997,27(7):1113-1122.
[22]ZANJANI ZADEH V,BOBKO C P.Nanomechanical characteristics of lightweight aggregate concrete containing supplementary cementitious materials exposed to elevated temperature[J].Constr Build Mater,2014,51:198-206.
[23]VANDAMME M,ULM F J,FONOLLOSA P.Nanogranular packing of C-S-H at substochiometric conditions[J].Cem Concr Res,2010,40(1):14-26.
[24]THOMAS J,RAMASWAMY A.Mechanical properties of steel fiber-reinforced concrete[J].J Mater Civ Eng,2007,19(5):385-392.
[25]焦楚杰,张季超,孙伟.钢纤维混凝土单轴受压试验研究[J].建筑科学,2005(5):1-5.JIAO Chujie,ZHANG Jichao,SUN Wei.Build Sci(in Chinese),2005(5):1-5.
[26]焦楚杰,詹镇峰,彭春元,等.混杂纤维混凝土抗压试验研究[J].广州大学学报(自然科学版),2007(4):70-73.JIAO Chujie,Zhan Zhenfeng,PENG Chunyuan,et al.J Guangzhou Univ:Nat Sci Ed(in Chinese),2007(4):70-73.
[27]YAO W,LI J,WU K.Mechanical properties of hybrid fiber-reinforced concrete at low fiber volume fraction[J].Cem Concr Res,2003,33(1):27-30.
[28]HUANG L,XU L H,CHI Y,et al.Experimental investigation on the seismic performance of steel-polypropylene hybrid fiber reinforced concrete columns[J].Constr Build Mater,2015,87(1-2):16-27.
[29]CHI Y,XU L H,ZHANG Y Y.Experimental study on hybrid fiber-reinforced concrete subjected to uniaxial compression[J].J Mater Civ Eng,2014,26(2):211-218.