多孔材料性能模型研究2:实验验证
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摘要
在三维网状多孔材料"八面体结构模型"及其系列基本物理、力学性能相关数理模型和表征方式基础上,本文对传导和拉伸等若干性能指标的数理关系验证进行了综述。重点讨论了数理关系的实践性、修正系数的合理性、对计算结果的影响、对应致密体的许用应力取值和塑性指数取值等问题。按照这种数理关系,通过多孔产品孔率等基本参量即可计算其电阻率等性能指标,实验结果证明了其可行性。本方法可以优越于有限元等复杂计算。
The "octahedral structure model" is introduced for three-dimensional reticulated porous materials, as well as the mathematical relations of their basic physical and mechanical properties. On this basis, the verification works about some performance relations, including the conductivity and tension, etc, are reviewed in this paper. A number of issues were discussed with the emphases on the practicality of these mathematical and physical relations, the rationality of the correction coefficients, the significant influence on the calculation results, and the allowable stress and the plastic index value of the corresponding dense body were also analyzed in details. According to this mathematical and physical relationship, the performance indexes such as the electrical resistivity of porous products can be calculated by the easily measurable basic parameters like the porosity. The experimental results prove this way feasible. Therefore, this method can be superior to the finite element and other complex computational methods.
The "octahedral structure model" is introduced for three-dimensional reticulated porous materials, as well as the mathematical relations of their basic physical and mechanical properties. On this basis, the verification works about some performance relations, including the conductivity and tension, etc, are reviewed in this paper. A number of issues were discussed with the emphases on the practicality of these mathematical and physical relations, the rationality of the correction coefficients, the significant influence on the calculation results, and the allowable stress and the plastic index value of the corresponding dense body were also analyzed in details. According to this mathematical and physical relationship, the performance indexes such as the electrical resistivity of porous products can be calculated by the easily measurable basic parameters like the porosity. The experimental results prove this way feasible. Therefore, this method can be superior to the finite element and other complex computational methods.
引文
[1] LIU P S,LIANG K M.Functional materials of porous metals made by P/M,electroplating and some other techniques[J].Journal of Materials Science,2001,36(21):5059-5072.
[2] 陈祥,李言祥.金属泡沫材料研究进展[J].材料导报,2003,17(5):5-8.CHEN X,LI Y X.Porous metals:research advances and applications[J].Materials Review,2003,17(5):5-8.
[3] ROSA M E.An introduction to solid foams[J].Philosophical Magazine Letters,2008,88(9/10):637-645.
[4] 刘培生.多孔材料引论[M].2版.北京:清华出版社,2013.LIU P S.Introduction to porous materials[M].2nd ed.Beijing:Tsinghua University Press,2013.
[5] LIU P S,CHEN G F.Porous materials:processing and appli-cations[M].Boston:Elsevier Science,2014.
[6] 刘培生,马晓明.多孔材料检测方法[M].北京:冶金工业出版社,2006.LIU P S,MA X M.Methods to measure porous materials [M].Beijing:Metallurgical Industrial Press,2005.
[7] 刘培生,崔光,程伟.多孔材料性能模型研究1:数理关系[J].材料工程,2019,47(6):42-62.LIU P S,CUI G,CHENG W.Study on the property model for porous materials 1:mathematical relations[J].Journal of Materials Engineering,2019,47(6):42-62.
[8] LIU P S,LI T F,FU C.Relationship between electrical resistivity and porosity for porous materials[J].Materials Science and Engineering:A,1999,268:208-215.
[9] LIU P S,LIANG K M.Preparation and corresponding structure of nickel foam[J].Materials Science and Technology,2000,16(5):575-578.
[10] BABJAK J,ETTLE V A,PASERIN V.Nickel foam:EP 0402738A2[P].1990-12-19.
[11] 美国金属学会.金属手册:第二卷[M].北京:机械工业出版社,1994:987.ASM(american society for metals).Metals handbook,Vol.2[M].Beijing:Machinery Industry Press,1994:987.
[12] LIU P S,LIANG K M.Evaluating electrical resistivity for high porosity metals[J].Materials Science and Technology,2000,16(3):341-343.
[13] LIU P S,CHEN H,LIANG K M,et al.Relationship between apparent electrical-conductivity and preparation conditions for nickel foam[J].Journal of Applied Electrochemistry,2000(10):1183-1186.
[14] LIU P S.The tensile strength of porous metals with high porosity[J].Journal of Advanced Materials,2000,32(2):9-16.
[15] ALY M S.Tensile properties of open-cell nickel foams[J].Materials & Design,2010,31:2237-2240.
[16] 刘培生,梁开明,顾守仁,等.多孔金属抗拉强度公式中的指数项取值[J].力学学报,2001,33(6):853-855.LIU P S,LIANG K M,GU S R,et al.The exponential item in formulas for calculating tensile strength of porous metal[J].Acta Mechanica Sinica,2001,33(6):853-855.
[17] LIU P S,LIANG K M,TU S W,et al.Relationship between tensile strength and preparation conditions for nickel foam[J].Materials Science and Technology,2001,17(9):1069-1072.
[18] LIU P S,FU C,LI T F.Relationship between elongation and porosity for high porosity metals[J].Transactions of Nonfe-rrous Metals Society of China,1999,9(3):546-552.
[19] 黄培云.粉末冶金原理[M].2版.北京:冶金工业出版社,1997.HUANG P Y.Principles of powder metallurgy[M].2nd ed.Beijing:Metallurgical Industry Press,1997.
[20] HAMIUDDIN M.Correction between mechanical properties and porosity of sintered iron and steels—a review[J].Powder Metallurgy International,1986,18(2):73-76.
[21] LIU P S,FU C,LI T F.Theoretical calculation of elongation after fracture for high porosity metals[J].Acta Metallurgica Sinica,1999,35(4):357-361.
[22] 刘文斌,张宏.塑性力学基础[M].北京:高等教育出版社,1986.LIU W B,ZHANG H.The basis of elastic-plastic mechanics[M].Beijing:Higher Education Press,1986.
[23] LIU P S.Tensile fracture behavior of foamed metallic materials properties[J].Materials Science and Engineering:A,2004,384 (1/2):352-354.
[24] YANG Q C,ZHANG M J,LIU P S.Macroscopic fracture beh-avior of nickel foam under tension[J].Multidiscipline Modeling in Materials and Structures,2016,12(1):110-118.
[25] LIU P S,FU C,LI T F,et al.Relationship between tensile strength and porosity for high porosity materials[J].Science in China,1999,42(1):100-107.
[26] GIBSON L J,ASHBY M F.Cellular solids:structure and prop-erties[M].2nd ed.Cambridge:Cambridge University Press,1999.
[27] ANDREWS E,SANDERS W,GIBSON L J.Compressive and tensile behavior of aluminum foams[J].Materials Science and Engineering:A,1999,270:113-124.
[28] GONG Z Y,LI Z Z.Materials mechanics[M].Beijing:Science Press,1999:112.
[29] DESHPANDE V S,FLECK N A.Isotropic constitutive models for metallic foams[J].Journal of the Mechanics and Physics of Solids,2000,48(6/7):1253-1283.
[30] LIU P S,FU C,LI T F.Approximate means for evaluating ten-sile strength of high porosity materials[J].Transactions of Nonferrous Metals Society of China,1999,9(1):70-78.
[31] LIU P S,WANG X S,LUO H Y.Relationship between tensile strength and porosity for foamed metals under equal speed biaxial tension[J].Materials Science and Technology,2003,19(6):985-987.
[32] LIU P S.Relationship between fracturing nominal stress and porosity for metal foams under biaxial tension[J].Science in China E,2003,46(5):546-550.
[33] LIU P S.Effect of preparation conditions on relative elongation of nickel foam[J].Materials Science and Technology,2004,20(5):669-672.
[34] 刘培生.泡沫金属双向承载的力学模型[J].中国有色金属学报,2006,16(4):567-574.LIU P S.Mechanical model for metallic foams under biaxial loads[J].The Chinese Journal of Nonferrous Metals,2006,16(4):567-574.
[35] LIU P S,CHEN G F.Mechanical relation of foamed metals under uniaxial and biaxial loads of collective tension and compression[J].Materials Science and Engineering:A,2009,507(1/2):190-193.
[36] LIU P S.Mechanical behaviors of porous metals under biaxial tensile loads[J].Materials Science and Engineering:A,2006,422(1/2):176-183.
[37] MAITI S K,ASHBY M F,GIBSON L J.Fracture toughness of brittle cellular solids[J].Scripta Metallurgica,1984,18(3):213-217.
[38] GIBSON L J,ASHBY M F,ZHANG J,et al.Failure surfaces for cellular materials under multiaxial loads:I.modelling[J].International Journal of Mechanical Sciences,1989,31(9):635-663.
[39] TRIANTAFILLOU T C,ZHANG J,SHERCLIFF T L,et al.Failure surfaces for cellular materials under multiaxial loads:II.comparison of models with experiment[J].International Journal of Mechanical Sciences,1989,31(9):665-678.
[40] LIU P S.Different theories application to foamed metals under biaxial equal-stress tension[J].Materials Science and Eng-ineering:A,2004,364:370-373.
[41] 刘培生,马晓明.高孔率泡沫金属材料疲劳表征模型及其实验研究[J].材料工程,2012(5):47-54.LIU P S,MA X M.Fatigue model for foamed metals with high porosity and corresponding experimental study[J].Journal of Materials Engineering,2012(5):47-54.
[42] 吴培英.金属材料学[M].北京:国防工业出版社,1987:81-83.WU P Y.Study on metal materials[M].Beijing:National Defence Industry Press,1987:81-83.
[43] 徐灏.疲劳强度[M].北京:高等教育出版社,1988:9-14,46-52,90,111-146.XU H.Fatigue strength[M].Beijing:Higher Education Press,1988:9-14,46-52,90,111-146.
[44] FRITTS D H.A discussion of the causes of blistering of sintered nickel hydroxide electrodes[J].Journal of Power Sources,1981,6(2):327-336.
[45] INGRAHAM M D,DEMARIA C J,ISSEN K A,et al.Low cy-cle fatigue of aluminum foam[J].Materials Science and Engineering:A,2009,504(1/2):150-156.
[46] HUANG J S,LIU S Y.Fatigue of isotropic open-cell foams under multiaxial loads[J].International Journal of Fatigue,2001,23(3):233-240.
[47] ZETTL B,MAYER H,STANZL-TSCHEGG S E,et al.Fatigue properties of aluminium foams at high numbers of cycles[J].Materials Science and Engineering:A,2000,292(1):1-7.
[48] SCHULTZ O,DES LIGNERIS A,HAIDER O,et al.Fatigue behavior,strength,and failure of aluminum foam[J].Advanced Engineering Materials,2000,2(4):215-218.
[49] 刘培生.多孔金属比表面积的计算方法[J].材料研究学报,2009,23(4):415-420.LIU P S.Calculation method for the specific surface area of por-ous metals[J].Chinese Journal of Materials Research,2009,23(4):415-420.
[50] 刘培生.多孔材料比表面积和孔隙形貌的测定方法[J].稀有金属材料与工程,2006,35(增刊2):25-29.LIU P S.Determining methods for specific surface area and pore morphology of porous materials[J].Rare Metal Materials and Engineering,2006,35(Suppl 2):25-29.
[51] 马立群,何德坪.新型泡沫铝的制备及其孔结构的控制[J].材料研究学报,1994,8(1):11-17.MA L Q,HE D P.Fabrication and pore structure control of new type aluminium foams[J].Chinese Journal of Materials Rese-arch,1994,8(1):11-17.
[52] CHEN B,LIU P S,CHEN J H.Influence of processing on sur-face morphology and specific surface area for the nickel foam made by electrodeposition[J].Multidiscipline Modeling in Mat-erials and Structures,2018,14(4):735-743.
[2] 陈祥,李言祥.金属泡沫材料研究进展[J].材料导报,2003,17(5):5-8.CHEN X,LI Y X.Porous metals:research advances and applications[J].Materials Review,2003,17(5):5-8.
[3] ROSA M E.An introduction to solid foams[J].Philosophical Magazine Letters,2008,88(9/10):637-645.
[4] 刘培生.多孔材料引论[M].2版.北京:清华出版社,2013.LIU P S.Introduction to porous materials[M].2nd ed.Beijing:Tsinghua University Press,2013.
[5] LIU P S,CHEN G F.Porous materials:processing and appli-cations[M].Boston:Elsevier Science,2014.
[6] 刘培生,马晓明.多孔材料检测方法[M].北京:冶金工业出版社,2006.LIU P S,MA X M.Methods to measure porous materials [M].Beijing:Metallurgical Industrial Press,2005.
[7] 刘培生,崔光,程伟.多孔材料性能模型研究1:数理关系[J].材料工程,2019,47(6):42-62.LIU P S,CUI G,CHENG W.Study on the property model for porous materials 1:mathematical relations[J].Journal of Materials Engineering,2019,47(6):42-62.
[8] LIU P S,LI T F,FU C.Relationship between electrical resistivity and porosity for porous materials[J].Materials Science and Engineering:A,1999,268:208-215.
[9] LIU P S,LIANG K M.Preparation and corresponding structure of nickel foam[J].Materials Science and Technology,2000,16(5):575-578.
[10] BABJAK J,ETTLE V A,PASERIN V.Nickel foam:EP 0402738A2[P].1990-12-19.
[11] 美国金属学会.金属手册:第二卷[M].北京:机械工业出版社,1994:987.ASM(american society for metals).Metals handbook,Vol.2[M].Beijing:Machinery Industry Press,1994:987.
[12] LIU P S,LIANG K M.Evaluating electrical resistivity for high porosity metals[J].Materials Science and Technology,2000,16(3):341-343.
[13] LIU P S,CHEN H,LIANG K M,et al.Relationship between apparent electrical-conductivity and preparation conditions for nickel foam[J].Journal of Applied Electrochemistry,2000(10):1183-1186.
[14] LIU P S.The tensile strength of porous metals with high porosity[J].Journal of Advanced Materials,2000,32(2):9-16.
[15] ALY M S.Tensile properties of open-cell nickel foams[J].Materials & Design,2010,31:2237-2240.
[16] 刘培生,梁开明,顾守仁,等.多孔金属抗拉强度公式中的指数项取值[J].力学学报,2001,33(6):853-855.LIU P S,LIANG K M,GU S R,et al.The exponential item in formulas for calculating tensile strength of porous metal[J].Acta Mechanica Sinica,2001,33(6):853-855.
[17] LIU P S,LIANG K M,TU S W,et al.Relationship between tensile strength and preparation conditions for nickel foam[J].Materials Science and Technology,2001,17(9):1069-1072.
[18] LIU P S,FU C,LI T F.Relationship between elongation and porosity for high porosity metals[J].Transactions of Nonfe-rrous Metals Society of China,1999,9(3):546-552.
[19] 黄培云.粉末冶金原理[M].2版.北京:冶金工业出版社,1997.HUANG P Y.Principles of powder metallurgy[M].2nd ed.Beijing:Metallurgical Industry Press,1997.
[20] HAMIUDDIN M.Correction between mechanical properties and porosity of sintered iron and steels—a review[J].Powder Metallurgy International,1986,18(2):73-76.
[21] LIU P S,FU C,LI T F.Theoretical calculation of elongation after fracture for high porosity metals[J].Acta Metallurgica Sinica,1999,35(4):357-361.
[22] 刘文斌,张宏.塑性力学基础[M].北京:高等教育出版社,1986.LIU W B,ZHANG H.The basis of elastic-plastic mechanics[M].Beijing:Higher Education Press,1986.
[23] LIU P S.Tensile fracture behavior of foamed metallic materials properties[J].Materials Science and Engineering:A,2004,384 (1/2):352-354.
[24] YANG Q C,ZHANG M J,LIU P S.Macroscopic fracture beh-avior of nickel foam under tension[J].Multidiscipline Modeling in Materials and Structures,2016,12(1):110-118.
[25] LIU P S,FU C,LI T F,et al.Relationship between tensile strength and porosity for high porosity materials[J].Science in China,1999,42(1):100-107.
[26] GIBSON L J,ASHBY M F.Cellular solids:structure and prop-erties[M].2nd ed.Cambridge:Cambridge University Press,1999.
[27] ANDREWS E,SANDERS W,GIBSON L J.Compressive and tensile behavior of aluminum foams[J].Materials Science and Engineering:A,1999,270:113-124.
[28] GONG Z Y,LI Z Z.Materials mechanics[M].Beijing:Science Press,1999:112.
[29] DESHPANDE V S,FLECK N A.Isotropic constitutive models for metallic foams[J].Journal of the Mechanics and Physics of Solids,2000,48(6/7):1253-1283.
[30] LIU P S,FU C,LI T F.Approximate means for evaluating ten-sile strength of high porosity materials[J].Transactions of Nonferrous Metals Society of China,1999,9(1):70-78.
[31] LIU P S,WANG X S,LUO H Y.Relationship between tensile strength and porosity for foamed metals under equal speed biaxial tension[J].Materials Science and Technology,2003,19(6):985-987.
[32] LIU P S.Relationship between fracturing nominal stress and porosity for metal foams under biaxial tension[J].Science in China E,2003,46(5):546-550.
[33] LIU P S.Effect of preparation conditions on relative elongation of nickel foam[J].Materials Science and Technology,2004,20(5):669-672.
[34] 刘培生.泡沫金属双向承载的力学模型[J].中国有色金属学报,2006,16(4):567-574.LIU P S.Mechanical model for metallic foams under biaxial loads[J].The Chinese Journal of Nonferrous Metals,2006,16(4):567-574.
[35] LIU P S,CHEN G F.Mechanical relation of foamed metals under uniaxial and biaxial loads of collective tension and compression[J].Materials Science and Engineering:A,2009,507(1/2):190-193.
[36] LIU P S.Mechanical behaviors of porous metals under biaxial tensile loads[J].Materials Science and Engineering:A,2006,422(1/2):176-183.
[37] MAITI S K,ASHBY M F,GIBSON L J.Fracture toughness of brittle cellular solids[J].Scripta Metallurgica,1984,18(3):213-217.
[38] GIBSON L J,ASHBY M F,ZHANG J,et al.Failure surfaces for cellular materials under multiaxial loads:I.modelling[J].International Journal of Mechanical Sciences,1989,31(9):635-663.
[39] TRIANTAFILLOU T C,ZHANG J,SHERCLIFF T L,et al.Failure surfaces for cellular materials under multiaxial loads:II.comparison of models with experiment[J].International Journal of Mechanical Sciences,1989,31(9):665-678.
[40] LIU P S.Different theories application to foamed metals under biaxial equal-stress tension[J].Materials Science and Eng-ineering:A,2004,364:370-373.
[41] 刘培生,马晓明.高孔率泡沫金属材料疲劳表征模型及其实验研究[J].材料工程,2012(5):47-54.LIU P S,MA X M.Fatigue model for foamed metals with high porosity and corresponding experimental study[J].Journal of Materials Engineering,2012(5):47-54.
[42] 吴培英.金属材料学[M].北京:国防工业出版社,1987:81-83.WU P Y.Study on metal materials[M].Beijing:National Defence Industry Press,1987:81-83.
[43] 徐灏.疲劳强度[M].北京:高等教育出版社,1988:9-14,46-52,90,111-146.XU H.Fatigue strength[M].Beijing:Higher Education Press,1988:9-14,46-52,90,111-146.
[44] FRITTS D H.A discussion of the causes of blistering of sintered nickel hydroxide electrodes[J].Journal of Power Sources,1981,6(2):327-336.
[45] INGRAHAM M D,DEMARIA C J,ISSEN K A,et al.Low cy-cle fatigue of aluminum foam[J].Materials Science and Engineering:A,2009,504(1/2):150-156.
[46] HUANG J S,LIU S Y.Fatigue of isotropic open-cell foams under multiaxial loads[J].International Journal of Fatigue,2001,23(3):233-240.
[47] ZETTL B,MAYER H,STANZL-TSCHEGG S E,et al.Fatigue properties of aluminium foams at high numbers of cycles[J].Materials Science and Engineering:A,2000,292(1):1-7.
[48] SCHULTZ O,DES LIGNERIS A,HAIDER O,et al.Fatigue behavior,strength,and failure of aluminum foam[J].Advanced Engineering Materials,2000,2(4):215-218.
[49] 刘培生.多孔金属比表面积的计算方法[J].材料研究学报,2009,23(4):415-420.LIU P S.Calculation method for the specific surface area of por-ous metals[J].Chinese Journal of Materials Research,2009,23(4):415-420.
[50] 刘培生.多孔材料比表面积和孔隙形貌的测定方法[J].稀有金属材料与工程,2006,35(增刊2):25-29.LIU P S.Determining methods for specific surface area and pore morphology of porous materials[J].Rare Metal Materials and Engineering,2006,35(Suppl 2):25-29.
[51] 马立群,何德坪.新型泡沫铝的制备及其孔结构的控制[J].材料研究学报,1994,8(1):11-17.MA L Q,HE D P.Fabrication and pore structure control of new type aluminium foams[J].Chinese Journal of Materials Rese-arch,1994,8(1):11-17.
[52] CHEN B,LIU P S,CHEN J H.Influence of processing on sur-face morphology and specific surface area for the nickel foam made by electrodeposition[J].Multidiscipline Modeling in Mat-erials and Structures,2018,14(4):735-743.