工程材料力学性质与其微结构关系研究
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摘要
材料力学性质依赖于材料微结构。本文针对两种常见工程材料，进行了以下工作：
第一部分研究了高聚物材料粘弹性力学性质与其微结构的关系。高聚物由晶态与非晶态两部分组成，其中晶态部分是晶片的集合，非晶态部分包含了大量随机取向的分子链。分子链在主方向是以化学键连接，垂直于分子链主方向以范德华力相结合，因此晶片的取向分布和分子链的取向分布将强烈地影响材料的宏观力学性质。引入取向分布函数ODF，我们分析了晶态部分弹性力学性质与晶片取向分布的关系，得到晶态部分有效弹性刚度张量与有效弹性柔度张量；建立分子链取向分布函数CODF，在Kelvin模型下，推导了非晶态部分的粘弹性力学性质与化学成分及其分子链的取向分布关系；并在Voigt模型下给出了包含晶片织构效应、分子链取向效应、晶态化学性质、非晶态化学性质的高聚物材料粘弹性本构方程。
第二部分研究了多相弹塑性复合材料力学性质与微结构的关系。多相单一颗粒材料集合而成的材料称为多相颗粒复合材料。多相颗粒材料的微结构包括单一组分的力学性能，颗粒的几何形状，颗粒之间的相互作用等。把多相颗粒复合材料中的任意颗粒看成夹杂，假设夹杂平均形状是球形，利用等效夹杂法和本征应变自洽法，给出了多相颗粒复合材料的宏观弹塑性应力-应变增量关系，寻找出多相颗粒复合材料的宏观弹塑性力学性质与各相颗粒材料力学性质的关系。实际材料中夹杂具有任意形状，夹杂形状分布会影响材料进入屈服的条件。假设屈服函数依赖于应力与夹杂形状分布，利用客观性原理讨论了由基体／夹杂组成的两相材料的屈服函数一般形式，包含五个材料常数。
The materials mechanics nature relies on the material microstructure. In view of two kind of common engineering material, this paper has carried on following work:
The first part has studied the relations of high polymer material visco-elasticity mechanical properties and the material microstructure. High Polymers is composed by the crystalline part and the non-crystalline part. Crystalline part is the set of chip; non-crystalline part is made of molecular chain. The Crystal itself has the anisotropic. The molecular chain in the principal direction is jointed by chemistry keying, vertical unifies in the molecular chain principal direction is connected by the van der Waals force, Therefore the crystalline orientation distribution and the molecular chain orientation distribution will intensely effect the material the macroscopic mechanical properties. We introduce orientation distribution function ODF, have respectively analyzed the crystalline elasticity theory nature and the crystalline orientation distribution relations under the Voigt model and the Reuss model, and then obtain the effective elastic rigidity tensor of crystalline. we has established molecular chain orientation distribution function CODF, and has inferred the non-crystalline state part under Kelvin model visco-elasticity mechanical properties and the chemical composition and the molecular chain orientation distribution relations. And gives containing the texture coefficient, the orientation coefficient, the crystalline state chemical property, the non-crystalline state chemical property effect high polymer material visco-elasticity constitutive equation. And gives contains the texture effect, the molecular chain orientation effect, the crystalline state chemical property, the non-crystalline state chemical property effect high polymer material visco-elasticity constitutive equation.
The second part has studied the relations of elasto-plasticity composite materials mechanical properties and the microstructure. Two materials is composed which by the matrix/inclusions, the inclusions shape distribution can affect the condition which the material enters submits. Our supposition submits the criterion to rely on the stress and the shape distribution, inclusions effect the yield function, using the principle of material frame-indifference contains infers the general form. Assume that a composite material is an aggregate of numerous several phase elasto-plastic grains, where any grain in the composite material only belongs to one phase material. In this paper, any grain in the composite material is taken as an inclusion. By the equivalent inclusion method and the self-consistent method on eigen-strain, we give the macroscopic constitutive relation of the composite material of several phase elasto-plastic grains. We find out the relations of material properties between the composite material and its tiny grains.
第一部分研究了高聚物材料粘弹性力学性质与其微结构的关系。高聚物由晶态与非晶态两部分组成，其中晶态部分是晶片的集合，非晶态部分包含了大量随机取向的分子链。分子链在主方向是以化学键连接，垂直于分子链主方向以范德华力相结合，因此晶片的取向分布和分子链的取向分布将强烈地影响材料的宏观力学性质。引入取向分布函数ODF，我们分析了晶态部分弹性力学性质与晶片取向分布的关系，得到晶态部分有效弹性刚度张量与有效弹性柔度张量；建立分子链取向分布函数CODF，在Kelvin模型下，推导了非晶态部分的粘弹性力学性质与化学成分及其分子链的取向分布关系；并在Voigt模型下给出了包含晶片织构效应、分子链取向效应、晶态化学性质、非晶态化学性质的高聚物材料粘弹性本构方程。
第二部分研究了多相弹塑性复合材料力学性质与微结构的关系。多相单一颗粒材料集合而成的材料称为多相颗粒复合材料。多相颗粒材料的微结构包括单一组分的力学性能，颗粒的几何形状，颗粒之间的相互作用等。把多相颗粒复合材料中的任意颗粒看成夹杂，假设夹杂平均形状是球形，利用等效夹杂法和本征应变自洽法，给出了多相颗粒复合材料的宏观弹塑性应力-应变增量关系，寻找出多相颗粒复合材料的宏观弹塑性力学性质与各相颗粒材料力学性质的关系。实际材料中夹杂具有任意形状，夹杂形状分布会影响材料进入屈服的条件。假设屈服函数依赖于应力与夹杂形状分布，利用客观性原理讨论了由基体／夹杂组成的两相材料的屈服函数一般形式，包含五个材料常数。
The materials mechanics nature relies on the material microstructure. In view of two kind of common engineering material, this paper has carried on following work:
The first part has studied the relations of high polymer material visco-elasticity mechanical properties and the material microstructure. High Polymers is composed by the crystalline part and the non-crystalline part. Crystalline part is the set of chip; non-crystalline part is made of molecular chain. The Crystal itself has the anisotropic. The molecular chain in the principal direction is jointed by chemistry keying, vertical unifies in the molecular chain principal direction is connected by the van der Waals force, Therefore the crystalline orientation distribution and the molecular chain orientation distribution will intensely effect the material the macroscopic mechanical properties. We introduce orientation distribution function ODF, have respectively analyzed the crystalline elasticity theory nature and the crystalline orientation distribution relations under the Voigt model and the Reuss model, and then obtain the effective elastic rigidity tensor of crystalline. we has established molecular chain orientation distribution function CODF, and has inferred the non-crystalline state part under Kelvin model visco-elasticity mechanical properties and the chemical composition and the molecular chain orientation distribution relations. And gives containing the texture coefficient, the orientation coefficient, the crystalline state chemical property, the non-crystalline state chemical property effect high polymer material visco-elasticity constitutive equation. And gives contains the texture effect, the molecular chain orientation effect, the crystalline state chemical property, the non-crystalline state chemical property effect high polymer material visco-elasticity constitutive equation.
The second part has studied the relations of elasto-plasticity composite materials mechanical properties and the microstructure. Two materials is composed which by the matrix/inclusions, the inclusions shape distribution can affect the condition which the material enters submits. Our supposition submits the criterion to rely on the stress and the shape distribution, inclusions effect the yield function, using the principle of material frame-indifference contains infers the general form. Assume that a composite material is an aggregate of numerous several phase elasto-plastic grains, where any grain in the composite material only belongs to one phase material. In this paper, any grain in the composite material is taken as an inclusion. By the equivalent inclusion method and the self-consistent method on eigen-strain, we give the macroscopic constitutive relation of the composite material of several phase elasto-plastic grains. We find out the relations of material properties between the composite material and its tiny grains.
引文
[1] I．M Word著．固体高聚物的力学性能．徐懋译．北京：科学出版社．1980．2
[2] 刘凤企．高分子物理．北京．高等教育出版社．1995．10
[3] Treloar the Physics of Rubber Elasticity. 3rd edition. Oxford University Press.
[4] 周光泉，刘孝敏．粘弹性理论．中国科技出版社 1996．
[5] Bunge H J. Texture of non-metallic Materials. [J].1991.Texture and Microstructures. 14(1):283.
[6] 王超群，胡广勇．双轴拉伸Bopp薄膜的织构研究 理化检验-物理分册 2004．40(2)
[7] 黄筑平 连续介质力学基础 北京：高等教育出版社 2003．2
[8] Roe R.J. Description of crystallite orientation in polycrystalline materials: Ⅲ, general solution to pole figures. 1965.
[9] Bunge H.J. Texture Analysis in Material Science: Mathematical Methods. London: Butterworths. 1982.
[10] L.C and Louck J.D. Angular Momentum In Quantum Physics. Cambridge. Cambridge University Press. 1984.
[11] Man.C-S. Notes on Quantitative Texture Analysis. Department of Mathematics.University of Kentucky, Lexington.
[12] Morris, P.R. Averaging fourth-rank tensors with weight functions. [J]. Appl Phys. 1969.40.447-448.
[13] Sayers, C.M. Ultrasonic velocities in anisotropic polycrystalline aggregates. J.Phys.,D, 1982. 15:2157-2167
[14] 黄模佳，Man，C．-S．立方晶粒各向异性集合的弹性本构关系．力学及其在木工程中的应用．清华大学出版，2002，107-116．
[15] 于同隐 何曼君 高聚物的粘弹性 上海科学技术出版社 1986．
[16] Perturbation approach to elastic constitutive relations of polycrystals.
[17] M．赫尔 群论：40-50 1981．3
[18] 张瑞明 钟志成 应用群论导引 武汉：华中科技大学出版社 2001．1
[19] K.Tashiro, M.Kobayashi and H. Tadokoro, macromolecules. 1978. 11.914.
[20] Man,C-S. Material tensors of weakly-textured aterials. In:Chien, W. et al Proceedings of the Third International Conference on Nonliner Mechanics. Shang hai University Press. Shang hai. 1998a. pp. 7-94.
[21] Man, C-S. On the constitutive equations of some weakly-textured polycrystals. Arch Rational Mech 1998.143.77-103.
[22] R．J．塞缪尔斯 美 结晶高聚物的性质．1984．7
[23] Man.C-S. On the constitutive equations of some weakly-textured poly-crystals.Arch Rational Mech 1998.143, 77-103.
[24] Huang, Mo. and Man,C-S. Constitutive relation of elastic polycrystal with quadratic texture dependence. [J] .Elasticity.2003. Vol.72, 183-212.
[25] 杨挺青 粘弹性力学 华中科技大学出版社 1990．6．
[1] 王仁 黄文彬 塑性力学引论 北京大学出版社．2003．07
[2] Taylor, G.I. Plastic strain in metals. J Inst.Met. 1938. Vol. 62. 307-324
[3] Sachs,G. Zur zbleilung einer fleissbedingung.Z. Verein Deut. 1928. Ing. Vol72.
[4] Man.C-S. On the correlation of elastic and plastic anisotropy in sheet metals .[J] Elasticity. 1995.Vol.39. 165-173.
[5] Man.C-S.Huang. Identification of material parameters in yield functions and flow rules for weakly textured sheets of cubic metals.International Jornal of Non-linear Mechanics. 2001.Vol.36..501-514.
[6] Hill,R. The elastic behavior of a crystallinaggregate.Proc.Phys.Soc.A65:349-354
[7] Eshelby. JD. The determination of the elastic field of an elliosidl inclusion,ande related problems. 1957. Proc.R.Soc A 241.376-396.
[8] Eshelby. JD. The determination of the elastic field of an elliosidl inclusion,ande related problems. 1957. Proc.R.Soc A 241.376-396.
[9] Kroner .E.Zur plastichen Verformung des.Vielkristalls. Acta Met. 1958.9:153-161.
[10] Budiansky.B.Wu.TY. The oretical prediction of plastic strains of polycrystals. In:Proc. 4th US Nat.Conger. Appel.Mech. 1962. 1175-1185
[11] Hill, R. A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 1965.213-222.
[12] Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech.Phys. Solids 13.1965.89—101.
[13] Hill. R. A self-consistent mechanic of materials. [J].M ech Phys Solids. 13. 1968.213-222.
[14] Hill R. On constitutive inequalities for simple materials. [J] Mech Phys Solids.16. 1972. 315-322.
[15] Budiansky. B.Wu.TY. Theoretical prediction of plastic strains of polycrystals. In: Proc.4th US Nat.Conger. Appel.Mech. 1962.1175-1185
[16] Nemat-Nasser, S. Hori.M. Micromechanics: Overall Properties of Heterogeneous Materials. 1993.North-Holland Amsterdam.
[17] Mura, T. Micromechanics of defects in solids.1987. Martinus Nijhoff Publishes. The Hague.
[18] 黄模佳，Man，C．-S．立方晶粒各向异性集合的弹性本构关系．力学及其在木工程中的应用，清华大学出版．2002．200．107-116．
[19] Mori T, Tanka Average stress in matrix and average elastic energy of materials with misfitting inclusions.Acta Metall.21.1973.571-574.
[20] Weng G J. Some elastic properties of reinforced solides, with special reference to isotropic ones containing spherical inclusions. Int J Eng Sci .22.1984.845-856.
[21] Benvensite Y. A new approach to the application of Mori-Tanaka's theory in cmposite materials.Me.6.1987.147-157.
[22] 黄克智 黄永刚 固体本构关系 清华大学出版社 1999．
[23] Ju, J.W. Chen, T.M. Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities, Acta Mechanica 1994.103,. 103-121.
[24] 吴永礼：计算固体力学方法，科学出版社，2003．
[25] 杨庆生：复合材料细观结构力学与设计，中国铁道出版社，2000。
[26] 王自强、段祝平：塑性细观力学，科学出版社，1995。
[27] Mojia Huang, Zhiwen Lan Constitutive relation of an orthorhombic polycrystal with the shape coefficients 固体力学学报 2005．Sinica21：608-618
[28] Man. C-S..Material tensors of weakly-textured aterials.In:Chien,W, et al Proceedings of the Third International Conference on Nonliner Mechanics. Shang hai University Press, Shang hai. 1998a. pp. 7-94.
[29] Man.C-S.On the constitutive equations of some weakly-textured polycrystals. Arch Rational Mech 143. 1998.77-103.
[2] 刘凤企．高分子物理．北京．高等教育出版社．1995．10
[3] Treloar the Physics of Rubber Elasticity. 3rd edition. Oxford University Press.
[4] 周光泉，刘孝敏．粘弹性理论．中国科技出版社 1996．
[5] Bunge H J. Texture of non-metallic Materials. [J].1991.Texture and Microstructures. 14(1):283.
[6] 王超群，胡广勇．双轴拉伸Bopp薄膜的织构研究 理化检验-物理分册 2004．40(2)
[7] 黄筑平 连续介质力学基础 北京：高等教育出版社 2003．2
[8] Roe R.J. Description of crystallite orientation in polycrystalline materials: Ⅲ, general solution to pole figures. 1965.
[9] Bunge H.J. Texture Analysis in Material Science: Mathematical Methods. London: Butterworths. 1982.
[10] L.C and Louck J.D. Angular Momentum In Quantum Physics. Cambridge. Cambridge University Press. 1984.
[11] Man.C-S. Notes on Quantitative Texture Analysis. Department of Mathematics.University of Kentucky, Lexington.
[12] Morris, P.R. Averaging fourth-rank tensors with weight functions. [J]. Appl Phys. 1969.40.447-448.
[13] Sayers, C.M. Ultrasonic velocities in anisotropic polycrystalline aggregates. J.Phys.,D, 1982. 15:2157-2167
[14] 黄模佳，Man，C．-S．立方晶粒各向异性集合的弹性本构关系．力学及其在木工程中的应用．清华大学出版，2002，107-116．
[15] 于同隐 何曼君 高聚物的粘弹性 上海科学技术出版社 1986．
[16] Perturbation approach to elastic constitutive relations of polycrystals.
[17] M．赫尔 群论：40-50 1981．3
[18] 张瑞明 钟志成 应用群论导引 武汉：华中科技大学出版社 2001．1
[19] K.Tashiro, M.Kobayashi and H. Tadokoro, macromolecules. 1978. 11.914.
[20] Man,C-S. Material tensors of weakly-textured aterials. In:Chien, W. et al Proceedings of the Third International Conference on Nonliner Mechanics. Shang hai University Press. Shang hai. 1998a. pp. 7-94.
[21] Man, C-S. On the constitutive equations of some weakly-textured polycrystals. Arch Rational Mech 1998.143.77-103.
[22] R．J．塞缪尔斯 美 结晶高聚物的性质．1984．7
[23] Man.C-S. On the constitutive equations of some weakly-textured poly-crystals.Arch Rational Mech 1998.143, 77-103.
[24] Huang, Mo. and Man,C-S. Constitutive relation of elastic polycrystal with quadratic texture dependence. [J] .Elasticity.2003. Vol.72, 183-212.
[25] 杨挺青 粘弹性力学 华中科技大学出版社 1990．6．
[1] 王仁 黄文彬 塑性力学引论 北京大学出版社．2003．07
[2] Taylor, G.I. Plastic strain in metals. J Inst.Met. 1938. Vol. 62. 307-324
[3] Sachs,G. Zur zbleilung einer fleissbedingung.Z. Verein Deut. 1928. Ing. Vol72.
[4] Man.C-S. On the correlation of elastic and plastic anisotropy in sheet metals .[J] Elasticity. 1995.Vol.39. 165-173.
[5] Man.C-S.Huang. Identification of material parameters in yield functions and flow rules for weakly textured sheets of cubic metals.International Jornal of Non-linear Mechanics. 2001.Vol.36..501-514.
[6] Hill,R. The elastic behavior of a crystallinaggregate.Proc.Phys.Soc.A65:349-354
[7] Eshelby. JD. The determination of the elastic field of an elliosidl inclusion,ande related problems. 1957. Proc.R.Soc A 241.376-396.
[8] Eshelby. JD. The determination of the elastic field of an elliosidl inclusion,ande related problems. 1957. Proc.R.Soc A 241.376-396.
[9] Kroner .E.Zur plastichen Verformung des.Vielkristalls. Acta Met. 1958.9:153-161.
[10] Budiansky.B.Wu.TY. The oretical prediction of plastic strains of polycrystals. In:Proc. 4th US Nat.Conger. Appel.Mech. 1962. 1175-1185
[11] Hill, R. A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 1965.213-222.
[12] Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech.Phys. Solids 13.1965.89—101.
[13] Hill. R. A self-consistent mechanic of materials. [J].M ech Phys Solids. 13. 1968.213-222.
[14] Hill R. On constitutive inequalities for simple materials. [J] Mech Phys Solids.16. 1972. 315-322.
[15] Budiansky. B.Wu.TY. Theoretical prediction of plastic strains of polycrystals. In: Proc.4th US Nat.Conger. Appel.Mech. 1962.1175-1185
[16] Nemat-Nasser, S. Hori.M. Micromechanics: Overall Properties of Heterogeneous Materials. 1993.North-Holland Amsterdam.
[17] Mura, T. Micromechanics of defects in solids.1987. Martinus Nijhoff Publishes. The Hague.
[18] 黄模佳，Man，C．-S．立方晶粒各向异性集合的弹性本构关系．力学及其在木工程中的应用，清华大学出版．2002．200．107-116．
[19] Mori T, Tanka Average stress in matrix and average elastic energy of materials with misfitting inclusions.Acta Metall.21.1973.571-574.
[20] Weng G J. Some elastic properties of reinforced solides, with special reference to isotropic ones containing spherical inclusions. Int J Eng Sci .22.1984.845-856.
[21] Benvensite Y. A new approach to the application of Mori-Tanaka's theory in cmposite materials.Me.6.1987.147-157.
[22] 黄克智 黄永刚 固体本构关系 清华大学出版社 1999．
[23] Ju, J.W. Chen, T.M. Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities, Acta Mechanica 1994.103,. 103-121.
[24] 吴永礼：计算固体力学方法，科学出版社，2003．
[25] 杨庆生：复合材料细观结构力学与设计，中国铁道出版社，2000。
[26] 王自强、段祝平：塑性细观力学，科学出版社，1995。
[27] Mojia Huang, Zhiwen Lan Constitutive relation of an orthorhombic polycrystal with the shape coefficients 固体力学学报 2005．Sinica21：608-618
[28] Man. C-S..Material tensors of weakly-textured aterials.In:Chien,W, et al Proceedings of the Third International Conference on Nonliner Mechanics. Shang hai University Press, Shang hai. 1998a. pp. 7-94.
[29] Man.C-S.On the constitutive equations of some weakly-textured polycrystals. Arch Rational Mech 143. 1998.77-103.