四向矩形编织复合材料几何细观结构和力学性能研究
|
摘要
编织复合材料是近二十年新出现的先进材料，具有许多优越性能，已被用于航空航天和一般工业。对其进行理论研究和性能预估，是日益重要的前沿课题。
本文详细研究了四向矩形编织复合材料的内部结构、表面结构和角柱结构。以矢量方法推导公式，解析确定纤维束的路径、接触点位置、接触线形状、过接触处的公法线方向，得到一些重要结果。从而为有限元分析计算提供了几何基础和所需数据。给出将材料划分为单胞的正确方法和更符合实际的单胞图形，消除了现有划分方法的几个不足，统一了单胞数的计算式。
发展出一种有限元方法，分析了这种材料在纵向拉伸下的力学响应。将纤维束划分为空间梁元，忽略基体。但把基体对纤维束的连接作用体现为纤维束相互接触处的固接，从而建立梁元节点位移约束关系，形成材料的结构增广刚阵。通过编程计算，得材料应变和模量等宏观力学量，还得纤维束的内力、内力矩、最大应力的值及位置、纤维束间的相互作用力等。计算结果与实验值吻合良好，证实了方法的有效可行。有可能成为其它载荷工况下的力学分析手段。
上述工作填补了该材料几何细观结构研究的一些空白，开辟了该材料模量和强度研究的新途径。本文将这两方面探索作了实质性推进。
Braided composites are advanced materials come out twenty years ago. Owing to their many superior behaviors, they have been used in aeronautics, astronautics and general industries. Theoretic approach and prediction for their performances have become increasingly important.
This dissertation investigates interior, surface and comer architecture of 4-directional rectangular braided composites in detail. Vector method is used to deduce mathematic expressions, the path of fiber tows in the material, position of contact point and shape of contact line between any two fiber tows, and common normal of any two fiber tows through their contact place, are all determined analytically, some important conclusions are drawn. These efforts result in provisions of geometric basis and data needed by following finite element analysis. Removing several shortcomings of existing methods dividing the material into unit cells, a correct division method and corresponding unit cell's graphics which are more approximate to the real, are proposed. Formulas to determine the numbers of unit-cells become unity.
A finite element method is developed to study mechanical response of composites under longitudinal tension. The fiber tows are divided into spatial beam units, and matrix of the materials is omitted. But matrix's effect on connecting fiber tows is expressed in adopted supposition that no relative displacements occur among all fiber tows at their contact points, which leads to establishment of constrained relation between node displacements of beam units, and leads to the formation of material's augmented structural-stiflf-matrix. Programming and calculating obtain the macro mechanical measurements such as strain and Young's module of the composites. Besides, forces and moments, stress's maximal value as well as occurring places in each fiber tow, force and moment exerted on any fiber tow by its adjacent fiber tows become all known. The numerical solutions agree with experiments well, proving the effectiveness and feasibility of the method. The method may be also available for other types of load bearing on t
he materials.
Work done above fills several gaps in study on geometric microstructure of the material, initiates a new way to analyze and predict the material's module and strength. For the both explorations, this dissertation has made a substantive progress.
本文详细研究了四向矩形编织复合材料的内部结构、表面结构和角柱结构。以矢量方法推导公式，解析确定纤维束的路径、接触点位置、接触线形状、过接触处的公法线方向，得到一些重要结果。从而为有限元分析计算提供了几何基础和所需数据。给出将材料划分为单胞的正确方法和更符合实际的单胞图形，消除了现有划分方法的几个不足，统一了单胞数的计算式。
发展出一种有限元方法，分析了这种材料在纵向拉伸下的力学响应。将纤维束划分为空间梁元，忽略基体。但把基体对纤维束的连接作用体现为纤维束相互接触处的固接，从而建立梁元节点位移约束关系，形成材料的结构增广刚阵。通过编程计算，得材料应变和模量等宏观力学量，还得纤维束的内力、内力矩、最大应力的值及位置、纤维束间的相互作用力等。计算结果与实验值吻合良好，证实了方法的有效可行。有可能成为其它载荷工况下的力学分析手段。
上述工作填补了该材料几何细观结构研究的一些空白，开辟了该材料模量和强度研究的新途径。本文将这两方面探索作了实质性推进。
Braided composites are advanced materials come out twenty years ago. Owing to their many superior behaviors, they have been used in aeronautics, astronautics and general industries. Theoretic approach and prediction for their performances have become increasingly important.
This dissertation investigates interior, surface and comer architecture of 4-directional rectangular braided composites in detail. Vector method is used to deduce mathematic expressions, the path of fiber tows in the material, position of contact point and shape of contact line between any two fiber tows, and common normal of any two fiber tows through their contact place, are all determined analytically, some important conclusions are drawn. These efforts result in provisions of geometric basis and data needed by following finite element analysis. Removing several shortcomings of existing methods dividing the material into unit cells, a correct division method and corresponding unit cell's graphics which are more approximate to the real, are proposed. Formulas to determine the numbers of unit-cells become unity.
A finite element method is developed to study mechanical response of composites under longitudinal tension. The fiber tows are divided into spatial beam units, and matrix of the materials is omitted. But matrix's effect on connecting fiber tows is expressed in adopted supposition that no relative displacements occur among all fiber tows at their contact points, which leads to establishment of constrained relation between node displacements of beam units, and leads to the formation of material's augmented structural-stiflf-matrix. Programming and calculating obtain the macro mechanical measurements such as strain and Young's module of the composites. Besides, forces and moments, stress's maximal value as well as occurring places in each fiber tow, force and moment exerted on any fiber tow by its adjacent fiber tows become all known. The numerical solutions agree with experiments well, proving the effectiveness and feasibility of the method. The method may be also available for other types of load bearing on t
he materials.
Work done above fills several gaps in study on geometric microstructure of the material, initiates a new way to analyze and predict the material's module and strength. For the both explorations, this dissertation has made a substantive progress.
引文
1. Jenn-Ming Yang, Chang-Long Ma & Tsu-Wei Chou. Fiber Inclination Model of Three-Dimentional Textile Structural Composites. Journal of Composite Materials, 1986, 472～484
2. Frank K. Ko & Christopher M.Pastore. Structure and Properties of an Integrated 3-D Fabric for Structural Composites. Composite Materials, 1985, 428～439
3. Frank K. Ko.Tensile Strength and Modulus of a Three-Dimensional Braid Composite. Proceedings of 2nd U. S. /Japan Conference on Composites, 1986, 392～403
4. Zhou Guangming, Wang Xinwei and Qiao Xin. Inclined Laminal Combination Model of 3D Braided Composites. Transaction of Nanjing University of Aeronautics and Astronautics, 1995(1), 8～14
5. Hui-Yu Sun and Xin Qiao. Prediction of the Mechanical Properties of Three-Dimentionally Braided Composites. Composites Science and Technology, 1997(57), 623～629
6．孙慧玉，吴长春，卞恩荣．三维编织复合材料面内刚度和强度性能研究．北京：复合材料学报，1998(4)，102～106
7. W. Li, M. Hammad & A. El-Shiekh. Structural Analysis of 3-D Braided Preforms for Composites. Part Ⅰ: The Four-step Preforms. Journal of the Textile Institute, 1990(4), 491～514
8. Y.Q. Wang & A. S. D. Wang. On the Topological Yarn Structure of 3-D Rectangular and Tubular Braided Preforms. Composites Science and Technology, 1994 (51), 575～586
9. You-Qi Wang & A. S. D. Wang. Microstructure/Property Relationships in Three-Dimentionally Braided Fiber Composites. Composites Science and Technology, 1995 (53), 213～222
10. Y. Q. Wang & A. S. D. Wang. Geometric Mapping of Yarn Structures Due to Shape Change in 3-D Braided Composites. Composites Science and Technology, 1995 (53), 213～222
11．吴德隆，郝兆平．五向编织结构复合材料的分析模型．北京：宇航学报，1993(3)，40～51
12. D. L. Wu. Three-Cell Model and 5D Braided Structural Composites. Composites Science and Technology, 1996(56), 225～233
13．沈怀荣，郑文龙．三维编织圆管力学性能及火箭级间段模拟结构承载能力研究．长沙：国防科技大学学报，1999(1)，8～12
14. Aleksander B. Macander, Roger M. Crane, etc. Fabrication and Mechanical Properties of Multidimensionally (X-D) braided Composite Materials. Composite Materials, 1986, 422～443
15. Wei Li & Aly El Shiekh. The Effect of Processes and Processing Parameters on 3-D Braided Preforms for Composites. 33th International SAMPE Symposium. 1988, 104～115
16. D. Liao, T. M. Tan & Frank K. Ko. Compressive Behavior of 3-D Braided Composites, PART1: Experimental Observations. 36th International SAMPE Symposium. 1991, 129～140
17. L. V. Smith & S. R. Swanson. Failure of Braided Carbon/Epoxy Composite under Biaxial Compression. Journal of Composite Materials, 1994 (12), 1158～1177
18. G. J. Filatovs, R. L. Sadler, etc, Fracture Behavior of A 3-D Braid Graphite/Epoxy Composite. Journal of Composite Materials, 1994 (6), 526～541
19．李嘉禄，肖丽华，董孚允，立体多向编织结构对复合材料性能的影响．北京：复合材料学报，1996(3)，71～75
20．黎观生，李建有，徐新．三维编织复合材料拉伸性能试验研究．北京：材料工程，1997(6)，20～41
21．卢子兴，冯志海，寇长河等．编织复合材料拉伸力学性能的研究．北京：复合材料学报，1999(3)，129～134
22．庞宝君，杜善义，韩杰才等．三维四向编织碳/环氧复合材料实验研究．北京：复合材料学报，1999(3)，137～141
23．三维编织工艺参数对复合材料拉伸性能的影响．北京：宇航材料工艺，2000(1)，55～58
24. Surya R. Kalidindi and Abdel Abusafieh. Longitudinal and Transverse Moduli and Strength of Low Angle 3-D Braided Composites. Journal of Composite Materials, 1996(8), 885～905
25. Vishnu s. Avva, Harold G. Allen, etc. Through-the-Thickness Tension Strength of 3-D Braided Composites. Journal of Composite Materials, 1994(1), 51～67
26. C.M. Pastore & F.K.Ko. Modelling of Textile Structural Composites, Part Ⅰ: Processing-science Model for Three-dimensional Braiding. Journal of the Textile Institute, 1990(4), 480～490
27. Terry C. Emehel. Prediction of Compression Strength of Laminated and Textile Composites Using A Tow Collapse Model. AIAA-96-1477-CP, 1468～1478
28. L. V. Smith & S. R. Swanson. Effect of Architecture on the Strength of Braided Tubes Under Biaxial Tension and Compression. Journal of Engineering Materials and Technology, 1996, 478～484
29．沈观林．复合材料力学．北京：清华大学出版社，1996，93
30．王震鸣，杜善义，张恒、范赋群．复合材料及其结构的力学、设计、应用和评价(第一册)．北京：北京大学出版社，1998，211
2. Frank K. Ko & Christopher M.Pastore. Structure and Properties of an Integrated 3-D Fabric for Structural Composites. Composite Materials, 1985, 428～439
3. Frank K. Ko.Tensile Strength and Modulus of a Three-Dimensional Braid Composite. Proceedings of 2nd U. S. /Japan Conference on Composites, 1986, 392～403
4. Zhou Guangming, Wang Xinwei and Qiao Xin. Inclined Laminal Combination Model of 3D Braided Composites. Transaction of Nanjing University of Aeronautics and Astronautics, 1995(1), 8～14
5. Hui-Yu Sun and Xin Qiao. Prediction of the Mechanical Properties of Three-Dimentionally Braided Composites. Composites Science and Technology, 1997(57), 623～629
6．孙慧玉，吴长春，卞恩荣．三维编织复合材料面内刚度和强度性能研究．北京：复合材料学报，1998(4)，102～106
7. W. Li, M. Hammad & A. El-Shiekh. Structural Analysis of 3-D Braided Preforms for Composites. Part Ⅰ: The Four-step Preforms. Journal of the Textile Institute, 1990(4), 491～514
8. Y.Q. Wang & A. S. D. Wang. On the Topological Yarn Structure of 3-D Rectangular and Tubular Braided Preforms. Composites Science and Technology, 1994 (51), 575～586
9. You-Qi Wang & A. S. D. Wang. Microstructure/Property Relationships in Three-Dimentionally Braided Fiber Composites. Composites Science and Technology, 1995 (53), 213～222
10. Y. Q. Wang & A. S. D. Wang. Geometric Mapping of Yarn Structures Due to Shape Change in 3-D Braided Composites. Composites Science and Technology, 1995 (53), 213～222
11．吴德隆，郝兆平．五向编织结构复合材料的分析模型．北京：宇航学报，1993(3)，40～51
12. D. L. Wu. Three-Cell Model and 5D Braided Structural Composites. Composites Science and Technology, 1996(56), 225～233
13．沈怀荣，郑文龙．三维编织圆管力学性能及火箭级间段模拟结构承载能力研究．长沙：国防科技大学学报，1999(1)，8～12
14. Aleksander B. Macander, Roger M. Crane, etc. Fabrication and Mechanical Properties of Multidimensionally (X-D) braided Composite Materials. Composite Materials, 1986, 422～443
15. Wei Li & Aly El Shiekh. The Effect of Processes and Processing Parameters on 3-D Braided Preforms for Composites. 33th International SAMPE Symposium. 1988, 104～115
16. D. Liao, T. M. Tan & Frank K. Ko. Compressive Behavior of 3-D Braided Composites, PART1: Experimental Observations. 36th International SAMPE Symposium. 1991, 129～140
17. L. V. Smith & S. R. Swanson. Failure of Braided Carbon/Epoxy Composite under Biaxial Compression. Journal of Composite Materials, 1994 (12), 1158～1177
18. G. J. Filatovs, R. L. Sadler, etc, Fracture Behavior of A 3-D Braid Graphite/Epoxy Composite. Journal of Composite Materials, 1994 (6), 526～541
19．李嘉禄，肖丽华，董孚允，立体多向编织结构对复合材料性能的影响．北京：复合材料学报，1996(3)，71～75
20．黎观生，李建有，徐新．三维编织复合材料拉伸性能试验研究．北京：材料工程，1997(6)，20～41
21．卢子兴，冯志海，寇长河等．编织复合材料拉伸力学性能的研究．北京：复合材料学报，1999(3)，129～134
22．庞宝君，杜善义，韩杰才等．三维四向编织碳/环氧复合材料实验研究．北京：复合材料学报，1999(3)，137～141
23．三维编织工艺参数对复合材料拉伸性能的影响．北京：宇航材料工艺，2000(1)，55～58
24. Surya R. Kalidindi and Abdel Abusafieh. Longitudinal and Transverse Moduli and Strength of Low Angle 3-D Braided Composites. Journal of Composite Materials, 1996(8), 885～905
25. Vishnu s. Avva, Harold G. Allen, etc. Through-the-Thickness Tension Strength of 3-D Braided Composites. Journal of Composite Materials, 1994(1), 51～67
26. C.M. Pastore & F.K.Ko. Modelling of Textile Structural Composites, Part Ⅰ: Processing-science Model for Three-dimensional Braiding. Journal of the Textile Institute, 1990(4), 480～490
27. Terry C. Emehel. Prediction of Compression Strength of Laminated and Textile Composites Using A Tow Collapse Model. AIAA-96-1477-CP, 1468～1478
28. L. V. Smith & S. R. Swanson. Effect of Architecture on the Strength of Braided Tubes Under Biaxial Tension and Compression. Journal of Engineering Materials and Technology, 1996, 478～484
29．沈观林．复合材料力学．北京：清华大学出版社，1996，93
30．王震鸣，杜善义，张恒、范赋群．复合材料及其结构的力学、设计、应用和评价(第一册)．北京：北京大学出版社，1998，211