Effective Elastic Properties of Transversely Isotropic Matrix Based Composites
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摘要: 细观力学的一个主要研究内容是求复合材料的等效弹性性能.常见的细观力学模型解析公式一般假定基体各向同性且只存在纤维和基体两相材料,实际复合材料的基体和纤维之间往往存在一个横观各向同性的界面相,该三相复合材料的等效性能可由两个两相复合材料性能的组合得到,这就需要求出横观各向同性基体复合材料的等效弹性常数.该文基于两相同心圆柱模型,首先导出了横观各向同性基体内应力与增强纤维内应力之间桥联矩阵的解析公式,与基于数值积分Eshelby张量得到的MoriTanaka桥联矩阵相符,再进一步获得了横观各向同性基体复合材料的5个弹性常数显式表达式.文中还给出了扩展的桥联模型显式公式.选用适当的桥联参数,两种模型所得结果十分接近.Abstract: One of the main objectives of micromechanics is to predict the effective elastic properties of composites. Most existent explicit micromechanics models are based on an assumption of isotropic matrices and on that only 2-phase constituent materials are involved. In reality, a composite may possess a 3rd interphase between the fiber and the matrix, which is generally transversely isotropic. Accordingly, the prediction of the elastic properties of a 3-phase composite can be achieved through the combination of 2 kinds of 2-phase composites, to which a micromechanics model with transversely isotropic matrix should be applicable. The explicit bridging tensor elements to correlate the internal stresses of a transversely isotropic matrix with those of a reinforcing fiber in a concentric cylinder assemblage (CCA) model were derived firstly. Then this obtained bridging tensor was used to deduce analytical formulae for all the 5 effective elastic moduli of the composite made with the transversely isotropic matrix. An extension of the bridging model applicable to fiber reinforced transversely isotropic matrix composites was achieved as well. With properly chosen bridging parameters, the predicted elastic moduli of the composite with the 2 models are quite close to each other.
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Key words:
- micromechanics /
- effective elastic property /
- anisotropic matrix /
- bridging tensor /
- bridging model
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[1] HASHIN Z. Analysis of composite materials: a survey[J]. Journal of Applied Mechanics,1983,50(3): 481-505. [2] UPADHYAY A, SINGH R. Prediction of effective elastic modulus of biphasic composite materials[J]. Modern Mechanical Engineering,2012,2(1): 6-13. [3] TSAI S W, HAHN H T. Introduction to Composite Materials [M]. Lancaster: Technomic Pubilishing Co, 1980. [4] BUDIANSKY B. On the elasticmoduli of some heterogeneous materials[J]. Journal of the Mechanics and Physics of Solids,1965,13(4): 223-227. [5] HILL R. A self-consistent mechanics of composite materials[J]. Journal of the Mechanics and Physics of Solids,1965,13(4): 213-222. [6] KERNER E H. The elastic and thermo-elastic properties of composite media[J]. Proceedings of the Physical Society Section B,1956,69(2): 807-808. [7] CHRISTENSEN R M, LO K H. Solutions for effective shear properties in three phase sphere and cylinder models[J]. Journal of the Mechanics & Physics of Solids,1979,27(4): 315-330. [8] MORI T, TANAKA K. Average stress in matrix and average elastic energy of materials withmisfitting inclusions[J]. Acta Metallurgica,1973,21(5): 571-574. [9] CHAMIS C C. Mechanics of composite materials-past, present and future[J]. Journal of Composites Technology & Research,1984,11(1): 3-14. [10] HUANG Z M. Simulation of the mechanical properties of fibrous composites by the bridging micromechanics model[J]. Composites Part A,2001,32(2): 143-172. [11] BENVENISTE Y. Exact results for the local fields and the effective moduli of fibrous composites with thickly coated fibers[J]. Journal of the Mechanics & Physics of Solids,2014, 71(1): 219-238. [12] GOTKHINDI T P, SIMHA K R Y. Transverse elastic response of bundled coated cylinders[J]. International Journal of Mechanical Sciences,2013,76: 70-85. [13] CHATZIGEORGIOU G, SEIDEL G D, LAGOUDAS D C. Effective mechanical properties of “fuzzy fiber” composites[J]. Composites Part B: Engineering,2012,43(6): 2577-2593. [14] HASEGAWA H, KISAKI M. The stress field caused by a circular cylindrical inclusion in a transversely isotropic elastic solid[J]. Journal of Applied Mechanics,2004,70(6): 825-831. [15] WANG Y C, HUANG Z M. Bridging tensor with an imperfect interface[J]. European Journal of Mechanics A: Solids,2015,56: 73-91. [16] GREBENYUK S N. The shear modulus of a composite material with a transversely isotropic matrix and a fibre[J]. Journal of Applied Mathematics & Mechanics,2014,78(2): 187-191. [17] ESHELBY J D. The determination of the elastic field of an ellipsoidal inclusion, and related problems[J]. Proceedings of the Royal Society of London,1957,241(1226): 376-396. [18] ESHELBY J D. The elastic field outside an ellipsoidal inclusion[J]. Proceedings of the Royal Society of London,1959,252(1271): 561-569. [19] WANG Y, HUANG Z. A new approach to a bridging tensor[J]. Polymer Composites,2014,36(8): 1417-1431. [20] HUANG Z M, ZHOU Y X. Strength of Fibrous Composites [M]. Zhejiang: Zhejiang University Press, 2011. [21] CHEN T, DVORAK G J, BENVENISTE Y. Stress fields in composites reinforced by coated cylindrically orthotropic fibers[J].Mechanics of Materials,1990,9(1): 17-32. [22] CHENG S, CHEN D. On the stress distribution inlaminae[J]. Journal of Reinforce Plast & Compos,1988,7(2): 136-144. [23] BENVENISTE Y, DVORAK G J, CHEN T. Stress fields in composites with coated inclusions[J]. Mechanics of Materials,1989,7(4): 305-317. [24] TIMOSHENKON S P, GOODIER J N. Theory of Elasticity [M]. New York: McGraw-Hill Book Company, 1970. [25] BENVENISTE Y. A new approach to the application of Mori-Tanaka’s theory in composite materials[J]. Mechanics of Materials,1987,6(2): 147-157. [26] GAVAZZI A C, LAGOUDAS D C. On the numerical evaluation of Eshelby’s tensor and its application to elastoplastic fibrous composites[J]. Computational Mechanics,1990,7(1): 13-19. [27] HUANG Z M, ZHANG C C. A critical assessment on the predictability of 12 micromechanics models for stiffness and strength of UD composites[C]//21st International Conference on Composite Materials.Xi’an, China, 2017.
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