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Numerical prediction of fiber mechanical properties considering random microstructures using inverse analysis with quasi-analytical gradients. (English) Zbl 1410.74090

Summary: An efficient and robust numerical scheme is reported that can inversely evaluate the elastic properties of fibers in unidirectional composites from the material properties of matrices and composite laminae. Considering the effect of microstructures such as random fiber arrangement, a set of finite element meshes are employed to represent the interaction between fiber and matrix. A lamina-scale cost function comprising the difference between the measured elastic properties, and the computed elastic properties of a unidirectional lamina is minimized to evaluate fiber properties. In the minimization process, quasi-analytical gradients derived from prediction formulae, such as the Chamis or Halpin-Tsai models, are adopted to greatly reduce the computation cost. To verify the proposed scheme in terms of accuracy, efficiency, and robustness, the elastic properties of T650-35 fiber in a T650-35/PMR-15 lamina are evaluated with various representative volume elements containing randomly distributed fibers and voids. The evaluation results obtained by the proposed scheme are compared with results in the literature, and the effects of microstructures are discussed.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
65K10 Numerical optimization and variational techniques
74M25 Micromechanics of solids
82D80 Statistical mechanics of nanostructures and nanoparticles

Software:

ABAQUS; Matlab
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Daniel, I. M.; Ishai, O., Engineering Mechanics of Composite Materials (2006), Oxford University Press: Oxford University Press New York
[2] J.C. Halpin, S.W. Tsai, Effects of environmental factors on composite materials, Air Force Material Laboratory Technical Report, AFML-TR 67-423, 1969.; J.C. Halpin, S.W. Tsai, Effects of environmental factors on composite materials, Air Force Material Laboratory Technical Report, AFML-TR 67-423, 1969.
[3] C.C. Chamis, Mechanics of composite materials: past, present, and future, NASA Technical Memorandum, 100793, 1984.; C.C. Chamis, Mechanics of composite materials: past, present, and future, NASA Technical Memorandum, 100793, 1984.
[4] Mori, T.; Tanaka, K., Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall., 21, 571-574 (1973)
[5] Chou, T.-W.; Nomura, S.; Taya, M., A self-consistent approach to the elastic stiffness of short-fiber composites, J. Compos. Mater., 14, 178-188 (1980)
[6] Sun, C.; Vaidya, R., Prediction of composite properties from a representative volume element, Compos. Sci. Technol., 56, 171-179 (1996)
[7] Benedikt, B.; Kumosa, M.; Predecki, P., An evaluation of residual stresses in graphite/PMR-15 composites by X-ray diffraction, Acta Mater., 53, 4531-4543 (2005)
[8] Benedikt, B.; Rupnowski, P.; Kumosa, M., Visco-elastic stress distributions and elastic properties in unidirectional composites with large volume fractions of fibers, Acta Mater., 51, 3483-3493 (2003)
[9] Karadeniz, Z. H.; Kumlutas, D., A numerical study on the coefficients of thermal expansion of fiber reinforced composite materials, Compos. Struct., 78, 1-10 (2007)
[10] Liu, X.; Wang, R.; Wu, Z.; Liu, W., The effect of triangle-shape carbon fiber on the flexural properties of the carbon fiber reinforced plastics, Mater. Lett., 73, 21-23 (2012)
[11] Park, S.-J.; Seo, M.-K.; Shim, H.-B., Effect of fiber shapes on physical characteristics of non-circular carbon fibers-reinforced composites, Mater. Sci. Eng. A, 352, 1-2, 34-39 (2003)
[12] Kuentzer, N.; Simacek, P.; Advani, S. G.; Walsh, S., Correlation of void distribution to VARTM manufacturing techniques, Composites Part A: Appl. Sci. Manuf., 38, 3, 802-813 (2007)
[13] Huang, H.; Talreja, R., Effects of void geometry on elastic properties of unidirectional fiber reinforced composites, Compos. Sci. Technol., 65, 13, 1964-1981 (2005)
[14] Guo, R.; Shi, H. J.; Yao, Z. H., Modeling of interfacial debonding crack in particle reinforced composites using Voronoi cell finite element method, Comput. Mech., 32, 1-2, 52-59 (2003) · Zbl 1042.74559
[15] Huang, Y.; Jin, K. K.; Ha, S. K., Effects of fiber arrangement on mechanical behavior of unidirectional composites, J. Compos. Mater., 42, 18, 1851-1871 (2008)
[16] Choi, J.; Shin, H.; Yang, S.; Cho, M., The influence of nanoparticle size on the mechanical properties of polymer nanocomposites and the associated interphase region: a multiscale approach, Compos. Struct., 119, 365-376 (2015)
[17] Liu, Y.; Greene, M. S.; Chen, W.; Dikin, D. A.; Liu, W. K., Computational microstructure characterization and reconstruction for stochastic multiscale material design, Comput.-Aided Des., 45, 1, 65-76 (2013)
[18] Ha, S. K.; Jin, K. K.; Huang, Y., Micro-mechanics of failure (MMF) for continuous fiber reinforced composites, J. Compos. Mater., 42, 18, 1873-1895 (2008)
[19] Miyagawa, H.; Mase, T.; Sato, C.; Drown, E.; Drzal, L. T.; Ikegami, K., Comparison of experimental and theoretical transverse elastic modulus of carbon fibers, Carbon, 44, 10, 2002-2008 (2006)
[20] Rupnowski, P.; Gentz, M.; Sutter, J.; Kumosa, M., An evaluation of the elastic properties and thermal expansion coefficients of medium and high modulus graphite fibers, Composites Part A: Appl. Sci. Manuf., 36, 3, 327-338 (2005)
[21] Ballard, M. K.; McLendon, W. R.; Whitcomb, J. D., The influence of microstructure randomness on prediction of fiber properties in composites, J. Compos. Mater., 48, 29, 3605-3620 (2014)
[22] Lu, J.; Zhu, P.; Ji, Q.; Feng, Q.; He, J., Identification of the mechanical properties of the carbon fiber and the interphase region based on computational micromechanics and Kriging metamodel, Comput. Mater. Sci., 95, 172-180 (2014)
[23] Bocciarelli, M.; Buljak, V.; Moy, C. K.S.; Ringer, S. P.; Ranzi, G., An inverse analysis approach based on a POD direct model for the mechanical characterization of metallic materials, Comput. Mater. Sci., 95, 302-308 (2014)
[24] Kamiński, M., Determination of sensitivity coefficients of the elastic effective properties for periodic fiber-reinforced composites using the response function method, Comput. Mater. Sci., 43, 4, 829-841 (2008)
[25] Xia, L.; Raghavan, B.; Breitkopf, P.; Zhang, W., Numerical material representation using proper orthogonal decomposition and diffuse approximation, Appl. Math. Comput., 224, 450-462 (2013) · Zbl 1334.74099
[26] Lim, J. H.; Charpentier, J.-B.; Sohn, D., Numerical evaluation of the coefficients of thermal expansion of fibers in composite materials using a lamina-scale cost function with quasi-analytical gradients, J. Mech. Sci. Technol., 29, 3, 1187-1197 (2015)
[27] Mishra, A. K.; Chakraborty, S., Development of a finite element model updating technique for estimation of constituent level elastic parameters of FRP plates, Appl. Math. Comput., 258, 84-94 (2015) · Zbl 1338.74103
[28] Arora, J., Introduction to Optimum Design (2004), Academic Press: Academic Press New York
[29] Matlab User’s Guide (R2014a), MathWorks, 2014.; Matlab User’s Guide (R2014a), MathWorks, 2014.
[30] Abaqus Analysis User’s Manual (6.14), Dassault Systèmes, 2014.; Abaqus Analysis User’s Manual (6.14), Dassault Systèmes, 2014.
[31] Swaminathan, S.; Ghosh, S.; Pagano, N., Statistically equivalent representative volume elements for unidirectional composite microstructures: part I - without damage, J. Compos. Mater., 40, 7, 583-604 (2006)
[32] Heinrich, C.; Aldridge, M.; Wineman, A. S.; Kieffer, J.; Waas, A. M.; Shahwan, K., The influence of the representative volume element (RVE) size on the homogenized response of cured fiber composites, Model. Simul. Mater. Sci. Eng., 20, 7, Article 075007 pp. (2012)
[33] Olsson, D. M.; Nelson, L. S., The Nelder-Mead simplex procedure for function minimization, Technometrics, 17, 1, 45-51 (1975) · Zbl 0295.65043
[34] Trias, D.; Costa, J.; Mayugo, J. A.; Hurtado, J. E., Random models versus periodic models for fibre reinforced composites, Comput. Mater. Sci., 38, 2, 316-324 (2006)
[35] Melro, A. R.; Camanho, P. P.; Pinho, S. T., Generation of random distribution of fibres in long-fibre reinforced composites, Compos. Sci. Technol., 68, 9, 2092-2102 (2008)
[36] Sohn, D.; Cho, Y.-S.; Im, S., A novel scheme to generate meshes with hexahedral elements and poly-pyramid elements: the carving technique, Comput. Methods Appl. Mech. Eng., 201-204, 208-227 (2013) · Zbl 1239.65074
[37] Bouhala, L.; Koutsawa, Y.; Makradi, A.; Belouettar, S., An advanced numerical method for predicting effective elastic properties of heterogeneous composite materials, Compos. Struct., 117, 114-123 (2014)
[38] Wongsto, A.; Li, S., Micromechanical FE analysis of UD fibre-reinforced composite with fibre distributed at random over the transverse cross-section, Composites Part A: Appl. Sci. Manuf., 36, 9, 1246-1266 (2005)
[39] Li, B.; Wang, B.; Reid, S. R., Effective elastic properties of randomly distributed void models for porous materials, Int. J. Mech. Sci., 52, 5, 726-732 (2010)
[40] Griffiths, D. V.; Paiboon, J.; Huang, J.; Fenton, G. A., Homogenization of geomaterials containing voids by random fields and finite elements, Int. J. Solids Struct., 49, 14, 2006-2014 (2012)
[41] Wang, X. F.; Wang, X. W.; Zhou, G. M.; Zhou, C. W., Multi-scale analyses of 3D woven composite based on periodicity boundary conditions, J. Compos. Mater., 41, 14, 1773-1788 (2007)
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