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Influence of Temperature-Dependent Resin Behavior on Numerical Prediction of Effective CTEs of 3D Woven Composites



3D woven composites are well known for their high strength, dimensional stability, delamination, and impact resistance. They are often used in aerospace, energy, and automotive industries where material parts can experience harsh service conditions including substantial variations in temperature. This may lead to significant thermal deformations and thermally-induced stresses in the material. Additionally, 3D woven composites are often produced using resin transfer molding (RTM) technique which involves curing the epoxy resin at elevated temperatures leading to accumulation of the processing-induced residual stress. Thus, understanding of effective thermal behavior of 3D woven composites is essential for their successful design and service. In this paper, the effective thermal properties of 3D woven carbon-epoxy composite materials are estimated using mesoscale finite element models previously developed for evaluation of the manufacturing-induced residual stresses. We determine effective coefficients of thermal expansion (CTEs) of the composites in terms of the known thermal and mechanical properties of epoxy resin and carbon fibers. We investigate how temperature sensitivity of the thermal and mechanical properties of the epoxy influences the overall thermal properties of the composite. The simulations are performed for different composite reinforcement morphologies including ply-to-ply and orthogonal. It is shown that even linear dependence of epoxy’s stiffness and CTE on temperature results in a nonlinear dependence on temperature of the overall composite’s CTE.


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Huang T, Wang Y, Wang G. Review of the Mechanical Properties of a 3D Woven Composite and Its Applications. Polym Plast Technol Eng 2018;57:740–56.

Tan P, Tong L, Steven GP, Ishikawa T. Behavior of 3D orthogonal woven CFRP composites. Part I. Experimental investigation. Compos Part A Appl Sci Manuf 2000;31:259–71.

Ikarashi Y, Ogasawara T, Aoki T. Effects of cyclic tensile loading on the rupture behavior of orthogonal 3-D woven SiC fiber/SiC matrix composites at elevated temperatures in air. J Eur Ceram Soc 2019;39:806–12.

Ma Z, Zhang P, Zhu J. Review on the fatigue properties of 3D woven fiber/epoxy composites: testing and modelling strategies. J Ind Text 2020.

Islam MS, Melendez-Soto E, Castellanos AG, Prabhakar P. Investigation of woven composites as potential cryogenic tank materials. Cryogenics (Guildf) 2015;72:82–9.

Wilkinson MP, Ruggles-Wrenn MB. Fatigue of a 3D Orthogonal Non-crimp Woven Polymer Matrix Composite at Elevated Temperature. Appl Compos Mater 2017;24:1405–24.

Sevostianov I. On the thermal expansion of composite materials and cross-property connection between thermal expansion and thermal conductivity. Mech Mater 2012;45:20–33.

Tan P, Tong L, Steven GP. Models for Predicting Thermomechanical Properties of Three-Dimensional Orthogonal Woven Composites. J Reinf Plast Compos 1999;18:151–85.

Ai S, Fu H, He R, Pei Y. Multi-scale modeling of thermal expansion coefficients of C/C composites at high temperature. Mater Des 2015;82:181–8.

Wang P, Zhang S, Li H, Kong J, Li W, Zaman W. Variation of thermal expansion of carbon/carbon composites from 850 to 2500°C. Ceram Int 2014;40:1273–6.

Dong K, Peng X, Zhang J, Gu B, Sun B. Temperature-dependent thermal expansion behaviors of carbon fiber/epoxy plain woven composites: Experimental and numerical studies. Compos Struct 2017;176:329–41.

Gou JJ, Gong CL, Gu LX, Li S, Tao WQ. The unit cell method in predictions of thermal expansion properties of textile reinforced composites. Compos Struct 2018;195:99–117.

Siddgonde N, Ghosh A. Thermo-mechanical modeling of C/C 3D orthogonal and angle interlock woven fabric composites in high temperature environment. Mech Mater 2020;148:103525.

Trofimov A, Le-Pavic J, Therriault D, Lévesque M. An efficient multi-scale computation of the macroscopic coefficient of thermal expansion: Application to the Resin Transfer Molding manufactured 3D woven composites. Int J Solids Struct 2021;210–211:162–9.

Drach B, Tsukrov I, Trofimov A, Gross T, Drach A. Comparison of stress-based failure criteria for prediction of curing induced damage in 3D woven composites. Compos Struct 2018;189:366–77.

Vasylevskyi K, Tsukrov I, Drach B, Buntrock H, Gross T. Identification of process-induced residual stresses in 3D woven carbon/epoxy composites by combination of FEA and blind hole drilling. Compos Part A Appl Sci Manuf 2020;130:105734.

Drach A, Drach B, Tsukrov I. Processing of fiber architecture data for finite element modeling of 3D woven composites. Adv Eng Softw 2014;72:18–27.

Wang Y, Sun X. Digital-element simulation of textile processes. Compos Sci Technol 2001;61:311–9.

Lomov S V, Ivanov DS, Verpoest I, Zako M. Meso-FE modelling of textile composites : Road map, data flow and algorithms. Compos Sci Technol 2007;67:1870–91.

Zhou E, Mollenhauer D, Iarve E. A realistic 3-D textile geometric model. Seventeenth Int Conf Compos Mater ICCM-17 2009:100–10.

Long AC, Brown LP. 8 - Modelling the geometry of textile reinforcements for composites: TexGen. In: Boisse P, editor. Compos. Reinf. Optim. Perform., Woodhead Publishing; 2011, p. 239–64.

Miao Y, Zhou E, Wang Y, Cheeseman BA. Mechanics of textile composites : Micro-geometry. Compos Sci Technol 2008;68:1671–8.

Whitcomb JD, Chapman CD, Tang X. Derivation of Boundary Conditions for Micromechanics Analyses of Plain and Satin Weave Composites. J Compos Mater 2000;34:724–47.

Tsukrov I, Giovinazzo M, Vyshenska K, Bayraktar H, Goering J, Gross T. Comparison of Two Approaches to Model Cure-Induced Microcracking in Three-Dimensional Woven Composites. Vol. 3 Des. Mater. Manuf. Parts A, B, C, ASME; 2012, p. 541.

Chamis CC. Mechanics of composite materials: Past, present, and future. J Compos Technol Res 1989;11:3–14.

Tsukrov I, Bayraktar H, Giovinazzo M, Goering J, Gross T, Fruscello M, et al. Finite element modeling to predict cure-induced microcracking in three-dimensional woven composites. Int J Fract 2011;172:209–16.

Tsukrov I, Drach B, Gross T. Effective stiffness and thermal expansion coefficients of unidirectional composites with fibers surrounded by cylindrically orthotropic matrix layers. Int J Eng Sci 2012;58:129–43.

Hashin Z, Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids 1963;11:127–40.

Hashin Z. Analysis of Properties of Fiber Composites With Anisotropic Constituents. J Appl Mech 1979;46:543–50.

Schapery RA. Thermal Expansion Coefficients of Composite Materials Based on Energy Principles. J Compos Mater 1968;2:380–404.

Brauner C, Block TB, Purol H, Herrmann AS. Microlevel manufacturing process simulation of carbon fiber/epoxy composites to analyze the effect of chemical and thermal induced residual stresses. J Compos Mater 2012;46:2123–43.

Karch C. Micromechanical Analysis of Thermal Expansion Coefficients. Model Numer Simul

Mater Sci 2014;04:104–18.

Drach B, Tsukrov I, Trofimov A. Comparison of full field and single pore approaches to homogenization of linearly elastic materials with pores of regular and irregular shapes. Int J Solids Struct 2016;96:48–63.

Morelle XP, Chevalier J, Bailly C, Pardoen T, Lani F. Mechanical characterization and modeling of the deformation and failure of the highly crosslinked RTM6 epoxy resin. Mech Time-Dependent Mater 2017;21:419–54.

Ewert A, Drach B, Vasylevskyi K, Tsukrov I. Predicting the overall response of an orthogonal 3D woven composite using simulated and tomography-derived geometry. Compos Struct 2020;243:112169.


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