A constitutive model of continuous carbon fiber reinforced thermoplastic polyether ether ketone composites in a wide temperature range
-
摘要: 连续碳纤维增强热塑性聚醚醚酮复合材料(CF/PEEK)具有抗冲击、易修复、耐高温等优异特性，是新一代航空航天热端结构的优选材料。PEEK基体的结晶特性使其在高于玻璃化转变温度(143℃左右)时仍具有较强承载能力，因此，CF/PEEK复合材料能够在200℃条件下长期服役。然而，CF/PEEK复合材料的成型温度域宽、服役温度范围广，高温条件下PEEK树脂会逐渐松弛，导致CF/PEEK复合材料呈现出与时间、温度、加载历史相关的各向异性黏弹性，对复合材料结构成型过程与服役历史的精细化设计带来了挑战。现有复合材料高温预测模型主要基于弹塑性本构的刚度折减方法，未充分考虑材料的各向异性松弛行为。发展了一种描述CF/PEEK复合材料力学性能随时间、温度演化的各向异性黏弹本构模型。通过表征热塑性PEEK树脂的松弛模量主曲线，基于广义Maxwell黏弹模型，获取泛温度域(25~200℃)热塑性PEEK的黏弹性本构参数，结合复合材料等效力学性能的半经验解法，给出了三维复合材料各向异性黏弹本构模型。通过与CF/PEEK复合材料的横向高温松弛实验和代表性体积单元(RVE)仿真模拟结果比较，证明了该模型的有效性。这一本构模型可用于CF/PEEK复合材料结构的成型过程仿真和高温力学性能设计。Abstract: As preferred high-temperature structural materials for the next generation aerospace craft, carbon fiber reinforced thermoplastic polyether ether ketone composite (CF/PEEK) has excellent properties, such as high impact resistance, repairability, high temperature resistance and so forth. Because of the crystallization characteristics, the PEEK matrix still has a high load-carrying capacity above the glass transition temperature (around 143℃), and therefore CF/PEEK composite can be used under long term operation at 200℃. However, due to the wide forming temperature range and service temperature range of CF/PEEK composites, PEEK resin will gradually relax at high temperature. Consequently, CF/PEEK composites will show obvious time-, temperature-, and loading history-dependent anisotropic viscoelasticity, which make it very hard to accurately design the forming history and service history of the composite structures. Currently, the existing high temperature prediction model of composites is usually based on the elastic-plastic constitutive stiffness reduction method, which does not fully consider the anisotropic relaxation behavior of the composites. An anisotropic viscoelastic constitutive model was developed to describe the time- and temperature- dependent properties of composites. The generalized Maxwell viscoelastic parameters of the PEEK resin were obtained by characterizing the relaxation modulus main curve in a wide temperature range (25~200℃). Then, by semi-empirical solution for equivalent mechanical properties of composite materials, a three-dimensional anisotropic constitutive model was developed. Finally, the developed model has been verified by comparing with the high temperature relaxation experiments and the finite element simulation by the representative volume element (RVE) along the transverse direction. Overall, the developed model can be used to simulate the forming process and design the high temperature mechanical properties of CF/PEEK composites.
-
图 1 广义Maxwell松弛模型
Figure 1. Generalized Maxwell relaxation model
E—Elastic modulus of spring; η—Viscosity of dashpot
图 2 聚醚醚酮(PEEK)及碳纤维/聚醚醚酮(CF/PEEK)松弛试样
Figure 2. Polyether ether ketone (PEEK) and carbon fiber/ polyether ether ketone (CF/PEEK) relaxation samples
图 6 CF/PEEK复合材料代表性体积单元模型
Figure 6. Representative volume element model of CF/PEEK composite
图 7 CF/PEEK复合材料纵向松弛曲线
Figure 7. Longitudinal relaxation curves of CF/PEEK composite material
RVE—Representative volume element
图 8 CF/PEEK复合材料在不同温度下的横向松弛曲线
Figure 8. Transverse relaxation curves of CF/PEEK composite materials at different temperatures
图 9 不同纤维体积分数的CF/PEEK复合材料横向松弛曲线
Figure 9. Transverse relaxation curves of CF/PEEK composites with different fiber volume fractions
Ef1/GPa Ef2/GPa μ12 μ23 G12/GPa G23/GPa 230 15 0.2 0.07 15 7 Notes：Ef1—Longitudinal modulus; Ef2—Transverse modulus; μ12—Poisson ratio in 12 directions; μ23—Poisson ratio in 23 directions; G12—Axial shear modulus; G23—Transverse shear modulus. 
下载: 导出CSV
表 2 PEEK广义Maxwell模型参数
Table 2. Generalized Maxwell model parameters of PEEK
Parameter Nonequilibrium branch Equilibrium
branch1 2 3 4 5 6 7 Modulus Ep/MPa 173.78 198.68 252.92 1431.96 1297.08 442.70 277.30 197.16 τiref /s 7.851 78.51 785.1 9159.5 39255 225100 2117000 — WLF parameters TR/K 373.15 C1 6.63 C2 148.21 Notes：τiref—Relaxation time; TR—Reference temperature; C1, C2—Constants related to materials.
下载: 导出CSV
-
[1] CEBE P, CHUNG S Y, HONG S. Effect of thermal history on mechanical properties of polyetheretherketone below the glass transition temperature[J]. Journal of Applied Polymer Science,1987,33(2):487-503. [2] WANG P, ZOU B, XIAO H, et al. Effects of printing parameters of fused deposition modeling on mechanical properties, surface quality, and microstructure of PEEK[J]. Journal of Materials Processing Technology,2019,271:62-74. doi: 10.1016/j.jmatprotec.2019.03.016 [3] 孙银宝, 李宏福, 张博明. 连续纤维增强热塑性复合材料研发与应用进展[J]. 航空科学技术, 2016, 27(5):01-07.SUN Yinbao, LI Hongfu, ZHANG Boming. Progress in research and application of continuous fiber reinforced thermoplastic composites[J]. Aeronautical Science & Technology,2016,27(5):01-07(in Chinese). [4] ZHU K, TAN H, WANG Y, et al. Crystallization and mechanical properties of continuous carbon fiber reinforced polyether-ether-ketone composites[J]. Fibers and Polymers,2019,20(4):839-846. doi: 10.1007/s12221-019-8791-5 [5] DIEZ-PASCUAL A M, NAFFAKH M, GOMEZ M A, et al. Development and characterization of PEEK/carbon nanotube composites[J]. Carbon,2009,47(13):3079-3090. doi: 10.1016/j.carbon.2009.07.020 [6] 肇研, 刘寒松. 连续纤维增强高性能热塑性树脂基复合材料的制备与应用[J]. 材料工程, 2020(8):49-61. doi: 10.11868/j.issn.1001-4381.2019.000209ZHAO Yan, LIU Hansong. Preparation and application of continuous fiber reinforced high-performance thermoplastic resin matrix composites[J]. Materials Engineering,2020(8):49-61(in Chinese). doi: 10.11868/j.issn.1001-4381.2019.000209 [7] 唐见茂. 航空航天材料发展现状及前景[J]. 航天器环境工程, 2013(2):115-121. doi: 10.3969/j.issn.1673-1379.2013.02.001TANG Jianmao. Development status and prospects of aerospace materials[J]. Spacecraft Environmental Engineering,2013(2):115-121(in Chinese). doi: 10.3969/j.issn.1673-1379.2013.02.001 [8] 邢丽英, 包建文, 礼嵩明, 等. 先进树脂基复合材料发展现状和面临的挑战[J]. 复合材料学报, 2016, 33(7):1327-1338.XING Liying, BAO Jianwen, LI Songming, et al. Development status and challenges of advanced resin matrix composites[J]. Acta Materiae Compositae Sinica,2016,33(7):1327-1338(in Chinese). [9] LI W, GAZONAS G, BROWN E N, et al. Thermomechanical model for monotonic and cyclic loading of PEEK[J]. Mechanics of Materials,2019,129(JAN.):113-138. [10] LEI M, HAMEL C M, CHEN K, et al. Thermomechanical behaviors of polyether ether ketone (PEEK) with stretch-induced anisotropy[J]. Journal of the Mechanics and Physics of Solids,2020,148:104271. [11] GABRION X, PLACET V, TRIVAUDEY F, et al. About the thermomechanical behaviour of a carbon fibre reinforced high-temperature thermoplastic composite[J]. Composites Part B: Engineering,2016,95:386-394. doi: 10.1016/j.compositesb.2016.03.068 [12] WANG C, SUN C T. Experimental characterization of constitutive models for PEEK thermoplastic composite at heating stage during forming[J]. Journal of Composite Materials,1997, 31(15):1480-1506. [13] 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. [14] SUN C T, VAIDYA R S. Prediction of composite properties from a representative volume element[J]. Composites Science & Technology,1996,56(2):171-179. [15] OTERO F, OLLER S, MARTINEZ X, et al. Numerical homogenization for composite materials analysis. Comparison with other micro mechanical formulations[J]. Composite Structures,2015,122:405-416. doi: 10.1016/j.compstruct.2014.11.041 [16] CHAMIS C C. Simplified composite micromechanics equations for hygral, thermal and mechanical properties [C]. Houston: The Thirty-eight Annual Conference of the Society of the Plastics Industry, 1983: 1-10. [17] AFFDL J, KARDOS J L. The Halpin-Tsai equations: A review[J]. Polymer Engineering & Science,1976,16(5):344-352. [18] GENIN G M, BIRMAN V. Micromechanics and structural response of functionally graded, particulate-matrix, fiber-reinforced composites[J]. International Journal of Solids and Structures,2009,46(10):2136-2150. doi: 10.1016/j.ijsolstr.2008.08.010 [19] YI Y M, PARK S H, YOUN S K. Asymptotic homogenization of viscoelastic composites with periodic microstructures[J]. International Journal of Solids & Structures,1998,35(17):2039-2055. [20] LEI M, HAMEL C M, YUAN C, et al. 3D printed two-dimensional periodic structures with tailored in-plane dynamic responses and fracture behaviors[J]. Composites Science and Technology,2018,159:189-198. [21] 梁军, 杜善义. 粘弹性复合材料力学性能的细观研究[J]. 复合材料学报, 2001, 18(1):97-100.LIANG Jun, DU Shanyi. Mesoscopic study on the mechanical properties of viscoelastic composite materials[J]. Acta Materiae Compositae Sinica,2001,18(1):97-100(in Chinese). [22] 任超, 陈建钧, 潘红良. 纤维增强复合材料黏弹性行为的预测模型[J]. 复合材料学报, 2012, 29(1):162-168.REN Chao, CHEN Jianjun, PAN Hongliang. Prediction model for viscoelastic behavior of fiber reinforced composites[J]. Acta Materiae Compositae Sinica,2012,29(1):162-168(in Chinese). [23] FRITZEN F, BOHLKE T. Reduced basis homogenization of viscoelastic composites[J]. Composites Science and Technology,2013,76:84-91. [24] 王震鸣, 游绍建. 单向复合材料弹性常数微观力学分析的探讨[J]. 复合材料学报, 1987, 4(4):72-78+102-103.WANG Zhenming, YOU Shaojian. Discussion on micromechanical analysis of elastic constants of unidirectional composites[J]. Acta Materiae Compositae Sinica,1987,4(4):72-78+102-103(in Chinese). [25] FLIEGENER S, HOHE J. An anisotropic creep model for continuously and discontinuously fiber reinforced thermoplastics[J]. Composites Science and Technology,2020,194:108168. doi: 10.1016/j.compscitech.2020.108168 [26] KAI Y, QI G, QI H J. Reduced time as a unified parameter determining fixity and free recovery of shape memory polymers[J]. Nature Communications, 2014, 5: 3066. [27] WILLIAMS M L, LANDEL R F, FERRY J D. The temperature dependence of relaxation mechanism in amorphous polymers and other glass forming liquid[J]. Journal of the American Chemical Society,1955,77(14):3701-3707. [28] KUKI Á, CZIFRAK K, KARGER-KOCSIS J, et al. An approach to predict the shape-memory behavior of amorphous polymers from dynamic mechanical analysis (DMA) data[J]. Mechanics of Time-Dependent Materials,2015,19(1):87-93. doi: 10.1007/s11043-014-9253-5 [29] PETTERMANN H E, DESIMONE A. An anisotropic linear thermo-viscoelastic constitutive law[J]. Mechanics of Time-Dependent Materials,2018,22:421-433. [30] GONZALEZ C, LLORCA J. Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: Microscopic mechanisms and modeling[J]. Composites Science and Technology,2007,67(13):2795-2806. doi: 10.1016/j.compscitech.2007.02.001 [31] NAYA F, GONZALEZ C, LOPES C S, et al. Computational micromechanics of the transverse and shear behavior of unidirectional fiber reinforced polymers including environmental effects[J]. Composites Part A Applied Science & Manufacturing,2017,92:146-157. [32] GITMAN I M, ASKES H, SLUYS L J. Representative volume: Existence and size determination[J]. Engineering Fracture Mechanics,2007,74(16):2518-2534. doi: 10.1016/j.engfracmech.2006.12.021 [33] LI S. Boundary conditions for unit cells from periodic microstructures and their implications[J]. Composites Science and Technology,2008,68(9):1962-1974. doi: 10.1016/j.compscitech.2007.03.035 [34] 张超, 许希武, 严雪. 纺织复合材料细观力学分析的一般性周期性边界条件及其有限元实现[J]. 航空学报, 2013, 34(7):1636-1645.ZHANG Chao, XU Xiwu, YAN Xue. General periodic boundary conditions for micromechanical analysis of textile composites and their finite element realization[J]. Acta Aeronautica Sinica,2013,34(7):1636-1645(in Chinese). [35] PDS A, MJH B, ASK A. Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates[J]. Composites Science and Technology,1998,58(7):1011-1022. doi: 10.1016/S0266-3538(98)00078-5 -
下载:
点击查看大图
图(9) / 表(2)
计量
- 文章访问数: 1558
- HTML全文浏览量: 894
- PDF下载量: 227
- 被引次数: 0
