A constitutive model of continuous carbon fiber reinforced thermoplastic polyether ether ketone composites in a wide temperature range
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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.
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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. 
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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.
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