Fatigue performance of fiber reinforced polymer composites under hygrothermal environment–A review
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摘要: 纤维增强树脂基复合材料在航空航天航海等领域受到广泛应用，湿热环境下长时间循环载荷的作用是复合材料结构设计必须面对的问题，对复合材料结构的强度和刚度有显著的影响。本文首先简要介绍复合材料的水分扩散机理，阐述湿热环境对其力学性能的退化机制。然后着重介绍了湿热环境下纤维增强树脂基复合材料疲劳性能的研究进展，梳理了影响纤维增强树脂基复合材料疲劳性能的湿热因素，总结归纳了存在的主要问题和挑战，为纤维增强树脂基复合材料未来的发展提供了思路。
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关键词:
- 纤维增强树脂基复合材料 /
- 疲劳性能 /
- 湿热环境 /
- 水分扩散 /
- 性能退化
Abstract: Fiber reinforced polymer composites are widely used in the fields of aeronautics, astronautics and marine technology engineering. Long-term cyclic load in hygrothermal environment is a critical problem for composite structural design and analysis, which has a significant impact on the strength and stiffness of composite structures. In the present review, by introducing moisture absorption model, performance degeneration of composites under hygrothermal environment was described. Following that, the review focused on the fatigue properties of composites under hygrothermal environment. The hygrothermal factors affecting the fatigue performance of fiber reinforced polymer composites were reviewed. The challenges and the existing problems were summarized. The future development of fiber reinforced polymer composites was finally discussed. -
图 10 未老化干燥试样和老化试样的拉伸强度和杨氏模量
Figure 10. Tensile strength and Yound’s modulud of unaged and dry and aged samples
图 11 在55℃海水中浸泡后纤维增强环氧树脂基复合材料的EDS-SEM和SEM图像
Figure 11. EDS-SEM and SEM images of fiber reinforced epoxy composites after exposure to seawater at 55℃
表 1 纤维和树脂的湿热膨胀系数
Table 1. Coefficient of hygrothermall expansion of fiber and resin
Material Thermal expansion coefficient Moisture expansion coefficient α1/℃−1 α2/℃−1 β Fiber CCF300 0.13×10−6[15] 2.7×10−6[15] — T300 −0.54×10−6[16], −0.7×10−6[17] 10.08×10−6[16],12×10−6[17] — HMS −0.99×10−6[16] 6.84×10−6[16] — P75 −1.35×10−6[16] 6.84×10−6[16] — P100 −1.40×10−6[16] 6.84×10−6[16] — T700-12K −0.52×10−6[18] 10.2×10−6[18] — Resin Urea-formaldehyde 2.5×10−5[19] — 2.01×10−3[19] N5208 11×10−5[20], 6×10−5[17] — 0.6[20] Resin matrix 4.39×10−5[19] — 2.68×10−3[19] Epoxy (solid) 11.0×10−5[21] — 2.68×10−3[21] Epoxy (liquid) 8.8×10−5[21] — 0.35[21] Notes: α1 and α2—Longitudinal and transverse thermal expansion coefficients, respectively; β—Moisture expansion coefficient. 
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表 2 复合材料吸湿模型
Table 2. Moisture absorption model of composites
Model Mathematical model Scope Characteristic Reference Fick model $\dfrac{{{M_{{t}}}}}{{{M_\infty }}} = \left\{ {1 - {\dfrac{8}{{{\text{π}}^2}}}\displaystyle\sum\limits_{j = 0}^\infty {\dfrac{{\exp \left[ { - {{\left( {2j + 1} \right)}^2}{{\text{π}}^2}\left( {\dfrac{{Dt}}{{{h^2}}}} \right)} \right]}}{{{{\left( {2j + 1} \right)}^2}}}} } \right\}$ Polymers; Single-ply composites Diffusivity is constant [25-26] Non-Fick model $\dfrac{{{M_{{t}}}}}{{{M_\infty }}} = \left( {1 + k\sqrt t } \right)\left\{ {1 - \dfrac{8}{{{{\text{π}}^2}}}\displaystyle\sum\limits_{j = 0}^\infty {\dfrac{{\exp \left[ { - {{\left( {2j + 1} \right)}^2}{{\text{π}}^2}\left( {\dfrac{{{D_{\mathrm{x}}}t}}{{{h^2}}}} \right)} \right]}}{{{{\left( {2j + 1} \right)}^2}}}} } \right\}$ Ambient temperature is below the glass transition temperature of the polymer Diffusivity is constant in the intial stage, while it is changes in the later stage [27] Langmuir type model $\dfrac{{{M_{{t}}}}}{{{M_\infty }}} = \left\{ {\dfrac{\beta }{{\gamma + \beta }}{{\rm{e}}^{ - {{\gamma t}}}}\left[ {1 - \dfrac{8}{{{{\text{π}}^2}}}\displaystyle\sum\limits_{l = 1}^{\infty \left( {odd} \right)} {\dfrac{{{{\rm{e}}^{ - {{k}}{{{l}}^{\mathrm{2}}}{{t}}}}}}{{{l^2}}}} } \right] + \dfrac{\beta }{{\gamma + \beta }}\left( {{{\rm{e}}^{ - {{\beta t}}}} - {{\rm{e}}^{ - {{\gamma t}}}}} \right) + \left( {1 - {{\rm{e}}^{ - {{\beta t}}}}} \right)} \right\}$ An initially dry one dimensional specimen Both the spatial distribution of moisture and total moisture uptake is a function of time. [28] Three-dimensional hindered diffusion model ${M^*} = 1 - \dfrac{{512\mu }}{{{{\text{π}}^6}}}\displaystyle\sum\limits_{P = 0}^\infty {\displaystyle\sum\limits_{Q = 0}^\infty {\displaystyle\sum\limits_{R = 0}^\infty {\dfrac{1}{{{{\left( {2P + 1} \right)}^2}{{\left( {2Q + 1} \right)}^2}{{\left( {2R + 1} \right)}^2}}}{{\rm{e}}^{ - {{\alpha t}}*}} - \left( {1 - \mu } \right){{\rm{e}}^{ - {{t}}*}}} } } $ Polymeric composites Physical or molecular interactions at the microscale lead to hindered diffusion [29] Thickness-dependent non-Fickian model $\dfrac{{{M_{{t}}}}}{{{M_\infty }}} = \phi \left\{ {1 - \exp \left[ { - 7.3{{\left( {\dfrac{{{D_{\mathrm{z}}}t}}{{{h^2}}}} \right)}^{0.75}}} \right]} \right\} + \left( {1 - \phi } \right)\left[ {1 - \left\{ {\exp \left[ {1 - {{\left( {\alpha \left\langle {t - {t_0}} \right\rangle } \right)}^{0.75}}} \right]} \right\}} \right]$ Multi-ply composites Coefficient of the time delay term, α, decrease with thickness [30] Time-varying diffusion coefficient model $\dfrac{{{M_{{t}}} - {M_{\mathrm{i}}}}}{{{M_\infty } - {M_{\mathrm{i}}}}} = 1 - \dfrac{8}{{{{\text{π}}^2}}}\displaystyle\sum\limits_{n = 0}^\infty {\dfrac{1}{{\left( {2n + 1} \right)}}} \exp \left\{ {\dfrac{{ - {{\left( {2n + 1} \right)}^2}{{\text{π}}^2}}}{{{h^2}}} \times \left\{ {{D_0}t + \displaystyle\sum\limits_{r = 1}^R {{D_{{r}}}\left[ {t + {\tau _{{r}}}\left( {{{\rm{e}}^{ - {{t/}}{{\mathrm{\tau }}_{{r}}}}} - 1} \right)} \right]} } \right\}} \right\}$ Polymer Diffusivity and boundary concentration vary continuously with time [31] Dual-diffusivity model $\dfrac{{{M_{{t}}}}}{{{M_\infty }}} = {V_{\mathrm{d}}}\left\{ {1 - \exp \left[ { - 7.3{{\left( {\dfrac{{{D_{\mathrm{d}}}t}}{{{h^2}}}} \right)}^{0.75}}} \right]} \right\} + \left( {{\mathrm{1 - }}{V_{\mathrm{d}}}} \right)\left\{ {{\mathrm{1 - }}\exp \left[ { - 7.3{{\left( {\dfrac{{{D_{\mathrm{l}}}t}}{{{h^2}}}} \right)}^{0.75}}} \right]} \right\}$ Two-phase structure Diffusion process is controlled only by the density of that phase [32] Modified dual-diffusivity model $\dfrac{{{M_{{t}}}}}{{{M_\infty }}} = {M_1}\left\{ {1 - \exp \left[ { - 7.3{{\left( {\dfrac{{{D_1}t}}{{{h^2}}}} \right)}^{0.75}}} \right]} \right\} + {M_2}\left\{ {{\mathrm{1 - }}\exp \left[ { - 7.3{{\left( {\dfrac{{{D_2}t}}{{{h^2}}}} \right)}^{0.75}}} \right]} \right\}$ Two-phase structure Density and hydrophilic character of both phases is different [33] Notes: Mt—Moisture content at the time t; M∞—Saturated moisture content; Mi—Initial moisture content; D—Diffusivity; Dx—Diffusivity in the x direction; t—Time of moisture absorption; h—Thickness of laminates; μ—Dimensionless hindrance coefficient; t*—Dimensionless parameter; φ—Fickian to non-Fickian maximum moisture content ratio; Dz—Moisture diffusivity that exhibits Fickian diffusion behavior; t0—Time of the initiation of non-Fickian moisture diffusion; D0—Unknown temperature-dependent Prony coefficients; τr—Corresponding retardation times; n—Number of terms in the Prony series; Dr, Dd—Diffusion coefficients of the less-dense and the dense phase, respectively; Vd—Volume fraction of the dense phase; M1, M2— Moisture content of the dense matrix and the less dense matrix, respectively; D1, D2—Diffusivity of the dense matrix and the less dense matrix, respectively; j, k, α, β, γ, l, P, Q, R—Parameter.
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