Experimental study and modeling of long-term viscoelastic behavior of resin matrix composite with consideration of physical aging effect
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摘要: 为充分掌握碳纤维增强环氧树脂基(CF/EP)复合材料的短时和长时变形特性,对一类碳纤维/环氧层合试样开展了蠕变试验研究。试验采用恒温、恒定载荷拉伸加载方式,获得了其在不同试验温度(25℃和50℃)、不同拉伸载荷水平(20%、30%和40%的拉伸极限强度值)下的应变变化规律。试验结果表明:该类材料的变形行为表现出显著的黏弹性特征,并且兼具蠕变温度效应与物理老化效应。加载初期的较短时间内,拉伸应变随时间逐渐增大,呈现出明显的蠕变变形第一、第二阶段特征;当加载时间超过其物理老化特征时间之后,在加载的大部分时间段内,这种与时间有关的变形则开始逐渐减小,呈现出清晰的物理老化特征。为了合理表征这种特殊的黏弹性变形行为,进一步构建了包含蠕变温度效应与物理老化效应的线性黏弹性理论模型。提出了可描述该复合材料黏弹性变形的本构关系,并给出了Prony级数近似解法,进而编写了相应的有限元材料子程序UMAT。仿真结果表明,所构建的理论模型能够合理地描述该类复合材料的黏弹性变形。Abstract: In order to better understand the short-term and long-term deformation behaviors of carbon fiber reinforced epoxy (CF/EP) composite materials, a series of tensile creep tests of a type of CF/EP laminated composite material under constant loads, typically, 20%, 30% and 40% of ultimate tensile strength and constant temperatures (25°C and 50°C) were conducted. The material deforms in a remarkable time-dependent way, and behaves both clearly creep temperature effect and physical aging phenomena. Specifically, the tensile strains increase during the short time duration after the tests begin, similar to creep deformation. When the testing time exceeds physical aging characteristic time, the tensile strains start to decrease during the most of loading period. To characterize reasonably this particular deformation behavior, a linear viscoelastic model was developed to describe both creep temperature effect and physical ageing effect. The related viscoelastic constitutive relations of this composite material were derived, and further numerically implemented using the Prony series. In addition, its numerical algorithm was proposed within a finite element framework, and numerical analysis was performed via UMAT subroutine. The new theoretical model is then verified by a comparison of experimental results to numerical ones.
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Key words:
- CF/EP /
- viscoelasticity /
- creep /
- physical aging /
- constitutive model
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表 1 CF/EP复合材料试样编号
Table 1. CF/EP composite sample labels under different load levels
Load level Label 20%UTS CF/EP-0.2 30%UTS CF/EP-0.3 40%UTS CF/EP-0.4 表 2 CF/EP复合材料试样黏弹性本构模型参数
Table 2. Parameters related to viscoelastic model of CF/EP composite specimen
n $ \lambda _n^{{\text{TE}}} $ $ S_n^{{\text{TE}}} $ $ \lambda _n^{{\text{AE}}} $ $ S_n^{{\text{AE}}} $ 1 0.1 0.346 0.1 −0.0927 2 0.01 0.074 0.01 −0.1881 3 0.001 0.157 0.001 −0.3321 4 0.0001 0.202 0.0001 −0.8055 5 0.00001 0.131 0.00001 −0.6237 6 0.000001 0.467 0.000001 −1.2105 HTSF ${a_{\text{H} } }(T) = \exp \left[ - 152.32 \times \left(\dfrac{1}{ {25} } - \dfrac{1}{T}\right)\right]$ VTSF ${a_{\text{v} } }(T) = 0.159 + 0.0405 T - 0.000273 {T^2}$ ASF ${a_{ {\text{te} } } }(t) = {\left(\dfrac{ { {t_{ {\text{e,ref} } } } } }{ { {t_{ {\text{e,ref} } } } + t} }\right)^{0.5} }$ CT ${t_{ {\text{e,ref} } } } = 655\;500$ Notes: n—Number of terms for each component in the transient compliance; $ \lambda _n^{{\text{TE}}} $ and $ \lambda _n^{{\text{AE}}} $—nth reciprocal of retardation time corresponding to $ S_n^{{\text{TE}}} $ and $ S_n^{{\text{AE}}} $; $ S_n^{{\text{TE}}} $ and $ S_n^{{\text{AE}}} $—nth coefficient of Prony series for each component in transient compliance of TE and AE; HTSF, aH—Horizontal temperature shift factor; VTSF, av—Vertical temperature shift factor; ASF, ate—Physical aging time shift factor; CT, te,ref—Physical aging characteristic time; t—Time; T—Temperature. -
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