Creep/recovery behavior analysis of wood-plastic composites based on fractional order viscoelastic model
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摘要: 木塑复合材料(WPC)是一种木质纤维增强聚合物的新型环保复合材料,为分析WPC在非恒定荷载下的变形行为,进行结构的长期变形设计,对WPC的蠕变/回复变形进行计算分析。采用叠加原理对比分析既有蠕变计算模型对WPC蠕变/回复的整体预测效果。结果表明,现有模型均不能良好预测其蠕变/回复行为。采用基于分数阶微积分的黏弹性模型对其蠕变/回复行为进行预测,提出一种双参数法的修正分数阶黏弹性模型。通过与已有实测数据对比表明,该模型能够准确反映WPC的静态黏弹性行为。结合实验数据,给出了不同WPC蠕变/回复模型的参数取值。Abstract: Wood-plastic composite (WPC) is a new kind of environment-friendly composite reinforced by wood fiber. In order to analyze the deformation behavior of WPC under the non-constant load and carry out effective design of long-term deformation of the structure, the creep/recovery deformation of WPC was analyzed. The superposition principle method was used to compare and analyze the overall prediction effect of the existing creep calculation model on WPC creep/recovery. The results show that none of the existing models can predict the creep recovery behavior well. The viscoelastic model based on fractional calculus was used to predict the creep/recovery behavior, and a modified fractional viscoelastic model with two-parameter method was proposed. The results show that the model can accurately reflect the static viscoelastic behavior of WPC. Based on the experimental data, the creep/recovery model parameters of different WPC materials were given.
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表 1 WPC分数阶模型拟合参数
Table 1. Fitting parameters of fractional order model of WPC
Test No. E0/MPa η0/(MPa·s) a η1/ (MPa·s) R2 10%-50WPC 3 613 36 828 0.184 3 447.6 0.999 10%-60WPC 5 997 6 774 056 0.216 5 188 0.998 10%-70WPC 6 798 35 157 0.262 12 186 0.999 20%-50WPC 2 688 27 011 701 0.226 28 377 0.997 20%-60WPC 5 388 5 674 429 0.214 32 700 0.994 20%-70WPC 7 747 9 872 0.244 71 360 0.994 30%-50WPC 2 001 754 019 0.246 35 462 0.981 30%-60WPC 5 056 1 132 038 0.256 48 518 0.990 30%-70WPC 7 637 1 402 0.246 77 392 0.935 Notes: E0—Elasticity coefficient; η0, η1—Viscous coefficients; 10%-50WPC—Stress level is 10% and the mass fraction of wood fiber is 50wt%; a—Fractional derivative order; R2—Goodness of fitting. 表 2 WPC Findley幂律模型蠕变回复阶段拟合参数
Table 2. Fitting parameters of Findley power law model in creep recovery stage of WPC
Test No. a b R2 10%-50WPC 0.098 0.111 9 0.990 10%-60WPC 0.063 0.125 8 0.979 10%-70WPC 0.060 0.088 3 0.833 20%-50WPC 0.094 0.198 2 0.752 20%-60WPC 0.144 0.114 3 0.996 20%-70WPC 0.113 0.109 5 0.987 30%-50WPC 0.656 0.073 5 0.988 30%-60WPC 0.191 0.132 5 0.984 30%-70WPC 0.134 0.131 1 0.991 Note: a, b—Model parameters after unloading. 表 3 WPC修正分数阶黏弹性模型蠕变回复阶段拟合参数
Table 3. Fitting parameters of fractional order model in creep recovery stage of WPC
Test No. E0/MPa η0/(MPa·s) a η1/(MPa·s) R2 10%-50WPC 31.0 130 0.30 1 227.50 0.995 10%-60WPC 54.4 31 0.22 574.49 0.990 10%-70WPC 99.1 1738 724 0.21 641.86 0.988 20%-50WPC 41.7 17 0.12 104.73 0.991 20%-60WPC 123.5 56 0.13 139.34 0.999 20%-70WPC 4 307.4 397 0.11 111.41 0.987 30%-50WPC 47.8 15 0.08 43.26 0.999 30%-60WPC 112.1 6 643 0.16 169.39 0.999 30%-70WPC 375.9 11 0.10 115.08 0.999 -
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