基于分数阶黏弹性模型的木塑复合材料蠕变/回复性能分析

梅生启; 唐广; 杨斌; 王元丰

doi:10.13801/j.cnki.fhclxb.20191230.002

基于分数阶黏弹性模型的木塑复合材料蠕变/回复性能分析

doi: 10.13801/j.cnki.fhclxb.20191230.002

梅生启^{1, 2, ,},
唐广^1,,
杨斌^1,,
王元丰^3,

1.
石家庄铁道大学　土木工程学院，石家庄 050043
2.
石家庄铁道大学　道路与铁道工程安全保障省部共建教育部重点实验室，石家庄 050043
3.
北京交通大学　土木建筑工程学院，北京 100044

基金项目: 国家自然科学基金(51778044)

详细信息

通讯作者:
梅生启，博士，讲师，研究方向为工程材料与结构的长期性能、动力性能　E-mail：cshqmei@stdu.edu.cn

中图分类号: TU531.6
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- 被引次数: 0
出版历程
- 收稿日期: 2019-10-09
- 录用日期: 2019-12-21
- 网络出版日期: 2019-12-31
- 刊出日期: 2020-08-15

Creep/recovery behavior analysis of wood-plastic composites based on fractional order viscoelastic model

MEI Shengqi^{1, 2
, ,},
TANG Guang^1
,,
YANG Bin^1
,,
WANG Yuanfeng^3
,

1.
School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
2.
Key Laboratory of Roads and Railway Engineering Safety Control of Ministry of Education, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
3.
School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

摘要

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。
- 木塑复合材料 /
- 蠕变 /
- 蠕变回复 /
- 分数阶黏弹性模型 /
- 双参数法
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.
- wood-plastic composite /
- creep /
- creep recovery /
- fractional order viscoelastic model /
- double parameters method

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图 1 材料蠕变/回复示意图

Figure 1. Material creep/recovery diagram

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图 2 广义Kelvin模型示意图

Figure 2. Diagram of generalized Kelvin model

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图 3 分数阶导数分形理论示意图

Figure 3. Schematic diagram of fractal theory of fractional derivatives

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图 4 分数阶模型

Figure 4. Fractional order model

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图 5 基于叠加原理方法的蠕变恢复计算

Figure 5. Creep recovery calculation based on superposition principle method

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图 6 模型计算木塑复合材料(WPC)蠕变结果(实测应变来自文献[7])

Figure 6. Creep of wood-plastic composite(WPC) calculated by the models (Measured strains were selected from Ref. [7])

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图 7 模型计算WPC蠕变结果(实测应变来自文献[8])

Figure 7. Creep of WPC calculated by the models (Measured strains were selected from Ref.[8])

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图 8 分数阶模型计算WPC蠕变结果(实测应变来自文献[7])

Figure 8. Creep of WPC calculated by fractional order model (Measured strains were selected from Ref.[7])

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图 9 分数阶模型计算WPC蠕变结果(实测数据来源于文献[8])

Figure 9. Creep of WPC calculated by fractional order model (Measured strains were selected from Ref.[8])

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图 10 基于叠加原理的WPC蠕变/回复全曲线(实测数据来源于文献[7])

Figure 10. Creep/recovery curves of WPC based on superposition principle (Measured strains were selected from Ref.[7])

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图 11 基于叠加原理的WPC蠕变/回复全曲线(实测数据来源于文献[8])

Figure 11. Creep/recovery curves of WPC based on superposition principle (Measured strains were selected from Ref.[8])

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图 12 基于叠加原理的分数阶模型预测WPC蠕变/回复全曲线(实测数据来源于文献[7])

Figure 12. WPC creep/recovery curves calculated by fractional model based on superposition principle (Measured strains were selected from Ref.[7])

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图 13 基于叠加原理的分数阶模型预测WPC蠕变/回复全曲线(实测数据来源于文献[8])

Figure 13. WPC creep/recovery curves calculated by fractional order model based on superposition principle (Measured strains were selected from Ref.[8])

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图 14 双参数法修正Findley模型计算WPC蠕变/回复全曲线(实测数据来源于文献[8])

Figure 14. WPC creep/recovery curves calculated by two-parameter method modified Findley model (Measured strains were selected from Ref.[8])

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图 15 双参数法修正分数阶模型计算WPC蠕变/回复全曲线(实测数据来源于文献[8])

Figure 15. WPC creep/recovery curves calculated by two-parameter method modified factional order model (Measured strains were selected from Ref.[8])

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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.

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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.

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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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