The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation
The moisture diffusion behaviors of 3D woven composites exhibit non-Fickian properties when they are exposed to a hydrothermal environment. Although some experimental works have been undertaken to investigate this phenomenon, very few mathematical works on non-Fickian moisture diffusion predictions...
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/5/1160 |
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| author | Hang Yu Chenhui Zhu Lu Yao Yan Ma Yang Ni Shenkai Li Huan Li Yang Liu Yuming Wang |
| author_facet | Hang Yu Chenhui Zhu Lu Yao Yan Ma Yang Ni Shenkai Li Huan Li Yang Liu Yuming Wang |
| author_sort | Hang Yu |
| collection | DOAJ |
| description | The moisture diffusion behaviors of 3D woven composites exhibit non-Fickian properties when they are exposed to a hydrothermal environment. Although some experimental works have been undertaken to investigate this phenomenon, very few mathematical works on non-Fickian moisture diffusion predictions of 3D woven composites are available in the literature. To capture the non-Fickian behavior of moisture diffusion in 3D woven composites, this study first utilized a time fractional diffusion equation to derive the percentage of moisture content of a homogeneous material under hydrothermal conditions. A two-stage moisture diffusion model was subsequently developed based on the moisture diffusion mechanics of both neat resin and 3D woven composites, which describes the initial fast diffusion and the long-term slow diffusion stages. Notably, the model incorporated fractional order parameters to account for the nonlinear property of moisture diffusion in composites. Finally, the weight gain curves of neat resin and the 3D woven composite were calculated to verify the fractional diffusion model, and the predicted moisture uptake curves were all in good agreement with the experimental results. It is important to note that when the fractional order parameter α < 1, the initial moisture uptake will become larger with a later slow down process. This phenomenon can better describe non-Fickian behavior caused by initial voids or complicated structures. |
| first_indexed | 2024-03-11T07:18:10Z |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T07:18:10Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
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| spelling | doaj.art-031e6ed274d6425280979448f2c8da9e2023-11-17T08:09:02ZengMDPI AGMathematics2227-73902023-02-01115116010.3390/math11051160The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion EquationHang Yu0Chenhui Zhu1Lu Yao2Yan Ma3Yang Ni4Shenkai Li5Huan Li6Yang Liu7Yuming Wang8School of Transportation and Civil Engineering, Nantong University, Nantong 226019, ChinaSchool of Transportation and Civil Engineering, Nantong University, Nantong 226019, ChinaSchool of Transportation and Civil Engineering, Nantong University, Nantong 226019, ChinaSchool of Textile and Clothing, Nantong University, Nantong 226019, ChinaShanghai Electro-Mechanical Engineering Institute, Shanghai 201109, ChinaSchool of Transportation and Civil Engineering, Nantong University, Nantong 226019, ChinaSchool of Transportation and Civil Engineering, Nantong University, Nantong 226019, ChinaSchool of Transportation and Civil Engineering, Nantong University, Nantong 226019, ChinaSchool of Transportation and Civil Engineering, Nantong University, Nantong 226019, ChinaThe moisture diffusion behaviors of 3D woven composites exhibit non-Fickian properties when they are exposed to a hydrothermal environment. Although some experimental works have been undertaken to investigate this phenomenon, very few mathematical works on non-Fickian moisture diffusion predictions of 3D woven composites are available in the literature. To capture the non-Fickian behavior of moisture diffusion in 3D woven composites, this study first utilized a time fractional diffusion equation to derive the percentage of moisture content of a homogeneous material under hydrothermal conditions. A two-stage moisture diffusion model was subsequently developed based on the moisture diffusion mechanics of both neat resin and 3D woven composites, which describes the initial fast diffusion and the long-term slow diffusion stages. Notably, the model incorporated fractional order parameters to account for the nonlinear property of moisture diffusion in composites. Finally, the weight gain curves of neat resin and the 3D woven composite were calculated to verify the fractional diffusion model, and the predicted moisture uptake curves were all in good agreement with the experimental results. It is important to note that when the fractional order parameter α < 1, the initial moisture uptake will become larger with a later slow down process. This phenomenon can better describe non-Fickian behavior caused by initial voids or complicated structures.https://www.mdpi.com/2227-7390/11/5/1160time-fractional diffusion equationnon-Fickian behaviorshygrothermal aging3D woven composite |
| spellingShingle | Hang Yu Chenhui Zhu Lu Yao Yan Ma Yang Ni Shenkai Li Huan Li Yang Liu Yuming Wang The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation Mathematics time-fractional diffusion equation non-Fickian behaviors hygrothermal aging 3D woven composite |
| title | The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation |
| title_full | The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation |
| title_fullStr | The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation |
| title_full_unstemmed | The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation |
| title_short | The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation |
| title_sort | two stage moisture diffusion model for non fickian behaviors of 3d woven composite exposed based on time fractional diffusion equation |
| topic | time-fractional diffusion equation non-Fickian behaviors hygrothermal aging 3D woven composite |
| url | https://www.mdpi.com/2227-7390/11/5/1160 |
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