The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation
Abstract
1. Introduction
2. Experiment
2.1. Materials
2.2. Moisture Uptake Experiment
3. Theory
3.1. Time Fractional Diffusion Equation
3.2. The Two-Stage Time Fractional Diffusion Model
4. Result and Discussion
4.1. The Results of the Time-Fractional Diffusion Equation
4.2. Moisture Uptake of Resin
4.3. Moisture Uptake of 3D Woven Composite
5. Conclusions
- (a)
- when α < 1, the moisture absorptions do not follow Fick’s law, exhibiting nonlinear properties. The moisture uptake rapidly increases at first, then develops slowly compared to Fickian diffusion.
- (b)
- The initial moisture uptake becomes quicker while α is smaller. It is worth noting that the intersection points of the curves (α = 0.25, 0.5 and 0.75) and the Fickian diffusion become larger with the increase of diffusivities D.
- (a)
- For neat resin, since the fast diffusion obeys Fick’s law, thus α = 1. The observed long-term diffusion of resin increases linearly, therefore, γ = 1.
- (b)
- However, for the 3D woven composite, α = 0.83 related to the voids and cracks, is fitted to represent the nonlinear property during non-Fickian diffusion. A linear tendency is found from the experimental observation during long-term hydrothermal aging, leading to γ = 1 for the 3D woven composite.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
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Materials | Length (mm) | Width (mm) | Thickness (mm) |
---|---|---|---|
Resin | 19.6 | 19.6 | 2.7 |
3D woven | 25.7 | 22.6 | 5.2 |
Material | Diffusivity (10−6 cm2/min) | M (%) | Parameters | |||
---|---|---|---|---|---|---|
Resin | 1.548 | 0.018 | 4.06 | 1.14 | 1 | 1 |
Material | Diffusivity (10−6 cm2/min) | M (%) | Fractional Parameters | |||
---|---|---|---|---|---|---|
WCa | 1.2. | 0.00054 | 1.2 | 0.7 | 0.83 | 1 |
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Yu, H.; Zhu, C.; Yao, L.; Ma, Y.; Ni, Y.; Li, S.; Li, H.; Liu, Y.; Wang, Y. The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation. Mathematics 2023, 11, 1160. https://doi.org/10.3390/math11051160
Yu H, Zhu C, Yao L, Ma Y, Ni Y, Li S, Li H, Liu Y, Wang Y. The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation. Mathematics. 2023; 11(5):1160. https://doi.org/10.3390/math11051160
Chicago/Turabian StyleYu, Hang, Chenhui Zhu, Lu Yao, Yan Ma, Yang Ni, Shenkai Li, Huan Li, Yang Liu, and Yuming Wang. 2023. "The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation" Mathematics 11, no. 5: 1160. https://doi.org/10.3390/math11051160
APA StyleYu, H., Zhu, C., Yao, L., Ma, Y., Ni, Y., Li, S., Li, H., Liu, Y., & Wang, Y. (2023). The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation. Mathematics, 11(5), 1160. https://doi.org/10.3390/math11051160