Approximation of Non-Linear Stress–Strain Curve for GFRP Tensile Specimens by Inverse Method
Abstract
:1. Introduction
2. Experiment and FEA Setup
2.1. Experimental Setup (ASTM D638-14)
2.2. Finite Element Analysis Setup
2.3. Inverse Methods
3. Optimization of Inverse Methods
Parameter Optimization
4. Results of Advanced Inverse Method
4.1. Advanced Inverse Method
4.2. Simulation and Optimization
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Center width of tensile specimen | |
Total width of tensile specimen | |
Thickness of tensile specimen | |
Length of tensile specimen | |
Total length of tensile specimen | |
Gauge length = Original distance between gage marks | |
Increment of distance between gage marks | |
Displacement in FEA | |
Radius | |
Reactive force | |
Engineering stress in experiment of ASTM D638-14 | |
Engineering strain in experiment of ASTM D638-14 | |
True stress in experiment of ASTM D638-14 | |
Engineering stress in FEA | |
Engineering strain in FEA | |
Maximum number of data points that express stress–strain | |
Order of data that express stress-strain, | |
Sequential stress values of the stress–strain curve derived from FEA | |
Sequential stress values of the stress–strain curve derived from an experiment | |
E | Young’s modulus |
Poisson’s ratio | |
Yield stress | |
Yield strain | |
Maximum number of material properties | |
Value that expresses the order of a material property, | |
Equation number of the inverse method, | |
Difference in the experiment and analysis for the engineering stress | |
Average of the differences between the experiment and the analysis | |
Average of the differences between the experiment and the analysis for the entire material properties | |
Material parameter of inverse model | |
Material parameter of advanced model | |
Maximum number of material parameters by inverse method | |
Value that expresses the order of a material parameter |
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Symbols | Units | wt 20% GF | wt 30% GF | wt 40% GF |
---|---|---|---|---|
MPa | 4082.40 | 4833.49 | 5717.59 | |
- | 0.35 | 0.38 | 0.4 | |
MPa | 7.25 | 8.08 | 10.62 | |
- | 0.0038 | 0.0037 | 0.0039 | |
1.05 | 1.11 | 1.21 | ||
MPa | 75.33 | 89.72 | 93.83 |
No. | Eq. | Applied S–S Curve Model | ||||
---|---|---|---|---|---|---|
wt 20% GF | wt 30% GF | wt 40% GF | ||||
1 | 1 | ASTM Engineering model | 13.54 | 17.00 | 15.75 | 15.43 |
2 | 3 | ASTM True model | 12.62 | 15.97 | 14.67 | 14.42 |
3 | 4 | Hollomon | 11.37 | 14.41 | 12.77 | 12.85 |
4 | 5 | Ludwik | 8.50 | 11.43 | 8.29 | 9.41 |
5 | 6 | Swift | 10.33 | 13.28 | 11.38 | 11.66 |
6 | 7 | Gosh | 1.87 | 2.85 | 2.06 | 2.26 |
7 | 8 | Voce | 1.32 | 1.39 | 1.91 | 1.54 |
8 | 9 | Hockett–Sherby | 26.59 | 33.03 | 30.51 | 30.05 |
No. | Eq. | Applied S-S Curve Model | ||||
---|---|---|---|---|---|---|
wt 20% GF | wt 30% GF | wt 40% GF | ||||
1 | 1 | ASTM Engineering model | 13.54 | 17.00 | 15.75 | 15.43 |
2 | 3 | ASTM True model | 12.62 | 15.97 | 14.67 | 14.42 |
3 | 4 | Hollomon | 0.96 | 1.20 | 1.18 | 1.11 |
4 | 5 | Ludwik | 0.68 | 1.09 | 0.82 | 0.86 |
5 | 6 | Swift | 0.57 | 0.77 | 0.71 | 0.69 |
6 | 7 | Gosh | 0.73 | 0.95 | 0.91 | 0.86 |
7 | 8 | Voce | 0.85 | 0.97 | 0.87 | 0.90 |
8 | 9 | Hockett–Sherby | 0.17 | 0.06 | 0.29 | 0.17 |
9 | 19 | Kim–Tuan | 0.12 | 0.16 | 0.32 | 0.20 |
10 | 20 | Swift–Voce | 0.11 | 0.15 | 0.29 | 0.18 |
11 | 21 | Ludwik–Voce | 0.38 | 0.26 | 0.45 | 0.36 |
12 | 22 | Swift Hockett–Sherby | 1.25 | 0.18 | 0.39 | 0.61 |
13 | 23 | Ludwik Hockett–Sherby | 0.18 | 0.21 | 0.38 | 0.26 |
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Shin, D.S.; Kim, Y.S.; Jeon, E.S. Approximation of Non-Linear Stress–Strain Curve for GFRP Tensile Specimens by Inverse Method. Appl. Sci. 2019, 9, 3474. https://doi.org/10.3390/app9173474
Shin DS, Kim YS, Jeon ES. Approximation of Non-Linear Stress–Strain Curve for GFRP Tensile Specimens by Inverse Method. Applied Sciences. 2019; 9(17):3474. https://doi.org/10.3390/app9173474
Chicago/Turabian StyleShin, Dong Seok, Young Shin Kim, and Euy Sik Jeon. 2019. "Approximation of Non-Linear Stress–Strain Curve for GFRP Tensile Specimens by Inverse Method" Applied Sciences 9, no. 17: 3474. https://doi.org/10.3390/app9173474