Computational Analysis of the Micromechanical Stress Field in Undamaged and Damaged Unidirectional Fiber-Reinforced Plastics Using a Modified Principal Component Analysis
Abstract
:1. Introduction
2. Materials and Methods
2.1. Specimen Preparation and Tensile Test
2.2. Computational Micromechanics Modeling
2.2.1. RVE for the Modified Mesh-Independent PCA Study
2.2.2. RVEs with Random Fiber Arrangements for the Micromechanical Stress Field Study
2.2.3. Micromechanical Damage Modeling Approaches
The Stiffness Degradation Model for the Matrix and Interface
Probabilistic Modeling of Fiber Breaks
2.3. Application of Principal Component Analysis for the Matrix Stress Field
2.3.1. Octahedral Stress Field Within the Matrix
2.3.2. Implementation of Principal Component Analysis (PCA)
3. Results and Discussion
3.1. Development of a Modified Mesh-Independent PCA
3.2. Analysis of the Micromechanical Stress Field of RVE with Random Fiber Arrangements
3.2.1. Validation of the RVE Models with Random Fiber Arrangements
3.2.2. Modified PCA of Transverse Tensile Strain Simulations (Matrix/Interface Damage)
3.2.3. Modified PCA of the Longitudinal Tensile Strain Simulations (Matrix/Interface Damage)
3.2.4. Modified PCA of the Longitudinal Tensile Strain Simulations (Fiber Breaks)
3.2.5. Modified PCA of the Longitudinal Tensile Strain Simulations (Matrix/Interface Damage and Fiber Breaks)
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
Appendix C
References
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Mechanical Properties | Toray T700 Carbon Fibers [29] | LY556/H917 Epoxy Matrix [30] | |
---|---|---|---|
Longitudinal modulus [GPa] | E∥ | 230 | 3.15 |
Transverse modulus [GPa] | E⊥ | 15 | - |
Longitudinal shear modulus [GPa] | G⊥∥ | 15 | 1.17 |
Transverse shear modulus [GPa] | G⊥⊥ | 7 | - |
Longitudinal Poisson’s ration [–] | ν⊥∥ | 0.2 | 0.35 |
Transverse Poisson’s ration [–] | ν⊥⊥ | 0.5 | - |
Tensile strength [MPa] | σf | 4900 | 93 |
Model Parameter | Matrix | Interface | |
---|---|---|---|
A | [–] | 1.0−6 | 5.0−19 |
n | [–] | 10.0 | 8.0 |
b | [–] | 0.5 | 0.5 |
[–] | 75.0 | 55.0 | |
[–] | 10.0 | 10.0 | |
[–] | 0.1 | 0.25 | |
[–] | 0.5 | 0.75 |
L [µm] | L0 [mm] | m [−] | [MPa] | γ [−] |
---|---|---|---|---|
2.0 | 30.0 | 3.38 | 4170 | 1.0 |
RVE Size | Longitudinal Strain 2% | Transverse Strain 2% | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Fibers | Integration Points | λ1 | λ2 | |λ1| | |λ2| | θ1 [°] | λ1 | λ2 | |λ1| | |λ2| | θ1 [°] |
1 | 2305 | 1.019 | 0.345 | 0.993 | 0.116 | 161.2 | 0.937 | 0.419 | 0.913 | 0.408 | 30.3 |
4 | 9220 | 1.441 | 0.489 | 0.993 | 0.116 | 161.2 | 1.325 | 0.592 | 0.913 | 0.408 | 30.3 |
9 | 20,745 | 1.765 | 0.599 | 0.993 | 0.116 | 161.2 | 1.622 | 0.725 | 0.913 | 0.408 | 30.3 |
25 | 57,625 | 2.278 | 0.773 | 0.993 | 0.116 | 161.2 | 2.094 | 0.936 | 0.913 | 0.408 | 30.3 |
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Lopez, N.R.; Çelik, H.; Hopmann, C. Computational Analysis of the Micromechanical Stress Field in Undamaged and Damaged Unidirectional Fiber-Reinforced Plastics Using a Modified Principal Component Analysis. Polymers 2024, 16, 3000. https://doi.org/10.3390/polym16213000
Lopez NR, Çelik H, Hopmann C. Computational Analysis of the Micromechanical Stress Field in Undamaged and Damaged Unidirectional Fiber-Reinforced Plastics Using a Modified Principal Component Analysis. Polymers. 2024; 16(21):3000. https://doi.org/10.3390/polym16213000
Chicago/Turabian StyleLopez, Nicolas Rozo, Hakan Çelik, and Christian Hopmann. 2024. "Computational Analysis of the Micromechanical Stress Field in Undamaged and Damaged Unidirectional Fiber-Reinforced Plastics Using a Modified Principal Component Analysis" Polymers 16, no. 21: 3000. https://doi.org/10.3390/polym16213000