Numerical Simulations of the Low-Velocity Impact Response of Semicylindrical Woven Composite Shells
Abstract
:1. Introduction
2. Material and Experimental Procedure
3. Damage Models
4. Finite Element Model
5. Numerical Results
6. Numerical–Experimental Correlation
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Symbol | Description | Symbol | Description |
Density | Shear hardening function | ||
Young’s modulus along fiber direction 1 | Axial damage thresholds | ||
Young’s modulus along fiber direction 2 | Shear damage threshold | ||
Though-thickness Young’s modulus | Tensile/compressive strength along the fiber directions | ||
In-plane shear modulus | Tensile/compressive damage variable along direction 1 | ||
Out of plane shear modulus | Tensile/compressive damage variable along direction 2 | ||
In-plane Poisson’s ratio | Shear damage variable | ||
Tensile strength along direction 1 | Elastic energy density | ||
Compressive strength along direction 1 | Characteristic length of the element | ||
Tensile strength along direction 2 | Plastic strain due to shear deformation | ||
Compressive strength along direction 2 | Elastic normal interlaminar stiffness | ||
In-plane shear strength | Elastic shear interlaminar stiffness | ||
Intralaminar fracture toughness along direction 1 and 2 | Elastic tangential interlaminar stiffness | ||
Parameter in the equation of shear damage | Maximum normal contact stress | ||
Maximum shear damage | Maximum 1st shear contact stress | ||
Coefficient in hardening equation | Maximum 2nd shear contact stress | ||
Power term in hardening equation | Interlaminar normal fracture toughness | ||
Axial damage activation function | Interlaminar 1st shear fracture toughness | ||
Shear damage activation function | Interlaminar 2nd shear fracture toughness | ||
Plasticity activation function | 𝜂 | Benzeggagh–Kenane exponent | |
Effective tensile/compressive stress | Friction coefficient | ||
Initial effective shear yield stress | M | Parameter defined for the cohesive zone model | |
Effective shear stress | Number of elements in the cohesive zone |
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Property | Symbol | Units | Value |
---|---|---|---|
Density | kg/m3 | 1900 | |
Stiffness properties | GPa | 21.9 | |
GPa | 21.9 | ||
GPa | 8.6 | ||
GPa | 3.4 | ||
GPa | 2.4 | ||
- | 0.14 | ||
Strength properties | MPa | 250 | |
MPa | 200 | ||
MPa | 40 | ||
Fracture toughness | N/mm | 4500 | |
Shear plasticity | - | 1 | |
MPa | 25 | ||
- | 800 | ||
- | 0.552 |
Property | Symbol | Units | Value |
---|---|---|---|
Stiffness properties | N/mm3 | 106 | |
Strength properties | MPa | 15 | |
MPa | 30 | ||
Fracture toughness | N/mm | 0.3 | |
N/mm | 0.6 | ||
- | 1.45 |
Max. Load (N) | Dif. 1 (%) | Max. Displacement (mm) | Dif. 1 (%) | Contact Time (ms) | Dif. 1 (%) | |
---|---|---|---|---|---|---|
With mass scaling | 797 | - | 11.5 | - | 23 | - |
Without mass scaling | 730 | 8.8 | 11.5 | 0 | 22.6 | 1.8 |
Mesh Size (mm) | Max. Load (N) | Difference (%) | Max. Displacement (mm) | Difference (%) | Contact Time (ms) | Difference (%) |
---|---|---|---|---|---|---|
0.3 | 797 | - | 11.5 | - | 23 | - |
0.5 | 818 | 2.6 | 11.5 | 0 | 23 | 0 |
1 | 828 | 3.8 | 11.5 | 0 | 23.5 | 2.2 |
2 | 806 | 1.1 | 11.5 | 0 | 23.1 | 0.4 |
Mesh Size (mm) | Maximum Load (N) | Maximum Displacement (mm) | Contact Time (ms) | ||||||
---|---|---|---|---|---|---|---|---|---|
Num. | Exp. | Error (%) | Num. | Exp. | Error (%) | Num. | Exp. | Error (%) | |
0.3 | 797 | 757 | 5.0 | 11.5 | 11.2 | 2.7 | 23 | 20.6 | 10.4 |
0.5 | 818 | 7.5 | 11.5 | 2.7 | 23 | 10.4 | |||
1 | 828 | 8.6 | 11.5 | 2.7 | 23.5 | 12.3 | |||
2 | 806 | 6.1 | 11.5 | 2.7 | 23.1 | 10.8 |
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Ferreira, L.M.; Coelho, C.A.C.P.; Reis, P.N.B. Numerical Simulations of the Low-Velocity Impact Response of Semicylindrical Woven Composite Shells. Materials 2023, 16, 3442. https://doi.org/10.3390/ma16093442
Ferreira LM, Coelho CACP, Reis PNB. Numerical Simulations of the Low-Velocity Impact Response of Semicylindrical Woven Composite Shells. Materials. 2023; 16(9):3442. https://doi.org/10.3390/ma16093442
Chicago/Turabian StyleFerreira, Luis M., Carlos A. C. P. Coelho, and Paulo N. B. Reis. 2023. "Numerical Simulations of the Low-Velocity Impact Response of Semicylindrical Woven Composite Shells" Materials 16, no. 9: 3442. https://doi.org/10.3390/ma16093442