A Dynamic Constitutive Model and Simulation of Braided CFRP under High-Speed Tensile Loading
Abstract
:1. Introduction
2. Dynamic Constitutive Model
2.1. Traditional Composite Constitutive Model
2.2. Modified Dynamic Constitutive Model
3. Finite Element Model
3.1. UMAT
3.2. Dynamic Tensile FE Model
4. Analysis of Simulation Results
4.1. Comparison of Experimental and Simulation Results
4.2. Stress and Failure Contour Maps
4.3. Analysis of the Strain Rate Effect on the Modulus and Strength
4.4. Additional Parametric Analysis
5. Conclusions
- The results simulated with the dynamic constitutive model were in good agreement with the stress–strain curves and strain distributions from the tests during different stages. In the linear elastic stage of the test, the strain distributions of the specimens were relatively uniform. When the strain value reached 0.012–0.013, the strain field turned non-uniform, and failure occurred in the form of a brittle fracture. For the [0/90/±45]3s lay-up, as the strain rate increased, the input modulus decreased, the tensile strength decreased, and the stress decreased under a constant displacement. Comparing the three lay-ups considered, the [0/90]12 lay-up resulted in the highest stress for a given displacement, with failure mainly consisting of fiber tensile fracture.
- For the same specimen, the strain rate was the lowest at both clamped ends and the largest at the middle section. On the contrary, the modulus was high on both ends and small in the middle. On the other hand, the strength was the smallest at the clamped ends, decreasing at the transition region and increasing again toward the middle section where the strain rate was high. Combined with the simulation of additional lay-ups, strain rates, and thicknesses, it was found that the fitting curve in the test is completely input into the dynamic constitutive model, which can better reflect the dynamic variation rules of the different material properties. It was also found that the tensile strength of the material and the slope of the curve increased as the percentage of 0/90 angle lay-ups increased, while as the percentage of ±45 angle lay-ups increased, the curve tended to fluctuate. As the strain rate increased, the slope of the curve decreased, and the strength of the material increased.
- The dynamic properties of woven CFRP have not yet been extensively studied. Different resins, fibers, and weaving methods can affect the dynamic properties of the material. In the field of rail transportation, the application of composite materials is gradually increasing. Research on dynamic constitutive models of composite materials enables a better simulation of the bearing capacity and energy absorption characteristics of the structure during train collisions, which may significantly promote the application of carbon fiber composites in other multiple fields.
Author Contributions
Funding
Conflicts of Interest
References
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Failure Mode | Failure Criteria | |
---|---|---|
Fiber tensile failure | (4) | |
Fiber compressive failure | (5) | |
Matrix tensile failure | (6) | |
Matrix compressive failure | (7) | |
Fiber-matrix shear-out failure | (8) | |
Matrix tensile delamination failure | (9) | |
Matrix compressive delamination failure | (10) |
Failure Mode | |||||||||
---|---|---|---|---|---|---|---|---|---|
Fiber tensile failure | 0.14 | 0.4 | 0.4 | 0.25 | 0.25 | 0.2 | 0 | 0 | 0 |
Fiber compressive failure | 0.14 | 0.4 | 0.4 | 0.25 | 0.25 | 0.2 | 0 | 0 | 0 |
Matrix tensile failure | - | 0.4 | 0.4 | - | - | 0.2 | 0 | 0 | 0 |
Matrix compressive failure | - | 0.4 | 0.4 | - | - | 0.2 | 0 | 0 | 0 |
Fiber-matrix shear-out failure | - | - | - | 0.25 | 0.25 | - | 0 | 0 | - |
Matrix tensile delamination failure | - | - | 0 | - | 0 | 0 | - | 0 | - |
Matrix compressive delamination failure | - | - | 0 | - | 0 | 0 | - | 0 | - |
Parameter | Assigned Value | Parameter | Assigned Value |
---|---|---|---|
64.00 GPa | 771.83 MPa | ||
64.00 GPa | 830.93 MPa | ||
10.30 GPa | 771.83 MPa | ||
4.97 GPa | 830.93 MPa | ||
4.97 GPa | 31.2 MPa | ||
3.50 GPa | 184 MPa | ||
0.066 | 107.7 MPa | ||
0.3 | 94.24 MPa | ||
0.3 | 94.24 MPa |
Different Lay-Ups | [0/90]12 | [±45/0/90/0/90]4 | [±45/0/90]6 | [±45/±45/0/90]4 | [±45]12 |
---|---|---|---|---|---|
Different strain rates/s−1 | 50 | 100 | 200 | 400 | 600 |
Different thicknesses/mm | 1.6 | 2 | 2.4 | 2.8 | 3.2 |
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Jin, W.; Zhang, Y.; Jiang, L.; Yang, G.; Chen, J.; Li, P. A Dynamic Constitutive Model and Simulation of Braided CFRP under High-Speed Tensile Loading. Materials 2022, 15, 6389. https://doi.org/10.3390/ma15186389
Jin W, Zhang Y, Jiang L, Yang G, Chen J, Li P. A Dynamic Constitutive Model and Simulation of Braided CFRP under High-Speed Tensile Loading. Materials. 2022; 15(18):6389. https://doi.org/10.3390/ma15186389
Chicago/Turabian StyleJin, Wei, Yingchuan Zhang, Lanxin Jiang, Guangwu Yang, Jingsong Chen, and Penghang Li. 2022. "A Dynamic Constitutive Model and Simulation of Braided CFRP under High-Speed Tensile Loading" Materials 15, no. 18: 6389. https://doi.org/10.3390/ma15186389