Unloading Model of Elastic–Plastic Half-Space Contacted by an Elastic Spherical Indenter
Abstract
:1. Introduction
2. Analysis Method
2.1. Hertzian Theory and Critical Indentation
2.2. Unloading Analysis
3. Validations
3.1. Finite Element Model
3.2. Hertzian Unloading
3.3. Residual Indentation
3.4. Residual Curvature Radius
3.5. Unloading Model
3.6. Comparisons with Existing Unloading Models
4. Applications
4.1. Contact Model
4.2. Impact Simulations
4.3. Nanoindentation Test
5. Conclusions
- A new unloading contact model of an elastic–perfectly plastic half-space indented by an elastic spherical sphere is presented analytically. The model can accurately predict the residual indentation and residual curvature radius after fully unloading.
- The assumptions and the unloading model have been demonstrated by numerical simulations. The proposed unloading can cover a wide range of indentations and material properties and is compared with existing unloading models.
- Combining the present unloading law with the existing contact loading model, cyclical behavior including loading and unloading can be predicted. The combined model has been verified by static FE simulations, low-velocity impact simulations and nanoindentation tests.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Case | (GPa) | (GPa) | (MPa) | |
---|---|---|---|---|
1 | 210 | 52 | 50 | 4 |
2 | 210 | 104 | 120 | 2 |
3 | 210 | 208 | 345 | 1 |
4 | 52.5 | 208 | 550 | 0.25 |
5 | 210 | 210,000 | 345 | 0.001 |
Case | -Fitting | -Equation (25) | Error (%) |
---|---|---|---|
1 | 36.68 | 36.57 | −0.30 |
2 | 37.53 | 37.26 | −0.72 |
3 | 39.28 | 39.20 | −0.20 |
4 | 41.12 | 40.55 | −1.39 |
5 | 36.37 | 36.28 | −0.25 |
Materials | Elastic Modulus (GPa) | (MPa) |
---|---|---|
1 | 100 ± 12 | 510 ± 23 |
2 | 77 ± 10 | 630 ± 22 |
3 | 58 ± 8 | 513 ± 19 |
4 | 70 ± 7 | 480 ± 4 |
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Xie, W.; Guo, Y.; Ding, H.; Yin, X.; Weng, P. Unloading Model of Elastic–Plastic Half-Space Contacted by an Elastic Spherical Indenter. Materials 2024, 17, 3018. https://doi.org/10.3390/ma17123018
Xie W, Guo Y, Ding H, Yin X, Weng P. Unloading Model of Elastic–Plastic Half-Space Contacted by an Elastic Spherical Indenter. Materials. 2024; 17(12):3018. https://doi.org/10.3390/ma17123018
Chicago/Turabian StyleXie, Wenhao, Yuanyuan Guo, Huaiping Ding, Xiaochun Yin, and Panpan Weng. 2024. "Unloading Model of Elastic–Plastic Half-Space Contacted by an Elastic Spherical Indenter" Materials 17, no. 12: 3018. https://doi.org/10.3390/ma17123018
APA StyleXie, W., Guo, Y., Ding, H., Yin, X., & Weng, P. (2024). Unloading Model of Elastic–Plastic Half-Space Contacted by an Elastic Spherical Indenter. Materials, 17(12), 3018. https://doi.org/10.3390/ma17123018