An Improved Correlation for the Estimation of the Yield Strength from Small Punch Testing
Abstract
:1. Introduction
2. Modeling of the Small Punch Test
2.1. Finite Element Modeling
2.2. Analytical Equations for the Linear Elastic Phase of the SP Test
2.3. Systematic Variation of the Tensile Parameters and Specimen Thickness
3. Results
4. Discussion
5. Conclusions
- The analytical elastic slope agrees very well with the finite element simulation;
- A modified elastic–plastic transition force was proposed for the empirical yield strength correlation, which provides a significantly reduced uncertainty as compared to the elastic–plastic transition force defined in the European standard;
- With the new definition of (Equation (11)), the yield strength correlation is widely independent of the SP geometry and the flow properties of the material.
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Effective lower die radius | |
Total uniform strain (nominal strain at ) | |
Radius of the contact area between punch and specimen | |
Contact radius associated with the reference force | |
Coefficient of variation (standard deviation divided by average) | |
Diameter of lower die receiving hole | |
Elasticity modulus | |
Punch force | |
Elastic–plastic transition force | |
Reference force for the analytical calculation of the elastic slope | |
Modified elastic–plastic transition force | |
FE | Finite element |
Specimens thickness | |
Hardening exponent of the true stress–plastic strain curve | |
Plate stiffness | |
Puncher radius | |
Parameter of the true stress–plastic strain curve | |
Yield strength | |
Ultimate tensile strength | |
Elastic slope of the small punch plate (analytical calculation) | |
SP | Small punch |
UTS | Ultimate tensile strength |
Central deflection at the specimen bottom (opposite to punch tip) | |
Punch tip displacement | |
Indentation depth of the punch as calculated by Hertzian contact theory | |
YS | Yield strength |
Empirical factor for the estimation of yield stress | |
True strain | |
Nominal strain | |
Poisson’s ratio | |
True stress | |
Nominal stress | |
Elasticity limit, true initial flow stress |
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Punch Diameter d = 2r (mm) | Receiving Hole Diameter D (mm) | Specimen Thickness h (mm) | Edge Size (mm) | Edge Type |
---|---|---|---|---|
2.5 | 4.0 | 0.2 … 0.6 | 0.2 | Chamfer |
Code | |||||||
---|---|---|---|---|---|---|---|
3106 | 296.3 | 60.8 | 35.4 | 300 | 333 | 1.11 | 6 |
3306 | 285.3 | 135.1 | 59.2 | 300 | 400 | 1.33 | 6 |
3506 | 275.2 | 193.9 | 69.1 | 300 | 450 | 1.5 | 6 |
6106 | 592.2 | 121.2 | 27.5 | 600 | 667 | 1.11 | 6 |
6303 | 504.2 | 311.3 | 185.9 | 600 | 800 | 1.33 | 3 |
6306 | 569.0 | 270.0 | 62.6 | 600 | 800 | 1.33 | 6 |
6312 | 587.7 | 298.6 | 22.1 | 600 | 800 | 1.33 | 12 |
6506 | 547.5 | 388.8 | 73.4 | 600 | 900 | 1.5 | 6 |
9106 | 887.9 | 179.2 | 39.4 | 900 | 1000 | 1.11 | 6 |
9306 | 851.0 | 404.9 | 66.2 | 900 | 1200 | 1.33 | 6 |
9506 | 816.3 | 585.3 | 78.3 | 900 | 1350 | 1.5 | 6 |
Simulation ID | ||||
---|---|---|---|---|
3106-h5 | 81.9 | 196.4 | 0.916 | 0.382 |
3306-h2 | 13.3 | 24.8 | 0.900 | 0.484 |
3306-h4 | 55.8 | 124.7 | 0.860 | 0.385 |
3306-h5 | 85.5 | 202.5 | 0.877 | 0.370 |
3306-h6 | 120.1 | 301.0 | 0.899 | 0.359 |
3506-h5 | 88.5 | 209.6 | 0.848 | 0.358 |
6106-h5 | 164.2 | 370.6 | 0.914 | 0.405 |
6303-h5 | 178.8 | 401.8 | 0.839 | 0.373 |
6306-h2 | 25.9 | 42.3 | 0.927 | 0.567 |
6306-h4 | 111.4 | 232.7 | 0.862 | 0.413 |
6306-h5 | 174.7 | 392.8 | 0.859 | 0.382 |
6306-h6 | 244.5 | 586.7 | 0.884 | 0.368 |
6312-h5 | 167.4 | 381.1 | 0.896 | 0.394 |
6506-h5 | 179.5 | 407.1 | 0.836 | 0.368 |
9106-h5 | 250.6 | 539.6 | 0.898 | 0.417 |
9306-h2 | 38.5 | 55.4 | 0.935 | 0.650 |
9306-h4 | 168.4 | 335.8 | 0.855 | 0.429 |
9306-h5 | 264.0 | 563.3 | 0.852 | 0.399 |
9306-h6 | 369.2 | 850.2 | 0.878 | 0.381 |
9506-h5 | 269.9 | 578.5 | 0.834 | 0.389 |
Dataset | ||||
---|---|---|---|---|
All data | 0.41 | 0.88 | 17.4% | 3.7% |
Sets | 0.37 | 0.88 | 2.5% | 1.9% |
Sets | 0.39 | 0.87 | 4.4% | 3.8% |
Sets | 0.41 | 0.86 | 4.4% | 0.3% |
Sets | 0.57 | 0.92 | 12.0% | 1.1% |
Simulation ID | ||||
---|---|---|---|---|
6306-D175-h250 | 42.7 | 95.5 | 0.88 | 0.39 |
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Altstadt, E. An Improved Correlation for the Estimation of the Yield Strength from Small Punch Testing. Metals 2023, 13, 1716. https://doi.org/10.3390/met13101716
Altstadt E. An Improved Correlation for the Estimation of the Yield Strength from Small Punch Testing. Metals. 2023; 13(10):1716. https://doi.org/10.3390/met13101716
Chicago/Turabian StyleAltstadt, Eberhard. 2023. "An Improved Correlation for the Estimation of the Yield Strength from Small Punch Testing" Metals 13, no. 10: 1716. https://doi.org/10.3390/met13101716
APA StyleAltstadt, E. (2023). An Improved Correlation for the Estimation of the Yield Strength from Small Punch Testing. Metals, 13(10), 1716. https://doi.org/10.3390/met13101716