Prediction of Fatigue Limit of Spring Steel Considering Surface Defect Size and Stress Ratio
Abstract
:1. Introduction
2. Equations for Predicting Fatigue Limit
3. Experimental Method
3.1. Material Used
3.2. Surface Hardness and Roughness
3.3. Fatigue Test
3.4. Observations of Fracture Surface
4. Results and Discussion
4.1. Result of Surface Hardness and Roughness
4.2. Fatigue Test Results
4.3. Effect of Stress Ratio on Fatigue Limit and
4.4. Observations of Fracture Surface
5. Prediction of Fatigue Limit
6. Conclusions
- (1)
- As the stress ratio increased from −1 to 0.4, the fatigue limit decreased under all slit conditions due to mean stress. The rate of decrease in the fatigue limit owing to the defects decreased as the stress ratio was increased.
- (2)
- Based on the test results for the smooth specimen and the 400-µm slit specimen, the stress-ratio dependence of the fatigue limit of the smooth specimen, , and the threshold-stress-intensity factor range, , of the investigated spring steel could be determined.
- (3)
- The results of the fatigue tests showed that the fatigue limit decreased as the defect size was increased, irrespective of the stress ratio. In the case of the 30 µm slit specimen, the fatigue limit did not decrease from only at R = 0.4. Thus, we found that the dimensions of the surface defects that did not result in a decrease in the fatigue limit were dependent on the stress ratio.
- (4)
- The modified El-Haddad’s equation, i.e., Equation (8), yielded values close to the experimental data for a wide range of values and stress ratios. Murakami’s equation, that is, Equation (4), yielded values close to the experimental data between and , but above it yielded non-conservative values with respect to the experimental results. Smith’s equation, that is, Equation (6), yielded highly non-conservative values near . Thus, the usefulness of the modified El-Haddad’s equation was clarified for a wide range of defect dimensions and stress ratios.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
stress range (twice stress amplitude) | |
fatigue limit | |
fatigue limit of smooth specimen | |
mean stress | |
ultimate tensile strength | |
0.2% offset yield strength | |
maximum stress intensity factor | |
threshold stress intensity factor range for long crack | |
shape factor | |
defect size | |
intrinsic defect size | |
square root of the area projected in the direction of principal stress | |
of critical defects which decrease the fatigue limit | |
of the transition defect between small and large defects | |
of intrinsic defect | |
HV | Vickers hardness |
stress ratio | |
material constant | |
a/c | aspect ratio |
arithmetic mean roughness | |
maximum height of roughness |
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C | Si | Mn | P | S | Cu | Ni | Cr | Fe |
---|---|---|---|---|---|---|---|---|
0.57 | 0.25 | 0.86 | 0.022 | 0.019 | 0.2 | 0.11 | 0.82 | Bal. |
−1 | 30 | 1080 | 1280 | 0.84 |
60 | 840 | 0.66 | ||
400 | 400 | 0.31 | ||
0 | 30 | 760 | 880 | 0.86 |
60 | 640 | 0.73 | ||
400 | 280 | 0.32 | ||
0.2 | 30 | 760 | 800 | 0.95 |
60 | 600 | 0.75 | ||
400 | 260 | 0.33 | ||
0.4 | 30 | 680 | 680 | 1.00 |
60 | 560 | 0.82 | ||
400 | 240 | 0.35 |
R (−) | ||
---|---|---|
−1 | 1280 | 10.61 |
0 | 880 | 7.57 |
0.2 | 800 | 6.79 |
0.4 | 680 | 5.90 |
R (−) | |||
---|---|---|---|
−1 | 5.25 | 51.7 | 163 |
0 | 6.55 | 55.7 | 163 |
0.2 | 6.05 | 54.2 | 163 |
0.4 | 6.91 | 56.7 | 163 |
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Ishii, T.; Takahashi, K. Prediction of Fatigue Limit of Spring Steel Considering Surface Defect Size and Stress Ratio. Metals 2021, 11, 483. https://doi.org/10.3390/met11030483
Ishii T, Takahashi K. Prediction of Fatigue Limit of Spring Steel Considering Surface Defect Size and Stress Ratio. Metals. 2021; 11(3):483. https://doi.org/10.3390/met11030483
Chicago/Turabian StyleIshii, Takehiro, and Koji Takahashi. 2021. "Prediction of Fatigue Limit of Spring Steel Considering Surface Defect Size and Stress Ratio" Metals 11, no. 3: 483. https://doi.org/10.3390/met11030483