Parameters
| Symbol | Name | Unit |
|---|---|---|
| almen_intensity | almen_intensity | — |
| coverage_pct | coverage_pct | % |
| sigma_a_MPa | sigma_a_MPa | MPa |
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DIN 2093 Shot Peening Correction: Improvement of Fatigue Strength by Residual Compressive Stress
1. Shot Peening Mechanism
Shot peening uses high-speed projectiles to impact the surface of disc springs, inducing cold plastic deformation, thereby introducing residual compressive stress in the surface layer, while also refining surface grains and slightly increasing hardness.
For disc springs: - Point OM (upper surface inner edge): The working stress is compressive stress. The residual compressive stress introduced by shot peening acts in the same direction as the working stress, causing the absolute value of the mean compressive stress to increase (unfavorable for Goodman correction). - Point I (lower surface outer edge): The working stress is typically tensile stress. The residual compressive stress introduced by shot peening can offset part of the working tensile stress, significantly improving the fatigue strength at this point.
Since fatigue cracks in disc springs often originate in the tensile stress zone at point I (especially for thick-section disc springs), the improvement effect of shot peening on point I is far greater than its adverse effect on point OM. Overall, this can increase the fatigue limit stress amplitude by 20 % to 40 %.
The fatigue limit curves (Haigh diagrams) in the DIN 2093 standard typically provide allowable stress values after shot peening treatment directly. However, if it is necessary to estimate the shot peening effect from unpeened data, the following correction formula can be used.
2. Shot Peening Correction Factor $k_p$
For disc springs, the correction of the fatigue limit by shot peening can be expressed as:
Where: - $\sigma_{A,shot}$ — Fatigue limit stress amplitude of the disc spring after shot peening (MPa) - $\sigma_{A,unshot}$ — Fatigue limit stress amplitude of the unpeened disc spring (only heat treated, oxidized surface) (MPa) - $k_p$ — Shot peening strengthening factor, typically taken as 1.2 ~ 1.4, depending on shot peening intensity, coverage, material hardness, and stress ratio
Recommended values (based on DIN 2093 empirical data):
| Disc Spring Thickness $t$ | $k_p$ Reference Value | Description |
|---|---|---|
| $t \le 1.25\ \text{mm}$ | 1.3 – 1.4 | Thin disc springs, significant shot peening effect |
| $1.25 < t \le 3.0\ \text{mm}$ | 1.2 – 1.3 | Medium thickness disc springs |
| $t > 3.0\ \text{mm}$ | 1.15 – 1.25 | Thick disc springs, residual compressive stress layer is relatively shallow, effect slightly reduced |
Note: The above factors are for the pulsating compression ($R=0$) fatigue limit. If the working stress ratio differs, it should be considered in conjunction with mean stress correction in the Goodman diagram.
3. Shot Peening Correction Based on the Goodman Relationship
If the Goodman linear relationship is used for fatigue verification in the design, the effect of shot peening can be reflected by increasing the fully reversed fatigue limit $\sigma_{-1}$ or directly correcting the allowable stress amplitude.
Goodman formula for unpeened condition:
After shot peening, $\sigma_{-1}$ increases to:
Therefore, the allowable stress amplitude becomes:
Similarly, if using the DIN 2093 fatigue limit diagram directly, simply read the curve corresponding to the shot peened condition; no additional calculation is required.
4. Effect of Shot Peening on Mean Stress at Point OM (Caution Required)
The residual compressive stress introduced by shot peening will increase the absolute value of the actual mean stress at point OM, which has a weakening effect on the allowable stress amplitude according to the Goodman correction. However, the standard fatigue limit diagrams (e.g., the Haigh diagram in DIN 2093) already include this effect. That is, the curves on the diagram are the final result that combines the enhancement in the tensile stress zone and the slight disadvantage in the compressive stress zone due to shot peening. Therefore, designers can directly use the data from the DIN 2093 shot peening curves without needing to separately deduct the stress increment at point OM.
If deriving from unpeened data independently, it is recommended to: - Apply the shot peening correction only for the fatigue assessment of the tensile stress at point I. - For point OM, still use the unpeened stress values for static strength verification (since the increase in compressive stress is not beneficial for static strength).
5. Practical Application Recommendations
- Prioritize using DIN 2093 standard charts: The standard clearly distinguishes between shot peened and unpeened fatigue curves. Select based on the actual manufacturing state of the disc spring during design.
- When charts are unavailable: Use the $k_p$ factor to correct the fatigue limit and maintain a sufficient safety margin ($S_D \ge 1.3$).
- Verification requirements: For critical applications, require the supplier to provide shot peening process parameters (intensity, coverage, arc height) and corresponding fatigue test reports.
- Avoid excessive shot peening: Excessive shot peening can cause surface micro-cracks or excessive cold work hardening, which can instead reduce fatigue performance. Follow DIN 2093 or process specifications.
Summary: The shot peening correction, represented by the factor $k_p \approx 1.2 \sim 1.4$, reflects its improvement on the fatigue limit of disc springs. During design, priority should be given to consulting the DIN 2093 shot peening curves. If extrapolating from unpeened data, correctly distinguish between the different effects on the tensile stress point (beneficial) and the compressive stress point (slightly unfavorable). Shot peening is one of the most economical and effective measures to improve the high-cycle fatigue performance of disc springs.