DIN 6796 Washer Fatigue Life Estimation

1. Background of Washer Fatigue Issues

The primary function of DIN 6796 disc spring washers is to provide axial elastic force in bolted connections, compensating for preload relaxation caused by embedding, thermal expansion, etc. They are generally considered static elastic elements designed for static loading. However, under the following operating conditions, washers may be subjected to alternating loads, posing a risk of fatigue failure:

• Bolted connections experience periodic external loads, causing pulsating changes in washer compression $s$.
• Equipment maintenance requires repeated tightening/loosening (repeated assembly and disassembly), leading to cyclic stress variations in the washer.
• In vibration environments, the washer participates in the system's elastic vibration, generating stress cycles.

For low-cone-angle ($h_0/t \le 0.9$) DIN 6796 washers, fatigue strength is relatively good, but evaluation is still necessary, especially when the working stress amplitude is large.

2. Stress Basis for Fatigue Analysis — OM Point

Fatigue cracks in disc washers typically originate at the OM point on the inner edge of the upper surface (high compressive stress zone) or the uM point on the inner edge of the lower surface (if tensile stress occurs). Since the uM point in DIN 6796 washers is mostly under compressive stress, the core of fatigue evaluation lies in the compressive stress pulsation at the OM point.

The stress at the OM point is calculated using the Almen‑Laszlo formula:

where:

Under alternating loads, the washer compression varies between $s_{min}$ and $s_{max}$, and the corresponding OM stress pulsates between $\sigma_{OM,min}$ and $\sigma_{OM,max}$ (both compressive, expressed in absolute values).

3. Fatigue Safety Factor and Allowable Stress Amplitude

Since fatigue data for washer materials (spring steel) are typically characterized by stress amplitude $\sigma_a$, under pulsating cycles:

($\sigma_m$ is the mean stress, expressed in absolute values when both are compressive)

The allowable stress amplitude can be determined using a Haigh diagram (Goodman correction). For quenched and tempered spring steel (e.g., 50CrV4), the material's rotating bending fatigue limit $\sigma_{bW} \approx 600 \sim 700$ MPa. Taking a safety factor $S_D = 1.5$ and considering factors such as size, notch effects, and surface quality, the allowable stress amplitude can be estimated as:

Since the OM point is under compressive stress, which is generally beneficial for fatigue life, the limit can be relaxed. In engineering practice, a simplified fatigue limit stress amplitude is often used:

Alternatively, the fatigue strength diagram from the disc spring standard (DIN 2093) can be directly applied. For low-cone-angle washers, the allowable stress amplitude is approximately 200 ~ 400 MPa.

4. Life Estimation Formula (Stress‑Life Method)

If the stress amplitude exceeds the fatigue limit, the washer enters the finite life region, and the number of cycles can be estimated using the Basquin equation:

where: - $N_f$ — number of cycles to failure - $\sigma_f'$ — fatigue strength coefficient (≈ $1.5 R_m$) - $b$ — fatigue strength exponent (typically $-0.05 \sim -0.12$ for steel)

Solving for life:

Engineering simplification: When $\sigma_a \le \sigma_{a,zul}$ (e.g., 200 MPa), it can be considered infinite life (> 2×10⁶ cycles). If $\sigma_a$ exceeds this value, the above formula should be used for estimation, or the number of cycles should be directly limited.

5. Calculation Example

Conditions:
DIN 6796 washer for M10 (parameters as before), bolt preload fluctuation causes compression to vary between $s_{min}=0.3$ mm ($\delta=0.2$) and $s_{max}=0.6$ mm ($\delta=0.4$).
From previous example data: - $|\sigma_{OM}(s=0.3)| = 1620$ MPa - $|\sigma_{OM}(s=0.6)| = 2774$ MPa

Then:

Using material 50CrV4, $R_m \approx 1800$ MPa, $\sigma_{bW} \approx 650$ MPa.
Goodman allowable stress amplitude:

Thus, $\sigma_a = 577$ MPa far exceeds the allowable value, indicating that under this pulsation amplitude, the washer will experience finite-life fatigue.

For safe operation, the pulsation amplitude should be reduced (narrowing the preload fluctuation) or the washer should be used only under static loading (i.e., $s$ nearly constant), which aligns with the "static load design" philosophy of DIN 6796 washers.

6. Design Guidelines and Conclusions

• DIN 6796 washers are designed for static elastic compensation and should not be used as cyclic springs under repeated large load variations.
• If stress fluctuations are unavoidable, the OM stress amplitude must be controlled to $\sigma_a \le 200 \sim 300$ MPa to ensure high-cycle fatigue life.
• When preload changes frequently (e.g., rapid repeated tightening/loosening), consider switching to dedicated disc springs (DIN 2093), whose fatigue characteristics are well-validated.
• Fatigue performance can be improved by reducing the working cone height ratio $\eta$, lowering the maximum compression, or using a higher fatigue-grade material.

Summary:
Although it is theoretically possible to estimate the fatigue life of DIN 6796 washers using the Basquin equation and Goodman diagram, their application range is narrow. In standard applications, DIN 6796 washers should be treated as static elastic elements. Fatigue life verification is only performed under special circumstances, and cyclic loading leading to high stress amplitudes should be avoided whenever possible.