DIN 6796 Temperature Derating: Effect of Operating Temperature on Flattening Force and Permissible Load

1. Nature of Temperature Effects

The material of DIN 6796 disc spring washers (typically spring steel such as C75S, 50CrV4) undergoes two significant changes at elevated temperatures:

• Decrease in elastic modulus $E$ → Reduced washer stiffness, lower force at the same compression, reduced flattening force $F_{flat}$.
• Decrease in yield strength $R_{p0.2}$ → Reduced permissible stress of the washer, lower maximum allowable load.

If room-temperature parameters are used directly for high-temperature connections, the washer may flatten due to insufficient load capacity or undergo excessive plastic deformation. Therefore, derating must be performed based on material properties at the operating temperature.

2. Effect of Temperature on Elastic Modulus and Yield Strength

2.1 Temperature Coefficient of Elastic Modulus

For most spring steels, within the range of 20°C to 300°C, the elastic modulus decreases approximately linearly with increasing temperature:

• $E_{20}$ — Elastic modulus at room temperature (20°C), ≈ 206 000 MPa
• $\alpha_E$ — Temperature coefficient of elastic modulus, for spring steel approximately $2.0\times10^{-4}\ \text{K}^{-1}$ (i.e., modulus decreases by about 2% per 100°C rise)
• $T$ — Operating temperature (°C)

2.2 Temperature Derating of Yield Strength

Yield strength decreases more significantly with increasing temperature, and thermal stability varies among materials. Reference data for common spring steel 50CrV4 (relative to room-temperature values):

For other materials (e.g., stainless steel, high-temperature alloys), consult their specific high-temperature strength data.

3. Temperature Derating Formula for Flattening Force

The theoretical flattening force is proportional to the elastic modulus:

Substituting the temperature coefficient of elastic modulus yields an approximately linear derating:

This formula is used directly to calculate the washer's flattening force at elevated temperatures. For example, at 150°C, the flattening force is approximately $1 - 2\times10^{-4} \times 130 \approx 0.974$ times the room-temperature value, i.e., a decrease of about 2.6%.

4. Temperature Derating of Maximum Permissible Load

The maximum permissible load of the washer is limited by the stress at the OM point, and the OM stress is approximately proportional to the load. At the same compression, stress is also proportional to the elastic modulus. However, the permissible stress itself is governed by the material's yield strength. Considering both factors, the permissible load should be derated according to the yield strength, while the effect of elastic modulus reduction on the force-stress relationship is approximately offset in low-cone-angle washers. Engineering practice adopts a simplification: the permissible load is directly derated by the yield strength ratio.

Alternatively, a more conservative approach uses elastic modulus derating, but since yield strength decreases more rapidly, yield strength derating is more critical.

Recommended dual verification:

• Calculate the high-temperature flattening force $F_{flat}(T)$, apply a safety factor $S_{flat} \ge 1.3$, obtaining permissible load $F_{zul}^{(1)} = F_{flat}(T)/S_{flat}$.
• Calculate permissible load based on high-temperature yield strength: $F_{zul}^{(2)} = F_{zul,20} \times \frac{R_{p0.2}(T)}{R_{p0.2,20}}$.
• Take the smaller value as the final permissible load $F_{zul}(T)$.

5. Temperature Correction of Bolt Preload

At elevated temperatures, not only does the washer capacity decrease, but the bolt's proof load also decreases with the reduction in yield strength. VDI 2230 requires using the high-temperature $R_{p0.2}$ to calculate the bolt's maximum allowable preload $F_{Mmax}$. Therefore, the design preload $F_{M,rec}$ at high temperatures should be derated accordingly.

Matching condition:

and the washer compression at minimum preload must still satisfy $s \ge 0.1h_0$.

6. Calculation Example

Room-temperature parameters (DIN 6796 washer for M10, 50CrV4): - $F_{flat,20} = 11\,000\ \text{N}$ - $F_{zul,20} = 11\,000/1.3 \approx 8\,460\ \text{N}$ (based on room-temperature yield strength $R_{p0.2,20}=1500\ \text{MPa}$) - Bolt maximum preload (grade 8.8 M10) original design $F_{Mmax} = 20\,000\ \text{N}$.

Operating condition: Operating temperature $T = 200°\text{C}$.

Material data: - Elastic modulus retention rate $1 - 2\times10^{-4} \times 180 = 0.964$ → $E(200°C) \approx 198\,600\ \text{MPa}$ - 50CrV4 $R_{p0.2}$ retention rate at 200°C ≈ 0.85 → $R_{p0.2}(200°C) \approx 1275\ \text{MPa}$

Washer derating: - Flattening force $F_{flat}(200°C) = 11\,000 \times 0.964 \approx 10\,600\ \text{N}$ - Permissible load (method 1) $F_{zul} = 10\,600 / 1.3 \approx 8\,154\ \text{N}$ - Permissible load (method 2) $F_{zul} = 8\,460 \times 0.85 \approx 7\,191\ \text{N}$

Taking the smaller value, $F_{zul}(200°C) \approx 7\,200\ \text{N}$.

The high-temperature proof load of the M10 grade 8.8 bolt at 200°C also requires corresponding derating but may still exceed 15 kN, which is greater than the washer's permissible load. Conclusion: At 200°C, the washer's permissible load drops to approximately 7.2 kN, unable to withstand the original 20 kN preload. The bolt preload must be reduced, or a washer with higher load capacity (e.g., L-type or multi-disc stack) must be used.

7. Design Recommendations

1. Obtain accurate material data: Acquire $E$ and $R_{p0.2}$ values at the operating temperature from the washer supplier or material standards.
2. Verify both flattening force and yield strength: Use the most conservative permissible load.
3. Consider differential thermal expansion: Preload changes due to thermal effects may superimpose on washer derating; handle comprehensively in VDI 2230 calculations.
4. Multiple tightening and relaxation: Oxide scale embedding at high temperatures may exacerbate settlement; appropriately reduce preload or schedule periodic retightening.
5. Alternative materials: For temperatures exceeding 250°C, consider heat-resistant alloy washers (e.g., Inconel X-750), but note that their elastic modulus and yield strength also vary with temperature.

Summary:
At elevated temperatures, the flattening force and permissible load of DIN 6796 washers must be derated according to the actual reduction in elastic modulus and yield strength. The core formulas are $F_{flat}(T)=F_{flat,20}\cdot E(T)/E_{20}$, and $F_{zul}(T)$ is taken as the smaller value from modulus correction and strength correction. Neglecting temperature derating will lead to washer overload failure.