DIN 6796 Elastic Modulus‑Temperature Curve

1. Mechanism of Temperature Effect on Elastic Modulus

The materials commonly used for DIN 6796 disc spring washers are quenched and tempered spring steels (e.g., C75S, 50CrV4, etc.). The elastic modulus $E$ of such materials originates from interatomic bonding forces. As temperature rises, atomic thermal vibrations intensify, reducing bonding stiffness and causing the $E$ value to decrease in a nearly linear manner.

Accurately understanding the variation of $E$ with temperature is fundamental for calculating the washer's flattening force, stiffness, stress, and for performing preload matching at elevated temperatures.

2. Elastic Modulus‑Temperature Formula for Spring Steel

Within the common bolted joint operating temperature range of $-40°C \sim 300°C$, the elastic modulus of spring steel can be described by the following formula:

Where: - $E(T)$ — Elastic modulus at temperature $T$ (°C) (MPa) - $E_{20} = 206\,000\ \text{MPa}$ — Standard elastic modulus at room temperature (20°C) - $\beta \approx 2.0 \times 10^{-4}\ \text{K}^{-1}$ — Temperature coefficient of elastic modulus (relative decrease per 1°C increase) - $T$ — Washer operating temperature (°C)

This coefficient is derived from DIN 2093 (disc springs) and general spring steel data, and is widely adopted in engineering practice.

3. Elastic Modulus‑Temperature Data Table

Based on the above formula, reference values of elastic modulus at common temperature points can be generated:

Note: The ratio can be directly calculated using $1 - \beta (T-20)$.

If the operating temperature exceeds 300°C, in addition to the continued decrease in elastic modulus, the material may undergo temper softening, leading to a sharp reduction in strength. The use of ordinary spring steel washers is generally no longer recommended.

4. Application in Washer Design

4.1 Temperature Correction of Flattening Force

The washer flattening force $F_{flat}$ is proportional to the elastic modulus, therefore:

Example: Room temperature flattening force $F_{flat,20} = 11\,000\ \text{N}$, at 150°C:

4.2 Temperature Correction of Stiffness

The washer tangent stiffness $k$ is also proportional to the elastic modulus:

The compliance $\delta_W(T) = 1/k(T)$ increases correspondingly. The compliance at the operating temperature must be used when calculating preload loss.

4.3 Temperature Correction of Stress

At the same compression, the stress at various points on the washer (e.g., the OM point) is also proportional to the elastic modulus. However, design is typically limited by the reduced allowable stress (determined by the high-temperature yield strength), rather than relying solely on the elastic modulus correction.

5. Temperature Characteristics of Other Washer Materials

If the DIN 6796 washer is made of stainless steel (e.g., 1.4310), its elastic modulus vs. temperature relationship differs from that of spring steel, and its absolute value is lower (room temperature $E \approx 190\,000\ \text{MPa}$). The corresponding $\beta$ value and room temperature $E$ for the specific material should be used in design.

When selecting non-standard materials, it is essential to obtain high-temperature elastic modulus data from the supplier.

6. Engineering Design Recommendations

• Always use $E(T)$ at the operating temperature for force, stiffness, and stress calculations to avoid errors from using room temperature parameters.
• When the temperature exceeds 150°C, although the elastic modulus decrease is only 2.6%, the yield strength derating is larger (approximately 5% to 10%). Both factors must be considered together to determine the allowable load.
• Experimental Verification: For critical high-temperature applications, perform high-temperature measurements of the washer's force‑deflection characteristics to confirm the calculations.
• Cyclic Temperature: If the joint experiences wide temperature cycles, the washer characteristics must be verified at both the maximum and minimum temperatures to ensure requirements are met across the entire temperature range.

Summary:
The elastic modulus of DIN 6796 washers decreases linearly with temperature and can be accurately described by $E(T) = E_{20}[1 - 2.0\times10^{-4}(T-20)]$. This curve is fundamental for calculating flattening force, stiffness, and stress at elevated temperatures. Together with the derating of the material's yield strength, it determines the safe operating range of the washer under high-temperature conditions.