DIN 6796 Settlement Estimation: Washer Creep + Surface Embedding + Thermal Expansion

1. Definition and Consequences of Settlement

During service of bolted connections, due to micro-plastic deformation, creep, and thermal effects, the effective axial length of the clamping system gradually shortens. This total shortening is called settlement $f_{total}$ (mm). It leads to a reduction in preload, potentially causing joint failure.

DIN 6796 disc spring washers, due to their spring characteristics, can compensate for part of the settlement, but the total settlement must still be estimated during design to assess whether the preload loss is within acceptable limits.

2. Components of Settlement

The total settlement is the superposition of the following three terms (the direction of preload loss is taken as positive):

• $f_Z$ — Surface embedding settlement (VDI 2230 conventional loss)
• $f_{creep}$ — Thickness reduction due to washer material creep
• $f_{th}$ — Equivalent axial displacement difference due to thermal expansion (taking the case that reduces preload)

3. Surface Embedding Settlement $f_Z$

VDI 2230 R4 provides the embedding amount (μm) for each contact pair, depending on surface roughness and treatment. The embedding surfaces in a connection include:

• Bolt head/nut and washer top surface
• Washer bottom surface and clamped part
• Interface between clamped parts
• Thread pair

Reference embedding amounts per surface:

where $n$ is the number of contact surfaces. For example, the washer has top and bottom surfaces, plus the thread pair, totaling at least 3 surfaces. For design, take the maximum possible value for each surface for a conservative estimate.

4. Washer Creep Settlement $f_{creep}$

Under sustained high stress (especially at elevated temperatures), DIN 6796 washer material (spring steel) undergoes minor creep deformation, leading to a reduction in free height. The creep amount depends on:

• Washer stress level (equivalent stress at OM point)
• Operating temperature $T$
• Load duration

Due to the lack of a general analytical formula, the following methods can be used for estimation in engineering:

4.1 High-Temperature Creep Data Method

For common spring steels (e.g., 50CrV4), manufacturers or material handbooks provide creep curves at specific temperatures and stresses. This is generally expressed as:

Multiplying the creep strain by the washer thickness $t$ gives the creep thinning amount:

Typical Reference: For 50CrV4 at 150°C and stress 1000 MPa, creep after 1000 hours is < 0.1% → $f_{creep} \approx 0.001 \times 1.5\text{ mm} = 1.5\text{ μm}$, usually negligible. However, when temperature > 200°C or stress is very high, a dedicated evaluation is required.

4.2 Simple Conservative Estimate

If detailed data is unavailable, for standard steel washers take:

For high temperature (> 200°C) or high stress, conservatively take $f_{creep} \approx 5 \sim 10$ μm, and verify with sample testing.

5. Equivalent Displacement from Thermal Expansion $f_{th}$

If the bolt and clamped parts have different coefficients of thermal expansion, a temperature change produces an expansion difference, altering the effective clamping length and thus the preload. The equivalent axial shortening that reduces preload is:

Where: - $\alpha_P, \alpha_S$ — Coefficients of thermal expansion of clamped parts and bolt (1/°C or 1/K) - $l_P, l_S$ — Respective effective thermal expansion lengths (mm), approximately equal to the clamping length $l_K$ - $\Delta T = T_{work} - T_{assembly}$ — Temperature change (positive for heating)

Only when this value is positive (clamped parts expand more than the bolt) does it cause preload loss, and it is included in $f_{th}$. If negative (bolt expands more), preload increases, and this is not counted as settlement loss, but the increased preload must be considered in strength checks.

Example: Aluminum clamped parts ($\alpha_P=23\times10^{-6}$/K), steel bolt ($\alpha_S=12\times10^{-6}$/K), $l_K=50$ mm, temperature rise 100°C:

6. Preload Loss Due to Total Settlement

The total settlement $f_{total}$ is converted into preload loss via the system stiffness:

• $\delta_S$ — Bolt compliance (mm/N)
• $\delta_P$ — Clamped part compliance (mm/N)
• $\delta_W$ — DIN 6796 washer compliance (mm/N), $\delta_W = 1/k_W$

Since the washer compliance is usually much larger than that of the bolt and clamped parts, the denominator is significantly increased. Therefore, for the same settlement amount, the preload loss with an elastic washer is much smaller than in a rigid connection. This is the core mechanism by which DIN 6796 compensates for settlement.

7. Calculation Procedure

1. Determine all contact surfaces in the connection and sum them to obtain $f_Z$.
2. Evaluate washer creep $f_{creep}$ (neglect at room temperature, look up data for high temperature).
3. Calculate the thermal expansion equivalent displacement $f_{th}$ (take positive loss value).
4. Calculate system compliances $\delta_S, \delta_P, \delta_W$.
5. Obtain preload loss $F_Z$, then update the minimum residual preload $F_{Mmin} = F_{Kerf} + (1-\Phi^*)F_A + F_Z$.

8. Example

Conditions: M10 bolt, grade 8.8, clamping length 40 mm.
Clamped parts: Steel, three contact surfaces, each with 4 μm embedding → $f_Z = 12$ μm.
Washer: DIN 6796, operating temperature 120°C, creep neglected.
Thermal expansion: Steel-steel, $\alpha$ similar, temperature difference 80°C → $f_{th} \approx 0$.

Total settlement $f_{total} = 12$ μm = 0.012 mm.

Compliances:
- Bolt $\delta_S \approx 1.0 \times 10^{-6}$ mm/N
- Clamped parts $\delta_P \approx 0.8 \times 10^{-6}$ mm/N
- Washer $\delta_W = 1/12\,000 \approx 8.3 \times 10^{-5}$ mm/N

Total compliance $\approx (0.000001 + 0.0000008 + 0.000083) = 8.48 \times 10^{-5}$ mm/N.

Preload loss:

Relative to a preload of 20 kN, the loss is only 0.7%, demonstrating that the elastic washer excellently compensates for embedding settlement.

Summary:
When estimating the settlement of a DIN 6796 washer connection, embedding, creep, and thermal expansion must be considered. Due to the high compliance of the washer, the preload loss caused by the total settlement is greatly reduced. Accurately calculating each component and checking the residual preload is key to ensuring long-term joint reliability.