Creep Rupture Life (Larson-Miller)
Creep Rupture Life (Larson-Miller)
Formula Expression
Parameters
| Symbol | Name | Unit |
|---|---|---|
| stress_MPa | stress_MPa | MPa |
| temp_C | temp_C | °C |
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Larson-Miller Parameter Method: Extrapolation of Creep Rupture Life
At high temperatures, creep-induced fracture is one of the primary failure modes for disc springs. The Larson-Miller parameter (LMP) is a time-temperature equivalence parameter that integrates the creep rupture life $t_r$ and operating temperature $T$ into a single parameter $P$, widely used to extrapolate short-term high-temperature accelerated test results to service life under long-term operating temperatures.
1. Core Formula
The basic expression of the Larson-Miller parameter is:
Where: - $P$: Larson-Miller parameter, approximately constant for a given material and stress level. - $T$: Absolute temperature (K), $T = \theta + 273.15$, where $\theta$ is temperature in Celsius. - $t_r$: Creep rupture life (h). - $C$: Material constant. For most metallic materials, $C \approx 20$. The accurate $C$ value should be obtained by fitting test data from at least two temperatures.
The core principle of this formula is that "under the same stress level, $P$ is approximately constant". This means that by conducting short-term creep tests at higher temperatures, the $P$ value can be calculated, and then the rupture life at the operating temperature can be derived.
2. Life Extrapolation Formula
From the Larson-Miller formula, the creep rupture life $t_r$ can be directly solved:
This formula is the cornerstone for predicting the life of high-temperature components in engineering. Its application logic is: 1. Obtain material data: Acquire the Larson-Miller master curve (i.e., the relationship diagram or table of $\sigma$ vs. $P$) for the target material at a specific stress level from material handbooks or suppliers. 2. Calculate the operating $P$ value: Based on the disc spring's operating stress $\sigma$, find the corresponding $P$ value from the master curve. 3. Extrapolate life: Substitute the operating temperature $T$ and the obtained $P$ value into the above formula to calculate the expected rupture life $t_r$.
3. Significance and Calibration of Material Constant $C$
The $C$ value represents the kinetic characteristics of material fracture at high temperatures. Although $C \approx 20$ is a good general initial value for many metals, calibration is necessary for precise design.
Calibration Method: For the same material under the same stress level, conduct creep rupture tests at least two different temperatures ($T_1, T_2$) to obtain the corresponding rupture lives $t_{r1}, t_{r2}$. Since $P$ is constant:
Solve for $C$:
4. Typical Material Larson-Miller Parameter Characteristics
The creep resistance of different materials is reflected by the position of the curve on the LMP plot. A larger $P$ value (or higher stress at the same $P$ value) indicates stronger creep resistance of the material.
| Material | Stress $\sigma$ Range (MPa) | $P$ Typical Range | Characteristics |
|---|---|---|---|
| 51CrV4 | 200 – 500 | 15,000 – 18,000 | Suitable only for low temperatures, low $P$ value |
| H13 | 300 – 800 | 18,000 – 22,000 | Excellent medium-temperature performance |
| Inconel 718 | 400 – 1000 | 24,000 – 28,000 | Extremely high $P$ value, superior long-term life at high temperatures |
Note: The $P$ value range is significantly affected by stress and material condition; refer to the ASME or material supplier's LMP diagram for specifics.
5. Calculation Example
Given: H13 disc spring, operating stress $\sigma = 400\ \text{MPa}$, operating temperature $T_{work} = 500^\circ C \ (773\ \text{K})$. Assume that by consulting the material's LMP master curve, $P = 21,500$ at this stress. Material constant $C = 20$.
Calculate expected rupture life:
This result indicates that, theoretically, the H13 disc spring has an extremely long creep life at 500°C under this stress level. In practical use, factors such as oxidation, fatigue, and creep-fatigue interaction must be considered, which can reduce life.
Accelerated test verification: If an accelerated test is conducted at 600°C (873 K) and the specimen fractures after 3,000 hours, then:
This $P$ value is more realistic. Then, back-calculate the life at 500°C:
The life expectancy is significantly shortened but still considerable. This shows that the accurate $P$ value must rely on testing; the initial assumption of $P = 21,500$ may be overly optimistic.
6. Application in Disc Spring Design
- Setting allowable stress: In high-temperature design, the allowable stress $\sigma_{allow}$ is often determined not by yield strength or fatigue, but by the 10,000-hour or 100,000-hour creep rupture strength. Using the LMP method, the allowable stress corresponding to the design life can be precisely calculated.
- Safety factor: Creep data exhibits significant scatter. In design, a safety factor for rupture life of $S_{creep} \ge 3 \sim 5$ is typically applied.
- Combined assessment: For disc springs under fixed displacement, creep leads to stress relaxation rather than fracture. In this case, the LMP parameter can be used for conservative estimation, but a more accurate analysis requires combining the Norton-Bailey relaxation equation.
Summary: The Larson-Miller parameter $P = T(C + \log t_r)$ serves as a bridge connecting temperature and creep rupture life. By leveraging its property of being constant under the same stress, it conveniently allows extrapolation of high-temperature accelerated test results to operating temperatures, making it a key tool for life assessment of high-temperature disc springs.