Miner's Rule (Cumulative Damage Rule)
Miner's Rule (Cumulative Damage Rule): Theoretical Foundations
What is Miner's Rule?
Professor, please teach me about Miner's Rule (the cumulative damage rule).
Palmgren-Miner's Rule (1945) evaluates cumulative fatigue damage under variable loading. Failure occurs when the sum of the damage ratios at each stress level reaches 1:
$n_i$ is the actual number of cycles at stress level $i$, $N_i$ is the S-N life at that stress level. Failure at $D = 1$.
It's just summing up the "consumption rate" for each level. So simple.
It's simple but has the problem of ignoring the load sequence effect. Life changes depending on whether the order is high stress → low stress or the reverse, but Miner's Rule does not capture this effect. Still, it's the standard in practice.
Summary
The "Mysterious 1.0" of Miner's Rule
The linear cumulative damage rule (Miner's rule) predicts failure when the damage sum reaches 1.0, but actual failure scatters between 0.3 and 3.0. This was a limitation Miner himself acknowledged when he published it in 1945. The main cause is the sequence effect: damage accumulates faster when large amplitude loads are applied first, and slower when the order is small → large.
Computational Methods for Miner's Rule (Cumulative Damage Rule)
Miner's Rule in FEM
1. FEM stress → Rainflow method for cycle extraction → S-N life $N_i$ for each $\Delta\sigma_i$ → $D = \sum n_i/N_i$
Automatically calculated in all fatigue software (nCode, fe-safe, FEMFAT).
Summary
The Key is Combination with the Rainflow Method
To use Miner's rule in practice, cycles are extracted from irregular load time histories using the rainflow method, the life Ni on the S-N curve for each amplitude is read, and the damage Σ(ni/Ni) is calculated. Since the 1990s, automotive manufacturers have developed in-house software to automatically process measurement data, enabling fatigue damage evaluation of 1 minute of actual driving data within 5 minutes.
Miner's Rule (Cumulative Damage Rule) in Practice
Miner's Rule in Practice
Used in all variable amplitude fatigue.
Practical Checklist
Example: Fatigue Life Evaluation of a Truck Axle
In actual truck axle design, the standard load spectrum from Japanese Industrial Standard JASO M 305 is combined with Miner's rule. For a 10-ton capacity vehicle, 10,000 km of driving corresponds to about 5 million cycles. Using load ratios of 3:5:2 for empty, fully loaded, and bump crossing, a design equivalent to a 1 million km life is possible.
Miner's Rule (Cumulative Damage Rule): Software & Solver Comparison
Tools
Differences in Miner's Rule Implementation Among Solver Vendors
In ABAQUS, ANSYS, and MSC Nastran, the default critical value for the linear cumulative damage rule (Miner's rule) is D=1.0, which is common. However, Simulia fe-safe recommends D=0.5 as the default, adopting a conservative setting aligned with the aerospace AS9100 standard. In practice, even with the same FE model, the allowable number of cycles can vary by a factor of 2 depending on solver choice.
Advanced Technology
Advanced Topics in Miner's Rule
Related Topics
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