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Inspectioneering Journal

FFS Forum: Miner’s Rule – A Primer on Linear Damage Accumulation

By Greg Garic, P.E., Senior Staff Consultant at Stress Engineering Services, Inc. This article appears in the November/December 2023 issue of Inspectioneering Journal.
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What’s the Point?

A basic S-N curve will fully define the fatigue life so long as all the load cycles are the same. For example, Figure 1 shows that for an alternating stress of 30-ksi, in this particular material, the fatigue life would be expected to be about 40,000 cycles.

If life were only so simple.

Figure 1. ASME Design Fatigue Curve for Carbon and Low Alloy Steels  [From: ASME B&PV Code, Section VIII, Division 2, Article 5.1, Figure 5-110.1 (2004)]
Figure 1. ASME Design Fatigue Curve for Carbon and Low Alloy Steels [From: ASME B&PV Code, Section VIII, Division 2, Article 5.1, Figure 5-110.1 (2004)]

In reality, the load is often not represented by a single value, but rather by a load spectrum. Perhaps the load is 30-ksi for 10,000 cycles, then 20-ksi for 10,000 cycles, etc. Or what if it is random, with a different stress value on every cycle? These more complicated scenarios happen to be more representative of many practical engineering problems.

We need a method to calculate the fatigue life in the presence of variable loads. Thus, we begin our discussion of Miner’s Rule, or more generally, damage accumulation modeling.

Where It All Began

As is often the case, Miner’s Rule didn’t start with Miner.

In 1907, SKF was founded as a bearing company. Arvid Palmgren joined the company as an engineer in 1917. SKF’s historical account indicates that Palmgren started out writing technical manuals, but he felt he didn’t have the technical detail he needed, so he began doing experiments and developing his own bearing theory. In 1924, Palmgren published “The Service Life of Ball Bearings” – probably the first theory on roller bearing life. It would become the standard for the bearing industry. Palmgren won a gold medal from the Royal Swedish Academy of Engineering Sciences (IVA) for his work. (The IVA is still around today: www.iva.se/en.)

Palmgren’s work included a damage accumulation model, but his work was specifically limited to bearings and didn’t become widely known in the broader metal fatigue world until it was picked up by Miner in the 1940s. Milton Miner’s 1945 publication of “Cumulative Damage in Fatigue” in the Journal of Applied Mechanics launched the method into popular usage.

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