Fatigue life and fatigue damage

The concepts of fatigue life and fatigue damage are common to both approaches to fatigue analysis. Fatigue life is often specified in terms of blocks of events or cycles to failure of a structure or specimen. In metal fatigue analysis, each individual block (or cycle) of the same amplitude is usually assumed to contribute equally to the fatigue damage that occurs in the structure.

For example, a constant amplitude fatigue test may last for 110,000 cycles before the specimen initiates a small crack. At that point, 100 percent of the crack initiation life has been used in the specimen, or the damage is equal to one. If each cycle contributes equally to damaging the specimen, then each cycle causes a damage of

Equation 1

The term Di is called the damage fraction of the cycle and Nfailure is the number of cycles to failure. Since each cycle was assumed to be equally damaging, the damage fraction for each cycle is the same. If all of the damage fractions are added, then

Equation 2

This linear addition of damage is called Palmgren-Miner's linear cumulative damage rule, or simply linear Miner’s rule. The right-hand side of Equation 2, here 1.0, is called the limit damage sum.

Some researchers have proposed other damage accumulation rules, including non-linear damage accumulation rules, in which cycles near the beginning of the loading history are weighted to have more or less of an effect on damage than cycles at the end of the loading history. Although these damage rules have been successful for certain laboratory situations, linear Miner’s rule has been demonstrated to be quite successful for a variety of loading situations and structures.

Damage fractions for cycles at different load levels can be obtained from S-N diagrams or damage parameter life curves, which will be discussed in detail in subsequent sections. For variable amplitude loading the damage fractions for the different cycles can be added together to calculate the total damage sustained. For example, a block or group of load cycles might consist of two cycles at stress level S1 and three cycles at stress level S2, as in figure below. The cycles to failure from a constant amplitude fatigue test for each stress level is 110,000 and 70,000 cycles, respectively.

Block Cycle Load History

The damage for the block is

Equation 3

The number of blocks to failure could then be calculated using Miner’s rule if the limit damage sum is 1.0 by

Equation 4

The number of blocks to failure can be found by solving for Nblocks, which in this case yields approximately 16.4 · 103 blocks to failure.

In certain cases, it may be appropriate to adjust the limit damage sum to values above or below 1.0. For values of the limit damage sum less than one, the number of blocks to failure will be calculated to be smaller, and likewise, for values greater than one, the number of blocks to failure will be calculated to be larger. Adjusting the limit damage sum can effectively make fatigue calculations more or less conservative. You can set this value in Simcenter 3D Specialist Durability using a Damage Sum Limit durability simulation object for any particular analysis.

The manner in which the damage fraction is determined for a given cycle is what distinguishes the stress-life and strain-life approaches.

Parameter	Unit	Preset To
Damage Sum Limit	1	1.0

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Fatigue life and fatigue damage, Simcenter 3D 2021.1 Series

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