# Theory of Cumulative Damage

The theory of cumulative damage assumes that a stress cycle with an alternating stress above the endurance limit inflicts a measurable permanent damage. It also assumes that the total damage caused by a number of stress cycles is equal to the summation of damages caused by the individual stress cycles.

## Linear Damage Rule

Assume that the S-N curve indicates that it takes N1 cycles at an alternating stress S1 to cause fatigue failure, then the theory states that each cycle causes a damage factor D1 that consumes 1/N1 of the life of the structure.

Moreover, if a structure is subjected to n1 cycles at S1 alternating stress and n2 cycles at S2 alternating stress, then the total damage factor D is calculated as:

D = (n1/N1 + n2/N2),

where N1 is the number of cycles required to cause failure under S1, and

N2 is the number of cycles required to cause failure under S2.

This rule is referred to as the Linear Damage Rule or the Miner's Rule. The damage factor, also called usage factor, represents the ratio of the consumed life of the structure. A damage factor of 0.35 means that 35% of the structure's life is consumed. Failure due to fatigue occurs when the damage factor reaches 1.0.

The linear damage rule does not consider the effects of load sequence. In other words, it predicts that the damage caused by a stress cycle is independent of where it occurs in the load history. It also assumes that the rate of damage accumulation is independent of the stress level. Observed behavior indicates that cracks initiate in a few cycles at high stress amplitudes, whereas almost all the life is spent on initiating the cracks at low stress amplitudes.

The linear damage rule is used in its simple form when you specify that fatigue events do not interact with each other in the properties of the study. When you set the interaction between events to random, the program uses the ASME code (ASME Boiler and Pressure Vessel Code, Edition 1983 (and later), section III, Division 1, Subsection NB) to evaluate the damage by combining event peaks.