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 to evaluate the damage by combining event peaks.
Related Topics
Performing
Fatigue Analysis
Setting
the Properties of Fatigue Analysis
Viewing
the Results of Fatigue Analysis