# What is the unit of measurement of fatigue damage in a structure?

I looking the specific meaning of fatigue damage in structures. I have one structure and which is subjected to repeated loading cycles. I want to see is this design is safe from fatigue point of view.

• – ja72 Sep 14 '16 at 21:07

Damage calculations use S-N curves, which define the number of cycles to failure, N(S), for stress range S.

The damage value itself can be thought of as the proportion of the fatigue life that is used up by 1 cycle of stress range S.

$$D(S) = \begin{cases} \dfrac{1}{N(S)} &\text{if }S > FL \\ 0 &\text{if }S \leq FL \end{cases}$$

$FL$ is the defined endurance limit below which no damage occurs.

There are 3 models of mean stress effects Goodman, Soderberg and Gerber. Each one has its own formulas. This is so because mean stress effects are handled by modifying each stress range according to a formula dependent on the mean stress level.

T-N curves are handled in a similar way. A T-N curve defines the number of cycles to failure, N(T), for effective tension range T. There is no analogue of endurance limit for T-N curves. Likewise there are no analogues of stress concentration factor and thickness correction factor. As for S-N curves, damage is defined as:

$$D(T) = \dfrac{1}{N(T)}$$

The summation of damage is then performed in an identical manner to that performed for S-N curves.

So that would be your unit: number of cycles before failure.

• first of all thank you for your effort, I am aware of all this stuff, My question is little different, i.e. suppose one structure is subjected to cyclic loading above FL, then as the number of cycle increase (bellow failure) what changes in the structure can be seen at macroscopic level, since the fatigue is consider to be linear cumulative damage, so where does the damage(hypothetically) stored in the structure? – Chirag Palan Sep 16 '16 at 4:44
• The fatigue is linear in the case we deal with linear tensor forces. In the case of cyclic bending, for example, distribution is no longer linear and damage will be done in a reverse-gaussian manner (more on the outer sides of the material and less near the middle of it). If you have a practical example I'm sure we could explain a lot better. In general situations, I personally use (along with other researchers) a SID (structural integrity damage) scale, witch measures integrity of a material between 0 and 100%. This becomes simple to apply to any material with known mechanical properties. – Overmind Sep 16 '16 at 6:41
• Thank you for explaining, I am having long flexible pipe and which subjected to the random loads. I have stress time history of the pipe, I just want to know is the minners rule is sufficient to calculate fatigue damage? or do I need to use some other method? – Chirag Palan Sep 18 '16 at 11:48
• In this case tension is way less relevant, so yes, Miner’s Rule / Cumulative Damage Models are the thing you'd want to apply. If you have time history/stats and you know the exact pipe material you could even get a good estimate of its remaining lifetime until damage exceeds a safety limit value. – Overmind Sep 19 '16 at 6:25

Typically you might use Miner's Rule and compute the Damage Fraction which is the percentage of predicted life consumed. It's a simplified model though and there are better ways using software like ALTA

• that is what i want to understand, As the number of loading cycles increase the damage index D increase, now what does that damage index meaning in regards of structure, i.e. if I talk about deflection as I increase load deflection increase in similar way as i increase number of loading cycles what does it show on the structures? I hope my question is clear – Chirag Palan Sep 14 '16 at 14:46
• Just as an aside, though the link leads to aerospacengineering.net, Miner's Rule is also applicable to structures (at least Brazilian codes make reference to it). – Wasabi Sep 14 '16 at 14:48
• @Wasabi aircraft and the like ARE structures – DLS3141 Sep 14 '16 at 14:50
• @DLS3141: Sure, but the loads and behavior of aircraft are quite distinct from structures. If nothing else, aircraft suffer significantly more violent dynamic loads than structures, meaning that fatigue is usually more of a concern for aircraft (but must also be checked in structures, of course). My comment was mainly to remove the issue of "ok, so this can be used to describe the behavior of an aircraft's wing, but how applicable is this to structures?" – Wasabi Sep 14 '16 at 15:02
• @Wasabi the structures and loads are different, but the idea of cumulative damage and its application to predicting life are the same. – DLS3141 Sep 14 '16 at 15:13