Fatigue Threshold Re-Visited

JULY 2018

Fatigue is one of the most common contributors to engineering and plant failures, particularly in engineering systems that experience some form of repetitive or cyclic loading. This fatigue phenomenon has been known for over a hundred years, and now, with the discipline of Fracture Mechanics, it is generally fairly well understood. However fatigue still accounts for over 80% of unexpected engineering failures, and despite efforts to understand fatigue and mitigate against it, its occurrence is frequent and ubiquitous. Perhaps one of the reasons for this is the general misunderstanding of fatigue threshold and its effect on fatigue life. To an extent, this was discussed in our August 2017 Tech Tip (available on our website), but this present article extends this and addresses a different issue referring to threshold dependence itself.

The background to Fracture Mechanics formulation and the Paris equation detailed in the August 2017 Technical Tip, showed the correlation between crack growth rate (da/dN) and cyclic stress intensity (ΔK) can be summarised in a linear relationship:

da/dN = C ΔKm

Where ‘C’ and ‘m’ are material and environmental parameters, peculiar to those particular fatigue conditions, materials and environment.  This so-called Paris equation’ is extremely useful as it can be determined experimentally.  Quite often the various parameters used in the equation are available in material databases and the values do not have to be determined experimentally.  The similar, but more accurate Forman equation takes account of the stress range ratio R (stress min/ stress max).  Both the Paris and Forman equations are very amenable to being integrated, using calculus, to allow the operational fatigue life of the component operating under the cyclic loading conditions to be determined. The integration of the equation in terms of cyclic load and material parameters ‘C’ and ‘m’ leads to the number of cycles to failure, a very useful and reliable measure of lifetime performance.  To calculate the fatigue life one also requires the probable initial flaw size as well as the critical flaw size at failure which can be estimated from the material fracture toughness. 
This methodology works very well, but is complicated in the low crack growth regime in the vicinity of so-called‘fatigue threshold’.  If the cyclic stress intensity is below this threshold condition, then fatigue does not occur.  Conversely, if the cyclic stress intensity is in excess of the threshold value (ΔKthres) then fatigue is bound to develop and cracking propagate.  

What is less well known, however, is what the specific threshold values for various materials and environments are.  These are not always readily available but can be determined experimentally in a good fracture mechanics laboratory or, to an extent, be looked up in sourcebooks.  Typical values for many steels and materials range between about 2 and 6 MPa√m, above which fatigue will definitely take place.  These threshold values can be reduced significantly by environmental effects to values approaching zero which implies fatigue cracks will initiate at even low values of cyclic stress.  This dependence on liquid or gaseous environment is presented in the August article but this reduction in the threshold stress intensity can also be influenced by a number of other factors including microstructure, surface finish, stress and residual stress.  Generally, the Paris equation plot (on a typical da/dN vs ΔK log-logplot) will be shifted to the left thus indicating that the stress, or loading conditions to initiate fatigue cracking are substantially reduced and micro-cracking can occur almost immediately.  In addition, in certain circumstances, the effect of corrosion and stress corrosion cracking type phenomena can exacerbate the initiation and accelerate the crack growth substantially in the middle regimes of crack growth.  
A surface which is not polished or slightly rough, thus providing small stress initiating stress concentration features, will also reduce threshold and hence the magnitude of the cyclic stresses required for initiation.  In addition, there are additional effects on fatigue due to waveform, mean level and frequency, which need to be considered when undertaking fatigue prediction estimates, although with less direct influence on the threshold itself.  A saw-tooth loading waveform with i) a slow ramp rate/rising stress and a fast stress reversal, as opposed to ii) a fast stress increase and slow return, leads to significantly shorter fatigue lives and needs to be taken into account.  Similarly, a loading profile with a higher sustained mean load will lead to shorter fatigue lifetimes.  Reductions in the loading frequency also leads to a shorter fatigue life (in the appropriate regimes), from the contribution of environmental attack on open cracks (which would not be the case in higher frequency cyclic loading, where the environment does not have time to dwell within open cracks and accelerate crack growth).
Although environmental factors almost always decrease threshold and increase crack growth rates, it is probably worth noting that in a propagating crack, closure, the local plasticity or oxide development within a crack may cause incomplete closing of the crack surfaces (so-called 'closure’) and so actually SLOW the crack growth rate down.  This phenomenon is more of a special case/rarity and should not be turned to as a means of slowing down fatigue cracking.
Although fatigue is often thought to be well understood the phenomenon of fatigue crack initiation and propagation is complex and often not well understood, which to a large extent accounts for the widespread occurrence of fatigue failures.  Factors affecting threshold, waveform, frequency, mean loads and environmental aspects all need to be taken into account to ensure accuracy when undertaking fatigue life prediction assessments.  

Published in Technical Tips by Origen Engineering Solutions on 1 July 2018