Fatigue Life Estimation
The failure of engineering components as a result of cyclic loading induced fatigue is widespread and probably one of the major causes of component failure. Some estimates indicate that close to 80% of all engineering failures are primarily due to fatigue. The fracture mechanics approach to quantifying fatigue, presented in our August 2017 and July 2018 technical tips, shows how fatigue crack growth rate can be characterized by the well-known Paris equation.
da/dN = C∆Km
The Paris equation relates the crack growth rate, da/dN, to the cyclic stress intensity ∆K, and material parameters C and m. If the values C and m for the particular material (and operating environment) in question are known, the expression can be integrated from an initial flaw size a0 (determined from NDT inspection or inspection limits) to critical flaw size, acrit, determined from the maximum stress and the material’s fracture toughness. This integration yields the number of cycles required to reach critical flaw size and inevitable failure.
Integration of the Paris equation is very useful, but often the load/stress data is not available in a format that can be integrated easily (e.g. a continuous sine wave loading with constant amplitude). It is much more common to have cyclic loading recorded from the component in question (be it a shaft of a motor driving a shredder, wave loading on a ship or the wind speed spectrum on today’s ubiquitous wind turbines) as a variable wave form of changing amplitude, mean and frequency, as well as duration. In such variable loading cases, it is appropriate to undertake the Paris ‘integration’ by means of an iterative summation process. Instead of re-arranging the above Paris equation as
and integrating between limits, the approach is rather to SUM crack growth per regime, for discrete bins, i.e.
In this case the increment in crack length could be summed numerically in a piece wise fashion for each stress intensity interval ∆K and the exact number of cycles for which it pertained. This approach allows the variable amplitude load data to be assessed and the crack increment for each load interval block to be calculated. By adding these ‘crack growth increments’ from the initial flaw size to the final (critical) flaw size, the number of iterations (ultimately cycles) to failure can be readily determined.
Using suitable computational techniques, the requisite numerical integration can be handled with relative ease. If suitable material data is available, the technique can be employed to predict fatigue life to the required accuracy, by applying the cyclic stresses in discrete load amplitude blocks which would characterise the load spectrum (and can be obtained from field testing).
The accuracy of the approach is dependent on how well the load data characterises the actual operating conditions, accurate modelling of the load sequencing, the availability of suitable material data and knowledge of the actual maximum initial flaw size – but can lead to meaningful and useful fatigue lifetime estimates.
Published in Technical Tips by Origen Engineering Solutions on 1 May 2019