PSI - Issue 19

A. Halfpenny et al. / Procedia Structural Integrity 19 (2019) 150–167 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The fatigue design of mechanical systems has historically followed a ‘deterministic’ process. That means, for a given set of inputs they will return a consistent set of fatigue life results with no scatter. In reality the inputs are statistically uncertain – they have an expected value and a variability. Deterministic design methods take no implicit account of uncertainty. In practice, the designer applies a safety factor to each input parameter to account for the uncertainty. Often an additional safety factor is also applied to the final result to allow for ‘modelling errors’. In most cases, the engineer is fairly certain that the simulation results are conservative, but cannot state with any confidence what the expected safety margin, reliability or failure rate will be. Furthermore, the uncertainty in safety margin makes it almost impossible to validate the simulation against a physical durability or reliability test. In comparison, a ‘Probabilistic Fatigue Simulation’ is ‘stochastic’ in nature. That means inputs are expressed using an expected value along with a probability distribution. The analysis is run repeatedly using a procedure known as ‘Monte Carlo’ simulation. A different set of input values is chosen randomly for each run based on the specified statistical distributions. This produces a number of life results. Post processing of these results provides a safe design where the reliability statistic can be determined with known confidence. This design process helps to avoid poor in service reliability whilst reducing over-design. The simulation is easily validated against physical tests. Validation includes the inherent scatter associated fatigue life as well as the mean time to failure. Furthermore, it is easy to see which uncertainties contribute most to the overall design conservatism allowing justification to study these uncertainties more thoroughly. A comparison between deterministic and stochastic design methods is given by [NAF 18] [NAF 19] and is illustrated in Fig. 1. This paper addresses the three stages of Probabilistic Fatigue and Reliability Simulation : - Uncertainty Quantification (UQ) of the input parameters - Stochastic fatigue simulation of individual components - Reliability simulation of individual components and a system

Fig. 1. Comparison between deterministic and stochastic design methods

 Uncertainty Quantification (UQ) In order to take advantage of Probabilistic Fatigue Simulation, uncertainties in the input and the analysis model must be properly estimated. There are two types of input uncertainty : - Reducible uncertainties (or epistemic uncertainties) - Irreducible uncertainties (or aleatoric uncertainties)