A Bayesian Framework for Estimation of Strain Life Lower Bounds and its Application to IN617

The practice of applying strain-life relationships to model materials subjected to low cycle fatigue conditions has been widely-accepted for the past seventy years. The Coffin-Manson rule employs a double, two-parameter power law equation to correlate cycles to failure to strain range (or vice versa). Plastic strain range dominates low life, while elastic strain dominates high life. In some settings with well-established materials, copious amounts of test data are available. The median response and the Coffin-Manson parameters are determined through regression. Scatter in both strain amplitude and fatigue life values are a consequence of material and specimen variation, test technician attributes or more. Recent initiatives have endeavored to transition deterministic approaches over to probabilistic analogies. Confidence bands, lower ones in particular, are useful for understanding reliability curves and implementing reliability-based design and optimization. In settings with accelerated product development schedules, intentionally sparse sets of test data are used to play “what if” scenarios in the context of life prediction. We propose a non-stationary variance to model deviations from the Coffin-Manson rule and use Bayesian statistical methods to estimate model parameter uncertainties. The proposed approach is applied to the calibration of strain-life parameters of the candidate material Inconel 617, a Ni-base alloy used is combustion equipment. When compared with constant variance (such as in traditional regression), the results show an improved characterization of the confidence bounds for fatigue life. This is important as it indicates that the methodology can be used to manage the number of coupon test to achieve an acceptable convergence.