A hybrid physics–Bayesian framework for fatigue design curves under cryogenic conditions with consideration of load ratio and residual stress

Fatigue performance is a critical design consideration for cryogenic structures used in the storage and transport of alternative fuels such as liquefied natural gas (LNG), ammonia, and captured CO₂. However, fatigue crack growth rate (FCGR) testing at cryogenic temperatures is expensive and prone to uncertainty due to complex experimental conditions. This study proposes a physics-informed Bayesian framework to improve the prediction and design of FCGR behaviour without extensive cryogenic testing. Four probabilistic models are developed: two Gaussian process (GP) regressions, a physics-informed Bayesian neural network (PIBNN), and a hybrid physics–GP fusion model. The framework explicitly incorporates temperature-dependent material properties, residual stress, load ratio, and crack closure mechanisms while utilising Bayesian inference to quantify epistemic and aleatory uncertainties. The physics-informed components constrain the model to physically admissible trends, improving extrapolation beyond the training data. Based on these models, Bayesian design curves are constructed to replace the traditional “mean + 2SD” rule, achieving a balanced level of conservatism with quantified confidence intervals. The proposed approach demonstrates reliable prediction of fatigue behaviour under untested cryogenic conditions, offering a data-efficient and mechanistically consistent tool for the design and integrity assessment of cryogenic structures.