Very high cycle fatigue (VHCF) tests are often performed by a high‐frequency fatigue test system, such as ultrasonic fatigue test machine. In the paper, simple VHCF tests and cumulative fatigue (low cycle fatigue plus VHCF) tests are performed to investigate the fatigue behaviour, respectively, for a low carbon manganese steel. The test results in Wöhler diagram show a large scatter in VHCF regime. Continuum damage mechanics model is extended to VHCF region to estimate the remaining fatigue life. A rapid fatigue failure probability prediction method is applied and extended to VHCF regime in order to evaluate the fatigue dispersion based on multi‐scales model and fatigue dissipation analysis.

Ultrasonic fatigue tests up to 10¹⁰ cycles were performed on a turbine engine titanium alloy (Ti-8Al-1Mo-1V) at the stress ratio (R) of −1 with smooth specimens and at R = −1, 0.1 and 0.5 with notched specimens. As a result, with increase of fatigue life, the source of reduced fatigue life caused by multi-point surface crack initiation changes from crack propagation stage to crack initiation stage in the high cycle fatigue regime. Notch effect further promotes the degeneration of high cycle and very high cycle fatigue strength at R > −1. The bilinear model, extended from the Goodman method, can better estimate the mean stress sensitivity of this titanium alloy. The fatigue mean stress sensitivity and fatigue-creep mean stress sensitivity of this material increased with the increase of fatigue life. The new model, based on the Murakami model, can provide more appropriate predictions for notch fatigue strength.

The effects of the secondary crystal orientations on the nickel-based single-crystal superalloy turbine blades were investigated. The stress concentration features were used for investigation of the optimal secondary crystal orientation leading to the higher strength of the single-crystal turbine blades. The crystal plastic finite element method coupled with micromechanics constitutive model is applied to study the effect of secondary crystal orientation on plastic deformation and mechanical behavior around the cooling holes and notches with the primary (load) orientation fixed at [001] direction. For nickel-based superalloy plates with holes or notches, the secondary crystal orientation effect on the strength needs to be clarified at various load levels. The maximum von Mises stress in the single-crystal alloy varies significantly with variation in the secondary crystal orientations. It was found that only two slip systems dominate the deformation process of the material owing to their favorable orientation with loading. The secondary orientation of 45° was identified with lowest resolved shear stress in the dominating slip systems and potential of producing higher strength for single-crystal turbine blades.