Creep-fatigue damage is caused by reversed loading at elevated temperature, which presents the interaction of fatigue and creep. This behaviour normally spans a wide range of industries, such as aerospace, nuclear and automotive industries. In general, the creep-fatigue evaluation may be conducted by performing the creep-fatigue test under the running conditions, but this is uneconomical. Typical practice is to apply numerical models to pre-evaluate creep-fatigue behaviour at the initial stage of design. However, these models cannot effectively and efficiently be applied to engineering design because of a poor balance between accuracy and economy. Consequently, there is value in developing a new creep-fatigue model to improve the limitations presented by the existing models.

The present work developed strain-based and stress-based unified creep-fatigue equations. This started from an investigation of the underlying physical justification of fatigue and creep. We introduced the concept of fatigue capacity to represent the combined damage of creep and fatigue. The relationships between relevant variables were extracted from the conventional models, and were then applied to constitute the numerical representation of creep fatigue based on the concept of fatigue capacity. Furthermore, the heat-treatment effect was included into the unified model by introducing the parameter of grain size. Then a method of extracting the coefficients was proposed. Specifically a moderating factor was introduced to transfer the creep damage under constant loading into an equivalent situation with cyclic loading, and the compatibility was included to give a better description of the pure-fatigue condition.

The unified creep-fatigue equations were validated on multiple materials, including 63Sn37Pb solder, 96.5Sn3.5Ag solder, 2024T3 aluminium alloy, stainless steel 316, stainless steel 304, Inconel 718 and GP91 casting steel, where the empirical data of creep rupture and creep fatigue were extracted from existing literature. The validation verified the numerical structure of the unified creep-fatigue models, and demonstrated that the unified formulations can be applied in multiple situations for multiple materials to describe creep-fatigue behaviour with high quality of fitting to empirical data.

The unified creep-fatigue equations have significant advantages compared to existing creep-fatigue models, when applied to engineering design. Specifically, the unified models can be applied in multiple situations for multiple materials, can cover the full range of conditions from pure fatigue to pure creep, and can provide an economical method for fatigue-life prediction. Application of the unified method to engineering design was demonstrated via application to a gas turbine blisk. Combining the unified model with finite element analysis (FEA) reduced the complexity of creep-fatigue simulation.

Further refinements of the unified model were made to develop a simplified strain-based creep-fatigue formulation, the benefit of which is less reliance on empirical data collection, hence greater economy. A grain-size modified Manson-Haferd parameter was likewise introduced.

Another development of the theory was towards more complex mean stress conditions. The unified creep-fatigue equations were originally developed for the situation with zero mean stress. The model was extended to non-zero mean-stress situation. This was based on the simplifying assumption that the strain-stress relations under the situations with/without mean-stress effect share the same characteristic.

A physical explanation was developed for the terms in the unified creep-fatigue formulation. The unified models may be explained by the underlying physical mechanisms. This was achieved by reference to the physical phenomena of diffusion creep and crack growth at the microstructural level. A graphical representation of the crack growth process was proposed. This conceptual model illustrates the whole process of damage accumulation from crack initiation to crack propagation, then to structural failure.

Overall, the strain-based and stress-based unified creep-fatigue equations provide an improved formulation for creep fatigue, where the improvements are evident in greater accuracy, improved economy of empirical testing, coverage of the three conditions (pure fatigue, pure creep, and creep fatigue), inclusion of grain size, and applicability to engineering design. The benefits are a more effective and efficient method for creep-fatigue life prediction.