1. Introduction

Creep-dominated creep-fatigue interaction is a long-term material failure mode that involves cyclic loading 1. Lack of fundamental understanding on this topic prevents us to commercialise the Generation IV high-temperature nuclear power plants with a design life of 60 years 2. Although the mechanistic-based descriptions of cavity nucleation, growth and coalescence under creep have been established 3, little attempt has been made to reveal the mechanism of cavity nucleation and its early-stage radius change under creep-fatigue interaction 4, 5.
The empirical relationship between cavity nucleation rate under creep and Monkman-Grant constant has been established by Davanas6, providing a good agreement with experimental data. But it is unclear about its suitability for creep-fatigue interaction. Cavitation under fatigue is known to be different from that under creep, in a sense that fatigue induced cavities are smaller in size but higher in their number density 5. There are creep-fatigue lifetime prediction models that consider the creep cavitation mechanism, e.g. Nam 7. However, the model cannot explain the positive relationship between the cavity nucleation and tensile hold time 8. Recent work by Wen, Srivastava9 and Barbera, Chen 10 used creep damage models to predict crack growth rate under creep-fatigue, by incorporating the late-stage cavity growth. However, they did not consider the physical process of cavity nucleation or early-stage growth.
Moreover, little knowledge has been gained regarding the cavity sintering. Compressive loading can cause the nucleated creep cavities shrink in radius and forces them to be removed completely under some circumstances 11, 12. This means that their number density after certain number of cycles is not the simple sum of nucleated cavities from each cycle. To the best of the authors’ knowledge, creep cavitation model considering both the nucleation and sintering events under creep-fatigue interaction does not exist so far.
The mechanism of cavity nucleation was initially proposed by Greenwood13, and developed further by Raj and Ashby14. It has been accepted that vacancies agglomerate and form stable nuclei assisted by local normal stress. The local normal stress can be significantly higher than the far-field stress15. One of the causes is grain boundary (GB) sliding induced stress concentration. Extensive cavitation was found in copper bi-crystals which had been subjected to pre-strain in favour of GB sliding followed by creep loading 16, 17. Min and Raj18 proposed a model to predict the local normal stress under creep-fatigue loading based on the GB sliding mechanism. By considering the creep effect on local normal stress, our model is capable of predicting the cavity nucleation under one-cycle creep-fatigue 19.
Modelling the early-stage radius change is key to understanding the sintering process under creep-fatigue. Note that sintering shares a high degree of commonality with the cavity growth. The classical growth models were established under either or both of vacancy diffusion and matrix deformation (Cocks 20, Cocks and Ashby21, Needleman and Rice 22, Chuang, Kagawa 23, Chen and Argon 24), and the growth rate is controlled by the far-field stress. Nevertheless, these models might not be suitable for the early-stage growth. First, the radius of nucleated cavities (~5 nm) is much smaller than those commonly defined ‘small’ cavities (~1 μm)3. This indicates that the vacancy flow near the cavities is highly sensitive to the local normal stress25. Second, the cavity growth mechanism map26 does not consider the role of GB sliding on the early-stage growth, despite its importance 25.
In this paper, the number density of cavities and their time evolution during multi-cycle creep-fatigue loading are modelled. The stress-controlled load waveform is considered because a higher creep damage would be generated in comparison with the strain-controlled one27, 28. Type 316 stainless steel is selected for twofold reasons: material parameters are available 18, 29-31 and its wide application to the power generation industry2, 29.