4. Discussion
4.1 Stress-strain curves
The typical stress-strain curve under cyclic creep is shown in Fig. 7, where \(\sigma^{\max}\) and \(\sigma^{\min}\) are of the peak and valley applied stresses, \(\ \sigma_{e}^{\max}\) and \(\sigma_{e}^{\min}\) are the upper and lower limits of the elastic domain respectively. The strain within the two adjacent cycles can be divided into four parts, as illustrated in Fig. 7 (a), including (I)\(\ \varepsilon^{r}\), the ratcheting deformation which contains elastic and plastic strains, loading from the lower-elastic limit to the peak stress; (II)\(\ \varepsilon^{c}\), which contains the creep strain generated during peak stress hold and a minor additional viscoplastic strain that is produced during the unloading process from peak stress to upper-elastic limit, In order to simplify the classification, the part of viscoplastic strain is considered as a continuation of creep. Previous works40,41 have concluded that the viscoplasticity of materials has a contribution to creep during the loading and unloading stage; (III)\(\ \varepsilon^{\text{re}}\ \), the total recovery strain when stress unloads from the upper-elastic limit to the valley stress and then reload to the lower-elastic limit; and (IV)\(\ \varepsilon^{\text{act}}\), the actual increased deformation compared to the last adjacent cycle.