Fig. 9 Evolutions of elastic modulus during the entire life under different unloading conditions: (a) loading and (b) unloading.
4.2.2 Creep strain \(\varepsilon^{c}\)
As above classification, the creep strain \(\varepsilon^{c}\) is calculated by the sum of the deformation during the peak stress hold time and a minor additional viscoplastic strain near the peak stress. As shown in Fig. 8 (b), the evolution of \(\varepsilon^{c}\) displays three stages obviously, as the creep strain decreases sharply after the first cycle and then keeps constant before increases again near fracture. The difference of the creep strain would result from the viscoplastic component, which can be affected by the changed unloading rate.
The maximum strain in one cycle is the sum of the ratcheting strain\(\varepsilon^{r}\)and creep strain \(\varepsilon^{c}\) as shown in Fig.7 (a).
Recovery strain \(\varepsilon^{re}\ \)in one cycle
4.3.1 Elastic recovery strain \(\ \varepsilon^{e}\)
Fig. 7 exhibits that the strain starts to reverse as the stress drops to the upper-elastic limit, which indicates the strain begins to recover. The elastic recovery strain \(\ \varepsilon^{e}\) mainly depends on the loading elastic modulus E and the upper-elastic limit\(\ \sigma_{e}^{\max}\), which can be calculated according to Eq. (5). The values and evolution of the loading elastic modulus have been mentioned and displayed in Fig. 9 (a). The upper-elastic limit can be obtained by applied peak stress and viscous stress according to Eq. (6). Therefore, the elastic recovery strain for different unloading rates is obtained in Fig. 10 (a), which also shows three distinct stages. The elastic recovery strain is slightly large for high unloading rate at the first cycle and then keeps constant with little difference in the stable stage before increases again at last. It means that the value of \(\varepsilon^{e}\) depends on the loading elastic modulus mainly and is hardly affected by the difference of the upper-elastic limit within the examined range of unloading rates.