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.