(13)
where reference stress σref is defined by the plastic limit load Po ,σref =σ0 (P/P0 );\(\varepsilon_{\text{ref}}^{p}\) and\({\dot{\varepsilon}}_{\text{ref}}^{c}\) are the reference plastic strain and reference creep strain rate at the corresponding reference stress, respectively; and K is the stress intensity factor.
The crack-tip hoop stresses at the maximum load and the end of hold time are compared with the RR stress in Fig. 13 at crack initiation (Δa = 0 mm) and growth (Δa = 2 mm). For the tension-tension loading case (specimen 1), shown in Fig. 13(a) and (b), the crack-tip stresses are slightly changed during the hold time, and are close to the RR stress both at crack initiation and growth. This suggests that the stress field is similar to that under pure creep condition. On the other hand, the tension-compression loading cases (specimen 3 and 5) show quite different crack-tip stresses from that under pure creep condition. For the tension-compression with long hold time (specimen 3), shown in Fig. 13(c) and (d), the crack-tip stresses decrease significantly during the hold time, and the crack-tip stress at the end of hold time is close to the RR stress both at crack initiation and growth. For the tension-compression with short hold time (specimen 5), shown in Fig. 13(e) and (f), the crack-tip stress remains similar during hold time and is much higher than the RR stress both at crack initiation and growth. The difference between tension-tension and tension-compression loading condition arises from initialization of the creep-relaxed stress caused by compressive loading, which is mentioned in Section 4.4. Furthermore, for tension-compression cases (specimen 3 and 5), the hoop stresses near the crack tip are close to or lower than the RR stress, due to formation of local creep-dominant zone, cyclic softening, and large deformation of crack tip (blunting). The effect of the cyclic softening is appreciable in the specimen 5 at crack growth, as shown in Fig. 13(f).