(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).