5. Discussion

## 5.1 The minimum creep strain rate over a wide range of stress levels for P91 high Cr alloy

The results shown in Figure 2 clearly demonstrated that Xu's modified hyperbolic sine law is the best for the P91 high Cr alloy over a wider range of stress levels.

It is pointed out that the introduction of σ<sup>q</sup> into the normal hyperbolic sine function, purposely, offers a capability to depict a wider range of curvatures between the minimum creep strain rate and stress level.

Furthermore, the value q = 2 found here for P91 is in similar order to those found for low Cr alloy [12] and for P92 [35]. It is worth to research any profound reason for this similarity.

It is reasonable to propose that, due to generic mathematical property (feature), the application of Xu's modified hyperbolic shin law should be further explored, particularly for a wider range of stress level cases.

Figure 15. The damage evolution with time [31].

#### 5.2 Creep cavity fracture model

#### 5.2.1 The determination of the creep cavitation coefficients

A set of creep cavitation model and creep cavity growth model were calibrated using the more representative X-ray synchrotron cavitation data. The predicted cavity size probability density is very close to the experimental measured one, indicated by Figure 3, and it can be concluded that the quality of creep cavitation models are good. Hence their application should also be reliable [12].

The predicted relationships of the number of cavity, the creep cavity growth, and creep damage variable with time can provide the insight of the evolution of the complex creep cavity damage process, and its use will lead to a clear and definite answers on (1) how to present creep cavity damage and (2) how to quantify it.

The obtained explicit creep cavity damage fracture model can be used for creep lifetime prediction and possible extrapolation.

#### 5.2.2 Trend of creep fracture lifetime coefficient U<sup>0</sup>

The creep lifetime coefficient U<sup>0</sup> is introduced in theoretically based cavitation nucleation, growth, and coalescence along the grain boundary. A clear trend shown Modeling of Creep Deformation and Creep Fracture DOI: http://dx.doi.org/10.5772/intechopen.89009

from the experimental data, in Figure 7, indicated that such creep cavity damage/ fracture modeling is scientifically sound and numerically reliable; hence it can be used for creep life time prediction and possible extrapolation.

Furthermore, theoretically, creep lifetime coefficient and lifetime, in log–log scale, is a linear relationship; and the experimental data strongly support that as shown in Figures 8 and 9. Hence the trend revealed by experimental data in Figures 8 and 9 could be used for lifetime prediction and very promising for lifetime extrapolation.

#### 5.2.3 Creep cavity fracture lifetime prediction over a stress range

The excellent agreement (87%) between the predicted creep lifetime and experimental measured one proved the reliability of creep lifetime prediction.

It needs to be reported here [33] that the stress of 180 MPa is of the high stress level and the stress of 120 MPa is of the lower stress level. Hence, the above excellent agreement is actually achieved between two stress levels. There is no stress breakdown phenomenon in this approach; actually, the stress-dependent effects will be taken into account by the values of the creep cavitation coefficients.

The success is underpinned by both the correct mathematical model and the direct using the most presentative cavitation data.

Furthermore, the creep cavitation modeling approach reported here should be generic and can be used for any other cavitation controlled damage and fracture problems such as ductile fracture, fatigue fracture, and creep and fatigue combined fracture.

## 5.3 Mesoscopic composite model of the simulation of creep cavity damage and fracture


#### 6. Conclusion

Modeling of creep deformation and creep facture is very challenging. However, research work report here has made some progress. These progress and suggestions for future work are presented as:

