**5. Brittle creep rupture**

Creep rupture is technically very important, because it determines the life of many plants operating at high temperatures. Two main mechanisms are distinguished: ductile rupture and brittle rupture. Ductile rupture is controlled by the exhaustion of the deformation capacity of the material. In this case the usual rupture criterion is that the creep strain reaches a critical value. The deformation takes place by dislocation mechanisms. The faster the dislocations move, the faster rupture occurs. Since ductile rupture does not involve cavitation, it is not reviewed here, but full details can be found elsewhere [53].

Rupture curves for dislocation creep are illustrated in **Figure 12** for the austenitic stainless steel 18Cr12NiTi (321H) at temperatures between 600°C and 775°C. The experimental creep rupture data cover times up to 100,000 h (11 years). The general overall behaviour is well described by the model predictions.

The second process brittle rupture is due to grain boundary decohesion. By far the most important mechanism in this respect is the formation and growth of cavities. It is well established that when the cavitated grain boundary area reaches a certain fraction of about 0.25, brittle rupture takes place [54]. The cavitated area fraction *A*cav can be computed from Ref. [43]

$$A\_{\rm cav} = \int\_{l\_{\rm \cdot}} \frac{d\mathbf{n}}{dt'} \langle t' \rangle \boldsymbol{\pi} \, R^2(t, t') dt'. \tag{20}$$

A continuous nucleation of cavities takes place. The number of cavities is directly proportional to the creep strain, Eq. (10). Once a cavity has nucleated it starts to grow after an incubation time *t* <sup>i</sup> that is a small fraction of the rupture time [52]. The growth is described with Eq. (16) with the reduced stress given by Eq. (19). When *A*cav has reached 0.25, rupture is assumed to take place.

The model predictions for brittle rupture for 18Cr12NiTi (321H) are shown in **Figure 13**. The predictions are compared to the same experimental data as in **Figure 12**. Again the overall

2*π D*<sup>0</sup> *K*f(*σ*red − *σ*0)

34 Study of Grain Boundary Character

and relative difference increase with time.

**5. Brittle creep rupture**

described by the model predictions.

*A*cav = ∫*<sup>t</sup>*

tion time *t*

to take place.

/ *<sup>L</sup>*<sup>2</sup> *<sup>R</sup>* <sup>+</sup> *<sup>ε</sup>* .

In general Eq. (19) has to be solved by iteration to find the new value of σred. This new value for σred is lower than that given by Eq. (17). This is illustrated in **Figure 10**: Both the absolute

The new constrained growth model is compared to experimental data for austenitic stainless steels in [52]. Some examples are given here in **Figure 11**. Growth data for 18Cr10Ni steel with and without Nb or Ti are shown. It can be seen that the growth data can be described with fair

Creep rupture is technically very important, because it determines the life of many plants operating at high temperatures. Two main mechanisms are distinguished: ductile rupture and brittle rupture. Ductile rupture is controlled by the exhaustion of the deformation capacity of the material. In this case the usual rupture criterion is that the creep strain reaches a critical value. The deformation takes place by dislocation mechanisms. The faster the dislocations move, the faster rupture occurs. Since ductile rupture does not involve cavitation, it is

Rupture curves for dislocation creep are illustrated in **Figure 12** for the austenitic stainless steel 18Cr12NiTi (321H) at temperatures between 600°C and 775°C. The experimental creep rupture data cover times up to 100,000 h (11 years). The general overall behaviour is well

The second process brittle rupture is due to grain boundary decohesion. By far the most important mechanism in this respect is the formation and growth of cavities. It is well established that when the cavitated grain boundary area reaches a certain fraction of about 0.25, brittle rupture takes place [54]. The cavitated area fraction *A*cav can be computed from Ref. [43]

(*t*')*π R*<sup>2</sup>

<sup>i</sup> that is a small fraction of the rupture time [52]. The growth is described with Eq.

A continuous nucleation of cavities takes place. The number of cavities is directly proportional to the creep strain, Eq. (10). Once a cavity has nucleated it starts to grow after an incuba-

(16) with the reduced stress given by Eq. (19). When *A*cav has reached 0.25, rupture is assumed

The model predictions for brittle rupture for 18Cr12NiTi (321H) are shown in **Figure 13**. The predictions are compared to the same experimental data as in **Figure 12**. Again the overall

(*t*, *t*')*dt*'. (20)

i *<sup>t</sup>* \_\_\_ *dn dt*'

accuracy. The lower growth rate according Eq. (19) is important in this respect.

not reviewed here, but full details can be found elsewhere [53].

(*σ*red) = *ε* .

(*σ*appl). (19)

**Figure 12.** Comparison of dislocation creep model rupture curves (ductile rupture) Refs. [53, 54] with experiments [55] for 18Cr12NiTi (321H). Model prediction and experiments at temperatures between 600°C and 775°C with 25°C interval.

time dependence of the rupture strength at different temperatures is well represented. In fact the differences between the model predictions for ductile rupture in **Figure 12** and brittle rupture **Figure 13** are not very large.

Ductile rupture is assumed to be controlling if the strain exhaustion occurs before *A*cav = 0.25 has been reached. On the other hand if the cavitation criterion is reached first, brittle rupture takes place. The results for ductile and brittle rupture are combined in **Figure 14**. For a given

**Figure 13.** Comparison of model rupture curves based on cavitation (Eq. (20), brittle rupture) [54] with experiments [55] for 18Cr12NiTi (321H). Model prediction and experiments at temperatures between 600°C and 775°C with 25°C interval.

**Figure 14.** Comparison of model rupture curves based on both dislocation creep (ductile rupture) and cavitation (brittle rupture) with experiments [55] for 18Cr12NiTi (321H). Model predictions and experiments at temperatures between 600°C and 775°C with 25°C interval.

temperature and stress the value from **Figure 12** is chosen if the (ductile) rupture time is shorter than the (brittle) rupture time in **Figure 13** and vice versa.

When brittle rupture is taken into account when modelling the creep rupture curves, there is an improvement in particular at high temperatures and low stresses.
