*3.3.2 Damage progression behavior of the notched specimen of the weld joint and the base metal*

The time sequential behavior of damage progression around a notch tip of the weld joint specimen for P91 steel observed by the in situ observational testing machine under creep condition with a temperature of 650° C is shown in **Figure 10**. These results show that the creep damage preferentially originated at the HAZ of the base metal side, however this damage was not a dominant damage of final fracture. After that, another creep damage newly originated from both of the upper and the lower notch tips. When this damage area spread over the whole ligament from the upper notch tip to the lower notch tip, final fracture occurred, that is, creep fracture of a weld joint notched specimen is not creep crack growth dominant but it is creep damage dominant, which related to the similarity law of creep deformation as is mentioned in the Section 3.3.1.

The time sequential behavior of damage progression around a notch tip of the base metal observed by the in situ observational testing machine under creep condition with a temperature of 650° C for P91 steel is shown in **Figure 11**.

*The Quantitative Estimation of Mechanical Performance on the Creep Strength… DOI: http://dx.doi.org/10.5772/intechopen.106419*

#### **Figure 10.**

*The time sequential behavior of damage formation around a notch tip of the weld joint specimen under creep condition with a temperature of 650°C and 113 MPa for P91 steel.*

#### **Figure 11.**

*The time sequential behavior of damage formation around a notch tip of the base metal under creep condition with a temperature of* 650° C *and 113 MPa for P91 steel.*

For the base metal, creep damage originated from a notch tip in the direction of shearing stress. When the damage area spread over the specimen width, final fracture occurred. However, damage progression behavior is different from that of the weld joint, creep fracture mechanism is also creep damage dominant, which also related to the similarity law of creep deformation as is mentioned in the Section 3.3.1.

#### *3.3.3 Experimental law of creep fracture life and creep strain rate*

As shown in **Figure 12**, a unique linear logarithmic relationship between creep fracture life and steady state creep strain rate, that is, the unique *QL*<sup>∗</sup> relationship was

**Figure 12.** *The relationship between logarithmic value of tf and dε=dt.*

found out both in base metal and weld joint, which means the weld joint is considered to have a similar property as that of base metal, that is, <sup>Δ</sup>*QL*<sup>∗</sup> <sup>¼</sup> 0.

As shown in **Figure 13**, the linear logarithmic relationship between the steady state creep strain rate and the applied stress was found out both for the base metal and the weld joint respectively.

From these experimental results, the following equations are obtained.

**Figure 13.** *The relationship between logarithmic value of dε=dt and applied stress, σ.*

*The Quantitative Estimation of Mechanical Performance on the Creep Strength… DOI: http://dx.doi.org/10.5772/intechopen.106419*

$$t\_f = 0.503\dot{\epsilon}^{-0.925} \tag{15}$$

$$
\dot{\varepsilon}\_{B} = \textbf{3.56} \times \textbf{10}^{-28} \sigma\_{B} \, ^{11.53} \, (\text{Base metal}), \tag{16}
$$

$$
\varepsilon\_W = \text{3.42} \times 10^{-19} \sigma\_W^{8.1} \text{ (Weld joint)}, \tag{17}
$$

where *tf* , *ε*\_*B*, *σB*, *εW*\_ and *σ<sup>W</sup>* is creep fracture life, steady state creep strain rate and applied stress for the base metal and weld metal respectively.

#### *3.3.4 The derivation of the converted stress and the converted stress ratio*

As shown in **Figure 12**, the *QL*<sup>∗</sup> relationship is written by Eq. (15) both of the base metal and the weld joint.

As shown in **Figure 13**, the linear logarithmic relationship between the steady state creep strain rate and the applied stress is given by Eq. (16) for the base metal.

Substituting Eq. (16) into Eq. (15), Eq. (18) is obtained for the base metal.

$$t\_{\rm fb} = 1.234 \times 10^{25} \sigma\_{\rm B}^{-10.67},\tag{18}$$

where *tfB* is the creep fracture life under applied stress, *σB*, for the base metal.

Using the experimental results of steady state creep strain rate, *ε*\_*<sup>W</sup>* of the weld joint and substituting it into *ε*\_ in Eq. (15), the fracture life, *tfweld* of the weld joint specimen corresponding with *ε*\_*<sup>W</sup>* is obtained.

Substituting *tfweld* into *tfB* in Eq. (18), the converted stress of the weld joint into that of the base metal, *σWCB*, with the same fracture life as *tfweld* is obtained by Eq. (19).

$$
\sigma\_{WCB} = t\_{fuel}^{-1\_{\tilde{1}0.67}} \times \left( \mathbf{1.234} \times \mathbf{10^{25}} \right)^{\dagger\_{0.67}} \tag{19}
$$

The converted stress ratio, *η*, is defined by Eq. (20).

$$
\eta = \frac{\sigma\_{WCB}}{\sigma\_W} \tag{20}
$$

The accuracy of predictive creep fracture life of the weld joint derived from the *QL*<sup>∗</sup> line is about 71% � 76% accuracy to the actual life as shown in **Table 4**.

The value of the converted stress ratio of the weld joint into that of the base metal, *η* ¼ *σWCB=σ<sup>W</sup>* is 1.39 and 1.41 for the case of 135 MPa and 113 MPa of *σ<sup>W</sup>* respectively as shown in **Table 4**. These results mean that the creep strength of the weld joint is lower than that of base metal of 39% and 41%, respectively. The scattering of the converted stress ratio is 0.7%. On the other hand, the value of the ratio of creep fracture life of the weld joint to that of the base metal is 0.052 and 0.035 respectively. The scattering of the creep fracture ratio is 20%.

From these results, the converted stress ratio is more accurate indicator of estimating the MPCS than the fracture life ratio from the point of the data scattering.

For creep ductile materials, the prediction of the creep fracture life of the target materials and the quantitative comparative estimation of the MPCS of the target materials to the control material are found to be possible measuring the steady state creep rate of the target materials by the short time range experiments.


#### **Table 4.**

*Converted stress and the ratio of converted stress to actual applied stress of the weld joint.*

## **4. Discussions**

## **4.1 Application of this theory to the case of C (T) specimens of the weld joint for P91 and P92 steels**

The *QL*\* map of the base metal and weld joint for the ASME grade P92 steel and ASME grade P91 steel are shown in **Figure 14** [14]. Weld metal is 12Cr steel and 9Cr steel, respectively.

**Figure 14.** *QL\*map of the base metal and weld joint for the P92 and P91 steels [14].*

*The Quantitative Estimation of Mechanical Performance on the Creep Strength… DOI: http://dx.doi.org/10.5772/intechopen.106419*

**Figure 15.**

*The prediction and derivation methods of creep fracture life and the converted stress of the weld joint into that of the base metal.*

These results showed that the *QL*\* line of the weld joint is parallel to and lower of Δ*QL*<sup>∗</sup> than that of the base metal. Therefore, one creep fracture test of the short range life is necessary to determine the value of Δ*QL*<sup>∗</sup> , after that, as shown in **Figure 15**, the converted stress of the weld joint in to the applied stress of base metal, *σWCB* and its ratio, η are feasible to obtain according to the flow chart given by **Figure 5**.
