**2.3 Derivation method of the converted stress and Δ***QL***<sup>∗</sup>**

For the case of creep ductile materials such as Cr-Mo-V steel, the similarity law of creep deformation and Eq. (8) described in the Section 2.1 and 2.2 are valid [11, 12]. For such case, the concept of the converted stress is defined and valid to conduct a quantitative estimation of the MPCS and the prediction of creep fracture life.

This section shows the derivation method of the converted stress. When the same similarity law of creep deformation is valid both for A and B materials, the relationship between *ln t*<sup>f</sup> and *ln ε*\_*<sup>s</sup>* in the *QL*<sup>∗</sup> map is unique as shown in **Figure 4** [12], where A material is a control material to make the *QL*<sup>∗</sup> line and B material is a target material to estimate MPCS.

The flow chart of the derivation method of the converted stress is shown in **Figure 5**. When the similarity law of creep deformation is valid, Eq. (8) is unique both for A and B materials and it was written by Eq. (9),

$$\mathbf{t}\_{\hat{f}} = \mathbf{M}\_1 \dot{\mathbf{e}}\_s^{-a},\tag{9}$$

where *M*<sup>1</sup> is creep ductility for A and B materials. Steady state creep rate for the A material is experimentally given by Eq. (10).

$$
\dot{\sigma\_{\rm SA}} = K\_A \sigma\_A^{m\_A} \tag{10}
$$

Using Eqns. (9) and (10), *tfA* is given by Eq. (11),

$$\mathbf{t}\_{\!\!\!\!A} = \mathbf{M}\_1 \mathbf{K}\_A \,^{-a} \sigma\_A^{-a m\_A} \tag{11}$$

where *tfA*, *εSA*\_ , *KA*, *σ<sup>A</sup>* and *mA* is the creep fracture life, the steady state creep strain rate, the material constant, the applied stress and power coefficient value of *σA*, obtained by creep tests for the A material, respectively.

When the steady state creep rate, *εSB*\_ for the B material is experimentally obtained by non-fracture test, substituting *εSB*\_ in to Eq. (9), the predictive creep fracture life, *tfB* for the B material is given by Eq. (12), because Eq. (9) is unique both for A and B materials.

$$t\_{\rm fb} = M\_1 \dot{\epsilon}\_{\rm SB}^{\cdot - a} \tag{12}$$

**Figure 4.** QL*\* line for A and B materials when the similarity law of creep deformation is valid both for A and B materials.*

**Figure 5.** *Flow chart of derivation method of the converted stress.*

Substituting *tfB* given by Eq. (12) into *tfA* in Eq. (11), the converted stress of the B material into that of the A material, *σBCA* is given by Eq. (13).

$$t\_{\!\!\!B} = M\_{\!\!1} A^{-a} \sigma\_{\!\!\! \!CA}^{-a \!\! m\_A} \tag{13}$$

where *σBCA* is the converted stress of the B material into that of the A material.

The converted stress of the B material into that of the A material, *σBCA* means applied stress which causes the equivalent steady state creep rate, *εSB*\_ for the A material given by Eq. (10).

Furthermore, the converted stress ratio, *η* is defined and it is written by Eq. (14).

$$\eta = \frac{1}{\eta^\*} = \frac{\sigma\_{BCA}}{\sigma\_B} \tag{14}$$

where *σ<sup>B</sup>* is actual applied stress for the B material, *η* <sup>∗</sup> is the converted strength, which is the inverse value of the converted stress ratio, η. η is a quantitative indicator of the MPCS.

For the case of *η*> 1*:*0, *σ<sup>B</sup>* <*σBCA* being valid, it means creep strength of the B material is lower than that of the A material.

For the case of *η*<1*:*0, *σ<sup>B</sup>* >*σBCA* being valid, it means creep strength of the B material is higher than that of the A material. The detailed derivation method is shown in **Figure 5**.

In addition, the concept of Δ*QL*<sup>∗</sup> is useful to discriminate the difference of the creep ductility caused by different materials or different local stress multi-axiality

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

**Figure 6.**

*The schematic illustration of the comparison of* QL*\* line between a notched specimen (C (T) specimen) and smooth specimen for Cr-Mo-v steel [12] and that between base metal and weld joint of C (T) specimen for P91 and P92 steels [14].*

characterized by *TF* <sup>¼</sup> <sup>3</sup>ð Þ *<sup>σ</sup>x*þ*σy*þ*σ<sup>z</sup> <sup>σ</sup>eq* <sup>¼</sup> <sup>3</sup>*σ<sup>P</sup> <sup>σ</sup>eq* such as weld joint, that is, the structural brittleness [13]. *σ<sup>P</sup>* is hydrostatic stress. *σeq* is equivalent stress.

Schematic illustration of experimental characteristics of Δ*QL*<sup>∗</sup> between a C (T) and a smooth specimens for Cr-Mo-V steel and a base metal and a weld joint of a notched specimen for P91 and P92 steels is shown in **Figure 6** [12, 14]. The difference in Δ*QL*<sup>∗</sup> between a C (T) and a smooth specimens is considered to be caused by the difference in compliance between a cracked specimen and a smooth specimen [12]. The difference in Δ*QL*<sup>∗</sup> between a base metal and a weld joint with a different weld metal will be caused by different local stress multi-axiality at the HAZ [8, 14]. For both cases, however, Δ*QL*<sup>∗</sup> , that is different creep ductility, exists, a parallel *QL*<sup>∗</sup> line appears [12, 14].

Using the concept of the converted stress and Δ*QL*<sup>∗</sup> , a quantitative estimation of MPCS and prediction of creep fracture can be conducted as shown in **Figures 5** and **6** mentioned in the Section 4.
