# Estimation of C* Integral for Mismatched Welded Compact Tension Specimen

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions in the chemical and petrochemical industries and in thermal power plants. Increasing the operating temperatures of the plant increases the energy efficiency, thus reducing CO

_{2}emissions. Higher operating temperatures and higher stresses increase the risk of welded structure failure due to creep conditions. It is therefore necessary to develop a method to predict the CCG in welded joints [3].

## 2. Numerical Analysis

#### 2.1. Geometry and Loading

^{−3/2}.

#### 2.2. Material Properties

_{BM}= 1 × 10

^{−20}(MPa)

^{−n}h

^{−1}and n

_{BM}= 7. To investigate the influence of material constraints on the C* integral in welded joints, different configurations of material mismatch in creep strain rate of BM, WM and HAZ were designed. The material creep properties for HAZ and WM were chosen so that the creep strain rate was lower or higher than that of BM. This was achieved by varying the constant A. The creep exponent n for BM, WM and HAZ was identical (n

_{BM}= n

_{WM}= n

_{HAZ}= 7). The effect of the mismatch in the creep properties for WM and HAZ relative to BM is expressed by the mismatch factor. These mismatch factors are defined as follows [18]:

_{WM}and MF

_{HAZ}factors are 10, 1 and 0.1, respectively. Thus, in order to investigate the effect of material constraints on the C* integral, nine possible combinations of material mismatch were considered, as shown in Table 1.

#### 2.3. Finite Element Analysis

_{I}and C* obtained by FE analyses with analytical solutions for CT specimen [22,23]. It is evident that the FE results provide confidence in the FE analyses for elastic and steady-state creep conditions.

## 3. Results and Discussion

_{HAZ}, MF

_{WM}and W/h on the factor φ for the ratio a/W = 0.5. It can be seen that MF

_{HAZ}has a strong influence on the factor φ for the considered values of MF

_{WM}and W/h. Values of φ are highest for creep-soft HAZ (MF

_{HAZ}= 0.1). It can be seen that these values are significantly higher than one, meaning that the C* integral is lower than the C* integral for a homogeneous CT specimen. A larger C* integral causes a higher rate of CCG. For a given value of MF

_{HAZ}, the factor φ is higher if MF

_{WM}is lower. For creep-hard HAZ (MF

_{HAZ}= 10), the values of φ are mostly lower than one, meaning that the C* integral is less than the C* integral for a homogeneous CT specimen. The influence of W/h on the φ factor is significant for creep-soft HAZ. The factor φ is higher for the larger HAZ width h (lower W/h ratio).

_{HAZ}and MF

_{WM}at the ratio W/h = 6.

_{HAZ}on φ are quite complex. For creep-hard HAZ (MF

_{HAZ}= 10), the values of φ are lower than one for all considered values of a/W. The value of φ becomes lower and asymptotically approaches a constant value as a/W increase. The value of MF

_{WM}has almost no effect on φ when a/W ≥ 0.7.

_{HAZ}= 1), the values of φ in the range 0.5 ≤ a/W ≤ 0.7 are higher than one if WM is creep-soft material (MF

_{WM}= 0.1). On the other side, for creep-hard WM (MF

_{WM}= 10) and range 0.5 ≤ a/W ≤ 0.7 the values of φ are lower than one. In both cases, for values of a/W > 0.7, the value of φ asymptotically approaches one. For creep match WM the value of φ is one for all considered values of a/W. This is expected because it is in fact a homogeneous material.

_{HAZ}= 0.1), the values of φ are significantly higher than one for all considered values of a/W. The value of φ becomes higher and asymptotically approaches a constant value as a/W increase. The value of MF

_{WM}has almost no effect on φ when a/W ≥ 0.7.

_{HAZ}and MF

_{WM}at the ratio W/h = 8. Thus, for a/W = 0.5 and MF

_{HAZ}= 10, the corresponding values of φ for W/h = 8 are higher than those for W/h = 6. Likewise, for a/W = 0.5 and MF

_{HAZ}= 0.1, the corresponding values of φ for W/h = 8 are lower than those for W/h = 6. In both cases, the value of φ asymptotically approaches a constant value as a/W increase. For a/W = 0.5 and MF

_{HAZ}= 1 and if WM is creep-soft material (MF

_{WM}= 0.1), the value of φ for W/h = 8 is higher than this for W/h = 6. For a/W = 0.5 and MF

_{HAZ}= 1 and if WM is creep-hard material (MF

_{WM}= 10), the value of φ for W/h = 8 is lower than this for W/h = 6. In the case where WM and HAZ are creep match materials, the value of φ is one for all considered a/W ratios.

_{HAZ}, MF

_{WM}and a/W for all W/h ratios, it can be generally concluded that there is a strong and complex influence of material and geometry constraints on the CCG rate. If the HAZ creep is a soft material, which is often the practice [18], the factor φ will have values higher than one. This means that the C* integral will be higher than the C* integral for homogenic material, so the CCG rate will also be higher. It is clear that a higher CCG rate means a shorter lifetime of the welded structure.

_{n}is quantity that depends on exponent n and the stress condition, ${\widehat{\sigma}}_{ij}$. and ${\widehat{\epsilon}}_{ij}$ are angular functions. Analyzing the diagrams in Figure 4, Figure 5 and Figure 6, it can be clearly concluded that the values of φ change with different combination of MF

_{HAZ}, MF

_{WM}, W/h and a/W. Different combinations of these parameters change the crack-tip constraint effect, and thus the magnitude of the crack-tip stress and strain rate. A higher magnitude of crack-tip stress and strain rate means a higher value of the C* integral, and thus a higher value of φ.

_{HAZ}, MF

_{WM}, a/W and W/h. This is the following expression:

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 4.**Dependence φ factor on MF

_{HAZ}, MF

_{WM}and W/h for a/W = 0.5: (

**a**) MF

_{WM}= 10; (

**b**) MF

_{WM}= 1; (

**c**) MF

_{WM}= 0.1.

**Figure 5.**Dependence φ factor on MF

_{HAZ}, MF

_{WM}and a/W for W/h = 6: (

**a**) MF

_{HAZ}= 10; (

**b**) MF

_{HAZ}= 1; (

**c**) MF

_{HAZ}= 0.1.

**Figure 6.**Dependence φ factor on MF

_{HAZ}, MF

_{WM}and a/W for W/h = 8: (

**a**) MF

_{HAZ}= 10; (

**b**) MF

_{HAZ}= 1; (

**c**) MF

_{HAZ}= 0.1.

MF_{WM} | MF_{HAZ} |
---|---|

10 | 0.1 |

10 | 1 |

10 | 10 |

1 | 0.1 |

1 | 1 |

1 | 10 |

0.1 | 0.1 |

0.1 | 1 |

0.1 | 10 |

K_{I}(FE)/K_{I} | 1.005 | |

C*(FE)/C* | n = 5 | 0.978 |

n = 10 | 0.982 |

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**MDPI and ACS Style**

Katinić, M.; Turk, D.; Konjatić, P.; Kozak, D. Estimation of *C** Integral for Mismatched Welded Compact Tension Specimen. *Materials* **2021**, *14*, 7491.
https://doi.org/10.3390/ma14247491

**AMA Style**

Katinić M, Turk D, Konjatić P, Kozak D. Estimation of *C** Integral for Mismatched Welded Compact Tension Specimen. *Materials*. 2021; 14(24):7491.
https://doi.org/10.3390/ma14247491

**Chicago/Turabian Style**

Katinić, Marko, Dorian Turk, Pejo Konjatić, and Dražan Kozak. 2021. "Estimation of *C** Integral for Mismatched Welded Compact Tension Specimen" *Materials* 14, no. 24: 7491.
https://doi.org/10.3390/ma14247491