# Effects of the Crack Tip Constraint on the Fracture Assessment of an Al 5083-O Weldment for Low Temperature Applications

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Constraint-based Failure Assessment

#### 2.1. The $J$-$Q$ Theory

#### 2.2. Modification of Failure Assessment Diagram (FAD)

## 3. Experimental Procedure

#### 3.1. Material and Tensile Test

#### 3.2. Fracture Toughness Test

## 4. Numerical Procedure

## 5. Results and Discussion

#### 5.1. Results of Fracture Toughness Test

#### 5.2. Discussion of $Q$ Parameter in CT Specimen

#### 5.3. Constraint-Based FAD for the Al 5083-O Weldment at Cryogenic Temperature

#### 5.4. Fracture Assessment for the Welded Joints of Al 5083-O with a Surface Flaw

## 6. Concluding Remarks

- The CTOD values of Al 5083-O at cryogenic temperature were higher than those at room temperature for both the base metal and weldments. In case of the weldment, the average CTOD values were 0.74 mm and 0.91 mm, at room and cryogenic temperatures, respectively. This was attributed to the slower crack opening behavior of the Al 5083-O weldment at cryogenic temperature than room temperature.
- The $Q\text{}$parameter decreases rapidly with increasing applied load. Moreover, the $Q$ parameter values for a shallow crack were calculated to be lower than the values of a deep crack. On the limit load, the $Q$ parameter values of the CT specimen corresponding to a/W = 0.2, 0.3, 0.4, and 0.5 at cryogenic temperature were found to be in the range between −0.55, −0.46, −0.37, and −0.29. No significant temperature effect in the $Q$ parameter was observed in the case of the Al 5083-O weldment.
- Based on the $J$-$Q$ approach, the critical J integral values of the CT specimen corresponding to a/W = 0.2–0.5 were determined using the modified RKR form. As expected, the critical J integral value were found to be inversely proportional to the $Q$ parameter as the crack length increased, with respect to the ligament of the CT specimen. The $\alpha $ and $k$ values, which are the constants of constraint-based FAD, for the Al 5083-O weldment at cryogenic temperature, were found to be 1.544 and 3.418, respectively. With the $J$-$Q$ locus calculated in this study for the weldment of Al 5083-O, the fracture toughness with different constraint levels at cryogenic temperature can be estimated readily. In other words, the critical J integral value can be evaluated conveniently using the $J$-$Q$ locus without requiring further fracture toughness tests.
- The conventional fracture assessment method based on BS 7910 Option 1 FAD produces excessively conservative results if the constraint effect is not considered properly. Based on this study, the maximum allowable stress for the welded plate with a surface flaw of Al 5083-O, which was calculated by the constraint-based FAD, is 29% higher than that obtained from the Option 1 FAD. Therefore, the constraint-based FAD procedure is essential for avoiding overly conservative prediction of the allowable stress from a practical point of view.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Schematic diagram of the relationship between the constraint and specimen geometry on the fracture toughness.

**Figure 3.**Comparison of the fracture assessment procedures between the conventional (BS 7910) and constraint-based (this study) approaches.

**Figure 4.**Dimensions of the compact tension (CT) specimen for the fracture toughness test (unit: mm).

**Figure 5.**(

**a**) Finite element model for the CT specimen; (

**b**) assignment of the material properties (a/W = 0.5).

**Figure 8.**Comparison of the $Q$ parameters for the weldment with respect to different a/W ratios at room and cryogenic temperatures.

**Figure 10.**Approximation of the crack tip constraint and ${K}_{mat}^{c}$ to obtain $\alpha $ and $k$ in Equation (13).

**Figure 11.**Comparison of the conventional and constraint-based FADs for various crack ligament ratios.

**Figure 13.**Constraint-based FADs for the welded plate of Al 5083-O with various crack configurations (

**a**) a/B = 0.2, (

**b**) a/B = 0.3, (

**c**) a/B = 0.4, and (

**d**) a/B = 0.5.

**Figure 14.**Failure assessment points for the welded plate of Al-5083 based on BS 7910 Option 1 and the constraint-corrected FADs, with different crack configurations (

**a**) a/c = 0.2; (

**b**) a/c = 0.3; (

**c**) a/c = 0.4; and (

**d**) a/c = 0.5.

**Figure 15.**Comparison of the residual strength distribution for the welded plate of Al 5083-O with different crack configurations at cryogenic temperature (

**a**) a/c = 0.2; (

**b**) a/c = 0.3; (

**c**) a/c = 0.4; and (

**d**) a/c = 0.5.

Si | Fe | Cu | Mn | Mg | Cr | Zn | Ti | Cr_{eq} | |
---|---|---|---|---|---|---|---|---|---|

Chemical composition (wt. %) | 0.07 | 0.20 | 0.02 | 0.60 | 4.80 | 0.07 | 0.01 | 0.02 | 0.223 |

Welding Method | Filler Metal | Groove Shape | Current [A] | Voltage [V] | Speed [cm/min] |
---|---|---|---|---|---|

MIG welding | ER5183 | Double V | 550 | 30 | 36 |

Material | Temp. | Yield Strength [MPa] | Tensile Strength [MPa] | Elastic Modulus [GPa] | Elongation [%] | Strain Hardening Exponent | Material Constant |
---|---|---|---|---|---|---|---|

Base metal | Room | 166 | 326 | 61 | 23 | 7 | 0.735 |

Cryogenic | 189 | 373 | 70 | 26 | 7.13 | 0.741 | |

Weld metal | Room | 157 | 307 | 61 | 20 | 6.83 | 0.777 |

Cryogenic | 175 | 365 | 75 | 23 | 6.43 | 0.857 |

Specimen (a/W = 0.5) | Temp. | CTOD (avg.) [mm] | Max. Load [kN] | CMOD [mm] |
---|---|---|---|---|

Base metal | Room | 0.70 | 46 | 2.50 |

Cryogenic | 0.83 | 57 | 3.03 | |

Weld metal | Room | 0.74 | 44 | 2.88 |

Cryogenic | 0.91 | 52 | 3.35 |

Flaw Type | a [mm] | 2c [mm] | a/B | a/c |
---|---|---|---|---|

5 × 50 | 5 | 50 | 0.2 | 0.2 |

7.5 × 60 | 7 | 60 | 0.3 | 0.25 |

10 × 100 | 10 | 100 | 0.4 | 0.2 |

12.5 × 100 | 12.5 | 100 | 0.5 | 0.25 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Moon, D.H.; Park, J.Y.; Kim, M.H.
Effects of the Crack Tip Constraint on the Fracture Assessment of an Al 5083-O Weldment for Low Temperature Applications. *Materials* **2017**, *10*, 815.
https://doi.org/10.3390/ma10070815

**AMA Style**

Moon DH, Park JY, Kim MH.
Effects of the Crack Tip Constraint on the Fracture Assessment of an Al 5083-O Weldment for Low Temperature Applications. *Materials*. 2017; 10(7):815.
https://doi.org/10.3390/ma10070815

**Chicago/Turabian Style**

Moon, Dong Hyun, Jeong Yeol Park, and Myung Hyun Kim.
2017. "Effects of the Crack Tip Constraint on the Fracture Assessment of an Al 5083-O Weldment for Low Temperature Applications" *Materials* 10, no. 7: 815.
https://doi.org/10.3390/ma10070815