# A Numerical Study into the Effect of Machining on the Interaction between Surface Roughness and Surface Breaking Defects on the Durability of WAAM Ti-6Al-4V Parts

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## Abstract

**:**

## 1. Introduction

- (i)
- Advanced manufacturing can be used to address the readiness challenges posed by parts obsolescence, diminishing sources of supply, and sustained operations in austere environments.
- (ii)
- If employed to the maximum extent, advanced manufacturing could transform battlefield logistics through on-demand fabrication of parts close to the point of need, thus reducing the large number of parts stored and transported around the world.

^{p}

_{thr})/(1 − K

_{max}/A)

^{1/2}

_{max}and K

_{min}are the maximum and minimum values of the stress intensity factor seen in the cycle, ∆K = (K

_{max}− K

_{min}) is the range of the stress intensity factor that is seen in a cycle, ΔK

_{thr}is the “effective fatigue threshold”, and A is the cyclic fracture toughness. A related formulation is given in [59], where it is shown to be able to represent the growth of cracks that nucleate from near surface porosity. As explained in [32], the terms ∆K

_{thr}and A are best interpreted as parameters that are chosen so as to fit the measured da/dN versus ∆K data.

_{thr}and A, then each of the da/dN versus ∆κ curves in the 30 different tests analysed in [48], the 34 different tests in [49], and the 13 different tests in [50] all collapse onto the same master curve. As such, for both conventionally and AM Ti-6Al-4V the values of D (=2.79 × 10

^{−10}) and p (=2.12) are true materials constants, and remain the same for each of these seventy seven tests. The mean value of A given in [49] for as-built AM Ti-6Al-4V surfaces is 62 MPa √m.

_{thr}and A then the da/dN versus ∆κ curves collapse to a single curve, to a wide range of conventionally manufactured, AM and cold spray additively manufactured (CSAM) materials are given in [53,54].

- (a)
- The effect of different AM processes;
- (b)
- The effect of different build directions;
- (c)
- The residual stress fields induced by the different manufacturing process;
- (d)

## 2. Materials and Methods

## 3. On the Interaction between Surface Roughness and Surface Breaking Defects on the Durability of WAAM Ti-6Al-4V Parts

^{−10}, p = 2.12, and A = 62 MPa $\sqrt{\mathrm{m}}$. As noted above, this value of A represents the mean value given in [49] for as-built AM Ti-6Al-4V. The durability analysis requires the stress intensity factor solutions along the crack front to be determined as the crack grows. The approach adopted in this study to determine the stress intensity factor solutions is as outlined in [60]. This is a semi-analytical approach which has the advantage that it only uses the uncracked finite element model, and that the cracks are not explicitly modelled; see [60] for more details.

## 4. Effect of Machining the Rough Surfaces

## 5. Conclusions

- Comparing the fatigue life-associated surfaces left in the unmachined state, the durability of an AM part appears to be a relatively strong function of the local radius of the curvature of the trough associated with the rough surfaces.
- Surfaces with tall narrow roughness exhibit the largest reductions in fatigue life and these cases do not overly benefit from partial machining of the surface.
- The size of the initial material discontinuities, porosity, lack of fusion, etc., associated with the AM process appears to strongly affect the fatigue life of the part.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**The effect of surface roughness on the fatigue life from an initial semi-elliptical defect size of 0.03 mm. Case 1 is the baseline specimen with no surface roughness.

**Figure 9.**The effect of surface roughness on the fatigue life from an initial semi-elliptical defect size of 0.254 mm. Case 1 is the baseline specimen with no surface roughness.

**Figure 10.**The assumed machined surface profile for case when the original peak to trough height was 0.363 mm.

**Figure 11.**The assumed machined surface profile for case when the original peak to trough height was 0.141 mm.

**Figure 12.**The local stress field associated with Case 5, which is the “machined” version of Case 6.

**Figure 13.**The local stress field associated with the Case 8, which is the “machined” version of Case 9.

**Figure 14.**An expanded view of the stress field associated with Figure 6.

d (mm) | Case | Surface Machined | T (mm) | Computed Life (Cycles) | |||
---|---|---|---|---|---|---|---|

Semi-Circular Surface Crack | Reduction * in Fatigue Life (% diff) | Corner (Quadrant) Crack | Reduction * in Fatigue Life (% diff) | ||||

1.57 | 1 | No | 0 | 16786 | Baseline | 16428 | Baseline |

2 | Yes | 0.071 | 9877 | 41.2 | 9610 | 41.5 | |

3 | No | 0.142 | 7418 | 55.8 | 8018 | 51.2 | |

4 | No | 0.1815 | 7112 | 57.6 | 6896 | 58.0 | |

5 | Yes | 0.1815 | 5699 | 66.0 | 6162 | 62.5 | |

6 | No | 0.363 | 2888 | 82.8 | 4971 | 67.7 | |

2.42 | 1 | No | 0 | 16786 | Baseline | 16428 | Baseline |

7 | No | 0.071 | 12585 | 25.0 | 13270 | 19.2 | |

8 | Yes | 0.071 | 10464 | 37.7 | 10578 | 35.5 | |

9 | No | 0.142 | 9765 | 41.8 | 10235 | 37.7 |

d (mm) | Case | Surface Machined | T (mm) | Computed Life (Cycles) | |||
---|---|---|---|---|---|---|---|

Semi-Circular Surface Crack | Reduction in Fatigue Life (% diff) from the Baseline | Corner (Quadrant) Crack | Reduction in Fatigue Life (% diff) from the Baseline | ||||

1.57 | 1 | No | 0 | 5875 | Baseline | 5639 | Baseline |

2 | Yes | 0.071 | 3275 | 44.3 | 3401 | 39.7 | |

3 | No | 0.142 | 2746 | 53.3 | 3058 | 45.8 | |

4 | No | 0.1815 | 2399 | 59.2 | 2186 | 61.2 | |

5 | Yes | 0.1815 | 2186 | 62.8 | 2468 | 56.2 | |

6 | No | 0.363 | 1135 | 80.7 | 1924 | 65.9 | |

2.42 | 1 | No | 0 | 5875 | Baseline | 5639 | Baseline |

7 | No | 0.071 | 4536 | 22.8 | 4701 | 16.6 | |

8 | Yes | 0.071 | 3693 | 37.1 | 3883 | 31.1 | |

9 | No | 0.142 | 3463 | 41.1 | 3730 | 33.9 |

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## Share and Cite

**MDPI and ACS Style**

Peng, D.; Jones, R.; Ang, A.S.M.; Champagne, V.; Birt, A.; Michelson, A.
A Numerical Study into the Effect of Machining on the Interaction between Surface Roughness and Surface Breaking Defects on the Durability of WAAM Ti-6Al-4V Parts. *Metals* **2022**, *12*, 1121.
https://doi.org/10.3390/met12071121

**AMA Style**

Peng D, Jones R, Ang ASM, Champagne V, Birt A, Michelson A.
A Numerical Study into the Effect of Machining on the Interaction between Surface Roughness and Surface Breaking Defects on the Durability of WAAM Ti-6Al-4V Parts. *Metals*. 2022; 12(7):1121.
https://doi.org/10.3390/met12071121

**Chicago/Turabian Style**

Peng, Daren, Rhys Jones, Andrew S. M. Ang, Victor Champagne, Aaron Birt, and Alex Michelson.
2022. "A Numerical Study into the Effect of Machining on the Interaction between Surface Roughness and Surface Breaking Defects on the Durability of WAAM Ti-6Al-4V Parts" *Metals* 12, no. 7: 1121.
https://doi.org/10.3390/met12071121