# Digital Scanning of Welds and Influence of Sampling Resolution on the Predicted Fatigue Performance: Modelling, Experiment and Simulation

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## Abstract

**:**

## 1. Introduction

- A framework for determining the scanning resolution needed for digital quality assurance of welded joints that is assessed on non-load carrying tee joints. The resolution requirements can then be directly incorporated in production for continuous quality assurance of welded structures.
- A modelling approach to predict the fatigue strength probability distribution based on measured weld geometry variation.

## 2. Experimental Investigation

#### 2.1. Topographic Scanning

#### 2.2. Weld Geometry Evaluation

^{®}qWeld (Winteria, Hudiksvall, Sweden) [32]. This is done to investigate and present the scatter in weld geometry for the investigated group of specimens independently from the simulations that is later carried out. This quality assurance system quantifies the weld geometry into geometric definitions as throat thickness, weld leg length, undercut, weld toe radius and weld toe angle using internal algorithms developed by Stenberg et al. [5,6]. The algorithm goes through each weld section with an internal algorithm which locates the weld toes and determines the weld toe radii and angle by a fitting routine. The accuracy of the method has been proven to be comparable to other commercial programs when the same reference block has been studied [5]. The accuracy has also been studied in [6]. The latter two geometrical parameters are presented in Figure 4 along the weld surface of specimen 24.

#### 2.3. Uniaxial Fatigue Testing

## 3. Probabilistic Fatigue Model

#### 3.1. Weakest-Link Area Model

#### 3.2. Multiaxial Considerations

## 4. Numerical Implementation of True Weld Geometry

_{p}) and the second corresponds to the cyclic loading of the specimen (prescribed rotation θ = π − θ

_{p}and applied nominal force F). Linear elastic material behaviour is implemented in the simulation model with a Young’s modulus of 200 GPa and a Poisson’s ratio of 0.3. The stress distribution for specimen 24 under cyclic loading is presented in Figure 11. The implemented simulation process is completely automated from start to finish to ensure that all specimens are analysed using the same conditions. The only manual input needed during the process is the location of the fatigue critical weld toe in the scanning data. The CPU (Intel(R) Core(TM) i9-10940X (14Core, 3.30GHz)/64GB RAM) simulation time for each specimen is around 1 h per specimen.

## 5. Evaluation of Failure Probability and Determination of Model Parameters

## 6. Influence of Sampling Resolution on Predicted Fatigue Failure Probability

#### 6.1. Sampling-Induced Uncertainty in Computed Fatigue Failure Probability

#### 6.2. Required Sampling Resolution

## 7. Concluding Remarks

- Digital scanning—the local weld geometries of more than 50 welded tee joints were measured with a high resolution of 50 μm.
- Fatigue testing—all measured specimens were fatigue tested at the same load level. The experimental fatigue failure probability was computed using median rank for each specimen that failed within 5 million cycles.
- Finite-element analysis—for each of the failed specimens during fatigue testing, the local stresses on the weld surface were computed from FE analysis using the Digital scanning data of the weld topography.
- Weakest-link failure probability—a two-parameter weakest-link area model was applied to model the fatigue failure probability based on the local stresses computed from the finite element analysis. The weakest-link parameters were determined by fitting the model probabilities to the experimental probabilities determined from the fatigue testing.
- Sensitivity analysis—the sensitivity of the computed Weakest-link failure probability to a reduction in sampling resolution was studied based on an arbitrarily chosen specimen. The digital scanning data was down-sampled to sampling resolutions in the range of 100 μm to 5 mm with different scanning start positions. A finite-element analysis was performed for each of the down-sampled scanned geometries and the corresponding failure probability was computed. The error and uncertainty in the computed probabilities due to the down-sampling was quantified and the required sampling resolution was determined by setting an allowable mean error.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${\alpha}_{\mathrm{wt}}$ | Weld toe angle | $k,q$ | Number of sub-areas and number of defects |

$\beta ,\lambda $ | Weibull shape and scale parameter | ||

${\Delta}_{\xi},{\Delta}_{\eta}$ | Element facet dimension | ${\mathrm{l}}_{\mathrm{ext},\mathrm{x}},{\mathrm{l}}_{\mathrm{ext},\mathrm{y}}$ | Extension of reference area |

${\theta}_{}$ | Rotational degree of freedom | $m$ | Basquin slope exponent |

${\theta}_{\mathrm{p}}$ | Plate angle | MSE | Mean square error |

${\lambda}_{0}$ | Fitting parameter | $n$ | Cycles to failure |

$\xi ,\eta $ | Local reference system parameters | ${n}_{\mathrm{seq}}$ | Number of scanning sequences |

${\rho}_{\mathrm{wt}}$ | Weld toe radius | ${n}_{\mathrm{spec}}$ | Number of tested specimens |

${\sigma}_{1}$ | Largest principal stress | ${p}_{\mathrm{f}}^{\mathrm{exp}}$ | Experimental failure probability |

$\mathrm{a}$ | Weld throat thickness | ${p}_{\mathrm{f}}^{\mathrm{WL}}$ | Weakest-link failure probability |

${A}_{\mathrm{ref}}$ | Reference surface area | $R$ | Fatigue load ratio |

${c}_{\mathrm{EM}}$ | Euler-Mascheroni constant | $r$ | Pearson correlation coefficient |

$dy,dz$ | Translational degree of freedom | ${s}_{\mathrm{eff}}$ | Effective stress amplitude |

${e}_{i}$ | Fitting error | ${s}_{\mathrm{equ}}$ | Equivalent stress amplitude |

$F$ | Applied nodal force | $\mathrm{w}$ | Specimen width |

${F}_{S}$ | Weibull probability distribution | $x$ | Spatial position |

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**Figure 3.**Sampling resolution (mm) for different combinations of scanning speeds (mm/s) and sampling frequencies (Hz).

**Figure 4.**(

**a**) Weld geometry definitions and (

**b**) variation measured by the Winteria

^{®}qWeld [32] system for specimen 24.

**Figure 8.**(

**a**) Measured area and (

**b**) reference area of the welded joint used in the Weakest-link area model.

**Figure 11.**Stress distribution at the weld surface of the specimen 24 (failure order 17 in Table 1) for a nominal stress of 180 MPa.

**Figure 12.**Numerical fatigue strength estimations at the corresponding fatigue life determined from experimental testing.

**Figure 13.**Resampling of scanning data by excluding weld profiles. Each row represents a sampled sequence including only the profiles with filled cells.

**Figure 14.**Influence of starting position on the model failure probability at different sampling resolutions. (

**a**) 200 μm sampling resolution, (

**b**) 250 μm sampling resolution, (

**c**) 500 μm sampling resolution, (

**d**) 1000 μm sampling resolution, (

**e**) 2000 μm sampling resolution.

**Figure 15.**Influence of sampling resolution on (

**a**) the computed Weakest-link failure probability of 1 digitally scanned specimen and (

**b**) the relative absolute error in the computed probability with respect to the highest resolution (50 μm). At each sampling resolution, different sampling sequences are marked by crosses.

**Table 1.**Fatigue test data for single-pass tee joint test specimens and median rank estimates. All specimens are fatigue-loaded at R = 0.1 and amplitude 180 MPa.

Failure Order i | Cycles [-] | Median Rank, ${\mathit{p}}_{\mathbf{f},\mathit{i}}^{\mathbf{exp}}$ | Failure Order i | Cycles | Median Rank, ${\mathit{p}}_{\mathbf{f},\mathit{i}}^{\mathbf{exp}}$ |
---|---|---|---|---|---|

1 | 296319 | 0.0187 | 20 | 796070 | 0.5267 |

2 | 319754 | 0.0455 | 21 | 844067 | 0.5535 |

3 | 358569 | 0.0722 | 22 | 874843 | 0.5802 |

4 | 450880 | 0.0989 | 23 | 875982 | 0.6070 |

5 | 479592 | 0.1257 | 24 | 911631 | 0.6337 |

6 | 491902 | 0.1524 | 25 | 942420 | 0.6604 |

7 | 499422 | 0.1791 | 26 | 978798 | 0.6872 |

8 | 554425 | 0.2059 | 27 | 998173 | 0.7139 |

9 | 577447 | 0.2326 | 28 | 1017389 | 0.7406 |

10 | 601596 | 0.2594 | 29 | 1067794 | 0.7674 |

11 | 621224 | 0.2861 | 30 | 1102915 | 0.7941 |

12 | 637281 | 0.3128 | 31 | 1159417 | 0.8209 |

13 | 644313 | 0.3396 | 32 | 1199808 | 0.8476 |

14 | 697257 | 0.3663 | 33 | 1259817 | 0.8743 |

15 | 707011 | 0.3930 | 34 | 1478800 | 0.9010 |

16 | 712686 | 0.4198 | 35 | 1563887 | 0.9278 |

17 | 739705 | 0.4465 | 36 | 1960249 | 0.9545 |

18 | 761384 | 0.4733 | 37 | 2418827 | 0.9813 |

19 | 781303 | 0.5 |

Parameter | Implemented Value |
---|---|

$\mathrm{a}$ | 4 mm |

$\mathrm{w}$ | 60 mm |

${\mathrm{l}}_{\mathrm{ext},\mathrm{x}}$ | 10 mm |

${\mathrm{l}}_{\mathrm{ext},\mathrm{y}}$ | 8 mm |

$\mathrm{t}$ | 6 mm |

${A}_{\mathrm{ref}}$ | 881.2 mm^{2} |

Weakest-Link Fitting Parameters | Accuracy Metrics | ||
---|---|---|---|

β (-) | λ_{0} (MPa) | $RMSE$ | r |

8.22 | 314 | 0.121 | 0.903 |

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**MDPI and ACS Style**

Hultgren, G.; Myrén, L.; Barsoum, Z.; Mansour, R.
Digital Scanning of Welds and Influence of Sampling Resolution on the Predicted Fatigue Performance: Modelling, Experiment and Simulation. *Metals* **2021**, *11*, 822.
https://doi.org/10.3390/met11050822

**AMA Style**

Hultgren G, Myrén L, Barsoum Z, Mansour R.
Digital Scanning of Welds and Influence of Sampling Resolution on the Predicted Fatigue Performance: Modelling, Experiment and Simulation. *Metals*. 2021; 11(5):822.
https://doi.org/10.3390/met11050822

**Chicago/Turabian Style**

Hultgren, Gustav, Leo Myrén, Zuheir Barsoum, and Rami Mansour.
2021. "Digital Scanning of Welds and Influence of Sampling Resolution on the Predicted Fatigue Performance: Modelling, Experiment and Simulation" *Metals* 11, no. 5: 822.
https://doi.org/10.3390/met11050822