Correction: Wang et al. Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile. Materials 2020, 13, 4639

Yixun Wang; Yuxiao Luo; Seiichiro Tsutsumi

doi:10.3390/ma14092433

The authors wish to revise the following from pages 16–18 in the text of Appendix B [1] due to the presence of incorrect information.

The correct text is shown below:

Appendix B

Formulas for calculating SCFs for T-shape welded joint and cruciform welded joint under tensile and bending stress.

(1): T-shape welded joint under tensile stress:

$K_{t} = 1 + 1.39418 \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1}))$

(A5)

where:

$\begin{array}{l} f (r_{1} / t) = & 1.824174 \cdot {(r_{1} / t)}^{- 0.145045} + 6.400210 \cdot {(r_{1} / t)}^{3} - 6.802011 \cdot {(r_{1} / t)}^{2} + 3.277059 \cdot (r_{1} / t) \\ - 2.692331 \end{array}$

$f (θ_{1}) = - 2.778232 \times 10^{- 1} \cdot {(π - θ_{1})}^{3} + 1.531999 \cdot {(π - θ_{1})}^{2} - 3.394907 \cdot (π - θ_{1}) + 4.967130$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & - 1.001612 \times 10^{1} \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} + 1.279269 \times 10^{1} \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} \\ + 5.761117 \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 1.181649 \end{array}$
(2): T-shape welded joint under bending stress:

$\begin{array}{l} K_{t} = & 1 - 1.129553 \cdot f (T / t) \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \\ \cdot f ((L_{1} / t) \cdot (L_{2} / t)) \cdot f (H / t) \end{array}$

(A6)

where:

$f (T / t) = - 9.622916 \times 10^{- 3} \cdot {(T / t)}^{3} - 3.157009 \times 10^{- 2} \cdot {(T / t)}^{2} + 1.848086 \times 10^{- 1} \cdot (T / t) + 2.433139$

$\begin{array}{l} f (r_{1} / t) = & 6.477191 \times 10^{- 1} \cdot {(r_{1} / t)}^{- 0.258620} + 2.860640 \cdot {(r_{1} / t)}^{3} - 3.689862 \cdot {(r_{1} / t)}^{2} \\ + 2.089786 \cdot (r_{1} / t) - 1.238719 \end{array}$

$\begin{array}{l} f (θ_{1}) = & 3.450624 \times 10^{- 3} \cdot {(π - θ_{1})}^{3} - 3.531382 \times 10^{- 2} \cdot {(π - θ_{1})}^{2} + 6.008736 \times 10^{- 2} \cdot (π - θ_{1}) \\ + 8.576512 \times 10^{- 2} \end{array}$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 3.532021 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{5.127981} - 8.442514 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} \\ + 8.645182 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + 1.481668 \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 3.814145 \times 10^{- 1} \end{array}$

$\begin{array}{l} f (L_{1} / t) = & - 1 . 140609 \times 10^{1} \cdot {(L_{1} / t)}^{3.036113} + 7.436459 \times 10^{- 2} \cdot {(L_{1} / t)}^{4} + 1.188223 \times 10^{1} \cdot {(L_{1} / t)}^{3} \\ - 8 . 150334 \times 10^{- 1} \cdot {(L_{1} / t)}^{2} + 2 . 933742 \times 10^{- 1} \cdot (L_{1} / t) + 2 . 718308 \times 10^{- 2} \end{array}$

$\begin{array}{l} f (L_{2} / t) = & 1.919634 \times 10^{1} \cdot {(L_{2} / t)}^{- 0.1508265} - 7.315526 \times 10^{- 1} \cdot {(L_{2} / t)}^{4} + 4.967357 \cdot {(L_{2} / t)}^{3} \\ - 8.382442 \cdot {(L_{2} / t)}^{2} - 5.482638 \cdot (L_{2} / t) + 4.359819 \times 10^{1} \end{array}$

$\begin{array}{l} f ((L_{1} / t) \cdot (L_{2} / t)) = & - 1.823407 \times 10^{- 1} \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} + 1.469586 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} \\ - 5.862377 \cdot ((L_{1} / t) \cdot (L_{2} / t)) - 8.301064 \end{array}$

$f (H / t) = - 1.913752 \times 10^{1} \cdot {(H / t)}^{3} + 7.690410 \cdot {(H / t)}^{2} - 5.994878 \times 10^{- 1} \cdot (H / t) + 1.201826$
(3): Cruciform welded joint under tensile stress:

$\begin{array}{l} K_{t} = & 1 + 9.355385 \times 10^{- 1} \cdot f (T / t) \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \cdot \\ f ((L_{1} / t) \cdot (L_{2} / t)) \cdot f (H / t) \end{array}$

(A7)

where:

$f (T / t) = - 4.241098 \times 10^{- 1} \cdot {(T / t)}^{3} + 1.392836 \cdot {(T / t)}^{2} - 1.072866 \cdot (T / t) + 5.223873$

$\begin{array}{l} f (r_{1} / t) = & - 2.214616 \cdot {(r_{1} / t)}^{0.5081972} + 3.365455 \cdot {(r_{1} / t)}^{3} - 4.439046 \cdot {(r_{1} / t)}^{2} + 3.726006 \cdot (r_{1} / t) \\ + 4.033244 \times 10^{- 1} \end{array}$

$f (θ_{1}) = - 7.886656 \times 10^{- 1} \cdot {(π - θ_{1})}^{3} + 2.966534 \cdot {(π - θ_{1})}^{2} - 5.878541 \cdot (π - θ_{1}) + 1.772818 \times 10^{1}$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 1.557408 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{- 0.1158765} + 3.821716 {((r_{1} / t) \cdot (π - θ_{1}))}^{3} \\ - 5.354226 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + 7.153383 \cdot ((r_{1} / t) \cdot (π - θ_{1})) - 1.529427 \end{array}$

$\begin{array}{l} f (L_{1} / t) = & 8.158610 \cdot {(L_{1} / t)}^{1.944849} - 1.90075 \times 10^{- 2} \cdot {(L_{1} / t)}^{4} + 2.021235 \times 10^{- 1} \cdot {(L_{1} / t)}^{3} - 7.977936 \cdot {(L_{1} / t)}^{2} \\ - 4.569099 \times 10^{- 1} \cdot (L_{1} / t) + 1.108427 \times 10^{- 1} \end{array}$

$\begin{array}{l} f (L_{2} / t) = & 1.020926 \times 10^{1} \cdot {(L_{2} / t)}^{0.09585178} + 3.856400 \times 10^{- 1} \cdot {(L_{2} / t)}^{4} - 2.432551 \cdot {(L_{2} / t)}^{3} \\ + 6.069561 \cdot {(L_{2} / t)}^{2} - 8.045796 \cdot (L_{2} / t) - 5.364472 \end{array}$

$\begin{array}{l} f ((L_{1} / t) \cdot (L_{2} / t)) = & - 2.421137 \times 10^{- 1} \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} + 5.706142 \times 10^{- 1} \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} \\ - 2.159502 \times 10^{1} \cdot ((L_{1} / t) \cdot (L_{2} / t)) - 2.240262 \end{array}$

$f (H / t) = 4.996101 \cdot {(H / t)}^{3} - 1.461031 \cdot {(H / t)}^{2} - 1.874919 \times 10^{- 1} \cdot (H / t) - 1.083093$
(4): Cruciform welded joint under bending stress:

$K_{t} = 1 + 1.20077 \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \cdot f ((L_{1} / t) \cdot (L_{2} / t))$

(A8)

where:

$f (r_{1} / t) = 1.245919 \cdot {(r_{1} / t)}^{- 0.1788861} + 5.187295 \cdot {(r_{1} / t)}^{3} - 5.888376 \cdot {(r_{1} / t)}^{2} + 2.948041 \cdot (r_{1} / t) - 2.024161$

$f (θ_{1}) = 4.518553 \times 10^{- 1} \cdot {(π - θ_{1})}^{3} - 4.169720 \cdot {(π - θ_{1})}^{2} + 6.471859 \cdot (π - θ_{1}) + 1.232356 \times 10^{1}$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 6.195167 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{1.958767} + 2.102936 \times 10^{- 1} \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} \\ - 6.258362 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + 4.307112 \times 10^{- 2} \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 1.578839 \times 10^{- 2} \end{array}$

$f (L_{1} / t) = 1.069048 \times 10^{- 1} \cdot {(L_{1} / t)}^{3} + 4.896665 \times 10^{- 1} \cdot {(L_{1} / t)}^{2} - 3.181390 \cdot (L_{1} / t) + 1.187674 \times 10^{1}$

$\begin{array}{l} f (L_{2} / t) = & 6.217977 \cdot {(L_{2} / t)}^{2.938345} + 8.220848 \times 10^{- 2} \cdot {(L_{2} / t)}^{4} - 5.872895 \cdot {(L_{2} / t)}^{3} - 5.835022 \times 10^{- 1} \cdot {(L_{2} / t)}^{2} \\ + 1.809699 \times 10^{- 1} \cdot (L_{2} / t) + 2.220297 \times 10^{- 2} \end{array}$

$\begin{array}{l} f ((L_{1} / t) \cdot (L_{2} / t)) = & - 9.639892 \times 10^{- 2} \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} - 2.213564 \times 10^{- 1} \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} \\ + 5.660853 \cdot ((L_{1} / t) \cdot (L_{2} / t)) + 3.300823 \times 10^{1} \end{array}$

The previously given text is shown below:

Appendix B

Formulas for calculating SCFs for T-shape welded joint and cruciform welded joint under tensile and bending stress.

(1): T-shape welded joint under tensile stress:

$K_{t} = 1 + 1.394 \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1}))$

(A5)

where:

$f (r_{1} / t) = 1.824 \cdot {(r_{1} / t)}^{- 0.145} + 6.400 \cdot {(r_{1} / t)}^{3} - 6.802 \cdot {(r_{1} / t)}^{2} + 3.277 \cdot (r_{1} / t) - 2.692$

$f (θ_{1}) = - 0.278 \cdot {(π - θ_{1})}^{3} + 1.532 \cdot {(π - θ_{1})}^{2} - 3.395 \cdot (π - θ_{1}) + 4.967$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & - 10.016 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} + 12.793 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + \\ 5.761 \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 1.182 \end{array}$
(2): T-shape welded joint under bending stress:

$\begin{array}{l} K_{t} = & 1 - 1.130 \cdot f (T / t) \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \cdot \\ f ((L_{1} / t) \cdot (L_{2} / t)) \cdot f (H / t) \end{array}$

(A6)

where:

$f (T / t) = - 0.010 \cdot {(T / t)}^{3} - 0.032 \cdot {(T / t)}^{2} + 0.185 \cdot (T / t) + 2.433$

$f (r_{1} / t) = 0.648 \cdot {(r_{1} / t)}^{- 0.259} + 2.861 \cdot {(r_{1} / t)}^{3} - 3.690 \cdot {(r_{1} / t)}^{2} + 2.090 \cdot (r_{1} / t) - 1.239$

$f (θ_{1}) = 0.003 \cdot {(π - θ_{1})}^{3} - 0.035 \cdot {(π - θ_{1})}^{2} + 0.060 \cdot (π - θ_{1}) + 0.086$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 3.532 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{5.128} - 8.443 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} + \\ 8.645 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + 1.482 \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 0.381 \end{array}$

$f (L_{1} / t) = - 11.406 \cdot {(L_{1} / t)}^{3.036} + 0.074 \cdot {(L_{1} / t)}^{4} + 11.882 \cdot {(L_{1} / t)}^{3} - 0.815 \cdot {(L_{1} / t)}^{2} + 0.293 \cdot (L_{1} / t) + 0.027$

$f (L_{2} / t) = 19.196 \cdot {(L_{2} / t)}^{- 0.151} - 0.732 \cdot {(L_{2} / t)}^{4} + 4.967 \cdot {(L_{2} / t)}^{3} - 8.382 \cdot {(L_{2} / t)}^{2} - 5.483 \cdot (L_{2} / t) + 43.598$

$f ((L_{1} / t) \cdot (L_{2} / t)) = - 0.182 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} + 1.470 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} - 5.862 \cdot ((L_{1} / t) \cdot (L_{2} / t)) - 8.301$

$f (H / t) = - 19.138 \cdot {(H / t)}^{3} + 7.690 \cdot {(H / t)}^{2} - 0.599 \cdot (H / t) + 1.202$
(3): Cruciform welded joint under tensile stress:

$\begin{array}{l} K_{t} = & 1 + 0.936 \cdot f (T / t) \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \cdot \\ f ((L_{1} / t) \cdot (L_{2} / t)) \cdot f (H / t) \end{array}$

(A7)

where:

$f (T / t) = - 0.424 \cdot {(T / t)}^{3} + 1.393 \cdot {(T / t)}^{2} - 1.073 \cdot (T / t) + 5.224$

$f (r_{1} / t) = - 2.215 \cdot {(r_{1} / t)}^{0.508} + 3.365 \cdot {(r_{1} / t)}^{3} - 4.439 \cdot {(r_{1} / t)}^{2} + 3.726 \cdot (r_{1} / t) + 0.403$

$f (θ_{1}) = - 0.789 \cdot {(π - θ_{1})}^{3} + 2.967 \cdot {(π - θ_{1})}^{2} - 5.879 \cdot (π - θ_{1}) + 17.728$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 1.557 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{- 0.116} + 3.822 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} - 5.354 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + \\ 7.153 \cdot ((r_{1} / t) \cdot (π - θ_{1})) - 1.529 \end{array}$

$f (L_{1} / t) = 8.159 \cdot {(L_{1} / t)}^{1.945} - 0.019 \cdot {(L_{1} / t)}^{4} + 0.202 \cdot {(L_{1} / t)}^{3} - 7.978 \cdot {(L_{1} / t)}^{2} - 0.457 \cdot (L_{1} / t) + 0.111$

$f (L_{2} / t) = 10.209 \cdot {(L_{2} / t)}^{0.096} + 0.386 \cdot {(L_{2} / t)}^{4} - 2.433 \cdot {(L_{2} / t)}^{3} + 6.070 \cdot {(L_{2} / t)}^{2} - 8.046 \cdot (L_{2} / t) - 5.364$

$f (H / t) = 4.996 \cdot {(H / t)}^{3} - 1.461 \cdot {(H / t)}^{2} - 0.187 \cdot (H / t) - 1.083$

$f ((L_{1} / t) \cdot (L_{2} / t)) = - 0.242 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} + 0.571 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} - 21.595 \cdot ((L_{1} / t) \cdot (L_{2} / t)) - 2.240$
(4): Cruciform welded joint under bending stress:

$\begin{array}{l} K_{t} = & 1 + 1.201 \cdot f (r_{1} / t) \cdot f (θ_{1}) \cdot f ((r_{1} / t) \cdot (θ_{1})) \cdot f (L_{1} / t) \cdot f (L_{2} / t) \cdot \\ f ((L_{1} / t) \cdot (L_{2} / t)) \end{array}$

(A8)

where:

$f (r_{1} / t) = 1.246 \cdot {(r_{1} / t)}^{- 0.179} + 5.187 \cdot {(r_{1} / t)}^{3} - 5.888 \cdot {(r_{1} / t)}^{2} + 2.948 \cdot (r_{1} / t) - 2.024$

$f (θ_{1}) = 0.452 \cdot {(π - θ_{1})}^{3} - 4.170 \cdot {(π - θ_{1})}^{2} + 6.472 \cdot (π - θ_{1}) + 12.324$

$\begin{array}{l} f ((r_{1} / t) \cdot (θ_{1})) = & 6.195 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{1.959} + 0.210 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{3} - 6.258 \cdot {((r_{1} / t) \cdot (π - θ_{1}))}^{2} + \\ 0.043 \cdot ((r_{1} / t) \cdot (π - θ_{1})) + 0.016 \end{array}$

$f (L_{1} / t) = 0.107 \cdot {(L_{1} / t)}^{3} + 0.490 \cdot {(L_{1} / t)}^{2} - 3.181 \cdot (L_{1} / t) + 11.877$

$f (L_{2} / t) = 6.218 \cdot {(L_{2} / t)}^{2.938} + 0.082 \cdot {(L_{2} / t)}^{4} - 5.873 \cdot {(L_{2} / t)}^{3} - 0.584 \cdot {(L_{2} / t)}^{2} + 0.181 \cdot (L_{2} / t) + 0.022$

$f ((L_{1} / t) \cdot (L_{2} / t)) = - 0.096 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{3} - 0.221 \cdot {((L_{1} / t) \cdot (L_{2} / t))}^{2} + 5.661 \cdot ((L_{1} / t) \cdot (L_{2} / t)) + 33.008$

The authors would like to apologize for any inconvenience caused to the readers by these changes.

Reference

Wang, Y.; Luo, Y.; Tsutsumi, S. Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile. Materials 2020, 13, 4639. [Google Scholar] [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© 2021 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 (https://creativecommons.org/licenses/by/4.0/).

Article Metrics

Citations

Article Access Statistics

Journal Statistics

Multiple requests from the same IP address are counted as one view.