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Determination of notch factors for welded butt joints based on numerical analysis and metamodeling

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Abstract

Fatigue evaluation based on the effective notch stress approach requires stress concentration factors for idealized notch geometries. In this paper, stress concentration factors are calculated numerically for different idealizations of the weld geometry. The joints covered here are one-sided Y-butt joints and two-sided DY-butt joints, each with partial and full penetration. The variable parameters of the finite element models are the weld flank angle, the notch radius, the sheet thickness, the ratio of weld seam width to sheet thickness, and the ratio of height of non-fused root face to sheet thickness. Existing estimation formulae for stress concentration factors will be compared with new methods for stress concentration factor estimation: (a) polynomial regression using mixed terms and (b) artificial neural networks. These two methods show similar or superior quality compared with the existing estimations which is expressed through lower estimation errors with respect to the numerically calculated stress concentration factors. The database for the regression analysis using methods (a) and (b) consists of a total of 11,871 design alternatives obtained by finite element analysis. In addition to the improved quality of prognosis, the range of allowable geometrical parameters is significantly increased compared with the existing formulae. The methods (a) and (b) provide a possibility to a fast estimation of stress concentration factors of sufficient quality for a large range of geometrical weld seam parameters. The presented formulae could also be part of a programmed solution.

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Notes

  1. ANSYS Mechanical™ is a trademark of ANSYS, Inc., Canonsburg, PA, USA, see http://www.ansys.com

  2. optiSLang® is a trademark of Dynardo GmbH, Weimar, Germany, see https://www.dynardo.de/software/optislang.hmtl

  3. ∘ indicates the elementwise Hadamard product, ⊘ the elementwise Hadamard division

Abbreviations

ANN [−]:

Artificial neural network

β [°]:

Flank angle

bi [−]:

Bias vectors for artificial neural networks

ck [−]:

Scalar multiplication parameter for the PRC method

d [mm]:

Total model depth

E [MPa]:

Young’s modulus

errrel [%]:

Relative error

F[N] :

Force

f [−]:

Ratio of weld seam width to sheet thickness

fk [−] :

Value of geometric multiplication parameter for the PRC method

g [−] :

Input vector for the ANN method

h [mm] :

Height of non-fused root face

Kf [−] :

Fatigue notch factor

Kt [−] :

Stress concentration factor

Kt, EST [−]:

Stress concentration factor, estimated

Kt, FEM [−]:

Stress concentration factor, calculated by FEM

kt [−] :

Stress concentration output vector of the ANN method

Kt, AKS [−]:

Stress concentration factor of Anthes et al. method

Kt, ANN [−]:

Stress concentration factor of the ANN method

Kt, LER [−] :

Stress concentration factor of Lehrke’s method

Kt, PRC [−] :

Stress concentration factor of the PRC method

Kt, RAI [−] :

Stress concentration factor of Rainer’s method

Kt, YL [−] :

Stress concentration factor of Yung and Lawrence’s method

Kw [−]:

Ratio of notch stress to structural stress

Kw, min [−]:

Minimum ratio of notch stress to structural stress

L [mm]:

Sheet length

M [N/mm] :

Moment

m [−]:

Weld angle exponent in Lehrke’s method

ν [−]:

Poisson ratio

Φi [−]:

Artificial neural network layer potential

PRC [−]:

Polynomial regression with coupling terms

r [mm]:

Notch radius

Sb [MPa]:

Nominal bending stress

St [MPa]:

Nominal tension stress

σe [MPa]:

Notch stress

σw [MPa]:

Structural stress

t [mm]:

Sheet thickness

u [−]:

Weld reinforcement

w [mm]:

Width of weld seam

Wi [−]:

Weight matrices of artificial neural networks

xi,gain [−]:

Gain input vector for artificial neural networks

xi,offset [−]:

Offset input vector for artificial neural networks

yo,gain [−]:

Gain output vector of artificial neural networks

yo,offset [−]:

Offset output vector of artificial neural networks

z [−]:

Ratio of height of non-fused root face to sheet thickness

b, bend:

Bending

t, tens:

Tension

f. p.:

Full penetration

k :

PRC method index

p. p.:

Partial penetration

r, root:

Root

toe:

Toe

Y :

Y-butt joint

DY:

DY-butt joint

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Funding

The IGF project 19450 N of FOSTA - Forschungsvereinigung Stahlanwendung e. V., Düsseldorf, is funded by the Federal Ministry of Economic Affairs and Energy via the AiF within the framework of the program for the promotion of the Industrielle Gemeinschaftsforschung (IGF) based on a resolution of the German Bundestag.

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Authors and Affiliations

  1. Department of Mechanical, Automotive and Aeronautical Engineering, Munich University of Applied Sciences, Dachauer Str. 98b, 80335, Munich, Germany

    Markus Oswald, Josef Neuhäusler & Klemens Rother

Authors
  1. Markus Oswald
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  2. Josef Neuhäusler
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  3. Klemens Rother
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Corresponding author

Correspondence to Markus Oswald.

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Recommended for publication by Commission XIII - Fatigue of Welded Components and Structures

Appendix

Appendix

Table 21 Regression formulae for PRC method for fully penetrated welds, Y-butt joint
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Table 22 Regression formulae for PRC method for partially penetrated welds at weld toe, Y-butt joint
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Table 23 Regression formulae for PRC method for partially penetrated welds at non-fused root face, Y-butt joint
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Table 24 Regression formulae for PRC method for fully penetrated welds, DY-butt joint
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Table 25 Regression formulae for PRC method for partially penetrated welds at weld toe, DY-butt joint
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Table 26 Regression formulae for PRC method for partially penetrated welds at non-fused root face, DY-butt joint
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Table 27 Neural network data for full penetration joints, Y-butt joints
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Table 28 Neural network data for partial penetration joints, Y-butt joints
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Table 29 Neural network data for full penetration joints, DY-butt joints
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Table 30 Neural network data for partial penetration joints, DY-butt joints
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Oswald, M., Neuhäusler, J. & Rother, K. Determination of notch factors for welded butt joints based on numerical analysis and metamodeling. Weld World 64, 2053–2074 (2020). https://doi.org/10.1007/s40194-020-00982-4

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