PSI - Issue 31

N.D. Bibbo et al. / Procedia Structural Integrity 31 (2021) 75–79 N. D. Bibbo et al. / Structural Integrity Procedia 00 (2019) 000–000

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critical plane. What makes MWCM unique is its method of assessing multiaxial fatigue. The MWCM approach assesses fatigue based on a modified SN-curve that is a hybrid between the uniaxial bending and uniaxial torsion SN-curves for a given material. The modified SN-curve is a function of the stress ratio � as seen in Eqn. 3 and is defined as the normal stress range Δ � divided by the shear stress range Δ for a given load cycle. � = Δ � Δ �3� Based on the stress ratio � and the SN-curve slopes � and � for uniaxial bending and torsion, a new modified SN-curve slope is calculated � as seen in Eqn. 4. It represents the first region before the knee-point in the SN-curve. � � � � = � � − � � ⋅ � + � �4� When shear stress ranges are smaller than the normal stress range, the damaging effects of the shear stress diminish. To account for this, when � > 1 , the modified slope � is set equal to the uniaxial bending slope � as seen in Eqn. 5. � � � � = � �5� Along with modifying the slope, the SN-curve is also shifted up or down depending on the stress ratio � . This is quantified by modifying the reference shear stress range Δ ��� at the number of cycles � based on Eqn. 6, using the reference shear stress range for uniaxial torsion Δτ and the reference normal stress range for uniaxial bending Δ � . Δ ��� � � � = � Δ � − Δτ� ⋅ � + Δ �6� For certain cases using the MWCM approach, it was found that if � is larger than the limit ������ as seen in Eqn. 7, that fatigue failure predictions where overconservative. Thus, a hard limit is set using Δ ��� � ����� � . ����� = Δ Δ � �7� There are further equations for the modification of the 2 nd Sn-curve slope region after the knee-point, however this is not relevant for use in the article, as all loads that are applied are within the region before the knee-point. 4. Notch stress method The notch stress method was developed for stress analysis of welded connections, particularly fatigue analysis. The approximation of weld stresses is challenging due weld geometry acting as a stress concentrator. Further, the inconsistencies of the weld manufacturing process make it next to impossible to model the weld accurately. The notch stress method has been introduced as a “best practice” modelling method of the weld toe or weld root, where the stresses typically are greatest. The notch stress method requires accurate modelling of the welded joint and the application of a fictitious rounding at the weld toe or weld root, either with a reference radius ��� of . 5 or 1 depending on the thickness of the welded component, Sonsino et. al. (2012). Use of the reference radius can be seen in Fig. 1 both for weld roots and weld toes.