PSI - Issue 45

Aditya Khanna et al. / Procedia Structural Integrity 45 (2023) 12–19 Khanna and Young / Structural Integrity Procedia 00 (2019) 000 – 000

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the dominant excitation frequencies are lower than the natural frequency of the first bending mode. The opposite is true when the dominant excitation frequencies are above the first natural frequency of the cantilever fitting.

Fixed-Free Beams - First Bending Mode

2

Displacement-based Velocity-based

1.5

1

0.5

Below resonance

Above resonance

0

Normalised stress per unit vibration

0

0.5

1

1.5

2

Frequency ratio, ω / ω n

Fig. 4. Off-resonant relationship between the dynamic stress and vibration amplitude around the first resonant mode. In the present work, the allowable vibration limit is expressed in terms of the dynamic displacement amplitude. For transverse (bending) vibrations, the allowable vibration displacement, , can be obtained in terms of the fatigue endurance limit for the appropriate weld or joint classification, , using the following general relationship (Wachel et al., 1990): < ( )( ) ( 2 ), (1) where is the safety margin used to determine the various “tiers” of the vibration rating system, is the geometry factor to be obtained using FEA and the parameters and are the length and diameter of the fitting. Note that the notch effect associated with the weld is incorporated by assuming a lower endurance limit for welded connections compared to the parent material and the stress concentration due to the joint geometry is incorporated in the geometry factor , obtained using FEA. The stress concentration factor ( ) accounts for any stress concentrating effects that are not otherwise accounted for in the analysis. 1.2. Hot-spot stress method for fatigue assessment The Hot-Spot Stress (HSS) method is the standard method for the design and fatigue assessment of welded joints in which likely crack initiation site is at the weld toe. As shown in Fig. 5, the HSS (obtained analytically, experimentally, or using FEA) includes the stress concentration due of the joint geometry but excludes the local non-linear stress distribution due to the notch-like weld toe geometry. The notch (non-linear) effect is instead incorporated by comparing the hot-spot stress to experimentally obtained fatigue strength of welded specimens of the same weld class. Various methods for the extrapolation of the stresses at the weld toe have been reviewed and compared in the past (Niemi et al., 2018; Doerk et. al, 2003). The surface stress extrapolation method, which is based on linear (or quadratic) extrapolation at two (or three) reference distances from the weld toe, has been shown to be sufficiently accurate for most practical purposes (BS 7608:2014). This method is also applied when determining the HSS experimentally using strain gauges. The HSS method reviewed here is not applicable to cases where the crack is expected to grow from the weld root and propagate through the weld throat. Good design practice aims to avoid situations where the crack is not visible before it has propagated through the weld (Niemi et al., 2018).