Locations of strain gauges for fatigue analysis of welded joints (2)

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Notes

^1. Formerly: Sumitomo light Metal Ind. Ltd.

^2. Expression of the design hotspot S–N curve is the same as for nominal stress. Since, in all standards, it is lowered by two standard deviations only from the mean S–N curve found from the deviations in experimental points, it is linear on both the logarithmic scales and the geometric stress range Δσ ( = σ_s.max − σ_s.min), a major factor influencing fatigue life, is expressed as follows:

Here, N is the number of iterations, K _s is a constant, and m is the inverse gradient of the S–N curve.

The constant amplitude fatigue limit is N = 5 × 10⁶ and when this is subjected to variable amplitude, it ranges from N = 5 × 10⁶ to m ₂ = m ₁+2, with a cut-off at N = 10⁸. If K _s is found from a fatigue classification FAT (N/mm²) of N = 2 × 10⁶ and m ₁, it is possible to calculate Δσ_s for the desired number of iterations N.

^3. In this paper¹⁴, the positions of the strain gauges in Figure 2(b) are 0.4, 0.5, and 0.8t.

^4. When geometric stress is found by FEM, the calculations usually assume an ideal welded joint, with no geometric irregularities or other misalignments, but it is necessary to incorporate those geometric irregularities that may be encountered. As for the components, the stress and stress gradient must be found at locations corresponding to the extrapolation points used for strain gauge measurements with adequate precision near the hotspots.

A short description of these is given as ‘Calculation of geometric stress’ in Section 2.2.3.2 of the IIW recommendations¹, and Ref. 4, by Niemi, is recommended as a guide to these.

^5. Since in a flat sheet welded structure for maritime use, the welded structural joints used in pipe assembly show little variation in SCF associated with the changes in the dimensions of the structure, there is some doubt as to whether the method of defining hotspot stress is logical. At the 202nd Conference of the Japan Shipbuilding Research Association¹⁷, there was a report of a study in which large experimental fatigue model specimens of 30 mm bracket doubler pad and stiffener assembled from TMCP steel sheet with main sheet thickness of T = 15 mm and with a yield stress of 36 kgf/mm² for the studies in which the first and second strain gauges were used at six different combinations of locations at differing distances from the weld toe.

Since the results, including the gradient of the hotspot S–N curve, showed a mean − 2σ⁻  (σ⁻ : standard deviation) line, which is closest to the T diagram of the UK DEn (in which the sheet thickness and toe angle are corrected), the following flat sheet welded structure is proposed. In this, the positions of the strain gauges are such that the first is 1.57√T ³ and the second is 4.9√T ³ from the weld toe and the hotspot S–N curve is as follows:

Here, Δσ: geometric stress range (kgf/mm²) N _f, number of iterations of fracture

When a Δσ of N = 2 × 10⁶ is found from Equation (6), it has an average of 106 N/mm² and − 2σ⁻  is 78 N/mm², findings which are similar to the values in Table 2 (EC 3) and Table 1 (IIW).

^6. The characteristic curve (or characteristic line), which is shown in Figure 6, is usually very similar to two standard deviations below the mean S–N line. This is based on a probability of survival of 95% calculated on the basis of a mean figure found from an interval estimate with a 75% confidence level. See Section 3.7 ‘How to find fatigue resistance by testing’ in Ref. 1.

^7. For tubular pipe welded joints, European standard EC 3² has specifications for butt, K, and N joints of tubular pipes and square pipes, and there are also IIW specifications¹ of fatigue classification by nominal stress for butt joints. Here, I describe only the tendency for parametric equations.

^8. When the brace wall thickness is t ₁ < 8 mm, it has a butt weld with leg lengths of t ₁ √2, and when t ^l>8 mm, it has a 45°single bevel groove and a root gap of 2 mm. When β = 1.0, the bead is ground flat so that the brace has a single bevel groove and the corner of the brace coincides with the chord surface. According to the European standard 25–72, steel pipes are to be Fe430D and Fe430B hot-rolled square pipes and welding is to be performed using rutile electrodes (ISO 2560), with three passes for fillet welding and four passes for butt welding. For the symbols used, see Table 5.