PSI - Issue 13

Adam Smith et al. / Procedia Structural Integrity 13 (2018) 566–570 Smith / Structural Integrity Procedia 00 (2018) 000 – 000

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2.2. Fatigue Crack Modelling Procedure for Calculating ERF

Fatigue crack modelling was carried out using FRANC3D software with Abaqus FEA used as the solver. The finite-element model generated in Abaqus FEA was imported into FRANC3D to allow a longitudinal surface breaking semi-circular crack to be embedded near one of the weld toes at the mid-width of the specimen (location A in Fig. 2(b)) by re-meshing a specified volume in the model (the shaded region in Fig. 2(b)). The volume of the model that contained the crack consisted of second-order tetrahedral elements away from the crack-tip, second-order brick elements near the crack tip, and second-order wedge elements at the crack-tip with the mid-side nodes shifted to the quarter points. FRANC3D was then used to ‘ grow ’ the fatigue crack based on the resultant stress-intensity factor range,  K, and the supplied crack-growth-rate data (da/dN- ∆ K). These simulations were carried out using mean da/dN- ∆ K data from tests conducted in air on similar quenched-and-tempered steel as described by Knop (2015). These data were applicable to the Q2(N) steel modelled in the present study because data in the literature (Knop (2015)) indicate that crack-growth rates are very similar amongst quenched-and-tempered steels. The initial crack size for the fracture-mechanics analysis was determined through an iterative process in which the growth of a fatigue crack in air was modelled for a variety of initial crack sizes until the N f value matched the number of cycles-to-failure obtained from fatigue testing in air (approximately 30800 cycles according to Fig. 1(a)). The failure criterion was determined using the failure assessment diagram described in BS 7910 (2015). The initial crack size determined from this analysis was then used for simulations of fatigue crack growth in aqueous 3.5 wt.% NaCl. FRANC3D was then used to carry out numerical simulations of corrosion-fatigue crack growth, but for these calculations, crack-growth rates (mean da/dN- ∆ K data) corresponding to freely corroding conditions in aqueous 3.5 wt.% NaCl at the required cycle frequency from Knop (2015) were used. These simulations were carried out for twelve different cycle frequencies ranging from 30 Hz to 7 × 10 − 7 Hz. The values of N f(E) were calculated also using the failure assessment diagram described in BS 7910 (2015). N f for the given stress range was then divided by N f(E) for a given frequency to determine the ERF. It was determined from the fracture-mechanics calculations that an initial surface crack length of 1.16 mm with a corresponding crack depth of 0.58 mm was required so that the number of cycles-to-failure in air resulted in the same value obtained experimentally (~30800, Fig. 1(a)). These initial crack dimensions were used for subsequent modelling in aqueous NaCl. Guidance in BS 7608 (2015) for fracture-mechanics analysis recommends an initial surface crack length of 0.20 mm to 0.50 mm. However, it is noted in BS 7608 (2015) that larger initial crack lengths (e.g. 1.16 mm) may be reasonable, presumably due to variations in weld quality. As expected, the crack in air (Fig. 3(a)) requires more cycles to grow to a given length and depth compared with the crack in aqueous NaCl at very low cycle frequencies (Fig. 3(b)), as the crack-growth rate in air is slower. It should be noted that the fatigue life in aqueous NaCl is expected to be essentially the same as in sea water because corrosion-fatigue crack-growth rates are essentially the same in both environments (Scott and Silvester (1975), Knop (2015)). Also, this study only considers a single idealised case to model crack growth. It is recognised that there are other variables with respect to crack growth in a tee-butt weld that need to be considered in future research (e.g. crack location, crack orientation, initial crack size and shape, growth/coalescence of multiple cracks, and crack-tip electrochemistry). Fracture-mechanics calculations for freely corroding tee-butt welded joints subjected to a stress range of 518 MPa are in excellent agreement with corresponding experimental data (Fig. 3(c)). Notably, the maximum calculated ERF is in alignment with the average maximum corrosion-fatigue crack-growth rate with respect to  K (within 1%), such that the ERF is about 6.7. The ERF corresponding to a cycle frequency of 0.001 Hz was calculated to be 5.7 (Fig. 3(c)), which is 1.9 times greater than the recommended ERF of 3 corresponding to wave loading in BS 7608 (2015). The modelling data indicates that the ERF is about 2.0 for a cycle frequency of 0.1 Hz, which is similar to the ERF of 3 given in BS 7608 (2015). This difference presumably arises because the ERF depends on a number of other variables, e.g. the applied stress range. As such, this highlights the need for further work to assess the influence of other test variables, besides the cycle frequency, on the ERF, such as (i) stress range, (ii) electrode potential, (iii) joint geometry, (iv) weld quality, and (v) variable amplitude loading. 3. Results and Discussion