Shot Peening Processes to obtain Nanocrystalline surfaces in metal alloys: D. D’Angela et alii, Frattura ed Integrità Strutturale, 60 (2022) 265-272; DOI: 10.3221/IGF-ESIS.60.18 265 Fatigue crack growth analysis of welded bridge details Danilo D’Angela University of Naples Federico II, Italy danilo.dangela@unina.it, http://orcid.org/0000-0002-8096-5202 Marianna Ercolino University of Greenwich, UK m.ercolino@gre.ac.uk, http://orcid.org/0000-0001-8678-0631 ABSTRACT. The paper investigates the fatigue crack growth in typical bridge weldments by means of numerical analysis. The extended finite element (XFEM) method is coupled with the low-cycle fatigue (LCF) approach in ABAQUS, and parametric analyses are carried out in order to assess the influence of the main sample/testing features on the fatigue life of the investigated structures. The numerical results are found to be robust and reliable by performing comparisons with past experimental data and regulation design correlations. KEYWORDS. Crack growth; Fatigue; Welded details; XFEM; ABAQUS. Citation: D’Angela, D., Ercolino, M., Fatigue crack growth analysis of welded bridge details, Frattura ed Integrità Strutturale, 60 (2022) 265-272. Received: 03.02.2022 Accepted: 07.02.2022 Online first: 08.02.2022 Published: 01.04.2022 Copyright: © 2022 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION atigue crack propagation is among the most critical damage mechanisms affecting metallic structures and infrastructures subjected to repeated loading [1–4]. Welded details are typically extremely sensitive to crack propagation phenomena. The welding process can generate flaws and defects in the vicinity of the weldment toe, and such pre-cracks can easily activate crack development [5] especially if the applied load is orthogonal to the crack surface (e.g., mode I fracture). Numerical simulation by means of finite element (FE) analysis is among the most reliable tools for the assessment of the fatigue crack propagation in metallic structures and for the estimation of their fatigue life [6–10]. The extended finite element method (XFEM) is among the most advanced technologies for simulating fracture phenomena, and several recent studies proved that it could be reliable also regarding fatigue crack propagation in metals [1,11–16]. Hedayati and Vajedi [15] developed robust modelling of crack propagation in slant cracked plates based and provided estimations of the fatigue life. Melson [17] analysed the fatigue response of aluminium crack plates and found that XFEM technology can be more reliable than other methodologies. Other authors [7,8] implemented subroutines for more accurate simulations, and they found reliable results. In spite of the available methodologies and the copious literature, there are still several issues affecting the FE analysis of fatigue and fracture phenomena, and novel approaches are needed to enhance the numerical analysis of F https://youtu.be/4VtFdxBPWi4 D. D’Angela et alii, Frattura ed Integrità Strutturale, 60 (2022) 265-272; DOI: 10.3221/IGF-ESIS.60.18 266 fatigue crack propagation in metallic structures. The available models are often extremely complex and not suitable for practitioners, and the modelling parameters are not often physical based. In many cases, the analyses require high computational costs and the numerical results have been validated only considering theoretical or analytical data. In order to cover this gap, a simple but reliable numerical model is presented in this study. The XFEM technology is coupled with low-cycle fatigue (LCF) approach and parametric analyses are performed in ABAQUS [18]. The case study consists of welded bridge details, which are critical systems undergoing fatigue crack propagation and are less studied in the literature. NUMERICAL MODELLING AND FATIGUE ANALYSIS three-dimensional model was built in ABAQUS coupling XFEM and LCF approach. In particular, the modelling was based on an improvement and extension of a pilot model developed by the authors considering bi-dimensional metallic plates [9,13]. The reference geometry, along with the initial crack, is shown in Figure 1a. S355 steel was assumed as a material. The structures consisted of (a) main plate, (b) gusset plate, and (c) main-to-gusset plate welded connection (Figure 1a). The main model had geometry dimensions W, L, δW, and δL equal to 60, 50, 10, and 8 mm, respectively; the initial crack length dimensions a and b were equal to 2 and 4 mm, respectively (Figure 1a). All surface connections between the parts were assumed to be perfectly tied. The initial plane pre-crack surface (a x b) was assigned to the model (main plate) according to the most common location and size of flaws/defects in welded details, i.e., at the toe of the weldment and orthogonally to the direction of the typically applied stress [5]. In particular, the main plate is assumed to carry the most significant load, which is applied along with the longitudinal direction of the latter. Therefore, the pre-crack (weldment defect) is perpendicular to the direction of the applied load, and it can develop and activate the crack propagation phenomena. Linear elastic homogeneous behaviour was assigned to the material according to the LEFM approach. The fracture response was implemented on the initial XFEM crack, according to Paris law (fatigue fracture criterion and surface behavior). The mixed- mode power law was used as a default ABAQUS model. The fatigue properties and the modelling parameters assumed for S355 steel are shown in Table 1, which were derived from the literature [19–21]. The boundary and loading conditions are shown in Figure 1.b. The stump cross sections of both main and gusset plates were fixed to simulate a symmetry condition. The cyclic loading P was applied to the reference middle section point, which was coupled to the whole surface by using a continuum distribution node-surface interaction. A cyclic frequency equal to 10 Hz was used, with a linear shape. Material Fatigue properties (mechanical) Modelling parameters (ABAQUS code) cp mp KC c3 c4 GC ( ) mp 0.5 m cycle MPa m          [-] 0.5 MPa m    4c m / cycles ( N / m )       [-] kN m       S355 steel 5.71E−13 3.56 45 3.54E−14 1.781 9.6 7 % nickel steel 2.17E−11 2.57 135 2.80E−12 1.285 90.0 7075-T6 aluminium alloy 3.33E−11 3.70 25 2.55E−13 1.850 9.0 Table 1: Fatigue properties of the investigated materials and model parameters. The numerical analysis consisted of two steps: general static and direct cyclic (LCF). The static analysis step was only performed to improve the convergence of the analysis, as it was previously found by pilot studies [9], as well as reported in the literature [22]. The static step included only one cycle, with negligible values of the applied force (no influence on the actual fatigue response). Several force values were applied to cover a wide range of applied stresses, i.e., from 75 to 325 MPa. This was aimed at evaluating the S-N curve, typically considered for the assessment of this typology of structures [5]. The model parts were partitioned (Figure 1c) to control the mesh size along with the distance from the FPZ. Only hexahedral elements (8-node linear brick elements) can be used in ABAQUS for three-dimensional modelling according to LCF- XFEM analysis, i.e., C3D8 (full integration) and C3D8R (reduced integration) elements [18]. The reduced integration elements are typically more used in the literature (than the full integration ones) since they were found to be accurate for A D. D’Angela et alii, Frattura ed Integrità Strutturale, 60 (2022) 265-272; DOI: 10.3221/IGF-ESIS.60.18 267 modelling crack propagation problems despite the gain in smaller computational costs [9,15,23]. Therefore, the mesh size analysis was performed considering this type of mesh. The mesh size of the model was assigned in the light of an expeditious convergence analysis. The mesh sizes are depicted in Figure 1c, where the sizes related to part A, B, C, and D were equal to 0.7 x 0.7 mm, 0.7 x 4.5 mm, 4.0 x 4.0 mm, and 4.5 x 4.5 mm. PARAMETRIC ANALYSIS he influence of several sample features was assessed considering the main model as a reference (defined as model m). Material, structure geometry, and initial crack dimension/shape were varied, defining six parametric models. 7075-T6 aluminium alloy and 7% nickel steel were considered as alternative materials for generating models M1 and M2. The related properties and modelling/analysis features are reported in Table 2. Two alternative structure geometries were considered, defining models G1 and G2, together with the main model geometry. In particular, the models have geometry W, L, dW, and dL equal to (G1) 120, 50, 10, and 8 mm, and (G2) 60, 50, 20, and 8 mm. Two alternative pre-crack dimensions were considered; the related models are defined C1 and C2; the models have dimensions a and b equal to (C1) 2 and 2 mm, and (C2) 2 and 8 mm. Constant-amplitude analyses were performed for all models from applied stress equal to 75 MPa up to 350 MPa, considering increments of 25 MPa. Overall, 72 analyses were performed. (a) (b) (c) Figure 1: (a) Geometry of the welded detail (W, L, δW, and δL) with initial pre-crack dimensions, (b) schematic of the boundary and loading conditions, and (c) mesh partitions and sizes resulting from the convergence analysis. T D. D’Angela et alii, Frattura ed Integrità Strutturale, 60 (2022) 265-272; DOI: 10.3221/IGF-ESIS.60.18 268 RESULTS AND DISCUSSION ig. 2 shows the comparison between the numerical and the experimental results [5], where the nominal stress approach was considered. Data having Nf lower than 1×103 cycles were not considered. The numerical results over 2.785 × 104 to 2.54012 ×106 cycles (e.g., ~75 to ~250 MPa) were fitted with very good accuracy (e.g., r2 > 0.995) using power law. This range of cycles is consistent with the typical values related to fatigue loading of such types of structures [5].The best-fit constants αm and βm were equal to 5.297×103 and -0.286, respectively. The experimental results are related to a large number (487) of fatigue tests on similar structures having the geometrical parameters W, L, δW, and δL ranging within 40 ÷ 170 mm, 50 ÷ 400 mm, 8 ÷ 20 mm, and 8 ÷ 20 mm, respectively. In Figure 2, the Eurocode 3 S-N (nominal stress approach) related to the investigated detail is also shown (nominal stress approach), i.e., C40 detail class curve [5,24]. The numerical results match with a good agreement the cloud of the experimental data, being on the safe side if the C40 class detail curve is considered. It is recalled that the experimental results are representative of an extremely wide range of geometries; furthermore, the numerical modelling considered a pre-crack with a definite geometry. Even though the validation of the model should be performed comparing cases having the same geometry/loading conditions, the numerical modelling is confirmed to be a reliable assessment of the fatigue life of complex welded details. This is supported by the log-log linear S-N correlation over the relevant stress-cycle ranges and by the location of the numerical data over the cloud of experimental results. As already mentioned, the model should be properly validated by considering specific case studies, e.g., as it was done with regard to the CT specimens. Figure 2: Comparison between the numerical results (red circles and red dashed line) and the experimental results (black dots and thin black and blu lines) reported by Aygül et al. [5] and Aygül [25], together with the C40 detail class curve (thick grey line) provided by Eurocode 3 [5,24]. The influence of the parametric variables was assessed by considering the S-N curves and both the parameters and the domain stress-cycle ranges related to the best-fit power laws. Figure 3 shows the results considering the variation of (a) the material (models M1 and M2), (b) the structural geometry (models G1 and G2), and (c) the pre-crack shape/dimension (models C1 and C2). The best-fit power laws (with related r2) are also shown. In particular, the data were fitted over the largest cycle interval that is associated with a power law having r2 larger than 0.950. The values of the related best-fit constants and the corresponding cycle ranges are given in Figure 3. “EL” in (b) represents the endurance limit, i.e., the fatigue life was larger than 108 cycles for stresses lower than the represented case. F D. D’Angela et alii, Frattura ed Integrità Strutturale, 60 (2022) 265-272; DOI: 10.3221/IGF-ESIS.60.18 269 Model ID α β r2 range of fitting from to [-] / 103 [-] [-] [cycles] / 103 [cycles] / 105 m 5.2971 -0.286 0.9979 27.85 25.4012 M1 1.9953 -0.252 0.9636 1.25 3.7826 M2 26.5302 -0.452 0.9991 16.36 4.0925 G1 8.1892 -0.329 0.9993 22.58 14.6633 G2 1.3941 -0.149 0.9592 71.43 69.6150 C1 6.0073 -0.305 0.9826 8.82 14.7419 C2 3.8580 -0.265 0.9815 9.73 21.2300 Table 2: Values of the best-fit constants defined in Figure 3. The material clearly affects the fatigue performance as well as the range in which the S-N data are stable (e.g., log-log linear). Model M1 shows a lower best-fit efficiency if compared to other cases. The geometry related to the double width of the main plate (M1) has S-N data (slightly) less performing than the main model, especially for larger numbers of cycles (e.g., larger than 105). It is recalled that all models have the same nominal applied stress; therefore, models G1 and G2 have a double total applied force with respect to the main model. If the main plate has a double thickness (i.e., model G2), the performance significantly improves, especially for larger numbers of cycles (e.g., larger than 105). For a low number of cycles, G2 has a performance comparable to the reference model m. The endurance limit (EL) is reached in model G2 corresponding to stresses lower than 125 MPa (not observed in other cases over the same stress range). Best-fit efficiency related to model G2 is reduced if compared to other cases, even though fewer data points were best-fitted. The size of the initial crack does not significantly affect the performance of the components. However, very interesting results are observed if model C1 is compared to the reference model m. C1 presents a (slightly) lower performance even though one of the dimensions of the initial crack is half the main model one. In particular, model C1 has the same crack dimensions a and b (equal 2 mm), whereas model m has the same C1 dimension for a and double for b. This confirms that the shape of the initial crack (e.g., a/b) is more significant than the area (a∙b) for the determination of the fatigue performance of the component. A similar result can be observed with regard to model C2, where b is equal to four times a. In fact, the fatigue performance is quite similar to model m (C1) for a higher (lower) number of cycles. This confirms that a component having an initial crack with a shape ratio (a/b) equal to 1/2 is (slightly) more critical than elements having larger or smaller ratios. Obviously, this trend is related to the specific application and the investigated conditions. The provided values of the best-fit parameters allow quantifying the differences in fatigue life estimations among the different models, and they allow assessing the fatigue performance of similar components by producing a quick estimation. Figure 4 shows the comparison between the numerical results (best-fit) related to (a) models m, G1, and G2 and (b) models m, C1, and C2 and the data related to the experimental database previously considered to assess the main model results [5,25]. Such models are compatible with the geometrical properties of the considered experimental database. The curve related to the detail class C40 is also shown [5,24]. It is recalled that the cloud of experimental data is related to a wide range of geometries, i.e., W, L, δW, and δL ranging within 40 ÷ 170 mm, 50 ÷ 400 mm, 8 ÷ 20 mm, and 8 ÷ 20 mm, respectively. However, the variation of the modelling geometry (W equal to 60 and 120 mm, and δW equal to 10 and 20 mm) approximately envelope the cloud of experimental data. In particular, the superior enveloping related to model G2 is qualitatively consistent with the fact that this case is associated with δW equal to 20 mm, which corresponds to the maximum value over the experimental case. Similarly, model G1, which is corresponding to W equal to 120 mm, shows results in the inferior part of the experimental cloud, which has maximum W equal to 170 mm. Such qualitative trends strengthen the robustness of the modelling approach, even though proper validation should be performed. D. D’Angela et alii, Frattura ed Integrità Strutturale, 60 (2022) 265-272; DOI: 10.3221/IGF-ESIS.60.18 270 (a) (b) (c) Figure 3: The influence of (a) material (models m, M1, and M2), (b) structure geometry (models m, G1, and G2), and (c) pre-crack shape/dimension (models m, C1, and C2) on the S-N results. CONCLUSIONS he study supplied simple but reliable three-dimensional modelling and cyclic analysis to simulate crack propagation in welded bridge details subjected to fatigue loading. The approach is based on XFEM technology coupled with LCF approach. S-N curves are provided for a wide range of welded bridge details. The numerical results are compared with both experimental results related to past studies and design curves provided by the regulations. Best-fit S-N curves are developed for enhancing the literature database. The study proves that the developed approach is suitable for various and complex applications, and it can be considered as a reference for similar implementations. T D. D’Angela et alii, Frattura ed Integrità Strutturale, 60 (2022) 265-272; DOI: 10.3221/IGF-ESIS.60.18 271 (a) (b) Figure 4: Comparison between the best-fit curves related to the numerical results (dotted and dashed lines) and the experimental results (black dots and thin blue and black lines) reported by Aygül et al. [5] and Aygül [25], together with the C40 detail class curve (thick grey line) provided by Eurocode 3 [5,24]: (a) models m, G1, and G2, and (b) models m, C1, and C2. ACKNOWLEDGMENTS omputation for the work presented in this paper was supported by the University of Greenwich High Performance Computer resources (https://www.gre.ac.uk/itand-library/hpc). The project was funded by the University of Greenwich under Seedling 2016 and REF 2017/2018 funds. REFERENCES [1] Bergara, A., Dorado, J. I., Martin-Meizoso, A., and Martínez-Esnaola, J. M. (2017). 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