Issue 42

P. Raposo et alii, Frattura ed Integrità Strutturale, 42 (2017) 105-118; DOI: 10.3221/IGF-ESIS.42.12 106 I NTRODUCTION he majority of fatigue models proposed in the literature are deterministic. Their application for design purposes requires additional safety margins defined with supplementary statistical arguments in order to allow the establishment of an appropriate safe design. In this paper, a probabilistic approach is applied to generate probabilistic S-N curves for notched details such as a notched plate (plate with circular hole) made of puddle iron from the Eiffel bridge, based on local strain fatigue approaches [1]. The plate with a circular hole is of interest since it shows similitudes with the riveted plates. Their study allows a better understanding of the fatigue behaviour of riveted joints. The model applied in this paper is an extension of the fatigue crack propagation model proposed by Noroozi et al. [2-4] which is based on a local strain approach to fatigue. The latter model, named as UniGrow model, is a fatigue crack propagation model based on residual stress considerations [2,3]. The selected model is applied in this paper to derive a probabilistic fatigue crack propagation field (p-S-N p field) for a detail tested under stress control and a null stress R-ratio. The fatigue crack propagation is considered a damaging process consisting on continuous crack initializations over adjacent material representative elements of a size, ρ*. Based on pure fatigue crack growth data, the material representative element size, ρ*, was previously estimated as can be consulted in references [5-9]. Probabilistic fatigue crack initiation fields (p-S-N i fields) are determined using an elastoplastic approach together with the material p-SWT-N fields. Predicted global p-S-N fields (combination of fatigue crack initiation and propagation phases) are compared with experimental S-N fatigue data for the notched plate, with a circular hole, made of puddle iron from the Eiffel bridge [10]. G ENERAL PROCEDURE TO GENERATE P –S–N–R FIELDS FOR NOTCHED DETAILS Description of the procedure he procedure proposed by Correia et al. [1] to derive probabilistic S–N–R fields for notched structural details or mechanical components is based on the assumption that crack path is discretized into elementary material blocks of length ρ*, placed along the assumed crack path (see Fig. 1). The process is then pictured according to the following steps: 1. Estimation of the p–SWT–N or p–ε a –N material fields, as described in next section, using experimental fatigue data from smooth specimens. These probabilistic fields will be the basis of the proposed model to evaluate the probabilistic S–N fields of the notched details. The selection of the damage parameter (SWT: Smith-Watson-Topper or ε a : strain amplitude) will depend on material/detail sensitivity to the mean stress or stress ratio. 2. Estimation of the elementary material block size, ρ*, using fatigue crack propagation data from fatigue crack propagation tests as for example using CT specimens, following the procedure by Noroozi et al. [2,3]. The elementary material block size is estimated using an iterative optimization procedure in order to result a good fit of the experimental fatigue crack propagation data, for several stress ratios, within the estimated S-N field. 3. Elastoplastic analysis of the uncracked detail in order to evaluate the average local stresses and strains at the first element block size ahead of the notch root. This step was performed in this research, using the finite element method (see Fig. 2). 4. Application of the p–SWT–N or p–ε a –N fields to derive the p–S–N i –R field representative of the macroscopic crack initiation, in the structural detail/mechanical component, which corresponds to the failure of the first elementary material block in the notch root. 5. Application of a modified version of the UniGrow model to evaluate the fatigue crack propagation in the structural detail, using the elementary material block size computed previously on step 2. The residual stress field required in the UniGrow model is computed in this paper using elastoplastic finite element analysis. 6. Computation of the p–S–N p –R field corresponding to the fatigue crack propagation in the notched detail/mechanical component (see Fig. 3). 7. Combination of probabilistic fields from steps 4 and 6 to evaluate the global p–S–N f –R field for the detail under analysis. The procedures adopted to compute the probabilistic S–N i –R and S–N p –R fields, for structural details are summarized in Figs. 2 and 3, respectively [1,5]. T T