Issue 31

J.A.F.O. Correia et alii, Frattura ed Integrità Strutturale, 31 (2015) 80-96; DOI: 10.3221/IGF-ESIS.31.07 92 The stress and strain fields along the y (load) direction assuming a material representative element of ρ* =55µm, a crack size a =15mm, a maximum load F max =5443.5N, and a stress R -ratio, R σ =0.0, obtained for the CT specimens using the elastoplastic finite element analysis, are illustrated in Fig. 14. It is clear the compressive stress field at the crack tip vicinity and at some extension of the crack wake. The stress and strain fields are shown at the end of the first loading reversal and at the end of the unloading reversal. Fig. 15 presents the residual stress intensity factor as a function of the applied stress intensity factor range obtained for the CT specimens made of S355 steel, using the numerical analysis. K residual  = ‐0.3935  K applied + 94.978 R 2  = 0.9987 K residual  = ‐0.3264  K applied + 83.854 R 2  = 0.9994 K residual  = ‐0.2212  K applied + 49.136 R 2  = 0.9999 ‐500 ‐400 ‐300 ‐200 ‐100 0 0 200 400 600 800 1000 1200 1400  K applied [N.mm ‐1.5 ] K residual  [N.mm ‐1.5 ] R=0.0 R=0.25 R=0.5 Figure 15: Residual stress intensity factor as a function of the applied stress intensity factor range obtained for the S355 steel (ρ*=5.5×10 -5 m). The elastic stress distributions presented a satisfactory agreement between the analytical and numerical results, for several crack sizes (measured from loading line), within a small distance from the crack tip. For higher distances, slight deviations are found for σ y stresses. For σ x stresses, the maximum deviation is found in the maximum absolute value. For small and high distances from the crack tip, the deviations on σ x stresses are minimal. Additional simulations with further mesh refinements did not produce noticeable changes in the elastic stress distributions, demonstrating a good mesh refinement. Besides the numerical solution for the elastoplastic analysis, results from the multiaxial Neuber’s analysis are also considered. Despite the same global trends are observed for the σ y and σ x stress distributions, deviations in maximum absolute values are verified in the elastoplastic stresses. In general, the analytical solutions lead to maximum absolute stresses higher than the elastoplastic FE analysis. σ x stresses are more stepped than the corresponding numerical stresses near the crack tip. Also, the analytical solution shows some instability near the crack tip. The analysis of the σ y stress distribution shows an inflection point which is related to the size of the plastic zone. The analytical solution does not show this behaviour, which is a clear limitation of the analytical approach. The compressive residual stresses decrease progressively with increasing stress ratio, making the applied stress intensity range more effective. The extension of the compressive residual stresses increases with the crack size. The numerical model always predicts a compressive stress region which is lower than that predicted using the analytical model. The comparison between the numerical and analytical results highlighted some inconsistencies in the analytical results. The analytical procedure produces reliable results at the crack notch root, but the residual stress distribution along the crack front path (away from the crack notch root) seems to be inconsistent, which is in part justified by the incapacity of the analytical model to handle the stress redistribution due to yielding. Therefore, the numerical solution, for the residual stresses, was adopted in the crack propagation prediction, based on the UniGrow model. A linear correlation between the residual stress intensity factor and the applied stress range is verified, for each stress R - ratio. This linear relation agrees with the proposition by Noroozi et al. [10]. p-da/dN-  K-R results and discussion The UniGrow model was applied to compute the fatigue crack propagation for the same experimental conditions used to derive the aforementioned fatigue crack propagation data. The residual stress intensity factor was computed based on compressive residual stress distribution from the finite element analysis, and using the weight function method [24], as proposed in the UniGrow model. The strain range and maximum stress required by the probabilistic strain-life or SWT-life