Issue 31

J.A.F.O. Correia et alii, Frattura ed Integrità Strutturale, 31 (2015) 80-96; DOI: 10.3221/IGF-ESIS.31.07 93 models were assessed using the analytical approach, applied to the first elementary material block, keeping the original structure of the UniGrow model. Average strain and stress values, along the first elementary material block, were used instead of peak values. The analytical solution produces reliable results at the crack tip notch root as verified in previous section. The original structure of the UniGrow model has some advantages: i) a direct correspondence with fracture mechanics based analyses, which facilitates the physical understanding of the process; ii) allows close form solutions for fatigue crack propagation laws in the same format of existing fracture mechanics approaches; iii) requires inexpensive computations. The elastoplastic finite element analysis was used for the derivation of the residual stresses which were afterwards used for the computation of the residual stress intensity factor, using the weight function method. The p-SWT-N or the p-ε a -N fields were used to derive the probabilistic fatigue crack propagation fields ( p-da/dN-  K-R fields). For each case, an independent identification of the elementary material block size, ρ* , was performed. Fig. 16 shows the probabilistic fatigue crack propagation fields that were obtained, for the S355 steel, using the p-ε a -N field. Fig. 17 illustrates the probabilistic fatigue crack propagation fields predicted for the S355 steel, resulting from the p-SWT-N field. An elementary material block size of 5.5×10 -5 m was found suitable for both p-SWT-N and p-ε a -N damage fields. Concerning the p-da/dN-  K-R fields predicted for the S355 steel, the field that resulted from the p-SWT-N damage model produced the best results. This observation is justified by the fact that the S355 steel shows a markedly stress ratio influence on fatigue crack propagation rates, requiring a fatigue damage model that is able to account for the mean stress effects.  K  [N.mm ‐3/2 ] da/dN  [mm/cycle] Experimental Data: R=0.0 P=0.01 P=0.05 P=0.50 P=0.95 P=0.99 1.0E‐6 1.0E‐3 1.0E‐2 200 1500 500 1.0E‐4 1.0E‐5 1000  K  [N.mm ‐3/2 ] da/dN  [mm/cycle] Experimental Data: R=0.25 P=0.01 P=0.05 P=0.50 P=0.95 P=0.99 1.0E‐6 1.0E‐3 1.0E‐2 200 1500 500 1.0E‐4 1.0E‐5 1000 a) b)  K  [N.mm ‐3/2 ] da/dN  [mm/cycle] Experimental Data: R=0.5 P=0.01 P=0.05 P=0.50 P=0.95 P=0.99 1.0E‐6 1.0E‐3 1.0E‐2 200 1500 500 1.0E‐4 1.0E‐5 1000 c) Figure 16: Probabilistic prediction of the fatigue crack propagation based the p-ε-N field, for the S355 steel: a) R σ =0; b) R σ =0.25; c) R σ =0.5.