Issue 31

J.A.F.O. Correia et alii, Frattura ed Integrità Strutturale, 31 (2015) 80-96; DOI: 10.3221/IGF-ESIS.31.07 88 be low, it was decided to postulate some fatigue data at the low- to very low-cycle fatigue domain, using the Morrow equation of the material, for that purpose. The Morrow equation is more reliable to perform extrapolations for very low number of cycles than the Weibull field since the Weibull field shows an abnormal asymptotic behaviour for very low- cycle fatigue. P ROBABILISTIC FATIGUE CRACK PROPAGATION RATES PREDICTIONS he probabilistic fatigue crack propagation rates predictions were based on the application of the UniGrow model to the CT specimens. The elementary material block size, ρ* , is required. A trial and error procedure was adopted in order to result a good agreement between the numerical and experimental da/dN vs.  K data, for the materials under consideration (see Fig. 4). The probabilistic fatigue crack propagation fields were evaluated using both the probabilistic ε a -N and SWT-N fields, for comparison purposes. The procedure to generate the probabilistic fatigue crack propagation fields was aforementioned and illustrated in the Fig. 5. Finite element analysis of the CT geometry In order to assess the accuracy of the simplified elastoplastic analysis proposed in the Unigrow model for the residual stress estimation, a bi-dimensional parametric finite element model of the CT specimen was built and used in an elastoplastic finite analysis, using ANSYS® 12.0 commercial code [31]. Fig. 8 illustrates the typical finite element mesh of the CT geometry with the respective boundary conditions. Figure 8: Typical finite element mesh of the CT specimen, using 6-noded quadratic triangular plane stress elements. Only ½ of the geometry is modelled, taking into account the existing plane of symmetry. Plane stress conditions were assumed since the thickness of specimens are relatively reduced (B=8mm). Plane stress quadratic 6-noded triangular elements were used in the analysis (SOLID183), with 3 integration points. In order to simulate the pin loading, rigid-to- flexible contact was used with a friction coefficient, µ =0.3. The pin was modelled as a rigid circle controlled by a pilot node, using TARGE169 elements. The surface of the holes was modelled as a flexible surface using CONTA172 elements. The Augmented Lagrange contact algorithm was used. The associative Von Mises (J2) yield theory with multilinear kinematic hardening was used to model the plastic behaviour. Fig. 9 shows the superposition of the Ramberg- Osgood relation [32] with the response of a finite element model reproducing a uniaxial stress state (single cubic element T