Issue 31

J.A.F.O. Correia et alii, Frattura ed Integrità Strutturale, 31 (2015) 80-96; DOI: 10.3221/IGF-ESIS.31.07 90 Maximum stress mesh 5 mesh 4 mesh 1 mesh 2 mesh 3  y [MPa] 1637.00 1772.00 1797.00 1926.90 1928.80 Dev. [%] -15.04 -9.04 -6.71 - 0.10  x [MPa] 419.70 423.83 416.67 417.89 417.78 Dev. [%] 2.83 1.42 -0.29 - -0.03 Table 3: Maximum elastic stresses for distinct finite element mesh densities for the S355 steel ( F max =5443.5N, a=10mm, ρ* =55µm). The finite element model was used to simulate a loading and unloading sequence. The residual stresses are computed from the stress field at the end of the unloading load step. Alternatively, the simplified analytical solution based on multiaxial Neuber’s approach [15] was implemented for comparison purposes. In this case, the residual stresses resulted from the subtraction of the cyclic elastoplastic stress range to the maximum elastoplastic stress, both computed in an independent way. The finite element model was initially applied to perform elastic and elastoplastic stress analyses in order to allow the comparison of the elastic and elastoplastic stress distributions, respectively with the Creager-Paris solution [22] and multiaxial Neuber’s approach [15]. According to the UniGrow model, the compressive residual stresses computed ahead the crack tip are assumed to be applied symmetrically, in the crack faces. Using the weight function method [24], the residual stress intensity factor, K r , was computed for the stress R -ratios considered in the experimental program. The elastic stress distributions from the numerical and analytical solutions for the CT specimens made of the S355 steel are compared in Fig. 11. Fig. 12 compares the elastoplastic stress distributions. The results were computed for a crack tip radius, ρ* =5.5×10 -5 m, which was found to be the best value for the S355 steel, that gives the best predictions for the crack growth rates, based on SWT fatigue damage probabilistic field. 0.0E+00 8.0E+08 1.6E+09 2.4E+09 3.2E+09 4.0E+09 0.0E+00 2.0E‐04 4.0E‐04 6.0E‐04 8.0E‐04 1.0E‐03 Distance from the crack tip [m] Elastic stress,  y  [Pa] FEM (a=10mm) CREAGER‐PARIS (a=10mm) FEM (a=15mm) CREAGER‐PARIS (a=15mm) FEM (a=20mm) CREAGER‐PARIS (a=20mm) R=0.0 0.0E+00 2.0E+08 4.0E+08 6.0E+08 8.0E+08 0.0E+00 2.0E‐04 4.0E‐04 6.0E‐04 8.0E‐04 1.0E‐03 Distance from the crack tip [m] Elastic stress,  x  [Pa] FEM (a=10mm) CREAGER‐PARIS (a=10mm) FEM (a=15mm) CREAGER‐PARIS (a=15mm) FEM (a=20mm) CREAGER‐PARIS (a=20mm) R=0.0 a) σ y stress distribution ( F max =5443.5N, ρ* =55µm). b) σ x stress distribution ( F max =5443.5N, ρ* =55µm). Figure 11: Elastic stress distribution ahead of the crack tip and along the crack plane line (y=0) for CT specimens made of the S355 steel: comparison between analytical and numerical results. Distinct crack sizes considered. 0.0E+00 2.0E+08 4.0E+08 6.0E+08 8.0E+08 0.0E+00 1.0E‐03 2.0E‐03 3.0E‐03 4.0E‐03 5.0E‐03 6.0E‐03 Distance from the crack tip [m] Elastoplastic stress,  y  [Pa] FEM (a=10mm) NEUBER (a=10mm) FEM (a=15mm) NEUBER (a=15mm) FEM (a=20mm) NEUBER (a=20mm) R=0.0 0.0E+00 1.0E+08 2.0E+08 3.0E+08 4.0E+08 5.0E+08 0.0E+00 1.0E‐03 2.0E‐03 3.0E‐03 4.0E‐03 5.0E‐03 6.0E‐03 Distance from the crack tip [m] Elastoplastic stress,  x  [Pa] FEM (a=10mm) NEUBER (a=10mm) FEM (a=15mm) NEUBER (a=15mm) FEM (a=20mm) NEUBER (a=20mm) R=0.0 a) σ y stress distribution ( F max =5443.5N, ρ* =55µm). b) σ x stress distribution ( F max =5443.5N, ρ* =55µm). Figure 12: Elastoplastic stress distribution ahead of the crack tip along the crack plane line (y=0) for CT specimens made of S355 steel: comparison between analytical and numerical results. Distinct crack sizes considered.