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J. Toribio et alii, Frattura ed Integrità Strutturale, 25 (2013) 130-137 ; DOI: 10.3221/IGF-ESIS.25.19 132 The simulations were performed for constant amplitude loadings at different SIF ranges  K = K max – K min , and ratios R = K min / K max , and the effect of a single overload was considered, too, along the following load cases: (I)  K = 2 K 0 , R = 0, (II)  K = K 0 , R = 0, (III)  K = K 0 , R = 0.5, (IV)  K = K 0 , R = 0, with an overload to K ov = 2 K 0 at a single cycle of the loading path, where the reference value K 0 = 30 MPa  m corresponds to loading regimes of fatigue cracking in steels [2,34]. The model of undeformed crack was parallel-flanks slot of the width b 0 with semicircular tip, Fig. 1( a ), as it has been repeatedly substantiated and used in analyses of cracks, e.g., by McMeeking [37], Needleman and Tvergaard [38], Rice et al. [39], or Toribio and Kharin [14,18-20]. The value of b 0 = 5  m was taken as a reasonable choice for steels [40]. Model design was subdued to ensuring the SSY in terms of the K -dominated crack tip autonomy [36]. The choice was made [19,20] in favor of full-scale specimens, which were double-edge-cracked panel (DECP) and central-cracked panel (CCP) under remote traction by uniform stress  ap , Fig. 1( b ). Due to specimen symmetries, the boundary-value problems were stated for the same region – a  X  W – a , 0  Y  H (Fig. 1( b ), shadowed), being a the initial crack size, 2 W and 2 H the panel width and height, respectively. Boundary conditions were posed according to the specimen symmetries and loading, Fig. 1( c ). To ensure the SSY, the model sizes were a = 15000 b 0 , a/W = 0.2 and W = H . The SIF calibrations were specified using the specimen geometry factor according to the compendium [41] for DECP and CCP, respectively. The textbook [34,36] estimation for the monotonic plastic zone dimension under plane strain, R Y = K 2 /(3   Y 2 ), renders for the chosen material, geometry and loading max{ R Y / a , R Y / H , R Y / W }  0.014 << 1, which ensures the SSY. Figure 1 : Model geometry and boundary conditions: ( a ) crack, ( b ) DECP and CCP specimens, ( c ) global view of the FE model of the specimen quarters shadowed in ( b ) with respective boundary conditions for CCP and DECP test-pieces, (d) near tip mesh refinement. Large-deformation elastoplastic solutions were generated using a finite element (FE) code with updated lagrangian formulation and additive decomposition of strain rates. The FE mesh design followed previous studies of large near tip deformations [37-39]. To overcome numerical problems associated with mesh degeneration at the crack tip, extensive trials were accomplished to ensure the solution mesh convergence for acceptable number of loading cycles. Re-meshing was considered to be not a suitable means to improve the FE model performance because of substantiated doubts [42] that, under the propensity to solution bifurcation of certain elastoplasticity problems due to their loss of ellipticity [43,44], small perturbations by re-meshing of the deformed tip shape in relation to the "true" one (yet unknown) can harm the results victim to pitfalls of a re-meshing technology. This later can break against mesh-sensitivity, which is rooted in the potential non-uniqueness of corresponding field solutions, to the extent that the relation between solution of the original continuum-mechanics problem and of its FE approximation may become questionable. To this end, it must not surprise to meet severe discrepancies between near tip deformations obtained using different mesh layouts, FE formulations and re-meshing procedures, which rendered crack faces folding without closure at the very first load cycles [17], as well as smooth surfaces arriving at closure at fairly large number of cycles [22, 23]. A variety of meshes permanently embedded in the material were explored attending the roles of FE size and shape, as well as of the interpolation order and integration scheme, as described elsewhere [42]. To postpone mesh degeneration, FE models of full-integration bi-linear quadrilateral elements were elaborated using rather high grade of element refinement