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J. Toribio et alii, Frattura ed Integrità Strutturale, 25 (2013) 130-137; DOI: 10.3221/IGF-ESIS.25.19 131 the experienced nonlinearity of the load-deformation curves (as obtained with the use of displacement or strain gauges, interferometry, or other devices to monitor deformations) “indicates that there is a progressive change in geometry of the specimen, which must be caused by the closing of the crack” [5]. This way, the very identification of PICC lacks of direct evidence and its responsibilities in FCG remain debatable. Since in situ visualization of the near-tip deformations is hardly feasible in the places where the plane-strain situation is approached, computational simulation turns out to be the right way to determine them. Accounting for both constitutive (inelasticity) and geometrical (large displacements and strains) nonlinearities is here essential. For cracks growing by means of local material rupture, the alteration of solid boundary via crack advance by bond breaking is the third nonlinearity. Then, the most precise revelation of the near tip situation would be achieved taking into account all three mentioned nonlinearities. Up to date, among available analyses of fatigue cracks, some of them have not accounted for large deformations (such as, e.g., [13, 15, 16]), whereas others (e.g., [14, 17-24]), although fulfilling this deficiency, presented partial data about cracks under cyclic loading. Anywise, common shortcoming is the lack of realistic treatment of the crack growth by means of bond breaking. This latter was simulated usually by cutting the material bonds fairly subjectively along finite-size steps via finite element node release to the analyst’s discretion at the bottom, mid or top points of designated loading cycles irrespectively of both the material and applied load (cf., e.g., [13, 16, 21, 24]), and thus, having hardly whatsoever to do with the physics of crack advance. The efforts involving more realistic mechanisms of material damage and bond breaking directly in the modeling of FCG have been undertaken since nearly a decade (e.g., [25, 26]) usually by substantial computational expenses. However, these relatively few attempts are at rather early stage of development and encounter conceptual and technical difficulties on the way to implement damage mechanics in large-deformation formulations. Finally, having difficulties with direct involvement of realistic material rupture modeling into simulation of FCG, another approach counts on the stress-, strain- or energy-based variables as fatigue damage monitors [27-30]. However, the evolution of a tip of a growing crack cannot be solved there straightforwardly. Obviously, ignoring any of the three commented nonlinearities worsens the resolution of the crack-tip fields. Disregard among them of the crack growth via bond breaking, modeling of which is surrounded by the most controversy, may have significance for the simulation outcome. However, would consequent inaccuracy be more or less substantial in comparison with faultiness of unrealistic modeling of the bond breaking merely by making use of a “virtual knife” in analyst’s hands has to be verified through much advanced analyses involving duly all three concerned nonlinearities. Meanwhile, among conceptual mechanisms of FCG, the one, which was suggested by Laird and Smith [31] and reaffirmed by Pelloux [32] and Neumann [33], and which was emphasized as the rational physical model for FCG in ductile materials [2, 10, 22, 23, 34, 35], relies solely on the near tip plastic deformations under cyclic loading without involvement of pull- apart bond breaking. Then, high-resolution large-deformation elastoplastic simulation is the right way to visualize this mode of FCG. Recent advances in large-strain elastoplastic analyses of cracks under cyclic loading [14,17-20,22,23] revealed various aspects of FCG according to the Laird-Smith concept. The scope of this paper is to narrate the results of modeling of cracks under cyclic loading, which are in particular association with the matter of PICC verification and assessment, and have not been revealed in previous presentations [14,18-20] of the performed simulations. Deformations near the crack subjected to mode I cyclic loading under plane strain and small scale yielding (SSY) are described with the intention to bring insight into some long-standing controversies about the crack blunting re-sharpening and PICC under load cycling. Model material parameters correspond here to medium-high strength steel. Notwithstanding, using common normalization techniques, generated solutions are applicable not to this sole material but to a similitude class fixed by the magnitudes of pertinent dimensionless parameters, such as the ratio of Young modulus E to the yield stress  Y , Poisson coefficient  , and so on. M ODELLING he results presented herein proceed from the extensive modeling of the mode I crack tip fields in elastoplastic material under SSY in terms of the crack tip autonomy dominated solely by the stress intensity factor (SIF) K [36]. Model design (geometry, loading and constitutive material model) and the large-strain analysis procedure were basically the same as presented and substantiated elsewhere [14,18-20]. Their outline is as follows. At large strains, material hardening approaches saturation, so that elastic perfectly-plastic constitutive model can be an acceptable approximation, provided the value of  Y corresponds not to the initial yield point, but to some saturation stress level, the "effective" yield stress as modified by strain-hardening. Then, the model of ideal elastoplastic solid having E = 200 GPa,  = 0.3 and  Y = 600 MPa with von Mises yield surface and associated flow rule was chosen. T