Issue 41

J. Toribio et alii, Frattura ed Integrità Strutturale, 41 (2017) 62-65; DOI: 10.3221/IGF-ESIS.41.09 63 N UMERICAL PROCEDURE or the study of fatigue propagation by plastic crack advance, a numerical simulation by the finite element method (FEM) under small scale yielding (SSY) was performed using the MSC.Marc software (nonlinear finite element code). Material was characterized as elastic–perfectly-plastic and the von Mises yield criterion was employed to define the plastic zone in the vicinity of the crack tip. Large strains and large geometry changes were used with an updated lagrangian formulation. Material properties (Young’s modulus E =200GPa, yield strength σ Y =600MPa and Poisson coefficient ν =0.3) were those associated with a typical high-strength steel. The geometry used in the computations is a symmetric double-edge-cracked panel under remote tension fatigue (Fig. 1). The undeformed crack was a parallel-flanks slot, where the kink length l 0 (representing 0.0012 times the total crack length) is deflected an angle α 0 (Fig. 2) and exhibits a semicircular shape (smooth blunting [9]) with b 0 =5µm, i.e., 0.055 l 0 . Four- node isoparametric quadrilateral elements (for plane strain applications) were used. Finally, a convergence study was performed to determine the optimal finite element mesh size and the most adequate number of steps required in the computations. (a) (b) Figure 1 : Finite element mesh: (a) general view; (b) crack tip. Figure 2 : Scheme and dimensions of the deflected crack kink. The key variable analyzed in this research work is the deflection angle of the kink in relation to the main crack. The four values α 0 =0, 15, 30 and 45º were used. The stress intensity factor (SIF) range used in the numerical procedure was Δ K =25MPam 1/2 (associated with the Paris regime of fatigue crack propagation). N UMERICAL RESULTS ig. 3 shows the cumulative equivalent plastic strain in the deformed geometry of the cracked solid with the deflected crack kink after the main crack. The initial geometry of the solid before loading ( initial crack profile ) is also shown. Results are obtained after applying 20 loading cycles (fatigue) with Δ K =25MPam 1/2 . It is observed how the crack, independently of the deflection angle, tends to propagate in mode I when subjected to remote mode I (opening) tensile loading. In addition, the distribution of cumulative equivalent plastic strain becomes more non-symmetric and exhibits more elevated values as the kink deflection angle increases. The crack deflection provokes a retardation effect in fatigue crack growth in global mode I, this effect being more pronounced for elevated deflection angle, as shown in Fig. 4. l α 0 0 b 0 F F