numero25

J. Toribio et alii, Frattura ed Integrità Strutturale, 25 (2013) 124-129 ; DOI: 10.3221/IGF-ESIS.25.18 126 for an elastoplastic material with von Mises yield surface and Ramberg-Osgood strain-hardening rule. Mixed isotropic- kinematic hardening was used to capture Bauschinger-type effects. Model parameters corresponded to the steel used in the experiments (Tab. 1). Finite deformation analysis of a plane strain crack under mode I (opening) load was confined to small scale yielding, so that the stress intensity factor K is the only variable governing the near tip mechanics [6]. The initial crack was modeled as a parallel-sided round-tip slit with initial height b 0 = 5  m in agreement with data for fatigue cracks in steels [7]. Simulated loading histories consisted of several zero-to-tension cycles with K max /K IC = 0.45, 0.60 and 0.80, followed by rising load representing the EAC tests. An updated Lagrangian formulation was used in the computations. Plastic zones developed fairly self-similar with a scaling factor of (K/  Y ) 2 , which is natural for the K-dominated crack-tip domain and coincides with the prediction by Rice [5]. At loading up to the first load reversal at K max , the monotonic plastic zone is defined by the equivalent von Mises stress  eq =  Y (Fig. 1, left) where  Y is the tensile yield stress. Because of strain hardening, after load reversal the  Y -stress based yield criterion must not indicate further where plastic flow really proceeds. The cyclic plastic zones are defined then by positive equivalent plastic strain rate,  eq p > 0 (Fig. 1, right). They are approximately the same at cyclic load minima ( reversed zones at K min = 0) and maxima ( forward zones at K max ), smaller than the monotonic zone and quite stable with the cycle number. X Y Z 1 Y XZ 1 Figure 3 : Monotonic (left) and cyclic (right) plastic zones at K = K max for K max /K IC = 0.6 (the grid spacing is 50  m). At rising load, plastic flow starts at K = 0.2K max after elastic reloading and develops identically as the cyclic zone does up to attaining the pre-cracking level of K = K max , when it bursts and advances as the monotonic plastic zone does. The near tip stress distributions differ substantially from estimation given by Rice [5]. They stabilize after few first cycles as soon as a steady state of alternating plastic flow is approached. Fig. 4 shows the evolution of the hydrostatic stress in the crack plane beyond the tip,  =  (x), where x is the distance to the crack tip in the deformed configuration of a solid, during monotonic loading in the EAC test after pre-cracking. This stress component is focused since it is determinant for HAC controlled by stress-assisted hydrogen diffusion driven by the gradient   towards maximum stress locations [8, 9]. Figure 4 : Hydrostatic stress distributions beyond the crack tip during monotonic loading at EAC test after fatigue pre-cracking at K max /K IC = 0.45 (dashed lines) and 0.80 (solid lines).