numero25

J. Toribio et alii, Frattura ed Integrità Strutturale, 25 (2013) 130-137 ; DOI: 10.3221/IGF-ESIS.25.19 133 and relying on suitable initial element shaping trying to ascertain the near tip deformation patterns yet to come in the deformed configuration in order to maintain the accumulated FE distortions within tolerable limits. R ESULTS AND D ISCUSSION enerated near tip solutions turned out to be fairly insensitive to the specimen geometry and loading in pertinent aspects. This way, the K -dominance over the crack tip zone was confirmed. For all geometry-and-loading cases, the crack-tip deformations evolved similarly to what is shown in Fig. 2. Plastic crack growth  a p is there appreciated as an advancement of the tip apex A 0 deeper into material. This way, the Laird-Smith conceptual scheme, which is considered to be one of the intrinsic mechanisms of FCG in ductile materials [2,31-35], is visualized. Simulations evidence that the crack does grow under cyclic loading, although with no bond breaking . Figure 2 : Crack tip deformations at unloading after accomplishing the first ( a ) and fifth ( b ) cycles of the load case I (DECP specimen); undeformed mesh fragment and tip contours are shown near the image center in ( a ) and in the bottom-left corner in ( b ), respectively, together with the positions of material points A 0 , B 0 and B 1 in the initial and deformed configurations. The plastic crack advancements  a p vs. cycle number N are presented in Fig. 3. The slopes of these curves render corresponding rates of plastic crack growth ( da / dN ) p . Its acceleration with  K is there evident, whereas the effect of R is rather vague. Calculated ( da / dN ) p values are of the order of 10 –6 m/cycle, which is proper for the Paris regime in steels [2,34]. The Paris-like equation ( da / dN ) p = C  K m fits the numerical results at m  2.25, which is reasonable for many alloys [34]. This mode of crack extension is sensible to an overload, which halts the crack advance (Fig. 3, load case IV). This way, the effects of  K and overload on FCG obtained by simulations agree with common experimental trends [2,34]. Figure 3 : Crack growth  a p vs. cycle number N along indicated loading routes in CCP specimen (the points correspond to the crack tip positions at the load cycle ends). No signs of PICC have ever occurred during simulated crack growth at R  0. Although cracks upon unloading shrink in a wake behind the tip more than at the tip itself in all load cases (Fig. 2), deformed crack faces have never and nowhere got to the initial crack width, and so, no contact between crack surfaces could be approached. This holds for an appreciable crack advancement  a p leaving a considerable plastic wake behind the tip, as it can be appreciated from Fig. 4 which displays crack penetration through substantial fraction of the plastic zones created in the first load cycle, the G