numero25
J. Toribio et alii, Frattura ed Integrità Strutturale, 25 (2013) 130-137; DOI: 10.3221/IGF-ESIS.25.19 134 forward (monotonic) and the reverse ones, as well as the move forward of the actual cyclic plastic zone together with the crack tip, having these zones determined according to the criterion of non-zero equivalent plastic strain rate [20]. Figure 4 : Plastic zones near the tip of the grown crack in the deformed solid configuration (meshed area) after accomplishing of 90 loading cycles along the route II: actual cyclic (reversed) plastic zone at the end of the 90th cycle (white contour line) and the material which was involved in plastic flow in the first loading cycle at its top (monotonic plastic zone, light-grey area) and bottom (reversed plastic zone at unloading, dark-grey area). Undeformed crack contour is present at the figure bottom. Although presented modeling agrees with experimental trends of FCG, crack advancement by blunting re-sharpening can hardly be the entire mechanism of every FCG occurrence, as far as fatigue cracks usually evidence, e.g., by means of fractography, the signs of material damage and fracture. This may be the reason why simulated solely plastic crack growth is insensitive to the load ratio or manifests negative crack growth rate after an overload (Fig. 3). FCG is seen [2,4,34] to proceed usually by various mechanisms of deformation, damage and bond breaking which go on synergistically. As well, crack closure upon unloading can arise owing to a series of causes, both intrinsic (such as fracture surface roughness originated from various microstructural damage and fracture events, or stress-induced phase transformations, etc.) and extrinsic (e.g., in-crack debris, oxides, and so long) ones. However, presented results imply that crack closure can be neither a necessary requisite nor a decisive factor for the mentioned FCG trends. Indeed, the plastic advancement of a crack behaves per se in agreement with well known experimental FCG trends, but with no signs of PICC . This latter may happen at larger number of cycles, as it occurred in simulations by Tvergaard [22,23], as well as may not. The supposed consequences of closure in FCG (e.g., the overload retardation or arrest [34]) do appear with no closure. Accordingly, the practiced indirect assessments of PICC-related issues from FCG behaviour [7] acquire a deal of spuriousness, which can make them artifacts. Displayed results fairly agree in all pertinent aspects with other large-strain analyses of cracks under cyclic loading [22,23], but challenge those small- and finite-strain simulations (such as, e.g., [13,16,21,24]), where crack growth was imposed by means of cutting the material arbitrarily with a "virtual knife" in analyst's hands counting on neither the material nor the applied load. So, all these latter models were intrinsically unable to render per se any effect of the loading route on FCG, such as the influence of K or overload. In contrast, presented modeling does this. Moreover, by virtue of the permanent gluing of FE meshes to the material, it is revealed here how the crack grows by plastic straining, which renders material transfer from the crack front onto its lateral surfaces, as it does a neighborhood of the material point B 1 in Fig. 2. Material "bricks" situated initially a little bit aside the top A 0 of the arc B 0 B 1 A 0 , which shapes the crack tip, move there sideways and build the crack flanks up, i.e., contribute to crack enlargement. This is lengthened additionally by stretching of these material “bricks”, which are placed to form the crack flanks, Fig. 5( a ), where large tensile plastic strain 0 p yy in the in-plane of the crack direction is observed, Fig. 5( b ), which implies negative axial strain YY XX < 0 near the crack tip by virtue of plane-strain large incompressible plasticity. This latter result agrees with experimental X-ray diffraction study of the strain fields near fatigue cracks, which reported the "negative anomaly" in yy strain behind the tip [45], but contradicts the results of small-strain numerical analysis [13] schematized in Fig. 5( c ). This way, performed large-deformation simulations discard the mechanism of PICC implied from the small-strain modeling [13], where material elements behind the crack tip underwent out-of-plane plastic stretching 0 p yy accompanied by shrinking along the crack surfaces 0 p p xx yy by virtue of the plane-strain incompressible plasticity, Fig. 5( c ). Accordingly, it was argued that this out-of-plane stretched material on the growing crack surfaces behind the tip could fill-
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