Issue 41

S. E. Ferreira et alii, Frattura ed Integrità Strutturale, 41 (2017) 129-138; DOI: 10.3221/IGF-ESIS.41.18 130 fatigue lives under variable amplitude loads (VAL). The  K eff idea has been used since then in many semi-empirical FCG models, among them the strip-yield models (SYM) that estimate K op and FCG lives using a suitable da/dN  K eff rule properly fitted to experimental data [5-9]. Works that support the da/dN  f (  K eff ) hypothesis are extensively reviewed e.g. by Kemp [10] and by Skorupa [11-12], but many other works question it. FCG delays or arrests after OLs under high R while the crack remains fully opened, always maintaining K min > K op [13]; constant FCG rates induced by fixed {  K , R }, but highly variable  K eff loadings [14-15]; cracks arrested at a given R that restart to grow at a lower R under the same  K eff [16]; or the R -insensibility of FCG in inert environments [17], are examples of FCG behaviors that cannot be explained by Elber's postulate. Although this work does not aim to support or to refute Elber's idea, neither to review the works that support or question it, it can be claimed that there is no doubt it still remains controversial. In view of such doubts, this work first uses well-proved strip-yield mechanics [5-9] to model some da/dN  K curves measured at low and high R . However, instead of just assuming that a reasonable description of some fatigue data confirms that the  K eff hypothesis is valid, the very same mechanics is then used to verify if the same data can be equally described by the alternative view that FCG, instead of controlled by  K eff , is due to damage accumulation ahead of the crack tip. This critical damage model (CDM) assumes that fatigue cracks grow by sequentially breaking small volume elements (VE) adjacent to the crack tip after they reach the critical damage the material can sustain. If properly applied, this alternative idea do not need the  K eff hypothesis or requires arbitrary data-fitting parameters [13, 18-20]. FCG MODELS our FCG models are studied following: (i) the critical damage model (CDM) proposed in [18-20]; (ii) a strip-yield model (SYM) based on [6]; (iii) a combination of the strip-yield with the critical damage model (SYM-CDM) using fracture mechanics tools; and (iv) a modified strip-yield critical damage model (mod SYM-CDM) proposed here. Fig 1 illustrates the CDM principles that allow the use of  N concepts, used to describe fatigue crack initiation, to model FCG as well. This simple model basically assumes that: (i) fatigue cracks grow by successively breaking small VE located ahead of their tips; (ii) such VE can be treated as tiny  N specimens fixed along the crack path; (iii) these VE accumulate fatigue damage induced by variable strain ranges, which increase as the crack tip approaches them; and (iv) the fracture of the VE adjacent to the crack tip occurs because it accumulated the entire damage the material can tolerate. Figure 1 : Schematics of the FCG process caused by successive fractures of the VE adjacent to the crack tip at every load cycle [2].