Issue 35

Chahardehi et al, Frattura ed Integrità Strutturale, 35 (2016) 41-49; DOI: 10.3221/IGF-ESIS.35.05 44 2) The effective stress intensity factor range  K eff is defined as a function of  K and R-ratio. This is the method employed by Walker [31], and by Kurihara [32] and Eason [33], in the form of an effective coefficient U where  K eff = U.  K . 3) Equations where the general form is similar to the Paris law but includes other terms such as the material toughness and K max , such as Forman’s equation [34], the relationship proposed by McEvily et al [35] and a number of other authors. For a review of some of the famous fatigue crack growth rate equations see the works of Bloom [36] and Huang [37]. The equations are mainly based on empirical plasticity-induced crack closure models. Additional mechanisms include asperity-induced and oxide-induced closure [36]. The Two Parameter models, e.g. as proposed by Vasudevan [38] can either be deemed to be among the second group of methods (above), or the third type of methods. Kurihara [32] predicts that for fully reversed loading (R = -1.0), only 39 percent of the stress intensity factor range is effective for crack growth. However, not many empirical models are based on experimental data for part compressive stresses (and fully compressive stresses, for that matter). Jones et al [23] found that by using a form of equation suggested by Eason [33], and finding the coefficients from experimental data, the effects of negative R-ratio on the fatigue crack growth rates for even the high stress range tests could be bounded by correlating the foregoing equation to only positive R-ratio test results and extending the resulting equations into negative R-ratio regime. F ACTORS A FFECTING FCG IN COMPRESSIONS - D ISCUSSION eal life applications where fatigue loading is involved present a number of complicating problems e.g. variable amplitude loading, and residual stresses, to name a couple, and some of there factor are examined in the rest of this section. The examination is by no means exhaustive, but each sub-section provides a meaningful understanding to the whole topic: Variable amplitude loading – effect of overload and underload Variable amplitude loading itself poses a number of complications. Variable amplitude cycles would in reality have a variable R-ratio, whereas cycle-by-cycle analysis using an R-ratio dependent growth law is tedious. Indeed, to overcome this particular issue, the loading histogram (stress range vs. number of occurrence) could be rearranged and grouped into separate subsets with similar R-ratios for ease of calculation. However, another complicating factor, which is less easily surmountable, is the influence of the previous stress cycle on the increment of growth. To demonstrate the effect of load history on fatigue, McEvily et al [39] argue that if several alloys are ranked in terms of fatigue crack growth resistance under constant amplitude loading conditions, the same order of rating may not apply under variable amplitude loading, based on findings of Minakawa et al [40]. This observation also confirms a deeper material dependence of fatigue behaviour. To provide an explanation for the effect of overload and underload (i.e. compressive overload), Silva proposed as a competition between a damage accumulation effect and a residual stress effect [41]. In a study by Stephens et al [42] it is experimentally shown that compressive loading greatly reduces the tensile overload effect. This is shown in Fig. 1 taken from Stephens [42]. McEvily et al [39] argue that “… the influence of compressive overloads or various combinations of compression-tension overloads is generally of lesser significance than a single tensile overload, an effect which can be related to a reduction of the crack opening level as the results of a compressive cycle.”. Material-dependence of the overload and underload behaviour Silva maintains that the difference in the sensitivity of different materials to negative loads may be due to the Bauschinger effect [41]. Based on test results, Silva [43] also found that materials exhibiting strong cyclic hardening and a high Bauschinger effect were strongly affected by the compressive load while materials exhibiting no cyclic hardening were relatively insensitive to applied compressive load. Jones et al [23] observe that experimental results found from a specific material do not necessarily generalise, i.e. do not predict the behaviour of other alloys because with the exception of corrosion-induced blunting, crack-tip blunting and crack-tip plasticity behaviour are governed by the toughness/yield ratio of the material. In their review of fatigue crack growth, Allen et al [44] argue that where stress ratio dependence is observed, such as the Forman equation [34], it is usually associated with additional cyclic crack extension by brittle fracture or microvoid coalescence. See for example [45-46]. Where neither mechanism is operative there is generally no stress ratio R