Issue 35

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 35 (2016) 456-471; DOI: 10.3221/IGF-ESIS.35.52 460 In the original Paris crack propagation equation [14] the driving parameters are C,  K and m. In Tab. 1 it is possible to see some other crack propagation equations for constant amplitude loading, which are modifications of the Paris equation, relating the mentioned parameters. Murthy et al. [20] discuss crack growth models for variable amplitude loading and the mechanisms and contribution to overload retardation. There are many authors which have been developing fatigue crack growth models for variable amplitude loading. Tab. 2 presents some authors and the application of their models. Yield Zone Concept Crack Closure Concept Wheeler [21] Elber [28] Willenborg, Engle, Wood [22] Bell and Creager (Generalized Closure) [29] Porter [23] Newman (Finite Element Method) [30] Gray (Generalized Wheeler) [24] Dill and Staff (Contact Stress ) [31] Gallagher and Hughes [25] Kanninen, Fedderson, Atkinson [32] Johnson [26] Budiansky and Hutchinson [33] Chang et al. [27] de Koning [34] Table 2 : Fatigue crack growth models [20]. R ETARDATION PHENOMENON orbly & Packman [35] present some aspects of the retardation phenomenon some of which are presented below. 1. Retardation increases with higher values of peak loading  peak for constant values of lower stress levels [36,37]. 2. The number of cycles at the lower stress level required to return to the non-retarded crack growth rate is a function of  K peak ,  K lower , R peak , , R lower and number of peak cycles [38]. 3. If the ratio of the peak stress to lower stress intensity factors is greater than l.5 complete retardation at the lower stress intensity range is observed. Tests were not continued long enough to see if the crack ever propagated again [38]. 4 . With a constant ratio of peak to lower stress intensity the number of cycles to return to non-retarded growth rates increases with increasing peak stress intensity [37,38]. 5 . Given a ratio of peak stress to lower stress, the number of cycles required to return to non-retarded growth rates decreases with increased time at zero load before cycling at the lower level [38]. 6. Increased percentage delay effects of peak loading given a percent overload are greater at higher baseline stress intensity factors [39]. 7 . Delay is a minimum if compression is applied immediately after tensile overload [40]. 8. Negative peak loads cause no substantial influence of crack growth rates at lower stress levels if the values of R > 0 for the lower stress [41]. 9. Negative peak loads cause up to 50 per cent increase in fatigue crack propagation with R = - 1 [40]. 10. Importance of residual compressive stresses around the tip of crack [42]. 11 . Low-high sequences cause an initial acceleration of the crack propagation at the higher stress level which rapidly stabilizes [43]. S MALL SCALE YIELD MODELS hile the basic layout of the small scale yield model has been established by Dill & Saff [44], only improvements introduced later by Newman [45] made this approach applicable to general variable amplitude loading. The small scale yield model employs the Dugdale [16] theory of crack tip plasticity modified to leave a wedge of plastically stretched material on the fatigue crack surfaces. The fatigue crack growth is simulated by severing the strip material over a distance corresponding to the fatigue crack growth increment as shown Fig. 2. In order to satisfy the compatibility between the elastic plate and the plastically deformed strip material, a traction must be applied on the C W