Issue 36

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 36 (2016) 201-215; DOI: 10.3221/IGF-ESIS.36.20 205 Yield Zone Concept Crack Closure Concept Wheeler [14] Elber [21] Willenborg, Engle, Wood [15] Bell and Creager (Generalized Closure) [22] Porter [16] Newman (Finite Element Method) [23] Gray (Generalized Wheeler) [17] Dill and Staff (Contact Stress ) [24] Gallagher and Hughes [18] Kanninen, Fedderson, Atkinson [25] Johnson [19] Budiansky and Hutchinson [26] Chang et al. [20] de Koning [27] Table 2 : Some Fatigue Crack Growth Models [13]. Retardation phenomenon It has been noted that, under certain conditions, the crack growth presents a slower rate, called retardation, due to several factors. Despite recent large increase in research into the retardation effects in crack propagation there are many aspects of load interaction phenomena that lack adequate explanations. It is presented here some several aspects of the retardation phenomenon by Corbly & Packman [28]. 1. Retardation increases with higher values of peak loading  peak for constant values of lower stress levels [29,30]. 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 [31]. 3. If the ratio of the peak stress to lower stress intensity factors is greater than l.5 retardation at the lower stress intensity range is observed. Tests were not continued long enough to see if the crack ever propagated again [31]. 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 [30,31]. 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 [31]. 6. Increased percentage delay effects of peak loading given a percent overload are greater at higher baseline stress intensity factors [32]. 7. Delay is a minimum if compression is applied immediately after tensile overload [33]. 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 [34]. 9. Negative peak loads cause up to 50 per cent increase in fatigue crack propagation with R = - 1 [33]. 10. Importance of residual compressive stresses around the tip of crack [35] 11. Low-high sequences cause an initial acceleration of the crack propagation at the higher stress level which rapidly stabilizes [36]. Small Scale Yield Models While the basic layout of the small scale yield model has been established by Dill & Saff [37], only improvements introduced later by Newman [38] made this approach applicable to general variable amplitude loading. The small scale yield model employs the Dugdale [12] 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. 4. In order to satisfy the compatibility between the elastic plate and the plastically deformed strip material, a traction must be applied on the fictitious crack surfaces in the plastic zone ( a  x < a afict ), as in the original Dugdale model, and also over some distance in the crack wake (a open  x < a), where the plastic elongations of the strip L(x) exceed the fictitious crack opening displacements V(x) . The compressive stress applied in the crack wake to insure L(x)=V(x) are referred to as the contact stresses. Ricardo et al. [39] discuss the importance in the determination of materials properties like crack opening and closing stress intensity factor. The development of crack closure mechanisms, such plasticity, roughness, oxide, corrosion, and fretting product debris, and the use of the effective stress intensity factor range, has provided an engineering tool to predict small and large crack growth rate behavior under service loading conditions. The major links between fatigue and fracture mechanics were done by Elber [21]. The crack closure concept put crack propagation theories on a firm foundation and