Issue 43

L.C.H. Ricardo, Frattura ed Integrità Strutturale, 43 (2018) 57-78; DOI: 10.3221/IGF-ESIS.43.04 65 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 [37]. 6. Increased percentage delay effects of peak loading given a percent overload are greater at higher baseline stress intensity factors [38]. 7. Delay is a minimum if compression is applied immediately after tensile overload [39]. 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 [40]. 9. Negative peak loads cause up to 50 per cent increase in fatigue crack propagation with R = - 1 [39]. 10. Importance of residual compressive stresses around the tip of crack [41] 11. Low-high sequences cause an initial acceleration of the crack propagation at the higher stress level which rapidly stabilizes [42]. Yield Zone Concept Crack Closure Concept Wheeler [20] Elber [27] Willenborg, Engle, Wood [21] Bell and Creager (Generalized Closure) [28] Porter [22] Newman (Finite Element Method) [29] Gray (Generalized Wheeler) [23] Dill and Staff (Contact Stress ) [30] Gallagher and Hughes [24] Kanninen, Fedderson, Atkinson [31] Johnson [25] Budiansky and Hutchinson [32] Chang et al. [26] de Koning [33] Table 2 : Fatigue Crack Growth Models [19]. Small Scale Yield Models While the basic layout of the small scale yield model has been established by Newman [29] and this approach was applicable to general variable amplitude loading. The small scale yield model employs the Dugdale [17] 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. 5. 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. The fatigue crack growth is simulated using the strip material as shown schematically in Fig. 5. Ricardo et al. [43] 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 Christensen [44] and Elber [45]. The crack closure concept put crack propagation theories on a firm foundation and allowed the development of practical life prediction for variable and constant amplitude loading, by such as experienced by modern day commercial aircrafts. Numerical analysis using finite elements has played a major role in the stress analysis crack problems. Swedlow [35] was one of the first to use finite element method to study the elastic-plastic stress field around a crack. The application of linear elastic fracture mechanics, i.e. the stress intensity factor range,  K , to the “small or short” crack growth have been studied for long time to explain the effects of nonlinear crack tip parameters. The key issue for these nonlinear crack tip parameters is crack closure. Analytical models were developed to predict crack growth and crack closure processes like Dugdale [17], or strip yield, using the plasticity induced approach in the models considering normally plane stress or strain effects. Schijve [36], discussing the relation between short and long cracks presented also the significance of crack closure and growth on fatigue cracks under services load histories.