Issue 43

L.C.H. Ricardo, Frattura ed Integrità Strutturale, 43 (2018) 57-78; DOI: 10.3221/IGF-ESIS.43.04 64                       2 1 2 I ys K a (2.29) Expression (2.29) is similar to Irwin’s expression, eq. (2.16). In addition, if r << a, plasticity corrections are not necessary. Fig. 4 compares the normalized stress intensity factors as per Irwin’s and Dugdale’s approximations. The curves significantly differ as σ/σ ys → 1 ; however, similarities occur at r < σ/σ ys ≤ 0.2 . This strongly suggests that both Irwin’s and Dugdale’s approximation methods should be used very carefully because their differences in normalized stress intensity factor . Figure 4 : Normalized Stress Intensity factor as function of stress ratio [16].            min max ( ) 1 m c C K da dN K K K K    max ( ) m c C K da dN K K    1 max ( ) ( ) m m da C K K dN Table 1 : Empirical Crack Growth Equations for Constant Amplitude Loading [18]. The models of Irwin [6,7] and Dugdale [17] give an idea of the size of the plastic zone but not of its shape. The size, in general, is estimated as a circle of certain diameter ( r y or r p ) obtained on the basis of reasoning given in the above models for crack-tip-plasticity. In these models the effect of the shape of the plasticity affected zones is not taken into account. In the original Paris crack propagation equation [18] 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. [19] discuss crack growth models for variable amplitude loading and the mechanisms and contribution to overload retardation. Tab. 2 presents some authors and the application of their models. Retardation phenomenon Corbly & Packman [34] 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 [35,36]. 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 [37]. 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 [37]. 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 [36,37].