Issue 41

S. E. Ferreira et alii, Frattura ed Integrità Strutturale, 41 (2017) 129-138; DOI: 10.3221/IGF-ESIS.41.18 134 (10) (11) Since the numerical model calculates fatigue damage at the central position of each VE, the crack increment induced by each load cycle is given by the location where the damage reaches one ahead of the crack tip. Therefore, the damage value of the new first element are calculated using a linear interpolation procedure. As the number of elements is unchanged, to keep the width sum of all elements equal to the pz size, the first and the last element can have a variable width. Moreover, since Eq. (6) reproduces the sigmoidal shape of da/dN  K curves, and since its only adjustable constant C can be directly calculated for any {  K , R } combination from the  N properties of the material, the CDM used here in fact have no data- fitting parameters (whereas the NASGRO FCG rule used at the SYM needs 4 of them). The C constant (Eq. 6) is found using several da/dN values calculated by SY-CDM procedures using C&M or SWT rules. This process is similar to the adopted by the original CDM. The main difference here is the replacement of a shifted HRR strain field by a strain field derived from the displacement field of the SYM. The new modification proposed here for the SY-CDM eliminates the need of assuming that the da/dN versus  K curve of the material is always described by McEvily’s rule Eq. (6). This can be achieved by assuming two new hypotheses, which are also based on the physics of the FCG process. The first supposes that there is a limit strain range below which the crack does not grow by fatigue, which is directly related to the SIF range threshold  K th . The second assumes the crack becomes unstable at a maximum plastic strain related to the critical stress intensity factor, or to the material toughness. These hypotheses are described by: (12) The plastic strain range calculated by Eq. (12) is used by the modified SY-CDM to calculate the damage at each element by Eq. (10) or (11). The interpolation routine was improved to work with a fixed number of elements (400) for any load condition and, due these hypotheses, one less step is required to estimate the FCG Finally, a major fringe-benefit of all CDMs used in this work must be emphasized: if they can reasonably estimate FCG rates for a given material, they do so using only its  N ,  K th , and K C properties, without the need for any adjustable data-fitting parameters. Therefore, these simple and sound models can indeed be called predictive , since they do not need or use actual FCG data points to estimate da/dN rates. The results presented next support this claim. E XPERIMENTAL RESULTS AND DISCUSSIONS hese four models are compared against experimental da/dN   K data measured at R  0.1 and R  0.7 for two materials, a 7075-T6 Al alloy and a 1020 low carbon steel, as described elsewhere [19]. These materials properties and the C values used by the C&P CDM (model i) are listed in Tab. 1. FCG rates predictions by the SYM (model ii) use material properties from NASGRO version 4.02, as shown in Tab. 2. But instead of using Poisson's coefficients to estimate the constraint factor  , its value was varied to verify its effect on FCG predictions. Values  3 for 7075 and  2 for the 1020 resulted in good approximations and are adopted here. The  K th (R) and K IC from Tab. 1 are used in Eq. 8, since they approximate the data better than the values listed in NASGRO. The constants C from Eq. (6), model (iii), are listed in Tab. 3. Material S Y (MPa) S U (MPa)  c (MPa)  c b c K IC (MPa  m)  K th (MPa  m) C (for  K in MPa  m) R  0.1 R  0.7 7075-T6 498 576 709 0.12 -0.056 -0.75 25.4 3.4 2.9 8.23e-09 1020 285 491 815 0.25 -0.114 -0.54 277 11.6 7.5 2.73e-10 Table 1 : Material properties [19] and C values obtained by several strain concentration rules.     1 ( ) ) ( 1 2 2 c y c N i i           1 max ( ) 1 2 ( ) ( ) 2 b c y c c N i i i           ,mod , , , ,max ( ) ( ) ( ) ( ) ( ) ( ) y y y th y cr y cr y i i i i i i                      T