Issue 50

M.F. Borges et al., Frattura ed Integrità Strutturale, 50 (2019) 9-19; DOI: 10.3221/IGF-ESIS.50.02 10 N UMERICAL M ODEL o study the effect of the yield stress on FCG, two materials were considered: the 7050-T6 aluminium alloy (AA) and the 304L stainless steel (SS). To avoid the influence of geometry and loading, the same CT specimen (see Fig. 1) and loading conditions were used. The specimen had a width, W, of 50 mm, an initial crack length, a 0 , of 24 mm, therefore a 0 /W is 0.48. To reduce numerical effort and since the specimen in question is symmetric relatively to two planes, only ¼ of the specimen was considered. Also to reduce the numerical effort, only a 0.1 mm of the thickness of the specimen was modelled. Adequate boundary conditions were implemented to reproduce the symmetry of the specimen and state of stress. Fig. 1b shows a lateral view of the specimen with symmetry conditions for plane stress state. For plane strain state an additional out of plane condition was implemented to avoid deformation along the thickness direction. The load was applied at the hole of the specimen and varied between 4.167 N and 41.67 N, therefore the load ratio was R=0.1 and K max , K min and  K were 18.3; 1.83 and 16.5 MPa.m 0.5 , respectively. Material Hooke´s law Voce law Armstrong-Frederick law E ν Y 0 Y Sat C Y C X X Sat [GPa] [-] [MPa] [MPa] [-] [-] [MPa] AA7050-T6 Reference 420.50 420.50 0.50Y 0 210.25 210.25 0.75Y 0 71.70 0.33 315.38 315.38 0 228.91 198.35 1.25Y 0 525.63 525.63 1.50Y 0 630.75 630.75 SS304L Reference 117 0.50Y 0 58.50 0.75Y 0 196 0.30 87.75 204 9 300 176 1.25Y 0 146.25 1.50Y 0 175.50 Table 1 : Material parameters used in the analysis of the effect of the yield stress on fatigue crack growth. The mechanical behavior of the materials was assumed to be elastic-plastic. The isotropic elastic domain was defined by the generalized Hooke’s law elastic parameters Young’s modulus (E) and Poisson’s ratio (ν). The plastic behavior was described by von Mises yield criterion coupled with a mixed hardening model using Voce isotropic and Armstrong- Frederick kinematic hardening laws, under an associated flow rule. Voce isotropic hardening law is given by:       p p 0 Sat 0 Y Y ε =Y + Y -Y [1-exp -C ε ] where Y 0 , Y Sat, and C Y are the material parameters of Voce law and p ε is the equivalent plastic strain. The Armstrong- Frederick kinematic hardening law can be written:   p sat X X =C -X -X ε σ        X σ   T