Issue 37

V. Anes et alii, Frattura ed Integrità Strutturale, 37 (2016) 124-130; DOI: 10.3221/IGF-ESIS.37.17 125 fundamental prerequisite to estimate fatigue damage under random loading conditions. The main focus was on the hypothesis that states the existence of a typical SSF damage map for each material family. T HEORY , MATERIALS AND METHODOLOGY ased on experiments the present authors have found out that fatigue damage from normal stresses have a damage scale different from the one found in shear stresses, especially under multiaxial loading conditions. Therefore, to compute a multiaxial damage parameter, both normal and shear stresses must be reduced to the same damage scale. In literature, this reduction is commonly performed using a constant; usually this constant is a function of uniaxial fatigue limits. However, results show that the damage scale between normal and shear stresses depends on the stress amplitude ratio  , and also on the stress level [8]. To account these findings in fatigue damage assessment, the present authors developed the SSF equivalent shear stress. This damage parameter is an equivalent shear stress, were its magnitude represents the fatigue damage of a given multiaxial loading. Eq. (1) shows the SSF model; in the left the SSF equivalent shear stress and at right the uniaxial shear SN curve [8].       max , b a f block ssf A N        (1) The   , a ssf   function shown in Eq. (1) is given in Eq. (2), this function is the so-called SSF damage map and aims to update the damage scale of normal stresses to the shear damage scale.                           2 3 2 3 4 5 , a a a a ssf a b c d f g h i (2) where  a is the normal stress component of a given biaxial loading and  is the stress amplitude ratio ( a a     ). The polynomial constants “ a ” to “ i " are determined through experiments. The values of these constants for the 42CrMo4 steel are the following:        a=2.69; b= 9.90E 03; c=1.69E 05; d= 9.52E 09; f= 5.99; g=11.72; h= 8.04; i=1.63 Generalization of the SSF damage map The SSF damage map, given by the 5 th polynomial function shown in Eq. (2) was obtained for the 42CrMo4 material and translates its cyclic behavior under different stress amplitude ratios and stress levels. Therefore, the SSF fatigue estimates for other materials must be done using their SSF damage maps, which must be previously obtained by experiments. However, within a given steel family it has been assumed that the SSF damage map does not vary significantly, thus the SSF damage map computed for a given material of this family can be used as a typical SSF damage map and can be shared between material of this family. This assumption has been tested with success in two high strength steels, the Ck45 and C40, and is tested here with the 1050QT and 304L steels. The 1050QT clearly belongs to the 42CrMo4 family because their mechanical properties are very alike; please see Tab. 1. However, the mechanical properties of the 304L stainless steel are clearly out of the high strength steels family [9], thus it is expected a lower performance in the SSF fatigue life correlations for this material. The use of the 42CrMo4 SSF damage map in other materials is not performed directly, in these cases the SSF damage map must be updated using the tensile ultimate stresses as shown in Eq. (3). ,42 4 ( , ) u eq u CrMo ssf                    (3) where   ,42 4 u u CrMo is the ratio between the material’s ultimate tensile stress (material that belongs to the 42CrMo4 family but its SSF damage map is unknown) and the ultimate tensile stress of the 42CrMo4 steel. The ultimate stress is a mechanical parameter that indicates clearly the steel family and has been used to estimate SN curves. Thus being the SSF damage map obtained based on the material SN curves under different stress amplitude ratios the use of the ultimate stress to perform this update was hypothesized and presented in [9]. B