Issue 37

P.S. van Lieshout et al., Frattura ed Integrità Strutturale, 37 (2016) 173-192; DOI: 10.3221/IGF-ESIS.37.24 181 Originally, [3] included a square root term in the hypothesis to try to account for the influence of the maximum stressed material volume on the local stress. However, this term was found to be unsuccessful and got removed from the equation [37]. The EESH defines a local equivalent stress  EESH , based on the Von Mises stress equivalent which is determined as a function of the phase angle  (see Eqs. 9-10). The interaction of the shear stresses acting at different material planes is incorporated by an effective shear stress term F which is also a function of the phase angle  . The effective shear stress is an integral of all shear stress components (i.e.  n ) acting on the material planes (in two dimensional space) defined by their angle of rotation  . Due to this integration procedure frequency induced non-proportionality is also covered in this hypothesis. However, as can be seen from Eq. 11, the calculations become significantly more complex once variable amplitude loading is encountered. Henceforth, damage calculation requires a local SN curve. Such a local SN-curve was constructed with experimental data from a welded flange-tube specimen in Sonsino & Kueppers (2001).                   0 0 EESH EESH F F (9)                2 2 2 0  3 EESH x y x y xy (10)            0 1 p F f d (11)                    , 1 :  1 :  n L s p n i s i for constant amplitude loading f for variable amplitude loading L  s whereby L sequence length of the load spectrum C OMPARATIVE STUDY he stress state at a location of interest can be analyzed at different levels. In the current literature different methods have been developed based on nominal stress [38, 9], hot spot stress [38-41] or structural stress [42-44] and notch stress [19, 45-47]. They differentiate amongst one another in the amount of local stress information. The nominal stress approach only considers the membrane component of stress induced by the macro-geometry of the joint, excluding stress concentrations [23]. The hot spot or structural stress approach considers an equilibrium-equivalent structural stress part as a composition of a membrane and bending stress component. It uses linear extrapolation towards the weld toe in order to account for the membrane and bending component of stress (or through-thickness linearization), excluding the effect of the notch at the weld-toe transition. This means that only those stress concentrations are being considered which are caused by the structural detail of the joint [40]. The effective notch stress approach accounts for the additional stress peak induced by the notch at the weld-toe transition (i.e. self-equilibrating notch stress part). Typically, the more local information is added the more accurate the fatigue lifetime estimates should become. However, at a certain point it is no longer worthwhile to add more local information because it cannot overcome statistical scatter in experiments [14]. This comparative study is based on nominal stresses. The reasoning behind this is that more local stress information (e.g hot spot/structural stress, notch stress) would require a specified joint geometry. The objective is to execute a comparative study which is independent of joint dimensions. Moreover, the results can be considered conservative because more local stress information would improve the accuracy. Constant amplitude loading Five different conceptual CA load cases have been established presuming harmonic sinusoidal loading, see Tab. 1. The stress amplitude ratio was set to    / 1/ 3 A A (with a normal stress amplitude of   100  A MPa ) and a frequency ratio of    / 1 f f . Load case 5 is an exception whereby the frequency ratio is set to 2 .