13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- As residual stresses are not considered in the Tanaka-Mura model according to Eq. (3), they are imposed as additional external loading. Therefore, the residual stresses are in the Tanaka-Mura equation implicitly evaluated through the average shear stress range on the slip band Δ߬̅ . Figure 3 shows the shear stress distribution and nucleated micro-cracks for a typical high cycle fatigue regime load level (450 MPa). In the beginning, micro-cracks tended to occur scattered in the model and form in larger grains that are favorably oriented and show higher shear stresses. But after a while, existing micro-cracks started coalescing, causing local stress concentrations and amplifying the likelihood of new micro-cracks forming near already coalesced cracks. 4. Modeling and analysis of crack propagation in welded stiffened panels It is well-known that the residual stress in a welded stiffened panel is tensile along a welded stiffener and compressive in between the stiffeners. Residual stresses may significantly influence the stress intensity factor (SIF) values and fatigue crack growth rate. A total SIF value, Ktot, is contributed by the part due to the applied load, Kapp, and by the part due to weld residual stresses, Kres, as given by equation (4): Ktot = Kappl + Kres (4) The so-called residual stress intensity factor, Kres, is required in the prediction of fatigue crack growth rates. The considered analysis method is based on the superposition rule of linear elastic fracture mechanics (LEFM). The finite element method (FEM) has been widely employed for calculating SIFs. For evaluating Kres, it is important to input correct initial stress conditions to numerical models in order to characterize residual stresses [22, 25]. In the FE software package ANSYS [26] the command INISTATE is used for defining the initial stress conditions. 4.1. Specimen’s geometry and loading conditions Fatigue tests with constant stress range and frequency were carried out on a stiffened panel specimen with a central crack, [23]. The specimen geometry is shown in Figure 4. The material properties of the used mild steel for welding are given in Table 1. Table 2 shows the fatigue test conditions applied in the experiment. The cross sectional area of the intact section, and the average stress range away from the notch, are denoted as, Ao and Δσo, respectively. The force range, and the stress ratio are denoted by ΔF = Fmax - Fmin, and R = Fmin/Fmax, respectively. The average applied stress range was Δσo = 80MPa. The initial notch length was 2a = 8mm and the loading frequency was 3 Hz. Table 1. Material properties E – Young’s modulus 206 000 MPa ν - Poisson’s coefficient 0.3 σo – Yield strength 235 MPa Table 2. Fatigue test conditions Ao [mm2] ΔF [N] Δσo [MPa] R 1200 96000 80 0,0204
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