( ) î í ì ³ < = 0 / 1 0 / 0 / m eq m eq m eq H f s s s s s s (13) FINITE ELEMENT ANALYSES Damage model performance under cycling loading has been firstly checked on a single axisymmetric 4 node element. The element size is 1.0 x 1.0 mm. The material is a 22NiMoCr37 steel of German production for which damage parameters were previously determined by Bonora et al. (1998). A cyclic imposed displacement with zero mean value dm=0 and amplitude da=0.2 mm has been applied until element failure. Response under isotropic and kinematic hardening is given in figure 1 together with the displacement evolution with time. Here, time is a fictitious variable since viscoplastic and time dependent behaviors have been neglected. Figure 1 – Single element response under cyclic loading: a) axial stress vs axial strain; b) equivalent plastic strain vs time; c) stress triaxiality vs time; d) active damage vs time; e) active strain vs time; f) imposed displacement vs time In figure 1 it is shown how the effective plastic strain, together with active damage, accumulates only when stress triaxiality is positive. In this case, where the imposed nominal strain amplitude is 20%, failure is expected to occur after 5 cycles. Subsequently, the model has been used to investigate damage evolution in round notched tensile bar (R = 2mm ) under reversal plastic flow loading conditions, figure 2a. At the present time a single test has been performed on SA 537 steel. An initial monotonic ramp up to 0.2 mm has been applied followed by sinusoidal cycling with an amplitude of 0.125 mm. The cycling frequency was 0.0125 Hz. Local deformation field across the notch has been monitored using an extensometer with a gage length of 10 mm. In figure 2b, the comparison between the finite element results and the experimental data is given in term of applied load versus displacement at the gauge. It is important to note that the FEM model incorporating damage is capable to reproduce the load cycle in the near notch region pretty well if kinematic hardening is used. Isotropic hardening results in a very narrow
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