In the present work, we postulate that a critical value of the stored plastic strain energy density (SPSED) is associated with fatigue failure in metals and is independent of the applied load. Unlike the classical approach of estimating the (homogenized) SPSED as the cumulative area enclosed within the macroscopic stress–strain hysteresis loops, we use crystal plasticity finite element simulations to compute the (local) SPSED at each material point within polycrystalline aggregates of a nickel-based superalloy. A Bayesian inference method is used to calibrate the critical SPSED, which is subsequently used to predict fatigue lives at nine different strain ranges, including strain ratios of 0.05 and −1, using nine statistically equivalent microstructures. For each strain range, the predicted lives from all simulated microstructures follow a lognormal distribution. Moreover, for a given strain ratio, the predicted scatter is seen to be increasing with decreasing strain amplitude; this is indicative of the scatter observed in the fatigue experiments. Finally, the lognormal mean lives at each strain range are in good agreement with the experimental evidence. Since the critical SPSED captures the experimental data with reasonable accuracy across various loading regimes, it is hypothesized to be a material property and sufficient to predict the fatigue life.
SummarySloshing water in the overhead water tank of a multi-storeyed building may be utilized to act as a tuned liquid damper for vibration control under wind and earthquake excitation. In conventional rectangular or circular water tanks, tuning presents difficulties as the sloshing frequency varies significantly with change in the depth of water in the tank. To address this issue, in this paper, we find shapes of tanks wherein the sloshing frequency is essentially independent of water depth over a large and useful range of water levels. Both two-dimensional as well as axisymmetric (three-dimensional) tank shapes are found. We use a direct boundary element method to find the sloshing frequencies in each case. In each case, a tentative simple analytical form for the tank shape is chosen with three free parameters, and these parameters are adjusted to obtain shapes where the first lateral sloshing frequency has negligible variation with water depth. For axisymmetric tanks, the circumferential (azimuthal) variation in field variables is restricted to the first harmonic, in the interest of lower computational effort. For both planar and axisymmetric cases, the working range of water depths is taken to be from 0.2 to 2 times the tank width. In both cases, the variation in first lateral sloshing mode frequency is found to be under 0.2% over the working range. In comparison, for constant width tanks such as the rectangular or circular ones, over the same range of water depths, the corresponding variation is more than 60 times greater.
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