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In this paper, by using the Armstrong- Frederick nonlinear kinematic hardening model, the ratchetting behavior of carbon steel piping elbows is described under conditions of steady internal pressure and dynamic moments out-of-plane at frequencies typical of seismic excitations. The elbows had an outside diameter of 60.3 mm and thicknesses of 3.91 and 5.54 mm. For each thickness two bend radius geometries (long and short) were studied. A pure out-of-plane bending moment applied at one end of a 90 welding elbow is reacted by a purely torsional moment at the other end. Three-dimensional elastic-plastic analyses by Armstrong-Frederick nonlinear kinematic hardening model are carried out to evaluate structural ratcheting behaviors. Initial, the rate of ratchetting is large and then it decreases with the increasing cycles. While there is practically no strain accumulation in the axial direction, the direction of highest ratcheting is along the hoop direction. The cyclic strain accumulation against response moment for each component is assessed. By Armstrong-Frederick model, the predicted ratchetting of low moments near is to the experimental results, while for the high moment, this model will over-predict the ratcheting strain.

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In this paper, three dimensional frequency analysis of moderately thick plate with considering the effect of a circular hole is presented by using of Three Dimensional theory of Elasticity and a numerical mesh-less method with radial point interpolation functions. Using this numerical method, the field variable (such as displacement) is interpolated just using nodes scattered in the plate domain. Because there is no relation between nodes, they can be scattered arbitrarily in the problem domain. The plate is made of a functionally graded material that is consists of two different phases of metal and ceramic. Mechanical properties of the plate change independently in the length, width and thickness directions of it using (according to) Mori-Tanaka model. The effects of radius of holes, different volume fraction exponents of functionally graded plate in three directions and different boundary conditions on natural frequencies of the plate is investigated by using of the code written in MATLAB and simulation in ABAQUS. The results have been compared with results in available papers and it shows the high accuracy of the method used in this present work.

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Strain accumulation of the components in power-plants and large industries, which causes physical and human costs, has been interested of many researchers in last decades, because of unexpected collapse of these components under periodic loads and internal pressure. In this study, the effect of four basic factors of piping elbow material, frequency of periodic loading (typically below 10 Hz), internal pressure of pipe and periodic dynamic moments on the amount strains accumulation of piping elbows have been considered. Also, the effect of factors variation listed above, on the amount of strains accumulation has been studied. Analyses done in this study, shows that increase in loading frequency, internal pressure and dynamic moments at the end of piping elbow, increases the amount of strains accumulation. Behavior of strain accumulation of two kinds of materials (carbon steel and stainless steel) was investigated in same condition. Studies showed that the strain accumulation in carbon steel are more than stainless steel due to differences in hardness behavior of these materials. The results showed that, stainless steel piping elbow has better performance compared to carbon steel.

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In this study, the strain ratcheting behavior of piping branch under the influence dynamic bending moments are evaluated. The Chaboche nonlinear kinematic hardening model and combined Armstrong-Fredrick model with isotropic rule are used to predict the plastic behavior of the piping branches. The results of FE method by using the hardening models have been compared with the results of the experimental method and Armstrong-Fredrick kinematic hardening results. The constant parameters of the hardening model and stress-strain data have been obtained from several stabilized cycles of specimens that are subjected to simulated seismic bending cycles. Both the FE and experimental results showed that the maximum strain ratcheting occurred on the flanks in the piping branch hoop stress direction just above the junction. The ratcheting strain rate increases with increase of the dynamic moment levels. The FE results show that initial rate of ratcheting is large and then it decreases with the increasing of loading cycles. In BMS1 sample, the FE hoop strain ratcheting data by using chaboche nonlinear kinematic hardening model comparing with the other hardening models to be near that found experimentally values. In BMS2 and BMS3 components, the FE hoop strain ratcheting data by using chaboche nonlinear kinematic hardening model and combined hardening model comparing with the A-F hardening model to be near that found experimentally values. The hoop strain ratcheting rate by Armstrong-Fredrick model gives overestimated values comparing with the experimental data.

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In this paper, finite element analysis with combined (nonlinear isotropic/AF kinematic hardening model) and chaboche hardening models are employed to investigate ratcheting behavior in stainless steel branch pipes under dynamic moments and internal pressure. Obtained results show that the maximum value of ratcheting strain takes place in the junction of branch pipes in the hoop stress direction. In this case, the rate of progressive strains increases with the increase of the bending moment levels in constant internal pressure. Furthermore, this study reveals that the geometry and dimensions of branch pipes have a significant impact on the rate of progressive strains. The bending moment levels to initiate strain accumulation phenomena will be increased with the increase of the dimensions of branch pipes. In the BSS1 sample, comparison between results obtained using progressive strains with combined and chaboche hardening models are much better than those of Armstrong-Fredrick hardening model and are near to the experimental data. Of course, in BSS2 sample, the behavior of ratcheting with combined hardening model is near the experimental results. For the BSS3 sample, the prediction of ratcheting with the chaboche hardening model is better than using the other strain hardening models and are near to the experimental data. Like the carbon steel samples studied in the recent paper, compared to the Armstrong-Frederick hardening model, the chaboche and combined hardening models exhibit an appropriate prediction and similar to experimental results in stainless steel samples.
 

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