The load separation concept is employed to determine the mixed mode plastic pl and COD pl factors for the tension plate with an inclined centre throughthickness crack for power law hardening materials. The separation parameters ij S are calculated from the FE computed load -plastic displacement (or COD) curves for each case. It is shown that the mixed mode plastic pl factor is a function of both the crack angle orientation (or the applied elastic parameter e M ) and the strain hardening exponent.
Vessels and containers for the storage, processing, and transport of oil and gas are refen'ed to as potentially dangerous entities, since they operate under pressure and at elevated and reduced temperatures and are subject to corrosion-active and aggressive media. Their strength is therefore based on specially developed, time-proven, and experimentally approved regulatory documents: roles, standards, and guide materials. Nevertheless, the need to perform additional calculations and investigations using methods of mathematical modeling frequently arises during both design and analysis of the serviceability of in-service vessels.Let us examine an actual problem associated with evaluation of the serviceability of a tower container at a gas processing Plant, which had been in the active zone of a fire that occurred in a nearby mill (Fig. 1).The height of the tower container is 38.37 m, and the profile of the container and the thickness of the housing vary over the height (see Fig. 1). The steel housing, which is covered by a layer of insulation 60 mm thick, takes up the load due to internal equipment situated in the upper section of the vessel, which is uniformly distributed over the height. The continuous wall of the mill, which encloses (shades) the lower section of the container is located between the container and fire zone. As a result of fireproofing measures adopted, the container remained virtually undamaged after the fire, with the exception of a small section of the housing located directly above the shaded portion of the vessel. Burnout of some of the insulation occurred in this section of the housing. Visual and measurement inspection indicated that the housing was severely deformed in this zone. The dimension of the deformed zone was -1 m, while the maximum residual deflection amounted to several centimeters.The primary goal of the mathematical modeling of the actual process was to determine the mechanism responsible for the apparent deformation of the vessel, reproduce the actual geometry of the deformed zone, and evaluate the vessel's serviceability, and the possibility of prolonging its service life without reconditioning.For this purpose, it is necessary to solve the following: 9 the nonlinear nonstationary problem of the distribution of the temperature field in the housing of the vessel during and after the fire; and 9 the nonlinear nonisothermal elastoplastic problem of the distribution of the time-dependent stress-strain state (SSS) of the vessel housing. Let us point out the most important characteristic features of the statement adopted for the thermal problem. Let us consider that emergency protection was depleted at the start of the fire; there was therefore no internal excess pressure in the vessel. The radiational effect of the flame front, which was located at a distance of 5 m from the surface of the vessel, was the basic source of the thermal effect on the vessel. The temperature of the front was assumed constant and equal to 1600 K. The thermal effect was instantaneous and acted over a p...
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