TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Ratcheting and strain ranges in the shakedown state with stress stiffening using the Simplified Theory of Plastic Zones T2 - International Journal of Pressure Vessels and Piping N2 - The behavior of elastic-plastic structures under cyclic loading can be determined by incremental elastic-plastic analyses where a given load histogram is analysed cycle-by-cycle until shakedown is achieved. Many cycles may be required for this, if a ratchet mechanism is causing plastic strains to accumulate in each cycle until either elastic or plastic shakedown is achieved. The complexity of the elastic-plastic response of a structure is further increased if geometric effects are present. It may be very costly to get the accumulated strains and strain ranges in the state of shakedown by incremental analyses so that simplified or direct methods have been developed as an alternative. The Simplified Theory of Plastic Zones (STPZ) has proven itself for estimating the required quantities in the state of elastic and plastic shakedown within the framework of the 1st order theory, i.e., if the equilibrium conditions are satisfied for the undeformed structure. It is shown in this paper, how the STPZ can be expanded to capture 2nd order effects introduced by the equilibrium of the deformed structure. Some examples are used to demonstrate its applicability and the quality of the results, but also its limitations with respect to determining the accumulated strains and elastic-plastic strain ranges. KW - Simplified theory of plastic zones KW - Cyclic strain accumulation KW - Shakedown KW - Ratcheting KW - Post-shakedown quantities KW - Stress stiffening Y1 - 2022 U6 - https://doi.org/10.1016/j.ijpvp.2022.104727 SN - 0308-0161 VL - 199 SP - 1 EP - 11 ER - TY - GEN A1 - Vollrath, Bastian A1 - Hübel, Hartwig T1 - Direct Analysis of Elastic-Plastic Strain Ranges and Accumulated Strains Considering Stress Stiffening T2 - ASME 2022 Pressure Vessels & Piping Conference N2 - Many pressure vessel and piping components have to withstand high internal pressures and are therefore thick-walled so that geometric effects such as stress stiffening need not be accounted for. However, thin-walled, or moderately thick structures may be sensitive to these effects. Design Codes such as the ASME Boiler and Pressure Vessel Code usually provide little guidance on when they are to be accounted for. In general, the effects of stress stiffening are difficult to estimate even for experienced engineers and can only be estimated by detailed finite element analyses. In the opinion of the authors, this effect deserves more attention. This is particularly true for simplified elastic-plastic methods for fatigue and ratcheting assessment of structures subjected to cyclic loading. Cyclic loading may cause elastic-plastic strains to accumulate if a ratcheting mechanism is present. After a number of cycles, strain accumulation may cease so that a state of either elastic or plastic shakedown is reached. Determination of accumulated strains, strain ranges and other quantities in the state of shakedown (post-shakedown quantities) by means of incremental analyses is costly, in particular if geometric effects such as stress stiffening play a role. Direct methods aim at providing estimates of the post-shakedown quantities, bypassing cycle-by-cycle analyses. These methods claim to deliver the post-shakedown quantities with high accuracy and low computational effort. The Simplified Theory of Plastic Zones can account for the combination of plasticity and stress stiffening. The theory is described and illustrated by examples. The Simplified Theory of Plastic Zones (STPZ) has proven itself for estimating the post-shakedown quantities in the state of elastic and plastic shakedown within the framework of the 1st order theory, i.e. if the equilibrium conditions are satisfied for the undeformed structure. In this paper, the results of elbows subjected to various loading parameters are compared, considering and neglecting stress stiffening. Thus, the results show the influence 2nd order effects can generate. It is further shown that the STPZ can capture 2nd order effects introduced by the equilibrium of the deformed structure. Some examples are used to demonstrate its applicability and the quality of the results, e.g. for a pipe bend subjected to cyclic in-plane bending. KW - STPZ KW - direct methods KW - ratcheting KW - stress stiffening Y1 - 2022 UR - https://asmedigitalcollection.asme.org/PVP/proceedings-abstract/PVP2022/86144/V001T01A020/1149647 SN - 978-0-7918-8614-4 U6 - https://doi.org/10.1115/PVP2022-84241 ER -