@misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Simplified Theory of Plastic Zones in the state of elastic shakedown with stress stiffening}, series = {European Journal of Mechanics - A/Solids}, volume = {95}, journal = {European Journal of Mechanics - A/Solids}, issn = {0997-7538}, doi = {10.1016/j.euromechsol.2022.104613}, pages = {15}, abstract = {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 strains and other quantities in the state of shakedown (post-shakedown quantities) by means of incremental analyses is costly. Direct methods such as the Simplified Theory of Plastic Zones (STPZ) aim at providing estimates of the post-shakedown quantities, bypassing cycle-by-cycle analyses. If geometric effects such as stress stiffening play a role, determination of accumulated strains even becomes more complicated. The STPZ has been further developed in order to account for the combination of plasticity and stress stiffening with respect to elastic shakedown. The theory is described and illustrated using examples such as a pipe bend subjected to cyclic in-plane bending. The implications of cyclic as opposed to constant stress stiffness are discussed. The effect of stress stiffening on ratcheting interaction diagrams (RID), separating regions of elastic and plastic shakedown in the space of loading parameters, is discussed.}, language = {en} } @misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Ratcheting and strain ranges in the shakedown state with stress stiffening using the Simplified Theory of Plastic Zones}, series = {International Journal of Pressure Vessels and Piping}, volume = {199}, journal = {International Journal of Pressure Vessels and Piping}, issn = {0308-0161}, doi = {10.1016/j.ijpvp.2022.104727}, pages = {1 -- 11}, abstract = {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.}, language = {en} } @misc{HuebelVollrath, author = {H{\"u}bel, Hartwig and Vollrath, Bastian}, title = {Effect of stress stiffness on elastic-plastic strain range}, series = {International Journal of Pressure Vessels and Piping}, volume = {192}, journal = {International Journal of Pressure Vessels and Piping}, issn = {0308-0161}, doi = {10.1016/j.ijpvp.2021.104421}, abstract = {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 the opinion of the authors, this effect deserves more attention. Therefore, the purpose of this paper is to illuminate the effect of stress stiffening by investigating some examples, with particular attention to elastic-plastic strain ranges and the plastic strain range enhancement factor Ke used for fatigue analyses.}, language = {en} }