TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Ratcheting caused by moving loads T2 - International Journal of Advanced Structural Engineering N2 - Progressive deformation (ratcheting) can occur as a response to variable loads as soon as the elastic limit is exceeded. If this is the case, strains and displacements accumulate in the event of cyclic loading in each load cycle. Widely known as triggers for ratcheting and already being considered in some design codes are configurations, in which a structure is subjected to at least two different types of load, namely a constant load (the primary load) and a superimposed cyclic load. In this paper, another mechanism that generates ratcheting is introduced. It can be attributed solely to the effect of a single load. In the simplest case, this can be explained by the successive activation of (an infinite number of) plastic hinges if a load of constant magnitude is moved in space. The increments of strains and displacements can decrease or increase from cycle to cycle, when the material is hardening, or if elastic foundation is present, or if the equilibrium condition is formulated for the deformed system (second-order theory) or if “large” rotations are taken into account (third-order theory). KW - Ratcheting KW - Progressive deformation KW - Shakedown KW - Traveling load KW - Moving temperature front Y1 - 2017 UR - http://link.springer.com/article/10.1007/s40091-017-0154-0/fulltext.html SN - 2008-6695 SN - 2008-3556 VL - 9 IS - 2 SP - 139 EP - 152 ER - TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Simplified determination of accumulated strains to satisfy design code requirements T2 - International Journal of Pressure Vessels and Piping N2 - In case of cyclic loading, strain may accumulate due to a ratcheting mechanism until the state of shakedown is possibly achieved. Design Codes frequently require strain limits to be satisfied at the end of the specified lifetime of the structure. In addition, the strain range is required for performing fatigue analyses in case of plastic shakedown. However, little guidance is usually provided by Design Codes on how the accumulated strains and strain ranges are to be calculated, and some of the guidelines implemented in Design Codes are not well founded and may therefore be misleading. This is, for example, true for the ASME B&PV Code, Section III. Of course, strains and strain ranges can be determined by means of incremental elastic-plastic analyses, which require to go step-by-step through many cycles of a given load histogram until the state of shakedown is reached. This is rather costly in terms of engineering time and numerical effort. As an alternative, simplified methods can be adopted, e.g. the Simplified Theory of Plastic Zones (STPZ) as used in the present paper. Being a direct method, effects from load history are disregarded. The theory is described shortly and illustrated by some examples. It is shown that the Simplified Theory of Plastic Zones is well suited to provide reasonable estimates of strains accumulated in the state of elastic and plastic shakedown at the cost of few linear elastic analyses. KW - Simplified elastic-plastic analysis KW - Simplified theory of plastic zones (STPZ) KW - Zarka's method KW - Shakedown KW - Ratcheting KW - Cyclic loading KW - Accumulated strains KW - Strain range KW - Residual stress Y1 - 2019 UR - https://www.sciencedirect.com/science/article/pii/S0308016118304617 U6 - https://doi.org/10.1016/j.ijpvp.2019.01.014 SN - 0308-0161 VL - 171 SP - 92 EP - 103 ER - TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Limited Versus Unlimited Strain Accumulation Due to Ratcheting Mechanisms T2 - Journal of Pressure Vessel Technology N2 - After distinguishing material ratcheting and structural ratcheting, different phenomena related to structural ratcheting are gathered. Ratcheting of elastic–plastic structures observed with stationary position of loads is distinguished from ratcheting with moving loads. Both categories are illustrated by examples. The effect of evolution laws for the internal variables describing kinematic hardening on the accumulation of strain due to a ratcheting mechanism, and whether the ratcheting mechanism ceases with the number of cycles so that the accumulated strains are limited, is discussed. Some conditions are shown, under which the Chaboche model can lead to shakedown. Scenarios where shakedown is guaranteed at every load level, or where it may or may not occur at a specific load level, or where it definitely cannot occur at any load level, are distinguished. Correspondingly, the usefulness of shakedown analyses, which are searching for maximum load factors assuring shakedown, or direct (or simplified) methods to obtain postshakedown quantities by avoiding incremental cyclic analyses is discussed. KW - Ratcheting KW - moving loads KW - cyclic loads KW - strain accumulation KW - hardening Y1 - 2019 UR - http://pressurevesseltech.asmedigitalcollection.asme.org/article.aspx?articleid=2725462 U6 - https://doi.org/10.1115/1.4042853 VL - 141 IS - 3 SP - 031206-1 EP - 031206-10 ER - TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Effect of stress stiffness on elastic-plastic strain range T2 - International Journal of Pressure Vessels and Piping 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 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. KW - Ke KW - Elbow KW - Strain range KW - Stress stiffening KW - Plasticity KW - Twice Yield Y1 - 2021 UR - https://www.sciencedirect.com/science/article/pii/S0308016121001174?via%3Dihub U6 - https://doi.org/10.1016/j.ijpvp.2021.104421 SN - 0308-0161 VL - 192 ER - TY - GEN A1 - Hübel, Hartwig A1 - Vollrath, Bastian T1 - Simplified Theory of Plastic Zones in the state of elastic shakedown with stress stiffening T2 - European Journal of Mechanics - A/Solids N2 - 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. KW - Cyclic strain accumulation KW - Shakedown KW - Ratcheting KW - Post-shakedown quantities KW - Stress stiffening KW - Geometric effects KW - Second order effects KW - Progressive buckling KW - Zarka's method Y1 - 2022 U6 - https://doi.org/10.1016/j.euromechsol.2022.104613 SN - 0997-7538 VL - 95 ER - 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 -