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Research Papers: Design and Analysis

Limited Versus Unlimited Strain Accumulation Due to Ratcheting Mechanisms

[+] Author and Article Information
Hartwig Hübel

Brandenburg University of Technology
Cottbus-Senftenberg,
Faculty 6,
Lipezker Str. 47,
Cottbus D-03048, Germany
e-mail: hartwig.huebel@b-tu.de

Bastian Vollrath

Brandenburg University of Technology
Cottbus-Senftenberg,
Faculty 6,
Lipezker Str. 47,
Cottbus D-03048, Germany
e-mail: bastian.vollrath@b-tu.de

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received August 8, 2018; final manuscript received February 11, 2019; published online March 25, 2019. Assoc. Editor: Oreste S. Bursi.

J. Pressure Vessel Technol 141(3), 031206 (Mar 25, 2019) (10 pages) Paper No: PVT-18-1148; doi: 10.1115/1.4042853 History: Received August 08, 2018; Revised February 11, 2019

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.

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Figures

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Fig. 1

Typical uniaxial stress–strain diagram and strain histogram at stress-controlled cyclic loading with nonlinear kinematic hardening including recovery terms (Chaboche model) during early cycles

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Fig. 2

Strain histogram at stress-controlled cyclic loading with nonlinear kinematic hardening (Chaboche model): effect of one of the five γ-parameters being zero or not zero

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Fig. 3

Multi-axial ratcheting: strain histogram in direction of force F (linear elastic—perfectly plastic material)

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Fig. 4

Thin-walled tube under constant axial force and cyclic displacement-controlled twist as example of multi-axial ratcheting: strain histogram in direction of force F (linear elastic—perfectly plastic material)

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Fig. 5

Classification of ratcheting phenomena

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Fig. 6

Two-bar model (nonlinear hardening material, Chaboche model): stress–strain diagram and strain histogram of the left bar (here ultimately leading to elastic shakedown after many cycles)

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Fig. 7

Bree-tube (multilinear kinematic hardening material): stress–strain diagram and strain histogram at outside surface in circumferential direction (here ultimately leading to plastic shakedown)

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Fig. 8

Pipe bend (linear kinematic hardening material): stress–strain diagram and strain histogram in circumferential direction at position close to the crown

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Fig. 9

Two-bar model reinforced by an elastic bar: stress–strain diagram of the left bar (state of plastic shakedown highlighted) and strain histogram

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Fig. 10

Continuous beam subjected to moving lateral force (linear elastic—perfectly plastic material): displaced configurations of the first five cycles and histogram of deflection in the middle of the right span

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Fig. 11

Cylindrical shell with axially moving hotspot (linear elastic—perfectly plastic material): displaced configurations of the first five cycles, and histogram of radial displacement in the middle of the moving distance

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Fig. 12

Rolling contact (linear elastic—perfectly plastic material): shear stress versus shear strain and shear strain histogram

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Fig. 13

Classification of types of elastic–plastic ratcheting and association with useful analysis methods

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Fig. 14

Effect of limited and unlimited kinematic hardening on shakedown

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