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Research Papers: Design and Analysis

A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Implementation and Comparison

[+] Author and Article Information
Alan Jappy

e-mail: alan.jappy@strath.ac.uk

Donald Mackenzie

e-mail: d.mackenzie@strath.ac.uk

Haofeng Chen

e-mail: haofeng.chen@strath.ac.uk
Department of Mechanical
and Aerospace Engineering,
University of Strathclyde,
Glasgow G1 1XQ, UK

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the Journal of Pressure Vessel Technology. Manuscript received August 20, 2012; final manuscript received April 8, 2013; published online October 29, 2013. Assoc. Editor: Wolf Reinhardt.

J. Pressure Vessel Technol 136(1), 011205 (Oct 29, 2013) (9 pages) Paper No: PVT-12-1133; doi: 10.1115/1.4024450 History: Received August 20, 2012; Revised April 08, 2013

Ensuring sufficient safety against ratcheting is a fundamental requirement in pressure vessel design. However, determining the ratchet boundary using a full elastic-plastic finite element analysis can be problematic and a number of direct methods have been proposed to overcome difficulties associated with ratchet boundary evaluation. This paper proposes a new lower bound ratchet analysis approach, similar to the previously proposed hybrid method but based on fully implicit elastic-plastic solution strategies. The method utilizes superimposed elastic stresses and modified radial return integration to converge on the residual state throughout, resulting in one finite element model suitable for solving the cyclic stresses (stage 1) and performing the augmented limit analysis to determine the ratchet boundary (stage 2). The modified radial return methods for both stages of the analysis are presented, with the corresponding stress update algorithm and resulting consistent tangent moduli. Comparisons with other direct methods for selected benchmark problems are presented. It is shown that the proposed method evaluates a consistent lower bound estimate of the ratchet boundary, which has not previously been clearly demonstrated for other lower bound approaches. Limitations in the description of plastic strains and compatibility during the ratchet analysis are identified as being a cause for the differences between the proposed methods and current upper bound methods.

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Topics: Stress
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Figures

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Fig. 1

Bree cylinder with capped end: dimensions

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Fig. 2

Ratchet boundary: Bree

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Fig. 3

Total equivalent stress Δθ = 500: left θ = 20, right θ = 520

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Fig. 4

Constraints for pressurized two-bar structure

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Fig. 5

Ratchet boundary F/P = 10

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Fig. 6

Ratchet boundary F/P = 15

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Fig. 7

Ratchet boundary F/P = 20

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Fig. 8

Modified yield strength F/P = 20, Δθ = 150 °C, left: hybrid; right: proposed methods

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Fig. 9

Equivalent total stress F/P = 15, left: Δθ = 0 °C; right: Δθ = 150 °C

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