Research Papers: NDE

A Fully Implicit, Lower Bound, Multi-Axial Solution Strategy for Direct Ratchet Boundary Evaluation: Theoretical Development

[+] 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
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 9, 2013; published online August 26, 2013. Assoc. Editor: Wolf Reinhardt.

J. Pressure Vessel Technol 135(5), 051202 (Aug 26, 2013) (11 pages) Paper No: PVT-12-1132; doi: 10.1115/1.4024449 History: Received August 20, 2012; Revised April 09, 2013

Ensuring sufficient safety against ratchet is a fundamental requirement in pressure vessel design. Determining the ratchet boundary can prove difficult and computationally expensive when using a full elastic–plastic finite element analysis and a number of direct methods have been proposed that overcome the difficulties associated with ratchet boundary evaluation. Here, a new approach based on fully implicit finite element methods, similar to conventional elastic–plastic methods, is presented. The method utilizes a two-stage procedure. The first stage determines the cyclic stress state, which can include a varying residual stress component, by repeatedly converging on the solution for the different loads by superposition of elastic stress solutions using a modified elastic–plastic solution. The second stage calculates the constant loads which can be added to the steady cycle while ensuring the equivalent stresses remain below a modified yield strength. During stage 2 the modified yield strength is updated throughout the analysis, thus satisfying Melan's lower bound ratchet theorem. This is achieved utilizing the same elastic plastic model as the first stage, and a modified radial return method. The proposed methods are shown to provide better agreement with upper bound ratchet methods than other lower bound ratchet methods, however limitations in these are identified and discussed.

Copyright © 2013 by ASME
Topics: Stress , Cycles
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Fig. 1

Bree diagram with inset stress–strain responses

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Fig. 2

Elastic residual and loaded stress vectors below yield

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Fig. 3

Elastic residual and loaded stress vectors above yield

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Fig. 4

Calculation of the maximum allowable constant equivalent stress

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Fig. 5

Pictorial representation of stage 2, X ≤ 1

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Fig. 6

Pictorial representation of stage 2, X > 1

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Fig. 8

Ratchet boundary plate with hole

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Fig. 9

Modified yield strength (Δθ/100 = 0.5): left method 2; right hybrid method

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Fig. 10

Residual stress, |p¯|, at a cyclic temperature (Δθ/100) = 0.5

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Fig. 11

Residual stress, |p¯|, at a cyclic temperature (Δθ/100) = 1.0

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Fig. 12

Residual stress, |p¯|, at a cyclic temperature (Δθ/100) = 2.5




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