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.

Copyright © 2014 by ASME
Topics: Stress
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Bree, J., 1967, “Elasto-Plastic Behaviour of Thin Tubes Subjected to Internal Pressure and Intermittent Heat Fluxes With Application to Fast Reactor Fuel Elements,” J. Strain Anal., 2, pp. 226–238. [CrossRef]
Chen, H. F., 2010, “Lower and Upper Bound Shakedown Analysis of Structures With Temperature-Dependent Yield Stress,” ASME J. Pressure Vessel Technol., 132, pp. 1–8
Staat, M., and Heitzer, M., 2001, “LISA a European Project for FEM-Based Limit and Shakedown Analysis,” Nucl. Eng. Des., 206, pp. 151–166. [CrossRef]
Martin, M., and Rice, D., 2009, “A Hybrid Procedure for Ratchet Boundary Prediction,“ July 26–30, Prague, Czech Republic, Paper No. PVP2009-77474 .
Abdalla, H. F., Megahed, M. M., and Younan, M. Y. A., 2007, “A Simplified Technique for Shakedown Limit Load Determination,” Nucl. Eng. Des., 237, pp. 1231–1240. [CrossRef]
Mackenzie, D., Boyle, J. T., and Hamilton, R., 2000, “The Elastic Compensation Method for Limit and Shakedown Analysis: A Review,” J. Strain Anal. Eng. Des., 35(3), pp. 171–188. [CrossRef]
Chen, H. F., 2010, “A Direct Method on the Evaluation of Ratchet Limit,” ASME J. Pressure Vessel Technol., 132(4), p. 041202. [CrossRef]
Jappy, A., Mackenzie, D., and Chen, H., 2012, “A Fully Implicit, Lower Bound, Multi-axial Solution Strategy for Direct Ratchet Boundary Evaluation: Theoretical Development,” July 15–19, Toronto, ON, Canada, Paper No. PVP2012-78314.
Melan, E., 1936, “Theorie Statisch Unbestimmter Systeme aus Ideal-Plastischem Bastoff,” Sitzungsber. Akad. Wiss. Wien, Abt., 145, pp. 195–218.
Koiter, W. T., 1960, “General Theorems for Elastic Plastic Solids,” Progress in Solid Mechanics, J. N.Sneddon and R.Hill, eds., North Holland, Amsterdam, Vol. 1, pp. 167–221.
Weichert, D., and PonterA., 2009, Limit States of Materials and Structures, Springer Science, Business Media, The Netherlands.
Chen, H., and Ponter, A., 2001, “A Method for the Evaluation of a Ratchet Limit and the Amplitude of Plastic Strain for Bodies Subjected to Cyclic Loading,” Eur. J. Mech. A/Solids, 20, pp. 555–571. [CrossRef]
Adibi-Asi, R., and Reinhardt, W., 2010, “Ratchet Boundary Determination Using a Noncyclic Method,” ASME J. Pressure Vessel Technol., 132(2), p. 021201. [CrossRef]
Martin, M., and Rice, D., 2009, “A Hybrid Procedure for Ratchet Boundary Prediction,” Vol. 1, Codes and Standards, July 26–30, 2009, Prague, Czech Repulblic, Paper No. PVP2009-77474, ASME J. Pressure Vessel Technol., pp. 81–88. Available at: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&frm=1&source=web&cd=2&ved=0CC4QFjAB&url=http%3A%2F%2Fproceedings.asmedigitalcollection.asme.org%2Fdata%2FConferences%2FPVP2009%2F70244%2F81_1.pdf&ei=laBHUsPrJuqi4AP9woGYBQ&usg=AFQjCNGWlhctXJ4CPzzLrSuWtRfiWWPEiw
Ure, J., Chen, H., Li, T., Chen, W., Tipping, D., and Mackenzie, D., 2011, “A Direct Method for the Evaluation of Lower and Upper Bound Ratchet Limits,” International Conference on the Mechanical Behaviour of Materials, June 5th–9th, Lake Como, Italy
Abou-Hanna, J., and McGreevy, T. E., 2011, “A Simplified Ratchet Limit Analysis Using Modified Yield Surface,” Int. J. Pressure Vessel Piping, 88, pp. 11–18. [CrossRef]
Nguyen-Tajan, T. M. L., Pommier, B., Maitournam, M. H., Houari, M., Verger, L., Du, Z. Z., and Snyman,M., 2003, “Determination of the Stabilized Response of a Structure Undergoing Cyclic Thermal-Mechanical Loads by a Direct Cyclic Method,” Abaqus Users' Conference Proceedings Munich Allemagne, Germany.
ABAQUS 6.10, 2010 SIMULIA Customer Conference, May 24, 2010, Providence, RI.
Gokhfeld, D. A., and Cherniavsky, O. F., 1980, Limit Analysis of Structures at Thermal Cycling, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands.
Polizzotto, C., 1993, “A Study on Plastic Shakedown of Structures: Part II—Theorems,” ASME J. Appl. Mech., 60, pp. 20–25. [CrossRef]
Simo, J. C., and Hughes, T. J. R, 2000, Computational Inelasticity, Springer-Verlag, NY.


Grahic Jump Location
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

Grahic Jump Location
Fig. 9

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



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