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.

References

References
1.
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
.10.1243/03093247V023226
2.
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
3.
Staat
,
M.
, and
Heitzer
,
M.
,
2001
, “
LISA a European Project for FEM-Based Limit and Shakedown Analysis
,”
Nucl. Eng. Des.
,
206
, pp.
151
166
.10.1016/S0029-5493(00)00415-5
4.
Martin, M., and Rice, D., 2009, “A Hybrid Procedure for Ratchet Boundary Prediction,“ July 26–30, Prague, Czech Republic, Paper No. PVP2009-77474 .
5.
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
.10.1016/j.nucengdes.2006.09.033
6.
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
.10.1243/0309324001514332
7.
Chen
,
H. F.
,
2010
, “
A Direct Method on the Evaluation of Ratchet Limit
,”
ASME J. Pressure Vessel Technol.
,
132
(4), p.
041202
.10.1115/1.4001524
8.
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.
9.
Melan
,
E.
,
1936
, “
Theorie Statisch Unbestimmter Systeme aus Ideal-Plastischem Bastoff
,”
Sitzungsber. Akad. Wiss. Wien
,
Abt.
,
145
, pp.
195
218
.
10.
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
.
11.
Weichert
,
D.
, and
Ponter
A.
,
2009
,
Limit States of Materials and Structures
,
Springer Science
,
Business Media
, The Netherlands.
12.
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
.10.1016/S0997-7538(01)01162-7
13.
Adibi-Asi
,
R.
, and
Reinhardt
,
W.
,
2010
, “
Ratchet Boundary Determination Using a Noncyclic Method
,”
ASME J. Pressure Vessel Technol.
,
132
(2), p.
021201
.10.1115/1.4000506
14.
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
15.
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
16.
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
.10.1016/j.ijpvp.2010.12.001
17.
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.
18.
ABAQUS 6.10, 2010 SIMULIA Customer Conference, May 24, 2010, Providence, RI.
19.
Gokhfeld
,
D. A.
, and
Cherniavsky
,
O. F.
,
1980
,
Limit Analysis of Structures at Thermal Cycling
,
Sijthoff & Noordhoff
, Alphen aan den Rijn, The Netherlands.
20.
Polizzotto
,
C.
,
1993
, “
A Study on Plastic Shakedown of Structures: Part II—Theorems
,”
ASME J. Appl. Mech.
,
60
, pp.
20
25
.10.1115/1.2900750
21.
Simo
,
J. C.
, and
Hughes
,
T. J. R
,
2000
,
Computational Inelasticity
,
Springer-Verlag
, NY.
You do not currently have access to this content.