The phenomenon of elastic follow-up in high temperature piping has a long history and rules to limit its significance in design are well established. However, most design rules, and numerous associated supporting studies, have been limited to a simple power-law of creep, with variations to account for time- or strain-hardening in primary creep. A common feature of the most studies of elastic follow-up in structures subject to power-law creep is that a plot of (maximum) stress against strain—a so-called isochronous stress– strain trajectory—is almost insensitive to the creep law (in particular, the stress exponent in the power-law) and is almost linear (until perhaps the later stages of stress relaxation). A limitation of the power-law is that it assumes to be valid across all stress ranges, from low through moderate to high, yet it is well known that this is not generally the case. This paper aims to investigate the effect of stress-range dependent material models on the nature of elastic follow-up: both a simple two-bar structure (common in studies of elastic follow-up) and a detailed finite element analysis of a piping elbow are examined. It is found that stress-range dependent material models can have a significant effect on the accepted characteristics of elastic follow-up.

References

References
1.
Robinson
,
E. L.
,
1955
, “
Steam Piping Design to Minimize Creep Concentration
,”
Trans. ASME
,
77
, pp.
1147
1162
.
2.
Severud
,
L. K.
,
1984
, “
A Simplified Method of Evaluation for Piping Elastic Follow-Up
,”
Proceedings of the 5th International Conference on Pressure Vessel Technology
,
ASME
,
San Fransisco
, Vol.
1
.
3.
Dhalla
,
A. K.
,
1984
, “
Numerical Estimate of Elastic Follow-Up in Piping: Inelastic Evaluation
,”
Design of Elevated Temperature Piping
(
PVP-Vol. 86
),
R. H.
Mallett
and
R. M.
Mello
, eds.,
ASME
,
New York
.
4.
Boyle
,
J. T.
, and
Nakamura
,
K.
,
1987
, “
The Assessment of Elastic Follow-Up in High Temperature Piping Systems—Overall Survey and Theoretical Results
,”
Int. J. Pressure Vessels Piping
,
29
, pp.
167
194
.10.1016/0308-0161(87)90049-4
5.
Kasahara
,
N.
,
2001
, “
Strain Concentration at Structural Discontinuities and Its Prediction Based on Characteristics of Compliance Change in Structures
,”
JSME Int. J. Ser. A
,
44
, pp.
354
361
.10.1299/jsmea.44.354
6.
Naugle
,
F. V.
,
1984
, “
Design Guidance for Elastic Follow-Up
,”
ASME J. Pressure Vessel Technol.
,
106
, pp.
32
36
.10.1115/1.3264306
7.
Hadidi-Moud
,
S.
, and
Smith
,
D. J.
,
2008
, “
Use of Elastic Follow-Up in Integrity Assessment of Structures
,”
Proceedings of the ASME Pressure Vessels & Piping Division Conference
,
Chicago, ASME PVP, New York
, Paper No. PVP2008-61754.
8.
Smith
,
D. J.
,
McFadden
,
J.
,
Hadidimoud
,
S.
,
Smith
,
A. J.
,
Stormonth-Darling
,
A. J.
, and
Aziz
,
A. A.
,
2010
, “
Elastic Follow-Up and Relaxation of Residual Stress
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
224
, pp.
777
787
.10.1243/09544062JMES1733
9.
Hadidi-Moud
,
S.
, and
Smith
,
D. J.
,
2010
, “
Estimation of Elastic Follow-Up in Structures
,”
Key Eng. Mater.
,
462
, pp.
361
365
.10.4028/www.scientific.net/KEM.462-463
10.
British Energy Plant Integrity Branch
,
2003
,
R5, Assessment Procedure for the High Temperature Response of Structures. Issue 3
,
British Energy Generation Ltd
,
Barnwood, UK
.
11.
Naumenko
,
K.
,
Altenbach
,
H.
, and
Gorash
,
Y.
,
2009
, “
Creep Analysis With a Stress Range Dependent Constitutive Model
,”
Arch. Appl. Mech.
,
79
, pp.
619
630
.10.1007/s00419-008-0287-5
12.
Boyle
,
J. T.
, “
Stress Relaxation and Elastic Follow-Up Using a Stress Range Dependent Constitutive Model
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Sci.
Published Online 21 October 2011.10.1177/0954406211425766
13.
Boyle
,
J. T.
, and
Spence
,
J.
,
1983
,
Stress Analysis for Creep
,
Butterworths
,
London
.
14.
Naumenko
,
K.
, and
Altenbach
,
H.
,
2007
,
Modelling of Creep for Structural Analysis
,
Springer
,
Berlin
.
15.
Evans
,
R. W.
, and
Wilshire
,
B.
,
1985
,
Creep of Metals and Alloys
,
Institute of Metals
,
London
.
16.
Robinson
,
E. L.
,
1943
, “
The 100,000-Hour Creep Test
,”
Mech. Eng.
,
65
, pp.
166
168
.
17.
Soderberg
,
C. R.
,
1936
, “
The Interpretation of Creep Tests for Machine Design
,”
Trans. ASME
,
58
, pp.
733
743
.
18.
Prandtl
,
L.
,
1928
, “
Ein Gedankenmodell zur kinematischen Theorie der festen Korper. Zeitsch
,”
Z. Angew. Math. Mech.
,
8
, pp.
85
106
.10.1002/(ISSN)1521-4001
19.
McVetty
,
P. G.
,
1943
, “
Creep of Metals at Elevated Temperatures—The Hyperbolic Sine Relation Between Stress and Creep Rate
,”
Trans. ASME
,
65
, pp.
761
769
.
20.
Nadai
,
A.
, and
McVetty
,
P. G.
,
1943
, “
Hyperbolic Sine Chart for Estimating Working Stresses of Alloys at Elevated Temperature
,”
Proc. ASTM
,
43
, pp.
735
745
.
21.
Garofalo
,
F.
,
1963
, “
An Empirical Relation Defining the Stress Dependence of Minimum Creep Rate in Metals
,”
Trans. Metall. Soc. AIME
,
227
, pp.
351
355
.
22.
Lemaitre
,
J.
, and
Chaboche
,
J.-L.
,
1994
,
Mechanics of Solid Materials
,
Cambridge University Press
,
Cambridge
.
23.
Boyle
,
J. T.
, “
The Creep Behavior of Simple Structures With a Stress Range Dependent Constitutive Model
,”
Arch. Appl. Mech.
, SpringerLink Online First™, 23 July 2011.
24.
Holdsworth
,
S.
,
2010
, “
Advances in the Assessment of Creep Data During the Past 100 Years
,”
Trans. Indian Inst. Met.
,
63
, pp.
93
99
.10.1007/s12666-010-0013-1
25.
Holdsworth
,
S. R.
,
Askins
,
M.
,
Baker
,
A.
,
Gariboldi
,
E.
,
Holmström
,
S.
,
Klenk
,
A.
,
Ringel
,
M.
,
Merckling
,
G.
,
Sandstrom
,
R.
,
Schwienheer
,
M.
, and
Spigarelli
,
S.
(on behalf of Working Group 1 of the European Creep Collaborative Committee),
2008
, “
Factors Influencing Creep Model Equation Selection
,”
Int. J. Pressure Vessels Piping
,
85
, pp.
80
88
.10.1016/j.ijpvp.2007.06.009
26.
Bolton
,
J.
,
2008
, “
A ‘Characteristic Strain’ Model for Creep
,”
Mater. High Temp.
,
25
, pp.
101
108
.10.3184/096034008X357573
27.
Boyle
,
J. T.
,
2011
, “
The Behavior of Structures Based on the Characteristic Strain Model of Creep
,”
Int. J. Pressure Vessels Piping
,
88
, pp.
473
481
.10.1016/j.ijpvp.2011.08.002
28.
Evans
,
R. W.
,
Parker
J. D.
, and
Wilshire
B.
,
1982
,
Recent Advances in Creep and Fracture of Engineering Materials and Structures
,
B.
Wilshire
and
D. R. J.
Owen
, eds.,
Pineridge Press
,
Swansea, UK
, pp.
135
184
.
29.
Levantovsky
,
A.
,
2011
, MAGICPLOT, http://magicplot.com/
30.
Nakamura
,
K.
, and
Boyle
,
J. T.
,
1987
, “
The Assessment of Elastic Follow-Up in High Temperature Piping Systems—Some Example Problems
,”
Int. J. Pressure Vessels Piping
,
29
, pp.
249
273
.10.1016/0308-0161(87)90020-2
31.
ABAQUS
,
2011
,
User’s Manual, Version 6.9
,
Dessault Systems Simulia Corp.
,
Providence, RI
.
32.
ANSYS
,
2009
,
Structural Analysis Guide, Version 12.1
.
ANSYS, Inc.
,
Canonsburg, PA
.
33.
JSME
,
2005
,
JSME S NC2 2005 Code for Nuclear Power Generation Facilities—Rules on Design and Construction for Nuclear Power Plants—Section II Fast Reactor Standards
,
JSME
.
You do not currently have access to this content.