Review of strain buckling

European Commission Directorate-General For The Information Society And Media Directorate-General For Research And Innovation

Description

Analysis methods
Nuclear energy and safety
Energy research

Informations

• Publié par: EUROPEAN-COMMISSION-DIRECTORATE-GENERAL-FOR-THE-INFORMATION-SOCIETY-AND-MEDIA-DI
• Nombre de lectures: 17
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Corrimission of the European Communities
nuclear science
and technology
x\
Review of strain buckling
Analysis methods
Report
\ '
EUR 11270 EN Commission of the European Communities
IJf
Review of strain buckling
Analysis methods
D. Moulin
Commissariat à l'énergie atomique
DEMT Saclay
BP 2
F-91190 Gif-sur-Yvette
Contract No RAP - 067 F
Final report
This work was performed under the
Commission of the European Communities
for the Codes and Standards Working Group,
Activity Group 2: 'Structural Analysis'
within the Fast Reactor Coordinating Committee
PARL Für?. Eiú'ioth.
Directorate-General '.C
Science, Research and Development
J
CL
JUP11270 EN 1987 Published by the
COMMISSION OF THE EUROPEAN COMMUNITIES
Directorate-General
Telecommunications, Information Industries and Innovation
Bâtiment Jean Monnet
LUXEMBOURG
LEGAL NOTICE
Neither the Commission of the European Communities nor any person acting on
behalf of then is responsible for the use which might be made of the
following information
Cataloguing data can be found at the end of this publication
Luxembourg: Office for Official Publications of the European Communities, 1988
ISBN 92-825-8046-6 Catalogue number: CD-NA-11270-EN-C
© ECSC-EEC-EAEC, Brussels · Luxembourg, 1988
Printed in Belgium CONTENTS
Page
1 - INTRODUCTION !
2 - SCOPE AND CONTENT OF THE REPORT 2
3 - MANUFACTURER'S PROBLEMS, REQUIREMENTS,
CONSTRUCTION CODES 3
3.1 - Illustration of a practical case
3.2 - Limitation of buckling in the presence
of imposed strain 5
3.3 - Review of construction codes 6
3.3.1 - ASME Code Section III
3.3.2 - ASME Code, Case N47 7
3.3.3 - ASME, Case N284
3.3.4 - Conclusion on standard construction
codes 8
4 - PROBLEMS ENCOUNTERED IN THE DEVELOPMENT OF
STRAIN BUCKLING ANALYSIS 9
4.1 - General
4.2 - Simple elastic problem of the heated beam
whose expansion is prevented
4.3 - Plastic problem of an embedded and uniformly
heated circular plate 13
4.4 - Consideration of residual stresses 15
4.5 - Problem of interaction with buckling under
load 18
4.5.1 - Temperature loading only
4.5.2 - Composite loading, Temperature
then load9
4.6 - Conclusions on the simple exemplary cases
presented 20
4.7 - Review of previous work2
4.8 - Conclusions4 Pa?e.
5 - RECENT WORK ON THERMAL BÜCKLING ANALYSIS METHODS 24
5.1 - Introduction 2
5.2 - Experimental methods5
5.2.1 - Effect of imposed strains that are
constant with time
5.2.2 - Effect of cyclic imposed strains 27
5.2.3 - Thermal fatigue buckling 29
5.2.4 - Conclusions 31
5.3 - Analytical methods
5.3.1 - Asymptotic theories2
5.3.2 - Simplified methods, Progressive
buckling of a beam
5.3.3 - Conclusions4
5.4 - Methods using computation codes 3
5.4.1 - Incremental methods
5.4.2 - Special methods 35
5.4.3 - Conclusions6
5.5 - Changes in dimensioning rules
6 - GENERAL CONCLUSIONS7
LIST OF REFERENCES 39
FIGURES 45
ANNEXES 7
IV 1 - INTRODUCTION
This report represents an attempt to review the mecha­
nical analysis methods reported in the literature to account
for the specific behaviour that we call buckling under strain.
In this report, this expression covers allg mechanisms
in which the strains imposed play a rôle, wether they act alone
(as in simple buckling under controlled strain), or wether they
act with other loadings (primary loading, such as pressure, for
example).
Attention is focused on the practical problems rele­
vant to LMFBR reactors. The components concerned are distin­
guished by their high slenderness ratios and by rather high
thermal levels, both constant and variable with time.
Conventional static buckling analysis methods are not
always appropriate for the consideration of buckling under
strain. New methods must therefore be developed in certain
cases.
It is also hoped that this review will facilitate the
coding of these analytical methods to aid the constructor in
his design task and to identify the areas which merit further
investigation.
- 1 -2 - SCOPE AND CONTENT OF THE REPORT
The objectives assigned to this study are aimed to
facilitate the possible writing of practical rules designed to
take account of buckling effects in the presence of imposed
strain, such as thermal stresses.
It is first necessary to define the problems of the
LMFBR reactor manufacturer as clearly as possible. The degree
of risk of this failure mode is related to the specificities of
construction and operation of this type of reactor, built of
large thin shell structures and withstanding low pressures but
high thermal stresses.
The construction codes normally consulted by the buil­
ders will then examined. These codes offer little operational
data to take account of this behaviour.
In the third phase, an illustration of the problems
encountered in developing rules designed to account for
buckling under strain will be provided in the light of a
review of previous works.
This will be followed by a precise description of the
latest analytical methods, many of them still under develop­
ment, by arbitrarily considering their classification in three
categories, in line with their implementation principles:
experimental, theoretical and numerical.
The final conclusion are intended to express an opi­
nion on the conditions of application of the methods described,
inasmuch as their degree of development permits. Their defi­
ciencies, if any, and further research and development needs,
will be indicated.
- 2 -3 - MANUFACTURER'S PROBLEMS, REQUIREMENTS, CONSTRUCTION CODES
In broaching the study of relatively recent mechanical
behaviour, it may be advisable to begin by examining the reali­
ty of the problem of buckling under strain. It is important to
determine the extent to which stresses due to imposed strain
may accelerate the appearance of buckling.
As a rule, buckling can be defined by the appearance
in the structure, above a certain loading level, often called
the critical loading, of a significant discontinuity in the
stress and strain distributions produced. This behaviour may
occur if compressive stresses exist. For example, it may be
manifested very significantly if the shape of the structure
changes with the appearance of folds and characteristic
wrinkles.
The acceleration of buckling due to imposed strains
has already been observed in other areas besides nuclear cons­
truction, where it has been the subject of specific develop­
ment. Roughly speaking, before going into further detail below,
these include problems of thermal buckling in the aerospace
field (local temperature rise due to air friction on fuselages
of thin stiffened shells) and in railway construction (thermal
expansion caused by heating by the sun and trainset/rail
friction).
3.1 - Illustration of a practical case
An interesting description of a practical case is
reported in the literature by Severud [1]. It concerns the
mechanical analysis of the thermal buckling of a LMFBR reactor
vessel containing liquid sodium. This overflow vessel (see
Figure 1) has a thickness-to-diameter ratio of about 5/1000 in
the cylindrical part. It is built of austenitic stainless steel
304. During a temperature excursion, it may receive cold
sodium, which produces a local compressive stress in the free
level area, elastically calculated at 204 MPa (or a strain of
0.13%) .
3 -The critical strain of a uniformly axially compressed
cylinder may reach a nominal value of 0.22%. This means a
margin that is just adequate with regard to a construction code
such as ASME Code Case N47 [2]. The author has nevertheless
wanted to provide wider margin values to comply with the
margins of an older code [3]. He indicates the means available
to improve the analysis of this risk, and lays special
attention on:
. a detailed analysis of the temperature fields during
thermal shock,
. the thermomechanical calculation of stresses and elastic
strains produced by this shock,
. the elastic bifurcation calculation of the hemispherical
end considered as a sphere, and of the cylinder conside­
red as a tore,
. the reduction of the bifurcation loads calculated above
to take account of plasticity,
. the empirical compilation of experimental results concer­
ning configurations approaching this thermal buckling to
determine a critical temperature.
This example provides a glance at the difficulties of
thermal buckling analysis, which lead the author to a relati­
vely complicated sequence of simple calculations.
Thermal buckling problems are found in some of the
main components of fast breeder reactors. These include the
main vessel of a pool type reactor whose thickness-to-diameter
ratio may be even smaller (1/1000), and which may be subjected
to a longitudinal and axisymmetric thermal gradient correspon­