iter structural design criteria for in-vessel components (sdc-ic)

ITER G 74 MA 8 01-05-28 W0.2
ITER STRUCTURAL DESIGN CRITERIA
FOR IN-VESSEL COMPONENTS
(SDC-IC)
APPENDIX B
GUIDELINES FOR ANALYSIS,
IN-VESSEL COMPONENTS

ITER G 74 MA 8 01-05-28 W0.2
SDC-IC, Appendix B. Guidelines for Analysis page ii

ITER G 74 MA 8 01-05-28 W0.2
TABLE OF CONTENTS
BÊ1000 GENERAL ............................................................................................................................ 1
B 1100 Introduction.......................................................................................................................................1
B 1110 Purpose.........................................................................................................................................1
B 1120 Organization.................................................................................................................................1
B 1130 Related documents.......................................................................................................................1
B2300 Criteria levels....................................................................................................................................1
BÊ2301 Load Combinations and Associated Criteria Levels .............................................................1
B2500 Stress definition and classification...................................................................................................2
BÊ2501 Mechanical stress.........................................................................................................................2
BÊ2502 General and local thermal stress in a shell..................................................................................2
BÊ 2503 Swelling induced stress ..........................................................................................................2
B 2510 Breakdown of stresses .................................................................................................................3
BÊ2513 Membrane stress .....................................................................................................................4
BÊ2514 Bending stress .........................................................................................................................5
BÊ2520 Classification of stresses obtained by elastic analysis................................................................6
B 2521 Primary stress..........................................................................................................................6
B 2521.1 Primary membrane stress ...............................................................................................7
B 2525 Secondary stress......................................................................................................................7
B 2526 Peak stress...............................................................................................................................7
B 2540 Stress Intensities / Equivalent stresses......................................................................................10
BÊ2540.1 Stress intensity - Maximum shear stress theory (Tresca) ...........................................10
BÊ2540.2 Stress intensity - Octahedral shear stress theory (von Mises) ....................................10
B 2541 Hydrostatic stress ( sH ).......................................................................................................11
B 2541.1 Triaxiality factor...........................................................................................................11
B 2550 Stress intensity ranges/Equivalent stress ranges..................................................................11
BÊ2550.1 Stress intensity range - Maximum shear stress theory................................................11
BÊ2550.2 Stress Intensity range - Octahedral shear stress theory...............................................14
B 2600 Strain definitions and classification ...............................................................................................16
B 2620 Calculation of equivalent strain ( e) .........................................................................................16
BÊ2630 Calculation of the equivalent strain range ( De )......................................................................16
B 2700 Terms related to limit quantities.....................................................................................................17
B 2750 Terms related to fatigue damage ...............................................................................................17
B 2752 Fatigue usage fraction V.......................................................................................................17
BÊ2752.1 Procedure for combination of cycles ...........................................................................17
B3000 Design rules for single-layer homogeneous structures .................................................. 20
B 3020 Methods of analysis ...................................................................................................................20
B 3021 Test to determine if nonlinear (finite deformation) analysis is needed ..............................21
B 3022 Negligible irradiation-induced swelling test........................................................................22
B 3023 Elastic Analysis....................................................................................................................23
B 3024 Inelastic analysis...................................................................................................................23
B 3024.1 Simplified inelastic analysis.........................................................................................23
B 3024.1.1 Elastic-irradiation-induced-creep analysis..........................................................23
B 3024.1.2 Neuber's rule ........................................................................................................26
B 3024.1.3 Elastic follow-up factor (r)..................................................................................27
BÊ3024.2 Elasto-plastic analysis of a structure subjected to a monotonic loading ....................29
BÊ3024.2.1 Use of the tensile curve .......................................................................................30
BÊ3024.2.2 Plasticity criterion................................................................................................31
BÊ3024.2.3 Flow rule ..............................................................................................................32
BÊ3024.2.4 Hardening rule .....................................................................................................33
BÊ3024.3 Elasto-plastic analysis of a structure subjected to cyclic loading...............................33
B 3024.4 Elasto-visco-plastic analysis of a structure subjected to cyclic loading.....................34
BÊ3024.5 Limit analysis (collapse load) ......................................................................................34
BÊ3025 Zones of calculation..............................................................................................................34
BÊ3026 Combination of analysis methods ........................................................................................35
SDC-IC, Appendix B. Guidelines for Analysis page iii

ITER G 74 MA 8 01-05-28 W0.2
B3030 Applicable rules - Flow of analysis...........................................................................................35
B3031 Master flow charts for satisfying design rules.....................................................................35
B 3040 Rules for the prevention of excessive deformation affecting functional adequacy ................36
BÊ3050 Negligible thermal creep test.....................................................................................................36
B 3100 LOW TEMPERATURE RULES...................................................................................................37
B 3101 Negligible irradiation-induced creep test.............................................................................37
B 3200 Rules for the prevention of M type damage ..................................................................................38
B 3211 Immediate plastic collapse and plastic instability ...............................................................38
B 3211.1 Elastic analysis (Immediate plastic collapse and plastic instability)..........................38
B 3211.1.1 Bending shape factor ...........................................................................................38
B 3211.2 Elasto-plastic analysis (Immediate plastic collapse)...................................................39
B 3212 Immediate plastic flow localization .....................................................................................39
B 3212.1 Elastic analysis (Immediate plastic flow localization)................................................39
B 3212.2 Elasto-plastic analysis (Immediate plastic flow localization) ....................................40
B 3213 Immediate local fracture due to exhaustion of ductility......................................................40
B 3213.1 Elastic analysis (Immediate local fracture due to exhaustion of ductility)...............40
B 3213.2 Elasto-plastic analysis (Immediate local fracture due to exhaustion of ductility) .....41
BÊ3214 Fast fracture..........................................................................................................................41
B 3214.1 Elastic analysis (Fast fracture)....................................................................................41
B 3214.2 Elasto-plastic analysis (Fast fracture).........................................................................42
B 3300 Rules for the prevention of C type damage (Levels A and C)......................................................42
B 3310 Progressive deformation or ratcheting ......................................................................................42
B 3311 Elastic analysis (Progressive deformation or ratcheting)....................................................42
B 3311.1 3Sm rule........................................................................................................................42
B 3311.2 Bree-diagram rule.........................................................................................................42
B 3312 Elasto-plastic analysis (Progressive deformation or ratcheting).........................................43
B 3320 Time-independent fatigue..........................................................................................................44
B 3322 Limits on fatigue damage .....................................................................................................44
B 3322.1 Calculation of the fatigue usage fraction: V( De).....................................................44
B 3322.2 Estimation of irradiation effects on fatigue usage fraction.........................................44
BÊ3322.2.1 Calculation of fatigue usage fraction - general...................................................44
BÊ3322.2.2 Procedure for estimating the fatigue curve.........................................................45
B 3323. Calculation of equivalent strain range De .........................................................................46
B 3323.1 Elastic analysis (Time-independent fatigue) ..............................................................46
B 3323.1.1 Elastic strain range...............................................................................................46
B 3323.1.2 Corrections for effects of plasticity.....................................................................47
B 3323.1.3 Combining Components......................................................................................51
B 3400 Rules for the prevention of buckling..............................................................................................52
B 3420 Buckling limits...........................................................................................................................52
B 3421 Immediate elasto-plastic instability under monotonic loading ...........................................52
B 3421.1 Elastic analysis (Immediate elasto-plastic instability )...............................................52
B 3421.1.1 Load-controlled buckling limits..........................................................................52
B 3421.1.2 Buckling diagrams...............................................................................................55
B 3421.1.2 Strain-controlled buckling limits ........................................................................60
B 3421.2 Elasto-plastic analysis (Immediate elasto-plastic instability).....................................60
B 3500 High Temperature Rules.................................................................................................................61
BÊ3800 Design Rules for bolted joints........................................................................................................62
BÊ3810 Methods of analysis ...................................................................................................................62
BÊ3811 Elastic analysis......................................................................................................................62
B 3812 Simplified elastic analysis ....................................................................................................63
B 3812.1 Simplified uniaxial analysis.........................................................................................64
B 3812.1.1 Effects of a temperature rise................................................................................65
B 3812.1.2 Effects of an external load applied to the bolted assembly................................66
B 3812.1.3 Effects of an external moment applied to the bolted assembly .........................67
BÊ3813 Elasto-plastic analysis...........................................................................................................69
SDC-IC, Appendix B. Guidelines for Analysis page iv

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BÊ1000 GENERAL
B 1100 INTRODUCTION
This document provides guidelines and procedures for analysis which should be used in
satisfying the rules presented in SDC-IC.
B 1110 Purpose
The purpose of appendix B is to provide analysis methods and guidelines compatible with the
design rules of SDC-IC. The primary intent of this document is to facilitate the designer /
analyst's job by providing widely accepted analysis guidelines and interpretation of the
design rules.
B 1120 Organization
Guidelines are presented in sections which are numbered, where appropriate, on a one-to-one
correspondence with those in the SDC-IC. Cross-reference and redundancy are kept to a
minimum.
General guidelines for elastic analysis and inelastic analysis are presented in sections B 3023
and B 3024, respectively.
B 1130 Related documents
Although this appendix is intended to be self-contained, references to SDC-IC, which contain
the design rules, are frequently made. Appendix C contains the rationale or justifications for
the design rules and may provide some insights into the interpretation of the analysis methods
presented here. Appendix A provides the materials design limit data used in the SDC-IC.
Irradiation-induced creep and stress-free swelling properties are given in MAR 1 and MPH-
IV 2 .
B2300 CRITERIA LEVELS
BÊ2301 Load Combinations and Associated Criteria Levels
Loading category and damage limits specified in the DRG1 3 shall be used for structural
analysis. Specification of loads and their combination that shall be used for analysis are given
in LS document 4 . Relationship between loading categories and criteria levels are given in IC
2200.
1 G 74 MA 10, Materials Assessment Report
2 G 74 MA 9, Materials Properties Handbook for In-vessel Components
3 G A0 GDRD 2, Design Requirements and Guidelines, Level 1
4 G A0 MA 1, Load Specification and Combination. Annex to DRG1.
SDC-IC, Appendix B. Guidelines for Analysis page 1

ITER G 74 MA 8 01-05-28 W0.2
Neutron irradiation effects (e.g. embrittlement, swelling, irradiation creep) must be included
in analysis.
B2500 STRESS DEFINITION AND CLASSIFICATION
BÊ2501 Mechanical stress
Mechanical stresses are stresses which result from the application of mechanical loads such
as internal pressure, weight, earthquakes and, where applicable, reactions of supports and
other components.
BÊ2502 General and local thermal stress in a shell
Thermal stresses are self-equilibrated stresses resulting from a non-uniform spatial
distribution of temperature or from the presence of materials with different thermal expansion
coefficients. For the purposes of applying stress criteria, two types of thermal stresses are
recognized: general thermal stresses and local thermal stresses, as defined in the following.
If a small portion of the shell is considered, that is, a portion whose dimensions
normal to the median surface does not exceed a few thicknesses, general thermal
stresses entail a general deformation (or strain) of this portion; local thermal stresses
do not induce such general deformation (or strain).
Examples of general thermal stress are
- stress produced by axial temperature distribution in a cylindrical shell,
- stress produced by temperature difference between a nozzle and the shell to which
it is attached,
- equivalent linear stress (IC 2515) distribution produced by a radial temperature
distribution in a cylindrical shell,
- equivalent linear stress (IC 2515) distribution produced by a through-thickness
temperature distribution in a constrained flat plate.
Examples of local thermal stress are
- the stress in a small hot spot,
- the non-linearly distributed (IC 2516) thermal stress, i.e., the difference between
actual stress and equivalent linear stress,
- thermal stress in a cladding material which has a different thermal expansion
coefficient than that of the base metal.
BÊ 2503 Swelling induced stress
These are self-equilibrated stresses resulting from a non-uniform spatial distribution of
fluence or from the presence of materials with different swelling laws. As with thermal
stresses (B2512), general and local swelling stresses can be distinguished. Swelling-induced
stresses are limited by relaxation due to irradiation-induced creep (IC 2151). Swelling can
SDC-IC, Appendix B. Guidelines for Analysis page 2

ITER G 74 MA 8 01-05-28 W0.2
also lead to large deformations of the structure which might require that all analysis include
the effects of finite deformation on stresses and strains (B 3021). On the other hand, under
certain circumstances (B 3022) if the temperature and neutron damages are sufficiently low,
the effects of irradiation-induced swelling may be neglected. If the effects of irradiationinduced
swelling is not negligible, the swelling-induced stress, including the relaxing effects
of irradiation-induced creep, has to be taken into consideration either by detailed inelastic
(elasto-visco-plastic) analysis or by elastic-irradiation-induced creep analysis (B 3024.1.1.1).
B 2510 Breakdown of stresses
The decomposition of stresses into membrane, bending, and peak categories is used for
elastic analysis of shell and beam-like structures because, for these types of structures,
different allowable stresses may be determined (by a simple limit analysis) for the different
stress categories. Primary membrane stress is limited by Sm. For primary bending stresses, a
bending shape factor K accounts for redistribution of stress due to plasticity. For peak
stresses, which are strain controlled, there is no limit for a ductile material apart from fatigue.
The line integration method used in IC 2513 - 2514 to decompose the stress components is
strictly applicable only to homogeneous shells. With some modification (see below) the
concept may be applied to beam-like structures. However, the concept of stress
decomposition cannot be generalized for a three-dimensional structure. The treatment of
these structure types is discussed below.
For a 3-D structure, depending on the structure and the loading, it is possible that the
analyst can use judgement to decompose the stresses and apply the rules for elastic analysis
directly. When this is not possible, the recommended approach is to compare the applied
loadings to the limit loadings that would cause failure, and to ensure that the safety factor on
the applied loading is consistent with the safety factors implied in the SDC-IC rules. An
elastic stress analysis is generally insufficient to determine the limit load. Therefore, for a
three-dimentional structure, it may be approporate to use the rules for elasto-plastic analysis
(ICÊ3211.2, ICÊ3212.2, IC 3213.2, and ICÊ3214.2). Alternatively, the assessment may be
based either on experiment or a nonlinear analysis of a representative structure.
The remainder of this section addresses stress decomposition in structures other than three
dimensional.
For single layer, homogeneous shells, each separate component of a stress tensor defined
along the supporting line segment can be decomposed into its membrane and bending
components. The rules for the decomposition of stresses in a single-layer homogeneous shell
are given in IC 2513 - 2514.
For shell or beam-like structures other than a single-layer homogeneous shell, the
decomposition of a stress component into its membrane and bending components is not
always straightforward, and a general rule for decomposition of stresses cannot be given.
The decomposition would depend on how the structure is modeled and the type of stress
analysis conducted, to derive the distribution of stresses through the thickness. In some
cases, the decomposition can be better implemented by an integration over an area rather than
along a supporting line segment.
As a simple example, consider a thick walled tube running along the x2 direction. If the tube
is analyzed as a shell, then the membrane and bending stress vary with position on the shell,
SDC-IC, Appendix B. Guidelines for Analysis page 3

ITER G 74 MA 8 01-05-28 W0.2
and a line integration through the thickness is used to calculate the breakdown of stresses at
any position. On the other hand, if the tube is analysed as a beam, then the membrane and
bending stress apply to the cross-section as a whole, and an area integral over the total crosssectional
area of the tube would be more appropriate.
Once a determination has been made as to which type of integration (line integral or area
integral) is more appropriate, a membrane stress component can be defined as the average or
mean value of that stress component along that line or area. The bending component of the
stress is a linearly varying stress which can be defined in such a way that its moment about
the centroid of the line segment or the area is the same as the moment of the total stress
component minus the membrane stress component about the centroid.
BÊ2513 Membrane stress
As an example of a structure other than a single layer homogeneous shell, consider the case
of a first wall design consisting of two face plates of thicknesses h1 and h2 separated by a
coolant channel of height hc where the coolant channels running along one direction (say x2
direction) are separated by regularly spaced webs á(Figure B 2513-1). In general, such a
structure is anisotropic but could be analyzed using various geometrical approximations.
X 3
SDC-IC, Appendix B. Guidelines for Analysis page 4
X 1
Figure BÊ2513-1: First wall cross-section
(1) At an elementary level, when x3 variation of stresses in the x1 direction can be
neglected, a slice of the first wall consisting of halves of two adjacent coolant channels
together with their face plates may be analyzed as a one-dimensional stress analysis
problem. The cross-section of interest is like an I-beam and the stress of interest is the
normal stress s22. For this case the membrane stress ( s22 ) has to be defined as the
m
average stress over the whole cross-section, i.e., based on an area integral.
1
( s ) = ò s
m A
22 22
A
dA (1)
where A is the area of cross-section.
(2) An alternative approach, when x3 variation of stresses in both directions are nonnegligible,
could be to analyze the structure as an isotropic, homogeneous, and multi-
h 1
h c
h 2

ITER G 74 MA 8 01-05-28 W0.2
layer plate consisting of many such coolant channels but ignoring the contribution of
the channel webs to the stiffnesses of the plate. For some applications, e.g., satisfying
the primary stress limits, this approximation is conservative. In this case, a supporting
line segment can be defined at all points of the plate but it will be discontinuous
because it will pass through the coolant channels. For such a multi-layer homogeneous
shell, the components (sij)m can be defined by the following equation:
+ ht
( ij ) = ( 1 )
m ò-h
ij 3
s / h s dx
(2)
b
where h = h1+ h2 = total solid thickness, excluding thickness of coolant
channels, if any, and hb and ht are the distances of the extreme surfaces from
the neutral plane.
Axis x3 contains the supporting line segment of length hb + ht. The origin of the x3 axis
is taken at the centroid, i.e.,
+ h
t
ò Jx ( 3) x3 dx3
= 0
(3)
-h
b
where Jx ( 3)
0
= ì if x 3 is in the coolant channel
í
î1
if x 3 is in the structure
(3) A third alternative could be the same as the previous one but without ignoring the
stiffnesses of the channel webs in the x2 direction. so that the first wall can be modelled
either as a multi-layer anisotropic plate or by using detailed finite-element analysis. In
this case, the membrane components of the normal stresses can be derived by using Eq.
2 for the s11 component and Eq. 1 for the s22 component. However, the membrane
components for the shear stresses s12 and s21 defined by these equations are generally
unequal.
BÊ2514 Bending stress
As in the case of membrane stress, for structures other than a single-layer homogeneous shell,
a general rule for decomposition of stresses into their bending components cannot be given.
The decomposition would depend on how the structure is modelled and the type of stress
analysis conducted to derive the distribution of stresses through the thickness. Results for the
three examples considered in section B 2513 are given below.
(1) The bending stress tensor is given (as a function of x3) by the following equation:
x3
s
ù
22 s
b ij x3dA ëê I ûú ò
(1)
( ) = é
A
where I x dA
= ò 3 2
A
and the origin of the x3 axis is at the centroid of the area A.
(2) The bending stress tensor is given (as a function of x3) by the following equation:
SDC-IC, Appendix B. Guidelines for Analysis page 5

ITER G 74 MA 8 01-05-28 W0.2
( ) = é
x3
s
ù +ht
ij s
b
h
ij x3 dx3
ëê ûú ò
(2)
I - b
+ h
=
-h
t
where I ò J( x3) x3 dx
2
b
and J(x3) is defined in B 2513.
Note: The bending shape factors for this case are given in Figure IC 3211-3
3
(3) In this case, the bending components of the normal stresses can be derived by using
Eq.2 for the s11 component and Eq. 1 for the s22 component. However, the bending
components for the shear stresses s12 and s21 defined by these equations are generally
unequal.
BÊ2520 Classification of stresses obtained by elastic analysis
General classifications for stresses are given in IC 2520.
B 2521 Primary stress
The primary stress is defined as that portion of the total stress which is required to satisfy
equilibrium with the applied loading and which does not diminish after small scale permanent
deformation. Small scale permanent deformation is taken to mean deformation which results
from plastic strains that are of the same order of magnitude as the elastic strains. If the
stresses do not diminish after such small plastic strains, then it is implied that the stresses
cannot be relaxed by small deformation and can lead to plastic instability and other damage.
Within a structure, any stress field (e.g., the elastic stress field or a lower bound stress field
for limit analysis) which balances the volumetric forces and the loads applied on the surface
(mechanical loads: pressure, forces, etc.) is an upper bound to the primary stress. This
property is useful in practice because the exact value of the primary stress is not always easy
to determine. Thus, the upper bound will, more often than not, be used instead of the true
primary stress. The exact value of the primary stress may be obtained by taking the smallest
stress field which balances the forces, that is, that which leads to the lowest value of the
maximum stress intensity in the structure.
Example: For a clamped edge beam with a uniformly distributed load (w), from elastic
analysis, an upper bound to primary bending stress (Pb) corresponds to the edge bending
moment of wL 2 /12, where L is the span. However, a better (i.e., lower) upper bound to the
primary bending stress, which can be obtained from limit analysis, corresponds to a bending
moment of wL 2 /16.
Generally, mechanical stresses (B2501) produced by mechanical loads are classified as
primary.
Note: If the elastic stress analysis is conducted using a finite-element technique, the primary
membrane and bending stresses at any section have to be determined using the procedures
given in IC 2513 and IC 2514, respectively (also, see sections B 2513 and B 2514).
SDC-IC, Appendix B. Guidelines for Analysis page 6

ITER G 74 MA 8 01-05-28 W0.2
B 2521.1 Primary membrane stress
The definition of membrane stress is straightforward for simple geometries, such as a solid
shell or a section with several parallel solid shells, as defined in IC 2513. However, for more
complex-shaped cross-section, the definition depends on how the geometry is modelled and
analysed (see section B 2513).
B 2525 Secondary stress
Stresses arising from differential thermal expansion and swelling, being deformationcontrolled,
are classified as secondary, except where the possibility of a large elastic follow
up (IC 2161) exists, in which case they should be classified as primary. General thermal (or
constrained swelling, B 2503) stresses (IC 2502) are generally classified as secondary.
Elasto-plastic analysis (B 3024) can be carried out to help distinguish between primary and
secondary stresses by applying the following principle:
"Any stress can be categorized as secondary, if it is likely to be redistributed in compliance
with the significant strain criteria given in IC 3312."
B 2526 Peak stress
Peak stress is that increment of stress which is additive to the primary and secondary stresses
by reason of local discontinuities (IC 3024) or local thermal (or constrained swelling, B
2503) stress (B 2502) including the effects of, if any, stress concentrations. In a ductile
material, peak stresses are objectionable only as a source of fatigue. However, in a lowductility
material (e.g., irradiated stainless steels), peak stress could also lead to local
cracking by exhaustion of ductility, and has to be guarded against.
Table B 2520-1 provides some guidance to the designer about stress classification. However,
the designer is ultimately responsible for specifying the final classification based on
assessment of the specific design situation.
SDC-IC, Appendix B. Guidelines for Analysis page 7

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Table B 2520-1: Stress classification for in-vessels components
Location Origin of stress Type of stress Classification Remarks
Everywhere
except at
discontinuities
Corners where
two flats meet
Internal/external
pressure
Thermal gradient
through thickness
Axial or
circumferential
thermal gradient
Axial,
circumferential
or throughthickness
swelling gradient
General
membrane
Bending
SDC-IC, Appendix B. Guidelines for Analysis page 8
Pm
Pb
Averaged across
section
Linear variation
across thickness
Bending Q Thermal stress,
deformation
controlled
Membrane/
Bending
Membrane/
Bending
Internal pressure General
Membrane
Differential
Swelling/
Temperature
Linearized stress
from bending
moment
Maximum stress
including stress
concentration
Membrane
Linearized
component of
bending
Maximum stress
including stress
concentration
Q Deformation
controlled
Q Deformation
controlled
Pm
Pb
Peak (F)
Q
Q
Peak (F)
Averaged across
section
linear variation
across thickness
Concentrated
Deformation
controlled
Deformation
controlled
Concentrated

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Table B 2520-1: Stress classification for in-vessels components (Cont'd)
Location Origin of stress Type of stress Classification Remarks
Junction with
end plug/cap or
near
attachments
Internal pressure Membrane
Channel Channel to
channel
interaction due to
temperature
difference across
flats (bowing)
Fillets between
flats
Near holes,
slits, etc.
Channel to
channel
interaction due to
swelling
Internal/external
pressure
Channel to
channel
interaction due to
swelling or
temperature
difference
Stresses from any
source
Bending
Bending
Bending
Membrane
Bending
SDC-IC, Appendix B. Guidelines for Analysis page 9
PL
Q
Q
Q
PL
Q
Averaged across
wall, acts at
immediate
vicinity of
junction
Due to constraint
at end,
deformation
controlled
Thermal stress,
deformation
controlled
Swelling induced
stress,
deformation
controlled
Averaged across
wall, acts at
immediate
vicinity
Due to
constraint,
deformation
controlled
Bending Peak (F) Concentrated at
fillet
Local
enhancement
Peak (F) Concentrated

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B 2540 Stress Intensities / Equivalent stresses
BÊ2540.1 Stress intensity - Maximum shear stress theory (Tresca)
For a stress tensor with Cartesian components sij (i and j = 1, 2, 3) and principal components
s1, s2 and s3, the maximum shear stresses are related to the differences in the principal
stresses as follows:
2t12, max = s1 - s2
2t23, max = s2 - s3
2t31, max = s3 - s1
The stress intensity at any point is defined as twice the largest absolute value of t12, max, t23,
max, t31, max and is denoted by s
( 1 2 2 3 3 1 )
s = max s - s , s - s , s - s
This formula can be applied to the total stress tensor as well as to the stress tensor
corresponding to a stress category or a combination of stress categories in the stress
classification of ICÊ2520. When the stress intensity of a combination of several tensors is to
be calculated, care must be taken to first sum the components of all tensors before calculating
the stress intensity. That is, one should calculate the stress intensity of the sum of the tensors,
not the sum of stress intensities.
BÊ2540.2 Stress intensity - Octahedral shear stress theory (von Mises)
For a stress tensor with Cartesian components sij (i and j = 1, 2, 3) and principal components
s1, s2 and s3, the stress intensity at any point is equal to the value obtained by using any one
of the following three equivalent expressions:
2
2
2
{ ( 11 22 ) + ( 22 - 33 ) + ( 33 - 11)
+ ( 12 + + ) }
2 2
23 31
2
s = 12. s - s s s s s 6 s s s
2
2
{ ( 1 2)
+ ( 2 - 3)
+ ( 3 - 1)
}
s = 12.
s - s s s s s
{
2
s = s + s + s - s . s - s . s - s . s } 12
1 2
2
3 2
1 2 2 3 3 1
The first expression is generally valid, whereas the following two can be used only after the
principal stresses have been determined. As before (BÊ2540.1), these formulae can also be
applied to the stress tensor corresponding to a combination of stress categories, in which
case, one should calculate the stress intensity of the tensor sum.
SDC-IC, Appendix B. Guidelines for Analysis page 10
2 12
12

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B 2541 Hydrostatic stress ( s H )
B 2541.1 Triaxiality factor
The triaxiality factor (TF) is defined as the ratio between the hydrostatic stress (IC 2541), sH,
and the von Mises or octahedral shear stress (B 2540.2) normalized to unity for uniaxial
loading. Tests have shown that the ductility of a material can be significantly reduced for a
stress field with a high positive (i.e., tensile hydrostatic stress) triaxiality factor, which
typically occurs at the tip of a notch. Therefore, all ductility-based design rules (IC 3212 and
IC 3213) should account for the triaxiality effects by adjusting the ductility (strain limit)
measured in uniaxial tests. For example, the S e rule for primary and secondary membrane
stresses (ICÊ3212.1) reduces the uniaxial uniform elongation by a factor of 2 to account for
biaxial membrane loading. The S d rule for local fracture due to exhaustion of ductility
(ICÊ3213.1) reduces the uniaxial true strain of rupture by a factor = TF to account for
triaxiality in a notch.
B 2550 Stress intensity ranges/Equivalent stress ranges
The rules for prevention of C-type damage require that calculated history of stress or strain at
any point in the structure be divided into cycles. The procedure for deducing the cycles from
the stress history is given in BÊ2752.1. Next, some of the rules require that the variation of
the stress tensor during a cycle be transformed into a scalar measure called the stress intensity
range. A simple procedure for calculating the stress intensity range, when the components of
the stress tensor vary directly in proportion to a scalar, is given in IC 2550.
More general procedures, to be used when the variation of the stress tensor is not so simple,
are given below for two common theories: maximum shear stress and octahedral shear stress.
BÊ2550.1 Stress intensity range - Maximum shear stress theory
The general procedure for calculating the stress intensity range using maximum shear stress
(Tresca) theory is as follows:
1) At each instant (t) within the cycle, calculate the components of the stress tensor
s(t) at the point concerned.
2) Calculate the tensor representing the stress difference s(t, t') for each pair of
instants (t) and (t') within the cycle. The components of the tensor are equal to the
difference between the components of tensors s(t) and s(t'):
s(t, t') = s(t) - s(t')
3) In accordance with ICÊ3224.4.2, calculate the stress intensity s( tt ,©) of tensor
s(t, t'). The stress intensity range is thus the greatest of the absolute values of the
following quantities:
S12(t, t') = s1(t, t') - s2(t, t')
SDC-IC, Appendix B. Guidelines for Analysis page 11

ITER G 74 MA 8 01-05-28 W0.2
S23(t, t') = s2(t, t') - s3(t, t')
S31(t, t') = s3(t, t') - s1(t, t')
Where indices 1, 2, 3 denote the principal directions of the tensor s(t, t').
Simplification:
If the principal directions of the tensors s(t) remain fixed with time, the principal
directions of tensor s(t, t') coincide with these directions for every pair of instants
(t) and (t') of the cycle. The principal stresses of s(t, t') can then be expressed by
the following equations:
s1(t, t') = s1(t) - s1(t')
s2(t, t') = s2(t) - s2(t')
s3(t, t') = s3(t) - s3(t')
4) For the cycle in question, the stress intensity range is equal to the greatest of the
quantities s tt , ©
( ) calculated for every pair of instants (t) and (t') of the cycle:
[ ] = [ ( ) - ( ) ]
Ds Max s t,© t Max s t s t©
tt ,© tt ,©
= ( )
( ) ( )
The search for the maximum value can be made easier if one of the two instants
defining the cycle is fixed. If tA is taken as the fixed instant, the stress range is
equal to the greatest of the quantities s(t, tA) calculated for each instant t of the
cycle. The stress intensity range is then given by:
[ ]
Ds Max s t s tA t
= ( ) - ( )
If the principal directions of the tensor s(t) remain fixed with time, the search for the stress
range using maximum shear stress theory can be carried out graphically in the plane of the
stress deviator s(t) (Figure BÊ2550-1). Indeed, the principal components of the stress deviator
s(t) can be expressed as functions of the principal stresses s1(t), s2(t), s3(t) as follows:
[ ]
( ) = ( ) - ( ) + ( ) + ( )
s t s t s t s t s t
1 1 1 2 3
[ ]
( ) = ( ) - ( ) + ( ) + ( )
s t s t s t s t s t
2 2 2 2 3
[ ]
( ) = ( ) - ( ) + ( ) + ( )
s t s t s t s t s t
3 3 1 2 3
In the plane of the stress deviator (Figure BÊ2550-1), define three coplanar axes 1, 2 and 3
with origin at the point O and with unit vectors r r r
i , j, and k inclined at an angle 120¡ to each
other. For a point M with Cartesian projection Ki on these axes, the following equation
OK = 32s ( t) i = 1to 3
i i
( )
SDC-IC, Appendix B. Guidelines for Analysis page 12
3
3
3

ITER G 74 MA 8 01-05-28 W0.2
describes a closed plane curve during the cycle in question. This closed plane curve is
contained within an hexagon (shown by dotted lines), the sides of which are parallel to the
directions of axes 1, 2 and 3. The greatest of distances d23, d31 and d12, measured parallel
to the directions of axes 1, 2 and 3 respectively between the sides of this hexagon divided by
2 3 gives the stress intensity range for the cycle concerned.
( ) = ( )
23 Ds Max d12, d23, d31
Ds = ( 2) ( )
12
Max D , D , D
r r r
i, j, k : unit vectors
1 2 3
Figure BÊ2550-1: Stress intensity range, maximum shear theory,
fixed principle directions
SDC-IC, Appendix B. Guidelines for Analysis page 13

ITER G 74 MA 8 01-05-28 W0.2
BÊ2550.2 Stress Intensity range - Octahedral shear stress theory
The general procedure for calculating the stress intensity range using the octahedral shear
stress (Von Mises) yield theory is as follows:
1) At each instant (t) of the cycle concerned, calculate the components of the stress
tensor s(t) at the point in question.
2) Calculate the tensor which represents the stress difference s(t, t') for each pair (t),
(t') of the cycle. The components of the tensor s(t, t') are equal to the difference
between the components of the tensors s(t) and s(t'):
s(t, t') = s(t) - s(t')
3) Using ICÊ3224.4.3, calculate the stress intensity s( tt , © ) of tensor s(t, t'):
{
2
[ 11 22 ] + [ 22 ( ) - 33(
) ]
( ) = ( ) - ( )
s tt ,© 12.
s tt ,© s tt ,© s tt ,© s tt ,©
Simplification:
[ s33 tt ,© s11
tt ,© ]
+ ( ) - ( )
6 [ s12 tt ,© s tt ,© s tt ,© ]}
2
2
23 31
2
+ ( ) + ( ) + ( )
2
If the principal directions of the stress tensors s(t) remain fixed with time, the
stress intensity s tt , ©
the stress deviator s(t):
s t s t s t s t s t 3
( ) is expressed as a function of the principal components of
[ ]
( ) = ( ) - ( ) + ( ) + ( )
1 1 1 2 3
[ ]
( ) = ( ) - ( ) + ( ) + ( )
s t s t s t s t s t
2 2 1 2 3
[ ]
( ) = ( ) - ( ) + ( ) + ( )
s t s t s t s t s t
Then
3 3 1 2 3
2
2
( ) = ( ( ) - ( ) ) + ( ( ) - ( ) ) + ( ( ) - ( ) )
s t,© t . s t s t© s t s t© s t s t©
SDC-IC, Appendix B. Guidelines for Analysis page 14
3
3
{ 2 2
3 3 }
32 1 1
12
2
2 12
4) For the cycle concerned, the stress intensity range denoted by Ds is equal to the
greatest of the quantities s( tt , © ) calculated for each pair of instants (t) and (t') of
the cycle:
Ds Max
tt ,©
s
[ ]
= ( tt ,© )
( )
The search for the maximum value can be made easier if one of the two instants
defining the cycle is fixed. If tA is taken as the fixed instant, the stress range is

ITER G 74 MA 8 01-05-28 W0.2
equal to the greatest of the quantities s(t, tA) calculated for each instant t of the
cycle. The stress intensity range is then given by: :
Ds Max
t
s
[ ttA ]
= ( , )
If the principal directions associated with the stress tensors s(t) remain fixed with time, the
search for the range using the octahedral shear stress theory may be carried out graphically
(Figure BÊ2550-2). In the plane of the stress deviator, define three coplanar axes 1, 2 and 3
with origin at the point O and with unit vectors r r r
i , j, and k inclined at an angle 120¡ to each
other. For a point M with Cartesian projection Ki on these axes, the following equation
OK = 3 2 S ( t) i = 1 to 3
i i
( )
describes a closed plane curve during the cycle concerned. The largest diameter of this curve
divided by 2 3 gives the stress intensity range for the cycle in question.
r r r
i, j, k : unit vectors
Figure BÊ2550-2: Stress intensity range, octahedral shear theory,
fixed principle directions
SDC-IC, Appendix B. Guidelines for Analysis page 15

ITER G 74 MA 8 01-05-28 W0.2
B 2600 STRAIN DEFINITIONS AND CLASSIFICATION
B 2620 Calculation of equivalent strain ( e)
For a strain tensor with Cartesian components eij (i and j = 1, 2, 3), the equivalent strain is
given by
2
e = { [ e11 - e22 ] + [ e - e ] + e - e
3
2
22 33 2
.
[ 12
] }
2 2
23 31
+ 6 e + e + e
2 1 2
[ ]
33 11 2
BÊ2630 Calculation of the equivalent strain range ( De)
The equivalent strain range De at a point is used to compute the fatigue usage fraction. A
simple procedure for calculating the equivalent strain range, when the components of the
strain tensor vary directly in proportion to a scalar, is given in IC 2630.
In general, when the components of the strain tensor do not vary in direct proportion to a
scalar, the strain range is calculated in the following way:
1) At each instant (t) of the cycle, calculate the components of the strain tensor e(t) at
the point examined:
e11(t); e22(t); e33(t); e12(t); e13(t); e31(t)
2) Calculate the strain range tensors e(t, t') for each pair of instants (t) and (t') of the
cycle. The components of tensor e(t, t') are equal to the difference between the
components of tensors e(t) and e(t'):
e(t, t') = e(t) - e(t')
3) Calculate the equivalent scalar strain range e tt , ©
using one of the following formulae:
{
( ) between the states (t) and (t')
2
2
e( tt ,© ) = . [ e11( tt ,© ) - e22 ( tt ,© ) ] + e22 ( tt ,© ) - e33(
tt ,© )
3
[ e33 tt ,© e11
tt ,© ]
+ ( ) - ( )
6 [ e12 tt ,© e tt ,© e tt ,© ] }
2
2
23 31
+ ( ) + ( ) + ( )
2
[ ]
2 1 2
SDC-IC, Appendix B. Guidelines for Analysis page 16
2

ITER G 74 MA 8 01-05-28 W0.2
{
2
2
e( tt ,© ) = . [ e1( tt ,© ) - e2( tt ,© ) ] + e2( tt ,© ) - e3(
tt ,© )
3
where
[ e2 tt ,© e3
tt ,© ] }
+ ( ) - ( )
2 12
[ ]
e11(t, t'), e12(t, t') are the components of tensor e(t, t'), and
e1(t, t'), e2(t, t'), e3(t, t') are the principal components of this tensor.
4) For the cycle examined, the strain range is equal to the greatest of the quantities
e tt , ©
( ) calculated for each pair of instants (t) and (t') of the cycle:
De Max
tt ,©
e
[ ]
= ( tt ,© )
( )
B 2700 TERMS RELATED TO LIMIT QUANTITIES
B 2750 Terms related to fatigue damage
B 2752 Fatigue usage fraction V
BÊ2752.1 Procedure for combination of cycles
The following procedure for combination of cycles is recommended to ensure that a random
sequence of cycles which could occur in the same time period are combined in such a way
that the calculated strain ranges are a maximum, therefore conservative in a fatigue
evaluation. For clarification, refer to the illustrated example below, which assumes that the
strain cycles are uniaxial.
1. If two types of strain cycles separately produce strain ranges which are lower than
those that would be produced by a single type of cycle formed by a concatenation
of these cycles, then the two cycles must then be combined into a single cycle
with the combined strain range.
2. If two types of cycles are combined in accordance with rule #1, and if n1 and n2
are the original numbers of cycles, and if n1 is less then n2, then the two types of
cycle should be combined for n1 cycles with a combined range, leaving (n2-n1)
cycles of the second type.
3. To preserve the total number of cycles, an additional number, n1, of cycles that
include the intermediate maxima and minima must be taken into account.
4. The above process should be repeated, if necessary, until no more combinations
are possible.
The following two figures illustrate these rules and explain the logic.
SDC-IC, Appendix B. Guidelines for Analysis page 17
2

ITER G 74 MA 8 01-05-28 W0.2
Figure BÊ2752-1: Original Cycles
Example of rule #1. Observe that Cycle 1 has a strain range of (50 + 10) = 60.
Cycle 2 has a strain range of (15+30) = 45. In accordance with rule #1 above,
however, a larger strain range (50 + 30) = 80 can be obtained by combining the
positive half of cycle 1 with the negative half of cycle 2. This gives combined
cycle 1Õ shown below.
Example of rule #2. Observe that the number of cycles of type 1 is 1000 and the
number of type 2 is 10,000. In accordance with rule #2, the number of cycles of
type 1Õ should be the smaller of these, or 1000. This leaves 10000 - 1000 - 9000
cycles of type 2Õ, as shown below.
Example of rule #3. The concatenation of original cycles 1 and 2 gives a variation
+50, -10, +15, -30. The combination of these in accordance with the above,
resulted in 1000 cycles with range +50 to -30. To account for the intermediate
maxima and minima, 1000 additional cycles with range +15 to -10 must be
included. These are the type 3Õ cycles shown below.
Figure BÊ2752-2: Combined Cycles
A generalization of the above procedure can be expressed as follows. In a history of random
cycles, select the first composite cycle as one having the maximum strain and the minimum
SDC-IC, Appendix B. Guidelines for Analysis page 18

ITER G 74 MA 8 01-05-28 W0.2
strain during the period. Remove that cycle from the history. Then, continue selecting
cycles, each time selecting the maximum and the minimum of the ones that remain.
SDC-IC, Appendix B. Guidelines for Analysis page 19

ITER G 74 MA 8 01-05-28 W0.2
B3000 DESIGN RULES FOR SINGLE-LAYER
HOMOGENEOUS STRUCTURES
The applicable rules depend on whether or not the effects of thermal creep are negligible. If
they are negligible, then the low temperature design rules (IC 3100) apply. If not, hightemperature
rules (IC 3600) are applicable.
B 3020 Methods of analysis
Two alternative types of analyses are permissible - elastic and inelastic. Elastic analysis
should be the method of first choice because it is much simpler. Inelastic analysis is more
complex and likely to encounter problems with convergence, accuracy, etc. Furthermore, the
validation of inelastic analysis methods, particularly those dealing with cyclic stresses in a
nonlinear material, requires extensive theoretical and experimental work.
The criteria to be used in conjunction with elastic analyses are purposely selected to be fairly
conservative. Other methods of analysis could be pursued if elastic analysis fails to
demonstrate compliance with the criteria.
In general, inelastic analyses methods should be adopted if the criteria based on elastic
analyses cannot be satisfied. These might include inelastic finite element analysis and
simplified inelastic analysis methods. Guidelines for satisfying limits for inelastic analysis
using simplified inelastic analysis methods are given in this chapter. Other simplified
analysis methods could be used provided they can be justified and shown to yield
conservative results. In general, inelastic finite element analyses should be conducted if the
simplified inelastic analysis methods fail to satisfy the criteria for inelastic analysis.
In general, elastic analysis is used to satisfy stress limits while inelastic analysis is used to
satisfy strain limits. This is because elastic analysis cannot calculate plastic strains directly,
rendering stress (and the equivalent elastic strain) as its only useful measure. Also, when an
inelastic analysis is performed in the range of interest, significant plastic strains can occur
with only small variation of stress, rendering strain a more useful measure. In addition to the
stress and strain limits needed to ensure structural integrity, fast fracture limits, fatigue limits,
buckling limit, and deformation limits for functional adequacy must be satisfied for both
types of analyses.
Both elastic and inelastic analyses may be conducted on the assumption that the
displacements and strain are infinitesimal (geometric linearity). However, the analyst should
verify that this assumption is reasonable, particularly in the presence of irradiation-induced
swelling and creep, because the design rules do not explicitly put a limit on these strains.
Guidance for verifying this assumption is given in B 3021. If the strains and displacements
become significant, an elasto-visco-plastic analysis, including finite deformation effects may
be needed.
The design rules have been separated into two classes - low-temperature rules (thermal creep
effects can be neglected) and high-temperature rules (thermal creep effects cannot be
neglected). To determine which rules are applicable, a test for negligible thermal creep
(IC3050) has been included.
Strain rate or time-dependent strain (or creep) effects are considered explicitly in the hightemperature
rules, with or without irradiation-induced swelling and creep. Generally, strain-
SDC-IC, Appendix B. Guidelines for Analysis page 20

ITER G 74 MA 8 01-05-28 W0.2
rate or time-dependent strain effects are ignored in the low-temperature rules. However, they
may become important in stress analysis (by introducing swelling-induced stress (B 2513)
and by redistributing stresses and strains), which is required before the low-temperature rules
can be applied, if significant amounts of irradiation-induced swelling and creep strains occur.
Therefore, before applying the low-temperature design rules, a determination has to be made
if the effects of irradiation-induced swelling (B 3022) and irradiation-induced creep (B 3101)
are negligible .
B 3021 Test to determine if nonlinear (finite deformation) analysis
is needed
The following procedure may be used to determine if nonlinear (finite deformation) analysis
is needed.
1) The total operating period of the component, throughout its life, and all loadings,
for which compliance with level A, C and D criteria is required, are taken into
account.
2) The total operating period is divided into N intervals of time. For each interval i,
of a duration ti, the thickness-averaged values of the maximum temperature
reached Tmi, the mean neutron flux Fmi, the mean neutron fluence Ftmi (or
displacement dose) and the corresponding allowable primary membrane stress
intensity Smi (from Table A.MAT.5.1 of appendix A) are noted.
3) To take full advantage of this rule, the intervals of time must be chosen in such a
way that the temperature and the flux change as little as possible throughout the
interval.
4) For each interval i, determine the neutron fluence Fts1i necessary to accumulate a
linear swelling strain (1/3 the volumetric swelling strain for isotropic swelling) of
2% at a temperature of Tmi and a neutron flux of Fmi from A.MAT.4.4 of
appendix A, and the neutron fluence Ftc1i necessary to accumulate an effective inreactor
creep strain of 2% at an effective stress of Smi (Tmi,Ftmi ), a temperature
of Tmi and a neutron flux of Fmi, from A.MAT.4.4 of appendix A.
5) Compute the following sum of the neutron fluence ratios for all N-intervals.
S
N
æ tmi
t
= å ç
+
è t t
F F
F
F
i = 1
mi
ci 1 si 1
ö
÷
ø
6) If the above sum, S, is greater than 1, then a nonlinear analysis involving large
displacement and strain may be needed.
Note 1: If the material displays an incubation period for swelling and the peak neutron
fluence in the component is less than the lowest incubation neutron fluence within the range
of temperature (not necessarily the maximum temperature) experienced by the component,
then checking for the swelling strain is not needed.
Note 2: Denote the maximum values of the thickness-averaged temperature, neutron fluence,
and Sm over the whole operating period (tmax) of the component by Tm, max, Ftm, max and Sm,
max, respectively. If the total creep strain accumulated at a stress Sm, max, temperature Tm,max,
SDC-IC, Appendix B. Guidelines for Analysis page 21

ITER G 74 MA 8 01-05-28 W0.2
neutron fluence Ftm, max, and average flux Fave (=Ftm, max/tmax) is less than 1%, then
checking of the creep strain is not needed. If there is a peak in the irradiation-induced creep
strain at a temperature

ITER G 74 MA 8 01-05-28 W0.2
Note 2: Tables for fts are provided in A.MAT.4.2 of appendix A.
Note 3: For ITER operating conditions, this test is satisfied, i.e., S < 1, for type 316L(N)
stainless steel and need not be checked.
B 3023 Elastic Analysis
This type of analysis is made assuming that:
- the behaviour of the material is linear-elastic,
- the material is homogeneous and isotropic,
- the displacements and strains are small,
- the initial or residual stresses are zero.
The behaviour of the material is determined by the Young's modulus, E, and Poisson's ration,
n, the shear modulus, G, is equal to E/2 (1 + n). The values of Young's modulus as a function
of temperature are given in A.MAT.2.2 of appendix A. The value of Poisson's ratio, given in
A.MAT.2.3 of appendix A, is generally equal to 0.3 but can vary in certain cases.
The effects of irradiation-induced swelling may be neglected (B 3022) if the total estimated
maximum irradiation-induced volumetric swelling strain at the end of design life is

ITER G 74 MA 8 01-05-28 W0.2
from all sources should be limited to satisfy the deformation limits for functional adequacy
(IC 3040).
Since irradiation-induced swelling and creep are time-dependent phenomena, deformations
and stress intensities are necessarily time-dependent. Generally, irradiation-induced creep
changes the initial elastic stress distribution by relaxing secondary (e.g., thermal or
constrained swelling stress) or peak stresses with accumulating neutron fluence. The relaxed
part of the secondary and peak stresses will reappear with reversed sign when the reactor is
shut down and the incremental loading is applied in reverse. These changes in stress
distribution should be accounted for in satisfying fatigue, ratchet, and buckling limits.
Constitutive equations for irradiation-induced creep and swelling for the ITER structural
materials are given in the ITER MPH-IV 2 . These equations should be used in a finiteelement
elastic-creep analysis of the component. In some cases, simplified constitutive
equations for irradiation-induced swelling and creep may be used, provided they can be
shown to give conservative results. Two such cases where stresses evolve with time are
discussed - one for swelling-induced stress (B 3024.1.1.1) and the other for relaxation of
thermal stress by irradiation-induced creep (B 3024.1.1.2).
B 3024.1.1.1 Swelling induced stress value
If the negligible swelling test of B 3022 is not satisfied, then stresses due to constrained
irradiation-induced swelling (B 2513) have to be considered. For computing stresses due to
fluence-dependent swelling, the relaxing effects of irradiation-induced creep has to be taken
into account irrespective of whether the negligible irradiation-induced creep test of B 3101 is
satisfied or not, because otherwise the elastically calculated swelling stresses could become
unrealistically large. Swelling strains, when constrained, give rise to stresses that, in general,
increase with fluence and ultimately reach steady-state values that are the results of a
dynamic equilibrium between the elastically driven constrained swelling stresses and the
relaxation effects of irradiation-induced creep. Such constrained swelling stresses are
classified as secondary stresses (ICÊ2525). In general, solving for constrained swelling
stresses would require an incremental thermal-elastic-creep analysis of the component. For
some isotropic materials, such as type 316 austenitic stainless steel, the constitutive equations
for the fluence driven creep and swelling strains can be approximated by
and
e
ij creep
( ft)
= BT ( , f)
S
3
2
eij
swelling 1 1 V 1
= d = AT ( , f) d
( ft)
3 V ( ft) 3
where
V = the volume,
ij
ij ij
A(T, f) and B(T, f) are coefficients for irradiation-induced swelling and
creep equations (see A.MAT.4.2 and A.MAT.4.3 of appendix
A), with T as temperature and f as neutron flux,
SDC-IC, Appendix B. Guidelines for Analysis page 24
(1)
(2)

ITER G 74 MA 8 01-05-28 W0.2
Sij = the deviatoric stress, and
dij = the Kronecker delta.
For these materials, the swelling stresses may be obtained by conducting a visco-elastic
analysis using the above equations. Alternatively, the following fully constrained steadystate
swelling stresses may be used as an upper bound.
For the case of uniaxial constraint,
Ds
s
( )
( )
æ AT,
f ö
= - ç
è 3BT,
f
÷
ø .
For the case of biaxial constraint,
Ds
æ 21 ( n) AT,
f ö
= - ç
d a b
è 3BT
f
÷ for , = 1,2
, ø
- ( )
( )
abs ab
To reduce the degree of conservatism (e.g., in the case of swelling strain gradient), an elastic
analysis of the component may be conducted using an imposed strain distribution defined as
follows.
For uniaxial loading,
De
s
=
( )
( )
æ AT,
f ö
ç
è 3EB
T,
f
÷
ø
For biaxial loading,
De
=
æ 21 ( - u) 2
AT ( , f)
ö
ç
d a b
è
3EB
T f ÷ for , = 1,2
( , )
ø
abs ab
In above, E and n are the Young's modulus and Poisson's ratio at temperature and fluence.
Note that if the mechanical and physical properties are not functions of temperature, the
above strains may be imposed by a fictitious temperature distribution obtained by dividing
the strain by the thermal expansion coefficient. If the mechanical and physical properties are
functions of temperature, then a method must be found (e.g., a user subroutine) to specify the
swelling strain directly. These secondary stresses together with others contribute to the total
stress (IC 2512). The stress tensor giving the maximum swelling stress intensity value
among the operating conditions should be selected.
B 3024.1.1.2 Relaxation of thermal stress by irradiationinduced
creep
At low temperatures, where thermal creep is negligible (B 3050), thermal stresses reach a
peak at the beginning of life and then decrease due to relaxation by irradiation-induced creep.
The analysis of relaxation of thermal stresses by irradiation-induced creep is straightforward,
since these stresses are fully developed in a very short period of time and then relaxation
takes over. The relaxed part of the thermal stresses will reappear during shutdown. During
SDC-IC, Appendix B. Guidelines for Analysis page 25

ITER G 74 MA 8 01-05-28 W0.2
relaxation, the sum of the incremental elastic strain and incremental irradiation-induced creep
strain is zero, i.e.,
e
ij
c
ij
eÇ + eÇ
= 0 (1)
If the material obeys the creep law given by Eq. 1 of B 3024.1.1.1, then denoting the initial
and relaxed thermal stresses by so and s respectively, Eq. (1) can be solved as follows:
for the uniaxial case,
( )
s = soexp -EB(
T, f) ft
(2)
and for the equi-biaxial case,
æ 3 EB( T, f) ftö
sij = sodij expç
-
÷
è 2 ( 1 - n)
ø
where i , j = 1,2
and E and n are the Young's modulus and Poisson's ratio.
If the material obeys a creep law different from Eq. (1) of B 3024.1.1.1 or if the initial
starting stress is more general than equi-biaxial, Eq(1) can be solved numerically if a closed
form solution cannot be obtained.
B 3024.1.2 Neuber's rule
Neuber's rule can be applied to estimate the maximum elasto-plastic stresses and strains at
notch roots. Consider a notch with an elastic stress concentration factor KT subjected to a
nominal (remote) uniaxial stress So and, for a linear elastic material, corresponding remote
uniaxial strain eo (eo = So/E). The elastically calculated peak stress (S) and strain (e) at the
notch root are given by
S = KTSo
e = KTeo
NeuberÕs rule states that, if we replace the linear elastic material with a material obeying a
uniaxial power-law constitutive equation,
s = Ae n ,
then, denoting the notch root maximum stress and strain by s and e,
s · e = S · e (1)
The above equations can be solved for the maximum stress and strain at the notch roots as
s = SK
e = eK
2n/( 1+
n)
o T
2/( 1+
n)
o T
SDC-IC, Appendix B. Guidelines for Analysis page 26
(3)
(2a)
(2b)

ITER G 74 MA 8 01-05-28 W0.2
Equations 2a-b have also been used extensively in fatigue analysis of notches by replacing
the stresses and strains by their respective ranges and by replacing KT with Keff, which is an
experimentally determined (material-dependent) effective stress concentration factor.
Neuber's rule in the form of Eq. 1 is used in satisfying the fatigue damage limit (IC 3322)
using the elastic fatigue analysis rule (B 3323.1).
Note: Neuber's rule as described here applies strictly to a power-law hardening material,
which implies that, in order to be applicable to an elastic-power-law hardening material, the
elastic strain at the notch root must be small compared to the plastic strain. Also, in a
multiaxial loading situation, the stresses and strains have to be replaced by their respective
scalar representations.
B 3024.1.3 Elastic follow-up factor (r)
The actual stress and strain at any point in an elasto-plastically deforming structure can be
expressed in terms of the elastically calculated stress at the same point by the use of a factor
R, defined as follows:
Ee
- s
R =
s - s
where
el
E = Young's modulus,
sel = elastically calculated stress
s and e = actual stress and total strain
The maximum value of R in the structure, which occurs at the point of maximum stress or
plastic strain, is called the Òelastic follow-up factorÓ, r. The term elastic follow-up (IC
2161) refers to the fact that the total strain includes plastic strains, which tend to be driven or
ÒfollowedÓ by the strain energy in the elastic part of the structure. In the literature (e.g.,
Roche), the elastic follow up factor has sometimes been defined in terms of a different factor
rÕ which is numerically equal to r Ð 1, with r defined as above. In general, the value of r
depends on the geometry of the structure, material stress-strain law, and the load level. When
defined as in Eq. (1), the maximum plastic strain in the structure (ep) can be expressed as
r
ep= sel - s
E
SDC-IC, Appendix B. Guidelines for Analysis page 27
(1)
[ ] (2)
Quite often, the actual stress s is much less than either Ee or the elastically calculated stress
sel, in which case the r-factor can be shown to be equal to the strain concentration factor due
to elastic follow-up, i.e.,
r
E e e
= = =
s
e
el el
K
e
A significant number of detailed inelastic analyses have been reported in the literature
indicating that, for general structures made of a reasonably strain-hardening ductile material
(3)

ITER G 74 MA 8 01-05-28 W0.2
and with maximum nominal stresses (P+Q) not exceeding the 3Sm limit (IC 3311.1), a
conservative value of r = 3. The design guide for the Monju reactor of Japan recommends a
default value of r=3 for creep-fatigue design. However, the r-factor methodology has not
been used in the fission reactor codes to design against fracture, because loss of ductility is
not a damage considered in these codes. Since, in the SDC-IC, we propose to use the r-factor
methodology to design against fracture, two factors have to be considered, both of which tend
to increase the value of r. They are (1) reduced or zero strain hardening capability of
materials under neutron irradiation (see Figure C 3024-6 of Appendix C) and (2) the elastic
stress that corresponds to fracture far exceeds the 3Sm limit.
Analysis of displacement-controlled three-point bend tests (see C 3024.1.3 of Appendix C) of
a beam made of a material with a bilinear stress-strain law has shown that the value of r as a
function of the peak plastic strain is bounded (£ 4) as long as the ratio of the tangent modulus
to Young's modulus (ET/E) is ³ 0.01. At lower values of ET/E ratio, the r value increases
with increasing peak plastic strain and, in particular, for an elastic-perfectly plastic material
(ET/E = 0), it increases indefinitely with increasing peak plastic strain.
Experimental results on three-point bend tests on irradiated type 304 stainless steel have
shown that the value of r can be large if the uniform elongation of the material is £ 1% (see C
3024.1.4 of Appendix C). When extrapolated from this set of data, the value of r should be £
4 when the uniform elongation ³ 2%. These results are in good agreement with the
analytically determined r as discussed in the previous paragraph.
In contrast to the three-point bend tests, single-edge notched tensile tests on irradiated type
304 stainless steel have shown that the value of r is relatively constant (» KT) even when the
uniform elongation is < 1% (see C 3024.1.3 of Appendix C). These results are in agreement
with r-values predicted analytically on the assumption that strain localization at the notch
cannot occur and that plastic strains remain distributed homogeneously at the notch root (see
C 3024.1.4 of Appendix C). However, because of the stiffness of the testing machine, these
specimens did not have the freedom to fail by sliding off at an angle starting at the notch. In
a load controlled test, depending on the notch geometry, strain localization could occur. This
must either be prevented by restricting the range of uniform elongation or accounted for by
increasing the r factor.
It is clear that the value of r can be quite sensitive to the component geometry and loading
mode. Therefore, in the design rules (IC 3212.1 and 3213.1), which use the r-factor
methodology for setting the limits on elastically calculated maximum stresses, the value of r
has been chosen conservatively. However, in any particular application, the designer is given
the option of using a lower value of r if it can be so justified.
The justification for a different r consists of estimating the peak values of strain and stress
conservatively using elasto-plastic analysis (B 3024.2), using Eq. 1 to evaluate R, and taking
r as the maximum R in the structure. The designer should use judgment in selecting a
suitable sub-model and loading of the structure. See BÊ3025 for a discussion of calculation
zones and sub-models. In addition, the designer should use an appropriate stress-strain law
that corresponds to the lowest work hardening (which, for steel, occurs at the maximum
fluence) under consideration. The analysis must be carried out either to the load level of
interest or to demonstrate that the r-value has peaked prior to reaching the load level of
interest.
SDC-IC, Appendix B. Guidelines for Analysis page 28

ITER G 74 MA 8 01-05-28 W0.2
BÊ3024.2 Elasto-plastic analysis of a structure subjected to a
monotonic loading
Elasto-plastic analysis should be conducted by using a validated finite-element analysis
program (e.g., ANSYS, ABAQUS, etc.) together with a validated material model
(constitutive law) and a structural model of quantified accuracy. Alternatively, the designer
may use any other analytical or numerical means that can be justified. Generally, an elastoplastic
analysis will be required under two conditions. First, if the designer intends to use a
lower value of the elastic follow-up factor r than is stipulated in the elastic analysis rules of
IC 3211.1, 3212.1, and 3213.1, the value of r has to be justified on the basis of elasto-plastic
analyses (B 3024.2). Second, if the designer cannot satisfy the elastic analysis rules of either
IC 3211.1, 3212.1, or 3213.1, the elasto-plastic analysis rules of IC 3211.2, 3212.2 or 3213.2
have to be satisfied using elasto-plastic analyses.
This section describes a simplified elasto-plastic analysis procedure applicable to monotonic
loading. This is applicable only if it can be ascertained that the following two conditions are
satisfied:
1) no unloading ever occurs in any part of the structure which undergoes plastic
strain,
2) at all points of the structure, the stress tensor components calculated elastically
vary simultaneously and proportionally to a single parameter.
A monotonic loading is one which evolves in a constantly increasing or decreasing manner.
For this type of analysis, the mathematical model of the material behaviour is based on the
following laws:
- homogeneity and isotropic behaviour of the material,
- von Mises yield criterion,
- the associated normality law for plastic strain: plastic flow rule,
- an isotropic strain hardening rule.
The material characteristics required for application of this model are:
- the minimum tensile curves as a function of temperature and fluence (A1.6.1),
- the Young's modulus and Poisson's ratio as a function of temperature and fluence
(A1.2.2).
The elasto-plastic analysis rules of IC 3211.1, 3212.2, and 3213.2, require the use of various
load factors (GiL) to be applied to mechanical loads, and strain factors (GiS) to be applied to
deformation-controlled loads (e.g., thermal load, swelling-induced load) before the elastoplastic
analysis is carried out. Although the application of a load factor to mechanical loads
is straightforward, for thermally-induced (or swelling-induced) loading, the strain factor is
applied to the loads induced by thermal strains (or swelling strains). In the latter case, it may
be necessary to artificially induce high strains concurrent with the use of realistic stiffness
and flow properties. The use of an "adjusted" thermal expansion coefficient is one technique
for enhancing the applied strains without affecting the associated stiffness and flow
properties. The treatment of swelling-induced stress is discussed in B 3024.1.1.1.
SDC-IC, Appendix B. Guidelines for Analysis page 29

ITER G 74 MA 8 01-05-28 W0.2
BÊ3024.2.1 Use of the tensile curve
To characterize the stress-strain response, this elasto-plastic model makes use of a Òminimum
tensile curve,Ó expressed as a relationship between the stress s* and the cumulative plastic
strain e p * at a given temperature. This relationship is obtained by subtracting the elastic
strain from the total strain of the tensile curve as shown in Figure BÊ3024-1 (below). The
minimum (lower bound) tensile curve is used to obtain a conservatively high estimate of the
plastic strain.
*
The curve ( s*; ep)
represents the strain hardening behaviour of the material. s* depends
*
on the current strain hardening state as represented by the cumulative plastic strain ep . In the
initial virgin state of the material, e p * = 0, s* equals the initial yield stress.
SDC-IC, Appendix B. Guidelines for Analysis page 30

ITER G 74 MA 8 01-05-28 W0.2
Figure BÊ3024-1: Use of tensile curve
BÊ3024.2.2 Plasticity criterion
The von Mises yield criterion can be expressed in terms of the stress intensity defined in
BÊ3254.1 and the stress s* determined in BÊ3024.2.1:
* *
s = s ( ep)
where
s = s s
3
© ij © ij
2
where s'ij is the deviatoric stress. Alternatively,
2
2
{ ( ) + ( 2 - 3)
+ ( 3 - 1)
}
s = . s - s s s s s
12 1 2
The behaviour of the material remains elastic as long as s < s*.
When s = s*,
the limit
of the elastic behaviour is reached and plastic strain can occur.
SDC-IC, Appendix B. Guidelines for Analysis page 31
2 12

ITER G 74 MA 8 01-05-28 W0.2
p
Plastic strain eij is calculated incrementally by using the flow rule given in ICÊ3024.2.3. In
the case of a material which can strain harden, the plastic strain modifies the yield criterion.
This modification is determined by means of the hardening rule given in ICÊ3024.2.4.
BÊ3024.2.3 Flow rule
p
The flow rule provides the incremental plastic strain de ij for a given incremental stress dsij.
The incremental plastic strain at any point can be obtained by using the following steps.
1) At the start of a step, the current stress, strain, and plastic strain at a given point
is known. By definition, the current stress is on the current yield surface which
is known:
2
3
* * 2
f( s©, ij s ) s© ij s© ij s
where
= - ( ) =
s'ij is the deviatoric stress.
SDC-IC, Appendix B. Guidelines for Analysis page 32
0,
2) For a given stress increment dsij , the deviatoric stress increment ds'ij can be
calculated. The point under consideration will undergo further plastic
deformation if s'ij ds'ij > 0. The stress increment will cause an elastic strain
increment only if s'ij ds'ij £ 0.
3) If further plastic deformation occurs, the plastic strain increment is determined
by the normality rule (Reuss equations)
de
p
ij
f
= dl = s© ij dl
s©
ij
.
Defining an equivalent plastic strain increment by
p
de =
p p
deijdeij 2
,
3
which can be written in an expanded form as
( ) + ( - ) + ( - )
2
de =
ì
2
2
í de11 - de22 de22 de33 de de
3 î
12
p p p
+
æ 2 2 2
( de ) + ( de ) + ( de
ö ü
6
è 12 23 31)
ø ý
þ
p p p p p p p 2
33 11
dl can be solved as
dl
d p
3 e
= *
2 s ,
and the incremental plastic strain components are then given by :
,

ITER G 74 MA 8 01-05-28 W0.2
de = s - 05 . s + s de
s
de = s - 05 . s + s de
s
de = s - 05 . s + s de
s
de 32 s de
s
de 32 s de
s
de
p
11 11 22 33
p
22 22 33 11
p
33 33 11 22
p
12 12
p
23 23
p
31
[ ( ) ]
[ ( ) ]
[ ( ) ]
= ( )
= ( )
= ( 32)
p
p
*
*
s31 de s
p *
4) The value of de p has to be determined iteratively by requiring that the resultant
incremental hardening ds * (obtained from the tensile curve) and the new stress
state must be on the new yield surface which is determined by the hardening rule
(BÊ3024.2.4) and which, for isotropic hardening, is given by,
* *
f ( s© ij + ds©, ij s + ds
) = 0
Note 1: The total stress tensor must also satisfy the equilibrium equations and the total
strains must satisfy the compatibility equations.
Note 2: In cases where the stress and strain ratios are maintained constant (radial loading),
the incremental stress-strain relationship (Reuss equations) can be integrated to give a
relationship between total plastic strain and stress (Hencky's equations). Although this may
simplify the calculations significantly, it must be remembered that Hencky's equations are
incorrect for general nonradial loading.
BÊ3024.2.4 Hardening rule
The hardening rule used during analysis of a structure subjected to monotonic loading is an
isotropic hardening rule. According to this rule, the yield surface expands but retains its
shape and origin. The expansion of the yield surface is determined by the variation of s*.
After calculating d p
e by an iterative procedure and determining the new value of the
*
cumulative plastic strain ep , a new value of s* is obtained with the curve in Figure BÊ3024-
1. It should be noted that s* is always positive in this model.
For monotonic proportional loading, kinematic hardening gives the same results.
BÊ3024.3 Elasto-plastic analysis of a structure subjected to cyclic
loading
A large number of possible analysis methods are now available, but none of them are today
qualified to describe all aspects of the cyclic behaviour of materials. The imposition of any
SDC-IC, Appendix B. Guidelines for Analysis page 33
p
p
p
*
*
*

ITER G 74 MA 8 01-05-28 W0.2
one of them would not appear necessary. Nevertheless, the used method used must be
justified.
B 3024.4 Elasto-visco-plastic analysis of a structure subjected to cyclic
loading
A large number of possible analysis methods are now available, but none of them are today
qualified to describe all aspects of the cyclic behavior of materials. The imposition of any
one of them would not appear necessary. Nevertheless, the method used must be justified.
Note: A combined elasto-visco-plastic analysis is necessary only when the effects of creep
and plasticity cannot be separated from one another. In many cases it is possible to separate
the effects as follows. Most models of plasticity are independent of time. If the time frame
for plastic stains is rapid compared with the time frame for creep, then one can assume that
creep strains are constant during a plastic loading period and that plastic strains are constant
during the creep periods between plastic loadings. If plasticity and creep effects are not
separable, then the formulation of the constitutive law becomes more difficult.
BÊ3024.5 Limit analysis (collapse load)
The deformation of a structure made of a rigid-perfectly plastic material increases without
bound at a loading level called the collapse load. Limit analysis methods can be used to
calculate the collapse load or a lower bound to the collapse load.
A given loading is less than or equal to the collapse load if there is a stress distribution which
satisfies the laws of equilibrium at all points that does not violate the material yield criterion
at any point. This theorem allows a lower bound to be defined for the collapse load.
In the case of elasto-plastic analysis and experimental analysis, the collapse load, by
convention, is defined as the loading for which the overall permanent deformation of the
structure equals the deformation which would occur by purely elastic behavior.
BÊ3025 Zones of calculation
In some cases it may be necessary for computational purposes to divide a component into
several zones for analyzing a single type of damage. In such cases, an overall analysis of the
component shall be carried out to determine the loads or displacements to be applied at the
boundaries of each zone for each load case considered. Care should be taken to ensure that
boundary conditions applied are sufficiently accurate or conservative. The accuracy may be
checked by a combination of the following:
a. showing that both stresses and displacements are consistent at the boundaries of
the zone;
b. refinement of the mesh.
Note: the application of displacement boundary conditions to a sub-model requires care.
Two examples are given below.
Say that an elastic analysis of a larger model is used to determine the displacement boundary
conditions for a smaller sub-model, yet the sub-model is expected to operate in the plastic
SDC-IC, Appendix B. Guidelines for Analysis page 34

ITER G 74 MA 8 01-05-28 W0.2
range. In this case, the elastic approximation of the sub-model region used to define the
boundary conditions will be too stiff, so the calculated boundary displacements will be too
small, and the plastic strains in the sub-model will be underestimated. The problem will be
much less severe if the plastic zone in the sub-model is completely embedded inside the
elastic material.
Similar problems can occur with mesh refinement. If a coarse mesh model is used to define
displacement boundary conditions for a fine mesh sub-model, the coarse mesh will be too
stiff, and stresses in the fine mesh sub-model will be underestimated.
BÊ3026 Combination of analysis methods
As a general rule, for reasons discussed above, the same analysis method (elastic or inelastic)
must be used for all parts of a component. A method other than that used for the entire
apparatus may be used locally provided the results of the two analysis methods are shown to
be consistent (with regard to both stresses and displacements) at the boundaries of the parts
examined.
B3030 Applicable rules - Flow of analysis
This section provides guidelines for on the procedure for conducting analyses required for
satisfying the design rules of SDC-IC.
B3031 Master flow charts for satisfying design rules
The flow chart for satisfying the design rules of SDC-IC is given in Figure IC 3030-1. Three
different event classes are considered in the flow chart. Definitions of these event classes are
given in IC 2220.
The flow chart for satisfying the low temperature design rules for a given operating
conditions is given in Figure IC3030-2. In order to use this flow chart, the negligible thermal
creep test of IC 3050 must first be satisfied. An additional flow chart for satisfying high
temperature design rules, when the test IC 3050 is not satisfied, will be provided in the future.
A more detailed flow chart for satisfying the limits for a given Criteria Level and for a given
damage mode, using various analysis options, is given in Figure B 3030-1.
In general, the degree of adherence to the flowchart procedures and the level of sophistication
of analysis are expected to vary with the design phase, being lesser in the conceptual design
phase and greater in the final design phase.
SDC-IC, Appendix B. Guidelines for Analysis page 35

ITER G 74 MA 8 01-05-28 W0.2
Start
Conduct Elastic-
Irradiation Creep
Analysis
(B 3024.1.1)
no
Select Damage Mode
Select Criteria Level
Check if finite
deformation
analysis necessary
(B 3021)
Is swelling negligible?
(B 3022)
yes
Is Irradiation-Creep
negligible?
(B 3101)
Conduct Elastic
Stress Analysis
(B 3023)
Elastic Analysis
Limits satisfied?
Criteria Satisfied
Stop
yes
yes
no
no
Include swelling stress
in analysis
(B 3024.1.1.1)
optional
Is Irradiation-Creep
negligible?
(B 3101)
Conduct Elasto-
Plastic Analysis
(B 3024.2)
Elasto-Plastic
Analysis Limits
Satisfied?
no
Criteria not satisfied
Redesign
Conduct Elasto-
Visco-Plastic
Analysis
(B 3024.5)
Figure BÊ3030-1 Analysis flow chart for satisfying the limits of a given
Criteria Level and damage mode at low temperatures
B 3040 Rules for the prevention of excessive deformation affecting
functional adequacy
yes
BÊ3050 Negligible thermal creep test
For a component or a part of a component, thermal creep is negligible over the total operating
period if the condition of the test performed using the following procedure is satisfied.
SDC-IC, Appendix B. Guidelines for Analysis page 36
yes
no

ITER G 74 MA 8 01-05-28 W0.2
1) The total operating period of the component, throughout the life of the component
is taken into account.
2) The total operating period is divided into N time intervals. For each interval i, of a
duration ti, the maximum temperature reached is denoted Ti,
3) To take full advantage of this rule, the intervals of time should be chosen in such a
way that the temperature changes as little as possible throughout each interval.
4) The time tci required for the material at a temperature Ti and at a stress 1.5 Sm(Ti,
0) to accumulate a thermal creep strain of 0.05% is obtained from the curves in
A.MAT.4.1 of Appendix A (Negligible thermal creep curve).
5) The effect of creep is negligible if the sum of the N ratios of duration ti to the
maximum time tci is less than 1:
N
å 1
i =
( ti/ tc)
£ 1
B 3100 LOW TEMPERATURE RULES
i
The low-temperature rules are applicable if the negligible thermal creep test B 3050 is
satisfied.
B 3101 Negligible irradiation-induced creep test
At low temperatures where thermal creep is negligible (B 3050), significant time (or neutron
fluence) dependent strain may still occur due to irradiation-induced creep. These strains may
relax thermal stresses and alter the stress-strain distribution in the component. However, if
the fluence at end-of-life is sufficiently low, the effects of irradiation-induced creep can be
ignored in the analysis. For a component or a part of a component, irradiation-induced creep
effects can be neglected over the total operating period if the condition of the test performed
using the following procedure is met.
1) The total operating period of the component throughout its life and for all loadings
including temperature and flux for which compliance with levels A and C criteria
is required, are taken into account.
2) The total operating period is divided into N time intervals. For each interval i, of a
duration ti, the maximum thickness-averaged temperature reached Tmi, the mean
neutron flux Fmi, the mean neutron fluence Ftmi and the corresponding value of
1.5Smi(Tmi, Ftmi) are noted.
3) To take full advantage of this rule, the time intervals must be chosen in such a
way that the temperature and the neutron flux change as little as possible
throughout the interval.
4) For each interval i, determine the neutron fluence Ftc2i necessary to accumulate
an effective in-reactor creep strain of 0.05% at an effective stress of 1.5Smi(Tmi,
SDC-IC, Appendix B. Guidelines for Analysis page 37

ITER G 74 MA 8 01-05-28 W0.2
Ftmi), a temperature of Tmi and a neutron flux of Fmi, from A.MAT.4.3 of
appendix A.
5) Compute the following sum of the time ratios for all N-intervals.
N
tmi
S = å t
f
f 2
i = 1
c i
6) If the above sum, S, is less than 1, then the effects of irradiation-induced creep
can be neglected and time- (or rate-) dependent stress analysis is not needed.
Otherwise, time (or rate) effects should be included using either elasticirradiation-induced-creep
analysis (B 3024.1.1) or, if plasticity effects are to be
considered at the same time, detailed elasto-visco-plastic analysis (B 3024.4).
Note: The above rule should be used with caution for determining whether irradiation
induced creep can relax bolt preloads significantly. For example, 0.05% creep strain
can cause a bolt stress relaxation of ~ 100 MPa in a material with Young's modulus
200 GPa.
B 3200 RULES FOR THE PREVENTION OF M TYPE DAMAGE
B 3211 Immediate plastic collapse and plastic instability
B 3211.1 Elastic analysis (Immediate plastic collapse and plastic
instability)
Eqs (1), (2), and (3) of IC 3211.1 are intended to guard against immediate plastic collapse by
general primary membrane (IC 2522) plus bending (IC 2523) stresses and by local primary
membrane stress (IC 2524), respectively. Note that the allowable stress Sm (IC 2723) has to
be evaluated at thickness-averaged temperature and neutron fluence and obtained from
Appendix A.
B 3211.1.1 Bending shape factor
The effective bending shape factor, Keff in Eq. 2 of ICÊ3211.1, depends on several variables,
including the amount of work-hardening in the material, the strain to failure, the definition of
Sm, and the safety factor that is desired. A detailed discussion of these variables is given in
Appendix C, section C 3211.1.1. The conclusion of this discussion is that for a material with
ample ductility, as is normally the case with unirradiated structural materials, then Keff is
given by
Keff = K (2a)
where K is the ratio of the maximum bending moment achievable, assuming rigid-perfectlyplastic
material, to the bending moment at initial yield, assuming linear elastic material with
the same yield stress. Values of K for simple section geometries are given in Figures IC
3211-1, -2, and -3.
SDC-IC, Appendix B. Guidelines for Analysis page 38

ITER G 74 MA 8 01-05-28 W0.2
For a material with reduced ductility, such as irradiated material, then Keff may be
approximated as
( )
( ) -
K = 1 + 2 K -1
K 1
eff eff × rect
where
SDC-IC, Appendix B. Guidelines for Analysis page 39
(2b)
K is the rigid-perfectly-plastic bending shape factor for the section
under consideration and
KeffÊrect is the effective bending shape factor for a rectangular cross section,
tabulated as a function of neutron fluence and temperature for each
material in A.MAT.5.2 of Appendix A. The equations used to
derive the tabulated values are given in Appendix C, section C
3211.1.1.
For a cross-section consisting of two plates separated by a distance comparable to the plate
thicknesses, as in the ITER first wall, the K-value can be obtained from Figure IC 3211-3.
For a cross section consisting of two thin skins separated by large distance, as in the ITER
vacuum vessel or cryostat, the theoretical value of K is 1.0, and Keff = 1.0 regardless of the
material properties. Thus, treating such a structure as a composite shape in bending is
equivalent to treating each skin independently as a membrane. However, if there are local
bending effects in a skin, such as might be caused by pressure loading inside the
corrugations, then separate analysis of the individual skin is required. In this case, each
separate skin then becomes a plate with rectangular cross section and K = 1.5. This
illustrates the point that the value of K depends on how the structure is idealized. In general,
the shape used for K must be consistent with the cross section upon which the stresses are
integrated to obtain the bending moment (or stress).
B 3211.2 Elasto-plastic analysis (Immediate plastic collapse)
If irradiation-induced swelling is not negligible (B 3022), then swelling together with
irradiation-induced creep have to be included in the stress analysis using either the simplified
inelastic method (B 3024.1.1.1 and B 3024.2) or elasto-visco-plastic analysis (B 3024.4).
However, the rules of IC 3211.2 should be applied using only the plastic strains, excluding
the irradiation-induced creep strain components, which are commonly held to be nondamaging.
B 3212 Immediate plastic flow localization
B 3212.1 Elastic analysis (Immediate plastic flow localization)
Values of Se as calculated by Eq. (1) are tabulated in Table A.MAT.5.3 of appendix A. Eq.
(1) of IC 3212.1 is intended to guard against plastic instability (necking) and plastic flow
localization due to a high primary plus secondary membrane loading. A conservative way of
satisfying this requirement might be to consider all membrane stresses, whatever the source
(i.e., primary or secondary), as primary. In that case, Eqs.(1), Eq. (2), Eq.(3), or Eq. (4) of IC
3211.1 becomes controlling and Eq. (1) of IC 3212.1 becomes redundant. However, if the
secondary stress is not expected to have a large elastic follow-up, then Eq.(1) may be used

ITER G 74 MA 8 01-05-28 W0.2
with an elastic follow-up factor r as defined in IC 2724. Note that when the uniform
elongation of the material drops below 2%, r1 is set equal to infinity, which effectively
implies that the secondary stresses are considered as primary.
If swelling is not negligible (B 3022), then swelling-induced stresses (B 3024.1.1.1) have to
be included with the secondary stresses.
In determining the allowable stress Se, both Su,min and eu have to be evaluated at the same
thickness-averaged fluence and temperature.
In general, this rule does not become controlling until the material has lost significant
uniform elongation due to irradiation. Up until then, this rule need not be satisfied, as
indicated by the entry "no limit" in Table A.MAT.5.3.
Note: The value of r1 for Eq. (1) has been chosen conservatively to be equal to 4 (IC 2724).
In some cases r1 may be shown to be much less than 4. The designer may choose to reduce
the conservativeness by using a smaller value of r1 if it can be justified using the procedure
given in B 3024.2.
B 3212.2 Elasto-plastic analysis (Immediate plastic flow localization)
If irradiation-induced swelling is not negligible (B 3022), then swelling together with
irradiation-induced creep have to be included in the stress analysis using either the simplified
inelastic method (B 3024.1.1.1 and B 3024.2) or elasto-visco-plastic analysis (B 3024.4).
However, the strain limits of IC 3212.2 should be applied to the plastic strain, excluding the
irradiation-induced creep strain components.
B 3213 Immediate local fracture due to exhaustion of ductility
B 3213.1 Elastic analysis (Immediate local fracture due to exhaustion
of ductility)
Equation (1) of IC 3213.1 has been provided to guard against cracking in regions of stress
concentration including peak stress effects while Eq. (2) is for guarding against cracking
excluding peak stress effects, e.g., cracking of extreme fibers in bending due to exhaustion of
ductility by irradiation. The allowable stresses Sd (T, ft, r2) and Sd (T, ft, r3) for the two
cases are given in A.MAT.5.4 of appendix A. The value of the elastic follow-up factor r2 has
been set on the basis of analysis of notched tensile tests (Appendix C 3024.1.4) and on the
assumption that KT = 4. The value of r3 has been chosen conservatively on the basis of
analysis of three-point bend tests (Appendix C 3024.1.4). As before, the designer may
choose to reduce the conservativeness by using a smaller value of r2 or r3 if it can be justified
using the procedure given in B 3024.2.
If swelling is not negligible (B 3022), then swelling-induced stresses (B 3024.1.1.1) have to
be included with the secondary stresses.
Note 1: For materials like 316L(N) stainless steel, the true strain at rupture remains high at
temperatures £ 400¡C and does not reduce significantly up to a fluence of 10 dpa. For these
materials, the PL+Pb+Q+F limit need not be checked because, cracking at notch roots due to
SDC-IC, Appendix B. Guidelines for Analysis page 40

ITER G 74 MA 8 01-05-28 W0.2
exhaustion of ductility is not a problem (the elastic follow up factor r2 remains bounded by
the stress concentration factor, irrespective of strain hardening capability).
Note 2: For materials that suffer severe loss of strain hardening capability (i.e., uniform
elongation) due to irradiation, the elastic follow up factor r3 can become very large in areas of
high elastic follow up and the Sd limit for PL+Pb+Q has to be checked. However, this rule
does not become controlling until the material has lost significant strain hardening capability
due to irradiation. Until then, this rule need not be checked, as indicated by the entry "no
limit" in Table A.MAT.5.4.
B 3213.2 Elasto-plastic analysis (Immediate local fracture due to
exhaustion of ductility)
If irradiation-induced swelling is not negligible (B 3022), then swelling together with
irradiation-induced creep have to be included in the stress analysis using either the simplified
inelastic method (B 3024.1.1.1 and B 3024.2) or elasto-visco-plastic analysis (B 3024.4).
However, the strain limit of IC 3213.2 should be applied only to the plastic strain, excluding
the irradiation-induced creep strain.
BÊ3214 Fast fracture
B 3214.1 Elastic analysis (Fast fracture)
For the elastic analysis rules to be strictly applicable, stresses everywhere have to remain
below yield. However, some local yielding may be permitted at the crack tip provided the
yielded zone is small compared to the crack length and the remaining ligament thickness.
Yielding is also permitted if the evaluation is carried out for a section sufficiently away from
the yielded region. In all cases, a mode I stress intensity factor KI has to be calculated for a
postulated surface crack of depth ao and minimum length 10ao subjected to the indicated
loading. The value of ao is given by
ao = Max[4au , h/4]
where au = largest undetectable crack by the NDE technique to be used
and h = thickness of section
For the global fast fracture case, the postulated crack should be oriented normal to the
maximum tensile component of the membrane stress due to all primary (PL) and primary plus
secondary loadings (PL+QL). The stress intensity factor may be obtained either from a
recognized handbook of stress intensity factors, or elastic finite element analysis.
For the local fast fracture case, the crack should be oriented normal to the maximum tensile
component of the local stress due to all primary and secondary loadings, including peak,
(PL+Pb+Q+F). The stress intensity factor should be calculated either by elastic finite element
analysis using crack tip singular elements or by any other method that can be justified to give
a conservative result.
SDC-IC, Appendix B. Guidelines for Analysis page 41

ITER G 74 MA 8 01-05-28 W0.2
Note: A conservative estimate for KI can be obtained by using the following expression for a
single-edge notched plate subjected to a uniform tensile stress s at infinity
K
I
1. 122
=
æ ao
1 -
ö
è h ø
3/ 2 s p
a
B 3214.2 Elasto-plastic analysis (Fast fracture)
o
If the postulated crack for fast fracture analysis is embedded in a yielded region, linear elastic
fracture mechanics methodology may give highly unconservative results. In such cases,
elasto-plastic fracture mechanics methodology should be used. Any procedure based on
elasto-plastic fracture mechanics (such as section XI of ASME, Appendix A16 of RCC-MR,
R6 rule) may be considered but its application shall be justified. Special attention shall be
given to the effect of thermal loads, complex loading modes, and spreading of plasticity. The
J-integral is an acceptable criterion for such cases. Most commercially available finite
element programs (e.g., ANSYS, ABAQUS, etc.) have the capability to compute the Jintegral
either by a contour integral method or by an energy method.
B 3300 RULES FOR THE PREVENTION OF C TYPE DAMAGE (LEVELS A
AND C)
B 3310 Progressive deformation or ratcheting
B 3311 Elastic analysis (Progressive deformation or ratcheting)
B 3311.1 3Sm rule
The 3Sm limit for the PL+Pb+D(P+Q) stresses ensures that the membrane and bending
stresses will shakedown after the first cycles of loading and unloading, thus ensuring that
there will be no overall (large scale) progressive deformation. Only peak stresses (F), which
are local in nature, may continue to cycle plastically. Peak stresses are considered in the
performance of fatigue evaluation and also for fracture in embrittled materials. Indeed, the
requirement that there be no overall progressive deformation is necessary to ensure that the
fatigue tests, which are conducted without progressive deformation, represent the behaviour
of the structure.
All cyclic stress ranges including the stress range due to disruption-induced electromagnetic
loading have to be added to the secondary stress range (see appendix C 3311.3). For annealed
austenitic stainless steels, if 0.9Sy controls the Sm value, some ratcheting strain may occur
until strain hardening increases the cyclic yield stress sufficiently to achieve shakedown.
B 3311.2 Bree-diagram rule
Since the Bree diagram approach is mathematically equivalent to the Efficiency diagram
approach of RCC-MR (see appendix C 3311), the Bree diagram rule was adopted for the
SDC-IC. However, the expression for the Bree diagram used in the SDC-IC is slightly
SDC-IC, Appendix B. Guidelines for Analysis page 42

ITER G 74 MA 8 01-05-28 W0.2
different from that in the ASME Code, Section III. In the SDC-IC, the normalizing factor for
the stresses is the average of the Sy values at the maximum and the minimum wall-averaged
temperature and neutron fluence during the cycle being evaluated for all values of Sm, In the
ASME Code, it is permissible to use 1.5ÊSm , instead of Sy , whenever it is greater than Sy.
The reason for choosing the Sy value in this way is to minimize the ratcheting strain
accumulated prior to shakedown and to assure that the allowable stresses determined by the
Bree diagram rule fall within (i.e., are conservative with respect to) those determined by the
Efficiency diagram rule of RCC-MR (see Appendix C 3311).
The Bree diagram approach is less conservative than the 3Sm rule. However, since the yield
stress rather than the proportional limit is used in the analysis, a small amount of ratcheting
strain (~ 0.2%) may occur until strain hardening raises the proportional limit to the yield
stress. If this is unacceptable, the 3Sm rule should be used instead.
B 3312 Elasto-plastic analysis (Progressive deformation or
ratcheting)
Rules for preventing progressive deformation based on elastic analysis are contained in
ICÊ3311. They require the partition of stresses into primary and secondary components. In
certain cases, this partition can lead to overly conservative results with regard to the
ratcheting resistance of the component. Elasto-plastic analysis could provide a less
conservative evaluation.
In order to check the limits on these strains, an elasto-plastic analysis, giving either the exact
value or an upper bound to the strains resulting from all the cycles envisaged, should be
carried out. This can be obtained:
- either by a cyclic elasto-plastic calculation until stabilization of stress-strain
response, or
- by extrapolated cyclic elasto-plastic calculation, using a validated method.
If a certain block of cycles (containing one or more types of cycles) is repeated periodically,
the block can be represented by one type of cycle (called the envelope cycle) which
sequentially adds all cycles in the block. (The individual cycles for which the linear stress
does not induce plastic strain may be excluded). The analysis can then be simplified as
follows:
- analyze in detail all the cycles inside one envelope cycle,
- compute a ratcheting strain increment in a single application of the envelope
cycle.
- the usage fraction for each type of envelope cycle is this ratcheting strain
increment multiplied by the number of times the envelope cycle is repeated,
divided by the allowable ductility term.
For the envelope cycle elasto-plastic analysis, and in the absence of explicit instructions, an
initial zero stress and strain condition may be assumed. However, the stress and strain
conditions at the beginning of each cycle contained within the envelope cycle are those
remaining at the end of the calculation of the previous cycle.
The permissible limits for the accumulated membrane and peak strains are given in IC 3312.
SDC-IC, Appendix B. Guidelines for Analysis page 43

ITER G 74 MA 8 01-05-28 W0.2
B 3320 Time-independent fatigue
B 3322 Limits on fatigue damage
B 3322.1 Calculation of the fatigue usage fraction: V( De)
Following the estimation of the "real" strain ranges De (B 3323) of each cycle, the fatigue
usage fraction V ( De)
at the point under consideration is determined in accordance with B
2752, using the fatigue curves in A---- for all loading cycles requiring compliance with levels
A and C criteria.
B 3322.2 Estimation of irradiation effects on fatigue usage fraction
If fatigue curves for irradiated material are not available, the fatigue usage fraction may be
estimated by using an empirical formula for estimating the fatigue curve (described below).
Following is a description of the general procedure for calculating the fatigue usage fraction,
followed by the detail of how the fatigue curve can be estimated.
BÊ3322.2.1 Calculation of fatigue usage fraction - general
- The complete loading history is considered to have N types of cycles.
- For each type of cycle j (j=1 to N), the total operating period is divided into Mj
time intervals, during each of which the temperature and fluence are assumed to
be constant.
- For each time interval k (k= 1 to Mj ), of duration tk, there are nk cycles of type j.
- The total number of cycles of type j during the complete loading history is then
M j
å 1
n = n
j k
k =
- The maximum temperature reached in time interval k (k= 1 to Mj ) is denoted by
Tk and the mean neutron flux is denoted by Fk.
- The maximum values of the temperature and neutron fluence reached during the
period under consideration should generally be used in the following estimation
procedures. However, since the irradiated material may display a ductilityminimum
as a function of temperature, care should be taken to ensure that the
fatigue damage is estimated conservatively.
- To take full advantage of this rule, the intervals of time must be chosen in such a
way that the neutron flux changes as little as possible throughout each interval.
- The cumulative fatigue usage fraction is the sum of the fatigue usage fractions
calculated for all types of strain cycles:
SDC-IC, Appendix B. Guidelines for Analysis page 44

ITER G 74 MA 8 01-05-28 W0.2
V
=
j=
1
é
ê
ê
ë
M
N j
å å
1
k =
n
N
k
( )
j k
ù
ú
ú
û
BÊ3322.2.2 Procedure for estimating the fatigue curve
- For each type of strain cycle j, the design allowable number of cycles ( N j ) k
corresponding to the temperature Tk and neutron fluence conditions of the interval
of time k, and corresponding to a strain range De, can be estimated by the
following general equation:
D F é
ù F é
e BNj AN
ëê k
ëê
e = ( )
b
c
p j
k
ûú + ( )
SDC-IC, Appendix B. Guidelines for Analysis page 45
ù
ûú
where, denoting the unirradiated values by the subscripts u and irradiated
values corresponding to the neutron fluence Ftk , by the subscripts i:
F e = elastic strain-life modification factor (£ 1)
= the ratio between the minimum irradiated ultimate tensile
strength, which is a function of temperature and neutron
fluence and the minimum ultimate tensile strength, which is a
function of temperature and independent of neutron fluence:
=
( S )
( S )
u i
u u
, for an irradiation hardening material,
F p = plastic strain-life modification factor (£ 1)
where
fk
( )
= f k
=
e
e
tru
tri
c
= the ratio between the minimum unirradiated ductility
(etruÊ=Ê etr ( T,0 k )), which is a function of temperature and
independent of fluence and the minimum irradiated ductility
(etriÊ=Ê etr ( Tk, Ftk
)), which is a function of temperature and
fluence,
A and B are the coefficients and b and c are the exponents that fit the design
fatigue curve (A1.5.4) for the unirradiated material, in the form of the
following equation:
b c
De = BN + AN

ITER G 74 MA 8 01-05-28 W0.2
A conservative approximation of the fatigue usage fraction can be obtained by
considering Fe = 0 . In that case, the fatigue usage fraction for the type of strain
cycle j is equal to the sum of the fatigue usage fraction for each interval k, which
is the ratio of the number of strain cycles nk to the maximum allowable number
( N j ) for this type of cycle, determined from the unirradiated fatigue curves,
k
multiplied by the correction factor f k:
N é M j
V = å êå
f
j=
1 ê
ëk
= 1
k
n
N
k
( )
j k
B 3323. Calculation of equivalent strain range De
ù
ú
ú
û
B 3323.1 Elastic analysis (Time-independent fatigue)
When elastic analysis is used to calculate the response of a structure, the range of strains
obtained does not account for plastic strains which would occur if the real behavior of the
material were taken into consideration . The method outlined below is aimed at providing an
estimate of the "real" strain range De on the basis of the results of the elastic analysis. This is
achieved by evaluating the amplification of the strain, and the resulting strain range, due to
plasticity as well as cyclic hardening or softening of the material as represented by the cyclic
stress-strain curves given in A.5.9.
( ( ) ) at
To apply the rules of this section, the total stress intensity range Dstot = D P + Q + F
the point under consideration and for each of the cycles must be calculated elastically, using
the procedure given in B 2550. This range can be obtained either by a sufficiently detailed
calculation of the region concerned or by using an appropriate stress concentration factor.
The value of the total effective strain range De is the sum of four scalar strains
De , De , De , De
:
1 2 3 4
De = De + De + De + De
1 2 3 4
These four terms are determined using a uniaxial cyclic stress-strain curve (see A.MAT.5.7 in
Appendix A) corresponding to the highest temperature (Tmax) and the lowest neutron fluence
(Ft)min at the point examined during the cycle concerned.
For cyclically hardening materials, the monotonic stress-strain curve is taken as a lower
bound of the cyclic curve.
For irradiation hardening materials, the virgin material cyclic curve is taken as a lower bound
of the irradiated material cyclic curve.
Calculation of De 1:
B 3323.1.1 Elastic strain range
SDC-IC, Appendix B. Guidelines for Analysis page 46

ITER G 74 MA 8 01-05-28 W0.2
D e 1 represents the strain range given by elastic analysis (path a-b in Diagram 1,
FigureÊBÊ3323-1).
Ds tot
Diagram 1
Ds
De 1
a b
Cyclic stress-strain
Curve
Figure B 3323-1: Determination of total strain range for fatigue
using elastic analysis. Step 1 - De1
D e 1 may be calculated on the basis of elastic analysis in accordance with the rules defined in
B 2630, or alternatively, the following formula may be used:
2
De1n Ds
3 1
= +
where
( ) ( tot E)
E = Young's modulus (A.MAT.2.2) at maximum temperature
Tmax and minimum fluence Ê(Ft)min during the cycle,
n = Poisson's ratio (A.MAT.2.3).
B 3323.1.2 Corrections for effects of plasticity
Calculation of De 2 (Cyclic Primary Stress):
De2 represents the plastic strain range due to cyclic primary stress (path b-c in Diagram 2,
FigureÊBÊ3323-2).
SDC-IC, Appendix B. Guidelines for Analysis page 47
De

ITER G 74 MA 8 01-05-28 W0.2
Diagram 2
Ds tot
D[P m +0.67(P b +P L -P m )]
Ds
a b
SDC-IC, Appendix B. Guidelines for Analysis page 48
De 2
Figure B 3323-2: Determination of total strain range for fatigue
using elastic analysis. Step 2 - De2
It can be determined using the following procedure:
- using the procedure outlined in BÊ2550, calculate the effective range of primary
stress,
[ ( ) ]
DP = D P + 067 . P + P - P
eff m b L m
- calculate a plastic strain range De2 corresponding to the effective range of
primary stress as follows:
· using the cyclic stress strain curves given in A.MAT.5.7, calculate the
total cyclic strain range Decyclic corresponding to the effective range
of primary stress D Peff .,
· calculate the plastic part of the total cyclic strain range as
De2 = D e
- DP
E
cyclic eff
The value of De2 is generally very low, but can nonetheless be important when an
appreciable elastic follow-up exists.
Calculation of De3:
D e 3 represents the "plastic" increase in strains along path c-d in Diagram 3, Figure BÊ3223-3.
c
De

ITER G 74 MA 8 01-05-28 W0.2
Diagram 3
Ds tot
Ds
a b
c
SDC-IC, Appendix B. Guidelines for Analysis page 49
d
De 3
Ds De = const
Figure B 3323-3: Determination of total strain range for fatigue
using elastic analysis. Step 3 - De3
Point (d) is the intersection point of the cyclic curve and the hyperbola D s . D e = constant
passing through point (c) with coordinates:
{ De1 + De2 ; Dstot
}
D e 3 has been derived from the above hyperbola such that
( )
( ) +
De = K -1De
De
3 e 1 2
The value of K e has been tabulated in appendix A as a function of Ds tot
Calculation of De4:
De4 represents the "plastic" increase in strain due to triaxiality. De4 is defined by the
following equation:
( )
De = K -1De
4 n 1
The value of the amplification coefficient Kn is evaluated, as shown in Diagram 4,
FigureÊBÊ3323-4, using the curves and tables in A.MAT.5.7 for temperature Tmax.
De

ITER G 74 MA 8 01-05-28 W0.2
Note 1:
Kn
Kn
1
Diagram 4
Dstot
Max (T, ft)
Figure B 3323-4: Determination of the Poisson's ratio factor Kn
for fatigue using elastic analysis
This method is strictly applicable in the case of an equi-biaxial stress field, such as the
skin effect during thermal shock. In other cases, the evaluation of De4 given above is
overly conservative . It may therefore be reduced by multiplying the value of Kn given in
Appendix A by the following coefficient:
Note 2 :
1 + 3 d 2 m 2
( ) 1 + 3 d 2 m 2
( )
where:
d
m
=
=
1 +
1 -
1 -
1 +
n
n
n
n
m = m K n
s - s
.
s + s
D D
D D
1 2
1 2
Ds1 = stress range calculated elastically in a principal direction.
Ds2 = stress range calculated elastically in the other principal
direction.
n = Poisson's ratio.
The initial slope of Diagrams 1 to 3 above must in reality be equal to 3 E/[2 (1 + n)]. In
fact, this is not the case with the curves given in Appendix A1, which are obtained from
uniaxial tests. In practice, this difference is negligible for the constructions shown in
diagrams 2 and 3.
SDC-IC, Appendix B. Guidelines for Analysis page 50
Ds

ITER G 74 MA 8 01-05-28 W0.2
B 3323.1.3 Combining Components
Adding the four strain components,
De = De + De + De + De
1 2 3 4
( ) +
( ) + -
( )
De = De + De + K -1
De De K 1 De
1 2 e 1 2 n 1
( ) +
De £ 1 + K - 1 + K -1
De De
e n
( 1 2)
= ( Ke + Kn
-1)
( De1 + De2)
The amplification coefficients Ke( Dstot, T, Ft)
and KnDstot, T, Ft
Appendix A.
( ) are tabulated in
SDC-IC, Appendix B. Guidelines for Analysis page 51

ITER G 74 MA 8 01-05-28 W0.2
B 3400 RULES FOR THE PREVENTION OF BUCKLING
The structures considered in this Section are thin shells, i.e., structures which can be
represented by a mean surface and a thickness.
The procedure given here for instability stress analysis for load-controlled buckling is based
on that in RCC-MR. Other methods may be used if they can be justified. RCC-MR does not
require instability analysis for strain-controlled buckling. However, as in ASME Code Case
N47, an instability analysis for strain-controlled buckling is required in the SDC-IC but with
smaller load factors than those for load-controlled buckling.
Note: The guidelines provided in sections B 3410 and B 3420 are applicable to static or
quasi-static buckling without any time or rate-dependent effects. If the loading under
consideration is due to a fast transient, e.g., electromagnetic loading during plasma
disruptions, dynamic effects may have a significant influence on buckling. Guidelines for
treating dynamic buckling and irradiation-induced creep buckling will be provided in the
future.
B 3420 Buckling limits
B 3421 Immediate elasto-plastic instability under monotonic
loading
B 3421.1 Elastic analysis (Immediate elasto-plastic instability )
B 3421.1.1 Load-controlled buckling limits
The method described in this Section is applicable to compute immediate (time-independent)
elasto-plastic instability of thin shells without stiffeners. It requires that an elastic analysis (B
3023) be performed on the nominal or "perfect" geometry of the structure subjected to the
loading in question (without load factors) and the following quantities be determined:
The procedure consists of
P m = primary membrane stress intensity.
PL + Pb
= primary membrane plus bending stress intensity.
1) obtaining the elastic bifurcation stress intensities of the nominal geometry using
standard eigenvalue analysis,
2) determining the instability stress intensities from the bifurcation stress intensities,
using factors that depend on the "imperfection" or deviation of the shell from its
nominal geometry and the yield stress of the material,
3) checking that the margin between the instability stress intensities and the primary
stress intensities equal or exceed the load factors.
1. Bifurcation analysis
SDC-IC, Appendix B. Guidelines for Analysis page 52

ITER G 74 MA 8 01-05-28 W0.2
The elastic bifurcation stress intensities are determined (e.g., by finite-element analysis) by
solving an eigenvalue problem, leading to a minimum positive eigenvalue lc which is the
multiplier by which the primary stress components need be multiplied to achieve bifurcation.
If the eigenvalue analysis yields a negative value of lc, instability cannot occur and further
instability analysis should be discontinued. Otherwise, the following bifircation stress
intensities are established:
2. Instability stress intensities
Critical membrane stress intensity
( Pm) c
= lc1 Pm
(1)
Critical membrane plus bending stress intensity
( L b ) =
c c ( L + b )
P + P l 2 P P
(2)
To determine the instability stress intensities, first the geometrical imperfection of the shell
has to be characterized from the tolerances given on the drawings in the Component Data
File.
This imperfection may be defined as being the largest distance separating the two mean
surfaces corresponding to the nominal geometry and a possible true geometry defined using
the tolerances. This distance (d) may be evaluated on the segment perpendicular to the
nominal geometry (Figure B 3421-1).
d
M' M
M = Nominal geometry
M' = Possible true geometry based on tolerances
MM' is perpendicular to the mean surface of the nominal geometry
d = Max (MM')
Figure B 3421-1: Distance ÒdÓ of imperfection in geometry
To simplify the analysis, it is possible to consider only a fraction of the previous value if it
can be shown that the neglected fraction of the tolerance has no effect on instability. Thus,
for a tube subjected to external pressure, only the ovalization tolerance is to be considered for
defining the imperfection, ignoring the tolerance on the mean diameter.
SDC-IC, Appendix B. Guidelines for Analysis page 53

ITER G 74 MA 8 01-05-28 W0.2
The deviation index is defined in terms of the distance d and the shell thickness h by
d = d/h
The reduction factors to be applied to the bifurcation stress intensities to account for the
effects of deviation index and plasticity on the instability stress intensities are determined
from buckling diagrams (see Figures B 3421.1.2-1a, -1b, -2a, and -2b in the following
section) which depend on
- whether the post-buckling behaviour of the structure is stable or unstable
- material
- temperature
To use the buckling diagrams, values of the following parameters are needed:
- the deviation index d,
( )
- x = ( P ) S or x = P + P S
m m c y L+ b L b c y
Straight lines Qm (or QL+b) with slopes xm (or xL+b) are drawn through the origin of a
buckling diagram, and their intersections with the curves D defined by d = constant are noted,
as shown in Figure B 3421-2 below.
Figure B 3421-2: Use of buckling diagrams
The intersections have coordinate values given by
and
( )
X = ( s ) ( P ) or X = ( s ) P + P (3)
m m I m c L+ b L+ b I L b c
SDC-IC, Appendix B. Guidelines for Analysis page 54

ITER G 74 MA 8 01-05-28 W0.2
Y s S or Y s S
(4)
= ( ) = ( )
m m I y L+ b L+ b I y
From Eqs. 1-4, the values of the instability membrane ( sm ) and membrane plus bending
I
( ) stress intensities and their corresponding load factors can be evaluated as follows:
sL+ b I
and
Load factors
( l ) =
m I
( )
s
P
m I
m
( s + )
( lL+
b) =
I P + P
L b I
L b
The final step in the buckling analysis consists of verifying that the buckling load factors are
equal to or greater than the design load factors (GL) as follows:
and
GL £ ( l m) (5)
I
GL L+ b I
£ ( )
l (6)
The design load factors (GL) for the various service levels are tabulated in Table IC 3421-1.
B 3421.1.2 Buckling diagrams
The buckling diagrams for unstable post-buckling behaviour are given in Figures B 3421-3a
and -3b, below. The buckling diagrams for stable post-buckling behaviour are given in
Figures B 3421-4a and -4b. The figures labeled "a" are the complete diagrams. The figures
labeled "b" provide more detail near the origin. These figures are applicable for annealed
unirradiated type 316 stainless steel between 20 - 700¡C. Note that before deciding on which
figure to use, the designer has to make a determination as to whether the post-buckling
equilibrium is stable or unstable. For example, the post-buckling behaviour is unstable for
circular cylindrical shells under axial compression or semi-spherical shell under external
pressure. On the other hand, post-buckling behaviour is stable for circular cylindrical shells
under external pressure or flat plate under in-plane compressive loading. If a determination
cannot be made, to be conservative, the buckling curves for unstable post-buckling behaviour
should be used.
SDC-IC, Appendix B. Guidelines for Analysis page 55

ITER G 74 MA 8 01-05-28 W0.2
Figure B 3421-3a: Unstable post-buckling behaviour diagram
SDC-IC, Appendix B. Guidelines for Analysis page 56

ITER G 74 MA 8 01-05-28 W0.2
Figure B 3421-3b: Unstable post-buckling behaviour diagram, details
SDC-IC, Appendix B. Guidelines for Analysis page 57

ITER G 74 MA 8 01-05-28 W0.2
Figure B 3421-4a: Stable post-buckling behaviour diagram
SDC-IC, Appendix B. Guidelines for Analysis page 58

ITER G 74 MA 8 01-05-28 W0.2
Figure B 3421-4b: Stable post-buckling behaviour diagram, details
SDC-IC, Appendix B. Guidelines for Analysis page 59

ITER G 74 MA 8 01-05-28 W0.2
B 3421.1.2 Strain-controlled buckling limits
Even though it is self-limiting, strain-controlled buckling must be avoided to guard against
failure by fatigue, excessive strain (ratcheting), and interaction with load-controlled
instability. For purely strain-controlled buckling, the effects of geometrical imperfections
and tolerances, whether initially present or induced by service, need not be considered in the
calculation of the instability strain. The procedure of B 3421.1.1 can be used to determine
the bifurcation strain and the instability strain after replacing
Pmand P L + Pbby QLand Q L + Qb,
respectively, and the design load factors GL by GS in
Table IC 3422-1
For thermally-induced, strain-controlled buckling, the strain factor is applied to the loads
induced by thermal strains. To determine the buckling (bifurcation) strain, it may be
necessary to artificially induce high strains concurrent with the use of realistic stiffness
properties. The use of an "adjusted" thermal expansion coefficient is one technique for
enhancing the applied strains without affecting the associated stiffness properties. The
plasticity correction for instability stress intensities may be obtained from the curves in the
buckling diagrams (Figs B 3421-3a/4b that correspond to d=0).
Although strain factors for strain-controlled buckling are less than load factors for loadcontrolled
buckling, for conditions where significant elastic follow-up may occur or where
load-controlled and strain-controlled buckling may interact, the load factors applicable to
load-controlled buckling shall be applied.
B 3421.2 Elasto-plastic analysis (Immediate elasto-plastic instability)
If the elastic buckling limits cannot be met, elasto-plastic buckling analysis may be
conducted. By its very nature it is a much more complex set of calculations than elastic
analysis. The basic procedure is as follows.
1) Obtain the elastic bifurcation stress intensities and modes of the nominal geometry
using standard eigenvalue analysis.
2) Determine a modified geometry by incorporating a defect with a shape of the
bifurcation mode corresponding to the lowest bifurcation load and with a
maximum amplitude (Fig. B 3400) that is consistent with the tolerances given in
the Component Data File.
3) If the maximum stress corresponding to the elastic bifurcation loading is in the
plastic range, the modified geometry may have to be constructed using an elastoplastic
bifurcation mode, which should be determined using the following
procedure.
- The pre-buckling equilibrium states of the structure subjected to proportional
loadings (lL) marked by a loading parameter l are calculated. This
calculation, made on the nominal geometry, should take into account the
effects of geometrical non-linearities and plasticity.
SDC-IC, Appendix B. Guidelines for Analysis page 60

ITER G 74 MA 8 01-05-28 W0.2
- For each loading value l, the coefficient k by which the corresponding stress
state should be multiplied, in order to obtain bifurcation, must be calculated.
If the stress state is "plastic", this coefficient should be calculated by replacing
Young's modulus by a modified modulus, at each point which has become
"plastic". It is recommended that the tangent modulus at the point concerned
be adopted as the modified modulus. Other values may also be used provided
that the choice can be justified.
- The elasto-plastic bifurcation load (lcL) is the load at which the multiplication
coefficient k is equal to 1; the deformation pattern (eigenmode) of this mode is
the bifurcation load to be taken into consideration.
- If the lowest elastic bifurcation load (Cbe) is much higher than the elastoplastic
bifurcation load (Cbi), a new "modified" geometry shall be constructed
like the one for the elastic case, but using the elasto-plastic bifurcation mode.
Unless otherwise justified, the elasto-plastic bifurcation mode must be used if
the elastic bifurcation load is 10 times greater than the elasto-plastic
bifurcation load (Cbe > 10 Cbi).
4) Conduct an incremental large-displacement elasto-plastic nonlinear analysis on
the modified geometry using the minimum stress-strain curves of the material and
loads applied proportionally after incorporating the appropriate load and strain
factors.
Instability is deemed to have occurred if the load-displacement curve reaches a maximum or
the maximum displacement exceeds acceptable limit, before the final load is reached.
Note: If finite element analysis is used, the basic approach is to increment the applied loads
until the solution begins to diverge. Care must be taken to use a sufficiently fine load
increment as the load approaches the expected buckling load. If the load increment is too
coarse the buckling load may not be accurate. It is important to keep in mind that an
unconverged solution does not necessarily mean that the load has reached a maximum. It
could also be caused by numerical instability. Tracking the load-displacement history of the
component can be helpful in deciding whether an unconverged load step represents actual
buckling or whether it reflects some other problem.
B 3500 High Temperature Rules
(Will be issued at a later date.)
SDC-IC, Appendix B. Guidelines for Analysis page 61

ITER G 74 MA 8 01-05-28 W0.2
BÊ3800 DESIGN RULES FOR BOLTED JOINTS
BÊ3810 Methods of analysis
BÊ3811 Elastic analysis
Detailed stress analysis of a bolted joint can be quite complex depending on the level of
detail to which the geometry and the loading of the joint is modelled. The complexity arises
from the fact that it is a non-integral connection using initially prestressed bolts which
requires that a discontinuity stress analysis be conducted to satisfy the compatibility of
deformations within the joint. This article provides guidelines for a general procedure for
analyzing a bolted joint. The designer may choose any other procedure that can be shown to
give conservative results.
In order to perform a discontinuity analysis of a bolted joint, the following information must
be available:
(1) the dimensions of the joint (including supports) and bolts,
(2) the material properties such as Young's Moduli, Poisson's ratios, and thermal
expansion coefficients of all components,
(3) mechanical loads, such as pressure, dead weight, bolt loads, and other externally
applied forces and moments on the joint, and
(4) temperature distribution in the component parts.
The discontinuity analysis of a bolted joint can be performed using standard procedures for
analysis of statically indeterminate structures satisfying equilibrium of forces and
compatibility of displacements at each interface. However, for a complex structure with
many bolts, interfaces, and shear keys, such an analysis may sometimes be unwieldy. In such
cases, a practical recourse is to analyze the structure by finite element analysis. Although
many commercial finite element codes provide sophisticated gap elements to simulate
realistic interfaces with friction, such analyses are inherently nonlinear and may be prone to
convergence problems. Since most joints are designed with bolt preloads such that gaps do
not develop at the interfaces due to service loading, simpler finite element models should be
adequate.
Depending on the finite element model of the joint, either beam elements or solid elements
may be used to model the bolts at the minimum bolt diameter or at the root of threads. The
detailed geometry of the threads in either the bolts or the flange need not be included in the
model. Designers should use judgment to set the appropriate boundary conditions at the joint
interfaces as well as the interfaces between the flange and the bolts. In all cases, the normal
displacements at the interfaces should be made continuous and, depending on the condition
of the interfaces, either the tangential displacements should also be made continuous (no
interfacial slippage) or the tangential shear stresses should be set equal to zero (lubricated
interface).
SDC-IC, Appendix B. Guidelines for Analysis page 62

ITER G 74 MA 8 01-05-28 W0.2
The initial stresses due to bolt preload can be obtained by finite element analysis using a
fictitious temperature drop of the bolts to simulate a lack of fit. The validity of the results
should be checked by ensuring that the normal stresses are compressive at each interface.
A major unknown in a bolted joint analysis is the redistribution of the normal pressure and
tangential stress at the joint interfaces due to service loading. As mentioned earlier, most
joints are designed such that gaps do not develop at the interfaces due to service loading.
Thus, as a first step, a global stress analysis of the joint should be conducted under all applied
mechanical and thermal loading (without the bolt pre-loading) and using either the no
slippage interfaces or lubricated interfaces, as discussed earlier. By superposition principle,
the total stresses in the structure are obtained by adding the stresses due to service loading to
those due to bolt preloads. The design bolt preloads should be chosen such that the total
normal stresses remain compressive at all interfaces under all loadings. Satisfying this
condition also ensures that the simplified analysis is valid. If gaps over significant areas of
the interfaces cannot be avoided due to some loadings, nonlinear gap elements may be
considered at the interfaces.
Often the stiffness of the flange is much greater than that of the bolts. In such cases, applied
mechanical loads (such as plasma disruption-induced electromagnetic loads) can be
accommodated in the joint by a reduction of interfacial pressure with relatively little change
in the bolt stress. However, bolt stresses can increase significantly if gaps develop at the
interfaces. On the other hand, bolt stresses can vary significantly with differential thermal
expansion (either due to temperature difference and/or due to difference in thermal expansion
coefficient) between the flange and the bolts even in the absence of gaps. Thus from a
standpoint of fatigue of the bolts in ITER blanket modules, cyclic thermal stresses of the
bolts are likely to be more critical than cyclic stresses due to electromagnetic loading during
plasma disruptions.
In fatigue analysis of the bolts, the range of the maximum concentrated stress at the root of
the threads is needed. This can be obtained by a local detailed elastic finite element analysis
of the bolt (including the threads) using the results from the global analysis to set the
boundary conditions. Alternatively, a fatigue strength reduction factor (Kf) (IC 2753) can be
used to estimate the maximum stress. In both cases, Neuber analysis (B 3024.1.3) can be
used to estimate the influence of plastic flow on the peak stress and strain ranges, as
discussed in IC 3851.2.1. Because of the presence of a high tensile mean stress, which is
known to have an adverse effect on fatigue life, a mean stress correction based on the
Goodman equation has been recommended.
B 3812 Simplified elastic analysis
A bolted connection can be visualized as two springs in parallel, one with stiffness K of the
assembled parts and the other with stiffness KB of the bolts. Expressions for stiffness factors
based on simplified uniaxial analysis of various types of joints are given in Appendix A6 of
RCC-MR. Alternatively, finite element analysis may be used to derive more accurate
stiffness factors for the connection. Finite element analysis will also be needed for
assemblies in which the assembled parts and bolts experience significant bending due to
applied loading.
If bending of the assembled parts and the bolts can be neglected, a uniaxial analysis can be
used. This simplified model may be applicable to a number of bolted assemblies for which
precise calculations are not needed.
SDC-IC, Appendix B. Guidelines for Analysis page 63

ITER G 74 MA 8 01-05-28 W0.2
B 3812.1 Simplified uniaxial analysis
Consider the simplified bolted assembly (with two parts connected by a threaded screw)
shown in Fig. B 3812-1. Although only a single screw connecting two parts are shown, the
following analysis can be extended to joints with n identical screws in parallel connecting J
number of parts in series. The stiffnesses of the individual bolts and the parts are given by
K
B0
EB0AB = , K
L
B
i0
Ei0Ai = , i = 1, 2,..., J
L
i
where EB0, and Ei0 are the moduli of elasticity of the bolt, and part i, respectively at initial
temperature q0. Denoting the initial combined stiffness of the parts by K0,
i= J
1 1
= å K Ki 0 i = 1 0
Denoting the initial elongation of the bolts by uB0, the total initial compression of the parts
by u0, and the initial bolt preload (per bolt) by PB0,
u
u
B0
0
P
=
K
nP
=
K
B0
B0
B0
B0
SDC-IC, Appendix B. Guidelines for Analysis page 64

ITER G 74 MA 8 01-05-28 W0.2
A
A
A
p I
1
B
2
P B
Fig. B 3812-1 Simplified bolted assembly used for uniaxial analysis.
SDC-IC, Appendix B. Guidelines for Analysis page 65
L 1
L 2
B 3812.1.1 Effects of a temperature rise
The free elongations of the bolts and the parts due to temperature rises DTB and
DT, respectively, from the initial temperature T0 are given by
DuB = LBaB DTB
Dui = Li ai DTi
for the bolts and
L B
P B
for the ith part, i = 1, 2, ..., J

ITER G 74 MA 8 01-05-28 W0.2
where aB and ai are the thermal expansion coefficients of the bolts and part
i at temperatures T0+DTB andT0+DTi, respectively.
The change in the bolt preload DPB (per bolt) due to the thermal expansion mismatch is given
by
KK éi=
J
ù
B
DPB= êå
LiaiDTi - LBaBDTBú K + nKBëêi=
1
ûú
where the stiffnesses are evaluated with Young's moduli at the final
temperatures and a positive sign denotes increase in tension and a negative
sign denotes decrease in tension.
If we include the change in the initial preload due to change in Young's moduli at final
temperatures, the final bolt preload (per bolt) is given by
KKB
K + nK
PB = DPB
+ ×
KK K + nK
0 B0
0 B0
B
B 3812.1.2 Effects of an external load applied to the bolted
assembly
If a tensile (or compressive) load N is applied along the symmetry axis of the bolted joint, the
load in the bolts increases (or decreases) by DNB (per bolt) and that in the assembled parts
decreases (or increases) by DN so that
SDC-IC, Appendix B. Guidelines for Analysis page 66
× P
- the total tensile load in each bolt = PB + DNB
- the total compressive load in the parts assembled = nPB - DN
- equilibrium of forces gives N = nDNB + DN
- compatibility of incremental axial deformations of the bolts and parts give
DNBDN =
K K
B
- total axial load in each bolt = P
B
B0
K
K nK N B
+
+
- total compressive load in assembled parts = nP
B
B
K
K nK N
-
+
nK
- to ensure that the assembled parts remain in compression, N < nP
æ
B 1 +
è K
Note: Validity of the above simplified analyses must be checked by ensuring that
(1) the applied mechanical and thermal loads do not cause the joint to become loose, i.e.,
joint contact pressure always remains positive
B
B
ö
ø

ITER G 74 MA 8 01-05-28 W0.2
(2) bending of the assembled parts do not cause a prying action on the bolts which may
lead to bending and increased tensile stress of the bolts. The flange thicknesses, bolt
spacing, distance from free edge and preload should be chosen so that such prying
action is reduced to a minimum.
B 3812.1.3 Effects of an external moment applied to the bolted
assembly
Consider a bolted assembly subjected to a bending moment My as shown in Fig. B 3812-2.
Assume that the section remains flat but rotates by an angle qy and that the interfaces
transmit the moment by a readjustment of the bolt loads and a redistribution of the interfacial
pressures which remain positive at all locations of the interfaces. Also, because of the
rotation of the section, each bolt will be subjected to a bending moment mBy which is applied
to the bolt by a redistribution of the interfacial pressure under the bolt head (or nut). Using a
similar uniaxial model as before, it can be shown that
q y
My
=
K 2 2
nR + K åx + x dA - x nKB + K
A ò
B
i= n
B
i = 1
2
Bi
A
( )
where A is the section area and RB is the rotational stiffness of the bolts. If
the section has a symmetry about the Y axis and the origin of the x axis lies
on it, then x =0, if not, then it is given by
i= n
K
K x
A
x
xdA
B å Bi + ò
i = 1 A
=
.
nK + K
B
In above K 1
= .
i= J
A Li
å E
i = 1
i
SDC-IC, Appendix B. Guidelines for Analysis page 67

ITER G 74 MA 8 01-05-28 W0.2
Y
M
y
x
Bi
ith Bolt
Fig. B 3812-2 Bolted assembly subjected to a bending moment
The changes in the bolt axial load and the maximum reduction in the interfacial pressure are
given by
DP = K q x -x
Dp
Bi B y Bi
( )
Kqy
= - x -x
A
( )
max max
SDC-IC, Appendix B. Guidelines for Analysis page 68
q y
y
Bi
where xmax is the maximum x value for the section.
The bending moment on each bolt is given by
mBy = RBqy,
where RB is the rotational stiffness of the bolt.
For computing RB, the bending of the bolt head (and the washer, if any) can be neglected,
i.e.,
R
B
EBd =
L
p
32
B
4
X

ITER G 74 MA 8 01-05-28 W0.2
where d is the nominal diameter of the bolt.
Similar expressions can be derived for an applied moment Mx about the x axis. To minimize
the stresses due to the applied bending moment, the bolts should be arranged as
symmetrically as possible.
For the above analysis to remain valid, the total interfacial pressure must not be negative
anywhere in the section or under the bolt heads. The minimum total pressure at the interfaces
between the parts assembled is (including the contribution of the applied axial force N)
p
( ) - -
nPB - N
A
Kq
A
( x x)
y
min =
max
Similarly, the minimum total pressure under the bolt head can be estimated by assuming a
linear pressure distribution to give
p
BH
( )
P N
B n m d
min
d d d d
=
4 + 32
2 2 4
p -
p -
( B ) -
1
By B
B 1 4
( )
where dB is the inscribed bolt head diameter and d1 is the diameter of the
hole.
To maintain positive pressures between the parts assembled and between the bolt head and
the part, we must have
pmin > 0
and
p BHmin > 0
BÊ3813 Elasto-plastic analysis
Detailed elasto-plastic analysis of a bolted joint can be highly complex and should be
attempted only if the elastic analysis rules cannot be satisfied. Since the superposition
principle cannot be used in elasto-plastic analysis, stresses due to bolt preloads as well as
service loads have to be determined together using an incremental approach (B 3024).
SDC-IC, Appendix B. Guidelines for Analysis page 69