ISO 27306:2009

INTERNATIONAL ISO
STANDARD 27306
First edition
2009-05-15
Metallic materials — Method of constraint
loss correction of CTOD fracture
toughness for fracture assessment of
steel components
Matériaux métalliques — Méthode de correction de perte de contrainte
du CTOD de la ténacité à la rupture pour l'évaluation de la rupture des
composants en acier
Reference number
©
ISO 2009
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.

©  ISO 2009
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2009 – All rights reserved

Contents Page
Foreword. iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 2
4 Symbols and units. 3
5 Principle. 4
6 Structural components of concern . 5
7 Assessment levels I, II and III . 6
7.1 General. 6
7.2 Level I: Simplified assessment. 6
7.3 Level II: Normal assessment . 7
7.4 Level III: Material specific assessment. 7
8 Equivalent CTOD ratio, β. 7
8.1 General. 7
8.2 Factors influencing the equivalent CTOD ratio, β . 7
8.3 Procedure for calculating the equivalent CTOD ratio, β, at assessment levels I to III . 8
8.3.1 General. 8
8.3.2 Surface crack case (CSCP or ESCP) . 8
8.3.3 Through-thickness crack case (CTCP or ETCP) . 8
Annex A (informative) Procedure for the selection of Weibull parameter m at level II assessment. 18
Annex B (informative) Analytical method for the determination of Weibull parameter m at level III
assessment . 21
Annex C (informative) Guidelines for the equivalent CTOD ratio, β. 26
Annex D (informative) Examples of fracture assessment using the equivalent CTOD ratio, β. 32
Bibliography . 53

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 27306 was prepared by Technical Committee ISO/TC 164, Mechanical testing of metals, Subcommittee
SC 4, Toughness testing — Fracture(F), Pendulum(P), Tear(T).

iv © ISO 2009 – All rights reserved

INTERNATIONAL STANDARD ISO 27306:2009(E)

Metallic materials — Method of constraint loss correction of
CTOD fracture toughness for fracture assessment of steel
components
1 Scope
In fracture assessments of steel structures containing cracks, it has generally been assumed that the fracture
resistance of fracture toughness specimens is equal to the fracture resistance of structural components.
However, such an assumption often leads to excessively conservative fracture assessments. This is due to a
loss of plastic constraint in structural components, which are subjected mainly to tensile loading. By contrast,
fracture toughness specimens hold a constrained stress state near the crack-tip due to bending loading. The
loss of constraint is significant for high strength steels with high yield-to-tensile ratios (= yield stress/tensile
strength) which have been extensively developed and widely applied to structures in recent years.
This International Standard specifies a method for converting the CTOD (Crack-Tip Opening Displacement)
fracture toughness obtained from laboratory specimens to an equivalent CTOD for structural components,
taking constraint loss into account. This method can also apply to fracture toughness assessment using the
stress intensity factor or the J-integral concept (see Clause 8).
This International Standard deals with the unstable fracture that occurs from a crack-like defect or fatigue
crack in ferritic structural steels. Unstable fracture accompanied by a significant amount of ductile crack
extension and ductile fractures is not included in the scope hereof.
The CTOD fracture toughness of structural steels is measured in accordance with any one of the established
test methods, ISO 12135:2002, BS 7448-1:1991 or ASTM E1290-99. The fracture assessment of a cracked
component is done using an established method such as FAD (Failure Assessment Diagram) in the
organization concerned, and reference is not made to the details thereof in this International Standard.
This International Standard can be used for eliminating the excessive conservatism frequently associated with
the conventional fracture mechanics methods and accurately assessing the unstable fracture initiation limit of
structural components from the fracture toughness of the structural steel. This is also used for rationally
determining the fracture toughness of materials to meet the design requirements of deformability of structural
components.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 12135:2002, Metallic materials — Unified method of test for the determination of quasistatic fracture
toughness
BS 7448-1:1991, Fracture mechanics toughness tests — Method for determination of KIc, critical CTOD and
critical J values of metallic materials
1)
ASTM E1290-99 , Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness
measurement
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 12135:2002 and the following apply.
3.1
CTOD of standard fracture toughness specimen
crack-tip opening displacement of standard fracture toughness specimen
δ
CTOD, as the fracture driving force, for the standard fracture toughness specimen (three point bend or
compact specimen) with 0,45 u (a /W) u 0,55, where a and W are the initial crack length and specimen width,
0 0
respectively
3.2
CTOD fracture toughness
crack-tip opening displacement fracture toughness
δ
cr
critical CTOD at the onset of brittle fracture in the standard fracture toughness specimen [δ (B) as defined in
c
ISO 12135:2002] with 0,45 u a /W u 0,55
3.3
CTOD of structural component
crack-tip opening displacement of structural component
δ
WP
CTOD, as the fracture driving force, for a through-thickness crack or a surface crack existing in a structural
component regarded as a wide plate
NOTE The CTOD of a surface crack is defined at the maximum crack depth.
3.4
critical CTOD of structural component
critical crack-tip opening displacement of structural component
δ
WP,cr
critical CTOD at the onset of brittle fracture in structural components
3.5
equivalent CTOD ratio
equivalent crack-tip opening displacement ratio
β
CTOD ratio defined by δ/δ , where δ and δ are CTODs of the standard fracture toughness specimen and
WP WP
the structural component, respectively, at the same level of the Weibull stress, σ
W
See Figure 1.
NOTE See Reference [1].
1) The procedure for calculating CTOD in ASTM E1290-08 is different from the one in ASTM E1290-1999. The new
ASTM E1290 procedure gives a somewhat different CTOD value compared to those calculated by ISO 12135:2002 and
BS 7448-1:1991. This International Standard employs ASTM E1290-99, which specifies the CTOD calculation procedure
similar to ISO 12135:2002 and BS 7448-1:1991.
2 © ISO 2009 – All rights reserved

3.6
Weibull stress
σ
W
fracture driving force defined with the consideration of statistical instability of microcracks in the fracture
process zone against brittle fracture
NOTE See Reference [2].
3.7
critical Weibull stress
σ
W,cr
Weibull stress at the onset of unstable fracture
3.8
Weibull shape parameter
m
material parameter used in the definition of the Weibull stress; one of two parameters describing the statistical
distribution of the critical Weibull stress, σ
W,cr
3.9
yield-to-tensile ratio
R
Y
ratio of yield strength (or 0,2 % proof strength), R , to tensile strength, R
p0,2 m
4 Symbols and units
For the purposes of this document, the following symbols, units and designations are applied in addition to
those in ISO 12135.
Symbol Unit Designation
a mm Depth of surface crack or half length of through-thickness crack in structural component
c mm Half length of surface crack in structural component
m 1 Weibull shape parameter
t mm Plate thickness
V mm Reference volume defined for Weibull stress
V mm Volume of fracture process zone
f
R — Yield-to-tensile ratio (= R /R )
Y p0,2 m
β — Equivalent CTOD ratio
β — Equivalent CTOD ratio for reference crack size
β — Equivalent CTOD ratio for target size of centre surface crack or double-edge surface
2c
crack
β — Equivalent CTOD ratio for target size of centre through-thickness crack or double-edge
2a
through-thickness crack
β — Equivalent CTOD ratio for target size of single-edge surface crack
c
β — Equivalent CTOD ratio for target size of single-edge through-thickness crack
a
Symbol Unit Designation
δ mm CTOD of standard fracture toughness specimen
δ mm Critical CTOD of standard fracture toughness specimen at onset of brittle fracture
cr
(CTOD fracture toughness)
δ mm CTOD at small-scale yielding limit for standard fracture toughness specimen
SSY limit
δ mm CTOD of structural component
WP
δ mm Critical CTOD of structural component at onset of brittle fracture
WP,cr
σ MPa Effective stress used for the calculation of Weibull stress
eff
σ MPa Weibull stress
W
σ MPa Critical Weibull stress at onset of brittle fracture
W,cr
5 Principle
This International Standard deals with the initiation of unstable fracture due to cleavage of structural steels. It
presents a method for converting the CTOD fracture toughness obtained from the standard fracture toughness
specimens [three-point bend or compact specimens with 0,45 u a /W u 0,55 and B (specimen thickness) = t
(plate thickness of structural component)], which are characterized by an extremely severe plastic constraint
in the vicinity of the crack-tip, to an equivalent critical CTOD for structural components, which are generally
characterized by less constraint. The reverse procedure is also possible with this method. Thus, this method
links fracture toughness tests and fracture performance assessments of structural components by taking
account of loss of plastic constraint in structural components, as shown in Figure 2.
NOTE 1 The fracture toughness specimen with a deep crack such as a /W = 0,7 presents a higher constraint near the
crack- tip than that with 0,45 u a /W u 0,55. The equivalent CTOD ratio β defined in this International Standard leads to a
conservative fracture assessment, if the user employs the deep cracked specimen with a /W > 0,55.
NOTE 2 This International Standard does not intend to address size and temperature effects nor the influence of data
[3]
scatter on the results. Refer to ASTM E1921 for guidance.
The CTOD fracture toughness (critical CTOD) of the standard fracture toughness specimen is determined in
accordance with any one of the established test methods, ISO 12135:2002, BS 7448-1:1991 or
ASTM E1290-99. The fracture assessment of a cracked component can be done using established methods
at the user’s discretion such as FAD (Failure Assessment Diagram) and CTOD design curve in the
organization concerned.
The critical CTOD of the standard fracture toughness specimen is converted to the critical CTOD of the
structural component using the equivalent CTOD ratio, β. The equivalent CTOD ratio, β , is defined as a
CTOD ratio, δ/δ , where δ and δ are CTODs of the standard fracture toughness specimen and the
WP WP
structural component, respectively, at the same level of the Weibull stress, σ . The equivalent CTOD ratio, β ,
W
is in the range 1 > β > 0.
The critical CTOD, δ , of the fracture toughness specimen is converted to the critical CTOD, δ , of the
cr WP,cr
structural component using β in the form
δ =δβ/ (1)
WP,cr cr
Furthermore, if the deformability, δ , required for the structural component is given, the material fracture
WP,req
toughness needed to meet the deformability requirement, δ , can be calculated as
req
δβ=⋅δ (2)
req WP, req
4 © ISO 2009 – All rights reserved

Equations (1) and (2) transfer the CTOD fracture toughness to the equivalent CTOD of the structural
component at the same fracture probability. The CTOD fracture toughness to be used for fracture
assessments shall be determined by agreement of the parties concerned, for instance, a minimum of three
test results.
The equivalent CTOD ratio, β, is dependent on the yield-to-tensile ratio, R , of the material, the Weibull shape
Y
parameter m, and the type and size of a crack in the structural component. In addition, β also depends on the
deformation level of the structural component, but its dependence is rather small in the deformation range
beyond small-scale yielding (SSY). The equivalent CTOD ratio, β, in this International Standard is specified in
this large deformation range, and given in nomographs.
The β-nomographs are physically effective in cases where both the standard fracture toughness specimen
and the structural component show unstable fracture. The nomographs are presented in Clause 8, where the
yield-to-tensile ratio, R , and the Weibull shape parameter, m, are in the range 0,6 u R u 0,95 and
Y Y
10 u m u 50 (R and m for structural steels are generally in this range). They are prepared on the conditions
Y
that the thickness, B, of the fracture toughness specimen is equal to the plate thickness, t, of the structural
component, and that there are no significant differences in fracture toughness through the thickness of the
steel being assessed. This procedure may also be applicable in cases where the crack size, yield-to-tensile
ratio, R , etc. of the structural component concerned are not within the range of the nomographs, provided
Y
that, β, is obtained by an appropriate procedure.
Three assessment levels (level I, level II and level III) for β are included in this method, as shown in Figure 3.
The details are described in Clause 7. The assessment level to be applied depends upon the agreement of
the parties concerned.
6 Structural components of concern
The structural components concerned in this International Standard are of the following four types regarded as
wide plates under tensile loading, as shown in Figure 4. The crack in the components should be sufficiently
small in comparison with the component dimensions (length, width) so as to ensure that the plate width effect
on the stress intensity factor is negligibly small.
CSCP (Centre surface crack panel): Wide plate component with a surface crack at the centre of the plate
under tensile loading
ESCP (Edge surface crack panel): Wide plate component with double-edge or single-edge surface crack
at the edge of the plate under tensile loading
CTCP (Centre through-thickness crack panel): Wide plate component with a through-thickness crack at
the centre of the plate under tensile loading
ETCP (Edge through-thickness crack panel): Wide plate component with double-edge or single-edge
through-thickness crack at the edge of the plate under tensile loading
NOTE These represent some important structural configurations. For instance, CSCP represents a shell or pipe
component with a flaw induced by crane scratch. ESCP is related to a beam or box component including a crack
originated from geometrical discontinuity by fatigue or seismic loading. CTCP and ETCP may correspond to an extreme
case of CSCP and ESCP where the surface crack grows in thickness direction to a large extent. Weld cracks such as lack
of fusion, undercut, cold cracking (hydrogen-induced cracking) and slag inclusion, etc. are more likely in weldments. But
this International Standard does not deal with the welded joints, because further investigation is necessary on the effects
of strength mismatch, residual stress and the crack-tip location with respect to welds. Embedded cracks are not
considered in this International Standard on the ground that embedded cracks are less likely in normal structural
components than surface cracks.
The loading condition is assumed to be substantially uniaxial and perpendicular to the crack plane. The
surface crack is assumed to be semi-elliptical, and the half-length, c, of the crack should be larger than the
crack depth, a (shallow surface crack). Surface cracks existing in structural components are not necessarily of
semi-elliptical type, but they should be idealized as semi-elliptical cracks by flaw assessment methods duly
authorized in the organization concerned.
Other components can be assessed if the equivalent CTOD ratio, β, is derived by a suitable method.
7 Assessment levels I, II and III
7.1 General
This International Standard proposes three levels for the assessment of the equivalent CTOD ratio, β.
Applicable assessment levels can be selected by agreement of the parties concerned. The details of the
assessments and required information are summarized in Table 1.
Table 1 — Assessment levels I, II and III of β and required information
Level I
Level II Level III
(Simplified
(Normal assessment) (Material specific assessment)
assessment)
⎯ Yield-to-tensile ratio, R ⎯ Yield-to-tensile ratio, R
Y Y
⎯ Crack type in structural ⎯ Crack type in structural
component component
Information
needed for None ⎯ Crack size (length, depth) ⎯ Crack size (length, depth)
assessment
⎯ Reference m-value (lower-bound ⎯ Stress-strain curve for finite
value) element (FE) analysis
⎯ Statistically determined m-value
0 < β < 1 (in most cases, 0 < β < 0,5) 0 < β (Level III) < β (Level II)
Equivalent
β = 0,5 β = f (R , a, c, m) for CSCP, ESCP β = f (R , a, c, m) for CSCP, ESCP
Y Y
CTOD ratio β
β = f (R , a, m) for CTCP, ETCP β = f (R , a, m) for CTCP, ETCP
Y Y
Constitutive equation and finite
a
For a long crack ,
a
For a long crack and R < 0,8, element size ahead of the crack-tip
Y
level II is
Remarks
level III is recommended. should be well defined in FE-
recommended.
analysis.
CSCP, ESCP: Centre and edge surface crack panels

CTCP, ETCP: Centre and edge through-thickness crack panels
a
Surface crack: 2c > 50 mm; Through-thickness crack: 2a > 25 mm,
2c: Surface crack length; 2a: Through-thickness crack length; m: Weibull shape parameter
Assessment levels I to III are applied in loading conditions beyond small-scale yielding (SSY). The δ
SSY limit
described in Figure 5 is the crack-tip opening displacement, δ , of the standard fracture toughness specimen
corresponding to the SSY limit specified in ISO 12135. When stress fields to build the same level of the
Weibull stress as in the fracture toughness specimen beyond δ are considered in a wide plate
SSY limit
structural component, constraint loss can be significant in the structural component. This International
Standard presents the equivalent CTOD ratio, β, under such loading conditions.
7.2 Level I: Simplified assessment
Level I assessment is applicable to cases where the information necessary for calculating β, such as the
mechanical properties of the structural component being assessed, the type and size of the assumed crack,
etc. is not fully available. At level I assessment, β = 0,5 is used as an upper-bound engineering approximation.
However, for a structural component that potentially includes a long crack (surface crack length 2c > 50 mm or
through-thickness crack length 2a > 25 mm), level II assessment is recommended because β may exceed 0,5
with a small shape parameter, m.
6 © ISO 2009 – All rights reserved

7.3 Level II: Normal assessment
Level II assessment is applicable to cases where the mechanical properties (yield-to-tensile ratio, R ) of the
Y
structural component being assessed and the type and size of the assumed crack are known, but the Weibull
shape parameter, m, is unknown. A lower-bound value for m is assumed for the assessment of β.
At level II, β-values are derived from nomographs as a function of the component crack type and size, material
yield-to-tensile ratio and the parameter m.
The use of a lower-bound m-value may lead to an excessive overestimation of β for cases where the
yield-to-tensile ratio R < 0,8, and the surface crack length 2c > 50 mm or the through-thickness crack length
Y
2a > 25 mm. Level III assessment is recommended in such cases.
7.4 Level III: Material specific assessment
Level III assessment is applicable to cases where the information for the assessment of β is fully known.
At level III, β-values are also derived from nomographs, but with a statistically determined m-value from a
sufficient number of fracture toughness test results.
Generally, the β-value at level III is smaller than that at level II.
8 Equivalent CTOD ratio, β
8.1 General
This clause describes a method for converting the CTOD of a standard fracture toughness specimen to the
[4]
equivalent CTOD of structural components by using the equivalent CTOD ratio, β .
8.2 Factors influencing the equivalent CTOD ratio, β
The equivalent CTOD ratio, β, based on the Weibull stress criterion, depends on the shape parameter, m, of
the material.
In addition, β is also influenced by the following factors, although the strength class and uniform elongation of
[4], [5]
the material have virtually no influence on β :
a) factors mainly controlling plastic constraint in the vicinity of the crack-tip:
⎯ yield-to-tensile ratio, R , of the material;
Y
⎯ crack type (CSCP, ESCP, CTCP, ETCP) and crack size (crack depth of surface crack and crack
length of through-thickness crack);
⎯ plate thickness (in the case of a deep surface crack);
b) factor exerting a volumetric effect:
⎯ length of surface crack.
NOTE The equivalent CTOD ratios, β, for CTCP and ETCP do not depend on the plate thickness, because the plate
thickness plays the same role in the evolution of the Weibull stresses for the CTCP (ETCP) and the fracture toughness
specimen, where the crack is of through-thickness type.
8.3 Procedure for calculating the equivalent CTOD ratio, β, at assessment levels I to III
8.3.1 General
The procedure for calculating the equivalent CTOD ratio, β, at assessment levels I to III is described below.
Equations (3), (4), (6) and (7) are applicable for the following crack sizes:
CSCP: 2c W 16 mm, 1 u a u 6 mm, t W 25 mm
ESCP: 2c W 24 mm, 1 u a u 6 mm, t W 25 mm
CTCP: 5 u 2a u 50 mm
ETCP: 5 u 2a u 30 mm
8.3.2 Surface crack case (CSCP or ESCP)
The procedure for calculating the equivalent CTOD ratio, β, for the surface crack is as follows.
Level I: β = 0,5
Level II: β is calculated, as shown in Figure 6, according to the following steps.
Step 1: Define the crack size (crack length 2c, depth a) and the material yield-to-tensile ratio, R .
Y
Step 2: Set the reference value (lower-bound value) of the shape parameter, m. Annex A can be
referred to when selecting the lower-bound m-value.
Step 3: Determine the equivalent CTOD ratio, β , for a reference crack size from the nomographs
shown in Figures 7 and 8 as a function of the m-value, crack depth, a, and the yield-to-tensile ratio, R .
Y
Step 4: Calculate the equivalent CTOD ratio, β = β , for the target crack length, 2c, using
2c
Equation (3) or Equation (4), depending on the type of crack:
km 2
()
CSCP
ββ==i24ck0 , m (3)
() ()
2c(CSCP) 0(CSCP) CSCP
exp⎡⎤0,1 m − 33 +1
()
⎣⎦
km() 2
ESCP
ββ==i()23ck0 , ()m (4)
2c(ESCP) 0(ESCP) ESCP
exp⎡⎤0,1 m − 40 +1
()
⎣⎦
In the case of single-edge surface crack of length c, the equivalent CTOD ratio, β = β , is given in the form
c
km( ) 2
ESCP
ββ= i()12 (5)
cc(ESCP) 2 (ESCP)
For t W 25 mm and 1 u a u 6 mm, the equivalent CTOD ratio, β, shows virtually no dependence on the
plate thickness, t.
Level III: β is calculated, as shown in Figure 6, with a statistically determined m-value.
8.3.3 Through-thickness crack case (CTCP or ETCP)
The procedure for calculating the equivalent CTOD ratio, β, for the through-thickness crack is as follows.
Level I: β = 0,5
8 © ISO 2009 – All rights reserved

Level II: β is calculated, as shown in Figure 6, according to the following steps.
Step 1: Define the crack length, 2a, and the material yield-to-tensile ratio, R .
Y
Step 2: Set the reference value (lower-bound value) of the shape parameter, m. Annex A can be
referred to when selecting the lower-bound m-value.
Step 3: Determine the equivalent CTOD ratio, β , for a reference crack size from the nomographs
shown in Figures 9 and 10 as a function of the m-value and the yield-to-tensile ratio R .
Y
Step 4: Calculate the equivalent CTOD ratio, β = β , for the target crack length 2a with Equation (6)
2a
or (7), depending on the type of crack:
0,4
ββ= i21a 3,8 (6)
()
2a(CTCP) 0(CTCP)
km, R −+0,57 3,1RR− 1,45
()
ETCP Y YY
ββ==i21ak1 , m,R (7)
() ()
2a(ETCP) 0(ETCP) ETCP Y
⎡⎤
exp −0,35 m−+10 1
()
⎣⎦
In the case of single-edge through-thickness crack of length a, the equivalent CTOD ratio, β = β , is given
a
in the form
ββ= 2 (8)
aa(ETCP) 2 (ETCP)
The equivalent CTOD ratio, β , of through-thickness cracks shows no dependence on the plate thickness.
Level III: β is calculated, as shown in Figure 6, with a statistically determined m-value.
1/2
In the case of the fracture assessment using the stress intensity factor K, β can be used for the constraint
loss correction. For the assessment based on the J-integral, β may be used as it is.
FE analysis of the Weibull stress for the fracture toughness specimen is required for determining the m-value
at level III assessment. A recommended procedure for the analytical determination of the m-value is described
in Annex B.
Annex C describes the guidelines for application of the equivalent CTOD ratio, β, at assessment levels I to III.
In cases where the crack size in structural components, yield-to-tensile ratio, R and the shape parameter, m
Y
of the material being assessed are not in the range of the nomographs in Figures 7 to 10, and are also outside
the applicable range of Equations (3), (4), (6) and (7), an equivalent CTOD ratio, β, obtained by a suitable
method, e.g. FE analysis of the target component, may be used.
Annex D presents examples of fracture assessments of structural components using the equivalent CTOD
[6]
ratio, β. Fracture assessment methods, such as FAD (Failure Assessment Diagram) or CTOD design
[7]
curve , which have been duly authorized in the organization concerned, may be used.
Figure 1 — Definition of the equivalent CTOD ratio, β, based on the Weibull stress fracture criterion

Figure 2 — Method of constraint loss correction to link fracture toughness tests and structural
performance evaluation
10 © ISO 2009 – All rights reserved

Figure 3 — Flow of fracture assessment of structural components from fracture toughness test results,
where three assessment levels of the equivalent CTOD ratio, β , are included for constraint loss
correction
Figure 4 — Standard fracture toughness specimens and wide plate components linked with the
equivalent CTOD ratio, β
12 © ISO 2009 – All rights reserved

Key
X applied stress σ /R
∞ p0,2
Y equivalent CTOD ratio β = δ/δ
WP
a
σ level corresponding to δ for standard fracture toughness specimen.
∞ SSY limit
Figure 5 — Assessment levels I, II and III of β for correcting constraint loss in wide plate components

Figure 6 — Flow chart for calculating the equivalent CTOD ratio, β
a)  CSCP (a = 1 mm; t W 25 mm): β versus m b)  CSCP (a = 1 mm; t W 25 mm): β versus R
0 0 Y
c)  CSCP (a = 3 mm; t W 25 mm): β versus m d)  CSCP (a = 3 mm; t W 25 mm): β versus R
0 0 Y
Figure 7 (continued)
14 © ISO 2009 – All rights reserved

e)  CSCP (a = 6 mm; t W 25 mm): β versus m f)  CSCP (a = 6 mm; t W 25 mm): β versus R
0 0 Y
Key
a crack depth R yield-to-tensile ratio
Y
2c surface crack length t plate thickness
m Weibull shape parameter β equivalent CTOD ratio for reference crack size, equal to δ/δ
0 WP
Figure 7 — Nomographs of equivalent CTOD ratio, β , for centre surface crack panel (CSCP)
a)  ESCP (a = 1 mm; t W 25 mm): β versus m b)  ESCP (a = 1 mm; t W 25 mm): β versus R
0 0 Y
Figure 8 (continued)
c)  ESCP (a = 3 mm; t W 25 mm): β versus m d)  ESCP (a = 3 mm; t W 25 mm): β versus R
0 0 Y
e)  ESCP (a = 6 mm; t W 25 mm): β versus m f)  ESCP (a = 6 mm; t W 25 mm): β versus R
0 0 Y
Key
R yield-to-tensile ratio
Y
a crack depth
t plate thickness
c length of edge surface crack
β equivalent CTOD ratio for reference crack size, defined as δ/δ
m Weibull shape parameter
0 WP
Figure 8 — Nomographs of equivalent CTOD ratio, β , for edge surface crack panel (ESCP)
16 © ISO 2009 – All rights reserved

a)  CTCP (2a = 13,8 mm): β versus m b)  CTCP (2a = 13,8 mm): β versus R
0 0 Y
Key
2a through-thickness crack length R yield-to-tensile ratio
Y
m Weibull shape parameter β equivalent CTOD ratio for reference crack size, defined as δ/δ
0 WP
Figure 9 — Nomographs of equivalent CTOD ratio, β , for centre
through-thickness crack panel (CTCP)
a)  ETCP (2a = 11 mm): β versus m b)  ETCP (2a = 11 mm):β versus R
0 0 Y
Key
a length of edge through-thickness crack R yield-to-tensile ratio
Y
m Weibull shape parameter β equivalent CTOD ratio for reference crack size, defined as δ/δ
0 WP
Figure 10 — Nomographs of equivalent CTOD ratio, β , for edge through-thickness crack panel (ETCP)
Annex A
(informative)
Procedure for the selection of Weibull parameter m at level II assessment
A.1 General
The procedure for the selection of the Weibull shape parameter m at level II assessment is described. The
shape parameter m is selected in the light of the average CTOD fracture toughness at the assessment
temperature.
A.2 Determination of average CTOD fracture toughness
In selecting the shape parameter m, the average (arithmetic mean) value of the CTOD fracture toughness
δ at the assessment temperature obtained with 25 mm thick test specimens shall be used.
cr,ave
In cases where no test data with 25 mm thick test specimens are available, the CTOD fracture toughness for a
[3], [8]
δ , which is calculated using Equations (A.1) and (A.2) , may be used.
25 mm thick specimen
cr,ave-25
1/ 4
⎧⎫
B
⎪⎪⎛⎞
δδ=+δ −δ ⋅ (A.1)
cr,ave-25⎨⎬min()cr,ave-B min
⎜⎟
⎝⎠
⎪⎪
⎩⎭
500⋅−1 ν
()
δ=⋅ K (A.2)
min min
RE⋅
p0,2
where
B is the test specimen thickness (mm);
δ is the average CTOD fracture toughness with test specimen thickness B (mm);
cr,ave-B
R is the yield strength (MPa);
p0,2
ν is Poisson’s ratio;
K is equal to 20 (MPa m ).
min
Note that Equations (A.1) and (A.2) are valid for the CTOD fracture toughness at brittle fracture initiation
without a significant amount of stable crack extension.
18 © ISO 2009 – All rights reserved

A.3 Determination of Weibull shape parameter m
A.3.1 Assessment of brittle fracture initiation of steel structure components from fracture
toughness of structural steel
In cases where the brittle fracture limit of steel components is to be assessed based on the fracture toughness
of the structural steel, the shape parameter m is selected as shown in Equation (A.3) depending on the
average CTOD fracture toughness, δ .
cr,ave-25
m = 10  for δ u 0,05 (mm) ⎫
cr,ave-25
(A.3)
⎬
m = 20  for δ > 0,05 (mm)
cr,ave-25
⎭
In Equation (A.3), the shape parameter m is selected provisionally as the lower-bound value of m so as to lead
to a conservative failure assessment in the light of a diagram for m and δ (Figure A.1) based on data
cr,ave −25
from Reference [1] and References [9] to [19].

Key
1 mild steel (R < 295 MPa)
p0,2
2 HT500 class (295 MPa u R < 440 MPa)
p0,2
3 HT600 class (440 MPa u R < 685 MPa)
p0,2
4 HT800 class (685 MPa u R < 885 MPa)
p0,2
m Weibull shape parameter
δ CTOD fracture toughness for a 25 mm thick specimen, expressed in millimetres
cr,ave-25
Figure A.1 — Relationship between Weibull parameter, m, and
average CTOD fracture toughness, δ
cr,ave-25
A.3.2 Determination of fracture toughness needed to meet design requirement of
deformability of structural components
In cases where the fracture toughness needed to meet the design requirement of deformability of structural
components is to be determined, the use of the lower-bound value in Equation (A.4) is recommended for
estimation of the required fracture toughness.
m = 10 (A.4)
In cases where the level of CTOD fracture toughness of the material can be estimated from the Charpy impact
test results or other properties, m may be selected as shown in Equation (A.3).
For additional information on the relationship between the Weibull parameter and the fracture toughness of
structural steels, see Reference [20].
20 © ISO 2009 – All rights reserved

Annex B
(informative)
Analytical method for the determination of Weibull parameter m at
level III assessment
B.1 General
This annex describes the analytical procedure for the determination of the Weibull shape parameter m that is
[9]
needed at level III failure assessment. A common procedure is shown in Figure B.1, and the recommended
methods in the Steps 1 to 3 are described in the following.
B.2 Fracture toughness test (Step 1)
Fracture toughness tests shall be performed using the three-point bend test specimen or the compact
specimen in accordance with ISO 12135. However, the initial crack length of the test specimen shall be within
the range of 0,45 u (a /W) u 0,55. The toughness tests (Table B.1) shall be performed with an adequate
number of specimens to determine the parameter m, and statistical data of the critical CTOD shall be obtained.
After testing, the fracture surface shall be observed, and the fact that brittle fracture occurred without stable
crack extension larger than 0,2 mm shall be confirmed.
[21], [22]
NOTE 1 In R/H/R6 Revision 3 – Appendix 17, a minimum number of 30 tests is recommended .
NOTE 2 The fracture toughness specimen with a deep crack such as a /W = 0,7 presents a higher constraint near the
crack-tip than that with 0,45 u a /W u 0,55. The equivalent CTOD ratio, β, defined in this International Standard leads to a
[23]
conservative fracture assessment, if the user employs the deep cracked specimen with a /W > 0,55 .
NOTE 3 One set of fracture toughness data obtained by the above specimen may give a non-unique m-value, if the
stress field near the crack-tip shows the singularity controlled by K or by the HRR (Hutchinson, Rice and Rosengren) field
within the range of the fracture toughness level measured. This non-uniqueness is related to the statistical characteristics
of toughness values, which follow a two-parameter Weibull distribution with a constant shape parameter (= 2 for the critical
CTOD), under the singular stress fields. In such a case, the use of two sets of specimens with high and low constraints,
e.g. deep-cracked and shallow-cracked specimens, is recommended to get a unique solution for m. The details of the
calibration procedure for m using two data sets is described in Reference [24].
Table B.1 — Fracture toughness testing
Number of test specimens Large enough for determination of Weibull parameter m with
statistical reliability
Items measured Force, P, and crack mouth opening displacement, V
g
Fracture toughness parameter Critical CTOD, δ
cr
B.3 FE-analysis of stress fields ahead of crack-tip in fracture toughness specimen
(Step 2)
B.3.1 General
The stress fields ahead of the crack-tip in the fracture toughness specimen shall be analysed by a finite
element method (FEM) that incorporates large deformation analysis. A guideline for obtaining sound
FE-results in terms of the stress-strain curve of material used and the FE-model is described in the following
subclauses.
B.3.2 Stress-strain curve for FE-analysis
B.3.2.1 Round-bar tensile testing
In order to obtain the stress-strain curve of the material for use in the FE-analysis, a round-bar tensile test
shall be performed in accordance with established International Standards for testing, such as the following:
ISO 6892:1998, Metallic materials — Tensile testing at ambient temperature;
ISO 15579:2000, Metallic materials — Tensile testing at low temperature.
The test shall be performed at the same temperature as that of the fracture toughness test in Step 1. During
the test, force and elongation between gauge marks shall be measured and recorded.
B.3.2.2 Equivalent stress-equivalent plastic strain curve for FE-analysis
Based on the results of the round-bar tensile test, the relationship between equivalent stress and equivalent
plastic strain to be used in the FE-analysis shall be determined in accordance with the following procedure.
a) Calculate the nominal stress-nominal plastic strain relationship, excluding the elastic strain component,
from the nominal stress-nominal strain curve measured in the strain range up to uniform elongation.
b) Convert the nominal stress-nominal plastic strain relationship to the true stress-true plastic strain
relationship (equivalent stress-equivalent plastic strain relationship) using the following equations.
s = σ(1 + ε) (B.1)
e = ln(1 + ε) (B.2)
where
s is the true stress;
e is the true strain;
σ is the nominal stress;
ε is the nominal strain.
NOTE Lüder's strain, if observed in the round-bar tension test, would be included in Equations (B.1) and (B.2).
c) Constitute the equivalent stress-equivalent plastic strain relationship beyond uniform elongation ε in the
T
form:
n
σ=+R 1/εα (B.3)
()
p0,2 p
where
σ is the equivalent stress;
ε is the equivalent plastic strain (plastic component of equivalent strain);
p
R is the yield stress;
p0,2
α and n are material constants (n being the strain hardening coefficient).
It
...