ISO/TR 10771-2:2008

TECHNICAL ISO/TR
REPORT 10771-2
First edition
2008-12-01

Hydraulic fluid power — Fatigue pressure
testing of metal pressure-containing
envelopes —
Part 2:
Rating methods
Transmissions hydrauliques — Essais de fatigue des enveloppes
métalliques sous pression —
Partie 2: Méthodes de classement



Reference number
ISO/TR 10771-2:2008(E)
©
ISO 2008

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ISO/TR 10771-2:2008(E)
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ISO/TR 10771-2:2008(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 2
4 Selection of material factors. 2
5 Determination of cyclic test pressure. 2
6 Conduct of fatigue test. 3
7 Rating by similarity. 4
8 Rating declaration. 4
9 Identification statement (reference to this part of ISO 10771) . 4
Annex A (informative) Material factor database. 5
A.1 Values of coefficient of variation, k , for commonly used metals . 5
o
A.2 Procedures used to establish values of coefficient of variation, k , for the metals listed in
o
Table A.1 . 5
Annex B (normative) Calculation of variability factor K . 13
V
B.1 General. 13
B.2 Method . 13
Annex C (informative) Proposal for an acceleration factor. 15
C.1 General. 15
7
C.2 Extrapolating data to 10 cycles . 15
C.3 Examples . 19
[9]
Annex D (informative) Basis of fatigue pressure rating . 21
D.1 Basis of pressure rating. 21
D.2 Statistical analysis theory. 22
D.3 Fatigue distribution data. 28
D.4 Data calculation example. 33
D.5 Raw data points for sample problem. 39
Bibliography . 40

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ISO/TR 10771-2:2008(E)
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.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
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/TR 10771-2 was prepared by Technical Committee ISO/TC 131, Fluid power systems, Subcommittee
SC 8, Product testing.
ISO/TR 10771 consists of the following parts, under the general title Hydraulic fluid power — Fatigue pressure
testing of metal pressure-containing envelopes:
⎯ Part 1: Test method
⎯ Part 2: Rating methods
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ISO/TR 10771-2:2008(E)
Introduction
In hydraulic fluid power systems, power is transmitted and controlled under pressure within a closed circuit. It
is important for the manufacturer and user of hydraulic components to have information on their global
reliability because of the importance of the fatigue failure mode and the relationship with their functional safety
and service life. This part of ISO 10771 provides a method for fatigue-testing in order to verify the rating of a
pressure-containing envelope.
During operation, components in a system can be subjected to loads that arise from:
⎯ internal pressure;
⎯ external forces;
⎯ inertia and gravitational effects;
⎯ impact or shock;
⎯ temperature changes or gradients.
The nature of these loads can vary from a single static application to continuously varying amplitudes,
repetitive loadings and even shocks. It is important to know how well a component can withstand these loads,
but this part of ISO 10771 addresses only the loads due to internal pressure.
There are several International Standards already in existence for pressure rating of individual components
(e.g. for determining maximum allowable rated pressure) and this part of ISO 10771 is not intended to replace
them. Instead, a method of fatigue verification is provided.
This part of ISO 10771 describes a universal verification test to give credibility to the many in-house and other
methods of determining the pressure rating of the components. Credibility is based upon the fundamental
nature of metal fatigue with its statistical treatment and a mathematical theory of statistical verification.
Nevertheless, it is necessary to have design knowledge of the component and its representative specimens to
maximize accuracy of the verification method. The use of this test method can reduce the risk of fatigue failure
for a hydraulic component regardless of sample size.
In order to rate components in accordance with this part of ISO 10771, it is necessary to propose a rating for
the component, select test specimens and select a test pressure. A fatigue test is then conducted in
accordance with ISO 10771-1. If the test is successful, the proposed rating is verified for the family of
components represented by the sample.
This part of ISO 10771 is based on ANSI/(NFPA) T 2.6.1, a standard which was developed and has been
used in the United States for over 25 years and has been adopted for use in Japan as JSME S006-1985. If
sufficient experience is gained in other parts of the world, and additional data on materials are obtained, this
part of ISO 10771 might be re-drafted as an International Standard in the future.
It should be noted that the test factors in Annex A are based on material data obtained from sources
originating in the USA. One of the objectives in issuing this part of ISO 10771 is to obtain material data from
other countries. The test factors are based only on the material properties and not on any tolerances of the
elements in the pressure-containing envelope.
Annex C describes a possible method for accelerating testing. The example shows how material property data
can be used to determine an acceleration factor and shows that they have to be carefully chosen. Another
objective of this part of ISO 10771 is to seek additional data as described in Annex C. Contributors are asked
to submit any available data to the secretary of ISO TC 131/SC 8.
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TECHNICAL REPORT ISO/TR 10771-2:2008(E)

Hydraulic fluid power — Fatigue pressure testing of metal
pressure-containing envelopes —
Part 2:
Rating methods
1 Scope
This part of ISO 10771 specifies a test method for fatigue rating of the pressure-containing envelopes of
components used in hydraulic fluid power systems, as tested under steady internal cyclic pressure loads in
accordance with ISO 10771-1.
This part of ISO 10771 is only applicable to components whose failure mode is the fatigue of any element in
the pressure-containing envelope, and that:
⎯ are manufactured from metals;
⎯ are operated at temperatures that exclude creep and low-temperature embrittlement;
⎯ are only subjected to pressure-induced stresses;
⎯ are not subjected to loss of strength due to corrosion or other chemical action;
⎯ can include gaskets, seals and other non-metallic components; however, these are not considered part of
the pressure-containing envelope being tested (see note 3 of 5.5 of ISO 10771-1:2002).
This part of ISO 10771 does not apply to piping as defined in ISO 4413 (i.e. connectors, hose, tubing, pipe).
NOTE See ISO 19879, ISO 6803 and ISO 6605 for methods of fatigue testing of tube connectors, hoses and hose
assemblies.
This part of ISO 10771 establishes a general rating method that can be applied to many hydraulic fluid power
components. In addition, EN 14359 has been developed for accumulators.
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 5598, Fluid power systems and components — Vocabulary
ISO 10771-1:2002, Hydraulic fluid power — Fatigue pressure testing of metal pressure-containing
envelopes — Part 1: Test method
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ISO/TR 10771-2:2008(E)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 5598, ISO 10771-1 and the
following apply.
3.1
rated fatigue pressure
P
RF
maximum pressure that a component pressure-containing envelope, selected at random, has been verified to
sustain for the rated cycle life without failure, with a known probability
3.2
assurance level
probability that the fatigue strength of a randomly selected test specimen exceeds its rated fatigue pressure
3.3
verification level
probability that the fatigue strength of a randomly selected test specimen is not less than its cyclic test
pressure
3.4
coefficient of variation
k
o
standard deviation of the fatigue strength distribution of a material at a given fatigue life, divided by its mean
[1]
NOTE Adapted from ISO 3534-1:2006 .
3.5
variability factor
K
V
ratio of cyclic test pressure to rated fatigue pressure
3.6
element
part of a component; for example, tie rods on a cylinder, end caps on a valve, bolts on a pump housing
4 Selection of material factors
4.1 Select a coefficient of variation, k , for each type of material in the pressure-containing envelope. The k
o o
factor should be obtained from fatigue tests on coupons for the particular temper of material used in the
pressure-containing envelope. The fatigue test method used to obtain this data should be in accordance with
a recognized national or International Standard.
4.2 As an alternative to testing the specific material, coefficients described in Annex A can be used for the
k factor.
o
5 Determination of cyclic test pressure
5.1 Select an assurance level for the fatigue pressure rating. A nominal value is 90 %.
5.2 Select a verification level for the fatigue pressure rating. A nominal value is 90 %.
NOTE See Annex D for a tutorial that describes these terms.
5.3 Select a number of component specimens to be tested, then determine the number of element
specimens that will be tested in the components.
NOTE The verification is independent of sample size because the test pressure compensates for different quantities.
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ISO/TR 10771-2:2008(E)
5.4 Determine the variability factor, K , for each element in the component using Table 1 and the procedure
V
described in the example given in Annex B. Use the largest K factor so obtained, for the calculations
V
described in the example.
5.5 Propose a rated fatigue pressure for the pressure-containing envelope of the component.
5.6 Calculate the cyclic test pressure, P , using Equation (1):
CT
PK=×P (1)
CT V RF
where
K is the variability factor;
V
P is the rated fatigue pressure of the component pressure-containing envelope.
RF
Table 1 — Variability factor, K (at a verification level of 90 %)

V
b
Assurance No. of Material coefficient of variation, k
o
level specimens

0 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28 0,30
a
n
1 1,001,09 1,20 1,321,461,631,832,082,382,773,29 — — — — —
2 1,001,08 1,16 1,261,381,521,681,882,132,452,87 — — — — —
99,9 %
3 1,00 1,07 1,15 1,23 1,34 1,46 1,61 1,78 2,01 2,29 2,66 3,18 — — — —
4 1,00 1,06 1,13 1,22 1,31 1,42 1,56 1,72 1,93 2,19 2,54 3,02 — — — —
5 1,00 1,06 1,13 1,20 1,29 1,40 1,53 1,68 1,87 2,12 2,44 2,89 — — — —
1 1,00 1,08 1,16 1,25 1,35 1,47 1,60 1,75 1,92 2,12 2,35 2,63 2,96 — — —
2 1,00 1,06 1,12 1,20 1,28 1,37 1,47 1,58 1,72 1,87 2,05 2,26 2,52 2,85 — —

99 %
3 1,00 1,05 1,11 1,17 1,24 1,32 1,40 1,50 1,62 1,75 1,90 2,09 2,31 2,59 2,94 —
4 1,00 1,05 1,10 1,15 1,21 1,28 1,36 1,45 1,55 1,67 1,81 1,98 2,18 2,43 2,74 3,16
5 1,00 1,04 1,09 1,14 1,20 1,26 1,33 1,41 1,51 1,62 1,75 1,90 2,08 2,31 2,60 2,98
1 1,00 1,05 1,11 1,17 1,23 1,29 1,36 1,44 1,52 1,60 1,69 1,79 1,89 2,00 2,12 2,25
2 1,00 1,04 1,07 1,11 1,16 1,20 1,25 1,30 1,35 1,41 1,47 1,54 1,61 1,69 1,77 1,86
90 % 3 1,00 1,03 1,06 1,09 1,12 1,16 1,19 1,23 1,28 1,32 1,37 1,42 1,48 1,54 1,60 1,67
4 1,00 1,02 1,05 1,07 1,10 1,13 1,16 1,19 1,23 1,26 1,30 1,34 1,39 1,44 1,49 1,55
5 1,00 1,02 1,04 1,06 1,08 1,11 1,13 1,16 1,19 1,22 1,25 1,29 1,33 1,37 1,41 1,46
a
Test twice the number of specimens if a 99 % verification level is chosen.
b
Use an interpolation of k values between those tabulated here, or calculate K from Equation (D.14) in Annex D.
o V
6 Conduct of fatigue test
5 7
6.1 Determine the number of cycles, between 1 × 10 and 1 × 10 , for which the component will be rated.
6.2 Subject the test specimens to a fatigue pressure test in accordance with ISO 10771-1 for the number of
cycles determined in 6.1, using the P calculated from Equation (1).
CT
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ISO/TR 10771-2:2008(E)
6.3 The fatigue pressure test is successful if all of the element specimens selected in 5.3 do not fail as
described in ISO 10771-1:2002, Clause 8.
7 Rating by similarity
It is permitted to extend a verified P to other components of similar shape if it can be shown that differences
RF
between those components and the components tested do not result in any reduction of their fatigue strength
capabilities. Examples of this are components that have smaller ports or different axial lengths but are
otherwise identical in geometry to the component tested.
8 Rating declaration
The P proposed in 5.5 will be verified if the requirements of 6.3 are met. A code should be applied to the
RF
component to declare its rating as:
P = P (in megapascals)/assurance level/verification level/K in the test/number of test cycles
RF RF V
EXAMPLE The rated fatigue pressure (12,5 MPa) of a component’s pressure-containing envelope that was tested at
6
an assurance level of 99 %, a verification level of 90 %, a K of 1,36 for 2 × 10 cycles, would be declared as:
V
6
P = 12,5 MPa/ 99 %/ 90 %/ 1,36/ 2 × 10 cycles
RF
9 Identification statement (reference to this part of ISO 10771)
Use the following statement in test reports, catalogues and sales literature when complying with this part of
ISO 10771:
“Method for fatigue pressure rating conforms to ISO TR 10771-2:2008, Hydraulic fluid power — Fatigue
pressure testing of metal pressure-containing envelopes — Part 2: Rating methods”.
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ISO/TR 10771-2:2008(E)
Annex A
(informative)

Material factor database
A.1 Values of coefficient of variation, k , for commonly used metals
o
Table A.1 tabulates data calculated from the sources listed in the bibliography.
Table A.1 — Values of coefficient of variation, k , for commonly used metals
o
k
Metal
o
Alloy, low 0,14
Carbon, plain 0,08
Steel
Nickel 0,10
Stainless 0,09
Tool 0,10
Iron 0,14
Aluminium (except unalloyed) 0,13
Unalloyed aluminium 0,23
Cobalt 0,13
Nonferrous Copper 0,09
Magnesium 0,17
1)
0,27
Monel
Titanium 0,12
A.2 Procedures used to establish values of coefficient of variation, k , for the metals
o
listed in Table A.1
A.2.1 Values of k were calculated from fatigue test data on test coupons that were published in the
o
references cited in the bibliography. The types of data taken from these references were one of the following:
a) Means, µ, and standard deviations, σ, of normal distributions;
b) parameters of Weibull distributions;
c) raw data points on S-N curves. From these data, individual coefficients of variation, k , were calculated at
o
6
10 cycles for:
1) normal distributions; k equals the standard deviation divided by the mean;
o

1) This is an example of a suitable product available commercially. This information is given for the convenience of users
of this document and does not constitute an endorsement by ISO of this product.
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ISO/TR 10771-2:2008(E)
2) Weibull distributions; k were calculated from a formula given in Reference [12]. The formula includes
o
a gamma function, the value of which was selected as a constant at 0,89 because its variations were
generally less than ± 2 % in the range of interest (a few data points went to a difference of ± 4 %);
3) S-N curves; the references had either included limit bands (assumed to be two sigma from the mean)
or actual standard deviation points. These were then used to calculate k in the same manner as a
o
normal distribution.
A.2.2 The resulting k values (shown as individual values in Table A.2 to Table A.13) include a mix of
o
notched and unnotched specimens, several different tempers, plus different methods of testing (e.g. axial,
rotating beam). However, only those tested at room temperature were used. No attempt was made to
segregate these data. It is reasoned that the components to be tested will have a variety of tempers and
notches, so an application of these published data to components can only be justified if the data are treated
statistically at a conservative value.
A.2.3 Therefore, the values given in Table A.1 were derived by assuming that all k data for a particular
o
metal group are part of a normal distribution, and a value that is greater than 90 % of this distribution was
selected. This ensures that the selection is substantially conservative. However, this part of ISO 10771 allows
the use of a more accurate k value, which is representative of the specific alloy and temper of the elements
o
being tested, if sufficient testing is performed to obtain those data, as described in 4.1. This approach will
likely yield a value that would be more advantageous for a particular application, but less than the
conservative values presented in Table A.1.
A.2.4 Table A.2 to Table A.13 describe all of the k calculations made from the data obtained from
o
Reference [10], Reference [11], and Reference [13] to Reference [17]. Most of the data are based on the
6
strength distribution at 10 cycles, but some data are at the endurance limit and these are identified in each
table, if applicable.
Table A.2 — Summary of k calculations for iron
o
a
k values
Type Reference Number of distributions
o
1)
[11] 1 0,0220
Armco
a a a a
0,0402; 0,042 ; 0,044 ; 0,0652; 0,126 ; 0,146 ;
Pearlitic (grey) [15];[17] 8
a
0,137
a a a a
Ferritic (malleable) [15];[17] 7 0,055 ; 0,0596; 0,0649; 0,065 ; 0,075 ; 0,109
a a a a a a
0,029 ; 0,040 ; 0,049 ; 0,065 ; 0,086 ; 0,094 ;
Nodular [15] 10
a a a a
0,095 ; 0,098 ; 0,173 ; 0,185
Fe; 5,5 % Mo; 2,5 %
[13] 2 0,0286; 0,0477
Cr; 0,5 % C
(k ) 90 % = 0,1335; (µ = 0,0771; σ = 0,0440)
Summary of all data
o
[13];[15];[11];[17] 28
above Conclusion: k value selected = 0,14
o

a
Data from reference [15] are at endurance limit.

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ISO/TR 10771-2:2008(E)
Table A.3 — Summary of k calculations for aluminium
o
a
k values
Alloy Reference Number of distributions
o
1) 0,0720
[13] 1
Duraluminum
356 [15] 2 0,038; 0,042
355 [14] 1 0,0766
1100 [14] 2 0,1742; 0,2377
0,017; 0,0400; 0,0527; 0,0534; 0,0541; 0,0556;
2014 [14];[15] 13 0,0702; 0,0732; 0,1152; 0,1164; 0,1215; 0,1386;
0,1400
0,026; 0,0498; 0,0542; 0,0561; 0,0613; 0,0708;
2024 [14];[15] 14 0,0717; 0,0765; 0,0825; 0,0974; 0,1039; 0,1190;
0,1404; 0,1840
2025 [14] 3 0,0347; 0,0549; 0,0947
2026 [14] 2 0,0507; 0,0834
2219 [14] 2 0,0701; 0,0705
5052 [14] 2 0,0845; 0,0914
5056 [14] 1 0,0947
5086 [14] 1 0,0640
5154 [14] 1 0,0662
5456 [14];[15] 2 0,012; 0,0708
6061 [14];[15] 4 0,018; 0,027; 0,0478; 0,087
7039 [14] 1 0,1405
0,040; 0,0505; 0,059; 0,0615; 0,0689; 0,0906;
7075 [14];[15] 8
0,1686; 0,2157
a a
0,0413 ; 0,0593
7076 [10] 2
7079 [14] 3 0,0560; 0,0942; 0,1486
7178 [14] 2 0,0484; 0,0881
R303 [14] 1 0,0434
0,0934; 0,1302
5 Mg Al [14] 2
7,5 Zn 2,5 Mg Al [14] 1 0,0570
Summary of all (k ) 90 % = 0,1390; µ = 0,0811; σ = 0,0452
o
[13];[14];[15];[10] 71
data above
(k ) 90 % = 0,1288; µ = 0,0775; σ = 0,0400
o
Conclusion: select k = 0,13 for alloyed
Remove the o
69
aluminium;
1100 data
select k = 0,23 for unalloyed
o
aluminium


a
Data from reference [10] are at endurance limit.

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ISO/TR 10771-2:2008(E)
Table A.4 — Summary of k calculations for low alloy steels
o
(containing silicon at less than 1 % and 1 or more of the following: nickel - less than 4 %;
chrome - less than 2 %; molybdenum - less than 0,5 %)
Number of
a
Alloy Reference k values

o
distributions
2340 [13] 6 0,0190; 0,0296; 0,0311; 0,0374; 0,0622 0,0696
3140 [13] 4 0,0145; 0,0283; 0,0435; 0,0919
4140 [13] 2 0,0650; 0,1102
4330 [10] 6 0,0313; 0,0372; 0,0498; 0,0644; 0,1063; 0,1129
0,0525; 0,0819; 0,1023; 0,1037; 0,1219; 0,1285;
4340 [13] 14 0,1301; 0,1335; 0,1428; 0,1438; 0,1476; 0,1484;
0,1600; 0,2035
4340 [11] 4 0,0253; 0,0301; 0,0321; 0,0627
0,0497; 0,0509; 0,0607; 0,0608; 0,0640; 0,0795;
4340 [10] 10
0,0822; 0,0833; 0,0880; 0,0966
0,0759; 0,0837; 0,0878; 0,0895; 0,1025; 0,1055;
4350 [10] 8
0,1209; 0,1213
AMS 5727 [13] 3 0,0341; 0,0385; 0,1002
(k ) 90 % = 0,1348; µ = 0,0812; σ = 0,0418
o
Summary of all data
[13];[11];[10] 57
above
Conclusion: k value selected = 0,14
o

a
Data from reference [10] are at endurance limit.

Table A.5 — Summary of k calculations for cobalt
o
Metal and alloy Reference Number of distributions k values

o
1)
Stellite 31 [14] 3 0,0771; 0,1202; 0,1472
S-816 (AMS5765) [13];[14] 4 0,0448; 0,0456; 0,0730; 0,0777
S-816 (AMS5534) [13] 1 0,0646
(k ) 90 % = 0,1269; µ = 0,0813; σ = 0,0355
Summary of all data
o
[13];[14] 8
above
Conclusion: k value selected = 0,13
o

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ISO/TR 10771-2:2008(E)
Table A.6 — Summary of k calculations for copper
o
Number of
a
Metal and alloy Reference k values

o
distributions
100 % Cu [14] 2 0,0522; 0,0804
70/30 Brass [14] 2 0,0153; 0,0735
Cu-7,3 AI BRNZ [14] 2 0,0496; 0,1037
a
AI Ni BRNZ [10] 1
0,0938
a
Beryllium [10] 1
0,0740
0,0153; 0,0173; 0,0181; 0,0185; 0,0200; 0,0211;
Copper casting alloys [16] 8
0,0234; 0,0514
(k ) 90 % = 0,0853; µ = 0,0455; σ = 0,0311
o
Summary of all data
[14];[16];[10] 16
above
Conclusion: k value selected = 0,09

o

a
Data from reference [10] are at endurance limit.

Table A.7 — Summary of k calculations for magnesium
o
Metal and alloy Reference Number of distributions k values

o
AZ31A [14] 1 0,0331
AZ31B [14] 1 0,0714
AZ61A [14] 3 0,0854; 0,1705; 0,1735
AZ80A-F [14] 1 0,0457
AZ81 [14] 2 0,0458; 0,0761
ZK60A [14] 1 0,1053
2,5 Al Mg [14] 3 0,1152; 0,1444; 0,1702
(k ) 90 % = 0,1694; µ = 0,1031; σ = 0,0517
Summary of all o
[14] 12
data above
Conclusion: k value selected = 0,17
o

Table A.8 — Summary of k calculations for plain carbon steel
o
k values
Group and alloy Reference Number of distributions
o
1045 [13] 3 0,0273; 0,0581; 0,0682
1050 [11] 1 0,0171
(k ) 90 % = 0,0739; µ = 0,0427; σ = 0,0244
o
Summary of all
[13];[11] 4
data above
Conclusion: k value selected = 0,08

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© ISO 2008 – All rights reserved 9

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ISO/TR 10771-2:2008(E)
Table A.9 — Summary of k calculations for stainless steel
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k values
Metal and alloy Reference Number of distributions
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321 [13] 3 0,0439; 0,0606; 0,0755
A-286 [13] 2 0,0958; 0,1303
347 [13] 4 0,0302; 0,0491; 0,0802; 0,1162
0,0163; 0,0180; 0,0230; 0,0313; 0,0313; 0,0315;
1)
[13] 14 0,0325; 0,0367; 0,0381; 0,0407; 0,0427; 0,0544;
Multimet N-155
0,0547; 0,0574
PH 15-7 [13] 2 0,0676; 0,0936
17-7 PH [13] 4 0,0135; 0,0145; 0,0168; 0,0505;
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