1、BRITISH STANDARD BS ISO 12107:2003 Metallic materials Fatigue testing Statistical planning and analysis of data ICS 77.040.10 BS ISO 12107:2003 This British Standard was published under the authority of the Standards Policy and Strategy Committee on 21 November 2003 BSI 21 November 2003 ISBN 0 580 4
2、2963 6 National foreword This British Standard reproduces verbatim ISO 12107:2003 and implements it as the UK national standard. It supersedes BS 3518-5:1996 which is withdrawn. The UK participation in its preparation was entrusted by Technical Committee ISE/NFE/4, Mechanical testing of metals, to S
3、ubcommittee ISE/NFE/4/6, Fatigue testing of metals, which has the responsibility to: A list of organizations represented on this subcommittee can be obtained on request to its secretary. Cross-references The British Standards which implement international publications referred to in this document ma
4、y be found in the BSI Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Search” facility of the BSI Electronic Catalogue or of British Standards Online. This publication does not purport to include all the necessary provisions of a contract. Users
5、are responsible for its correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. aid enquirers to understand the text; present to the responsible international/European committee any enquiries on the interpretation, or proposals for change, a
6、nd keep the UK interests informed; monitor related international and European developments and promulgate them in the UK. Summary of pages This document comprises a front cover, an inside front cover, the ISO title page, pages ii to v, a blank page, pages 1 to 26, an inside back cover and a back cov
7、er. The BSI copyright notice displayed in this document indicates when the document was last issued. Amendments issued since publication Amd. No. Date Comments Reference number ISO 12107:2003(E)INTERNATIONAL STANDARD ISO 12107 First edition 2003-03-15 Metallic materials Fatigue testing Statistical p
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13、bwww.is.o groii BSISO12107:2003 iiiContents Page Foreword iv Introduction v 1 Scope 1 1.1 Objectives 1 1.2 Fatigue properties to be analysed. 1 1.3 Limit of application . 1 2 Normative references . 1 3 Terms and definitions. 2 3.1 Terms related to statistics 2 3.2 Terms related to fatigue . 2 4 Stat
14、istical distributions in fatigue properties. 3 4.1 Concept of distributions in fatigue . 3 4.2 Distribution of fatigue life. 3 4.3 Distribution of fatigue strength . 4 5 Statistical planning of fatigue tests 4 5.1 Sampling 4 5.2 Number of specimens to be tested . 6 5.3 Allocation of specimens for te
15、sting 6 6 Statistical estimation of fatigue life at a given stress . 7 6.1 Testing to obtain fatigue life data 7 6.2 Plotting data on probability paper. 7 6.3 Estimating distribution parameters 9 6.4 Estimating the lower limit of the fatigue life. 9 7 Statistical estimation of fatigue strength at a
16、given fatigue life. 10 7.1 Testing to obtain fatigue strength data 10 7.2 Statistical analysis of test data 10 7.3 Estimating the lower limit of the fatigue strength . 11 7.4 Modified method when standard deviation is known . 11 8 Statistical estimation of S-N curve. 12 8.1 Fatigue testing to obtain
17、 S-N data . 12 8.2 Statistical analysis of S-N data. 12 8.3 Estimating the lower limit of the S-N curve. 13 8.4 Verifying the adequacy of the linear model13 9 Test report 14 9.1 Presentation of test results 14 9.2 Related information 15 Annex A (informative) Examples of applications 16 Annex B (info
18、rmative) Statistical tables . 22 Annex C (informative) Combined method for statistical estimation of a full S-N curve 24 Bibliography . 26 BSISO12107:2003iv Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). T
19、he 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-go
20、vernmental, 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.
21、 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 v
22、ote. 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 12107 was prepared by Technical Committee ISO/TC 164, Mechanical testing of metals, Subcommi
23、ttee SC 5, Fatigue testing. BSISO12107:2003 vIntroduction It is known that the results of fatigue tests display significant variations even when the test is controlled very accurately. In part, these variations are attributable to non-uniformity of test specimens. Examples of such non-uniformity inc
24、lude slight differences in chemical composition, heat treatment, surface finish, etc. The remaining part is related to the stochastic process of fatigue failure itself that is intrinsic to metallic engineering materials. Adequate quantification of this inherent variation is necessary to evaluate the
25、 fatigue property of a material for the design of machines and structures. It is also necessary for test laboratories to compare materials in fatigue behaviour, including its variation. Statistical methods are necessary to perform these tasks. They include both the experimental planning and procedur
26、e to develop fatigue data and the analysis of the results. BSISO12107:2003INTENRATIONAL TSANDADR IS:70121 O3002(E)1Metallic materials Fatigue testing Statistical planning and analysis of data 1 Scope 1.1 Objectives This International Standard presents methods for the experimental planning of fatigue
27、 testing and the statistical analysis of the resulting data. The purpose is to determine the fatigue properties of metallic materials with both a high degree of confidence and a practical number of specimens. 1.2 Fatigue properties to be analysed This International Standard provides a method for the
28、 analysis of fatigue life properties at a variety of stress levels using a relationship that can linearly approximate the materials response in appropriate coordinates. Specifically, it addresses: a) the fatigue life for a given stress, and b) the fatigue strength for a given fatigue life. The term
29、“stress” in this International Standard can be replaced by “strain”, as the methods described are also valid for the analysis of life properties as a function of strain. Fatigue strength in the case of strain-controlled tests is considered in terms of strain, as it is ordinarily understood in terms
30、of stress in stress-controlled tests. 1.3 Limit of application This International Standard is limited to the analysis of fatigue data for materials exhibiting homogeneous behaviour due to a single mechanism of fatigue failure. This refers to the statistical properties of test results that are closel
31、y related to material behaviour under the test conditions. In fact, specimens of a given material tested under different conditions may reveal variations in failure mechanisms. For ordinary cases, the statistical property of resulting data represents one failure mechanism and may permit direct analy
32、sis. Conversely, situations are encountered where the statistical behaviour is not homogeneous. It is necessary for all such cases to be modelled by two or more individual distributions. An example of such behaviour is often observed when failure can initiate from either a surface or internal site a
33、t the same level of stress. Under these conditions, the data will have mixed statistical characteristics corresponding to the different mechanisms of failure. These types of results are not considered in this International Standard because a much higher complexity of analysis is required. 2 Normativ
34、e 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 3534 (all parts), Statistics Voc
35、abulary and symbols BSISO12107:20032 3 Terms and definitions For the purposes of this document, the terms and definitions given in ISO 3534 and the following apply. 3.1 Terms related to statistics 3.1.1 confidence level value 1 of the probability associated with an interval of statistical tolerance
36、3.1.2 degree of freedom number calculated by subtracting from total number of items of test data the number of parameters estimated from the data 3.1.3 distribution function function giving, for every value x, the probability that the random variable X is less than or equal to x 3.1.4 estimation ope
37、ration made for the purpose of assigning, from the values observed in a sample, numerical values to the parameters of a distribution from which this sample has been taken 3.1.5 population totality of individual materials or items under consideration 3.1.6 random variable variable that may take any v
38、alue of a specified set of values 3.1.7 sample one or more items taken from a population and intended to provide information on the population 3.1.8 size n number of items in a population, lot, sample, etc. 3.1.9 standard deviation positive square root of the mean squared deviation from the arithmet
39、ic mean 3.2 Terms related to fatigue 3.2.1 fatigue life N number of stress cycles applied to a specimen, at an indicated stress level, before it attains a failure criterion defined for the test 3.2.2 fatigue limit fatigue strength at infinite life BSISO12107:2003 33.2.3 fatigue strength value of str
40、ess level S, expressed in megapascals, at which a specimen would fail at a given fatigue life 3.2.4 specimen portion or piece of material to be used for a single test determination and normally prepared in a predetermined shape and in predetermined dimensions 3.2.5 stress level S intensity of the st
41、ress under the conditions of control in the test EXAMPLES Amplitude, maximum, range. 3.2.6 stress step d difference between neighbouring stress levels, expressed in megapascals, when conducting the test by the staircase method 4 Statistical distributions in fatigue properties 4.1 Concept of distribu
42、tions in fatigue The fatigue properties of metallic engineering materials are determined by testing a set of specimens at various stress levels to generate a fatigue life relationship as a function of stress. The results are usually expressed as an S-N curve that fits the experimental data plotted i
43、n appropriate coordinates. These are generally either log-log or semi-log plots, with the life values always plotted on the abscissa on a logarithmic scale. Fatigue test results usually display significant scatter even when the tests are carefully conducted to minimize experimental error. A componen
44、t of this variation is due to inequalities, related to chemical composition or heat treatment, among the specimens, but another component is related to the fatigue process, an example being the initiation and growth of small cracks under test environments. The variation in fatigue data is expressed
45、in two ways: the distribution of fatigue life at a given stress and the distribution of strength at a given fatigue life (see 1 to 5). 4.2 Distribution of fatigue life Fatigue life, N, at a given test stress, S, is considered as a random variable. It is expressed as the normal distribution of the lo
46、garithm of the fatigue life. This relationship is: () 2 11 exp d 2 2 x x x x x Px x = (1) where x = log N and xand xare, respectively, the mean and the standard deviation of x. Equation (1) gives the cumulative probability of failure for x. This is the proportion of the population failing at lives l
47、ess than or equal to x. Equation (1) does not relate to the probability of failure for specimens at or near the fatigue limit. In this region, some specimens may fail, while others may not. The shape of the distribution is often skewed, displaying even BSISO12107:20034 greater scatter on the longer-
48、life side. It also may be truncated to represent the longest failure life observed in the data set. This International Standard does not address situations in which a certain number of specimens may fail, but the remaining ones do not. Other statistical distributions can also be used to express vari
49、ations in fatigue life. The Weibull4distribution is one of the statistical models often used to represent skewed distributions. Figure 1 shows an example of data from a fatigue test conducted with a statistically based experimental plan using a large number of specimens (see 5). The shape of the fatigue life distributions is demonstrated for explanatory purposes. 4.3 Distribution of fatigue strength Fatigue strength at
