1、 ISO 2012 Metallic materials Fatigue testing Statistical planning and analysis of data Matriaux mtalliques Essais de fatigue Programmation et analyse statistique de donnes INTERNATIONAL STANDARD ISO 12107 Second edition 2012-08-15 Reference number ISO 12107:2012(E) ISO 12107:2012(E) ii ISO 2012 All
2、rights reserved COPYRIGHT PROTECTED DOCUMENT ISO 2012 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
3、at the address below or ISOs 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 copyrightiso.org Web www.iso.org Published in Switzerland ISO 12107:2012(E) ISO 2012 All rights reserved iii Contents P
4、age 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 T erms and definitions . 2 3.1 Terms related to statistics . 2 3.2 Terms related to fatigue . 3 4 Statistical distributions in fatigue propertie
5、s 3 4.1 Concept of distributions in fatigue . 3 4.2 Distribution of fatigue life 4 4.3 Distribution of fatigue strength . 5 5 Statistical planning of fatigue tests 5 5.1 Sampling 5 5.2 Allocation of specimens for testing . 6 6 Statistical estimation of fatigue life at a given stress . 6 6.1 Testing
6、to obtain fatigue life data 6 6.2 Plotting data on normal probability paper 6 6.3 Estimating distribution parameters 7 6.4 Quantitative evaluation of the assumption of normality 7 6.5 Estimating the lower limit of the fatigue life 7 7 Statistical estimation of fatigue strength at a given fatigue lif
7、e . 8 7.1 Testing to obtain fatigue strength data . 8 7.2 Statistical analysis of test data 8 7.3 Estimating the lower limit of the fatigue strength 9 7.4 Modified method when standard deviation is known 9 8 Statistical estimation of the S-N curve . 9 8.1 Introduction . 9 8.2 Estimation of regressio
8、n parameters 13 8.3 Analysis approach 15 8.4 Calculation of the lower tolerance limit .21 8.5 Experimental plan for the development of S-N curves 22 9 Test report .22 9.1 Presentation of test results 22 9.2 Fatigue strength at a given life 22 9.3 S-N curve 23 Annex A (informative) Examples of applic
9、ations .24 Annex B (informative) Statistical tables .34 Bibliography .36 ISO 12107:2012(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 o
10、ut 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 c
11、ollaborates 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
12、 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 elemen
13、ts 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, Subcommittee SC 5, Fatigue testing. This second edition cancels and replac
14、es the first edition (ISO 12107:2003), which has been technically revised. iv ISO 2012 All rights reserved ISO 12107:2012(E) Introduction 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 attri
15、butable to non-uniformity of test specimens. Examples of such non- uniformity include 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
16、. Adequate quantification of this inherent variation is necessary to evaluate the 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
17、 to perform these tasks. This International Standard includes a full methodology for application of the Bastenaire model as well as other more sophisticated relationships. It also addresses the analysis of runout (censored) data. ISO 2012 All rights reserved v Metallic materials Fatigue testing Stat
18、istical planning and analysis of data 1 Scope 1.1 Objectives This International Standard presents methods for the experimental planning of fatigue testing and the statistical analysis of the resulting data. The purpose is to determine the fatigue properties of metallic materials with both a high deg
19、ree of confidence and a practical number of specimens. 1.2 Fatigue properties to be analysed This International Standard provides a method for the analysis of fatigue life properties at a variety of stress levels using a relationship that can linearly approximate the materials response in appropriat
20、e coordinates. Specifically, it addresses a) the fatigue life for a given stress, and b) the fatigue strength for a given fatigue life. The term “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 funct
21、ion of strain. Fatigue strength in the case of strain-controlled tests is considered in terms of strain, as it is ordinarily understood in terms of stress in stress-controlled tests. 1.3 Limit of application This International Standard is limited to the analysis of fatigue data for materials exhibit
22、ing homogeneous behaviour due to a single mechanism of fatigue failure. This refers to the statistical properties of test results that are closely related to material behaviour under the test conditions. In fact, specimens of a given material tested under different conditions may reveal variations i
23、n failure mechanisms. For ordinary cases, the statistical property of resulting data represents one failure mechanism and may permit direct analysis. Conversely, situations are encountered where the statistical behaviour is not homogeneous. It is necessary for all such cases to be modelled by two or
24、 more individual distributions. An example of such behaviour is often observed when failure can initiate from either a surface or internal site at the same level of stress. Under these conditions, the data will have mixed statistical characteristics corresponding to the different mechanisms of failu
25、re. These types of results are not considered in this International Standard because a much higher complexity of analysis is required. Finally, for the S-N case (discussed in Clause 8), this International Standard addresses only complete data. Runouts of censored data are not addressed. 2 Normative
26、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 Vocab
27、ulary and symbols INTERNATIONAL STANDARD ISO 12107:2012(E) ISO 2012 All rights reserved 1 ISO 12107:2012(E) 3 T erms and definitio ns 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 confid enc e l eve l val
28、ue 1 of the probability associated with an interval of statistical tolerance 3.1.2 degrees of freedom number calculated by subtracting from the total number of observations the number of parameters estimated from the data 3.1.3 distribution function function giving, for every value x, the probabilit
29、y that the random variable X is less than or equal to x 3.1.4 estimation operation 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
30、items under consideration 3.1.6 random variable variable that may take any value 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 mean sum of
31、 all the data in a population divided by the number of observations 3.1.10 sample mean sum of all the data in a sample divided by the number of observations 3.1.11 standard deviation positive square root of the mean squared standard deviation from the mean from a population. 3.1.12 estimated standar
32、d deviation positive square root of the mean squared standard deviation from the mean of a sample. 2 ISO 2012 All rights reserved ISO 12107:2012(E) 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 failu
33、re criterion defined for the test 3.2.2 fatigue limit fatigue strength at long life NOTE Historically, this has usually been defined as the stress generating a life at 10 7cycles. 3.2.3 fatigue strength value of stress level S at which a specimen would fail at a given fatigue life NOTE This is expre
34、ssed in megapascals. 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 stress under the conditions of control in the test EXAMPLES Amplitude, maxi
35、mum, range. 3.2.6 stress step d difference between neighbouring stress levels when conducting the test by the staircase method NOTE This is expressed in megapascals. 4 Statistical distributions in fatigue properties 4.1 Concept of distributions in fatigue The fatigue properties of metallic engineeri
36、ng 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 in appropriate coordinates. These are generally either log- lo
37、g 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 component of this variation is due to inequalities, related to chemi
38、cal 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 are expressed in two ways: the distribution of fatigue life at a given st
39、ress and the distribution of strength at a given fatigue life (see References 1 to 5). ISO 2012 All rights reserved 3 ISO 12107:2012(E) 4.2 Distribution of fatigue life Fatigue life, N, at a given test stress, S, is considered as a random variable. It is frequently observed the distribution of fatig
40、ue life values at any stress is normal in the logarithmic metric. That is, the logarithms of the life values follow a normal distribution (See 6.4). This relationship is: Px x x x x x x 12 1 2 d 2exp (1) where x = log N and xand xare, respectively, the mean and the standard deviation of x. Formula (
41、1) gives the cumulative probability of failure for x. This is the proportion of the population failing at lives less than or equal to x. Formula (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
42、. The shape of the distribution is often skewed, displaying even greater scatter on the longer-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,
43、but the remaining ones do not. Other statistical distributions can also be used to express variations in fatigue life. The Weibull 4 distribution is one of the statistical models often used to represent skewed distributions. On occasion, this distribution may apply to lives at low stresses, but this
44、 special case is not addressed in this International Standard. 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 Reference 5). The shape of the fatigue life distributions is demonstrated for explanatory
45、 purposes. Y X Key X cycles to failure Y stress amplitude, in MPa Figure 1 Concept of variation in a fatigue property Distribution of fatigue life at given stresses for a 0,25 % C carbon steel tested in the rotating-bending mode 4 ISO 2012 All rights reserved ISO 12107:2012(E) 4.3 Distribution of fa
46、tigue strength Fatigue strength at a given fatigue life, N, is considered as a random variable. It is expressed as the normal distribution: Py y y y y y y 1 2 exp 1 2 d 2(2) where y = S (the fatigue strength at N ), and yand yare, respectively, the mean and the standard deviation of y. Formula (2) g
47、ives the cumulative probability of failure for y. It defines the proportion of the population presenting fatigue strengths less than or equal to y. Other statistical distributions can also be used to express variations in fatigue strength. Figure 2 is based on the same experimental data as Figure 1.
48、 The variation in the fatigue property is expressed here in terms of strength at typical fatigue lives (see Reference 5). Y X Key X cycles to failure Y stress amplitude, in MPa Figure 2 Concept of variation in a fatigue property Distribution of fatigue strength at typical fatigue lives for a 0,25 %
49、C carbon steel tested in the rotating-bending mode 5 Statistical planning of fatigue tests 5.1 Sampling It is necessary to define clearly the population of the material for which the statistical distribution of fatigue properties is to be estimated. Specimen selection from the population shall be performed in a random fashion. It is also important that the specimens be selected so that they accurately repres
