1、BRITISH STANDARDBS EN 843-5:2006Advanced technical ceramics Mechanical properties of monolithic ceramics at room temperature Part 5: Statistical analysisThe European Standard EN 843-5:2006 has the status of a British StandardICS 81.060.30g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g4
2、4g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42g43g55g3g47g36g58BS EN 843-5:2006This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 January 2007 BSI 2007ISBN 978 0 580 4
3、9983 8National forewordThis British Standard was published by BSI. It is the UK implementation of EN 843-5:2006. It supersedes DD ENV 843-5:1997 which is withdrawn. The UK participation in its preparation was entrusted to Technical Committee RPI/13, Advanced technical ceramics.A list of organization
4、s represented on RPI/13 can be obtained on request to its secretary.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application.Compliance with a British Standard cannot confer immunity from legal obligations.Amendments i
5、ssued since publicationAmd. No. Date CommentsEUROPEAN STANDARDNORME EUROPENNEEUROPISCHE NORMEN 843-5December 2006ICS 81.060.30 Supersedes ENV 843-5:1996 English VersionAdvanced technical ceramics - Mechanical properties ofmonolithic ceramics at room temperature - Part 5: StatisticalanalysisCramiques
6、 techniques avances - Proprits mcaniquesdes cramiques monolithiques temprature ambiante -Partie 5: Analyse statistiqueHochleistungskeramik - Mechanische Eigenschaftenmonolithischer Keramik bei Raumtemperatur - Teil 5:Statistische AuswertungThis European Standard was approved by CEN on 11 November 20
7、06.CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such nationalstandards may be obtained on
8、application to the Central Secretariat or to any CEN member.This European Standard exists in three official versions (English, French, German). A version in any other language made by translationunder the responsibility of a CEN member into its own language and notified to the Central Secretariat ha
9、s the same status as the officialversions.CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Roman
10、ia,Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATIONCOMIT EUROPEN DE NORMALISATIONEUROPISCHES KOMITEE FR NORMUNGManagement Centre: rue de Stassart, 36 B-1050 Brussels 2006 CEN All rights of exploitation in any form and by any means reservedworld
11、wide for CEN national Members.Ref. No. EN 843-5:2006: EEN 843-5:2006 (E) 2 Contents Page Foreword3 1 Scope 4 2 Normative references 4 3 Terms and definitions .4 3.1 Flaws .4 3.2 Flaw distributions 5 3.3 Mechanical evaluation.5 3.4 Statistical terms .6 3.5 The Weibull distribution7 4 Symbols 8 5 Sign
12、ificance and use .10 6 Principle of calculation .11 6.1 Maximum likelihood method 11 6.2 Bias correction.12 6.3 Confidence interval12 7 Procedure .13 7.1 Graphical representation of data .13 7.2 Determination of Weibull parameters by maximum likelihood method.13 7.3 Determination of limits of the co
13、nfidence interval.14 8 Test report 14 Annex A (informative) Relationship between characteristic strengths of test pieces or components of different size or shape, or with different stress fields applied 15 Annex B (informative) FORTRAN program for calculating Weibull parameters.17 Annex C (informati
14、ve) PASCAL program for calculating Weibull parameters23 Annex D (informative) BASIC program for calculating Weibull parameters .28 Annex E (normative) Unbiasing factors for estimation of Weibull modulus, m33 Annex F (normative) Confidence factors for characteristic strength, 0.34 Annex G (normative)
15、 Confidence factors for Weibull modulus, m36 Annex H (informative) Worked examples38 Annex I (informative) Example test report 43 Bibliography 45 EN 843-5:2006 (E) 3 Foreword This document (EN 843-5:2006) has been prepared by Technical Committee CEN/TC 184 “Advanced technical ceramics”, the secretar
16、iat of which is held by BSI. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by June 2007, and conflicting national standards shall be withdrawn at the latest by June 2007. This document supersedes E
17、NV 843-5:1996. EN 843 Advanced technical ceramics Mechanical properties of monolithic ceramics at room temperature comprises six parts: Part 1: Determination of flexural strength Part 2: Determination of Youngs modulus, shear modulus and Poissons ratio Part 3: Determination of subcritical crack grow
18、th parameters from constant stressing rate flexural strength tests Part 4: Vickers, Knoop and Rockwell superficial hardness Part 5: Statistical analysis Part 6: Guidance for fractographic investigation At the time of publication of this Revision of Part 5, Part 6 was available as a Technical Specifi
19、cation. According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, La
20、tvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom. EN 843-5:2006 (E) 4 1 Scope This part of EN 843 specifies a method for statistical analysis of ceramic strength data in terms of a two-parameter Weib
21、ull distribution using a maximum likelihood estimation technique. It assumes that the data set has been obtained from a series of tests under nominally identical conditions. NOTE 1 In principle, Weibull analysis is considered to be strictly valid for the case of linear elastic fracture behaviour to
22、the point of failure, i.e. for a perfectly brittle material, and under conditions in which strength limiting flaws do not interact and in which there is only a single strength-limiting flaw population. If subcritical crack growth or creep deformation preceding fracture occurs, Weibull analysis can s
23、till be applied if the results fit a Weibull distribution, but numerical parameters may change depending on the magnitude of these effects. Since it is impossible to be certain of the degree to which subcritical crack growth or creep deformation has occurred, this European Standard permits the analy
24、sis of the general situation where crack growth or creep may have occurred, provided that it is recognized that the parameters derived from the analysis may not be the same as those derived from data with no subcritical crack growth or creep. NOTE 2 This European Standard employs the same calculatio
25、n procedures as method A of ISO 20501:2003 1, but does not provide a method for dealing with censored data (method B of ISO 20501). 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies.
26、For undated references, the latest edition of the referenced document (including any amendments) applies. EN 843-1:2006, Advanced technical ceramics Mechanical properties of monolithic ceramics at room temperature Part 1: Determination of flexural strength EN ISO/IEC 17025, General requirements for
27、the competence of testing and calibration laboratories (ISO/IEC 17025:2005) 3 Terms and definitions For the purposes of this document, the terms and definitions given in EN 843-1:2006 and the following apply. NOTE Definitions of additional statistical terms can be found in ISO 2602 2, ISO 3534-1 3,
28、or other source literature on statistics. 3.1 Flaws 3.1.1 flaw inhomogeneity, discontinuity or structural feature in a material which when loaded provides a stress concentration and a risk of mechanical failure NOTE 1 This could be, for example, a grain boundary, large grain, pore, impurity or crack
29、. NOTE 2 The term flaw should not be taken as meaning the material is functionally defective, but rather as containing an inevitable microstructural inhomogeneity. 3.1.2 critical flaw flaw acting as the source of failure EN 843-5:2006 (E) 5 3.1.3 extraneous flaw type of flaw observed in the fracture
30、 of test pieces manufactured for the purposes of a test programme which will not appear in manufactured components NOTE For example, damage from machining when this process will not be used in the manufacture of components. 3.2 Flaw distributions 3.2.1 flaw size distribution spread of sizes of flaw
31、3.2.2 critical flaw size distribution distribution of sizes of critical flaws in a population of tested components 3.2.3 compound critical flaw distribution flaw distribution which contains more than one type of strength controlling flaw not occurring in a purely concurrent manner (3.2.4) NOTE An ex
32、ample is when every test piece contains flaw type A and some contain additionally a second independent type B. 3.2.4 concurrent critical flaw distribution competing critical flaw distribution. Multiple flaw distribution where every test piece contains representative defects of each independent flaw
33、type which compete with each other to cause failure 3.2.5 exclusive critical flaw distribution multiple flaw distribution created by mixing and randomizing test pieces from two or more versions or batches of material where each version contains a single strength-controlling flaw population NOTE For
34、example, each test piece contains defects exclusively from a single distribution, but the total data set reflects more than one type of strength-controlling flaw. 3.2.6 competing failure mode distinguishably different type of fracture initiation event that results from concurrent (competing) flaw di
35、stributions (3.2.4) 3.3 Mechanical evaluation 3.3.1 fractography analysis of patterns and features on fracture surfaces, usually with the purpose of identifying the fracture origin and hence the flaw type 3.3.2 proof test application of a predetermined stress to a test piece or component over a shor
36、t period of time to ascertain whether it contains a serious strength-limiting defect NOTE This enables the removal of potentially weak test pieces or components from a batch. This procedure modifies the failure statistics of the survivors, such that the two-parameter Weibull distribution is typicall
37、y no longer valid. EN 843-5:2006 (E) 6 3.3.3 population mean average of all strength results in a population 3.3.4 sample mean average of all strength results from a sample taken from the population 3.3.5 strength population ensemble of fracture strengths 3.4 Statistical terms 3.4.1 bias consistent
38、numerical offset in an estimate relative to the true underlying value, inherent in most estimating methods NOTE For the maximum likelihood method of estimation, the magnitude of the bias decreases with increasing sample size. 3.4.2 confidence interval interval for which it can be stated with a given
39、 confidence level that it contains at least a specified proportion of the population of results, or estimates of parameters defining the population NOTE For example, estimates of Weibull modulus and characteristic strength from a batch of test pieces. 3.4.3 confidence level required probability that
40、 any one estimate will fall within the confidence interval 3.4.4 estimate well-defined value that is dependent on the variation of strengths in the population NOTE The resulting value for a given population can be considered an estimate of a distribution parameter associated with the population as a
41、 whole. 3.4.5 probability density function function f(x) is a probability density function for the continuous random variable x if: 0)( xf (1) and: = 1)( dxxf (2) such that the probability, P, that the random variable x assumes a value between a and b is given by: =xxxmxfmm(4) 00)( = xxf (5) NOTE 1
42、This corresponds with a cumulative distribution function as follows: 0exp1)( = xxxFm(6) 00)( = xxF (7) where m is the Weibull modulus or shape parameter ( 0); is the scale parameter ( 0). NOTE 2 The random variable representing the fracture strength of a ceramic test piece will assume only positive
43、values, and the distribution is asymmetric about the mean. These characteristics rule out the use of the normal distribution amongst others and point to the use of the Weibull distribution or similar skewed distributions. The assumption made in this European Standard is that the Weibull distribution
44、 will approximate to the true distribution of strengths observed. NOTE 3 This European Standard is restricted to the use of the two-parameter Weibull distribution. Other forms, such as the three-parameter method which assumes the existence of a non-zero minimum value for x, are outside the scope of
45、this European Standard. EN 843-5:2006 (E) 8 NOTE 4 The population mean x is related to by: 11xm= +(8) where is the gamma function. The gamma function is sometimes represented by a non-integral factorial: 111mm+ =(9) 3.5.2 Weibull modulus measure of the width of the Weibull distribution defined by pa
46、rameter m in Equation (4) 3.5.3 Weibull characteristic strength strength value at a probability of failure of 0,632 NOTE 1 If the random variable representing the strength of a ceramic test piece is characterized by the above equations, then the probability that a test piece will not sustain a nomin
47、al stress nom, i.e. has a nominal strength f= nom, is given by the cumulative distribution function: 0exp10=fmffP (10) 00 =ffP (11) where Pfis the probability of failure; 0is the Weibull characteristic strength. NOTE 2 Defined in the above manner, the Weibull characteristic strength depends on the t
48、est piece geometry and on the multiaxiality of the stress field applied. NOTE 3 When testing three-point and four-point bend test pieces from the same population, different values of 0will be derived, reflecting different stressed volumes or surface areas in the two geometries. See Annex A for infor
49、mation on the theoretical relationship between strengths of test pieces of different stressed volumes or areas. NOTE 4 Caution is needed in the use of Weibull statistical parameters beyond the population from which they are derived. 4 Symbols For the purposes of this document, the following symbols apply. A component surface area EN 843-5:2006 (E) 9 Aeffeffective component surface area b unbiasing factor for Weibull modulus es
