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、4g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42g43g55g3g47g36g58Licensed Copy: Wang Bin, na, Wed Apr 04 07:43:02 GMT+00:00 2007, Uncontrolled Copy, (c) BSIBS EN 843-5:2006This British Standard was published under the authority
3、 of the Standards Policy and Strategy Committee on 31 January 2007 BSI 2007ISBN 978 0 580 49983 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 It supersedes DD ENV 843-5:1997 which is withdrawn.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
4、entrusted to Technical Committee RPI/13, Advanced technical ceramics.A list of organizations 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.Co
5、mpliance with a British Standard cannot confer immunity from legal obligations.Amendments issued since publicationAmd. No. Date CommentsLicensed Copy: Wang Bin, na, Wed Apr 04 07:43:02 GMT+00:00 2007, Uncontrolled Copy, (c) BSIEUROPEAN STANDARDNORME EUROPENNEEUROPISCHE NORMEN 843-5December 2006ICS 8
6、1.060.30 Supersedes ENV 843-5:1996 English VersionAdvanced technical ceramics - Mechanical properties ofmonolithic ceramics at room temperature - Part 5: StatisticalanalysisCramiques techniques avances - Proprits mcaniquesdes cramiques monolithiques temprature ambiante -Partie 5: Analyse statistique
7、Hochleistungskeramik - Mechanische Eigenschaftenmonolithischer Keramik bei Raumtemperatur - Teil 5:Statistische AuswertungThis European Standard was approved by CEN on 11 November 2006.CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving
8、 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 application to the Central Secretariat or to any CEN member.This European Standard exists in three official versions (
9、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 has the same status as the officialversions.CEN members are the national standards bodies of Austria, Belgium, Cyprus, C
10、zech Republic, Denmark, Estonia, Finland, France,Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania,Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATIONCOMIT EUROP
11、EN 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 reservedworldwide for CEN national Members.Ref. No. EN 843-5:2006: ELicensed Copy: Wang Bin, na, Wed Apr 04 07:43:02 GMT+00:00 2007
12、, Uncontrolled Copy, (c) BSIEN 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 Significance and use .10 6 Prin
13、ciple 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 confidence interval.14 8 Test
14、 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 (informative) PASCAL program for calc
15、ulating 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) Confidence factors for Wei
16、bull modulus, m36 Annex H (informative) Worked examples38 Annex I (informative) Example test report 43 Bibliography 45 Licensed Copy: Wang Bin, na, Wed Apr 04 07:43:02 GMT+00:00 2007, Uncontrolled Copy, (c) BSIEN 843-5:2006 (E) 3 Foreword This document (EN 843-5:2006) has been prepared by Technical
17、Committee CEN/TC 184 “Advanced technical ceramics”, the secretariat 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
18、withdrawn at the latest by June 2007. This document supersedes ENV 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 an
19、d Poissons ratio Part 3: Determination of subcritical crack growth 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
20、 Revision of Part 5, Part 6 was available as a Technical Specification. 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, Finlan
21、d, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom. Licensed Copy: Wang Bin, na, Wed Apr 04 07:43:02 GMT+00:00 2007, Uncontrolled Copy, (
22、c) BSIEN 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 Weibull distribution using a maximum likelihood estimation technique. It assumes that the data set has been obtained from a series of tests under nom
23、inally identical conditions. NOTE 1 In principle, Weibull analysis is considered to be strictly valid for the case of linear elastic fracture behaviour to 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 t
24、here is only a single strength-limiting flaw population. If subcritical crack growth or creep deformation preceding fracture occurs, Weibull analysis can still be applied if the results fit a Weibull distribution, but numerical parameters may change depending on the magnitude of these effects. Since
25、 it is impossible to be certain of the degree to which subcritical crack growth or creep deformation has occurred, this European Standard permits the analysis of the general situation where crack growth or creep may have occurred, provided that it is recognized that the parameters derived from the a
26、nalysis 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 calculation 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 r
27、eferences 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. EN 843-1:2006, Advanced technical ceram
28、ics Mechanical properties of monolithic ceramics at room temperature Part 1: Determination of flexural strength EN ISO/IEC 17025, General requirements for the competence of testing and calibration laboratories (ISO/IEC 17025:2005) 3 Terms and definitions For the purposes of this document, the terms
29、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, or other source literature on statistics. 3.1 Flaws 3.1.1 flaw inhomogeneity, discontinuity or structural feature in a material which when loaded
30、 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. NOTE 2 The term flaw should not be taken as meaning the material is functionally defective, but rather as containing an inevitable microstructu
31、ral inhomogeneity. 3.1.2 critical flaw flaw acting as the source of failure Licensed Copy: Wang Bin, na, Wed Apr 04 07:43:02 GMT+00:00 2007, Uncontrolled Copy, (c) BSIEN 843-5:2006 (E) 5 3.1.3 extraneous flaw type of flaw observed in the fracture of test pieces manufactured for the purposes of a tes
32、t 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 3.2.2 critical flaw size distribution distribution of
33、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 example is when every test piece contains flaw type A an
34、d 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 type which compete with each other to cause failure 3.
35、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 example, each test piece contains defects exclusively
36、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 distributions (3.2.4) 3.3 Mechanical evaluation 3.3.1 fr
37、actography 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 short period of time to ascertain whether it contains a se
38、rious 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 typically no longer valid. Licensed Copy: Wang Bin, na, Wed Ap
39、r 04 07:43:02 GMT+00:00 2007, Uncontrolled Copy, (c) BSIEN 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 Sta
40、tistical terms 3.4.1 bias consistent 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 fo
41、r which it can be stated with a given 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 confi
42、dence level required probability that 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 paramete
43、r associated with the population as a 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
44、: =xxxmxfmm(4) 00)( = xxf (5) NOTE 1 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
45、test piece will assume only positive 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 Stan
46、dard is that the Weibull distribution 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 v
47、alue for x, are outside the scope of this European Standard. Licensed Copy: Wang Bin, na, Wed Apr 04 07:43:02 GMT+00:00 2007, Uncontrolled Copy, (c) BSIEN 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 represent
48、ed by a non-integral factorial: 111mm+ =(9) 3.5.2 Weibull modulus measure of the width of the Weibull distribution defined by parameter 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
49、of a ceramic test piece is characterized by the above equations, then the probability that a test piece will not sustain a nominal 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 test
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