EN 843-5:2006
(Main)Advanced technical ceramics - Mechanical properties of monolithic ceramics at room temperature - Part 5: Statistical analysis
Advanced technical ceramics - Mechanical properties of monolithic ceramics at room temperature - Part 5: Statistical analysis
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 nominally 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 there 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 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 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 calculation procedures as method A of ISO 20501:2003, but does not provide a method for dealing with censored data (method B of ISO 20501).
Hochleistungskeramik - Mechanische Eigenschaften monolithischer Keramik bei Raumtemperatur - Teil 5: Statistische Auswertung
Dieser Teil von EN 843 legt ein Verfahren für die statistische Auswertung von Festigkeitsdaten von Keramik in Form einer Zweiparameter-Weibull-Verteilung mit einem Schätzwert nach der Maximum-Likelihood-Methode fest. Es wird vorausgesetzt, dass der Datensatz aus einer Prüfreihe unter nominell identischen Bedingungen gewonnen wurde.
ANMERKUNG 1 Prinzipiell ist die Weibull-Analyse nur streng gültig bei linear-elastischem Bruchverhalten bis zum Punkt des Versagens, d. h. für einen vollkommen spröden Werkstoff, und unter Bedingungen, unter denen die Festigkeit begrenzende Fehler nicht in Wechselwirkung stehen und unter denen es nur eine einzige Festigkeit begrenzende Fehler-Grundgesamtheit gibt.
Tritt vor Brüchen subkritisches Risswachstum oder Kriechverformung auf, kann die Weibull-Analyse immer noch ange¬wendet werden, wenn die Ergebnisse einer Weibull-Verteilung folgen, numerische Parameter können sich aber abhängig von der Größe dieser Effekte verändern. Da es unmöglich ist, mit Sicherheit das Ausmaß des Auftretens von subkri¬tischem Risswachstum oder Kriechverformung anzugeben, lässt diese Europäische Norm die Analyse der allgemeinen Situation zu, in der Risswachstum oder Kriechen aufgetreten sein können, vorausgesetzt, dass berücksichtigt wird, dass die aus der Analyse abgeleiteten Parameter nicht die gleichen sein können wie die aus den Daten ohne subkritisches Risswachstum oder Kriechen abgeleiteten.
ANMERKUNG 2 Diese Europäische Norm wendet die gleichen Verfahrensweisen bei der Berechnung an wie Verfahren A von ISO 20501:2003 [1], liefert jedoch kein Verfahren, das sich mit zensierten Daten beschäftigt (Verfahren B von ISO 20501).
Céramiques techniques avancées - Propriétés mécaniques des céramiques monolithiques à température ambiante - Partie 5: Analyse statistique
La présente partie de l'EN 843 décrit une méthode d'analyse statistique des données de résistance mécanique des céramiques, sous forme d'une répartition de Weibull à deux paramètres en utilisant une technique d'estimation du maximum de vraisemblance. Cette méthode suppose que l'ensemble de données a été obtenu à partir d'une série d'essais effectués dans des conditions nominalement identiques.
NOTE 1 En principe, l'analyse de Weibull n'est jugée strictement valable que dans le cas d'un comportement élastique linéaire à l'instant de la rupture, c'est-à-dire pour un matériau parfaitement fragile, et dans des conditions où les défauts limitant la résistance mécanique n'interagissent pas et où n'existe qu'une seule population de défauts limitant la résistance mécanique.
Si une propagation sous-critique de la fissure ou une déformation par fluage précède la rupture, l'analyse de Weibull peut encore être appliquée si les résultats s'adaptent à une répartition de Weibull, mais les paramètres numériques peuvent varier selon l'amplitude de ces effets. Étant donné qu'il est impossible d'être certain de l'amplitude de la propagation sous-critique de la fissure ou de la déformation par fluage, la présente Norme européenne permet d'analyser la situation générale dans laquelle une propagation de la fissure ou un fluage a pu se produire, sous réserve qu'il soit reconnu que les paramètres déduits de l'analyse peuvent ne pas être identiques aux paramètres déduits des données obtenues sans propagation sous-critique de la fissure ou sans fluage.
NOTE 2 La présente Norme européenne utilise les mêmes procédures de calcul que celles de la méthode A de l'ISO 20501:2003 [1], mais ne fournit aucune méthode traitant des données tronquées (méthode B de l'ISO 20501).
Sodobna tehnična keramika - Monolitna keramika - Mehanske lastnosti pri sobni temperaturi – 5. del: Statistična analiza
General Information
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Standards Content (Sample)
SLOVENSKI STANDARD
01-maj-2007
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SIST ENV 843-5:2000
6RGREQDWHKQLþQDNHUDPLND0RQROLWQDNHUDPLND0HKDQVNHODVWQRVWLSULVREQL
WHPSHUDWXUL±GHO 6WDWLVWLþQDDQDOL]D
Advanced technical ceramics - Mechanical properties of monolithic ceramics at room
temperature - Part 5: Statistical analysis
Hochleistungskeramik - Mechanische Eigenschaften monolithischer Keramik bei
Raumtemperatur - Teil 5: Statistische Auswertung
Céramiques techniques avancées - Propriétés mécaniques des céramiques
monolithiques a température ambiante - Partie 5: Analyse statistique
Ta slovenski standard je istoveten z: EN 843-5:2006
ICS:
81.060.30 Sodobna keramika Advanced ceramics
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EUROPEAN STANDARD
EN 843-5
NORME EUROPÉENNE
EUROPÄISCHE NORM
December 2006
ICS 81.060.30 Supersedes ENV 843-5:1996
English Version
Advanced technical ceramics - Mechanical properties of
monolithic ceramics at room temperature - Part 5: Statistical
analysis
Céramiques techniques avancées - Propriétés mécaniques Hochleistungskeramik - Mechanische Eigenschaften
des céramiques monolithiques à température ambiante - monolithischer Keramik bei Raumtemperatur - Teil 5:
Partie 5: Analyse statistique Statistische Auswertung
This 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 this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on 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 translation
under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official
versions.
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, Romania,
Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36 B-1050 Brussels
© 2006 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 843-5:2006: E
worldwide for CEN national Members.
Contents Page
Foreword.3
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 distribution.7
4 Symbols.8
5 Significance and use .10
6 Principle of calculation .11
6.1 Maximum likelihood method .11
6.2 Bias correction.12
6.3 Confidence interval.12
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 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 calculating Weibull parameters.23
Annex D (informative) BASIC program for calculating Weibull parameters .28
ˆ
Annex E (normative) Unbiasing factors for estimation of Weibull modulus, m .33
Annex F (normative) Confidence factors for characteristic strength, σˆ .34
ˆ
Annex G (normative) Confidence factors for Weibull modulus, m .36
Annex H (informative) Worked examples.38
Annex I (informative) Example test report .43
Bibliography .45
Foreword
This document (EN 843-5:2006) has been prepared by Technical 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 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 Young’s modulus, shear modulus and Poisson’s 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 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, 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.
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 nominally 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 there 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 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 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 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 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.
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 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], 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.
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
3.1.3
extraneous flaw
type of flaw observed in the fracture 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
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 example 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 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 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 distributions
(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 short 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 typically no longer valid.
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 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 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 pro
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