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GB/T 40005-2021: Weibull statistics for strength data of fine ceramics
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Weibull statistics for strength data of fine ceramics
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Basic data | Standard ID | GB/T 40005-2021 (GB/T40005-2021) | | Description (Translated English) | Weibull statistics for strength data of fine ceramics | | Sector / Industry | National Standard (Recommended) | | Classification of Chinese Standard | Q32 | | Word Count Estimation | 30,376 | | Issuing agency(ies) | State Administration for Market Regulation, China National Standardization Administration | GB/T 40005-2021: Weibull statistics for strength data of fine ceramics---This is a DRAFT version for illustration, not a final translation. Full copy of true-PDF in English version (including equations, symbols, images, flow-chart, tables, and figures etc.) will be manually/carefully translated upon your order.
(Weibull statistical analysis method for the strength data of fine ceramics)
ICS 81.60.30
Q32
National Standards of People's Republic of China
Weibull statistical analysis method for the strength data of fine ceramics
[ISO 20501.2019,Fineceramics(advancedceramics,advancedtechnical
Released on 2021-05-21
2021-12-01 implementation
State Administration of Market Supervision and Administration
Issued by the National Standardization Management Committee
Weibull statistical analysis method for the strength data of fine ceramics
1 Scope
This standard specifies the parameter estimation method of the probability distribution of the uniaxial strength data of fine ceramics characterized by brittle failure.
Note. The failure strength of fine ceramics is treated as a continuous random variable. Under normal circumstances, samples with fixed geometric dimensions fail under loading.
The load at the time of failure is recorded, and the resulting failure stress is used to estimate the parameters related to the overall distribution.
This standard applies to the two-parameter Weibull distribution based on failure strength. In addition, this standard limits test samples (tensile, bending, plus
The load ring, etc.) is subject to uniaxial stress. 6.4 and 6.5 outline the method of correcting Weibull parameter estimation deviation, and from all fractures originating from a single defect
The overall (ie, single failure mode) data set calculates the confidence interval for these estimates. For samples where the fracture originates from multiple independent defect populations
(For example, competitive failure mode), the methods of bias correction and confidence interval calculation in 6.4 and 6.5 are not applicable.
2 Normative references
The following documents are indispensable for the application of this document. For dated reference documents, only the dated version applies to this article
Pieces. For undated reference documents, the latest version (including all amendments) is applicable to this document.
GB/T 3358.1 Statistical vocabulary and symbols Part 1.General statistical terms and terms used in probability (GB/T 3358.1-
2009, ISO 3534-1.2006, IDT)
3 Terms and definitions
The following terms and definitions defined in GB/T 3358.1 apply to this document.
3.1 Defects overall
3.1.1
Flaw
Areas with inhomogeneous or discontinuous features in the material are likely to cause stress concentration and fracture under external load.
Note. When the defect becomes the source of material failure, the defect is the key factor of material failure.
3.1.2
Censoreddata
Intensity data (ie a sample) includes delayed observations caused by multiple competing or coexisting defects.
Note. Fracture analysis clearly shows that there are three types of concurrent defect distributions in a sample (the sample can also contain any number of concurrent defect distributions), respectively
Denoted as distribution A type, distribution B type and distribution C type. According to the fracture analysis, the strength of each sample corresponds to a defect distribution leading to failure. in
When estimating the characteristic parameters of the intensity distribution related to the defect distribution type A, all samples should be included in the analysis (not just due to the distribution of type A defects).
Failed samples) to ensure the efficiency and accuracy of the obtained parameter estimates. The strength of the failed sample due to the distribution B type (or distribution C type) defect can be
It is regarded as a right censored observation relative to the distribution type A defect, and the distribution type A defect is delayed due to the failure of the distribution type B (or distribution type C) defect
The resulting failure, limiting or censoring the distribution of type A defect information in the sample [2]. Samples damaged by defects in distribution type B (or distribution type C)
Among them, the most severe distribution type A defect dominates with a higher intensity (and therefore on the right) the observed failure intensity. However, there is currently no information about this intensity difference
Information of different levels. This standard's method of analyzing censored data can use incomplete information to provide effective and relatively unbiased estimates of distribution parameters.
3.1.3
Competing failure modes
Different types of fracture source phenomena caused by coexistent (competitive) defect distribution.
t The normalized value of the confidence interval for calculating the Weibull feature intensity defined by formula (17)
UF unbiased factor
V The volume of the sample subjected to tensile stress
V0 unit volume
Veff effective volume
β Weibull scale parameter
σ uniaxial tensile stress
σ^ Estimated average intensity
σj Maximum stress when the jth sample fails
σ0 Weibull material scale parameter defined by formula (7) (strength corresponds to unit volume or area)
σ^0 Estimated value of Weibull material scale parameter
σθ Weibull characteristic intensity defined by formula (5) (related to the test sample)
σ^θ Estimated value of Weibull characteristic intensity
5 Significance and use
5.1 This standard can be used by experimenters to estimate Weibull distribution parameters of strength data. These parameters describe the fracture of fine ceramics for different purposes.
The statistical distribution of strength can be used for reliability evaluation during mechanical design. The intensity value depends on the sample size and geometry. Parameter Estimation
The value can be calculated by (m^,σ^θ) of a given geometric shape sample, but it is recommended that the report be converted into an estimate of material-specific parameters (m^,σ^0)
value. In addition, different defect distributions (for example, failure due to inclusions or processing damage) have their own unique strength distribution parameters. For typical
Please refer to Appendix C for details on the conversion of estimated values of sample parameters of any shape and defect distribution.
5.2 This standard provides two data processing methods, A and B, for different purposes.
Method A is suitable for simple analysis of samples whose dominant strength defects are known or assumed to come from a single population. So there is no need for fracture points
Analysis to identify defect types and classify different samples. This method is suitable for simple material screening.
Method B is suitable for the design and analysis of final parts, that is, there is a general situation of competitive defects. This method requires fracture analysis
Defect origin of dominant strength, determine the overall type of defect.
5.3 Method A analyzes the intensity data set and obtains the estimated value of Weibull modulus m^ and the estimated value of characteristic intensity σ^θ and its confidence interval if any
If necessary, the average intensity can also be calculated. Finally, the failure data is shown graphically in the test report. When the confidence interval is large, the result of the analysis should not be
It is used to analyze situations that are extrapolated beyond the existing confidence interval. Effective extrapolation analysis (about effective volume Veff and/or small failure probability)
The premise is that the defects of all samples are of the same type.
5.4 Method B is to characterize the origin of fracture by fracture analysis of each failed sample. Filter out the outliers of each defect distribution. If all
Defects originate from a single defect distribution, and the unbiased estimate of Weibull modulus, the confidence zone of Weibull modulus and Weibull characteristic intensity estimate can be calculated
between. If the fracture originated from one or more defect types, separate relevant data sets for each defect type, and compare these data sets separately
Perform censoring analysis. The failure data is shown graphically in the final test report. When using the analysis results for design purposes, it should be noted that the assumptions are
The part and the sample have the same defect type.
6 Method A. Maximum likelihood method parameter estimation of a single defect population
6.1 Summary
This standard is based on the maximum likelihood method for parameter estimation (see References [13], [14], [20] and [21]). Use maximum likelihood
The parameter estimate obtained is unique (two-parameter Weibull distribution), and as the number of samples increases, the statistical estimate
The calculation method more effectively approximates the real population.
Appendix E
(Informative appendix)
Analysis of samples with uncertain sources of fracture
E.1 Four options
E.1.1 Overview
7.2.2 describes the four options a) ~ d) when the experimenter encounters an uncertain fracture source during fracture analysis. E.1.2~E.1.5 further
These four options are defined, and the applicable and non-applicable situations are listed.
E.1.2 Option a)
Option a) involves using all available fracture analysis information to subjectively classify samples of unknown fracture sources as previously identified fracture sources
classification. Many samples with unknown fracture sources have partial fracture information but are considered insufficient for correct identification and classification. (It should be pointed out that
The degree of certainty required for "correct identification" of fracture source defects varies among different fracture analysts). under these circumstances,
Option a) allows the experimenter to use incomplete fracture analysis information to assign unidentified fracture sources to the previously determined defect classification. Such as
If partial fracture analysis information is available, this option is preferred. For example, the fracture analysis of a tensile sample shows that the fracture originated from the surface of the sample
Or it is very close to the surface of the sample, but the fracture initiation defect cannot be "correctly identified". Other samples from the same sample were determined to be due to lack of processing
Sink and fail. Usually processing damage is often difficult to identify. Therefore, in this case, use option a) and infer that the origin of the sample fracture is
The work injury is reasonable. The test report should clearly record each sample of unknown fracture source classified by this (or any other) option. however,
The conclusion about the processing damage in this example may be wrong; for example, the fracture initiation defect may be a "typical microscopy" located near the surface of the specimen.
Structural features" (mainstreammicrostructuralfeature)[3][12] (usually difficult to distinguish and identify). This misclassification is lacking in
It is inevitable that the source of the fracture is correctly identified.
E.1.3 Option b)
Option b) Designate unidentified fracture sources as the most similar strength sample fracture source classification. The samples with the closest intensity should have "correct knowledge"
The fracture source of “Don’t” [not use options a)~d)]. Take the tensile sample crushed at the time of failure as an example, the fracture source has been destroyed and lost, but the fracture
The crack is obviously caused by internal defects. Other samples in the sample mainly contain inclusions and macropores, which are correctly identified volume distribution fractures.
Source classification. When sorting all the breaking strengths, the samples that are closest to the strength of the samples with unknown breaking sources are the ones that are damaged by inclusions. Make
Use option b) to classify this sample as an inclusion. When the samples are arranged in order of breaking strength, the coexisting (competitive) defect distribution
The same fault sources tend to be grouped together, and the rationality of choosing b) increases. Therefore, for randomly unidentified samples, the most likely to break
The source classification is the classification of the samples with the closest intensity. If the above example changes slightly, option b) may be inappropriate. For example, the most intense
The fracture source classification of the close sample is a processing defect, then option b) will lead to a conclusion that is inconsistent with the fracture analysis result, that is, the failure is caused by the internal
Caused by a defect. The conclusion of the fracture analysis takes precedence over the conclusion of option b).
E.1.4 Option c)
Option c) Assume that the unidentified fracture source belongs to a new and unclassified defect type, and analyze these fracture sources in the censored data
As a separate defect distribution. This situation may occur when the fracture analyst cannot identify the type of defect because of the characteristics of the defect.
The signs are very subtle and difficult to distinguish. In this case, the fracture analyst may always be unable to locate, identify and classify the source of the fracture. Hard to identify
The types of defects include processing damage, atypical areas with a large number of micro-pores, and typical microstructure features. Option c) can be used for a group with similar
Or unidentified fracture source samples with obvious associated characteristics. Unfortunately, in many cases, option c) is incorrect. Use this option to
It can cause major errors in parameter estimation; for example, when several unidentified fracture source samples are concentrated in the high-strength part of the intensity distribution. These ones
The fracture source may belong to a previously determined classification, but small fracture source defects are more difficult to locate, or due to large fragments caused by high-strength samples.
Lost. If you use option c) to classify these high-strength samples as new defects, there will be errors in the parameter estimation of the correct defect classification.
Know the magnitude of the bias error.
E.1.5 Option d)
Option d) involves removing samples with unknown fracture sources from the samples (ie removing the corresponding data points from the intensity list). Unless it is clear
For the reasons, this choice is rarely appropriate, and this standard does not recommend it. Option d) Only when the sample with unknown fracture source is in the full intensity distribution
Valid for random distribution within the range and defect classification. Few reasonable physical processes can produce such random selection. Options
A reasonable example of d) is a data set containing 50 samples, of which the first 10 fractured samples (in order of testing) are in the test
Later, it was misplaced or destroyed before the fracture analysis. Therefore, these unidentified samples are produced through a random process.
In other words, the 10 intensity values are randomly distributed through the remaining 40 intensity values, and the 10 fracture source classifications pass the remaining 40 fracture source classes.
Type random distribution. (In this example, option b) can also be considered. When the uncertainty of the source of sample fracture is due to the high-strength test sample
If it is maliciously crushed and caused by the loss of fragments containing the fracture source, option d) is inappropriate. This situation mostly occurs when the intensity distribution is high
Therefore, it is uncertain that the fracture source will not show randomness of strength.
E.2 How to correctly apply the four options
E.2.1 When there is partial fracture analysis information, it is best to choose option a) so that this information can be used as far as possible in the classification of the fracture source. Options
d) It should be used only in abnormal situations where it can be proved that the source of unknown fracture is randomly generated.
E.2.2 There may be cases where multiple options are used in a single data set; for example, in 5 samples with unknown fracture sources, 3 samples
It can be classified according to partial fracture analysis information [option a)], and the remaining 2 samples have no fracture analysis information, you can use option b)
sort.
E.2.3 When a set of data contains samples of unknown fracture sources, the test report (see Chapter 9) should fully describe these samples and which ones are used.
These options classify the samples.
E.2.4 If unidentified fracture sources often appear in the low-strength part of the strength distribution, then special attention is required. Strength analysis is usually outside
The result is lower intensity and lower failure probability than the observed data set. Appropriate statistical evaluation and designation of the fracture source of the low-strength part
Classification is particularly important because low-intensity distributions usually dominate this type of extrapolation.
E.2.5 When there are only a few unknown fault sources, the impact of misclassification is small. When there are more than 5% or 10% of unknown fracture sources,
A large amount of statistical deviation may occur in parameter estimation. When used in design, it is important to select the appropriate option from E.1.2 to E.1.5
Yes, and should be carefully demonstrated in the test report. In this design application, it is best to analyze the possibility of multiple options; for example, one
Among the 50 samples in the group, there are 10 samples of unknown fracture source (without partial fracture information), you can use option b) for analysis first, and then use
Use option c) for analysis. The results of the two analyses can be used to estimate the service behavior of the designed components. If you need to use components
For conservative predictions of service behavior, it is advisable to use the more conservative results of the two analyses.
E.2.6 Finally, if most or all of the samples in the sample contain unknown fracture sources, the analysis of censored data according to this standard is
impossible. The intensity should be plotted on the Weibull probability axis. If the data shows obvious curvature (upward concave), this is two or more coexisting
The characteristics of defect distribution, then the method described in this standard can be used after further refinement.
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