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**Significance and Use**

5.1 Two- and three-parameter formulations exist for the Weibull distribution. This practice is restricted to the two-parameter formulation. An objective of this practice is to obtain point estimates of the unknown Weibull distribution parameters by using well-defined functions that incorporate the failure data. These functions are referred to as estimators. It is desirable that an estimator be consistent and efficient. In addition, the estimator should produce unique, unbiased estimates of the distribution parameters (6). Different types of estimators exist, including moment estimators, least-squares estimators, and maximum likelihood estimators. This practice details the use of maximum likelihood estimators.

5.2 Tensile and flexural specimens are the most commonly used test configurations for graphite. The observed strength values depend on specimen size and test geometry. Tensile and flexural test specimen failure data for a nearly isotropic graphite (7) is depicted in Fig. 1. Since the failure data for a graphite material can be dependent on the test specimen geometry, Weibull distribution parameter estimates (m^, σ^_{θ}) shall be computed for a given specimen geometry.

5.3 Many factors affect the estimates of the distribution parameters. The total number of test specimens plays a significant role. Initially, the uncertainty associated with parameter estimates decreases significantly as the number of test specimens increases. However, a point of diminishing returns is reached where the cost of performing additional strength tests may not be justified. This suggests a limit to the number of test specimens for determining Weibull parameters to obtain a desired level of confidence associated with a parameter estimate. The number of specimens needed depends on the precision required in the resulting parameter estimate or in the resulting confidence bounds. Details relating to the computation of confidence bounds (directly related to the precision of the estimate) are presented in 8.3 and 8.4.

**1. Scope**

1.1 This practice covers the reporting of uniaxial strength data for graphite and the estimation of probability distribution parameters for both censored and uncensored data. The failure strength of graphite materials is treated as a continuous random variable. Typically, a number of test specimens are failed in accordance with the following standards: Test Methods C565, C651, C695, C749, Practice C781 or Guide D7775. The load at which each specimen fails is recorded. The resulting failure stresses are used to obtain parameter estimates associated with the underlying population distribution. This practice is limited to failure strengths that can be characterized by the two-parameter Weibull distribution. Furthermore, this practice is restricted to test specimens (primarily tensile and flexural) that are primarily subjected to uniaxial stress states.

1.2 Measurements of the strength at failure are taken for various reasons: a comparison of the relative quality of two materials, the prediction of the probability of failure for a structure of interest, or to establish limit loads in an application. This practice provides a procedure for estimating the distribution parameters that are needed for estimating load limits for a particular level of probability of failure.

**2. Referenced Documents** *(purchase separately)* The documents listed below are referenced within the subject standard but are not provided as part of the standard.

**ASTM Standards**

C565 Test Methods for Tension Testing of Carbon and Graphite Mechanical Materials

C651 Test Method for Flexural Strength of Manufactured Carbon and Graphite Articles Using Four-Point Loading at Room Temperature

C695 Test Method for Compressive Strength of Carbon and Graphite

C749 Test Method for Tensile Stress-Strain of Carbon and Graphite

C781 Practice for Testing Graphite and Boronated Graphite Materials for High-Temperature Gas-Cooled Nuclear Reactor Components

D4175 Terminology Relating to Petroleum Products, Liquid Fuels, and Lubricants

D7775 Guide for Measurements on Small Graphite Specimens

E6 Terminology Relating to Methods of Mechanical Testing

E178 Practice for Dealing With Outlying Observations

E456 Terminology Relating to Quality and Statistics

**ICS Code**

ICS Number Code 71.060.10 (Chemical elements); 73.040 (Coals)

**UNSPSC Code**

UNSPSC Code 11101507(Graphite)

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**DOI:** 10.1520/D7846-16

**Citation Format**

ASTM D7846-16, Standard Practice for Reporting Uniaxial Strength Data and Estimating Weibull Distribution Parameters for Advanced Graphites, ASTM International, West Conshohocken, PA, 2016, www.astm.org

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