Journal of Testing and Evaluation, Vol. 37, No. 3Paper ID JTE101649

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George D. Quinn,1 Brian T. Sparenberg,2 Philip Koshy,3 Lewis K. Ives,1 Said Jahanmir,4 and

Dwayne D. Arola2

Flexural Strength of Ceramic and Glass Rods

ABSTRACT: Flexural testing is the most common method used to measure the uniaxial tensile strength of ceramics and glasses. Althoughstandard test methods have been developed for rectangular specimens, cylindrical rod specimens may be preferred in many cases. This paper sum-marizes how rods have been tested in the past, identifies key experimental errors and remedies, and serves as the foundation for a new standard testmethod for ceramics and glasses.

KEYWORDS: ASTM C-1684, ceramics, cradles, glass, flexural strength, three-point loading, four-point loading, brittle materials, standard,rods, cylindrical specimens, errors, silicon nitride, strain gage, Weibull statistics, wedging error, concentrated load error, friction error, largedeflection, contact cracks, initial curvature error, eccentric loading error, wrong span error, poor articulation, contact point tangency shifterror

Introduction

Flexural strength testing has long been a staple technique for mea-suring the uniaxial tensile strength of brittle materials such as ce-ramics and glasses. Direct tension tests are less commonly used dueto the large test piece size, the high costs of specimen fabricationand testing, and the difficulties of gripping without misalignments.Both three- and four-point flexure configurations are used as shownin Fig. 1. Four-point is preferred for most applications and it isoften qualified by an additional descriptor relating the fractionalsize of the moment arm, a, to the outer span length, Lo. For ex-ample, 14 -point four-point is the case of a=Lo /4. The flexuralstrength test generates data for many purposes including materialcharacterization, materials development, and design. Results fromone size and testing configuration can be scaled to alternative con-figurations and sizes by Weibull statistical analysis, provided thatkey assumptions are fulfilled. Done improperly, flexural strengthtesting can give faulty data with excessive variability and errorsthat can reach the order of tens of percent. The errors can be eithersystematic or random.

It is widely recognized that brittle material strengths are statisti-cal in nature. Specimen-to-specimen strength differences arisefrom variations in the flaws and the microstructure. Hence, it is nec-essary to use sample sets of ten or more specimens for even thesimplest of goals such as determining an average strength for ma-terial ranking, material development, or materials specification pur-poses. Random and systematic testing errors can generate faultydata that obscure or spoil even these simple tasks. Such errors canalso contaminate data for other tests such as fracture toughness ex-periments that use precracked beams in bending. If the goal of thetesting is to estimate the intrinsic strength scatter of a material, anysuperimposed testing variability will render estimates incorrect.The use of statistics to account for variability from an assigned

Manuscript received January 3, 2008; accepted for publication February 19,2009; published online March 2009.

1National Institute of Standards and Technology, Gaithersburg, MD 20899.2University of Maryland, Baltimore, MD 21250.3Now with McMaster University, Hamilton, Ontario, L8S 4L7 Canada.4

Now with MITI Heart, Albany, NY 12205.

Copyright 2009 by ASTM International, 100 Barr Harbor Drive, PO Box C700, Wpyright by ASTM Int'l (all rights reserved); Mon Apr 20 14:51:24 EDT 2009wnloaded/printed byphanie MacGilfrey (Mohawk Innovative Technology Inc.) pursuant to License Agre

cause, i.e., the materials intrinsic flaw and microstructural varia-tions, is different from the normal usage of statistics in experimen-tal work. This creates a requirement that the experimental error ofceramic strength test data must be negligible compared to the in-trinsic material variability.

Galileo Galilei analyzed the bending configuration in some de-tail in his book Dialogues Concerning Two New Sciences and con-cluded in Proposition 4 on day 3: In cylinders of equal length the resistance to fracture increases in the same ratio as the cube ofthe diameter [1]. Flexure testing has traditionally emphasizedrectangular specimens which could be sliced and diamond wheelground quite easily. At one time a myriad of testing and specimenconfigurations abounded and experimental errors were severe orunknown. Duckworths seminal paper in 1951 [2] was the first toidentify many of the errors in flexural strength testing of ceramics.He and his colleagues expanded the work in 1976 [3]. Jayatilakahad a section on flexure in his 1979 book [4] that identified fiveerrors. Baratta and colleagues [5,6], in the 1980s refined and addedto these error analyses and paved the way for the adoption of stan-dard procedures for advanced or technical ceramics [712]. Todaythe most common testing configuration is a 3 mm by 4 mm crosssection rectangular specimen on 20 mm by 40 mm span four-pointflexure fixtures, but 10 mm by 30 mm spans are sometimes used inAsia. Three-point testing is still an option, but four-point is pre-ferred since more material is exposed to high stress. An in-depthreview of flexure strength testing was presented by Quinn and Mor-rell [13]. We estimated that over 90 % of flexure testing on ceramicsis done with rectangular specimens. Rod specimens are preferred insome cases particularly if the material is made or utilized in a roundshape.

Glass rods have commonly been tested in flexure often due totheir low cost and convenience. ASTM International has a standardfor flexure strength of glass rods, C158 [14], that was originallyprepared in 1940. Fixed loading points of approximately 3 mm ra-dius are prescribed, but a cautionary note about high contactstresses is included. The support edges may have a curvature ofapproximately 76 mm in the plane of the bearing edge to aid align-ment of the specimens, as shown in Fig. 2. The specimen size isoptional although the minimum diameter must be 4.76 mm

3/16 in.. The length to diameter ratio has to be 10 or greater. El-

est Conshohocken, PA 19428-2959. 1

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2 JOURNAL OF TESTING AND EVALUATION

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liptical cross section and slightly bowed specimens are allowed.The moment arm has to be at least four times the diameter. A seri-ous shortcoming is there is no provision for friction relief. In addi-tion, the curved knife edges alleviate but do not eliminate the con-tact stresses of the crossed cylindrical surfaces.

The strength of electrical porcelains or insulating whitewaresalso is often measured with cylindrical rods in flexure. Even

FIG. 1Flexure testing is commonly done in three-point (a) or four-point con-figurations (b). The fractional location of the inner loading points relative to theoverall span is used to specify the configuration. For example, with a=Lo/4, theconfiguration is deemed 14-point four-point flexure.

FIG. 2Schematic of a test fixture for gl

pyright by ASTM Int'l (all rights reserved); Mon Apr 20 14:51:24 EDT 2009wnloaded/printed byphanie MacGilfrey (Mohawk Innovative Technology Inc.) pursuant to License Agre

Weibull [15] cited porcelain rod strengths to support his statisticalmodel. Porcelain specimens of length 155178 mm 6 in.7 in.with 25 mm 1 in. diameter were common and were usuallyloaded in three-point mode on a 127 mm 5 in. outer span. Thisconfiguration was listed as one of many tentative test methods ina fascinating 1928 topical issue of the Journal of the American Ce-ramic Society [16]. Very few details of the fixturing were given inthe early papers, but fixed knife edges were the norm. An ASTMInternational standard for whitewares, C674 [17], has large speci-mens suitable for whitewares and was originally prepared in 1971to replace two earlier standards. It includes an option for testing153 mm13 mm 6 in.0.5 in. long cylindrical rods of diameters6.4 mm 1/4 in. to 28.6 mm 1.125 in.. Fixtures with fixed knifeedges located 127 mm 5 in. apart or 76 mm 3 in. for the6.4 mm diameter rods are specified.

Many advanced or technical ceramics have been tested in rodflexure form. Often the ceramic is in the form of extruded rods thatare broken in their as-fabricated state. The flexure configuration isideal for measuring the effects of surface condition on strength ofstructural ceramics. Strengths of transversely and longitudinallyground rods with a variety of grinding steps and annealing treat-ments are commonly compared. The present study was part of aNIST project to characterize grinding and machining damage inground advanced ceramics and glasses [1820]. Thermal shock in-vestigations on advanced ceramics frequently utilized cylindricalflexure specimens in order to create symmetric thermal gradientsand to eliminate edge effects.

A few studies compared flexure strengths of cylindrical andrectangular specimens for the same material. Sometimes the datawere comparable and in other cases they were not. One study onporcelain [21] suggested round rod test data were superior, but thiswas probably due to the warpage of the rectangular specimens andthe use of nonarticulating fixtures or due to intrinsic strength differ-ences between the two specimen types. Cylindrical and square as-fired reaction bonded silicon nitride specimens were tested forcomparison by Newnham [22]. Four-point flexure was applied to50 mm long specimens with either 4 mm by 4 mm square or 4 mmdiameter cross sections. The strengths were quite similar and dif-fered by no more than 5 %. The cylindrical specimens should havebeen 8 % stronger on the basis of the Weibull effective volumes.Ne