Astm stp 844 1984

METHODS FOR ASSESSING THE STRUCTURAL RELIABILITY OF BRITTLE MATERIALS A symposium sponsored by ASTM Committee E-24 on Fracture Testing San Francisco, Calif., 13 Dec 1982 ASTM SPECIAL TECHNICAL PUBLICATION 844 Stephen W Freiman, National Bureau of Standards, and C, Michael Hudson, NASA Langley Research Center, editors ASTM Publication Code Number (PCN) 04-844000-30 1916 Race Street, Philadelphia, Pa 19103 # Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:11:39 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorize Librarj of Congress Cataloging in Publication Data ^4elhllds for assessing the structural rcliahilitv of brittle materials (AS IM special lechnical publication; 844) -ASTM publication code number (PCN) 04-844000-30.•' Includes bibliographies and index I Fracture mechanics—Congresses Brittleness— Congresses Ceramic materials—Congresses I Freiman S W II Hudson, C M III A S I M Committee F-24 on Fracture I'esting IV Series TA409.M4b l%4" 620.1'126 8,3-7,1253 ISBN 0-803l-02b5-8 C o p y r i g h t (?) b y AMEI^ICAN SOCII-MY POK T E S I I N G AND MArEKLA[.,s 1984 Library of C o n g r e s s C a t a l o g C a r d N u m b e r : 83-73253 NOTE The Society is not responsible, as a body for the statement.s and opinions advanced in this publication ;tl in B.iliinuirc Md, (b) Ociober l')«4 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:11:39 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions auth Foreword The symposium on Methods for Assessing the Structural Reliability of Brittle Materials was held on 13 Dec 1982 in San Francisco Calif The event was sponsored by ASTM Committee E-24 on Fracture Testing Stephen W Freiman National Bureau of Standards, and C Michael Hudson, NASA Langley Research Center, presided as chairmen of the symposium and also ser\'ed as editors of this publication Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:11:39 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions auth Related ASTM Publications Fractography of Ceramic and Metal Failures, STP 827 (1984), 04-827000-30 Fracture Mechanics for Ceramics, Rocks, and Concrete, STP 745 (1981) 04-745000-30 Fractography and Materials Science, STP 733 (1981), 04-733000-30 Fracture Mechanics Applied to Brittle Materials (11th Conference), STP 678 (1979), 04-678000-30 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:11:39 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions auth A Note of Appreciation to Reviewers The quality of the papers that appear in this pubHcation reflects not only the obvious efforts of the authors but also the unheralded, though essential, work of the reviewers On behalf of ASTM we acknowledge with appreciation their dedication to high professional standards and their sacrifice of time and effort ASTM Committee on Publications Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:11:39 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further rep ASTM Editorial Staff Janet R Schroeder Kathleen A Greene Rosemary Horstman Helen M Hoersch Helen P Mahy Allan S Kleinberg Susan L Gebremedhin Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:11:39 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorize Contents Introduction Failure from Contact-Induced Surface Flaws—DAVID B MARSHALL Controlled Indentation Flaws for Construction of Toughness and Fatigue Master Maps^ROBERT F COOK AND BRIAN R LAWN 22 Fatigue Properties of Ceramics with Natural and Controlled Flaws: A Study on Alumina—ARMANDO C GONZALEZ, HEIDI M U L T H O P P , ROBERT F COOK, BRIAN R LAWN, AND STEPHEN W FREIMAN 43 Statistical Analysis of Size and Stress State Effects on the Strength of an Alumina Ceramic—D K SHETTY, A R ROSENFIELD, AND W H DUCKWORTH 57 Dynamic and Static Fatigue of a Machinable Glass Ceramic— MATTHEW B MAGIDA, KATHERINE A FORREST, AND THOMAS M HESLIN 81 Effect of Multb«gion Crack Growth on Proof Testing— SHELDON M WIEDERHORN, STEPHEN W FREIMAN, EDWIN R FULLER, JR., AND HERBERT RICHTER 95 Discussion 116 Fracture Mechanics Analysis of Defect Sizes—GERALD G TRANTINA 117 Effect of Temperature and Humidity on Delayed Failure of Optical Glass Fibers—JOHN E RITTER, JR., KARL JAKUS, AND ROBERT C BABINSKI 131 Discussion 141 Subthreshold Indentation Flaws in the Study of Fatigue Properties of Ultrahigh-Strength Glass—TIMOTHY P DABBS, CAROLYN J FAIRBANKS, AND BRIAN R LAWN 142 Lifethne Prediction for Hot-Pressed Silicon Nitride at High Temperatures—THEO FETT AND DIETRICH MUNZ Copyright Downloaded/printed University by ASTM 154 Int'l (al by of Washington (University Static Fatigue in High-Performance Ceramics—GEORGE D QUINN 177 Requiiements for Flexure Testing of Brittle Materials— FRANCIS I BARATTA 194 Summary 223 Index 227 Copyright Downloaded/printed University by by of STP844-EB/Oct 1984 Introduction How can we ensure that ceramic components designed for gas turbine engines, human prostheses, optical communication lines, and many other varied applications will survive the in-service stresses imposed on them? This symposium on Methods for Assessing the Structural Reliability of Brittle Materials was organized under the auspices of two subcommittees of ASTM Committee E-24 on Fracture Testing—Subcommittee E24.06 on Fracture Mechanics Applications and Subcommittee E24.07 on Fracture Toughness of Brittle Nonmetallic Materials—for the purpose of providing a forum for discussion of current and proposed procedures for using fracture mechanics data in the design of structures made from essentially brittle materials One of the major concerns in the development of new ceramic components is a lack of knowledge regarding the nature of the flaws that can ultimately lead to failure Many of the papers in this volume address this question, as well as the question of the extent to which data obtained on large cracks in fracture mechanics specimens can be used to predict the behavior of "real" flaws The use of crack growth rate data in lifetime prediction and proof-test schemes is also emphasized The field of structural reliability prediction is a fast-moving one Even as this book goes to print, the methods of data acquisition and analysis are being further refined Nevertheless, the editors feel that this volume provides a very useful compilation of papers describing the current state of the science in this field Stephen W Freiman National Bureau of Standards, Washington, D.C 20234; symposium chairman and editor C Michael Hudson NASA Langley Research Center, Hampton, Va 23665; symposium chairman and editor Copyright by ASTM Downloaded/printed by Copyright 1984 b y A S I M International University of Washington Int'l (all www.astm.org (University rights of reserved); Washington) Wed pursuant 216 STRUCTURAL RELIABILITY OF BRITTLE MATERIALS (a) Rectangle with Rounded Corners (b) Rectangle with Chamfered Corners FIG 5—Beam cross section TABLE 12—Percent error in determining flexure stress." b d 1.0 2.0 4.0 0.1 0.4 0.9 1.5 2.4 5.4 9.7 0.1 0.2 0.4 0.8 1.2 2.6 4.6 0 0.1 0.2 0.4 0.6 1.3 2.2 0.1 0.2 0.5 0.9 1.4 2.0 3.4 5.2 0.1 0.1 0.3 0.5 0.7 1.0 1.7 2.6 0.1 0.1 0.1 0.2 0.4 0.5 0.9 1.3 r/d When neglecting corner radii 0,02 0.04 0.06 0.08 0.10 0.15 0.20 c/d When neglecting 45° chamfer 0.01 0.02 0.03 0.04 0.05 0.06 0.08 0.10 'All errors are negative Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:11:39 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized BARATTA ON REQUIREMENTS FOR FLEXURE TESTING 217 Weibull Parameter Estimate and Sample Size The type of analysis that has been used with varying degrees of success to relate failure strengths of brittle materials is attributed to Weibull [/ 7] Many investigators have used this approach to relate strength levels of various types of specimen configurations either on a stressed volume or surface area basis [26] The reader is cautioned that confirmation of such an analysis or lack thereof may well depend on a number of factors, including the test material As examples of such correlation and lack of it, Weibull statistical correlation was justified [26] for reaction-bonded silicon nitride but inappropriate, as reported by Lewis [27], in alumina fabricated by several processes A computer program for statistical evaluation of composite materials is available in Ref 28 This program determines the desirability of a particular probability density function in predicting fracture strength of ranked empirical data The candidate functions include normal, log normal, and Weibull Root mean square error results can be tabulated for each function comparison The effects of statistical ranking can be readily listed in the computer output The data mean and standard deviations with corresponding levels of confidence can be included in the printed results The Weibull parameters, obtained from the maximum likelihood method, and corresponding confidence intervals can be obtained from this program [28] Since a Weibull-type analysis is applicable in many instances, a discussion of Weibull parameter estimates and sample size determination is appropriate and given in the paragraphs to follow Different techniques will produce somewhat different results, according to McLean and Fisher [29], when estimating the Weibull parameters Two statistical methods had been used during preliminary analysis of hot-pressed silicon nitride material strength data, and the results indicated that the estimates of the characteristic value OQ (or scale parameter) were very close whereas the Weibull slope estimates vary and thus would yield considerable differences in the component strength requirement The following is quoted directly from Ref 29 (except for changed reference and figure numbers as appropriate for this paper), because it succinctly addresses the question of proper sample size: "The exact confidence intervals for the parameters are based on the distributions obtained by Monte Carlo methods presented in Thoman et al [30] It is not unexpected that the uncertainty in the estimation of a parameter will increase as the sample size decreases This uncertainty, however, has rarely been quantified The width of the confidence intervals for the parameters is a measure of the uncertainty and aids in the selection of the sample size of a test." Figures and are drawn from Ref 30 "and show the 90% confidence bounds for the Weibull slope and the characteristic value." (Figure differs from that given in Ref 29 in that two additional M values were computed and shown.) "The bounds for the Weibull slope are a function of sample size only, while for the characteris- Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:11:39 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 218 STRUCTURAL RELIABILITY OF BRITTLE MATERIALS :>u UJ 40 \ > a 30 a 20 a '^ 10 ul O ôã -10 o Ê -20 Ui ' If -30 90% CONFIDENCE BAND o « -40 _1 -50 UJ -60 7ol 20 40 60 80 100 120 NUMBER OF SAMPLES FIG 6—Weibull slope error versus sample size 20 40 60 Number of Samples 80 100 120 FIG 7—Characteristic value error versus sample size—90% confidence bands Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:11:39 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions a BARATTA ON REQUIREMENTS FOR FLEXURE TESTING 219 tic value they are a function of both the sample size and the Weibull slope As can be seen from the graphs, the error or uncertainty in estimates from small sample sizes is very large Important judgments and significant analysis should not be based on small samples Sample sizes of at least 30 should be used for all but the most preliminary investigations An uncertainty of +10% in Weibull slope requires more than 120 samples This uncertainty is not peculiar to just ceramics, but is intrinsic to the statistical analysis of data, whether that data be material strength or the life of some electronic component The choice of sample size depends on many factors including cost and time of testing and the degree of conservatism which is acceptable, but erroneous judgments may be made and unacceptable designs pursued if the sample sizes are too small." Loading Speed It is well known that brittle materials are strain-rate and environment sensitive, and thus speed of loading will influence the stress at which failure of the beam occurs To choose a "static" speed, which would ensure no strainrate effect, would increase the susceptibility of some materials to the effect of environment on fracture strength, and, conversely, a high rate of loading will cause a reverse trend Nevertheless, most materials testing facilities utilize testing machines that allow a choice of test speeds, for example, 0.2, 0.5, and 1.0 mm/min Therefore, it is possible to recommend one reference strain rate dependent upon the specimen sizes, and the following formulation for the strain rate e allowed this objective to be realized in Ref for different sizes of four-point and three-point loaded beams: e = -^ (19) where t is the time of the applied load; but since the speed of loading is i y/t, then e= — y (20) where J is the deflection of the beam and s is the constant speed of the testing machine Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:11:39 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 220 STRUCTURAL RELIABILITY OF BRITTLE MATERIALS The deflection at the load points of a four-point loaded beam is „ , 31 - 4a ,,., Recalling that Pa = 2