Astm stp 1409 2002

STP 1409 Fracture Resistance Testing of Monolithic and Composite Brittle Materials J A Salem, G D Quinn, and M G Jenkins, editors ASTM Stock Number: STPI409 ASTM International 100 Barr Harbor Drive PO Box C700 West Conshohocken, PA 19428-2959 Printed in the U S A Library of Congress Cataloging-in-Publication Data Fracture resistance testing of monolithic and composite brittle materials / J.A Salem, G.D Quinn, and M.G Jenkins, editors p cm "ASTM stock number: STP1409." Includes bibliographical references and index ISBN 0-8031-2880-0 Brittleness -Congresses Fracture mechanics -Congresses L Salem, J A (Jonathan A.), 1960- IL Quinn, G D (George D.) II1.Jenkins, Michael G., 1958TA418.16.F73 2002 620.1' t 26 0.3 M P a / s Water Rates of 0.03 to 30 MPa/s Ot 0.0207 + 0.0020 0.0620 + 0.0031 0.0243 + 0.0025 fl 2.2747 + 0.0048 2.2950 + 0.0034 2.2451 + 0.0037 n 47.3 + 4.8 15.1 + 0.8 40.1 + 4.2 D 188.2 + 2.1 197.2 + 1.6 175.8 + 1.5 DOF 52 48 18 SALEM AND JENKINS ON SLOW CRACK GROWTH PARAMETERS (c (1-4)-I DOFf,= N I - + N - 223 (16) where c = SD~I/N,~j so ,/uoj + soL/u (17) and N is the number of test specimens This results in a somewhat lower degrees-offreedom for t than direct pooling of the DOF's for the rates above and below 0.3 MPa/s (i.e., 80 instead of 100) Despite this, the t statistic of 2.07 at 99% confidence is substantially smaller than that associated with the data (11.13), implying a statistically significant difference in slope at much better than 99% confidence Effect of Stressing Rate on Strength Variation Another aspect of using linear regression to calculate the SCG parameters is the requirement that the data is normal and identically distributed The transformation of slow crack growth data into a log-log space should accomplish this requirement This can be examined by observing the standard deviation of the strength as a function of stress rate in log space Table summarizes the standard deviations along with F statistics for comparing the deviations The standard deviations are relatively similar and the F statistics small No statistically significantly difference can be detected at reasonable confidence levels (i.e., > 90%), implying little change in standard deviation of strength with stress rate in log-log space Effect of Test Environment If tests are conducted in a manner that minimizes or eliminates Region 11 of the SCG curve, then Region I is extended toward Region I / / a n d the errors induced by averaging can be minimized while stress rates approaching those specified in ASTM C 1368 are used This will allow the timesaving benefit of dynamic fatigue to be realized along with accurate parameter estimates for component life prediction This effect can be observed in the data of Sudreau: dynamic fatigue of mullite in water at rapid rates results in A = 0.5 x 1015 and n = 36, whereas the actual Region I parameters, as measured with the double torsion relaxation method, are A = 0.3 x 1015 and n = 41 for air andA = 0.5 x 10 15 and n = 43 for water The dynamic fatigue results for water are in good agreement with the actual Region I parameters However, the dynamic parameters generated in air (A = 0.3 x 10-8 and n = 19) are not because a significant Region II exists and is averaged into the results 224 FRACTURETESTING OF MONOLITHIC/COMPOSITE MATERIALS Thus by using a 100% concentration of the corrosive medium (water), the diffusion rate is increased, Region rl is minimized and more realistic SCG parameters are determined for efficient stress rates In order to experimentally verify the effect of concentration for the alumina, additional tests were conducted in distilled water at rates 0.03 and 30 MPa/s The resultant data is shown in Figure and the calculated SCG parameters are listed in Table Note the relatively good agreement between the standard deviations and the slopes of the ultra-slow rate data generated in air and the data generated in water at typical rates The significance of the small differences can be determined by using Eqs 14 and 16 The statistics are listed in Table and imply that the null hypotheses of equivalent standard deviations and equivalent slopes cannot be rejected Thus testing in water at typical rates results in a slope not significantly different from that measured in air at ultra-slow rates for reasonable confidence levels Although no significant difference can be detected between the slopes, the level of the curve for water appears to be lower (about 7% at 0.3 MPa/s) This is probably the result of a longer Region I causing more crack growth and a larger crack size on beginning Region Ill The crack growth associated with stress intensities for Region 11 in air is increased in water due to the higher concentration of corrosive medium Table - Statistics for comparison of slopes of SCG curves estimated from data measured in air with stress rates above and below 0.3 MPa/s The null hypotheses for the statistics F and t can be rejected with high confidence Parameter DOF F (Data) 90% 95% 99% Confidence Confidence Confidence Level Level level F 48/52 2.29 1.60 1.75 2.10 t 80 11.13 1.66 1.99 2.64 Table - Comparison of standards deviations in log space for various stress rates The null hypotheses for the statistics F cannot be rejected with high confidence Stress Rate MPa/s Standard Deviation 36 0.0206 0.36 0.00036 F DOF (Data) F 95% F 90% 36 vs 0.00036 24/18 1.20 2.50 2.15 0.0211 0.36 vs 0.00036 19/18 1.26 2.58 2.20 0.0188 0.36 vs 36 19/24 1.05 2.35 2.04 Rates Compared 225 SALEM AND JENKINS ON SLOW CRACK GROWTH PARAMETERS Strain Rate, e-9 300 275 250 ca fl_ 225 e-8 i o v zx 9 o D1RAS D2RGB D2RAS D2RAS D1RAS D2RGB D2RAS 1Is e-7 e-6 e-5 i i t t e-4 (2s) O : ~2 (5) Water Water Water Oil 200 e (5) 03 -q 175 (19) m ca ii 150 125 0.0001 v (10) ' ' ''""l 0.001 i ' '''""l 0.01 Stress ' '''""l 0.1 Rate, ' ''" d, i 10 i 100 MPa/s Figure - Experimentally measured failure stress as a function of stress rate for alumina The number of specimens tested is given in parenthesis Implications for Preloading Preloading is a useful tool for reducing the test time required to fail a specimen [8] The drawback is that large preloads may compound errors caused by excessively fast stress rates because the starting stress intensity factor may be above that for Region I and the resultant time spent in Region I of the SCG curve is thus truncated (see Figure 1) For the data of Sudreau, Region I of the mullite ends at -65% of the maximum stress intensity factors measured (i.e., the fracture toughness) For the silicon nitride, Region I ends at -90% of the maximum stress intensity factor measured Apparently the degree of acceptable preloading depends on the shapes and sizes of the SCG regions Experimental examination of this effect is left to further study 226 FRACTURETESTING OF MONOLITHIC/COMPOSITEMATERIALS Table - Statistics for comparison of slopes of dynamic fatigue curves estimated from data measured in air with ultra-slow stress rates (i.e