ULTRASONIC ASSESSMENT OF MICROCRACK DAMAGE IN CERAMICS

Transcription

1 ULTRASONIC ASSESSMENT OF MICROCRACK DAMAGE IN CERAMICS Y. C. Chu, M. Hefetz1and S. I. Rkhlin The Ohi State University Department f Welding Engineering Clumbus, Ohi INTRODUCTION The inherent brittleness f ceramics ften results in catastrphic failure due t micrcrack damage caused by thermal treatment r mechanical lading. Extensive theretical and experimental studies have been perfrmed t analyze micrcrack damage in ceramics caused by thermal shck [1-7]. Hasselman [1,2] prpsed a simple mdel describing the strength behavir f ceramic materials as a functin f thermal shck temperature difference 6.T. The imprtant characteristic parameter in this mdel is the critical temperature difference, 6.Tc Fr thermal shck temperature differences less than 6.T c (stage I, Fig. 1) ceramics retain their strength. Thermal shcks with temperature differences equal t 6.T c (stage II) are characterized by unstable crack prpagatin and instantaneus decreases in strength. Abve 6.Tc is a plateau f cnstant strength (stage III), where cracks are subcritical and gradual decrease in strength is bserved at higher thermal shck temperatures (stage IV). As shwn experimentally [3,6], the actual behavir depends n the cmpsitin and the micrstructure f the material. The appearance f micrcracks in the material can be cnsidered as the appearance f a secnd phase, which leads t mechanical prperty (elastic mduli and strength) changes. The effective elastic mdulus f a cracked medium depends n crack shape, density, and preferred rientatin [8,9]. This makes pssible ultrasnic assessment f ceramic degradatin under thermal shck. This wrk reprts n different ultrasnic techniques fr assessment f damage initiatin and severity. During crack nucleatin and subcriticallength stages (stages II and III), we use the Rayleigh critical angle methd t assess damage initiatin (critical temperature difference). Fr samples thermally shcked frm higher temperatures (stage IV), we use in additin the bulk ultrasnic wave methd t characterize the macrscpic elastic prperties f the damaged material. The mduli measured by bth techniques are cmpared with each ther and with thse predicted using damage theries. SAMPLE PREPARATION The materials used in the study were cmmercial alumina 7.5 em diameter 0.47 em thick discs supplied by Crs Ceramics and Si3N4 reactin bnded silicn nitride (RBSN) fabricated by the NASA Lewis Research Center. Alumina specimens were cut lnw with RAFAEL, Haifa, Israel. Review f Prgress in Quantitative Nndestructive Evaluatin, Vl. 12 Edited by D.O. Thmpsn and D.E. Chimenti, Plenum Press, New Yrk,

2 STAGE I (NO CRACK PROPAGATION) ::I: I (!) Z La.J a::: I Vl STAGE II (UNSTABLE CRACK PROPAGATION) STAGE III (MICROCRACKS ARE SUBCRITICAL) t:::.tc (CRITICAL TEMPERATURE DIFFERENCE) THERMAL SHOCK TEMPERATURE DIFFERENCE t:::.t (OC) Fig. 1 Schematic representatin f strength behavir as a functin f severity f thermal shck as predicted by thery [IJ. with a diamnd blade t rughly 2.5 by 2.5 cm with thickness 4.7 mm and the RBSN specimens were cut t 12.8 by 28 mm with thickness 6.15 mm. Thermal shck treatment was dne by hlding the samples fr at least 15 minutes in an electric furnace maintained at a predetermined temperature, and then quenching them in ice water. Different severities f thermal shck were achieved by varying the temperature f the sample befre quenching in temperature ranges t 800 C fr alumina and t 1000 C fr RBSN. DAMAGE ASSESSMENT BY RAYLEIGH CRITICAL ANGLE MEASUREMENTS Mnlithic RBSN samples were measured after thermal shcks frm different elevated temperatures were measured using the Rayleigh critical angle methd. The Rayleigh critical angle measurements were perfrmed in the duble reflectin mde shwn in Fig. 2. The ultrasnic signal is reflected by the sample surface, then by the cylindrical reflectr and returned t the transducer after the secnd reflectin frm the sample surface. The amplitude f the dubly-reflected signal was recrded as a functin f the rtatin angle. It is knwn that the Rayleigh critical angle OR crrespnds t a dip in this reflectin cefficient curve (amplitude versus incident angle). The Rayleigh wave velcity VR can be calculated via Snell's law [10]: where Va is the sund speed in water. VR = Vl sin OR (1) We fund that the reductin in the Rayleigh wave velcity due t thermal shck is very similar t the reductin in the ultimate bending strength. Fig. 3 shws the reductin in Rayleigh wave velcity and ultimate bending strength [11] in the same graph. It is nted that the ultrasnically-measured data crrelate well with fur-pint bending tests. This means that the Rayleigh critical angle methd might be useful fr examining the effect f damage n the ultimate strength f ceramic materials and fr determinatin f the critical temperature fr thermal shck. It is als very imprtant that the critical temperature crrespnding t damage initiatin can be determined with cnfidence by the ultrasnic methd. Fr RBSN ceramics it is clear that the critical temperature fr thermal shck is abut 400 C. 2176

3 212 -:r r-= z >= 0.40 u LU -'... LU '" 0.20 Rayleigh Critical Angle \:.00 +rn"ttt"'"fttt-rrn-rrr.trtt-rrrrj INCIDENT ANGLE (dg.) Fig. 2. Diagram f Rayleigh critical angle measurements..' >- I Ū 0 Ultrasnic Measurements...J w > Ultimate strength w r > 0.. -< ---*--<\ 340 E- \. ::x:: ::x:: \ l- e.!) e.!) Z W \...J \ w >- 0:: -< \ I- 0:: (I) \ 0 '- --.JIII w w I e_ N -< :J «::> 0:: z THERMAL SHOCK TEMPERATURE (OC) Fig. 3. Effect f thermal shck n Rayleigh wave velcities and ultimate bending strength [11] f RBSN ceramics. It seems that fr RBSN ceramics the temperature range tested crrespnds t stages I t III f Hasselman's strength reductin mdel (Fig. 1) fr thermal shck damage. Thus we cnclude that the effect f damage due t thermal shck frm temperatures belw 1000 DC fr RBSN ceramics is mainly n surface rather than bulk prperties. When thermal shck temperatures increase abve 1000 DC (stage IV), severe damage is expected. Fr Al 20 3 all fur stages may be bserved using Rayleigh waves [12] in the temperature range belw 800 D. 2177

4 DAMAGE ASSESSMENT BY BULK ULTRASONIC WAVE MEASUREMENTS Previus studies n thermal shck damage in alumina [2,3,12J have shwn that its thermal shck critical temperature is abut 200 t 300 C and substantial grwth in crack density and length begins when thermal shck temperatures are abve 500 DC. T prduce a unifrm distributin f micrcracks in the alumina sample, thermal shck temperatures were set at 600, 700 and 800 C. Samples were evaluated after thermal shck treatment using the bulk ultrasnic wave methd. Bulk velcity measurements were perfrmed in the duble transmissin mde as illustrated schematically in Fig. 4. The ultrasnic signal is transmitted thrugh the sample, reflected by the back reflectr and returned t the transducer after the secnd thrugh-transmissin. The measurements were perfrmed with reference t nrmal incidence. This is a mdificatin f the duble-thrugh-transmissin methd described by Rkhlin and Wang [13J, where reference measurements were made alng acustic paths withut the sample. The phase velcity at nrmal incidence is measured with high precisin by verlapping multiple reflected signals frm the frnt and back surfaces f the sample. The phase velcities in the samples at refractin angle Or (crrespnding t the incident angle Oi shwn in Fig. 4) are calculated using the phase velcity in the nrmal directin Vn and the time delay change fr the rtated sample (due t the acustic path length change in the sample relative t that at nrmal incidence): V/(O ) = [_1 6t - (6t + 6tOJCOSOi 6te;(26t + 6tOJ]_1/2 0, r V2 + h V + 4h2 n 0 (2) Here Vn is the phase velcity in the samples at nrmal incidence, h is the thickness f the sample, 6t = 2h(1/Vc, - I/Vn), and 6t; is the difference in the time-f-flight measurements between nrmal incidence and arbitrary blique incidence at angle Oi t = 2h(---) v" v" I BACK REFLECTOR D tn D SAMPLE 4 T/R I". Or' Ie ' I T/R 6tBi = tn - tbi Fig. 4. Diagram f the self-reference bulk wave methd. 2178

5 Table 1. Effect f thermal shck damage n elastic prperties f alumina samples. Elastic prperties Cll,GPa C 22, GPa C 33, GPa C44, GPa C55, GPa Withut thermal shck Thermal shck at 600 DC Thermal shck at 700 DC Thermal shck at 800 DC , , 10.5,... VI '" iii iii 0 0 '" '" 10.0 '-" >!:: u g 9.5 LJ > N therml shck Thermal shck frm 600 C "''''''''''''' Therml shck frm 700 C Therml shck frm 800 C REFRACTION ANGLE (deg.) 90 Fig. 5. Lngitudinal wave velcity versus refractin angle fr different thermal shck temperatures. The lngitudinal wave velcity measurements at different angles t the sample surface nrmal are summarized in Fig. 5. The lngitudinal velcity is given versus refracted angle in the sample (angle f deviatin frm the sample surface nrmal). The data are given fr different thermal shck temperatures including data fr the sample withut thermal shck. Strng dependence f velcity n angle f prpagatin can be bserved in the thermal shck temperature range tested. Due t the preferred crack rientatin the ultrasnic velcity in the directin nrmal t the sample surface is less sensitive t the damage. The velcities f waves prpagating in directins near nrmal t the micrcracks (higher refractin angle) are much mre sensitive t the damage. The elastic cnstants f the material have been calculated using nnlinear least square ptimizatin [13] t btain the best fit between the slutin f the Christffel equatin and the experimentally-measured velcity. The data are summarized in Table 1 fr nrmal and shear mduli. One can see that fr damaged materials the mdulus C 33, where the 3 axis is perpendicular t the sample surface, has nly a small change, while the mduli in the plane parallel t the surface (C ll and C 22 ) change significantly. Thus ne may infer the preferred micrdamage rientatin frm ultrasnic data. DAMAGE MODELING AND DETERMINATION OF MICROCRACK DENSITY As discussed earlier ceramic micrcracks caused by thermal shck treatments 2179

6 0.10, , 0.08 LLI 0.06 If) If) LLI 0.04 iii z LLI t--,-----,,----,---,--,...--r----r--; THERMAL SHOCK TEMPERATURE (OC) Fig. 6. The dimensinless crack density determined frm ultrasnic data versus the thermal shck temperature. are aligned nrmal t the sample surface. Such a preferred crack rientatin allws us t assume that the micrcracks in ceramic samples caused by thermal shck are tw-dimensinally-riented slit cracks. Fr samples with micrcracks caused by thermal shck, it is reasnable t assume that the cracks are arbitrarily riented in the 1-2 plane (but with a preferred rientatin in the 3 directin). Assuming the nndamaged material is istrpic with Yung's mdulus E and Pissn's rati v, the dimensinless crack density fr slit cracks with width 2a and length 1 can be expressed in terms f the elastic prperties f damaged and nndamaged materials [9]: =Na21= 4(1-EdE) (3) 71"2(1 - Etv;/ E) where Et is the transverse Yung's mdulus f the damaged material and N is the number f cracks per unit vlume. Thus we can determine the dimensinless crack density frm the abve equatin by measuring the elastic prperties with and withut thermal shck. The elastic prperties f the nndamaged sample can be determined frm the averaged ultrasnic velcities (VL=10.7 km/s and VT=6.2 km/s) and the density (3.96 g/cm 3 ). Using the elastic prperties f alumina samples after thermal shck frm different temperatures (Table 1), we can calculate the dimensinless crack density crrespnding t different thermal shck temperatures. The results f this calculatin are shwn in Fig. 6 where the dimensinless crack density is pltted as a functin f thermal shck temperature. As ne can see frm the figure the crack density increases rapidly as the thermal shck temperature increases. This indicates increase in the number f cracks per unit vlume and grwth f the crack size. The ultrasnically-measured elastic prperties f cracked samples and thse calculated using the damage mdel are shwn in Figs. 7 and 8 fr the transverse Yung's mdulus Et and axial shear mdulus G a, respectively. In bth figures the results are nrmalized t the mduli f the nndamaged material. The slid line is the calculated elastic mdulus f the damaged material as a functin f dimensinless crack density using the damage mdel. The square pints crrespnd t experimentally-determined transverse (t the crack surfaces) mduli f the damaged samples. The results fr the axial shear mdulus btained independently using Rayleigh 2180

7 1.50 -, , Damage thery DDDDD Er frm bulk wave data 1.00 W'0.75 L.I ,--.--.,--,-----,-, DIMENSIONLESS CRACK DENSITY Fig. 7. Transverse Yung's mdulus f a damaged material versus crack density. Slid line is thery and pints are experiment , , Damage thery DDDDD G. (bulk wave data) AAAAA G. (surface wave data [12]) 1.00 re;-:: j H r-.., r--,--.---,,--r--i DIMENSIONLESS CRACK DENSITY Fig. 8. Shear mdulus alng crack directin f a damaged material versus crack density. Slid line is thery, pints are experiment (triangles crrespnd t the Rayleigh wave methd [12] and squares t the bulk wave methd). critical angle measurements [12] are als shwn in Fig. 8 (triangles). As ne can see the experimental results btained frm tw different measurements (bulk and Rayleigh angle methds) agree well. The ultrasnically-determined axial shear mduli behave similarly t thse calculated using the damage thery but there is a systematic shift between these tw at different crack densities. This difference may be due t micrcrack branching, whereas the mdel assumes plane cracks vertically riented. SUMMARY This study fcuses n nndestructive assessment f micr crack damage in ceramics caused by thermal shck. Bth ultrasnic bulk wave and surface wave methds have been used fr assessment f thermal shck damage in ceramics. The fundatin 2181

8 f ultrasnic damage assessment lies in the effect f damage n elastic prperties. Since the earlier stages f thermal shck damage are lcated near the surface, Rayleigh critical angle measurements have been fund t be mst apprpriate fr estimatin f ultimate strength reductin and critical temperature f thermal shck. Fr severe damage caused by thermal shck (the later stages) the angular dependence f bth transverse and lngitudinal velcities has been fund t be affected by thermal shck damage. Experimental results n tw different ceramic materials shw that Si3N4 RBSN ceramics have better thermal shck resistance than alumina. The dimensinless crack density in damaged alumina samples was determined frm the reductin f elastic mduli due t thermal shck damage via an apprpriate damage mdel. The results indicate that the crack density increases rapidly as the thermal shck temperature increases. ACKNOWLEDGMENTS This wrk was supprted in part by NASA Lewis Research Center under grant #NAG The authrs appreciate Mr. Len Ewald f Crs Ceramics fr supplying the alumina samples, and Dr. G. Y. Baaklini f NASA Lewis Research Center fr supplying the RBSN samples. REFERENCES 1. D. P. H. Hasselman, J. Am. Ceram. Sc. 52, 600 (1969). 2. D. P. H. Hasselman, J. Am. Ceram. Sc. 53, 490 (1970). 3. T.K. Gupta, J. Am. Ceram. Sc., 55, 249 (1972). 4. A.G. Evans, Prc. Br. Ceram. Sc. 25, 217 (1975). 5. H.A. Bahr, G. Fischer, and H.J. Weiss, J. Mater. Sci. 21,2716 (1986). 6. E. H. Lutz, M.V. Swain, and N. Claussen, J. Am. Ceram. Sc. 74,19 (1991). 7. M. Oguma and T. Mtmiya, Nippn Seramikkusu Kykai Gakujutsu Rmbunshi 97, 778 (1989). 8. B. Budiansky and R.J. O'Cnnell, Int. J. Slids Structures 12, 81 (1976). 9. N. Laws and J. R. Brckenbrugh, Int. J. Slids Structures 23,1247 (1987). 10. F.1. Becker and R. L. Richardsn, in Research Techniques in Nndestructive Testing, edited by R.S. Sharpe (Academic Press, Lndn, 1970), pp R. T. Bhatt, NASA TM-I01356 (1988). 12. M. Hefetz and S. I. Rkhlin, J. Am. Ceram. Sc. 75, 1839 (1992). 13. S.1. Rkhlin and W. Wang, J. Acust. Sc. Am. 91,3303 (1992). 2182