Fracture behavior of silicon nitride ceramics subjected to hypervelocity impact

Fracture behavior of silicon nitride ceramics subjected to hypervelocity impactN.Kawai *,K.Tsurui,D.Shindo,Y.Motoyashiki,E.SatoInstitute of Space and Astronautical Science,Japan Aerospace Exploration Agency,3-1-1Yoshinodai,Chuo,Sagamihara,Kanagawa 252-5210,Japana r t i c l e i n f oArticle history:Received 10August 2010Received in revised form 13January 2011Accepted 14January 2011Available online 22January 2011Keywords:Hypervelocity impact Impact-induced damage Two-stage light-gas gun Silicon nitride ceramicsa b s t r a c tA new advanced ceramic thruster made of monolithic silicon nitride ceramics was developed for the planetary exploration spacecraft AKATSUKI (PLANET-C)at Institute of Space and Astronautical Science (ISAS),Japan Aerospace Exploration Agency (JAXA).To ensure its operation onboard the spacecraft,the reliability of the ceramic thruster against micrometeoroid hypervelocity impact has been investigated.Silicon nitride plates were impacted by spheres of stainless-steel and other materials with 0.2e 0.8-mm diameters in the velocity range up to 8.0km/s using a two-stage light-gas ing crater depth data under various impact conditions,the penetration equation of silicon nitride was determined.The impacted samples showed fracture patterns of three types:cratering,cratering with spallation,and perforation.These fracture patterns were well categorized by the multiple forms of the penetration equation.Ó2011Elsevier Ltd.All rights reserved.1.IntroductionA thruster is a small rocket engine used to control the attitude and orbit of a spacecraft.To achieve higher thrust performance,increased combustion temperature and a decreased mass of thruster components must be attained.Institute of Space and Astronautical Science (ISAS),Japan Aerospace Exploration Agency (JAXA)devel-oped a new advanced ceramic thruster made of monolithic silicon nitride for the planetary exploration spacecraft AKATSUKI (PLANET-C),sent on a Venus climate orbiter mission [1].Silicon nitride ceramic is an ideal structural material for high-temperature appli-cations such as heat engine and heat recovery system components because of its outstanding high-temperature strength,corrosion and erosion resistance,and chemical stability,coupled with low density.The design and veri fication of the ceramic thruster were conducted with consideration of its quasi-static strength under launching and firing conditions [1].In addition,its reliability against micromete-oroid impact has also been veri fied to ensure the operation of the planetary exploration spacecraft [2].For this study,following the veri fication under the thruster condition [2],the failure behavior of silicon nitride subjected to hypervelocity impact was investigated.Hypervelocity impact experiments were performed on a silicon nitride plate in the velocity range up to 8.0km/s.The impact failure morphology of the silicon nitride was examined.The penetration equation of silicon nitride was derived from the hypervelocity impact test data and analysis.2.Hypervelocity impact experimentThe material used in this study is a commercially available gas-turbine-grade silicon nitride,SN282,manufactured by Kyocera Corp.,which is densi fied via gas-pressure sintering with Lu 2O 3as a sintering additive and toughened with microstructures tailored to achieve elongated grain structures.The bulk density is 3.38Mg/m 3.The elastic modulus,bulk modulus,shear modulus,and Poisson ’s ratio are 316GPa,244GPa,123GPa,and 0.28,respectively [3].Impacted targets were 30mm Â50mm or 50mm square plates with five different thicknesses:1.0,1.5,2.0,2.5and 3.0mm.Hypervelocity experiments were performed using a two-stage light-gas gun at ISAS/JAXA [4],with the exception of the two highest velocity experiments performed at the White Sands Test Facility of the NASA Johnson Space Center [5].The projectiles used were spheres of stainless-steel ðr ¼7:89Mg =m 3Þ,Al ðr ¼2:78Mg =m 3Þ,Al 2O 3ðr ¼3:90Mg =m 3Þ,glass ðr ¼2:20Mg =m 3Þ,WC ðr ¼14:50Mg =m 3Þ,Pt ðr ¼21:10Mg =m 3Þand Ir ðr ¼22:70Mg =m 3Þof 0.2e 0.8-mm diameters.These projectiles were launched using a buckshot technique [6]or a single microparticle launching technique [4,5].The sample-plate was mounted on an acrylic frame with an adhesive tape so that there was a free rear surface and the sample was fixed in a practically uncon fined manner.The resulting crater depths for unperforated samples were measured using a laser microscope.Some samples were cut along the impact axis using a diamond saw to examine the internal damage.The cut samples were embedded in an epoxy resin and the sectioned surfaces were polished before optical microscope observations.*Corresponding author.Tel.:þ815033627539;fax:þ81427598461.E-mail address:nkawai@isas.jaxa.jp (N.Kawai).Contents lists available at ScienceDirectInternational Journal of Impact Engineeringjo urn al homepag e:/locate/ijimpeng0734-743X/$e see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/j.ijimpeng.2011.01.003International Journal of Impact Engineering 38(2011)542e 5453.Results3.1.Impact failure morphologyIn these experiments,fracture patterns of three types were observed:cratering,cratering with rear surface spallation,and perforation.The cross-sections along the impact axis of the impacted samples revealing three fracture patterns are,respec-tively,shown in Fig.1.In the case of the cratering-only fracture (Fig.1(a)),highly deformed and damaged silicon nitride,the white region in the images,was observed immediately beneath the crater.Numerous conical cracks propagated inside the sample from this damaged region.The horizontal planer cracks were also observed below the middle plane of the impacted sample.In the case of rear surface spallation with cratering,spall frac-tures of two kinds were observed.The first one is thin planar spall fracture (Fig.1(b)),which was usually observed in metal [7,8].This thin planar fracture near the rear surface is induced by a rarefaction wave formed by the re flection of a shock wave from the rear free surface.The formation of this spall fracture is associated with the shock wave propagation.Therefore the thin planar spall is formed during the early stages of impact crater formation.The thin planar spallation was observed only in the thick samples impacted at greater than 5.5km/s,indicating that a suf ficiently strong shock wave to trigger the planar spallation reaches the rear free surface in these impact conditions.Another rear surface spallation is a conical spall fracture (Fig.1(c)),in which many conical cracks that had propagated from crater were observed;some cracks reached the rear surface.The horizontal cracks were much more numerous than in the cratering-only case.Although thin planar spall fracture would also occur in this fracture pattern,the dominant fracture resulted from connec-tion of the extended conical cracks and horizontal cracks.Thecrack-propagation velocity is slower than the shock wave velocity propagated into the silicon nitride.Therefore,the conical spall fracture is formed later than the thin planar spall fracture.This fracture sequence was shown by the numerical simulation of the hypervelocity impact of silicon nitride using a hydrocode [9].In the case of perforation fracture (Fig.1(d)),the through-hole was formed by linking the front-surface crater and the rear surface conical spall.Some cracks that had propagated from the through-hole were also observed.3.2.Crater depthAll the experimental data are summarized in Table 1and Table 2.In Fig.2,the crater depth P c (mm)normalized by the projectile diameter d p (mm)is plotted versus the projectile velocity v p (km/s).In the case of the stainless-steel projectile,the normalized crater depth shows good correlation against the projectile velocity,independently of projectile diameters.Simple power-law fitting to all data of stainless-steel projectile yieldsP ss d p¼0:69v 0:64p ;(1)where P ss is crater depth (mm)by the impact of a stainless-steel projectile.The correlation coef ficient of this equation is 0.89.This simple power-law forces the crater depth to zero at v p ¼0although the critical velocity for penetration is expected to be greater than zero.However,previous studies [10,11]show that the critical velocity for crater formation of silicon nitride impacted by ceramics spheres with 1mm diameter is about 80m/s.The impact velocities of this study (from 1.5to 8.3km/s)are considerably higher than the critical velocity.Therefore,the effect of the critical velocity on the crater formation is considered to be negligible in this study.The differences of the crater depths between the stain-less-steel projectile and other materials are caused by differences of the projectiledensity.Fig.1.Cross-sections of the silicon nitride plate subjected to hypervelocity impact for failure patterns of different types.(a)Only cratering.Target thickness is 3.0mm and a 0.3-mm stainless-steel sphere was impacted at 4.43km/s.(b)Thin planar spallation.Target thickness is 2.0mm and a 0.3mm-aluminum sphere was impacted at 6.61km/s.(c)Conical spallation.Target thickness is 1.5mm and a 0.5-mm stainless-steel sphere was impacted at 1.94km/s.(d)Perforation.Target thickness is 1.5mm and a 0.5-mm stainless-steel sphere was impacted at 3.26km/s.Table 1Experimental data of hypervelocity impact tests on silicon nitride ceramics using stainless-steel projectiles.ProjectileSilicon nitride targetShot No.Material d p /mm v p /km/s t t /mm Fracture type P c /mm 652Stainless-steel0.304.05 2.0Crater0.455968 4.16 1.0Perforation e 969 4.30 1.5Conical Spall 0.5171004 4.41 1.0Perforation e 838 4.43 3.0Conical Spall 0.564376 5.63 1.5Conical Spall 0.60642206a 0.40 6.83 2.0Perforation e 42207a 8.31 2.0Perforation e 10090.501.94 1.5Conical Spall 0.6081315 1.96 1.5Conical Spall 0.42113202.19 2.0Crater0.4811006 2.80 1.0Perforation e 1335 2.85 2.5Conical Spall 0.6961205 2.86 3.0Crater0.8051333 3.02 2.0Conical Spall 0.6911323 3.06 2.0Conical Spall 0.6101326 3.26 2.0Conical Spall 0.7301325 3.31 3.0Crater0.8151556 3.38 1.5Perforation e 1553 3.52 2.0Conical Spall 0.8351317 3.79 1.5Perforation e 1559 3.79 2.0Conical Spall 0.7971563 3.85 2.0Perforation e 1329 4.12 2.5Conical Spall 0.8371562 4.25 2.0Perforation e 10130.801.351.0PerforationeaPerformed at the White Sands Test Facility of the NASA Johnson Space Center.N.Kawai et al./International Journal of Impact Engineering 38(2011)542e 5455434.DiscussionThe penetration equations for hypervelocity impacts are usually formulated as a power-law equation of the projectile diameter,the projectile density and the projectile velocity [12e 16].The crater depth data normalized by the projectile diameter for the stainless-steel projectiles are well fitted by the power-law equation of projectile velocity,as shown in Fig.2.Therefore,the exponent for d p is assumed to be 1.0in this study.The effect of the projectile density on the crater formation is estimated from the differences of the crater depths between stainless-steel projectile and other material paring the crater depth data of Al,Ir and Al 2O 3projectiles to the estimated crater depths of stainless-steel projectile with the same velocity and diameter,the exponent for the projectile density is calculated for each data point asP c ss¼r p r ssa;(2)where r p denotes the projectile density (Mg/m 3),r ss represents thedensity of stainless-steel (Mg/m 3)and a stands for the exponent for the projectile density.The values of P ss were estimated using Eq.(1).After calculation of a for each data point of Al,Ir and Al 2O 3projec-tiles,the a was determined to be 0:73Æ0:19as an average value.In Fig.3,the crater depth normalized by d p and r 0:73pare plotted against the projectile velocity.The graph shows good correlation between the normalized crater depth and projectile velocity for all projectile materials.By fitting the data to the power-law form for the projectile velocity,the penetration equation for silicon nitride is determined asP c ¼0:142d p r 0:73pv 0:67p :(3)The correlation coef ficient for this equation is 0.95.The standard deviation of the exponent of v p is Æ0:07.Some penetration equa-tions for metal,glass,and thermal protection materials have been proposed [13e 16].The exponents of projectile velocity in these equations are about 2/3and show only slight differences each other.In the case of the exponents of projectile density,previous studies show a range of values from about 0.3to 0.7because of the limited variation of projectile density in the data set used by different researchers [13,14].The exponents of projectile velocity and density for silicon nitride are also consistent with these previous results.The penetration equation has been used to assess the fracture resistance of a thin target [12,15,16].The plate thickness necessary to prevent fracture,t f (mm),is usually expressed in terms of a multiple of the penetration equation:t f ¼kP c ,where k is the factor depending on the fracture pattern.In Fig.4,the fracture patterns observed in this study are shown in the t t /d p /r p versus v p plane,where t t is the target thickness (mm).The values of the factor k were determined to express the boundaries of fracture patterns on the morphology map shown in Fig.4.As a result,the equations for the critical thickness of silicon nitride to prevent the conical spallation and the perforation are determined as follows:t f ¼0:142kd p r 0:73pv 0:67p ;(4)k ¼2:4Æ0:2to prevent the perforation ;k ¼3:7Æ0:2to prevent the conical spallation :The calculated t f using each k is depicted in Fig.4:a dashed line and a dashed-dotted line represent the target thickness to prevent the conical spallation and the perforation,respectively.BothcalculatedFig.2.Relation between penetration depth to projectile diameter ratio and projectilevelocity.The dashed line shows power-low fitting to the data of the stainless-steel projectile (Eq.(1)).Fig.3.Penetration depth to projectile diameter ratio as a function of projectile velocity with projectile density scaling.The dashed line shows the penetration equation of silicon nitride determined in this study (Eq.(3)).Table 2Experimental data of hypervelocity impact tests on silicon nitride ceramics using Al,Al 2O 3,Glass,WC,Pt and Ir projectiles.ProjectileSilicon nitride target Shot No.Material d p /mm v p /km/s t t /mm Fracture type P c /mm 577Al0.205.06 2.0Crater 0.147478 5.10 3.0Crater 0.1556566.42 2.0Crater0.1906490.30 6.61 2.0Planer Spall 0.350657Al 2O 30.20 5.41 2.0Crater0.2446510.30 5.78 2.0Planer Spall 0.429835Glass 0.30 4.03 2.0Crater 0.199966 4.23 1.5Crater0.154661WC 0.50 5.51 2.5Perforation e 1331Pt 0.33 3.94 1.0Perforation e 1217Ir0.391.501.5Conical Spall0.514N.Kawai et al./International Journal of Impact Engineering 38(2011)542e 545544curves represent the boundaries of fracture patterns very well.The values of k for metallic target have been estimated as 2.0for perfo-ration and 2.2for rear surface spallation [12,16].The k for spallation of silicon nitride is much bigger than that of metal.This is because the spall strength of ceramics is lower than that of metal.In contrast,the k for perforation of silicon nitride is little bigger than that of metal.The perforation occurs by connecting the crater and rear-side spallation.As mention above,ceramics are vulnerable to spallation.In contrast,the high hardness and compressive strength of ceramics are effective in preventing the penetration.It is expected that the difference of k for perforation between silicon nitride and metal become relatively small as a result of the combination of their penetration and spallation resistances.In the case of the thin planar spallation,the equation for the boundary of fracture pattern can not be determined in this study because of the scarcity of data points for this fracture pattern.To reveal the thin planar spallation,the target thickness must be suf fi-ciently thick to avoid the conical spallation.Furthermore,the projectile velocity must be high enough to generate a shock wave that is suf ficiently strong to trigger the planar spallation at the rear surface.The data points for the thin planar spallation observed in this study follow this trend.The expected boundary between the cratering and the thin planar spallation is shown as a dotted line in Fig.4.From these results,we can predict the fracture pattern of the silicon nitride subjected to hypervelocity impact using the pene-tration equation and k values.ConclusionIn this study,to determine the hypervelocity impact-induced fracture behavior of silicon nitride,hypervelocity impact tests wereperformed on a silicon nitride plate by impacting spheres of stainless-steel and other materials with 0.2e 0.8-mm diameters in the velocity range up to 8.0km/s.The penetration equation was determined using crater depth data under various impact condi-tions:P c ¼0:142d p r 0:73p v 0:67p.Impact-induced fracture patterns of three types were observed:cratering,cratering with spallation,and perforation.The boundaries of these fracture patterns were well described by the multiple form of the penetration equation deter-mined in this study:t f ¼kP c ,k ¼2:4for the perforation,and k ¼3:7for the conical spallation.Consequently,the fracture pattern of the silicon nitride subjected to hypervelocity impact can be pre-dicted using the obtained penetration equation.AcknowledgmentsThe authors are grateful to S.Hasegawa for his technical assis-tance with hypervelocity impact experiments.This research was supported by the Space Plasma Laboratory,ISAS,JAXA.References[1]Sawai S,Sato E,Uesugi KT,Furukawa K,Mishima H,Morishima K,et al.Development of ceramic based 500N class bipropellant thruster.In:Proc.the 56th International Astronautical Congress,IAC-05e C4.3.01;2005.[2]Motoyashiki Y,Hasegawa S,Okudaira K,Sato E.Micrometeoroid impact onceramic thin components for interplanetary probe.Int J Impact Eng 2008;35:1666e 71.[3]Dandekar DP,Casem DT,Motoyashiki Y,Sato E.Shock response of siliconnitride.In:Elert ML,Buttler WT,Furnish MD,Anderson WW,Proud WG,editors.Shock compression of condensed matter e 2009.New York:AIP;2009.p.985e 8.[4]Kawai N,Tsurui K,Hasegawa S,Sato E.Single microparticle launching methodusing two-stage light-gas gun for simulating hypervelocity impacts of micrometeoroids and spacedebris.Rev Sci Instrum 2010;81:115105.[5]Crews JL,Christiansen EL.The NASA JSC hypervelocity impact test facility(HIT-F),AIAA Paper 92e 1640;1992.[6]Taylor EA,Tsembelis K,Hayhurst CJ,Kay L,Burchell MJ.Hydrocode modellingof hypervelocity impact on brittle materials:depth of penetration and conchoidal diameter.Int J Impact Eng 1999;23:895e 904.[7]Shockey DA,Curran DR,DeCarli PS.Damage in steel plates from hypervelocityimpact.I.Physical changes and effects of projectile material.J Appl Phys 1975;46:3766e 75.[8]Moritoh T,Matsuoka S,Ogura T,Nakamura KG,Kondo K,Katayama M,et al.Dynamic failure of steel under hypervelocity impact of polycarbonate up to 9km/s.J Appl Phys 2003;93:5983e 8.[9]Kawai N,Kakimoto Y,Motoyashiki Y,Sato E.Damage evaluation of siliconnitride components subjected to hypervelocity impact.In:Schäfer F,Hier-maier S,editors.Proc.11th hypervelocity impact symposium,in press.[10]Akimune Y,Katano Y,Matoba K.Spherical-impact damage and strengthdegradation in silicon nitrides for automobile turbocharger rotors.J Am Ceram Soc 1989;72:1422e 8.[11]Shin HS,Maekawa I.Characterization of particle impact damage and residualstrength degradation behaviors in structural ceramics.JSME Int J A 1995;38:116e 22.[12]Cour-Palais BG.Hypervelocity impact in metals,glass and composites.Int JImpact Eng 1987;5:221e 37.[13]Herrmann W,Wilbeck JS.Review of hypervelocity penetration theories.Int JImpact Eng 1987;5:307e 22.[14]Yu SB,Sun GC,Tan QM.Experimental laws of cratering for hypervelocityimpacts of spherical projectiles into thick target.Int J Impact Eng 1994;15:67e 77.[15]Christiansen EL,Friesen L.Penetration equations for thermal protectionmaterials.Int J Impact Eng 1997;20:153e 64.[16]Cour-Palais BG.A career in applied physics:apollo through space station.Int JImpact Eng 1999;23:137e68.Fig.4.Failure morphology map against the target thickness to projectile diameter ratio with projectile density scaling and the projectile velocity.The dashed line represents the target thickness to prevent conical spallation (Eq.(4)).The dashed-dotted line represents the target thickness to prevent perforation (Eq.(4)).The dotted line shows the expected boundary between the cratering and thin planar spallation.N.Kawai et al./International Journal of Impact Engineering 38(2011)542e 545545。