Acta mater.Vol.47,No.18.pp.4711-4725,1999 On behalf of Acta metallurgica In PI:S13596454(99)00246-3 1359-645499520.00+0.00 PERGAMON CYCLIC FATIGUE OF INTRINSICALLY BRITTLE CERAMICS IN CONTACT WITH SPHERES D. K KIMT, Y.G. JUNGH, L M. PETERSON and B R. LAWN Materials Science and Engineering Laboratory, National Institute of Standards and Technology Gaithersburg. MD 20899, U.S.A. Received 24 March 1999; accepted 28 July 1999) Abstract--Contact damage modes in cyclic loading with spheres are investigated in three nominally brittle mall numbers of cycles and low loads consists of tensile-driven macroscopic cone cracks ("brittle"mode) dary damage at lar loads consists of shear-driven distributed micro damage (quasi-plastic"mode), with attendant radial cracks and a new form of deeply penetrating subsidi- first mode, based on time-integration of slow growth of cone cracks, is presented. This model provides relations for the remaining strength in terms of number of cycles and naterials design. Extrapolations of these relation ative, highlighting the need for further underst mics. Comparison with static contact data indicates a strong mechanical (as opposed to chemical "y mponent in the cyclic fatigue in the quasi-plastic region. Published by Elsevier Science Lid on behalf of Keywords: Structural ceramics; Fracture; Fatigue; Yeild phenomena; Microstructure 1 INTRODUCTION with spheres, where the stress field is largely com- Fatigue properties are important in any long-term, pressive and of uncommonly high intensity (i.e. in large-scale structural applications where cyclic loads excess of GPa)[16-21]. Earlier studies on damage are experienced. Such properties have been accumulation and fracture around notches in com- measured in several ceramics using conventional pressive loading constitute a precedent for such pre-cracked tensile test specimens or bend bars[I- effects [22-24. Contact fatigue is relevant to bear- 91. A key element of the fatigue response is micro- ings and engine components [21] dental restor structure:fine, homogeneous ceramics, character- ations [25, 26] and analogous biomechanical ized by crack-size-invariant toughness values replacements (hip joints, heart valves), and other undergo cyclic fatigue by time-integrated, chemi- applications where loads are concentrated. two dis- cally-enhanced slow crack growth [10] coarse, het- tinct contact damage modes have been identified [18]:(i) in homogeneous ceramics, well-defined cone erogeneous ceramics, characterized by R-curves, cracks (brittle"mode);(i)in heterogeneous cer- undergo fatigue mainly by time- independent mech- anical degradation of grain bridging or other crack- amics, microdamage within diffuse but well-defined yield zones (quasi-plastic" mode). Again, in the tip shielding mechanism [11-15. The competitive brittle materials the fatigue is attributable to chemi- roles of chemical and mechanical processes in the fatigue responses of ceramics is an issue of continu. cally-driven, time-independent slow crack growth, ing debate. whereas in the quasi-plastic materials it appea be governed primarily by a mechanical component tigue effects in ceramics can be even more dependent on number of cycles rather than on time ly evident in Hertzian-type contact loading [271. Both damage modes are deleterious to the remaining strength of the material. However, the gUest Scientist from: Department of Materials Science mechanics of the associated fatigue processes and Engineering, Korea Advance Science and remain obscure Technology, Yusong, Taejon 305-701, Korea. Present address: Department of Ceramic Science and n this paper we present results of a fatigue study Engineering. Changwon National University, Chang with spherical indenters on nominally brittle cer- S, i.e. relatively homogeneous ce
CYCLIC FATIGUE OF INTRINSICALLY BRITTLE CERAMICS IN CONTACT WITH SPHERES D. K. KIM{, Y.-G. JUNG{, I. M. PETERSON and B. R. LAWN} Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, U.S.A. (Received 24 March 1999; accepted 28 July 1999) AbstractÐContact damage modes in cyclic loading with spheres are investigated in three nominally brittle ceramics, soda-lime glass, porcelain and ®ne-grain silicon nitride, in moist environments. Initial damage at small numbers of cycles and low loads consists of tensile-driven macroscopic cone cracks (``brittle'' mode). Secondary damage at large numbers of cycles and high loads consists of shear-driven distributed microdamage (``quasi-plastic'' mode), with attendant radial cracks and a new form of deeply penetrating subsidiary cone cracks. Strength tests on indented specimens are used to quantify the degree of damage. Both damage modes degrade the strength: the ®rst, immediately after cone crack initiation, relatively slowly; the second, after development of radial cracks, much more rapidly. A fracture mechanics model describing the ®rst mode, based on time-integration of slow growth of cone cracks, is presented. This model provides simple power-law relations for the remaining strength in terms of number of cycles and contact load for materials design. Extrapolations of these relations into the quasi-plastic region are shown to be non-conservative, highlighting the need for further understanding of the deleterious quasi-plastic mode in tougher ceramics. Comparison with static contact data indicates a strong mechanical (as opposed to chemical) component in the cyclic fatigue in the quasi-plastic region. Published by Elsevier Science Ltd on behalf of Acta Metallurgica Inc. Keywords: Structural ceramics; Fracture; Fatigue; Yeild phenomena; Microstructure 1. INTRODUCTION Fatigue properties are important in any long-term, large-scale structural applications where cyclic loads are experienced. Such properties have been measured in several ceramics using conventional pre-cracked tensile test specimens or bend bars [1± 9]. A key element of the fatigue response is microstructure: ®ne, homogeneous ceramics, characterized by crack-size-invariant toughness values, undergo cyclic fatigue by time-integrated, chemically-enhanced slow crack growth [10]; coarse, heterogeneous ceramics, characterized by R-curves, undergo fatigue mainly by time-independent mechanical degradation of grain bridging or other cracktip shielding mechanism [11±15]. The competitive roles of chemical and mechanical processes in the fatigue responses of ceramics is an issue of continuing debate. Fatigue eects in ceramics can be even more strongly evident in Hertzian-type contact loading with spheres, where the stress ®eld is largely compressive and of uncommonly high intensity (i.e. in excess of GPa) [16±21]. Earlier studies on damage accumulation and fracture around notches in compressive loading constitute a precedent for such eects [22±24]. Contact fatigue is relevant to bearings and engine components [21], dental restorations [25, 26] and analogous biomechanical replacements (hip joints, heart valves), and other applications where loads are concentrated. Two distinct contact damage modes have been identi®ed [18]: (i) in homogeneous ceramics, well-de®ned cone cracks (``brittle'' mode); (ii) in heterogeneous ceramics, microdamage within diuse but well-de®ned yield zones (``quasi-plastic'' mode). Again, in the brittle materials the fatigue is attributable to chemically-driven, time-independent slow crack growth, whereas in the quasi-plastic materials it appears to be governed primarily by a mechanical component, dependent on number of cycles rather than on time [27]. Both damage modes are deleterious to the remaining strength of the material. However, the mechanics of the associated fatigue processes remain obscure. In this paper we present results of a fatigue study with spherical indenters on nominally brittle ceramics, i.e. relatively homogeneous ceramics with no signi®cant R-curve, using an indentation±strength Acta mater. Vol. 47, No. 18, pp. 4711±4725, 1999 Published by Elsevier Science Ltd On behalf of Acta Metallurgica Inc. Printed in Great Britain PII: S1359-6454(99)00246-3 1359-6454/99 $20.00 + 0.00 {Guest Scientist from: Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Yusong, Taejon 305-701, Korea. {Present address: Department of Ceramic Science and Engineering, Changwon National University, Changwon, Kyungnam 641-773, Korea. }To whom all correspondence should be addressed. 4711
4712 KIM et al: CYCLIC FATIGUE OF BRITTLE CERAMICS test procedure. This procedure involves two steps: single-cycle contacts falls off abruptly beyond a cyclic contacts on specimen surfaces using a hard critical load for cone crack formation, and there sphere of given radius, at prescribed frequency and after declines continuously and slowly with increas- maximum load; ( ii) inert strength measurement of ing contact load, in accordance with traditional the contact-damaged specimens. The first step indentation equilibrium fracture mechanics. One allows characterization of the actual damage pro- study with spheres in sustained static loading over cess-the second step enables quantification of the prescribed contact durations (static fatigue")on damage severity. Glass is an ideal model brittle ma- glass in water [31] reported a rate-dependent re- terial because of its well-documented indentation duction of the critical load for initiation of cone strength properties in single-cycle sphere loading cracks and subsequent propagation of the cone [28-31( see Section 2.1), as well as its availability cracks, with corresponding steady depression in the of essential crack velocity parameters for data ensuing strength levels. Those rate effects were analysis (from Vickers indentation fracture studies found to be entirely consistent with time-integrated [32-34]). Moreover, the transparency of glass allows chemically-enhanced slow crack growth, in accord- for direct observations of the fracture damage from ance with expectation for brittle solids. Another the contact tests and the response of this damage in study with impacting spheres [30 reported strength subsequent strength tests. Other brittle ceramics degradation characteristics similar to those in static selected for study include: a translucent dental por- loading. In that case the main features of the degra lain, because of its brittleness and its amenability dation could be accounted for by introducing a to limited subsurface observation [25, 26]; and a simple relation between impact velocity and impul- relatively strong bearing-grade silicon nitride [35], sive load into the indentation fracture mechanics included to expand the range of toughness values. However, in this latter study some irregularities in The bulk of the contact fatigue tests are conducted the detailed strength response were noted. particu n moist environments, to highlight any chemical larly with smaller and denser spheres-these irregu- effect larities were correlated with the appearance of Using an indentation fracture analysis, we con- plasticity-induced radial cracks from sphere pen- firm that the initial stages of strength degradation etration into the impact surface, in a manner first are indeed consistent with chemically-enhanced observed by Phillips (cited in Ref. [38] and later low growth of classical cone cracks, integrated quantified by Swain and Hagan [39 over the duration of the fatigue test (brittle" Later, strength degradation studies from single region). The analysis provides simple power-law re- cycle sphere contacts were extended to relatively lations for evaluating cyclic lifetimes in this region. homogeneous polycrystalline ceramics [35, 40-44 However, beyond a critical number of cycles, a Again, cone cracking was identified as the principa more deleterious mechanism of degradation comes mode of damage, with similar abrupt strength into play, signaling the imminent demise of the ma- decrements at critical contact loading. In more het terial. This second mode is shown to be associated erogeneous ceramics, quasi-plastic damage also with the onset of distributed subsurface microdam- degraded the strength, initially without the abrupt age, with attendant development of more dangerous falloff [27]however, in these materials the pro- radial cracks (quasi-plastic region). Comparison spect of microcrack coalescence within the damage of the cyclic fatigue data with static fatigue data zone was identified as a potential source of ultimate confirms a strong mechanical component in the cyc- rapid strength decline in more severe indentation lic damage buildup in the latter region. These events [27], e.g. in single-cycle overload, multi-cycle results highlight both the strengths and limitations contacts [21], or high-velocity impact [45]. of traditional fracture mechanics concepts in fatigue analysis, especially in the context of lifetime design, 2.2. Fracture mechanics analysis and foreshadow a totally dominant quasi-plastic Consider the application of indentation fracture mode of failure in tougher, more heterogeneous cer- mechanics to the analysis of strength degradation from cyclic contacts with spheres, Fig. 1. Begin with the assumption that the material is ideally brittle, so that the degradation is caused exclusively by failure from cone cracks. The cone fracture is 2. CONTACT FATIG assumed to be subject to slow crack growth during DEGRADATION he cyclic contact loading according to a power- law velocity function, as previously considered in static 2. 1. Background loading [31 but now with the time integral taken The first indentation-strength studies with over a periodic contact history. We defer, until cal indenters were carried out on soda-lime later, consideration of failure from any secondary glass, the quintessential brittle material, in mode of damage ycle indentation [28, 29, 36, 37]. Generall Thus. assume that the crack extends trength of surface- damaged glass specimens from cordance with a basic power-law crack velocity
test procedure. This procedure involves two steps: (i) cyclic contacts on specimen surfaces using a hard sphere of given radius, at prescribed frequency and maximum load; (ii) inert strength measurement of the contact-damaged specimens. The ®rst step allows characterization of the actual damage processÐthe second step enables quanti®cation of the damage severity. Glass is an ideal model brittle material because of its well-documented indentation± strength properties in single-cycle sphere loading [28±31] (see Section 2.1), as well as its availability of essential crack velocity parameters for data analysis (from Vickers indentation fracture studies [32±34]). Moreover, the transparency of glass allows for direct observations of the fracture damage from the contact tests and the response of this damage in subsequent strength tests. Other brittle ceramics selected for study include: a translucent dental porcelain, because of its brittleness and its amenability to limited subsurface observation [25, 26]; and a relatively strong bearing-grade silicon nitride [35], included to expand the range of toughness values. The bulk of the contact fatigue tests are conducted in moist environments, to highlight any chemical eect. Using an indentation fracture analysis, we con- ®rm that the initial stages of strength degradation are indeed consistent with chemically-enhanced slow growth of classical cone cracks, integrated over the duration of the fatigue test (``brittle`` region). The analysis provides simple power-law relations for evaluating cyclic lifetimes in this region. However, beyond a critical number of cycles, a more deleterious mechanism of degradation comes into play, signaling the imminent demise of the material. This second mode is shown to be associated with the onset of distributed subsurface microdamage, with attendant development of more dangerous radial cracks (``quasi-plastic'' region). Comparison of the cyclic fatigue data with static fatigue data con®rms a strong mechanical component in the cyclic damage buildup in the latter region. These results highlight both the strengths and limitations of traditional fracture mechanics concepts in fatigue analysis, especially in the context of lifetime design, and foreshadow a totally dominant quasi-plastic mode of failure in tougher, more heterogeneous ceramics. 2. CONTACT FATIGUE AND STRENGTH DEGRADATION 2.1. Background The ®rst indentation±strength studies with spherical indenters were carried out on soda-lime silicate glass, the quintessential brittle material, in singlecycle indentation [28, 29, 36, 37]. Generally, the strength of surface-damaged glass specimens from single-cycle contacts falls o abruptly beyond a critical load for cone crack formation, and thereafter declines continuously and slowly with increasing contact load, in accordance with traditional indentation equilibrium fracture mechanics. One study with spheres in sustained static loading over prescribed contact durations (``static fatigue'') on glass in water [31] reported a rate-dependent reduction of the critical load for initiation of cone cracks and subsequent propagation of the cone cracks, with corresponding steady depression in the ensuing strength levels. Those rate eects were found to be entirely consistent with time-integrated chemically-enhanced slow crack growth, in accordance with expectation for brittle solids. Another study with impacting spheres [30] reported strength degradation characteristics similar to those in static loading. In that case the main features of the degradation could be accounted for by introducing a simple relation between impact velocity and impulsive load into the indentation fracture mechanics. However, in this latter study some irregularities in the detailed strength response were noted, particularly with smaller and denser spheresÐthese irregularities were correlated with the appearance of plasticity-induced radial cracks from sphere penetration into the impact surface, in a manner ®rst observed by Phillips (cited in Ref. [38]) and later quanti®ed by Swain and Hagan [39]. Later, strength degradation studies from singlecycle sphere contacts were extended to relatively homogeneous polycrystalline ceramics [35, 40±44]. Again, cone cracking was identi®ed as the principal mode of damage, with similar abrupt strength decrements at critical contact loading. In more heterogeneous ceramics, quasi-plastic damage also degraded the strength, initially without the abrupt fallo [27]Ðhowever, in these materials the prospect of microcrack coalescence within the damage zone was identi®ed as a potential source of ultimate rapid strength decline in more severe indentation events [27], e.g. in single-cycle overload, multi-cycle contacts [21], or high-velocity impact [45]. 2.2. Fracture mechanics analysis Consider the application of indentation fracture mechanics to the analysis of strength degradation from cyclic contacts with spheres, Fig. 1. Begin with the assumption that the material is ideally brittle, so that the degradation is caused exclusively by failure from cone cracks. The cone fracture is assumed to be subject to slow crack growth during the cyclic contact loading according to a power-law velocity function, as previously considered in static loading [31] but now with the time integral taken over a periodic contact history. We defer, until later, consideration of failure from any secondary mode of damage. Thus, assume that the cone crack extends in accordance with a basic power-law crack velocity 4712 KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS
KIM et al: CYCLIC FATIGUE OF BRITTLE CERAMICS Pn generic form [47, 48 K(c)=do(tc)/Fc) where c is the crack dimension measured along the downward crack coordinate s and F(c) is a dimen sionless Greens function, with F0. Suppose now that the indenter is subject to some time-dependent contact load P(n. Assume that a ring crack initiates from a surface flaw of character istic size cr and begins to extend downward accord attain instability by writing u=dc/dr in equation and co th ions(2)and (3) Ro 0 dc/le/FOn Static load SIze c= cF at time I= Ie for cone crack pop-in is determinable from the 0 limiting equilibrium condition K= To in equation (3). Since the extension to depth cF is generally Multi-cycle 10c small compared to the final con we regard this phase of the crack evolution as initiation In the special case of periodic loading to pea load P over n cycles at frequency f, corresponding Fig. 1. Schematic of Hertzian contact of radius r and n cycles at load P. Beyond ith wc to an indentation time I=n/f, equation(4)reduces threshold load. damage consists of ks. surface ring radius Ro plus, under severe loading conditions, sub- (nPN)=[(N) Ro/G(N )uo(2n/RS/To/(1-2v)1 un over n normal contacts at frequency ests, and static loading over prescribed hold times I, are also run where subscript c denotes critical number of cycles Ie to pop-in at fixed P; or, alternatively, critical load p at fixed n. The G and h terms are dimen- sionless integrals [10 D=L0(K/70)(K<To) G(N)= [P(o/P] d(n where To(Ke)is the single-value material toughness defining the upper limit of the velocity range, and N and o are velocity exponent and coefficient, re- H(N)= d(c/Ro)/(c/Ro)Fc/Ro).(6b) spectively. We consider two stages in the kinetic rack evolution in relation to the ensuing strength Equation (5) degradation properties: initiation, determining the ing relative to threshold load at which strength undergoes an initiation in single-cycle contact, i.e. P=Pi at sequent continued strength loss at post-threshold n= 1: 2. 2. Cone crack initiation. The radial tensile stress do acting at the surface coordinate ro of a ne=(P1/P)(fixed P (7b) prospective cone crack from contact with a sphere of radius r at load P(Fig. 1)for a material of pois- The quantity Pi has the functional form sons ratio v is [46 IC,N, Do, Ro, To, v). We will obtain an explicit re- lation for this function in Section 5. Strictly, PI o=1-2)P/RG (2)also depends on cr and ce, but these dependencies are small because of the stabilizing effect of the The corresponding stress-intensity factor has the diminishing stress field in cone initiation, such that
function u u0 K=T0 N K 0. Suppose now that the indenter is subject to some time-dependent contact load P0 t. Assume that a ring crack initiates from a surface ¯aw of characteristic size cf and begins to extend downward according to equation (1). We may solve for the time to attain instability by writing u dc=dt in equation (1) and combining with equations (2) and (3): u0 1 ÿ 2n=2p1=2 R2 0T0 N tc 0 P 0 tN dt cF cf dc=c1=2 F cN 4 where the instability crack size c cF at time t tc for cone crack pop-in is determinable from the limiting equilibrium condition K T0 in equation (3). Since the extension to depth cF is generally small compared to the ®nal cone crack size, we regard this phase of the crack evolution as ``initiation''. In the special case of periodic loading to peak load P over n cycles at frequency f, corresponding to an indentation time t n=f, equation (4) reduces to nP Nc H N fR0=G N u02p1=2 R3=2 0 T0= 1 ÿ 2nN 5 where subscript c denotes critical number of cycles nc to pop-in at ®xed P; or, alternatively, critical load Pc at ®xed n. The G and H terms are dimensionless integrals [10] G N 1 0 P 0 ft=P N d ft 6a H N cF=R0 cf =R0 d c=R0= c=R0 1=2 F c=R0N: 6b Equation (5) may be further reduced by normalizing relative to the value of critical load for cone initiation in single-cycle contact, i.e. P P1 at n 1: Pc P1=n1=N fixed n 7a nc P1=P N fixed P: 7b The quantity P1 has the functional form P1 f, N, u0, R0, T0, n. We will obtain an explicit relation for this function in Section 5. Strictly, P1 also depends on cf and cF, but these dependencies are small because of the stabilizing eect of the diminishing stress ®eld in cone initiation, such that Fig. 1. Schematic of Hertzian contact test, with WC sphere of radius r and n cycles at load P. Beyond threshold load, damage consists of cone cracks, surface ring radius R0; plus, under severe loading conditions, subsurface quasi-plastic deformation zone. Cyclic fatigue tests are run over n normal contacts at frequency f. Comparative single-cycle tests, and static loading tests over prescribed hold times t, are also run. KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS 4713
KIM et al: CYCLIC FATIGUE OF BRITTLE CERAMICS the crack spends most of its lifetime in the inter- crack [equation(8)it is now the final stage of mediate stages of growth [38, 47 growth that is rate limiting. 2.2. 2. Cone crack propagation Equations (10)and(Il) indicate that relative to of fatigue for specimens containing well-developed cyclic contact tests, static contact tests run at the cone cracks has been given in an earlier study [20]. same maximum load P yield the same strengths a We reproduce that analysis here, with minor modifi- at anequivalent"contact time cations The stress-intensity factor for (13) cone cI may be approximated by the traditional roesler re- noting that GcsI [0sP'(OsP and Gs=l lation [28, 49] (P= P=constant) in equation(6a)(Appendix) where z is a dimensionless geometry coefficie 3. CONTACT FATIGUE EXPERIMENTS This relation is a far-field approximation, vali 3. Materials selection the limit c> Ro--note that it is independent of Ro Soda-lime glass laths 90 mmx 19.0 mmx5.65 mm and sphere radius r. For a time-dependent load P(n we insert equation(8) into equation (1) were cut with a diamond scribe from as-receive obtain the cone crack size c after time I commercial window plate. The laths were beveled at their top edges(the edges opposite the scribed 3N/ dc= Do(z/To) [P(]dr surfaces) to minimize edge failures in the sub- sequent strength tests, and annealed to re spurious residual stresses [28 with co the equilibrium crack size at K=To in Bars 3 mmx 4 mm x 25 mm of a feldspathic por equation(8)at critical time l= ne/f to pop-in. celain in use for dental restorations (Vita Mark Il For periodic loading over n cycles at frequency f, Vita Zahnfabrik, Bad Sackingen, Germany)were we integrate to obtain ground from large blocks. Top surfaces of the bars were finished with a I um diamond paste polish 3N/2+=[(3N/2+1)G(N )uonf(zPTo)"(10) The microstructure consists of a glass matrix with in the limit n>ne and N> I, with G(N) defined in reinforcing sanidine crystals and residual frit par- equation(6a) ticles of dimension 1-7 um [25, 26 The"inert"strength of a specimen containing a Bars of the same dimension and surface finish as well-formed cone crack is given by the familia lin were prepared from blocks of a bear- Griffith relation ing-grade silicon nitride from an earlier study(there eferred to as M-Si3N4)[35]. In this material the (11) microstructure consists of a bimodal distribution of elongated B grains of length 4.0 um and diameter where y is a crack geometry parameter. Below the 0.5 um(70 vol %)and equiaxed a grains of mean threshold for cone crack initiation [equations(7a) size 0.5 um (20 vol %) with oxynitride glassy and(7b)). the strength is considered to be deter- bonding phase(e10 vol % mined by the surface flaw size, c= cr. Above the threshold, the functional dependence an, P) is 3.2. Contact lesting determined by inserting equation (10)into equation The center regions of the top surfaces were sub- (11). Normalizing relative to the value of the jected to contact testing. For the glass specimens, a strength a=0I for contacts that produce cone light pre-abrasion was first made at the prospective cracks at critical load P= Pi at n= l, we obtain, contact sites with 400-mesh Sic grit to provide an in the limit N> 2/3 adequate density of flaws for ring-crack nucleation 28, 30, 31]. In the other materials, the intrinsic flaw a=01(P1/n/P)(fixed m) (12a) population associated with the microstructure obviated the need for any such pre-abrasion treat- n=I(P,/PGo](fixed a). (12b) ment 25,35 The contacts were made using tungsten carbide Note that even though n may vary over many dec- (wC) spheres of radius r=3.18 or 1.98 mm on a ades, a is not expected to be sensitive to n for typi- servo-hydraulic universal testing machine (Model cally large values of M 8502, Instron Corp, Canton, MA). Cyclic tests As in the preceding subsection, the quantity an were run in repeat loading in haversinusoidal an be expressed in functional form, form up to n=10 at frequency f=10 Hz, between aI(, N, Uo. Ro, To v). Again, an explicit relation for specified maximum and minimum loads(the latter, this quantity will be derived in Section 5. Strictly, typically 20 N, primarily to prevent the contact I also depends on co, but this dependency is small from wandering). Comparative static tests because of the stability of the well-developed cone also made over hold times t=n/f(Fig. 1), to iso-
the crack spends most of its lifetime in the intermediate stages of growth [38, 47]. 2.2.2. Cone crack propagation. A simple analysis of fatigue for specimens containing well-developed cone cracks has been given in an earlier study [20]. We reproduce that analysis here, with minor modi®- cations. The stress±intensity factor for the cone crack may be approximated by the traditional Roesler relation [28, 49] K wP=c3=2 8 where w is a dimensionless geometry coecient [50]. This relation is a far-®eld approximation, valid in the limit cwR0Ðnote that it is independent of R0 and sphere radius r. For a time-dependent load P0 t we insert equation (8) into equation (1) to obtain the cone crack size c after time t c c0 c3N=2 dc u0 w=T0 N t tc P 0 tN dt 9 with c0 the equilibrium crack size at K T0 in equation (8) at critical time tc nc=f to pop-in. For periodic loading over n cycles at frequency f, we integrate to obtain c3N=21 3N=2 1G N u0n=f wP=T0 N 10 in the limit nwnc and Nw1, with G(N) de®ned in equation (6a). The ``inert'' strength of a specimen containing a well-formed cone crack is given by the familiar Grith relation s T0=cc1=2 11 where c is a crack geometry parameter. Below the threshold for cone crack initiation [equations (7a) and (7b)], the strength is considered to be determined by the surface ¯aw size, c cf. Above the threshold, the functional dependence s(n, P) is determined by inserting equation (10) into equation (11). Normalizing relative to the value of the strength s s1 for contacts that produce cone cracks at critical load P P1 at n 1, we obtain, in the limit Nw2=3 s s1 P1=n1=NP 1=3 fixed n 12a n P1=P s1=s 3 N fixed s: 12b Note that even though n may vary over many decades, s is not expected to be sensitive to n for typically large values of N. As in the preceding subsection, the quantity s1 can be expressed in functional form, s1 f, N, u0, R0, T0, n. Again, an explicit relation for this quantity will be derived in Section 5. Strictly, s1 also depends on c0, but this dependency is small because of the stability of the well-developed cone crack [equation (8)]Ðit is now the ®nal stage of growth that is rate limiting. Equations (10) and (11) indicate that relative to cyclic contact tests, static contact tests run at the same maximum load P yield the same strengths s at an ``equivalent'' contact time tS GCn=f 13 noting that GCR1 [0RP0 tRP] and GS 1 (P0 P constant) in equation (6a) (Appendix). 3. CONTACT FATIGUE EXPERIMENTS 3.1. Materials selection Soda-lime glass laths 90 mm19.0 mm5.65 mm were cut with a diamond scribe from as-received commercial window plate. The laths were beveled at their top edges (the edges opposite the scribed surfaces) to minimize edge failures in the subsequent strength tests, and annealed to remove any spurious residual stresses [28]. Bars 3 mm4 mm25 mm of a feldspathic porcelain in use for dental restorations (Vita Mark II1 , Vita Zahnfabrik, Bad Sackingen, Germany) were ground from large blocks. Top surfaces of the bars were ®nished with a 1 mm diamond paste polish. The microstructure consists of a glass matrix with reinforcing sanidine crystals and residual frit particles of dimension 1±7 mm [25, 26]. Bars of the same dimension and surface ®nish as the porcelain were prepared from blocks of a bearing-grade silicon nitride from an earlier study (there referred to as M-Si3N4) [35]. In this material the microstructure consists of a bimodal distribution of elongated b grains of length 4.0 mm and diameter 0.5 mm (170 vol.%) and equiaxed a grains of mean size 10.5 mm (120 vol.%), with oxynitride glassy bonding phase (110 vol.%). 3.2. Contact testing The center regions of the top surfaces were subjected to contact testing. For the glass specimens, a light pre-abrasion was ®rst made at the prospective contact sites with 400-mesh SiC grit to provide an adequate density of ¯aws for ring-crack nucleation [28, 30, 31]. In the other materials, the intrinsic ¯aw population associated with the microstructure obviated the need for any such pre-abrasion treatment [25, 35]. The contacts were made using tungsten carbide (WC) spheres of radius r 3:18 or 1.98 mm on a servo-hydraulic universal testing machine (Model 8502, Instron Corp., Canton, MA). Cyclic tests were run in repeat loading in haversinusoidal waveform up to n 107 at frequency f=10 Hz, between speci®ed maximum and minimum loads (the latter, typically 20 N, primarily to prevent the contact from ``wandering''). Comparative static tests were also made over hold times t n=f (Fig. 1), to iso- 4714 KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS
KIM et al. CYCLIC FATIGUE OF BRITTLE CERAMICS 4715 late any mechanical contribution to the damage ad n). The indentation damage evolution was ulation. In most cases the tests were conducted nitored on a video recorder in distilled water to enhance the fatigue effect; other tests were conducted in laboratory air (relative humidity≈50%) 4. RESULTS In some cases the WC spheres themselves showed signs of deformation, especially in extended tests on 9.1. Strength des data and silicon nitride [35]. and so were rotated periodically es of the strength degradation tests are plotted for glass/water, porcelain/water and silicon 3.3. Strength tests nitride air in Figs 2-4. Data points with error bars Strength tests were conducted on the contact- are experimental means and standard deviations of damaged bar specimens in four-point flexure, with a minimum five specimens at each specified number the contact surface on the tensile side. The outer of cycles n or maximum contact load P. and inner span dimensions used in the flexure tests symbols represent failures from natural flaws, filled e 61 and 27 mm for the glass laths, 20 and symbols failures from indentation sites; in the latter 10 mm for the other ceramics to obtain "inert strengths" the contact sites were first dried in war air and covered with a drop of dry silicone oil, and he specimens then broken in fast fracture(<20 ms) (a)Glass/water 3,18mm [33]. All specimens were examined in a low-power ermine the source of failure. i.e damage site or"natural"flaw. Any edge failures 200N (more common in the glass specimens) were dis- carded from the data poo P=500N Selected surface contact damage sites in all ma terials were subjected to close examination by high- power optical microcopy, both before and after I (b) Porcelain/water flexure testing. Most observations were made in gold coating the indented surfaces. In the transpar- 6 Iso damage;and similarly in the translucent porcelain, a o reflection mode. in Nomarski illumination. after ent glass the damage sites were also examined irectly in transmission mode to observe subsurface after grinding and polishing the specimens from the P=500N back surface to a final thickness <500 um Subsurface side views were also obtained by grinding and polishing cross sections down to the 1500 indentation mid-planes [51] and viewing in optical (c)SiN//air icroscopy. Again, in the glass the damage was amenable to viewing in both reflection and trans 1000 mission microscopy, in the porcelain, by grinding 000N and polishing the specimens from both sides down to the mid-plane, to net thickness <500 um. 500 (Bonded-interface specimens [52, 53], in which spe- P=2200N prior to indentation, were not employed here because of concern that environmental specie might penetrate the interface and produce artifacts) Number of contact cycles, n the cross sections were etched of 12% HF acid to highlight damage features In situ observations of the damage zone crack cycles n, indentation with WC spheres of radius r, at maxi uring the indentation-strength tests These obser. porcelain in water;(e) silicon nitride ng ass id awater: (b) growth were made in selected glass specimens re means and standard deviations, minimum five speci ations were made using a stereo-zoom microscope mens per point. Filled symbols indicate failures fro with back lighting, either directly through the side indentation sites-grey symbols fro surface or from below using a mirror to redirect the mbols from radial cracks. Unfilled symbols indicate fail- res from natural flaws-box at left axis and horizonta light source (in the latter case with the con- dashed line are"laboratory"strengths (unindented speci tact surface precoated with gold to enhance reflec- mens). Solid curves are theoretical fits to data
late any mechanical contribution to the damage accumulation. In most cases the tests were conducted in distilled water to enhance the fatigue eect; other tests were conducted in laboratory air (relative humidity 150%). In some cases the WC spheres themselves showed signs of deformation, especially in extended tests on silicon nitride [35], and so were rotated periodically. 3.3. Strength tests Strength tests were conducted on the contactdamaged bar specimens in four-point ¯exure, with the contact surface on the tensile side. The outer and inner span dimensions used in the ¯exure tests were 61 and 27 mm for the glass laths, 20 and 10 mm for the other ceramics. To obtain ``inert strengths'' the contact sites were ®rst dried in warm air and covered with a drop of dry silicone oil, and the specimens then broken in fast fracture (<20 ms) [33]. All specimens were examined in a low-power microscope to determine the source of failure, i.e. damage site or ``natural'' ¯aw. Any edge failures (more common in the glass specimens) were discarded from the data pool. 3.4. Damage morphology Selected surface contact damage sites in all materials were subjected to close examination by highpower optical microcopy, both before and after ¯exure testing. Most observations were made in re¯ection mode, in Nomarski illumination, after gold coating the indented surfaces. In the transparent glass the damage sites were also examined directly in transmission mode to observe subsurface damage; and similarly in the translucent porcelain, after grinding and polishing the specimens from the back surface to a ®nal thickness <500 mm. Subsurface side views were also obtained by grinding and polishing cross sections down to the indentation mid-planes [51] and viewing in optical microscopy. Again, in the glass the damage was amenable to viewing in both re¯ection and transmission microscopy; in the porcelain, by grinding and polishing the specimens from both sides down to the mid-plane, to net thickness <500 mm. (Bonded-interface specimens [52, 53], in which specimens are pre-sectioned and restored into contact prior to indentation, were not employed here because of concern that environmental species might penetrate the interface and produce artifacts). Some of the cross sections were etched in a solution of 12% HF acid to highlight damage features. In situ observations of the damage zone crack growth were made in selected glass specimens during the indentation±strength tests. These observations were made using a stereo-zoom microscope with back lighting, either directly through the side surface or from below using a mirror to redirect the light source (in the latter case with the upper contact surface precoated with gold to enhance re¯ection). The indentation damage evolution was monitored on a video recorder. 4. RESULTS 4.1. Strength degradation data and analysis Results of the strength degradation tests are plotted for glass/water, porcelain/water and silicon nitride/air in Figs 2±4. Data points with error bars are experimental means and standard deviations of a minimum ®ve specimens at each speci®ed number of cycles n or maximum contact load P. Un®lled symbols represent failures from natural ¯aws, ®lled symbols failures from indentation sites; in the latter Fig. 2. Inert strength s as a function of number of contact cycles n, indentation with WC spheres of radius r, at maximum loads P indicated: (a) soda-lime glass in water; (b) porcelain in water; (c) silicon nitride in air. Data points are means and standard deviations, minimum ®ve specimens per point. Filled symbols indicate failures from indentation sitesÐgrey symbols from cone cracks, black symbols from radial cracks. Un®lled symbols indicate failures from natural ¯awsÐbox at left axis and horizontal dashed line are ``laboratory'' strengths (unindented specimens). Solid curves are theoretical ®ts to data. KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS 4715
4716 KIM et al. CYCLIC FATIGUE OF BRITTLE CERAMICS case, grey symbols represent failures from cone termined from previous(Vickers indentation)stu- cracks and black symbols from radial cracks dies [32-34], with just P, and a, as adjustable Section 4.2). Open boxes at left axis and associated parameters; for the other materials, N, PI and al horizontal dashed lines are strengths of unindented are all treated as adjustable parameters. The fitted pecimens. Solid curves through the data are theor- curves are consistent with the main data trends in etical fits the cone crack region, within the data scatter 4.1.1. Cyclic contact fatigue tests. Figure 2 shows 4.1.2. Cyclic vs static fatigue tests. Figure 4 com- lots of o(n) data for each material/environment pares a(n)data for cyclic and static tests, again for system, for indentations at specified sphere radius r, the same material/environment systems, with the at two selected loads P. In each case the two loads time scale for the cyclic data determined as are selected so as to straddle the single-cycle cone [= Gen/f according to equation(13). Chosen values crack threshold value, PI(see Table 1, later ). Gen- of n and P are such that degradation occurs within erally, at the higher of the two selected P values thethe first cycle. In the region of the first strength strength is substantially degraded within the first decrement the data overlap, within the scatter bars cycle--in this case, failures originate from indenta- However, in the region of the second strength tion sites at all n. At the lower of the P values the decrement the cyclic data diverge markedly below strength shows no degradation initially, correspond ing to failures away from the contact sites at natu- ral flaws (indicating that any initial flaw extension rior to ring-crack instability is too minor to a)Glass/water grade the strength); but beyond a critical number les (ne) the strength again declines above a 100 er of cycles(n>ne). Spec be made of the data for porcelain/water at the lower load P= 200N in Fig. 2(b)in this case P lies so close to Pi that the failures are stochastical distributed between cone crack and natural-faw gins. her n values the strength data show noticeable accelerating decline. This second region 200 (b) Porcelain/water =3.18mm becomes clearly evident after only a few hundred cycles at P= 500 N in the glass/water and porce- 2 150 lain/water systems; in the silicon nitrideair system it becomes apparent only after n10 cycles at the ases the glass and porcelain specimens fail during d the contact test itself (arrows). Figure 3 shows analogous o(P) results for the l material/environment systems, an 0 same specified sphere radius r, comparing data after longed cycling at specified numbers of cycles (e)Si3N4/air r=1.98mm (n>1)with those in single-cycle loading (n= 1) These results confirm a significant degradation in 1000 "乎“基”“T““““-“1 strength from the cycling. In the glass/water and porcelain/water systems the cyclic data fall withi the domain of the second strength decrement ove the entire range of P(cf. Fig. 2), and so tend to fall beneath the predicted curve; conversely, in the sili- con nitride/air system the cyclic data remain within 0001500 00 the bounds of the first strength decrement at all P. The solid curves in Figs 2 and 3 are best fits of Contact load, P(N) the initial degradation region corresponding to fail- indentation with WC spheres of radie of contact are from cone cracks (i.e. grey symbols), using N, water;(c) silicon nitride/ air. Data points are means and PI and a1 as parameters. Vertical solid lines indi- standard deviations, minimum five specimens per point cate critical ne or Pc values for cone crack initiation Filled symbols indicate failures from indentation sites- lequations(7a)and(7b)); the solid curves at ne >1 grey symbols from cone cracks, black symbols from radial nd Pe>I represent strength degradation functions cracks. Unfilled symbols indicate failures from natural faws-box at left axis and horizontal dashed line are for failure from these cone cracks [equations(12a)"laboratory"strengths (unindented specimens). Solid and(12b)] For soda-lime glass, N=17.9 is prede- urves are theoretical fits to data
case, grey symbols represent failures from cone cracks and black symbols from radial cracks (Section 4.2). Open boxes at left axis and associated horizontal dashed lines are strengths of unindented specimens. Solid curves through the data are theoretical ®ts. 4.1.1. Cyclic contact fatigue tests. Figure 2 shows plots of s(n) data for each material/environment system, for indentations at speci®ed sphere radius r, at two selected loads P. In each case the two loads are selected so as to straddle the single-cycle cone crack threshold value, P1 (see Table 1, later). Generally, at the higher of the two selected P values the strength is substantially degraded within the ®rst cycleÐin this case, failures originate from indentation sites at all n. At the lower of the P values the strength shows no degradation initially, corresponding to failures away from the contact sites at natural ¯aws (indicating that any initial ¯aw extension prior to ring-crack instability is too minor to degrade the strength); but beyond a critical number of cycles (nc) the strength again declines above a critical number of cycles (n > nc). Special note may be made of the data for porcelain/water at the lower load P = 200 N in Fig. 2(b)Ðin this case P lies so close to P1 that the failures are stochastically distributed between cone crack and natural-¯aw failure origins. At higher n values the strength data show a noticeable accelerating decline. This second region becomes clearly evident after only a few hundred cycles at P = 500 N in the glass/water and porcelain/water systems; in the silicon nitride/air system it becomes apparent only after n1107 cycles at the comparatively high load P = 2200 N. In extreme cases the glass and porcelain specimens fail during the contact test itself (arrows). Figure 3 shows analogous s(P) results for the same material/environment systems, and at the same speci®ed sphere radius r, comparing data after prolonged cycling at speci®ed numbers of cycles (nw1) with those in single-cycle loading (n 1). These results con®rm a signi®cant degradation in strength from the cycling. In the glass/water and porcelain/water systems the cyclic data fall within the domain of the second strength decrement over the entire range of P (cf. Fig. 2), and so tend to fall beneath the predicted curve; conversely, in the silicon nitride/air system the cyclic data remain within the bounds of the ®rst strength decrement at all P. The solid curves in Figs 2 and 3 are best ®ts of equations (7a), (7b), (12a) and (12b) to the data in the initial degradation region corresponding to failure from cone cracks (i.e. grey symbols), using N, P1 and s1 as parameters. Vertical solid lines indicate critical nc or Pc values for cone crack initiation [equations (7a) and (7b)]; the solid curves at nc > 1 and Pc > 1 represent strength degradation functions for failure from these cone cracks [equations (12a) and (12b)]. For soda-lime glass, N 17:9 is predetermined from previous (Vickers indentation) studies [32±34], with just P1 and s1 as adjustable parameters; for the other materials, N, P1 and s1 are all treated as adjustable parameters. The ®tted curves are consistent with the main data trends in the cone crack region, within the data scatter. 4.1.2. Cyclic vs static fatigue tests. Figure 4 compares s(t) data for cyclic and static tests, again for the same material/environment systems, with the time scale for the cyclic data determined as t Gcn=f according to equation (13). Chosen values of n and P are such that degradation occurs within the ®rst cycle. In the region of the ®rst strength decrement the data overlap, within the scatter bars. However, in the region of the second strength decrement the cyclic data diverge markedly below Fig. 3. Inert strength s as a function of contact load P, indentation with WC spheres of radius r, at number of cycles n indicated: (a) soda-lime glass/water; (b) porcelain/ water; (c) silicon nitride/air. Data points are means and standard deviations, minimum ®ve specimens per point. Filled symbols indicate failures from indentation sitesÐ grey symbols from cone cracks, black symbols from radial cracks. Un®lled symbols indicate failures from natural ¯awsÐbox at left axis and horizontal dashed line are ``laboratory'' strengths (unindented specimens). Solid curves are theoretical ®ts to data. 4716 KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS
KIM et al. CYCLIC FATIGUE OF BRITTLE CERAMICS 4717 Note that whereas the as(n) function extrapolates (a)Glass/water =3.l8m P=500N through the data over the complete time range, con- firming a predominantly chemical fatigue com- ponent in the static fatigue, the ac(o) function again declines to lower values beyond the second decre- ment 4.2. Damage morphology Cyclic Figure 5 shows surface and section optical micro- graphs of indentation damage sites in the three test (n= 1)and multi-cycle (n>1)loading. The glass P=500N [Fig. 5(a) and porcelain [Fig. 5(b)] are viewed in 习150 transmitted light, the latter after back-thinning: the silicon nitride is viewed in reflected light [Fig. 5(c) Static The loads and sphere radii chosen here highlight he transformation in damage mode(cf. Figs 2 and from simple, well-defined cone cracks just out- ide the contact in the single-cycle state to accumu- lated damage below the contact, with attendant 103 106 radial cracks as well as incipient material removal in the multi-cycle state. 1500s;N/r P-2200N failure origins at indentation damage sites in (a) 1000 glass and (b) porcelain strength specimens, in sequences of increasing n. The loads and sphere radii are again chosen to highlight the transform- ation in damage mode. At n= l the fracture path occur well outside the contact circle. consistent with failure from cone cracks. At intermediate n the frac- ture paths tend to move closer to the contact circle 00 ( more evident here in the Effective contact time, t(s) builds up within the contact area and begins to compete with the cone crack for dominance as a indentation. wC spheres of radius r, at maximum glass the fracture origin occurred outside and inside loads p indicated. Inert strength as a function of num be lain/water:(c)silicon nitride/air. Equivalent time axis for ability at P= 500 N and n= 105-cf. Fig. 3(a). At yclic test data computed as Gcnf. Data points are means large n the fracture paths intersect the indentation nd standard deviations, minimum five specimens per indicative of failures from radial cracks. Similar ob- oint. Circles are cyclic data, triangles static data-grey ymbols from cone cracks, black symbols from radial servations have been reported previously for the cracks. Box at left axis and horizontal dashed line are silicon nitride [44] and are not reproduced here: suf- ""laboratory" strengths (unindented specimens). Solid fice it to say that in this material the failure initiates curves are theoretical predictions from cone crack model. from cone cracks over the data range except at the highest value of n and P in Fig. 2 the static data, indicating the onset of a significant In situ observations of the indentation damage mechanical degradation component in the fatigue. sites during the strength tests provided more defini Equation (12a)is used to generate the solid tive confirmation of the failure origins in the trans- curves odn and os() in Fig. 4, using the calibrated parent glass specimens. In specimens with light parameters in Table I along with appropriate evalu- damage the failure initiated at the base of the cone tions of Gc(N)(Appendix).t Using equation(13) cracks and spread laterally and upward, forming to plot the time axis for the static data reduces the the characteristic inward-pointing cusp-like trace ado and os(n data to universal curves in the outside the contact on the upper surface seen in region just beyond the first strength decrement. Fig. 6 at n=l. This kind of failure occurred rapidly, with little extension before instability. In specimens with heavy damage, the failure was con- fActually, including the factor Gc() in equation (13) firmed to initiate from the edge of a favorably muscule shifts of the cyclic fatigue curves oriented radial crack (relative to the tension axis) uld still result in almost indistinguishable cyclic and The radial cracks extended outward 20%in dimension prior to failure, indicating a stabilizing
the static data, indicating the onset of a signi®cant mechanical degradation component in the fatigue. Equation (12a) is used to generate the solid curves sC(t) and sS(t) in Fig. 4, using the calibrated parameters in Table 1 along with appropriate evaluations of GC(N) (Appendix).{ Using equation (13) to plot the time axis for the static data reduces the sC(t) and sS(t) data to universal curves in the region just beyond the ®rst strength decrement. Note that whereas the sS(t) function extrapolates through the data over the complete time range, con- ®rming a predominantly chemical fatigue component in the static fatigue, the sC(t) function again declines to lower values beyond the second decrement. 4.2. Damage morphology Figure 5 shows surface and section optical micrographs of indentation damage sites in the three test materials, comparing damage after single-cycle (n 1) and multi-cycle (nw1) loading. The glass [Fig. 5(a)] and porcelain [Fig. 5(b)] are viewed in transmitted light, the latter after back-thinning; the silicon nitride is viewed in re¯ected light [Fig. 5(c)]. The loads and sphere radii chosen here highlight the transformation in damage mode (cf. Figs 2 and 3): from simple, well-de®ned cone cracks just outside the contact in the single-cycle state to accumulated damage below the contact, with attendant radial cracks as well as incipient material removal, in the multi-cycle state. Figure 6 shows re¯ection optical micrographs of failure origins at indentation damage sites in (a) glass and (b) porcelain strength specimens, in sequences of increasing n. The loads and sphere radii are again chosen to highlight the transformation in damage mode. At n 1 the fracture paths occur well outside the contact circle, consistent with failure from cone cracks. At intermediate n the fracture paths tend to move closer to the contact circle (more evident here in the porcelain), as damage builds up within the contact area and begins to compete with the cone crack for dominance as a starting ¯aw in the ¯exural ®eld. [In the case of glass the fracture origin occurred outside and inside the contact circle with approximately equal probability at P = 500 N and n 103Ðcf. Fig. 3(a).] At large n the fracture paths intersect the indentation, indicative of failures from radial cracks. Similar observations have been reported previously for the silicon nitride [44] and are not reproduced here: suf- ®ce it to say that in this material the failure initiates from cone cracks over the data range except at the highest value of n and P in Fig. 2. In situ observations of the indentation damage sites during the strength tests provided more de®nitive con®rmation of the failure origins in the transparent glass specimens. In specimens with light damage the failure initiated at the base of the cone cracks and spread laterally and upward, forming the characteristic inward-pointing cusp-like trace outside the contact on the upper surface seen in Fig. 6 at n 1. This kind of failure occurred rapidly, with little extension before instability. In specimens with heavy damage, the failure was con- ®rmed to initiate from the edge of a favorably oriented radial crack (relative to the tension axis). The radial cracks extended outward 120% in dimension prior to failure, indicating a stabilizing Fig. 4. Comparison of cyclic and static contact fatigue, indentation with WC spheres of radius r, at maximum loads P indicated. Inert strength as a function of number of contact cycles for: (a) soda-lime glass/water; (b) porcelain/water; (c) silicon nitride/air. Equivalent time axis for cyclic test data computed as GCn/f. Data points are means and standard deviations, minimum ®ve specimens per point. Circles are cyclic data, triangles static dataÐgrey symbols from cone cracks, black symbols from radial cracks. Box at left axis and horizontal dashed line are ``laboratory'' strengths (unindented specimens). Solid curves are theoretical predictions from cone crack model. {Actually, including the factor GC(N) in equation (13) causes only minuscule shifts of the cyclic fatigue curves along the logarithmic time axis in Fig. 4, so that omitting it would still result in almost indistinguishable cyclic and static functions. KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS 4717
4718 KIM et al: CYCLIC FATIGUE OF BRITTLE CERAMICS Table 1. Fracture parameters for each material Soda-lime glass Silicon nitride 22 1900 650 factor in the crack driving force. Examination in tact stresses has been well documented in earlier ossed polars revealed the presence of considerable Vickers indentation studies [54-56] residual stress around the more heavily damaged Analogous surface observations of damage sites tes. Such a stabilizing influence from residual con- at high loads P in fast single-cycle contact tests 104 300um n=1 n=5×103 300um n三 n=10 300um Fig. 5. Optical micrographs of Hertzian indentation sites, comparing damage after single-cycle (n=D) ycle(n>1)loading: (a) soda-lime glass/water 500N, r=3. 18 mm);(b)porcelainw (P=500 N. r=3.18 mm);(c) silicon nitride/air(P= 2200 N, r=1.98 mm). Surface views: glass ar lain viewed in transmitted light (porcelain after back-surface thinning ) silicon nitride in reflected (Nomarski contrast, after gold coating). Note appearance of radial cracks at contact periphery
factor in the crack driving force. Examination in crossed polars revealed the presence of considerable residual stress around the more heavily damaged sites. Such a stabilizing in¯uence from residual contact stresses has been well documented in earlier Vickers indentation studies [54±56]. Analogous surface observations of damage sites at high loads P in fast single-cycle contact tests or Table 1. Fracture parameters for each material Material N P1 (N) s1 (MPa) Soda-lime glass 17.9 228 90 Porcelain 30 205 120 Silicon nitride 22 1900 650 Fig. 5. Optical micrographs of Hertzian indentation sites, comparing damage after single-cycle (n 1) and multi-cycle (nw1) loading: (a) soda-lime glass/water (P = 500 N, r=3.18 mm); (b) porcelain/water (P = 500 N, r=3.18 mm); (c) silicon nitride/air (P = 2200 N, r=1.98 mm). Surface views: glass and porcelain viewed in transmitted light (porcelain after back-surface thinning), silicon nitride in re¯ected light (Nomarski contrast, after gold coating). Note appearance of radial cracks at contact periphery after cycling. 4718 KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS
KIM et al. CYCLIC FATIGUE OF BRITTLE CERAMICS 4719 (a) (b) n 300um n=103 n n=5×1 Fig. 6. Optical micrographs of Hertzian indentation failure sites in broken inert strength specimens. celain/water. Flexural tension axis horizontal. Surface views, reflected light (Nomarski contrast, after gold coating). Note how fracture origins begin outside the contact circle at low n, and move inside as at equivalent test durations I in extended constant of some rate effect in the radial crack initiation pre load tests revealed no obvious signs of radial crack- cess. ing in any of the materials. Howeve Half-surface and section optical micrographs of ing the fact that the predicted strength function in damage zones in the glass and porcelain in the equations (12a)and (12b) fits the data over the heavy damage region are shown in Fig. 7, for tests entire range of P at n= l in Fig. 3 and the static at load P= 140 N. The sections are viewed in data over the entire range of test time I in Fig. 4, transmitted light, the porcelain after thinning from the failure paths in the glass and porcelain did tend both sides down to the mid-plane. Secondary cone to intersect the contact zone at large P and t(black cracks propagate steeply downward from well symbols in Figs 3 and 4), suggesting the existence within the contact circle. The surface traces of these
at equivalent test durations t in extended constant load tests revealed no obvious signs of radial cracking in any of the materials. However, notwithstanding the fact that the predicted strength function in equations (12a) and (12b) ®ts the data over the entire range of P at n 1 in Fig. 3 and the static data over the entire range of test time t in Fig. 4, the failure paths in the glass and porcelain did tend to intersect the contact zone at large P and t (black symbols in Figs 3 and 4), suggesting the existence of some rate eect in the radial crack initiation process. Half-surface and section optical micrographs of damage zones in the glass and porcelain in the heavy damage region are shown in Fig. 7, for tests at load P = 140 N. The sections are viewed in transmitted light, the porcelain after thinning from both sides down to the mid-plane. Secondary cone cracks propagate steeply downward from well within the contact circle. The surface traces of these Fig. 6. Optical micrographs of Hertzian indentation failure sites in broken inert strength specimens, after indentation at P = 500 N, r=3.18 mm, for n values indicated: (a) soda-lime glass/water; (b) porcelain/water. Flexural tension axis horizontal. Surface views, re¯ected light (Nomarski contrast, after gold coating). Note how fracture origins begin outside the contact circle at low n, and move inside as damage intensi®es at large n. KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS 4719
KIM et al. CYCLIC FATIGUE OF BRITTLE CERAMICS 5. DISCUSSION a 5./ General We have shown that intrinsically brittle materials, specifically soda-lime glass, porcelain and silicon nitride, are susceptible to fatigue in contacts with spheres. The strength degradation plots in Section 4. I usefully quantify this fatigue, thereby providing a basis for materials evaluation in applications involving concentrated oscillating loads. For this purpose, it is convenient to condense data from such plots onto a "master diagram-accordingly in Fig. 8 we replot some of the curves from Fig. 2, along with companion curves for a glass-infiltrated 250m alumina and yttria-tetragonal-polycrystal zirconia from a study on dental ceramics [26]. It is clear that materials like silicon nitride and zirconia, by virtue of their intrinsic toughness, occupy a high position (b) in such a diagram, and present themselves as perior candidates for bearing materials Nevertheless, even the strongest and toughest ma- terials are susceptible, to a greater or lesser extent to some degree of degradation moreover there are other considerations such as cost and aesthetics (e. g. dental restorations), that may in some cases constrain selection to the lower portions of the plot. We shall return to the issue of materials design We have also demonstrated the existence of at least two modes of damage in nominally brittle cer- amics. The first mode is classical cone fracture. dri- ven in moist environments by chemically-enhanced slow crack growth. Cone fracture accounts for the first stage of degradation in the strength plots-the 500um Fig. 7. Half-surface(refiected light) and side-section(trans 2000 of hertzian indentati soda-lime glass/water (P=140 N, r=3.18 mm. n=I Y-TZP(P= 1000N n=5x 10). Deep penetrating cracks form beneath the near-surface damage zone. Bars denote outer and inner Si3N4(P=1000N ontact diameters secondary cracks appear to correlate with the inner radius of the Hertzian contact, associated with the 3 400 minimum load used in the cyclic tests--inserting Alumina(P= 1000N Hertzian relation between contact radius a and load P, aaPl/s [58] yields ainner/ Porcelain(P= 500 with the relative scale of the annular zone for the 0 Glass(P= 500N indent on glass in Fig. 7(a). Interestingly, these deep cracks do not appear to participate in the sub- sequent flexural failure, possibly because they extend down into the compressive zone of the flex- Number of cycles, ure field in the strength testing: however, they may Fig. 8. Master diagram comparing contact fatigue re- be the cause of failure during extended contact fati- sponses a(n) for selected materials, at specified contact gue testing at high P and n(arrows, Fig. 2) load P: data for soda-lime glass, porcelain and silicon nitride from Fig. I: data for a glass-infiltrated alumina such analogous subsidiary cone cracks and zirconia(Y-TZP)from a companion study [26]. Solid observed in comparative static loading lines denote brittle region. (Note break in strength axis
secondary cracks appear to correlate with the inner radius of the Hertzian contact, associated with the minimum load used in the cyclic testsÐinserting Pmin=Pmax10:14 (20 N/140 N) into the classical Hertzian relation between contact radius a and load P, aAP1=3 [58] yields ainner=aouter10:5, consistent with the relative scale of the annular zone for the indent on glass in Fig. 7(a). Interestingly, these deep cracks do not appear to participate in the subsequent ¯exural failure, possibly because they extend down into the compressive zone of the ¯exure ®eld in the strength testing; however, they may be the cause of failure during extended contact fatigue testing at high P and n (arrows, Fig. 2). No such analogous subsidiary cone cracks were observed in comparative static loading. 5. DISCUSSION 5.1. General We have shown that intrinsically brittle materials, speci®cally soda-lime glass, porcelain and silicon nitride, are susceptible to fatigue in contacts with spheres. The strength degradation plots in Section 4.1 usefully quantify this fatigue, thereby providing a basis for materials evaluation in applications involving concentrated oscillating loads. For this purpose, it is convenient to condense data from such plots onto a ``master diagram''Ðaccordingly, in Fig. 8 we replot some of the curves from Fig. 2, along with companion curves for a glass-in®ltrated alumina and yttria-tetragonal-polycrystal zirconia from a study on dental ceramics [26]. It is clear that materials like silicon nitride and zirconia, by virtue of their intrinsic toughness, occupy a high position in such a diagram, and present themselves as superior candidates for bearing materials. Nevertheless, even the strongest and toughest materials are susceptible, to a greater or lesser extent, to some degree of degradation. Moreover, there are other considerations, such as cost and aesthetics (e.g. dental restorations), that may in some cases constrain selection to the lower portions of the plot. We shall return to the issue of materials design later. We have also demonstrated the existence of at least two modes of damage in nominally brittle ceramics. The ®rst mode is classical cone fracture, driven in moist environments by chemically-enhanced slow crack growth. Cone fracture accounts for the ®rst stage of degradation in the strength plotsÐthe Fig. 8. Master diagram comparing contact fatigue responses s(n) for selected materials, at speci®ed contact load P: data for soda-lime glass, porcelain and silicon nitride from Fig. 1; data for a glass-in®ltrated alumina and zirconia (Y-TZP) from a companion study [26]. Solid lines denote brittle region. (Note break in strength axis.) Fig. 7. Half-surface (re¯ected light) and side-section (transmitted light) views of Hertzian indentation sites in: (a) soda-lime glass/water (P = 140 N, r=3.18 mm, n=104 ); (b) porcelain/water (P = 500 N, r=3.18 mm, n 5 104). Deep penetrating cracks form beneath the near-surface damage zone. Bars denote outer and inner contact diameters. 4720 KIM et al.: CYCLIC FATIGUE OF BRITTLE CERAMICS