indentation precracking of y-tzp: implications to r-curves and strength

Materials Science and Engineering A245 (1998) 267–276

Indentation precracking of Y-TZP: implications toR-curves and strength

Jorge Alcala *, Marc AngladaUni6ersidad de Castilla-La Mancha, ETS, Ingenieros Industriales, Campus Uni6ersitario s/n, 13071 Ciudad Real, Spain

Received 9 July 1997; received in revised form 3 October 1997

Abstract

Fracture resistance curves generated with indentation cracks and semielliptical surface cracks which are free of precrackingeffects are compared. The differences are related to the presence of an uncracked ligament at the center of the indent induced bythe inelastic zone. The role of crack shape on the R-curve behavior is also studied experimentally with through-thickness andsemielliptical surface cracks. The R-curves and crack growth thresholds obtained with semielliptical cracks are correlated withfailure strength and life limits measured with smooth (uncracked) specimens. © 1998 Elsevier Science S.A. All rights reserved.

Keywords: Indentation precracking; R-curves; Y-TZP

1. Introduction

A variety of ceramic materials are known to increasetheir fracture toughness with crack extension [1,2]. Suchan increase in fracture resistance (R-curve) providesflaw tolerance characteristics to ceramics and narrowstheir strength distributions [3–5]. When the amount ofstable crack growth is larger than the length of smallpre-existing flaws, unstable fracture is dictated by thecharacteristics of the R-curve and not by the size of theflaws [6,7]. An R-curve behavior is induced by mecha-nisms such as transformation toughening or crack-bridging which ‘shield’ the crack tip from externalloads.

Evaluation of R-curve behavior can be made usingspecimens containing long through-thickness cracks.However, these results may differ from those of smallcracks [8–10]. As small pre-existing flaws trigger failurein most ceramic components, the characterization ofthe short-crack phenomena becomes particularly rele-vant. In R-curve studies, short-crack effects are com-monly related to (i) differences in the level ofcrack-shielding which builds-up in long and shortcracks and (ii) break down of continuum mechanics

due to the interaction of crack tip fields with mi-crostructural features.

Since the R-curve behavior is a result of closingtractions which develop at the crack tip region due totoughening mechanisms, the crack-shielding effects in-duced by such tractions depend on the crack shape andsize. Crack shape issues become relevant in the assess-ment of short-crack effects because experiments withshort cracks are usually conducted with semiellipticalshapes and the results compared with those of longthrough-thickness cracks.

An important experimental problem in studying thegrowth of short cracks in ceramic materials is that thesecracks are difficult to detect. To overcome thisdifficulty, artificial techniques such as indentation pre-cracking are commonly applied to introduce smallsemielliptical cracks. The main drawback of such tech-niques lies in the calibration of the parameters describ-ing the residual stress field [11–14]. In addition, recentresults in alumina show that the behavior of artificialindentation cracks may be inherently different to thatof ideal short cracks [12]. A comprehensive study ofthis aspect is still not available in transformation tough-ened ceramics.

This work was conducted with the following objec-tives: (i) to evaluate the influence of crack shape in thedevelopment of transformation toughening usingsemielliptical and through-thickness cracks; (ii) to de-

* Corresponding author. Fax: +34 26 295361; e-mail: [email protected]

0921-5093/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved.

PII S0921-5093(97)00726-0

J. Alcala, M. Anglada / Materials Science and Engineering A245 (1998) 267–276J. Alcala, M. Anglada / Materials Science and Engineering A245 (1998) 267–276268

termine whether the R-curve generated with indenta-tion cracks is different to that measured with ideallysemielliptical cracks in a transformation toughened ce-ramic, and to postulate mechanisms for possible dis-crepancies; (iii) to examine strength evaluations in thecontext of the R-curve behavior.

2. Material selection

The material selected for this study is a 2.8 mol.%Y-TZP (polycrystalline yttria-stabilized tetragonal zir-conia) [15]. A heat treatment at 1100°C for 45 minreverts tetragonal to monoclinic (t–m) transformationwithout inducing any other microstructural change [15].

The following issues favored the selection of thisparticular material. (i) The possibility of removing priorcrack-shielding in a systematic fashion enabling a directcomparison of crack growth results obtained with dif-ferent crack shapes. (ii) A small scale transformationzone. In Y-TZP, the transformation zone is of the orderof 10 mm, when crack length is much larger than thiszone, crack-shielding is independent of crack length[16,17]. (iii) Reduced sensitivity to microstructurallyrelated short-crack effects. Since the grain size of Y-TZP is of the order of 0.5 mm and the cracks understudy are at least two orders of magnitude larger thanthis dimension, the material can be regarded as acontinuum. The latter two issues give a possibility forneglecting the influence of crack size on R-curve evalu-ations with Y-TZP and focus exclusively on crackshape effects.

Prior experiments with this material with indentationcracks indicated that the R-curve saturates after only20 mm of stable crack extension [18]. However, stablecrack extensions larger than 1 mm were also observedin environmentally assisted crack growth studies[15,19,20], indicating that crack growth results are load-ing rate sensitive. Thus, it is possible to experimentallycontrol the shape of the R-curve by changing theloading rate.

3. Experimental procedure

All mechanical tests were conducted in a laboratoryenvironment of :55% relative humidity at :20°Cusing a self-aligning four-point bending fixture withinner and outer spans of 20 and 40 mm, respectively(Fig. 1). The specimens were heat treated before testingto revert the phase transformation induced during pre-cracking, and polished to a 1 mm finish.

Failure strength and life limits were determined withsmooth (uncracked) specimens. These specimens hadsimilar dimensions as those used in the crack growthexperiments (Fig. 1). Cyclic life tests were conducted in

a resonant testing system using a sinusoidal waveform,loading frequency of 250 Hz, and minimum-to-maxi-mum load ratio, R, of 0.1. Failure strength and staticlife limit were evaluated with a servo-hydraulic testingmachine operated under load control. The failurestrength was determined at loading rates of 20 and 200MPa s−1 with eight different specimens. At such load-ing rates, unstable fracture was attained after :50 and5 s of monotonic loading., respectively.

3.1. Precracking techniques for through-thicknesscracks

A load-bridge indentation technique was used tointroduce long through-thickness cracks into bend bars[15], Fig. 1(a). The crack length to specimen widthratio, a/W, was :0.4; additional specimens containingcracks with a/W=0.2 were also prepared. Before test-ing, these cracks were allowed to propagate underconstant loads and four-point bending conditions formore than 0.4 mm. A short through-thickness notch,a/W:0.1, was then carefully machined to remove theindentation starter crack used for load-bridge precrack-ing. Such a procedure was used to overcome load-bridge precracking effects [15].

Fig. 1. Specimen dimensions and load application (a) through-thick-ness cracks; (b) surface cracks.

J. Alcala, M. Anglada / Materials Science and Engineering A245 (1998) 267–276J. Alcala, M. Anglada / Materials Science and Engineering A245 (1998) 267–276 269

3.2. Indentation precracking and crack geometrydetermination

A Vickers indenter was used to introduce small sur-face cracks into bend bars, Fig. 1(b). The subsurfacecrack geometry of indentation cracks was determinedby means of a stepwise grinding procedure [21]. Grind-ing was systematically conducted to different depthsusing diamond wheels and the crack profile measuredby optical microscopy after polishing. Crack geometrywas studied for a range of indentation loads between150 and 400 N in as-indented specimens as well as inheat treated specimens. The results, presented here forthe first time, showed that initial radial-type cracksevolved to semielliptical ones after the heat treatment at1100°C. However, even after such heat treatment, thecenter (core) of the indentation remained uncracked(see Section 4.2). This change in crack shape is relevantto the following indentation-based precrackingtechniques (see Section 4.2).

Ideally semielliptical surface cracks, free of indenta-tion effects, were produced by indentation precracking,possible external loading, heat treatment and finalgrinding of the specimen. In the first precracking se-quence, a series of two to four Vickers indents wereplaced in the tensile surface of the specimens with aconstant load of 150 or 400 N. The diagonals of theimprints were aligned parallel to the long axis of thespecimens within 5°. These cracks were then allowed togrow under four-point bending. After the heat treat-ment of the specimens, the indented surface was groundand polished until semielliptical cracks (without theinner ligament) were produced. In the second sequenceapplied to produce ideally semielliptical cracks, the stepin which the indentation cracks were allowed to growunder external loads was excluded from the procedure.The main difference between the above sequences lies inthe eccentricity of the final cracks obtained after grind-ing the specimens, Section 4.2. An intrinsic advantageof these procedures is the removal of the residual stressfield which is a consequence of the inelastic zone under-neath the imprint.

Specimens for R-curve experiments containing as-in-dented cracks were prepared by placing three to fouraligned indents with loads ranging from 150 to 400 Ninto the tensile surfaces of the bend bars. Indentationcracks were also introduced into additional specimensby a series of three or four indentations at a load of 400N. These 400 N cracks were then allowed to growunder four-point bending prior to testing. It is empha-sized that in these two precracking sequences, the un-cracked ligament remains underneath the imprint,however, the ligament radius to crack length ratio ismuch smaller when the cracks are grown under externalloads.

3.3. R-cur6e e6aluations with through-thickness cracks

Crack growth experiments were conducted underload control using a servo-hydraulic testing machine.An attempt was made to keep the loading rates, K: , at0.1 and 1.0 MPam s−1. (However, because of thecrack growth, these rates varied between 0.09–0.13MPam s−1 and 0.9–1.3 MPam s−1, respectively).Experiments were conducted under (i) continuouslyincreasing load until unstable fracture and (ii) by steploading, where the maximum load systematically in-creased in each consecutive loading–unloading step. Inthe former case, crack extension was monitored in situusing an optical microscope connected to a videorecorder with a resolution of 5 mm. For stepped loadingconditions, crack length was measured only upon un-loading by optical microscopy. The influence of theloading rate on crack propagation was also determinedwith stepped loading experiments by decreasing theloading rate of subsequent steps by half or by a tenth.

3.4. Crack growth experiments with semiellipticalcracks

R-curve assessments with semielliptical cracks wereconducted by loading specimens to failure and then bymeasuring the extension of the remaining cracks. Theseexperiments were conducted under four-point bendingconditions with an electromechanical testing machineoperated under load control. The R-curve was con-structed by calculating the final value of K for thesurviving cracks using the Newman and Raju equation[22] and by plotting the results in terms of the corre-sponding crack extensions [23]. The values of crackeccentricity, e, used in K calculations were determinedby the stepwise grinding procedure, and the results wereconfirmed by fracture surface observations. These ob-servations also rendered the final value of e at unstablefracture. The eccentricity of the surviving cracks interms of crack extension was estimated by interpola-tion, using the initial and final values of e for the actualtest under consideration. This procedure is fairly accu-rate since only large crack extensions, measured withcracks induced at identical indentation loads to thattriggering failure, can change e enough so that the valueof K is significantly modified. The final value of e forsuch cracks is close to that determined at the fracturesurfaces and, therefore, close to the maximum pointused in the interpolation.

A total of four to six specimens were prepared foreach of the precracking sequences described in Section3.2. A loading rate was used which gives an initial K: of0.1 MPam s−1 in the largest crack of the specimen.This value increased up to 0.13 MPam s−1 at un-stable fracture. In specimens containing cracks of sev-eral lengths, these conditions yielded an initial K which


Table 1Crack growth results

K for unstable for unstableK for crack growth K for static crack growthfracture (MPa m) initiation (MPa m)initiation (MPa m)

1 MPa m s−10.1 MPa m s−1 0.1 MPa m s−1 1 MPa m s−1

3.0Through-thickness cracks 3.7 5.0 5.0 2.7— 5.4 —3.0 2.7–3.1Surface cracks

was higher than 0.07 MPam s−1 in the smallestcrack.

Crack growth initiation under constant loads wasalso determined using a device designed to enable insitu crack extension measurements under four-pointbending [24]. In this case, the applied load was heldconstant for :60 min and systematically increaseduntil crack growth initiation was detected.

4. Results

4.1. Through-thickness cracks

The crack growth results determined undermonotonic loading with specimens precracked toa/W=0.4 are similar to those obtained for a/W=0.2.This validates the assumption that when prior crack-shielding is removed by the heat treatment of thespecimens, the R-curve of Y-TZP is not affected by theinitial crack size, Section 2. Crack growth initiation wasdetected for K:3.0 MPam at K: =0.1 MPam s−1,and for K:3.7 MPam at K: =1 MPam s−1. Un-stable fracture was always triggered at 5 MPam,Table 1.

The R-curve shifts to lower values of K with adecrease in loading rate, Fig. 2, consistent with thehypothesis of environmentally assisted crack growth.This result also confirms that toughening developmentin Y-TZP is controlled by the loading rate. Fig. 2 showsthe R-curve obtained with a specimen subjected tostepped loading at K: =0.1 MPam s−1. This curvelies at lower values of K than those corresponding tospecimens tested under continuous loading conditions,specially for long crack extensions. Under stepped load-ing, crack propagation restarted at an applied K smallerthan the maximum imposed in the previous loadingstep. This behavior further decreases the slope of theR-curve.

An R-curve plot constructed with a crack growthexperiment under static loading conditions [15] is in-cluded in Fig. 2. In this case, crack growth occursunder a constant applied load and K increases as aconsequence of crack propagation. Crack growth com-mences at K=2.7 MPam, and for any value of K, the

corresponding crack extension is much larger than thatdetermined under monotonic loading. This is also con-sistent with environmentally assisted crack growth.

4.2. Semielliptical cracks

The indentation crack profile determined by stepwisegrinding is shown in Fig. 3. As indentation load in-creases, the crack profile evolves to half-penny due to atendency of the radial cracks to converge. However,within the indentation load range applied in this study(150–400 N), a semielliptical profile was not achieved.Similar results have been previously reported in Y-TZPmaterials [25–27]. The crack profile after the heat treat-ment of the specimens is also presented in Fig. 3. Whilethe radial crack system induced with indentation loadshigher than 150 N extended inwards upon annealing,the material immediately underneath the imprint re-mained uncracked.

Fig. 4 shows the crack profiles produced by allowingan indentation crack induced at 400 N to propagateunder four-point bending prior to testing. These are ingood agreement with the crack growth marks detectedon the fracture surfaces. Note that when the surface ofthe specimens were ground to remove the ligament, theresulting cracks were shallow and their value of e,defined as crack depth to half of the surface cracklength (c) ratio, was smaller than 0.6. The value of e isthe only difference between cracks propagated underexternal loads and those in which this step was omittedprior to surface grinding (yielding e=0.5–0.6 and e=0.4, respectively). The initial and final crack profilesdetected at the fracture surfaces after a crack growthexperiment are shown in Fig. 5.

Fig. 6 shows the different R-curves obtained withsurface cracks. Among these curves, the one generatedwith cracks in the as-indented state was the steepest.The R-curve determined with specimens containingcracks which were propagated under external loads andwith specimens where the indentation ligament wasremoved by grinding, represent the lower bound curvefor semielliptical cracks. However, K for crack growthinitiation and for unstable fracture were not influencedby the precracking procedure. These values of K are:3.0 and 5.4 MPam, respectively, Table 1. It is


Fig. 2. R-curves determined with specimens containing through-thickness cracks.

noted that a systematic effect of crack eccentricity onR-curve assessments was not found for the range ofeccentricities examined in the present investigation.

Fig. 6 also shows a comparison of the results foundwith through-thickness cracks with those of semiellipti-cal cracks. This comparison indicates that (i) the Krange for stable crack growth is similar for both ge-ometries and (ii) after the initial 50 mm of crack exten-sion, the slope of the R-curve determined withsemielliptical cracks is :1.8 times of that found withthrough-thickness cracks.

Crack growth commencement under constant loadswith surface cracks where the ligament was previouslyremoved occurred for K\2.7 MPam, Table 1. Inthis case, crack growth was detected only after someholding period at the applied load. This indicates thatcrack growth initiates at the deepest point of the crack

periphery and gradually extends towards the free sur-face, (see Section 5.2).

4.3. Strength-life

A dependency of failure strength on loading rate wasclearly detected in this investigation, Table 2. This isattributed to the presence of environmentally assistedcrack growth effects. As shown in Fig. 7 and Table 2,the cyclic life limit of the material was 550 MPa whilethe static life limit was 850 MPa. Such a large differ-ence between cyclic and static life limits indicates thatcyclic loading strongly reduced the load bearing capac-ity of the material. Fig. 7 also shows that the static lifecurve remains relatively constant at 850 MPa, which isthe lower bound limit for the failure strength deter-mined at the lowest loading rate.


Fig. 3. Original indentation crack geometry induced at different load levels (left) and evolution during heat treating (right).

5. Discussion

5.1. R-cur6e of semielliptical cracks

The initial indentation crack geometry in Y-TZPevolves to a semielliptical configuration upon high tem-perature annealing; however, the cracks do not con-verge underneath the imprint. The presence of such anuncracked ligament appears to be the only factor thatdifferentiates the crack growth behavior determinedwith as-indented cracks to that of ideally semiellipticalcracks. The difference between these two R-curves islarge, Fig. 6. This is because as-indented cracks areassumed to be ideally semielliptical in the computationof K. This assumption is usually made in crack growthstudies in Y-TZP (see, for example, [18]), however, inview of present results, it does not seem to be accurate.

The effect of the uncracked ligament on crack growthcan be hypothesized as that of a spring loaded incompression in the center of the indent [29]. When

external loads are applied, the spring starts to unloadreducing its initial wedging effects at the crack tip. Atsufficiently high applied loads, the ligament may experi-ence some level of tensile loads before failing. Thiscrack-bridging hypothesis is consistent with the shiftingto higher values of K of the R-curve measured withcracks in the as-indented state, Fig. 6. It may be arguedwhether tensile stresses are effectively applied to theligament before indentation cracks trigger the finalfailure of the specimen. Present results show that theligament is actually subjected to tensile loads becauseits radius decreases after some crack growth. This pointwas evidenced by scanning electron microscopy (SEM)observations of the imprints and by the application ofthe successive grinding procedure used here primarily toassess crack eccentricity.

In the present study all specimens were heat treatedbefore testing. This considerably relieved the initialwedging effects provided by the ligament. (Measure-ments of the crack opening displacement at the verticesof the cracks showed a marked decrease after the heat

Fig. 4. Crack shapes reached by allowing a crack induced at a load of400 N to propagate under external loads.

Fig. 5. Failure marks indicating the initial crack profile obtained aftercrack growth under external loads and surface grinding (i) and thefinal crack length at unstable fracture conditions (f).


Fig. 6. R-curve plots determined with semielliptical surface cracks induced by the indentation-based precracking procedures under study, andcomparison with the results found with through-thickness cracks. All tests were conducted at K: =0.1 MPam s−1.

treatment which is indicative of residual stress reliev-ing [15]). Hence, the occurrence of crack-bridgingeffects before failure of the specimen under externalloads is facilitated here. It is noted that a completeremoval of residual stresses was not achieved because,if this was the case, the ligament would fail beforethe measurement of stable crack growth. The resultsin Fig. 6 also indicate that the R-curve generated withindentation cracks which were extensively grown underexternal loads prior to testing is similar to that ofideally semielliptical cracks. This is likely due to adecrease in crack-bridging effects in the formerspecimens where the ligament radius to crack lengthratio is small as compared with cracks in the as-in-dented state.

5.2. Through-thickness 6ersus ideally semiellipticalcracks

Present results show that crack growth commences atthe same value of K regardless of loading type (K: =0.1MPam s−1 or constant loading) or crack shape. Sucha similarity in crack growth initiation for differentcrack geometries seems to be a consequence of theremoval of prior crack-shielding effects. In the absenceof prior shielding, the value of K at the crack tip isequal to that applied under external loads. Hence,cracks of different shapes are expected to start growingat identical values of the applied K. Also, since themaximum value of K triggering unstable fracture wasnot particularly influenced by the crack geometry,Table 1, the maximum fracture toughness seems to be aproperty of the material under study.

The R-curve behavior of ideally semielliptical cracksis approximately linear after the initial 30 mm of crackextension until its saturation at :250 mm, Fig. 6. Inthis range, the slope of the R-curve is about twice ofthat determined with through-thickness cracks. Sincethe inducement of crack-shielding in ceramic materialsis generally associated with mechanisms which developat the crack wake, the way in which wake area increasesas a result of crack extension should play an importantrole in the development of crack-shielding. The largerslope of the R-curve plot determined with semiellipticalcracks might be associated with the further increase inwake area provided by such crack shape. Simple geo-metrical considerations have been set up as a basis toassess crack shape effects [30]. In an attempt to com-pare toughening development for different crack ge-ometries, the change in wake area with respect to crackextension normalized by the instantaneous wake area(dA/Adc) can be proposed as a meaningful parameter[30]. This parameter yields 1/c and 2/c for through-thickness cracks and semielliptical cracks, respectively.Experimental support for the use of this parameter todescribe the influence of crack shape in tougheningdevelopment is provided here as the difference in thevalue of the parameter for though-thickness and semiel-liptical cracks is similar to that detected between theslopes of the R-curves generated with these crackshapes.

In the case of an ideally semielliptical crack subjectedto static loads, crack growth initiation at the surface ofthe specimen occurred after some holding period, Sec-tion 4.2. This observation seems related to the smallvalue of the initial eccentricity of the semielliptical


Table 2Strength-life results

Cyclic limit (MPa)Strength at 20 MPa s−1 (MPa) Static limit (MPa)Strength at 200 MPa s−1 (MPa)

550900950 8501100950

crack under consideration. As e50.6, crack growth isexpected to commence at the deepest point of the crackperiphery and, after the consequent increase in K, toinitiate at the surface of the specimen [31]. If this resultis considered in the context of R-curve evaluations, thevalue of K may be underestimated as e could increasemostly at the beginning of the experiment. However,since the calculation of K based on the maximum stablecrack extension inferred from fracture surface observa-tions and load to failure was in very good agreementwith the values obtained with surviving cracks, thepossible unaccounted increase of crack eccentricity isnot expected to play an important role in the results.(Such a K calculation from fracture surface observa-tions could be accomplished for crack extensions asshort as 90 mm).

5.3. Correlation between crack growth and strength-liferesults

It is generally accepted that failure occurs at a loadlevel where (i) the applied value of K (Ka) becomestangent to the R-curve (Kr), and (ii) the increase intoughening is smaller than the increment of Ka withcrack extension (i.e. Ka=Kr and dKr/dc5dKa/dc [5,6]).By considering the propagation results of ideally semiel-liptical cracks, the intersection of the R-curve with Ka isrepresented in Fig. 8 for different applied stresses ande=0.6. The substitution of crack extension for cracklength in Fig. 8 can be performed on the basis that (i)the R-curve of the material is not influenced by theinitial crack length, and (ii) crack growth experiments

were conducted upon removal of prior crack-shieldingeffects. (The initial toughness can then be regarded asan intrinsic value of the bulk material which is indepen-dent of crack length [5,27]).

Fig. 8 indicates that cracks with half surface lengthsmaller than 300 mm are only expected to sample theinitial part of the R-curve, comprising Kr values smallerthan 4 MPam. As cracks of half surface length of upto 700 mm were used in this investigation, the presentcrack growth experiments are not affected by suchcrack size issues. It is noticed that it is precisely the highsteepness of the R-curve associated with Y-TZP whichhas been regarded as the underlying reason for the highfailure strength of this material and its sensibility uponprocessing flaws [6,32].

When correlating strength-life results with fracturemechanics evaluations, it is important to bear in mindthat the similarity between the failure strength deter-mined at 20 MPa s−1 and the static life limit (900 and850 MPa, respectively), cannot account for the largedifference between the maximum fracture toughnessand static crack growth threshold (5 and 3 MPa m,respectively). It is worth noting that by extrapolatingthe tangency condition illustrated in Fig. 8 into smallstrength-controlling cracks, these are expected to triggerfailure under monotonic loads at a similar stress levelthat yields to static crack growth initiation, in agree-ment with the above strength results. Furthermore,after an increase of an order of magnitude in loadingrate, the relative increment in the value of K for crackgrowth initiation (from 3.0 to 3.8 MPam) is similar

Fig. 8. Schematic of the R-curve showing its intersection with theapplied K for different surface crack lengths and applied stresses.Fig. 7. Stress-time to failure curves under cyclic and static loads.


to that detected on the failure strength (from 900 to1100 MPa). These observations confirm that as a resultof the shape of the R-curve of the material, its strengthis dictated by the commencement of crack propagationunder monotonic or static loading. Such a correspon-dence points out that failure under static andmonotonic loading is governed by a similar populationof pre-existing flaws and hence, that static crack nucle-ation is not a relevant process [33].

Although the application of the tangency conditionswith the R-curve evaluated with surface cracks rendersa good correlation between strength and fracture me-chanics assessments, the following issues may affect thiscorrespondence. (i) Strength-controlling natural flawsmay be blunt. This aspect is expected to increase theresistance of the flaws to crack growth initiation, fur-ther supporting the consideration that failure is associ-ated with crack growth commencement. If cracknucleation mechanisms were present, the bluntness ofthe flaws could play a role in the interpretation of theresults. (ii) Although an identification of failure originsin smooth specimens could not be achieved in thepresent work, previous investigations have related fail-ure in Y-TZP materials to the presence of small surfaceflaws of 30–80 mm in size [33]. Cracks of such lengthscould still be susceptible to the development of short-crack effects when compared with the transformationzone size of the material. However, the relative influ-ence of this issue in the strength-life results of Y-TZPmay be small if unstable fracture conditions arestrongly related to the commencement of crack growth.This aspect is independent of transformationtoughening.

The fatigue life limit which is :550 MPa, is antici-pated to correlate well with the fatigue threshold deter-mined with through-thickness cracks at K=2.3MPam [15]1. This assumption implies that the staticlife limit, determined at :850 MPa, would be relatedto a static crack growth threshold of K=3.6 MPam.However, such a value of K is much larger than theactual static threshold of the material (evaluated at Kbetween 2.7 and 3.0 MPam). Although the exactorigin of this discrepancy is not clear, it is possible thatthe mechanisms controlling the propagation of naturalflaws under cyclic conditions include damage accumula-tion [15]. In contrast with the results under static loadswhere crack nucleation mechanisms do not seem to berelevant, damage accumulation under cyclic loads could

sharpen the radius of curvature of natural flaws andease their propagation at a lower stress level.

6. Summary

A comparison between R-curve results generatedwith long (through-thickness) cracks and those ofsemielliptical surface cracks was conducted in Y-TZP.This is a candidate material for such a comparisonsince ‘fresh’ crack tips (free of crack shielding due tot–m transformation) can be readily obtained by re-course to heat treatments. Since crack size issues do notinfluence the fracture behavior of the material, presentR-curves are considered to show exclusively the depen-dence of toughening build-up on the crack shape. Thisis a fundamental point in the ongoing debate of short-crack effects in ceramics where crack growth resultsgenerated with semielliptical cracks are compared withthose of long through-thickness cracks. Present resultsprovide experimental support for the use of an empiri-cal parameter (increase in wake area normalized by theinstantaneous wake area) to quantify the developmentof crack shielding with different crack shapes.

It is shown that the kidney-like indentation crackgeometry developed in Y-TZP evolves to semiellipticalafter the heat treatment of the specimen, and that aligament underneath the imprint remains uncrackedeven after large extensions of the indentation precracks.Techniques involving the heat treatment of indentedspecimens, surface grinding and propagation of inden-tation cracks under external loads are used to produceideally semielliptical cracks (i.e. cracks which do notcontain a central ligament). For simplicity, previousstudies in Y-TZP have modeled indentation cracks asbeing semielliptical. Present work shows that the as-sumption of a semielliptical shape in the calculation ofK is not appropriate because the propagation of theindentation cracks under external loads is greatly af-fected by the uncracked ligament. These results arepotentially relevant for the application of indentationprecracking in fracture mechanics assessments in brittlematerials where indentation cracks do not convergeunderneath the imprint, such as other transformationtoughened ceramics, cermets and glasses.

The paper shows that loading rate markedly affectsR-curve evaluations in Y-TZP. This is related to thepresence of environmentally assisted crack growth ef-fects in the material. As crack growth may occur atvalues of K smaller than those of prior loading steps,the determination of crack length by sequentially un-loading the specimen (as in the compliance technique)may shift the R-curve plot to larger crack extensions.Although it is commonly accepted that the environmentcan facilitate crack growth in many ceramics, clearexperimental evidence showing the influence of loading

1 Although cyclic crack growth experiments were not conductedwith surface cracks, the similarity in the value of K determined forstatic or monotonic crack growth initiation with through-thicknessand surface cracks is expected to hold under cyclic loading. This ispredicated on the hypotheses that the crack size is large comparedwith the transformation zone size, and that prior crack-shieldingeffects have been removed.


rate on the R-curve behavior is seldom reported in theliterature. Such experimental evidence is provided inthis investigation.

Strength-life results under monotonic and static load-ing correlate well with fracture mechanics evaluations.The results indicate that failure is triggered by thecommencement of crack growth, and that the influenceof static crack nucleation mechanisms in the mechanicalresponse of the material is small. On the other hand,crack nucleation mechanisms may affect the cyclic lifelimit of Y-TZP.

Acknowledgements

The authors thank M. Marsal for help in the opera-tion of the SEM. We are grateful to U. Ramamurty forhelp in writing the manuscript. This work was sup-ported by the Spanish agency CICYT under grantMAT93-0328. Additional financial support was pro-vided by the Research Agency of Catalonia (DGR) andthe Spanish Ministry of Education and Science.

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indentation precracking of y-tzp: implications to r-curves and strength

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