J O U R N A L O F M A T E R I A L S S C I E N C E L E T T E R S 2 1, 2 0 0 2, 1145 – 1147

Micro- and macro-indentation fracture toughness of alumina

L. C. LIM∗Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent,Singapore 119260, SingaporeE-mail: mpelimlc@nus.edu.sg

A. MUCHTARMechanical and Materials Engineering Department, Universiti Kebangsaan Malaysia, 43600 Bangi, Malaysia

The indentation technique has evolved as an economi-cal and convenient technique for determining the frac-ture toughness of brittle solids [1–13]. In this technique,measurements are taken from the surface cracks ema-nating from the apexes of the indentation, and suitableexpressions are used to compute the fracture toughnessof the material concerned. Over the years, various mod-els have been developed for different crack systemsproduced by the indentation. However, these modelsconsidered either Palmqvist [4, 11, 13] or half-pennycrack only [1, 2, 6, 9]. One therefore must determinethe actual crack system produced by the indentation andapply the appropriate equations to calculate the fracturetoughness.

More recently, Liang et al. [12] have proposed auniversal model which applies to both the Palmqvistand half-penny cracks, thus enabling one to computethe fracture toughness without determining the type ofcracks produced by the indentation. Using Liang et al.’smodel, the present authors [14] have shown that thefracture toughness values of alumina determined by theindentation technique at low loads, i.e. via the micro-indentation test, correlate well with those obtainedfrom the conventional but more elaborated techniques[15, 16].

In a subsequent work [17], we investigated the cracknucleation and propagation events in both the micro-and macro-indentations of brittle solids by means ofthe finite element method (FEM), using elements ex-hibiting cohesive post-failure behaviours and aluminaas the model material. The results show that at low in-dentation loads, median cracks nucleate at full loadingwhile Palmqvist cracks nucleate only during the un-loading stage and that they may or may not join upto form a half-penny crack depending on the indenta-tion load. In contrast, at high indentation loads, bothmedian and Palmqvist cracks nucleate separately andjoin up to form a half-penny crack during the loadingstage. More interestingly, our FEM results show that anannulus of tensile stressed region gradually developsduring intermediate to later stages of unloading of themacro-indentation, as shown in Fig. 1. The formationof this annular tensile region is a result of the differ-ential elastic recovery behavior of the cracked materialbeneath the indentation impression and the surround-ing uncracked material. Although similar tensile stress

∗Author to whom all correspondence should be addressed.

patterns are produced in the surface region adjacent tothe indentation impression, such an annulus of tensilestress and hydrostatic tension does not develop substan-tially in the micro-indentation (see Fig. 5 of Ref. [17]).

The evolution of the annular tensile region in themacro-indentation process provides a conducive en-vironment for the formation and propagation of othercrack systems not modelled by the indentation fracture

Figure 1 Iso-stress contour plots (in MPa) of (a) maximum principalstress and (b) hydrostatic stress at full unloading of a macro-indentationin alumina (indentation load = 45 kgf; maximum depth of penetration =28.6 µm), as viewed on the face of which the top edge containing the apexof the indentation impression. Note the annulus of tensile stressed mate-rial and of hydrostatic tension in (a) and (b), respectively, separating thecracked material beneath the indentation impression and the surround-ing uncracked material. Such an annulus of tensile stress and hydrostatictension does not develop substantially in the micro-indentation.

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Figure 2 Fracture toughness of alumina of three different grain sizesdetermined by the indentation technique at different loads. All data wereobtained from well-behaved apex cracks produced by the indentations.

toughness expressions, such as deep lateral cracks, shal-low lateral cracks and secondary radial cracks [17]. Aquestion thus arises as to the validity of fracture tough-ness values determined by the indentation technique atmoderate to high loads although only data with well-defined apex cracks are used in such measurements.

To check the above, indentation fracture toughnesstests were carried out on pure alumina samples viaboth the micro-indentation and macro-indentation tech-niques. The detailed experimental procedures used canbe found in Ref. [14]. The loads used for the micro-indentation were 0.3, 0.5, 1 and 2 kgf, and those for themacro-indentation were 15, 30 and 45 kgf. After the in-dentation, specimens showing well-defined apex crackswere selected for crack length measurement, and Lianget al.’s expression was used for the fracture toughnesscomputation.

The results are shown in Fig. 2. In this figure, thedata points for the micro-indentation represent aver-aged values of at least 6 indentations for each test loadperformed on the same specimen, while those for themacro-indentation represent individual test result. Thisis because each macro-indentation test requires a biggersurface area on the alumina sample and thus not manyindentations can be performed. The crack length mea-surements were made immediately after the indentationtests to eliminate potential slow crack growth associ-ated with the environmental effect [7]. Only data withwell-behaved apex cracks were shown in Fig. 2.

Fig. 2 shows that the fracture toughness values de-termined by the macro-indentation technique are con-sistently higher than those determined by the micro-indentation technique, the former ranging from 4.3to 5.3 MPa

√m while the latter averaging about

3.4 MPa√

m.The high “apparent” fracture toughness values ob-

tained from the macro-indentation can be attributed tothe activation of other cracking systems beneath the sur-face of the material, as prediction by our FEM results

[17]. This is confirmed by an increased incidence ofother crack systems and chipping in some samples (seeFig. 7 of Ref. [17]), although such test data were dis-carded in the fracture toughness computations.

The present work shows that for brittle solids likealumina, high indentation loads should be avoided infracture toughness determination by means of the in-dentation technique. In other words, although micro-indentation technique produces well-behaved cracksand reasonably accurate fracture toughness values, thevalues obtained by the macro-indentation technique aresubstantially higher due to the formation of other cracksystems not modelled by the indentation fracture tough-ness expressions beneath the surface. A reliable ap-proach will be to perform the indentation tests with de-creasing loads until a constant but conservative fracturetoughness value is attained. Note also that proper pro-cedures must be observed in conducting the indentationtests, namely, the surface of the material must be stress-free and crack measurement must be made soon af-ter the test to avoid possible environment-assisted slowcrack growth [7].

Another interesting observation made in the presentwork is the effect of grain size on the “apparent” frac-ture toughness of alumina. As shown in Fig. 2, al-though the fracture toughness determined by the micro-indentation technique decreases with increasing grainsize, an opposite trend was observed for the macro-indentation. Examination of the samples after the in-dentation showed that at high indentation loads, thetendency for lateral cracking and chipping increasedwith the grain size of alumina but such was not de-tected at low indentation loads. The observed “im-proved” fracture toughness with increasing grain size inmacro-indentation tests can thus be attributed to an in-creased tendency for the activation of additional cracksystems not modelled by the indentation fracture tough-ness expression. Their activation can be attributed tothe decreased crack nucleation resistance of the largergrain material as well as the higher local stress con-centration effect associated with the high anisotropyin elastic constants of alumina [14, 18]. When cracksystems other than the primary radial cracks are sup-pressed, the fracture toughness of alumina determinedby the micro-indentation decreases monotonically withincreasing grain size, while the fracture mode changesgradually from predominantly intergranular to a mixedmode [14].

In summary, the present work shows that althoughonly data with well-defined surface radial cracks weretaken for fracture toughness calculations, the macro-indentation technique gives higher fracture toughnessvalues for brittle solids due to the formation of ad-ditional crack systems beneath the surface. With de-creasing indentation loads, the formation of additionalcrack systems is suppressed accordingly, and the frac-ture toughness values eventually attain a constant butconservative value. It is proposed that for reliablefracture toughness determination, the indentation loadshould be decreased until a constant but conservativevalue is obtained. For pure alumina, micro-indentationtests with a load between 0.3 to 1.0 kgf sufficefor the purpose, provided that proper experimental

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procedures are observed in specimen preparation andcrack measurement.

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Received 14 Februaryand accepted 17 April 2002

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