September 1981 A Critical Evaluation ,of Indentation Techniques for Measuring Fracture Toughness: I 533 ’H. P. Kirchner and R. M. Gruver, “Fracture Mirrors in Alumina Ceramics,” *“F. F. Lange, “Stress Induced Martensitic Reaction: 11,” Rockwell Intemation- ibid., 27 [6] 1433-46 (1973). al Science Center Tech. Rept. No. 3 (SC 5117.3TR). Contract NOOOl4-77-C-0441 ‘H.P. Kirchner, “The Strain Intensity Criterion for Crack Branching in Ce- ul , 1978). ramics,” Eng. Fracr. Mech. 10 [2] 283-88 (1978). (J 2h.J. Green, P. S. Nicolson, and J. D. Embury; pp. 541-53 in Fracture Mechanics ’R. W. Rice and W. J. McDonough; “Ambient Strength and Fracture of ZrO,,” of Ceramics, Vol. 2. Edited by R. C. Bradt, D. P. H. Hasselman and F. F. Lange. Mech. Behav. Muter. 394-403 (1972). Plenum, New York, 1974. 6R. C. Garvie, R. H. Hannink, and R. T. Pascoe, “Ceramic Steel?” Nature ,,N. Claussen, “Fracture Toughness of Al20, with an Unstabilized ZrO, Dispersed (London), 258 155371 703-704 (1975). Phase,” J. Am. Ceram. Soc., 59 [1-21 49-51 (1976). ‘R.C. Garvie, R. H. J. Hannink, R. R. Hughan, N. A. McKinnon, R. T. Pascoe, ”H. P. Kirchner, R. C. Garvie, R. M. Gruver, and D. M. Richard, “Localized and R. K. Shinger, “Strong and Partially Stabilized Zirconia Ceramics,” J. Aus. Impact Damage on Transformation Toughened Zirconia,” Muter. Sci. Eng. , 40, 49-57 11979) Ceram. Soc. 13 [I] 8-11 (1977). ._ I,\.,.,,. *D. L. Porter and A. H. Heuer, “Mechanisms of Toughening Partially Stabilized 24R.F. Pabst; pp. 555-66 in Ref. 21. Zirconia Ceramics (PSZ),” J. Am. Ceram. Soc., 60 [3-4] 183-84 (1977). 25F.W. Smith, A. F. Emery, and A. S. Kobayashi, “Stress-Intensity Factors 9R.C. Garvie, R.R. Hughan, and R.T. Pascoe; pp. 263-74 in Processing for Semicircular Cracks, Part 2 - Semi-Infinite Solid,” J. Appl. Mech., ME, [I21 of Crystalline Ceramics, Edited by Palmour 111, R. R. Davis, and T. M. Hare. H. 95L-5911967). ~~ ~ I- Plenum, New York, 1978. 26A.F. Liu. “Stress Intensity Factor for a Comer Flaw,” Eng. Fract. Mech., 4 %.T. Pascoe, R. H. J. Hannink, and R. C. Garvie; pp. 447-54 in Science of 175-79 (1972). Ceramics 9. Edited by K. J. de Vries. Nederlandse Keramische Vereniging, The ”R. T. Pascoe and R. C. Garvie; pp. 774-84 in Ceramic Microstructures ’76. Netherlands, 1977. Edited by R. M. Fulrath, Westview Press, Boulder, Colo., 1977. ”R. C. Garvie, R. H. J. Hannink, and C. Urbani, ‘.Fracture Mechanics Study of a 28J. J. Mecholsky, R. W. Rice, and S. W. Freiman, “Prediction of Fracture Energy Transformation Toughened Alloy in the CaO-ZrO, System,” Presented at the 4th and Flaw Size in Glasses from Measurements of Mirror Size,” J. Am. Ceram. Soc., ClMTEC Meeting, Saint-Vincent, Italy (May, 1979). 57 5101 44C-43 (1974). ’*T. Gupta; pp. 877-89 in Fracture Mechanics of Ceramics, Vol. 4.Edited by R. C. A. G. Evans, A. H. Heuer, and D. L. Porter, pp. 529-56 in Fracture 1977, Vol. Bradt, D. P. H. Hasselman, and F. F. Lange. Plenum, New York, 1978. 1. Edited by D. M. R. Taplin. University of Waterloo Press, Waterloo, Canada, 1977. ‘’G.K. Bansal and A. H. Heuer, “Precipitation in Partially Stabilized Zirconia,” J. ”E. Hombogen, “Martensitic Transformation at a Propagating Crack,” Acra Am. Ceram. Soc., 58 [5-61 235-38 (1975). Metall., 26, 147-52 (1978). I4N. Claussen, “Comments on ‘Precipitation in Partially Stabilized Zirconia’,” ’IG. K. Bansal and W. H. Duckwor!!, “Fracture Stress as Related to Flaw and ibid., 59 [MI179 (1976). Fracture Mirror Sizes,” J. Am. Ceram. Soc., 60 17-81 304-10 (1977). ”D. L. Porter, G. K. Bansal, and A. H. Heuer, “Reply,” ibid., pp. 17%82. ’,H. P. Kirchner and R. M. Gruver, “Fractographic Criteria for Subcritical Crack Growth Boundaries in Alumina.” 63 11980). IbR.W. Rice, “Further Discussion Of ‘Precipitation in Partially Stabilized Zir- 96% .13-41 1 16%74~~ ~ ---, 33F. E. Buresh; pp. in Ref.’ conia’.” 60 15-61 280 (1977). 835-47 12. ibid.. 34F.W. Kleinlein and H. Hubner; pp. 883-91 in Fracture 1977, Vol. 3. Edited by I’D. L. Porter adA. H. Heuer,“‘Reply to Further Discussion of ‘Precipitation in D. M. R. TaDlin. Universitv of Waterloo Press. Waterloo. Canada. 1977. Partially Stabilized Zirconia’,” ibid., pp. 28C-81, a5K. Krii and F. W. Kfeinlein, “Influence ‘of the Testing-Rate on Slow Crack ”C. A. Andersson and T. K. Gupta, “Martensitic Transformation Toughening of Growth in Alumina with Different Grain Sizes,” Ber. Deutsch. Keram. Ges., 57, Zro,”; for abstract see Am. Ceram. SOC.Bull.. 57 ._131 312 (1978).. , 22-26 (1980). 19k F. Lange, “Microstructurally Developed Toughening Mechanisms in Ceramics: 36M.V. Swain; to be published in Fracture Mechanics of Ceramics, Vols. 5 & 6. I, Fracture Toughness,” Rockwell International Science Center Tech. Rept. No. 2 (SC Edited by R. C. Bradt, A. G. Evans, D. P. H. Hasselman, and F. F. Lange. Plenum, 5117.2TR). Contract NooO14-77-0441 (July, 1978). New York, 1981. A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements G.R. ANSTIS, P. CHANTIKUL, B. R. LAWN,* and D. B. MARSHALL *’* Department of Applied Physics, School of Physics, University of New South Wales, New South Wales 2033, Australia The application of indentation techniques to the evaluation of considerable potential as a microprobe for quantitatively charac- fracture toughness is examined critically, in two parts. In this terizing mechanical properties. In comparison with more flrst part, attention is focused on an approach which involves conventional testing techniques, the sharp-indenter concept offers direct measurement of Vickers-produced radial cracks as a a unique simplicity and economy in test procedure, at little cost in function of indentation load. A theoretical basis for the method reliability. A recent survey of various fracture mechanics methods is first established, in terms of elasticlplastic indentation frac- currently under investigation for applications to brittle materials” ture mechanics. It is thereby asserted that the key to the radial is useful for placing indentation fracture in some perspective in crack response lies In the residual component of the contact this regard. fkld. This residual term has important implications concerning This study concerns itself with an evaluation of sharp-indenter the crack evolution, including the possibility of postindentation techniques in the determination of one vitally important fracture slow growth under environment-sensitive conditions. Frac- parameter for ceramics, namely the toughness K,. Two ap- tographic observations of cracks in selected “reference” mater- proaches, presented in separate parts, are examined: in Part I, the Ys are used to determine the magnitude of this effect and to determination is made from direct measurements of the crack traces investigate other potential complications associated with de- on the indented surfaces, using the indentation fracture theory as a partures from ideal indentation fracture behavior. The data straightforward basis for calculation. In Part II,’* values are ob- from these observations provide a convenient calibration of the tained indirectly from the strengths of indented flexural test indentation toughness equations for general application to pieces, in conjunction with a unified indentation-fracture/tensile- other well-behaved ceramics. The technique is uniquely failure formulation. The chief object of the study is to explore hpie in procedure and economic in its use of material. the advantages and limitations of each of these two alternative approaches. 1. Introduction The idea that the size of indentation cracks might be used to quantify toughness was actually recognized by Palmqvist, on em- HE advent of indentation fracture mechanics’ has provided a pirical grounds, long before the above-mentioned analytical frac- T fundamental basis for analyzing the apparently complex ture mechanics methods were developed. I3,l4 Palmqvist worked deformation/fracture response of ceramics to controlled sharp- with metal carbides and used a Vickers diamond pyramid indenter contact events .*-Io With this development in analytical under- to produce the crack patterns. With considerable insight, he was standing has come a growing realization that the sharp indenter has able to establish some of the most important variables in the frac- ture process, including hardness. Extension of the approach to Received October 22, 1980 revised copy received March 3, 1981. Supported by the Australian Research Grants Committee, the Australian De- glasses and ceramics has been surprisingly slow in coming. Indeed, papent of Defence, and the U. S. Office of Naval Research. the first attempt to use indentation methods for determining frac- Member, the American Ceramic Society. ‘Now with the Materials and Molecular Research Divisiw, Lawrence Berkeley ture parameters in more brittle materials was made using the Hertz- Lboratory. Berkeley, California 94720. ian cone crack geometry produced by spherical 534 Journal of the American Ceramic Society-Anstis et al. Vol. 64, No. 9 11. Background Theory Figure 1 shows a schematic of the indentation deformation/ fracture pattern for the Vickers geometry: P is the peak load and a and c are characteristic dimensions of the “plastic” impression and the radiahedian crack, respectively. From simplistic dimensional analysis it can be demonstrated that these parameters relate directly to the hardness H and toughness K, of the indented material: H=P/ad2 (la) ___/ K, =P 1poc ’I’ t---2c where a. and Po are to be regarded as numerical constants: for -I 2at- Vickers indenters a0=2 if a is taken as the impression half- diagonal and if H is identified with the mean contact (load- invariant) pressure; Pocorresponds to a complex geometrical factor for penny-like systems, incorporating interaction effects due to the presence of the specimen free surface, multiple-plane crack con- figuration, etc., and is usually determined by experimental cali- bration.