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Erschienen in: Experimental Mechanics 1/2018

15.08.2017 | Brief Technical Note

A New Formula for Evaluating Indentation Toughness in Ceramics

verfasst von: D. J. Ma, L. Sun, L. Z. Wang, J. L. Wang

Erschienen in: Experimental Mechanics | Ausgabe 1/2018

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Abstract

The Lawn-Evans-Marshall model for Vickers-induced crack driving force is widely applied for determining fracture toughness of ceramic materials, yet its simplification that the volumes of Vickers impression and equivalent expanding cavity merely depend on the half-diagonal length of residual impression will bring significant error. In this work, the model is modified by considering the influence of elastic recovery in depth after completely unloading on the volumes. As a result, a new expression for crack driving force is obtained and correspondingly a new fracture toughness formula is presented based on the modified model, which is expressed as the well-known Anstis formula with a different constant multiplied by the ratio of residual impression depth to the maximum indentation depth. Both finite element analysis and experimental results demonstrate the effectiveness of the proposed formula and, especially, that it works much better than Anstis formula on materials with large ratio of hardness to elastic modulus.

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Literatur
1.
Zurück zum Zitat Evans AG, Charles EA (1976) Fracture toughness determinations by indentation. J Am Ceram Soc 59:371–372CrossRef Evans AG, Charles EA (1976) Fracture toughness determinations by indentation. J Am Ceram Soc 59:371–372CrossRef
2.
Zurück zum Zitat Lawn BR, Evans AG, Marshall DB (1980) Elastic/plastic indentation damage in ceramics: the median/radial crack system. J Am Ceram Soc 63:574–581CrossRef Lawn BR, Evans AG, Marshall DB (1980) Elastic/plastic indentation damage in ceramics: the median/radial crack system. J Am Ceram Soc 63:574–581CrossRef
3.
Zurück zum Zitat Anstis GR, Chantikul P, Lawn BR, Marshall DB (1981) A critical evaluation of indentation techniques for measuring fracture toughness: I, direct crack measurements. J Am Ceram Soc 64:533–538CrossRef Anstis GR, Chantikul P, Lawn BR, Marshall DB (1981) A critical evaluation of indentation techniques for measuring fracture toughness: I, direct crack measurements. J Am Ceram Soc 64:533–538CrossRef
4.
Zurück zum Zitat Lankford J (1982) Indentation microfracture in the Palmqvist crack regime: implications for fracture toughness evaluation by the indentation method. J Mater Sci Lett 1:493–495CrossRef Lankford J (1982) Indentation microfracture in the Palmqvist crack regime: implications for fracture toughness evaluation by the indentation method. J Mater Sci Lett 1:493–495CrossRef
5.
Zurück zum Zitat Niihara K (1983) A fracture mechanics analysis of indentation-induced Palmqvist crack in ceramics. J Mater Sci Lett 2:221–223CrossRef Niihara K (1983) A fracture mechanics analysis of indentation-induced Palmqvist crack in ceramics. J Mater Sci Lett 2:221–223CrossRef
6.
Zurück zum Zitat Laugier MT (1987) New formula for indentation toughness in ceramics. J Mater Sci Lett 6:355–356CrossRef Laugier MT (1987) New formula for indentation toughness in ceramics. J Mater Sci Lett 6:355–356CrossRef
7.
Zurück zum Zitat Dukino RD, Swain MV (1992) Comparative measurement of indentation fracture toughness with Berkovich and Vickers indenters. J Am Ceram Soc 75:3299–3304CrossRef Dukino RD, Swain MV (1992) Comparative measurement of indentation fracture toughness with Berkovich and Vickers indenters. J Am Ceram Soc 75:3299–3304CrossRef
8.
Zurück zum Zitat Gong JH, Wang JQ, Guan ZD (2002) Indentation toughness of ceramics: a modified approach. J Mater Sci 37:865–869CrossRef Gong JH, Wang JQ, Guan ZD (2002) Indentation toughness of ceramics: a modified approach. J Mater Sci 37:865–869CrossRef
9.
Zurück zum Zitat Field JS, Swain MV, Dukino RD (2003) Determination of fracture toughness from the extra penetration produced by indentation-induced pop-in. J Mater Res 18:1412–1419CrossRef Field JS, Swain MV, Dukino RD (2003) Determination of fracture toughness from the extra penetration produced by indentation-induced pop-in. J Mater Res 18:1412–1419CrossRef
10.
Zurück zum Zitat Scholz T, Schneider GA, Munoz-Saldana J, Swain MV (2004) Fracture toughness from submicron derived indentation cracks. Appl Phys Lett 84:3055–3057CrossRef Scholz T, Schneider GA, Munoz-Saldana J, Swain MV (2004) Fracture toughness from submicron derived indentation cracks. Appl Phys Lett 84:3055–3057CrossRef
11.
Zurück zum Zitat Beshish GK, Florey CW, Worzala FJ, Lenling WJ (1993) Fracture toughness of thermal spray ceramic coatings determined by the indentation technique. J Therm Spray Technol 2:35–38CrossRef Beshish GK, Florey CW, Worzala FJ, Lenling WJ (1993) Fracture toughness of thermal spray ceramic coatings determined by the indentation technique. J Therm Spray Technol 2:35–38CrossRef
12.
Zurück zum Zitat Lima MM, Godoy C, Modenesi PJ, Avelar-Batista JC, Davison A, Matthews A (2004) Coating fracture toughness determined by Vickers indentation: an important parameter in cavitation erosion resistance of WC–co thermally sprayed coatings. Surf Coat Technol 177-178:489–496CrossRef Lima MM, Godoy C, Modenesi PJ, Avelar-Batista JC, Davison A, Matthews A (2004) Coating fracture toughness determined by Vickers indentation: an important parameter in cavitation erosion resistance of WC–co thermally sprayed coatings. Surf Coat Technol 177-178:489–496CrossRef
13.
Zurück zum Zitat Chen J, Bull SJ (2007) Loading rate effects on the fracture behaviour of solar control coatings during nanoindentation. Thin Solid Films 516:128–135CrossRef Chen J, Bull SJ (2007) Loading rate effects on the fracture behaviour of solar control coatings during nanoindentation. Thin Solid Films 516:128–135CrossRef
14.
Zurück zum Zitat Chicot D, Duarte G, Tricoteaux A, Jorgowski B, Leriche A, Lesage J (2009) Vickers indentation fracture (VIF) modeling to analyze multi-cracking toughness of titania, alumina and zirconia plasma sprayed coatings. Mater Sci Eng A 527:65–76CrossRef Chicot D, Duarte G, Tricoteaux A, Jorgowski B, Leriche A, Lesage J (2009) Vickers indentation fracture (VIF) modeling to analyze multi-cracking toughness of titania, alumina and zirconia plasma sprayed coatings. Mater Sci Eng A 527:65–76CrossRef
15.
Zurück zum Zitat Favache A, Libralesso L, Jacques PJ, Raskin JP, Bailly C, Nysten B, Pardoen T (2014) Fracture toughness measurement of ultra-thin hard films deposited on a polymer interlayer. Thin Solid Films 550:464–471CrossRef Favache A, Libralesso L, Jacques PJ, Raskin JP, Bailly C, Nysten B, Pardoen T (2014) Fracture toughness measurement of ultra-thin hard films deposited on a polymer interlayer. Thin Solid Films 550:464–471CrossRef
16.
Zurück zum Zitat Marshall DB, Lawn BR (1977) An indentation technique for measuring stresses in tempered glass surfaces. J Am Ceram Soc 60:86–87CrossRef Marshall DB, Lawn BR (1977) An indentation technique for measuring stresses in tempered glass surfaces. J Am Ceram Soc 60:86–87CrossRef
17.
Zurück zum Zitat Lawn BR, Fuller ER (1984) Measurement of thin-layer surface stresses by indentation fracture. J Mater Sci 19:4061–4067CrossRef Lawn BR, Fuller ER (1984) Measurement of thin-layer surface stresses by indentation fracture. J Mater Sci 19:4061–4067CrossRef
18.
Zurück zum Zitat Gruninger MF, Lawn BR, Farabaugh EN, Wachtman JB (1987) Measurement of residual stresses in coatings on brittle substrati by indentation fracture. J Am Ceram Soc 70:344–348CrossRef Gruninger MF, Lawn BR, Farabaugh EN, Wachtman JB (1987) Measurement of residual stresses in coatings on brittle substrati by indentation fracture. J Am Ceram Soc 70:344–348CrossRef
19.
Zurück zum Zitat Zeng K, Rowcliffe D (1994) Experimental measurement of residual stress field around sharp indentation in glass. J Am Ceram Soc 77:524–530CrossRef Zeng K, Rowcliffe D (1994) Experimental measurement of residual stress field around sharp indentation in glass. J Am Ceram Soc 77:524–530CrossRef
20.
Zurück zum Zitat Zeng K, Rowcliffe D (1995) Vickers indentations in glass—I. Residual stress fields and iso-stress contour maps. Acta Metall Mater 43:1935–1943CrossRef Zeng K, Rowcliffe D (1995) Vickers indentations in glass—I. Residual stress fields and iso-stress contour maps. Acta Metall Mater 43:1935–1943CrossRef
21.
Zurück zum Zitat Zhang TY, Chen LQ, Fu R (1999) Measurements of residual stresses in thin films deposited on silicon wafers by indentation fracture. Acta Mater 47:3869–3878CrossRef Zhang TY, Chen LQ, Fu R (1999) Measurements of residual stresses in thin films deposited on silicon wafers by indentation fracture. Acta Mater 47:3869–3878CrossRef
22.
Zurück zum Zitat Kese K, Rowcliffe DJ (2003) Nanoindentation method for measuring residual stress in brittle materials. J Am Ceram Soc 86:811–816CrossRef Kese K, Rowcliffe DJ (2003) Nanoindentation method for measuring residual stress in brittle materials. J Am Ceram Soc 86:811–816CrossRef
23.
Zurück zum Zitat Tandon R (2007) A technique for measuring stresses in small spatial regions using cube-corner indentation: application to tempered glass plates. J Eur Ceram Soc 27:2407–2414CrossRef Tandon R (2007) A technique for measuring stresses in small spatial regions using cube-corner indentation: application to tempered glass plates. J Eur Ceram Soc 27:2407–2414CrossRef
24.
Zurück zum Zitat Bull SJ (2011) Analysis methods and size effects in the indentation fracture toughness assessment of very thin oxide coatings on glass. C R Mec 339:518–531CrossRef Bull SJ (2011) Analysis methods and size effects in the indentation fracture toughness assessment of very thin oxide coatings on glass. C R Mec 339:518–531CrossRef
25.
Zurück zum Zitat Mao WG, Wan J, Dai CY, Ding J, Zhang Y, Zhou YC, Lu C (2012) Evaluation of microhardness, fracture toughness and residual stress in a thermal barrier coating system: A modified Vickers indentation technique. Surf Coat Technol 206:4455–4461 Mao WG, Wan J, Dai CY, Ding J, Zhang Y, Zhou YC, Lu C (2012) Evaluation of microhardness, fracture toughness and residual stress in a thermal barrier coating system: A modified Vickers indentation technique. Surf Coat Technol 206:4455–4461
26.
Zurück zum Zitat Leonardi A, Furgiuele F, Wood RJK, Syngellakis S (2010) Numerical analysis of brittle materials fractured by sharp indenters. Eng Fract Mech 77:264–276CrossRef Leonardi A, Furgiuele F, Wood RJK, Syngellakis S (2010) Numerical analysis of brittle materials fractured by sharp indenters. Eng Fract Mech 77:264–276CrossRef
27.
Zurück zum Zitat Lee JH, Gao YF, Johanns KE, Pharr GM (2012) Cohesive interface simulations of indentation cracking as a fracture toughness measurement method for brittle materials. Acta Mater 60:5448–5467CrossRef Lee JH, Gao YF, Johanns KE, Pharr GM (2012) Cohesive interface simulations of indentation cracking as a fracture toughness measurement method for brittle materials. Acta Mater 60:5448–5467CrossRef
28.
Zurück zum Zitat Hyun HC, Rickhey F, Lee JH, Kim M, Lee H (2015) Evaluation of indentation fracture toughness for brittle materials based on the cohesive zone finite element method. Eng Fract Mech 134:304–316CrossRef Hyun HC, Rickhey F, Lee JH, Kim M, Lee H (2015) Evaluation of indentation fracture toughness for brittle materials based on the cohesive zone finite element method. Eng Fract Mech 134:304–316CrossRef
29.
Zurück zum Zitat Ma DJ, Wang JL, Sun L (2016) Methodology for measuring fracture toughness of ceramic materials by instrumented indentation test with Vickers indenter. J Am Ceram Soc 100:2296–2308CrossRef Ma DJ, Wang JL, Sun L (2016) Methodology for measuring fracture toughness of ceramic materials by instrumented indentation test with Vickers indenter. J Am Ceram Soc 100:2296–2308CrossRef
30.
Zurück zum Zitat Leonardi A, Furgiuele F, Syngellakis S, Wood RJK (2009) Analytical approaches to stress intensity factor evaluation for indentation cracks. J Am Ceram Soc 92:1093–1097CrossRef Leonardi A, Furgiuele F, Syngellakis S, Wood RJK (2009) Analytical approaches to stress intensity factor evaluation for indentation cracks. J Am Ceram Soc 92:1093–1097CrossRef
31.
Zurück zum Zitat Hill R (1950) The mathematical theory of plasticity. Clarendon Press, Oxford Hill R (1950) The mathematical theory of plasticity. Clarendon Press, Oxford
32.
Zurück zum Zitat Wiederhorn SM (1969) Fracture surface energy of glass. J Am Ceram Soc 52:99–105CrossRef Wiederhorn SM (1969) Fracture surface energy of glass. J Am Ceram Soc 52:99–105CrossRef
33.
Zurück zum Zitat Ma DJ, Song ZK, Guo JH, Chen W (2011) A high precision instrumented indentation tester and the calculation method of diamond indenter press against the sample depth. CN. Patent CN102288500A Ma DJ, Song ZK, Guo JH, Chen W (2011) A high precision instrumented indentation tester and the calculation method of diamond indenter press against the sample depth. CN. Patent CN102288500A
34.
Zurück zum Zitat Ma DJ, Ong CW (2010) Analytical relationship among nominal hardness, reduced Young's modulus, the work of indentation, and strain hardening exponent. J Mater Sci 45:2530–2533CrossRef Ma DJ, Ong CW (2010) Analytical relationship among nominal hardness, reduced Young's modulus, the work of indentation, and strain hardening exponent. J Mater Sci 45:2530–2533CrossRef
Metadaten
Titel
A New Formula for Evaluating Indentation Toughness in Ceramics
verfasst von
D. J. Ma
L. Sun
L. Z. Wang
J. L. Wang
Publikationsdatum
15.08.2017
Verlag
Springer US
Erschienen in
Experimental Mechanics / Ausgabe 1/2018
Print ISSN: 0014-4851
Elektronische ISSN: 1741-2765
DOI
https://doi.org/10.1007/s11340-017-0325-8

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