Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-27T18:18:40.307Z Has data issue: false hasContentIssue false

Fracture sequences during elastic–plastic indentation of brittle materials

Published online by Cambridge University Press:  12 April 2019

Robert F. Cook*
Affiliation:
Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

A fracture analysis is developed for crack initiation sequences occurring during sharp indentation of brittle materials. Such indentations, generated by pyramidal or conical loading, generate elastic and plastic deformation. The analysis uses a nonlinear elements-in-series model to describe indentation load–displacement responses, onto which lateral, radial, cone, and median crack initiation points are located. The crack initiation points are determined by extension and application of a contact stress-field model coupled to the indentation load, originally developed by Yoffe, in combination with crack nuclei coupled to the indentation displacement to arrive at an explicit fracture model. Parameters in the analysis are adapted directly from experimental fracture and deformation measurements, and the analysis outputs are directly comparable to experimental observations. After adaptation, crack initiation loads and sequences during indentation loading and unloading of glasses and crystals are predicted by the model from material modulus, hardness, and toughness values to within about 25% of peak contact load. This work is dedicated to George M. Pharr IV on the occasion of his 65th birthday in recognition of his contributions to indentation mechanics.

Type
Article
Copyright
Copyright © Materials Research Society 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
Gayle, A.J. and Cook, R.F.: Mapping viscoelastic and plastic properties of polymers and polymer–nanotube composites using instrumented indentation. J. Mater. Res. 31, 2347 (2016).CrossRefGoogle ScholarPubMed
Cook, R.F.: A flexible model for instrumented indentation of viscoelastic–plastic materials. MRS Commun. 8, 586 (2018a).CrossRefGoogle Scholar
Cook, R.F.: Model for instrumented indentation of brittle open-cell foam. MRS Commun. 8, 1267 (2018b).CrossRefGoogle Scholar
Cook, R.F. and Pharr, G.M.: Direct observation and analysis of indentation cracking in glasses and ceramics. J. Am. Ceram. Soc. 73, 787 (1990).CrossRefGoogle Scholar
Cook, R.F., Liniger, E.G., and Pascucci, M.R.: Indentation fracture of polycrystalline cubic materials. J. Hard Mater. 5, 190 (1994).Google Scholar
Tandon, R., Green, D.J., and Cook, R.F.: Surface stress effects on indentation fracture sequences. J. Am. Ceram. Soc. 73, 2619 (1990).CrossRefGoogle Scholar
Tandon, R. and Cook, R.F.: Cone crack nucleation at sharp contacts. J. Am. Ceram. Soc. 75, 2877 (1992).CrossRefGoogle Scholar
Tandon, R. and Cook, R.F.: Indentation crack initiation and propagation in tempered glass. J. Am. Ceram. Soc. 76, 885 (1993).CrossRefGoogle Scholar
Chaudhri, M.M. and Enomoto, Y.: In situ observations of indentation damage in single crystals of MgO. Wear 233–235, 717 (1999).CrossRefGoogle Scholar
Thurn, J., Morris, D.J., and Cook, R.F.: Depth-sensing indentation at macroscopic dimensions. J. Mater. Res. 17, 2679 (2002).CrossRefGoogle Scholar
Thurn, J. and Cook, R.F.: Indentation-induced deformation at ultramicroscopic and macroscopic contacts. J. Mater. Res. 19, 124 (2004a).CrossRefGoogle Scholar
Yoshida, S., Kato, M., Yokota, A., Sasaki, S., Yamada, A., Matsuoka, J., Soga, N., and Kurkjian, C.R.: Direct observation of indentation deformation and cracking of silicate glasses. J. Mater. Res. 30, 2291 (2015).CrossRefGoogle Scholar
Oyen, M.L. and Cook, R.F.: Load–displacement behavior during sharp indentation of viscous–elastic–plastic materials. J. Mater. Res. 18, 139 (2003).CrossRefGoogle Scholar
Cook, R.F. and Oyen, M.L.: Nanoindentation behavior and mechanical properties measurement of polymeric materials. Int. J. Mater. Res. 98, 370 (2007).CrossRefGoogle Scholar
Yoffe, E.H.: Elastic stress fields caused by indenting brittle materials. Philos. Mag. A 46, 617 (1982).CrossRefGoogle Scholar
Lathabai, S., Rödel, J., Dabbs, T., and Lawn, B.R.: Fracture mechanics model for subtheshold indentation flaws: Part I equilibrium fracture. J. Mater. Sci. 26, 2157 (1991).CrossRefGoogle Scholar
Cook, R.F.: Fracture mechanics of the scratch strength of polycrystalline alumina. J. Am. Ceram. Soc. 100, 1146 (2017).CrossRefGoogle Scholar
Howes, V.R.: Surface strength of coated glass. Glass Technol. 15, 148 (1974).Google Scholar
Arora, A., Marshall, D.B., Lawn, B.R., and Swain, M.V.: Indentation deformation/fracture of normal and anomalous glasses. J. Non-Cryst. Solids 31, 415 (1979).CrossRefGoogle Scholar
Marshall, D.B. and Lawn, B.R.: Residual stress effects in sharp contact cracking Part 1: Indentation fracture mechanics. J. Mater. Sci. 14, 2001 (1979).CrossRefGoogle Scholar
Lawn, B.R., Dabbs, T.P., and Fairbanks, C.J.: Kinetics of shear activated indentation crack initiation in soda-lime glass. J. Mater. Sci. 18, 2785 (1983).CrossRefGoogle Scholar
Alcalá, J.: Instrumented micro-indentation of zirconia ceramics. J. Am. Ceram. Soc. 83, 1977 (2000).CrossRefGoogle Scholar
Thurn, J. and Cook, R.F.: Mechanical and thermal properties of physical vapor deposited alumina films: II, elastic, plastic, fracture and adhesive behavior. J. Mater. Sci. 39, 4809 (2004b).CrossRefGoogle Scholar
Sakai, M., Hakiri, N., and Miyajima, T.: Instrumented indentation microscope: A powerful tool for the mechanical characterization in microscales. J. Mater. Res. 21, 2298 (2006).CrossRefGoogle Scholar
Chiang, S.S., Marshall, D.B., and Evans, A.G.: The response of solids to elastic/plastic indentation. I. Stresses and residual stresses. J. Appl. Phys. 53, 298 (1982a).CrossRefGoogle Scholar
Chiang, S.S., Marshall, D.B., and Evans, A.G.: The response of solids to elastic/plastic indentation. II. Fracture initiation. J. Appl. Phys. 53, 312 (1982b).CrossRefGoogle Scholar
Chen, X., Hutchinson, J.W., and Evans, A.G.: The mechanics of indentation induced lateral cracking. J. Am. Ceram. Soc. 88, 1233 (2005).CrossRefGoogle Scholar
Rhee, Y-W., Kim, H-W., Deng, Y., and Lawn, B.R.: Brittle fracture versus quasi plasticity in ceramics: A simple predictive index. J. Am. Ceram. Soc. 84, 561 (2001).CrossRefGoogle Scholar
Feng, G., Qu, S., Huang, Y., and Nix, W.D.: An analytical expression for the stress field around an elastoplastic indentation/contact. Acta Mater. 55, 2929 (2007).CrossRefGoogle Scholar