Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-20T20:34:28.408Z Has data issue: false hasContentIssue false
  • English
  • Français

Fracture mode transitions in brittle coatings on compliant substrates as a function of thickness

Published online by Cambridge University Press:  03 March 2011

Herzl Chai  and
Brian R. Lawn
Herzl Chai
Affiliation:
Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Brian R. Lawn*
Affiliation:
Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
*
a)Address all correspondence to this author.e-mail: brian.lawn@NIST.gov
Get access

Abstract

The fundamentally changing nature of fracture in brittle coatings on compliant substrates with diminishing coating thickness is examined. Attention is focused on cracking induced by concentrated loading with a spherical indenter at the top surface. It is shown that the fracture mode undergoes transitions, from top-surface ring cracking around the contact (“thick-coating” region) to bottom-surface radial cracking at the lower ceramic surface (“intermediate” region) and, finally, back to surface ring cracking (“thin-coating” region). These transitions reflect a progressively changing stress field in the layer structures and highlight the differences in failure mechanism that may be anticipated at the large- and small-scale levels. Simple fracture relations are derived for each mode, expressing critical loads in terms of coating thickness relative to contact or sphere radius, coating strength and coating/substrate modulus mismatch. Data from finite element simulations and contact experiments on model ceramic/polymer bilayer systems are used to validate the basic elements of the analytical relations and to quantify deviations. Implications of the transitional behavior in relation to the strength of brittle coating/film systems are discussed.

Keywords

Contact stressBilayersBrittle coatings
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 6 , June 2004 , pp. 1752 - 1761
Copyright
Copyright © Materials Research Society 2004

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

REFERENCES

1Diao, D.F., Kato, K. and Hokkirigawa, K.: Fracture Mechanisms of Ceramic Coatings in Indentation. Trans ASME J. Tribology 116, 860 (1994).Google Scholar
2Weppelmann, E. and Swain, M.V.: Investigation of the Stresses and Stress Intensity Factors Responsible for Fracture of Thin Protective Films during Ultra-Micro Indentation Tests with Spherical Indenters. Thin Solid Films 286, 111 (1996).Google Scholar
3An, L., Chan, H.M., Padture, N.P. and Lawn, B.R.: Damage-Resistant Alumina-Based Layer Composites. J. Mater. Res. 11, 204 (1996).CrossRefGoogle Scholar
4Hayashi, K. and Yuan, F.: Elastic-Plastic Analysis of Stresses and Initiation of Cracks in a Ceramic Coating under Indentation by an Elastic Sphere. ASME J. Tribology 120, 463 (1998).CrossRefGoogle Scholar
5Wang, J.S., Sugimura, Y., Evans, A.G. and Tredway, W.K.: The Mechanical Performance of DLC Films on Steel Substrates. Thin Solid Films 325, 163 (1998).CrossRefGoogle Scholar
6Anderson, R., Toth, G., Gan, L. and Swain, M.V.: Indentation Response and Cracking of Sub-Micron Silica Films on a Polymeric Substrate. Eng. Fract. Mech. 61, 93 (1998).CrossRefGoogle Scholar
7Hainsworth, S.V., McGurk, M.R. and Page, T.F.: The Effect of Coating Cracking on the Indentation Response of Thin Hard-Coated Systems. Surf. Coat. Technol. 102, 97 (1998).CrossRefGoogle Scholar
8Chai, H., Lawn, B.R. and Wuttiphan, S.: Fracture Modes in Brittle Coatings with Large Interlayer Modulus Mismatch. J. Mater. Res. 14, 3805 (1999).Google Scholar
9Begley, M.R., Evans, A.G. and Hutchinson, J.W.: Spherical Indentation of Thin Elastic Films on Elastic–Plastic Substrates. Int. J. Solids Struct. 36, 2773 (1999).CrossRefGoogle Scholar
10Rhee, Y-W., Kim, H-W., Deng, Y. and Lawn, B.R.: Contact-Induced Damage in Ceramic Coatings on Compliant Substrates: Fracture Mechanics and Design. J. Am. Ceram. Soc. 84, 1066 (2001).CrossRefGoogle Scholar
11Zhao, H., Hu, X., Bush, M.B. and Lawn, B.R.: Cracking of Porcelain Coatings Bonded to Metal Substrates of Different Modulus and Hardness. J. Mater. Res. 16, 1471 (2001).CrossRefGoogle Scholar
12Souza, R.M., Sinatora, A., Mustoe, G.G.W. and Moore, J.J.: Numerical and Experimental Study of the Circular Cracks Observed at the Contact Edges of the Indentations of Coated Systems with Soft Substrates. Wear 251, 1337 (2001).Google Scholar
13Chai, H. and Lawn, B.R.: Cracking in Brittle Laminates from Concentrated Loads. Acta Mater. 50, 2613 (2002).CrossRefGoogle Scholar
14Deng, Y., Lawn, B.R. and Lloyd, I.K.: Characterization of Damage Modes in Dental Ceramic Bilayer Stuctures. J. Biomed. Mater. Res. 63B, 137 (2002).CrossRefGoogle Scholar
15Lawn, B.R., Deng, Y., Miranda, P., Pajares, A., Chai, H. and Kim, D.K.: Overview: Damage in Brittle Layer Structures from Concentrated Loads. J. Mater. Res. 17, 3019 (2002).CrossRefGoogle Scholar
16Abdul-Baqi, A. and Giessen, E.v.d.: Numerical Analysis of Indentation-Induced Cracking of Brittle Coatings on Ductile Substrates. Int. J. Solids Struct. 39, 1427 (2002).CrossRefGoogle Scholar
17Chai, H.: Fracture Mechanics Analysis of Thin Coatings under Spherical Indentation. Int. J. Fract. 119, 263 (2003).CrossRefGoogle Scholar
18Soloukhin, V.A., Brokken-Zijp, J.C.M. and With, G.D.: Subsurface Cracking During Indentation on Hybrid Coatings on Polycarbonate. J. Mater. Res. 18, 507 (2003).CrossRefGoogle Scholar
19Hseuh, C-H. and Miranda, P.: Modeling of Contact-Induced Radial Cracking in Ceramic Bilayer Coatings on Compliant Substrates. J. Mater. Res. 18, 1275 (2003).Google Scholar
20Hseuh, C-H. and Miranda, P.: Master Curves for Hertzian Indentation on Coating/Substrate Systems. J. Mater. Res. 19, 94 (2004).CrossRefGoogle Scholar
21Frank, F.C. and Lawn, B.R.: On the Theory of Hertzian Fracture. Proc. Roy. Soc. Lond. A299, 291 (1967).Google Scholar
22Lawn, B.R.: Indentation of Ceramics With Spheres: A Century After Hertz. J. Am. Ceram. Soc. 81, 1977 (1998).CrossRefGoogle Scholar
23Timoshenko, S. and Woinowsky-Krieger, S.: Theory of Plates and Shells (McGraw-Hill, New York, 1959).Google Scholar
24Miranda, P., Pajares, A., Guiberteau, F., Deng, Y. and Lawn, B.R.: Designing Damage-Resistant Brittle-Coating Structures: I. Bilayers. Acta Mater. 51, 4347 (2003).Google Scholar
25Johnson, K.L.: Contact Mechanics (Cambridge University Press, London, U.K., 1985).CrossRefGoogle Scholar
26Zhang, Y. and Lawn, B.R.: Long-Term Strength of Ceramics for Biomedical Applications. J. Biomed. Mater. Res. B. (in press).Google Scholar
27Lawn, B.R.: Fracture of Brittle Solids (Cambridge University Press, Cambridge, U.K., 1993).Google Scholar
28Rhee, Y-W., Kim, H-W., Deng, Y. and Lawn, B.R.: Brittle Fracture Versus Quasiplasticity in Ceramics: A Simple Predictive Index. J. Am. Ceram. Soc. 84, 561 (2001).Google Scholar
29Lawn, B.R.: Hertzian Fracture in Single Crystals with the Diamond Structure. J. Appl. Phys. 39, 4828 (1968).Google Scholar
30Chai, H.: Fracture Mechanics Analysis of Thin Coatings under Plane-Strain Indentation. Int. J. Solids Struct. 40, 591 (2003).CrossRefGoogle Scholar
31Guiberteau, F., Padture, N.P. and Lawn, B.R.: Effect of Grain Size on Hertzian Contact in Alumina. J. Am. Ceram. Soc. 77, 1825 (1994).CrossRefGoogle Scholar
32Miranda, P., Pajares, A., Guiberteau, F., Cumbrera, F.L. and Lawn, B.R.: Role of Flaw Statistics in Contact Fracture of Brittle Coatings. Acta Mater. 49, 3719 (2001).CrossRefGoogle Scholar
33Lee, C-S., Kim, D.K., Sanchez, J., Miranda, P., Pajares, A. and Lawn, B.R.: Rate Effects in Critical Loads for Radial Cracking in Ceramic Coatings. J. Am. Ceram. Soc. 85, 2019 (2002).CrossRefGoogle Scholar
34Kim, H-W., Deng, Y., Miranda, P., Pajares, A., Kim, D.K., Kim, H-E. and Lawn, B.R.: Effect of Flaw State on the Strength of Brittle Coatings on Soft Substrates. J. Am. Ceram. Soc. 84, 2377 (2001).Google Scholar
35Johnson, K.L., O’Connor, J.J. and Woodward, A.C.: The Effect of Indenter Elasticity on the Hertzian Fracture of Brittle Materials. Proc. R. Soc. Lond. A334, 95 (1973).Google Scholar