Skip to main content
Log in

A Parametric Study of Hertzian Contact Stresses in Pyrolytic Carbon/Graphite Composite

  • Published:
Cardiovascular Engineering: An International Journal

Abstract

A mechanical heart valve (MHV) prosthesis made of pyrolytic carbon (PyC) coated graphite is a long-term implant that operates continuously for lifetime in patient's body. The ceramic-like PyC coating is brittle and is prone to contact damages. The high-level local contact stress may lead to the initiation of microcracks, as well as accelerated propagation of preexisting cracks. In this paper, the effect of changing coating parameters on Hertzian contact stresses is investigated for a trilayer PyC/graphite laminate undergoing a spherical indentation test, by means of a finite element analysis. It is shown that by suitably changing Young's modulus, Poisson's ratio, and the thickness of the coating material, the stress levels at critical locations can be greatly modified. This can be accomplished effectively within a small range of variations of the coating parameters. Low Young's modulus, large Poisson's ratio, and relatively thick coating are found to be beneficial in general. The results obtained may be useful in the design of MHV components for improving resistance against contact-induced damages by elaborately controlling the deposition process of PyC coating.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  • Bokros JC. Deposition, structure, and properties of pyrolytic carbon. In Walker PL, Ed, Chemistry and Biophysics of Carbon, Vol 5. New York: Marcel Dekker, 1969, pp 1–118.

    Google Scholar 

  • Bokros JC, LaGrange LC, and Schoen FJ. Control of structure of carbon for use in bioengineering, chemistry, and physics of carbon. In Walker PL, Ed, Chemistry and Biophysics of Carbon, Vol 9. New York: Marcel Dekker, 1973, pp 103–165.

    Google Scholar 

  • Dimitri WR and Williams BT. Fracture of the Duromedics mitral valve housing with leaflet escape. J Card Surg 31: 41–46, 1990.

    Google Scholar 

  • Ely JL, Stupka J, and Haubold AD. Pyrolytic carbon indentation crack morphology. J Heart Valve Dis 5(Suppl I): S65–S71, 1996.

    Google Scholar 

  • Gilpin CB, Haubold AD, and Ely JL. Finite element analysis of indentation tests on Pyrolytic carbon. J Heart Valve Dis 5(Suppl I): S72–S78, 1996.

    Google Scholar 

  • Hamilton GM and Goodman LE. The stress field created by a circular sliding contact. J Appl Mech 33: 371–376, 1966.

    Google Scholar 

  • Hertz H. Hertz's Miscellaneous Papers. London: Macmillan, 1896.

    Google Scholar 

  • Hu S, Chen Z, and Mecholsky JJ, Jr. On the Hertzian fatigue cone crack propagation in ceramics. Int J Frac 79: 295–307, 1996.

    Google Scholar 

  • Huber MT. Zur theorie der ber¨uhrung fester elastischer körper. Ann Phys 14: 153–163, 1904.

    Google Scholar 

  • Jitcharoen J and Padture NN. Hertzian-crack suppression in ceramics with elastic-modulus-graded surfaces. J Am Ceram Soc 81: 2301–2308, 1998.

    Google Scholar 

  • Kocer C and Collins RE. Angle of Hertzian cone cracks. J Am Ceram Soc 81: 1736–1742, 1998.

    Google Scholar 

  • Lawn BR. Indentation of ceramics with spheres: A century after Hertz. J Am Ceram Soc 81: 1977–1994, 1998.

    Google Scholar 

  • Lee CS and Lawn BR. Effect of tangential loading on critical conditions for radial cracking in brittle coatings. J Am Ceram Soc 84: 2719–2721, 2001.

    Google Scholar 

  • Ma L. Studies on Pyrolytic Carbon for Biomedical Application, PhD dissertation, University of California, Los Angeles, California, 1997.

    Google Scholar 

  • Matthewson MJ. Axi-symmetric contact on thin compliant coatings. J Mech Phys Solids 29: 89–113, 1981.

    Google Scholar 

  • Matthewson MJ. The effect of a thin compliant protective coating on Hertzian contact stresses. J Phys D 15: 237–249, 1982.

    Google Scholar 

  • Rhee YW, Kim HW, Deng Y, and Lawn BR. Contact-induced damage in ceramic coatings on compliant substrates: Fracture mechanics and design. J Am Ceram Soc 84: 1066–1072, 2001.

    Google Scholar 

  • Ritchie RO. Fatigue and fracture of pyrolytic carbon: A damage-tolerant approach to structural integrity and life prediction in “ceramic” heart valve prostheses. J Heart Valve Dis 5(Suppl I): S1–S31, 1996.

    Google Scholar 

  • Warren PD, Hills DA, and Dai DN. Mechanics of Hertzian cracking. Trib Int 28: 357–362, 1995.

    Google Scholar 

  • Zeng K, Breder K, and Rowcliffe DJ. The Hertzian stress field and formation of cone cracks-I. Theoretical approach. Acta Metall Mater 40: 2595–2600, 1992a.

    Google Scholar 

  • Zeng K, Breder K, and Rowcliffe DJ. The Hertzian stress field and formation of cone cracks-II. Determination of fracture toughness. Acta Metall Mater 40: 2601–2605, 1992b.

    Google Scholar 

  • van der Zwaag S and Field JE. The effect of thin hard coatings on the Hertzian stress field. Phi Mag 46: 133–150, 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, C., Hwang, N.H.C. & Lin, Y.K. A Parametric Study of Hertzian Contact Stresses in Pyrolytic Carbon/Graphite Composite. Cardiovascular Engineering 2, 49–56 (2002). https://doi.org/10.1023/A:1020977202446

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020977202446

Navigation