DOI QR코드

DOI QR Code

Evaluation of Indentation Fracture Toughens in Brittle Materials Based on FEA Solutions

유한요소해에 기초한 취성재료의 압입파괴인성평가

  • Hyun, Hong Chul (Dept. of Mechanical Engineering, Sogang Univ.) ;
  • Lee, Jin Heang (Reactor Mechanical Engineering Division, Korea Atomic Energy Research Institute) ;
  • Felix, Rickhey (Dept. of Mechanical Engineering, Sogang Univ.) ;
  • Lee, Hyungyil (Dept. of Mechanical Engineering, Sogang Univ.)
  • Received : 2013.06.06
  • Accepted : 2013.09.16
  • Published : 2013.12.01

Abstract

In this study, we proposed an indentation evaluation method for fracture toughness using cohesive finite element simulations. First, we examined the effect of material properties (yield strain, Poisson's ratio, and elastic modulus) on crack size during Vickers indentation and then generated a regression formula that explains the relations among fracture toughness, indentation load, and crack size. We also proposed another indentation formula for fracture toughness evaluation using the contact size a and E/H (H: hardness). Finally, we examined the relation between the crack size and the indenter shapes. Based on this, we can generate from the formula obtained using the Vickers indenter a formula for an indenter of different shapes. Using the proposed method, fracture toughness is directly estimated from indentation data.

본 논문에서는 cohesive zone 모델을 이용한 유한요소해석에 기초해 압입 파괴인성 평가식을 제시한다. 먼저 Vickers 압입균열해석에 기초해 다양한 물성변수(항복변형률 ${\varepsilon}_o$, 푸아송비 ${\nu}$, 영률 E)의 들이 균열크기에 미치는 영향을 분석하고, 파괴인성을 압입 시 측정되는 최대하중과 균열길이로 나타낼 수 있는 수식을 회귀로 얻었다. 아울러 접촉길이 a, E/H (H: 경도) 등을 추가 압입변수로 선정해 다양한 형태의 파괴인성평가법을 제시했다. 이후 동일 압입하중에서 압입자각 및 압입자 형태와 균열 크기의 관계를 분석해 Vickers 압입 파괴인성평가법을 다양한 압입자 형태로 확장했다. 본 연구에서 제안된 평가식을 이용하면 압입시험으로 얻어지는 데이터로부터 바로 취성재료의 파괴인성을 예측할 수 있다.

Keywords

References

  1. Lawn, B.R. and Wilshaw, T.R., 1975, "Indentation Fracture: Principles and Applications," Journal of Materials Science, Vol. 10, pp. 1049-1081. https://doi.org/10.1007/BF00823224
  2. Evans, A.G. and Charles, E.A., 1976, "Fracture Toughness Determinations by Indentation," Journal of the American Ceramic Society, Vol. 59, pp. 371-372 https://doi.org/10.1111/j.1151-2916.1976.tb10991.x
  3. Lawn, B.R. and Evans, A.G., 1977, "A Model for Crack Initiation in Elastic/Plastic Indentation Fields," Journal of Materials Science,Vol. 12, pp. 2195-2199. https://doi.org/10.1007/BF00552240
  4. Lawn, B.R., Evans, A.G., and Marshall, D.B., 1980, "Elastic/Plastic Indentation Damage in Ceramics: The Median/Radial Crack System," Journal of the American Ceramic Society, Vol. 63, pp. 574-581. https://doi.org/10.1111/j.1151-2916.1980.tb10768.x
  5. Anstis, G.R., Chantikul, P., Lawn, B.R. and Marshall, D.B., 1981, "A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements," Journal of the American Ceramic Society, Vol. 64, pp. 533-538. https://doi.org/10.1111/j.1151-2916.1981.tb10320.x
  6. Chiang, S.S., Marshall, D.B., and Evans, A.G., 1982a, "The Response of Solids to Elastic/Plastic Indentation. 1. Stresses and Residual Stresses," Journal of Applied Physics, Vol. 53, pp. 298-311. https://doi.org/10.1063/1.329930
  7. Chiang, S.S., Marshall, D.B., and Evans, A.G., 1982b, "The Response of Solids to Elastic/Plastic Indentation. II. Fracture Initiation," Journal of the American Ceramic Society, Vol. 53, pp. 312-317.
  8. Tanaka, K., 1987, "Elastic/plastic indentation hardness and indentation fracture toughness: the inclusion core model," Journal of Materials Science, Vol. 22, pp. 1501-1508. https://doi.org/10.1007/BF01233154
  9. Cook, R.F. and Pharr, G.M., 1990, "Direct Observation and Analysis of Indentation Cracking in Glasses and Ceramics," Journal of the American Ceramic Society, Vol. 73, pp. 787-817. https://doi.org/10.1111/j.1151-2916.1990.tb05119.x
  10. Pharr, G.M., 1998, "Measurement of Mechanical Properties by Ultra-low Load Indentation," Materials Science and Engineering A, Vol. 253, pp. 151-159. https://doi.org/10.1016/S0921-5093(98)00724-2
  11. Zhang, W. and Subhash, G., 2001, "Finite Element Aalysis of Iteractiong Vckers Identations on Bittle Materials," Acta Materialia, Vol. 49, pp. 2961-2974. https://doi.org/10.1016/S1359-6454(01)00198-7
  12. Tang, Y., Yonezu, A., Ogasawara, N., Chiba, N. and Chen, X., 2008, "On Radial Crack and Half-penny Crack Induced by Vickers Indentation," Proceedings of the Royal Society A, Vol. 464, pp. 2967-2984
  13. Jang, J. and Pharr, G.M., 2008, "Influence of Indenter Angle on Cracking in Si and Ge During Nanoindentation," Acta Materialia, Vol. 56, pp. 4458-4469 https://doi.org/10.1016/j.actamat.2008.05.005
  14. Quin, G.D. and Bradt, R.C., 2007, "On the Vickers Indentation Fracture Toughness Test," Journal of the American Ceramic Society, Vol. 90, pp. 673- 680. https://doi.org/10.1111/j.1551-2916.2006.01482.x
  15. Palmqvist, S., 1957, "Method of Determining the Toughness of Brittle Materials, Particularly Hardmetals," Jernkontorets Ann141, 300-307.
  16. Hill, R., 1950, The mathematical theory of plasticity. Oxford University Press, Oxford, UK.
  17. Laugier, M.T., 1985, "The Elastic/Plastic Indentation of Ceramics," Journal of Materials Science Letters, Vol. 4, pp. 1539-1541. https://doi.org/10.1007/BF00721390
  18. Jang, J. and Pharr, G.M., 2008, "Influence of Indenter Angle on Cracking in Si and Ge During Nanoindentation," Acta Materialia, Vol. 56, pp. 4458-4469. https://doi.org/10.1016/j.actamat.2008.05.005
  19. Niihara, K., 1983, "A Fracture Mechanics Analysis of Indentation-induced Palmqvist Cracks in Ceramics," Journal of Materials Science Letters, Vol. 2, pp. 221-223. https://doi.org/10.1007/BF00725625
  20. Ponton, C.B. and Rawlings, R.D., 1989a, "Vickers Indentation Fracture Toughness Test: Part 1. Review of Literature and Formulation of Standardised Indentation Equations," Materials Science and Technology, Vol. 5, pp. 865-872. https://doi.org/10.1179/mst.1989.5.9.865
  21. Ponton, C.B. and Rawlings, R.D., 1989b, "Vickers Indentation Fracture Toughness Test: Part 2. Application and Critical Evaluation of Standardised Indentation Toughness Equations," Materials Science and Technology, Vol. 5, pp. 961-976. https://doi.org/10.1179/mst.1989.5.10.961
  22. Lee, J.H., Gao, Y., Johanns, K.E. and Pharr, G.M., 2012, "Cohesive Interface Simulations of Indentation Cracking as a Ftracture Toughness Measurement Method for Brittle Materials," Acta Materialia, Vol. 60, pp. 5448-5467. https://doi.org/10.1016/j.actamat.2012.07.011
  23. Hyun, H.C., Lee, J.H., Lee, H., Kim, D.H. and Hahn, J., 2012, "An Analysis on Cracking Characteristics with Indenter Geometry Using Cohesive Zone Model," Trans. Korean Soc. Mech. Eng. A, (submitted)