Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T01:55:56.217Z Has data issue: false hasContentIssue false
  • English
  • Français

Strain Gradient Effect in Cone Indentation

Published online by Cambridge University Press:  11 February 2011

Anthony A. DiCarlo ,
Henry T. Y. Yang  and
Srinivasan Chandrasekar
Anthony A. DiCarlo
Affiliation:
Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106
Henry T. Y. Yang
Affiliation:
Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106
Srinivasan Chandrasekar
Affiliation:
School of Industrial Engineering, Purdue University, West Lafayette, IN 47907–1287
Get access

Abstract

A size effect is known to exist in the strength and hardness of metals at small length scales. For example, the hardness of a pyramid indentation at the macro-scale is constant and typically independent of indentation size due to the self-similar feature of the indentation. But, at the meso-scale, this hardness has been observed to increase with decreasing indentation size. This increase has been attributed to the influence of strain gradient on the flow stress. At this point, the contribution of a rotational gradient to the hardness is unclear.

This study investigates the sensitivity of the hardness to rotational strain gradients through a Cosserat continuum. Finite element simulation of cone indentation is employed to conduct this investigation. The effect of varying indentation strain fields is modeled using indentation with cones of varying angles. The results demonstrate the role of rotational gradients in indentation.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 741: Symposium J – Nano- and Microelectromechanical Systems (NEMS and MEMS) and Molecular Machines , 2002 , J5.35
Copyright
Copyright © Materials Research Society 2003

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

1. Pethica, J. B., Huctings, R., and Oliver, W. C., “Hardness measurement at penetrations as small as 20 nm,” Philosophical Magazine A, Vol. 48, No. 4, p. 593–606 (1983).Google Scholar
2. Atkinson, M., “Phenomenology of the size effect in hardness tests with a blunt pyramidal indenter”, Journal of Materials Science, Vol. 33, No. 11, p. 2937–2947 (1998).Google Scholar
3. Gerberic, W. W., Yu, W., Kramer, D., Strojny, A., Bahr, D., Lilleodden, E., Nelson, J., “Elastic loading and elasto-plastic unloading from nanometer level indentations for modulus determinations”, Journal of Materials Research, Vol. 13, No. 2, p. 421–439 (1998).Google Scholar
4. Petzold, M., Landgraf, J., Futing, M., and Olaf, M. J., “Application of atomic force microscope of microindentation testing”, Thin Solid Films, Vol. 264, No. 2, p. 153–158 (1995).Google Scholar
5. Doerner, M. F. and Nix, W. D., “A method for interpreting the data from depth-sensing indentation instruments,” Journal of Material Research, Vol. 1, No. 4, p. 601–609 (1986).Google Scholar
6. Ashby, M. F., “The deformation of plastically non-homogeneous alloy,” Philosophical Magazine, Vol. 21, p. 399–424 (1970).Google Scholar
7. Stelmashenko, N. A., Brown, M. G., Milman, L. M., Yu, V., “Microindentationss on W and Mo oriented single crystals: An STM study,: Acta Metall. Mater., Vol. 41, No. 10, P. 2855–2865 (1993).Google Scholar
8. Nix, W. D. and Gao, H., “Indentation size effects in crystalline matereials: a law for strain gradient plasticity,” Journal of the Mechanics and Physics of Solids, Vol. 46, No. 3, p. 411–425 (1998)Google Scholar
9. Fleck, N. A., Muller, G. M., Ashby, M. F., and Hutchinson, J. W., “Strain gradient plasticity: Theory and experiements,” Acta Metall. Meter., Vol. 42, No. 2, p. 475–487 (1994).Google Scholar
10. Li, Z. Y., Chandrasekar, S., and Yang, H. T., “A generalized load-penetration relation for sharp indenters and the indentation size effect.” Transactions of the ASME, Vol. 69, p. 394–396 (2002).Google Scholar
11. Shu, J. Y. and Fleck, N. A., “The prediction of a size effect in microindentation,” International Journal of Solids and Structures, Vol. 35, No. 13, p 1363–1383 (1998)Google Scholar
12. Cosserat, E. and Cosserat, F., Theorie des Corps Deformables, Herman, ParisGoogle Scholar
13. Brulin, O. and Hsieh, R. K. T., Mechanics of micropolar media, Singapore: World Scientific, (1982).Google Scholar
14. Dietsche, , Steinmann, P., and Willam, K., “Micro-polar elastoplasticity and its role in localization.”, International Journal of Plasticity, Vol. 9, p. 813–831 (1993)Google Scholar
15. Ristinmaa, M. and Vecchi, M., “Use of couple-stress theory in elasto-plasticity.” Computer Methods in Applied Mechanics and Engineering, Vol. 136, p. 205–224 (1996)Google Scholar
16. Fleck, N. A., Muller, G. M., Ashby, M. F., and Hutchinson, J. W., “Strain gradient plasticity: Theory and experiements,” Acta Metall. Meter., Vol. 42, No. 2, p. 475–487 (1994).Google Scholar
17. Iordache, M-M. and Willam, K., “Localized failure analysis in elastoplastic Cosserat continua.” Computer Methods in Applied Mechanics and Engineering. Vol. 151, p. 559–586 (1998).Google Scholar
18. ABAQUS. ABAQUS/standard 5.8 Hibbitt, Karlsson and Sorensen, Inc., Providence, RI, 1996.Google Scholar
19. Begley, M. R. and Hutchinson, J. W., “The mechanics of size-dependent indentation,” Journal of Mechanics and Physics of Solids, Vol. 46 No. 10. P2049–2068 (1998).Google Scholar
20. Zhang, T-Y and Xu, W-H, “Surface effects on nanoindentation,” Journal of Material Research, Vol. 17, No. 7, pp. 1715–1720 (2002).Google Scholar