Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-06-06T00:06:11.124Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments and Simulations of Directionally dependent Fracture along Copper/Sapphire Interfaces

Published online by Cambridge University Press:  15 February 2011

Jeffrey W. Kysar
Jeffrey W. Kysar*
Affiliation:
Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138
Get access

Abstract

To test the hypothesis that the brittleness and ductility of crystalline materials are controlled by a competition between dislocation nucleation and cleavage failure at a crack tip, Rice et al. [1] designed a four-point bend copper/sapphire bicrystal which has two cracks that propagate along the interface in opposing directions. They predicted, on the basis of the Rice-Thomson model [2], that the specimen would exhibit a directionally dependent fracture behavior; that is, one crack would propagate more readily than the other. Beltz and Wang [3] carried out the experiments and reported that the specimen exhibits a directionally dependent fracture behavior in accordance with the predictions. In the present work, these experiments are repeated independently and it is shown that the orientation of the experimentally observed directionally dependent behavior is opposite that of the predicted orientation. Furthermore, we show that Beltz and Wang incorrectly measured the orientation of the directional dependence in their experimental results. A correct interpretation of their results is consistent with the present work.

Taking advantage of the transparent sapphire, the normal crack opening displacement (NCOD) profile of both cracks is measured with optical interferometry. The measurements show that, away from the very tip of the crack, the NCOD takes the form of a constant angle, irrespective of load level. The opening angle of the apparently brittle crack is smaller than that of the apparently ductile crack. Complementary measurements of the very tip of the crack with Atomic Force Microscopy show that the near-tip crack opening profiles of the brittle and ductile cracks differ significantly.

The specimen is analyzed with the Finite Element Method, taking into account the elastic and plastic properties of the single crystal constituents. Since the very essence of the observed phenomenon is one of crack growth, the two cracks are simulated as they grow quasistatically along the interface. The asymptotic deformation fields, characteristic of single crystals, of the growing interfacial cracks are identified. The stress and strain fields, as well as the NCOD, are calculated. We present a plausible explanation of the directional dependence of fracture on the basis of the continuum plastic fields surrounding the quasistatically growing cracks.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 539: Symposium M – Fracture & Ductile vs. Brittle Behavior - Theory, Modelling… , 1998 , 299
Copyright
Copyright © Materials Research Society 1999

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

1. Rice, J. R., Suo, Z., and Wang, J.-S. (1990). “Mechanics and thermodynamics of brittle interfacial failure in bimaterial systems.” Acta-Scripta Metallurgica Proceedings Series, Ruhle, M., Evans, A. G., Ashby, M. F., and Hirth, J. P., eds., Pergamon Press, Oxford, 269–294.Google Scholar
2. Rice, J. R., and Thomson, R. (1974). “Ductile versus brittle behaviour of crystals.” Phil. Mag., 29(1), 73–97.Google Scholar
3. Beltz, G. E., and Wang, J.-S. (1992). “Crack direction effects along copper/sapphire interfaces.” Acta metall. mater, 40(7), 1675–1683.Google Scholar
4. Wang, J.-S., and Anderson, P. M. (1991). “Fracture behavior of embrittled F.C.C. metal bicrystals.” Acta metall. mater, 39(5), 779–792.Google Scholar
5. Vehoff, H., Stenzel, H., and Neumann, P. (1987). Metallkade, 78, 550.Google Scholar
6. Wang, J.-S., and Mesarovic, S. D. (1995). “Directional dependence of corrosion fatigue of iron-silicon bicrystals.” Acta metall. mater, 43(10), 3837–3849.Google Scholar
7. Elssner, G., Korn, D., and Rühle, M. (1994). “The influence of interface impurities on fracture energy of UHV diffusion bonded metal-ceramic bicrystals.” Scripta metall. mater, 31(8), 1037–1042.Google Scholar
8. Beltz, G. E., and Rice, J. R. (1992). “Dislocation nucleation at metal-ceramic interfaces.” Acta metall, mater, 40(Supplement), S321–S331.Google Scholar
9. Kysar, J. W., PhD thesis, Harvard University, 1998.Google Scholar
10. Rogers, K. A., Trumble, K. P., Dalgleish, B. J., and Reimanis, I. E. (1994). “Role of oxygen in microstructure development at solid-state diffusion-bonded Cu/A1203 interfaces.” J. Am. Ceram. Soc., 77(8), 2036–2042.Google Scholar
11. Reimanis, I. E., Trumble, K. P., Rogers, K. A., and Dalgleish, B. J. (1997). “Influence of Cu2O and CuAO2 interphases on crack propagation at Cu/α-Al2O3 interfaces.” J Am. Ceram. Soc., 80(2), 424–432.Google Scholar
12. Turner, M. R., and Evans, A. G. (1996). “An experimental study of the mechanisms of crack extension along an oxide/metal interface.” Acta mater, 44(3), 863–871.Google Scholar
13. Beltz, G. E., (private communication).Google Scholar
14. Wang, J.-S., (private communication).Google Scholar
15. Laird, C. (1967). “The influence of metallurgical structure on the mechanisms of fatigue crack propagation.” Fatigue crack propagation, Special Technical Publication 415, American Society for Testing and Materials, 131–168.Google Scholar
16. Liang, Y.-M., and Liechti, K. M. (1995). “Toughening mechanisms in mixed-mode interfacial fracture.” Int. J. Solids Structures, 32, 957–978.Google Scholar
17. Wang, J.-S. (1995). “Interfacial fracture toughness of a copper-alumina system and the effect of the loading phase angle.” Mech. Mater., 20(3), 251–259.Google Scholar
18. Neumann, P. (1974). “New experiments concerning the slip processes at propagating fatigue cracks--l.” Acta Metall., 22, 1155–1165.Google Scholar
19. Green, G., and Knott, J. F. (1975). “On effects of thickness on ductile crack growth in mild steel.” J. Mech. Phys. Solids, 23, 167–183.Google Scholar
20. Turner, M. R., and Evans, A. G. (1996). “An experimental study of the mechanisms of crack extension along an oxide/metal interface.” Acta mater, 44(3), 863–871.Google Scholar
21. Mao, S. X., and Evans, A. G. (1997). “The influence of blunting on crack growth at oxide/metal interfaces.” Acta metall. mater, 45(10), 4263–4270.Google Scholar
22. McClintock, F. A., and Irwin, G. R. (1965). “Plasticity aspects of fracture mechanics.” ASTM STP 381, 84–113.Google Scholar
23. Rice, J. R. (1982). “Elastic-plastic crack growth.” Mechanics of Solids, Hopkins, H. G. and Sewell, M. J., eds., Pergamon Press, Oxford, 539–562.Google Scholar
24. Mesarovic, S. D., and Kysar, J. W. (1996). “Continuum aspects of directionally dependent cracking of an interface between copper and alumina crystals.” Mech. Mater, 23, 271–286.Google Scholar
25. ABAQUS/Standard User's Manual, (1998). Version 5.7, Hibbit, Karlsson and Sorensen, Inc., Pawtucket, RI, USA.Google Scholar
26. Huang, Y. (1991). “A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program.” Mech Report 178, Division of Applied Sciences, Harvard University, Cambridge, Massachusetts.Google Scholar
27. Kysar, J. W. (1997). “Addendum to “A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program, Mech Report 178,”.”, Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts.Google Scholar
28. Peirce, D., Asaro, R. J., and Needleman, A. (1983). “Material rate dependence and localized deformation in crystalline solids.” Acta Metall., 31, 1951.Google Scholar
29. Bassani, J. L., and Wu, T.-Y. (1991). “Latent hardening in single crystals II. Analytical characterization and predictions.” Phil. Trans. R. Soc. Lond A, 435, 21–41.Google Scholar