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A Theory for Elastic Potential Energy Change and Applied Stresses Accompanying Phase Transformation

Published online by Cambridge University Press:  05 May 2011

Huang Hsing Pan
Huang Hsing Pan*
Affiliation:
Department of Civil Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan 807, R.O.C.
*
*Associate Professor
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Abstract

A theory is proposed to derive the resultant elastic potential energy change in the systems accompanying phase transformation for a finite concentration of inclusions. Based on the thermodynamic equilibrium, this elastic potential energy due to the interaction of ellipsoidal inclusions is employed to evaluate the critically applied stress that induces phase transformation. It is shown that the material system with the disc inclusions is easier to get the stress-induced transformation than that with other shapes. The inclusions with 3-D random orientation are the most effective one to have toughness increments. The height of the transformation zone strongly depends on the volume concentration and the shape of the inclusions. As compared with the experimental data, the theory is in an acceptable range of accuracy.

Keywords

Phase transformationApplied stressElastic potential energy
Type
Articles
Information
Journal of Mechanics , Volume 16 , Issue 3 , September 2000 , pp. 169 - 176
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2000

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References

REFERENCES

1Evans, A. G. and Heuer, A. H., “Review — Transformation Toughening in Ceramics: Martensitic Transformations in Crack-Tip Stress Fields,” Journal of American Ceramics Society, 63, pp. 241–248 (1980).CrossRefGoogle Scholar
2Evans, A. G., “Perspective on the Development of High-Toughness Ceramics,” Journal of American Ceramics Society, 73, pp. 187–206 (1990).Google Scholar
3Evans, A. G. and Cannon, R. M., “Toughening of Brittle Solids by Martensitic Transformations,” Acta metallurgica, 34, pp. 761–800 (1986).Google Scholar
4Mura, T., Micromechanics of Defects in Solids, 2nd Edn., Martinus Nijfoff, Dordrecht (1987).CrossRefGoogle Scholar
5Tandon, G. P. and Weng, G. J., “Average Stress in the Matrix and Effective Moduli of Randomly Oriented Composites,” Composite Science and Technology, 27, pp. 111–132 (1986).CrossRefGoogle Scholar
6Eshelby, J. D., “The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Relation Problem,” Proceedings of the Royal Society, London, A241, pp. 376–396 (1957).Google Scholar
7Mori, T. and Tanaka, K., “Average Stress in the Matrix and Average Elastic Energy of Materials with Misfitting Inclusions,” Acta metallurgica, 21, pp. 571–574 (1973).CrossRefGoogle Scholar
8Khachaturyan, A. G., Theory of Structural Transformations in Solids, Wiley-Interscience (1983).Google Scholar
9Bunge, H. J., Texture Analysis in Materials Science, Butterworth, p. 21 (1982).Google Scholar
10McMeeking, R. M. and Evans, A. G., “Mechanics of Transformation-Toughening in Brittle Materials,” Journal of American Ceramics Society, 65, pp. 242–246 (1982).Google Scholar
11Hsueh, C. H. and Becher, P. F., “Some Consi-derations of Nonideal Transformation-Zone Profile,” Journal of American Ceramics Society, 71, pp. 494–497 (1988).Google Scholar
12Porter, D. L. and Heuer, A. H., “Mechanisms of Toughening Partially Stabilized Zirconia,” Journal of American Ceramics Society, 60, pp. 183–184 (1977).CrossRefGoogle Scholar
13Lange, L. L., “Transformation Toughening,” Journal of Materials Science, 17, pp. 225–262 (1982).CrossRefGoogle Scholar
14Budiansky, B., Hutchinson, J. W. and Lambropoulos, J. C., “Continuum Theory of Dilatant Transformation Toughening in Ceramics,” International Journal of Solids Structures, 19, pp. 337–355 (1983).CrossRefGoogle Scholar
15Lambropoulos, J. C., “Shear, Shape and Orientation Effects in Transformation Toughening,” International Journal of Solids Structures, 22, pp. 1083–1106 (1986).Google Scholar
16Porter, D. L., Evans, A. G. and Heuer, A. H., “Transformation-Toughening in Partially-Stabilized Zirconia,” Acta metallurgica, 27, pp. 1649–1654 (1979).CrossRefGoogle Scholar
17Evans, A. G., Burlingame, N., Drort, N. and Kriven, W. M., “Martensitic Transformations in Zirconia-Particle Size Effects and Toughening,” Acta metallurgica, 29, pp. 447–456 (1981).Google Scholar