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Continuum Damage Mechanics for Thermo-Piezoelectric Materials

Published online by Cambridge University Press:  05 May 2011

X.-H. Yang ,
Y. Zhang ,
Y.-T. Hu  and
C.-Y. Chen
X.-H. Yang*
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
Y. Zhang*
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
Y.-T. Hu*
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
C.-Y. Chen*
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
*
*Associate Professor
**Graduate student
***Professor
***Professor
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Abstract

With rapidly increasing use of piezoelectric materials in high-temperature environment, it is becoming increasingly important for reliable design of piezoelectric devices to study thermo-electroelastic damage and fracture mechanism. As the first step, a thermo-piezoelectric damage constitutive model is presented from continuum damage mechanics and effective properties of a damaged material are connected with both damages and the initial coefficients according to the theorem of energy equivalence in this paper. Then the finite element equations for a thermo-electroelastic damage problem are given by use of the virtual work principle. Finally, as a numerical illustration example, damage fields around a crack-tip in a three-point bending PZT-5H beam subjected to different thermal loads are calculated and analyzed. It is shown from both the damage curves and contours that influence of environmental temperature on the mechanical damage distribution is great but slight on the electrical damage.

Keywords

Thermo-piezoelectric materialMechanical and electrical damagesDamage constitutive relationThree-point bending beam.
Type
Articles
Information
Journal of Mechanics , Volume 22 , Issue 2 , June 2006 , pp. 93 - 98
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2006

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References

REFERENCES

1.Sih, G. c. and Zuo, J. Z., “Multiscale Behavior of Crack Initiation and Growth in Piezoelectric Ceramics,” J. Theoretical Appi. Fract. Mech., 34, pp. 123–141 (2000).Google Scholar
2.Shang, F. L., “Thermal Stress around a Penny-Shaped Crack in a Thermopiezoelectric Solid,” Computational Materials Science, 26, pp. 197–201 (2003).Google Scholar
3.Wang, B. L. and Li, J., “Thermal Stress and Intensity Release in Ferroelectric Materials by Multiple Cracking,” ActaMaterialia, 53, pp. 785–799 (2005).Google Scholar
4.Shang, F., Kuna, M. and Kitamura, T., “Theoretical Investigation of an Elliptical Crack in Thermopiezoelectric Material,” Part I: Analytical Development, J. Theoretical Appl. Fract. Mech., 40, pp. 237–246 (2003).CrossRefGoogle Scholar
5.Park, S. B. and Sun, C. T., “Fracture Criteria of Piezoelectric Ceramics,” J. Am. Ceram. Soc., 78, pp. 1475–1480 (1995).Google Scholar
6.Heyer, V., Schneider, G. A., Balke, H., Drescher, J. and Bahr, H. A., “A Fracture Criterion for Conducting Cracks in Homogeneously Poled Piezoelectric PZT-PIC 151 Ceramics,” Acta Mater., 46, pp. 6615–6622 (1998).CrossRefGoogle Scholar
7.Gao, H., Zhang, T. Y. and Tong, P., “Local and Global Energy Release Rates for an Electrically Yielded Crack in a Piezoelectric Ceramic,” J. Mech. Phys. Solids, 45, pp. 491–510 (1997).Google Scholar
8.Sze, K. Y. and Pan, Y. S., “Nonlinear Fracture Analysis of Piezoelectric Ceramics by Finite Element Method,” Engng. Fracture Mech., 68, pp. 1335–1351 (2001).Google Scholar
9.Yang, X. H., Chen, C. Y. and Hu, Y. T., “Analysis of Damage near a Conducting Crack in a Piezoelectric Cerami,” Acta Mechanica Solida Sinica, 16, pp. 147–154 (2003).Google Scholar
10.Yang, X. H., Dong, L., Wang, C., Chen, C. Y. and Hu, Y. T., “Transversely Isotropic Damage around Conducting Crack-Tips in a Four-Point Bending Piezoelectric Beam,” Applied Mathematics and Mechanics, 26, pp. 431–440 (2005).Google Scholar
11.Yang, X. H., Dong, L., Chen, C. Y., Wang, C. and Hu, Y. T., “Damage Extension Forces and Piezoelectric Fracture Criteria,” Journal of Mechanics, 20, pp. 277–283 (2004).CrossRefGoogle Scholar
12.Yang, X. H., Chen, C. Y., Hu, Y. T. and Wang, C., “Combined Damage Fracture Criteria for Piezoelectric Ceramics,” Acta Mechanica Solida Sinica, 18(1), pp. 21–27 (2005).Google Scholar
13.Yu, S. W. and Qin, Q. H., “Damage Analysis of Thermopiezoelectric Properties: Part I —Crack Tip Singularities,” J. Theoretical Appl. Fract. Mech., 25, pp. 263–277 (1996).CrossRefGoogle Scholar
14.Yu, S. W. and Qin, Q. H., “Damage Analysis of Thermopiezoelectric Properties: Part II — Effective Crack Model,” J. Theoretical Appl. Fract. Mech., 25, pp. 279–288 (1996).CrossRefGoogle Scholar
15.Huang, J. H., “Micromechanics Determinations of Thermoelectroelastic Fields and Effective Thermoelectroelastic Moduli of Piezoelectric Composites,” Matrials Science and Engineering, 39, pp. 163–172 (1996).Google Scholar
16.Qm, Q. H., Mai, Y. W. and Yu, S. W., “Effective Moduli for Thermopiezoelectric Materials with Microcracks,” International Journal of Fracture, 91, pp. 359–371 (1998).Google Scholar
17.Yang, X. H. and Shen, W., “An Advanced Dynamic Three-Dimensional Finite Element Method to Simulate Deformation-Damage Process of Laminates under Impact,” Engng. Fracture Mech., 49, pp. 631–638 (1994).Google Scholar
18.Altay, G. A. and Dökmeci, M. C., “Fundamental Varialtional Equations of Discontinuous Thermopiezoelectric Fields,” Int. J. Engng. Sci., 34, pp. 769–782 (1996).Google Scholar