J integral computation for piezo-ceramics
Keywords:
Finite element computation, energy-domain-integral method, piezo-electricity, piezoceramics, PZJ-4H, PZT-SHAbstract
Piezo-ceramics are brittle; they can fail untimely due to the propagation of flaws or defects produced during their manufacturing process. ln this paper, we propose a numerical estimate of a J -integral generalized to electro-mechanical processus, wich will prove useful in designing a propagation criterion. To that end, we use the finite-element method to solve the piezo-electric problem, providing thus displacements and coordinates of elements that constitute the chosen integration path. Then the computation of J is achieved by using the energydomain- integral methodfor piezo-ceramics such as PZT-4H and PZT-SH.
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References
[AND 91) ANDERSON T.L., "Fracture mechanics fundamentals and application ", CRC
PRESS, BOSTON, 1991.
[DAS 94) DASCALU C. , MAUGIN G.A., "Energy-release rates and path independent integrais
in electroelastic crack propagation", International Journal of Engineering Sciences,
vol. 32, 1994, p. 755-765.
[DAS 95) DASCALU C. , MAUGIN G.A., "On the energy of electric fracture", Z angew
Mathematics and Physics, vol. 46, 1995, p. 355-365.
[DEE 80) DEEG W.F., "The analysis of dislocation, crack and inclusion problems in piezoelectric
solids ", 1980, Stanford University, Stanford, California.
[CHU 89] CHUNG H.T., SHIN, KIM, Journal of American Ceramics Society, vol. 72, 1989,
p. 327.
[DHA 81) DHATT G., TouzoT G., "Une présentation de la méthode des éléments finis",
MALOINE S.A, 1981, LES PRESSES DE L'UNIVERSITÉ LAVAL, QUEBEC.
[MAU 93] MAUGIN G.A., "Material inhomogeneities in elasticity ", Chapman & Hall, London,
[MAU 95) MAUGIN G.A., "Material forces: concepts and applications", Applied Mechanics
Reviews, vol. 48, 1995, p. 213-245.
[MCM 87) MCMEEKING R.M., International Journal ofSolids and Structures, vol. 62, 1987,
p. 3116.
[MCM 90] MCMEEKING R.M., "Integral for the analysis of electrically induced mechanical
stress at cracks in elastic dielectrics ", International Journal of Engineering Sciences,
vol. 28, 1990, p. 605-613.
[MIK 90) MIKHAILOV G.K. PARTON V.Z., "Electromagnetoelasticity
,HEMISPHERE,NEW-YORK, 1995.
[PAK 90) PAK Y.E., "Crack extension force in a piezoelectric material", Journal of Applied
Mechanics, vol. 57, 1990, p. 647-653.
[PAK 86) PAK Y.E., HERMANN G., "Conservation laws and the material momentum tensor
for the elastic dielectric ", International Journal of Engineering Sciences, vol. 24, 1986,
p. 1365-1374.
[PAK 92] PAK Y.E., "Linear electroelastic fracture mechanics of piezoelectric materials ",
International Journal of Fracture, vol. 54, 1992, p. 79-100.
[PAR 95] PARTON V.Z., "Fracture mechanics of piezoelectric materials ", Acta Astronautica,
vol. 3, 1995, p. 671-683.
[RIC 71) RICE J.R., "A path-independent integral and the approximation analysis on strain
concentration by notches and cracks ", Journal of Applied Mechanics, vol. 35, 1968,
p. 379-386.
[SUN 95] SUN C.T., PARK S.B., "Effect of electric field on fracture of piezoelectric ceramics",
International Journal of Fracture, vol. 70, 1995, p. 203-216.
[SUO 92) SUO, Kuo C.M., BARNETT D.M., WILLIS J.R., "Fracture mechanics for piezoelectric
ceramics", Journal of Mechanics and Physics of Solids, vol. 40, 1992, p. 39-765.
[TON 96) TONG- YI ZANG , PPIN TONG, "Fracture mechanics for a mode III crack in a piezoelectric
material ", International Journal of Solids and Structures, vol. 33, 1996, p. 343.
[ZIE 71] ZIENCKIEWICZ O.C., ''The finite element method in engineering sciences", Mc
GRAW HILL, London, 1971.
