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On the crack face boundary conditions in electromechanical fracture and an experimental protocol for determining energy release rates. (English) Zbl 1154.74378

Summary: The fracture mechanics of electromechanical materials has been investigated for well over a decade, yet there still exists controversy over the appropriate crack face boundary conditions for non-conducting cracks. In this paper an experimental protocol for measuring the energy release rate in a non-linear reversible electromechanical body is proposed and summarized. The potential results from the proposed experimental approach are capable of shedding light on the true physical nature of the conditions prevailing at the crack surface and in the space within the crack. The experimental procedure is simulated numerically for a linear piezoelectric specimen in a four point bending configuration subjected to electrical loading perpendicular to the crack. The focus of these investigations is on a comparison between the commonly used exact crack face boundary condition and the recently proposed energetically consistent boundary conditions. To perform the numerical calculation with a wide range of electrical and mechanical loadings, two efficient finite element formulations are presented for the general analysis of crack problems with non-linear crack face boundary conditions. Methods for the numerical determination of the crack tip energy release rate and the simulation of the experimental method for obtaining the total energy release rate are developed. Numerical results for the crack tip and total energy release rate are given for both the exact and energetically consistent boundary conditions. It is shown that the crack tip energy release rate calculated under energetically consistent boundary conditions is equal to the total energy release rate generated from the simulated experimental method. When the exact boundary conditions are used, there is no such agreement.

MSC:

74R10 Brittle fracture
74F15 Electromagnetic effects in solid mechanics
74-05 Experimental work for problems pertaining to mechanics of deformable solids
74S05 Finite element methods applied to problems in solid mechanics
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References:

[1] Allik, H.; Hughes, T. J.R., Finite element method for piezoelectric vibration, Int. J. Numer. Methods Engrg., 2, 151-157 (1970)
[2] Anderson, T. L., Fracture Mechanics Fundamental and Applications (1991), CRC Press: CRC Press Boca Raton, FL
[3] Deeg, W.F., 1980. The analysis of dislocation, crack and inclusion problems in piezoelectric solids. PH.D. Thesis, Stanford University; Deeg, W.F., 1980. The analysis of dislocation, crack and inclusion problems in piezoelectric solids. PH.D. Thesis, Stanford University
[4] Dunn, M. L., The effects of crack face boundary conditions on the fracture mechanics of piezoelectric solids, Engrg. Fract. Mech., 48, 25-39 (1994)
[5] Hao, T. H.; Shen, Z. Y., A new electric boundary condition of electric fracture mechanics and its application, Engrg. Fract. Mech., 47, 793-802 (1994)
[6] Haug, A.; McMeeking, R. M., Cracks with surface charge in poled ferroelectrics, Eur. J. Mech. A Solids, 25, 24-42 (2006) · Zbl 1084.74042
[7] Heyer, V.; Schneider, G. A.; Balke, H.; Drescher, J.; Bahr, H. A., A fracture criterion for conducting cracks in homogeneously poled piezoelectric PZT-PIC 151 ceramics, Acta Mat., 46, 6615-6622 (1998)
[8] Landis, C. M., A new finite element formulation for electromechanical boundary value problems, Int. J. Numer. Methods Engrg., 55, 613-628 (2002) · Zbl 1076.74556
[9] Landis, C. M., Energetically consistent boundary conditions for electromechanical fracture, Int. J. Solids Struct., 41, 6291-6315 (2004) · Zbl 1120.74755
[10] Li, F. Z.; Shih, C. F.; Needleman, A., A comparison of methods for calculating energy release rates, Engrg. Fract. Mech., 21, 2, 405-421 (1985)
[11] Li, W., 2006. On the crack face boundary conditions in electromechanical fracture and an experimental protocol for determining energy release rates, Master’s Thesis, Rice University; Li, W., 2006. On the crack face boundary conditions in electromechanical fracture and an experimental protocol for determining energy release rates, Master’s Thesis, Rice University
[12] McMeeking, R. M., Crack tip energy release rate for a piezoelectric compact tension specimen, Engrg. Fract. Mech., 64, 217-244 (1999)
[13] McMeeking, R. M., The energy release rate for a Griffith crack in a piezoelectric material, Engrg. Fract. Mech., 71, 1149-1163 (2004)
[14] Pak, Y. E., Linear electro-elastic fracture mechanics of piezoelectric materials, Int. J. Fract., 54, 79-100 (1992)
[15] Parks, D. M., A stiffness derivative finite element technique for determination of crack tip stress intensity factors, Int. J. Fract., 10, 4, 487-502 (1974)
[16] Parton, V. Z., Fracture mechanics of piezoelectric materials, Acta Astronaut., 3, 671-683 (1976) · Zbl 0351.73115
[17] Schneider, G., 2006. Private communications; Schneider, G., 2006. Private communications
[18] Suo, Z.; Kuo, C. M.; Barnett, D. M.; Willis, J. R., Fracture mechanics for piezoelectric ceramics, J. Mech. Phys. Solids, 40, 739-765 (1992) · Zbl 0825.73584
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