Crack analyses in conducting and non-conducting piezoelectric solids
Jan Sladek1
, Vladimir Sladek1, Milan Zmindak2, Slavomir Hrcek2
1Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia.
2Faculty of Mechanical Engineering, University of Zilina, 01026 Zilina, Slovakia.
DOI:
https://doi.org/10.7494/cmms.2015.1.0523
Abstract:
The stress intensity factor and electric displacement intensity factor for cracks in conducting and non-conducting piezoelectric materials is investigated. Transient dynamic crack problems are analyzed. The coupled governing partial differential equations (PDE) for stresses, electric displacement field and electric current are satisfied in a local weak-form on small fictitious subdomains. Local integral equations are derived for a unit function as the test function on circular subdomains. All field quantities are approximated by the moving least-squares (MLS) scheme. The influence of the electric conductivity on the stress intensity and electric intensity factors is shown in numerical examples for an edge crack in a finite strip under a pure mechanical impact load with Heaviside time variation.
Cite as:
Sladek, J., Sladek, V., Zmindak, M., & Hrcek, S. (2015). Crack analyses in conducting and non-conducting piezoelectric solids. Computer Methods in Materials Science, 15(1), 198-203. https://doi.org/10.7494/cmms.2015.1.0523
Article (PDF):
Keywords:
Meshless approximation, Local integral equations, Intensity factors, Impermeable boundary conditions
Publication dates:
Received: 23.09.2014, accepted: 17.12.2014, published: 28.12.2014
Publication type:
Original scientific paper
References:
Auld, B.A., 1973, Acoustic Fields and Waves in Solids, John Wiley and Sons, New York, 357-382.
Davi, G., Milazzo, A., 2001, Multidomain Boundary Integral Formulation for Piezoelectric Materials Fracture Mechanics, Int J Solids Struct, 38, 2557-2574.
Enderlein, M., Ricoeur, A., Kuna, M., 2005, Finite Element Techniques for Dynamic Crack Analysis in Piezoelectrics, Int J Fracture, 134, 191-208.
Garcia-Sanchez, F., Saez, A., Dominguez, J., 2005, Anisotropic and Piezoelectric Materials Fracture Analysis by BEM, Comput Struct, 83, 804-820.
Garcia-Sanchez, F., Zhang, Ch., Sladek, J., Sladek, V., 2007, 2-D Transient Dynamic Crack Analysis in Piezoelectric Solids by BEM, Comp Mater Sci, 39, 179-186.
Govorukha, V., Kamlah, M., 2004, Asymptotic Fields in the Finite Element Analysis of Electrically Permeable Interfacial Cracks in Piezoelectric Biomaterials, Arch Appl Mech, 74, 92-101.
Gross, D., Rangelov, T., Dineva, P., 2005, 2D Wave Scattering by a Crack in a Piezoelectric Plane Using Traction BIEM, SID: Structural Integrity & Durability, 1, 35-47.
Gruebner, O., Kamlah, M., Munz, D., 2003, Finite Element Analysis of Cracks in Piezoelectric Materials Taking into Account the Permittivity of the Crack Medium, Eng Fract Mech, 70, 1399-1413.
Hu, Y., Zeng, Y., Yang, J.S., 2007, A Mode III Crack in a Piezoelectric Semiconductor of Crystals with 6mm Symmetry, Int J Solids Struct, 44, 3928-3938.
Hutson, A.R., White, D.L., 1962, Elastic Wave Propagation in Piezoelectric Semiconductors, J Appl Phys, 33, 40-47.
Kuna, M. 2006, Finite Element Analyses of Cracks in Piezoelectric Structures – a Survey, Arch Appl Mech, 76, 725-745.
Pak, Y.E., 1990, Crack Extension Force in a Piezoelectric Material, J Appl Mech, 57, 647-653.
Pan, E., 1999, A BEM Analysis of Fracture Mechanics in 2D Anisotropic Piezoelectric Solids, Eng Anal Bound Elem, 23, 67-76.
Park, S.B., Sun, C.T., 1995, Effect of Electric Field on Fracture of Piezoelectric Ceramics, Int J Fracture, 70, 203-216.
Sladek, J., Stanak, P., Han, Z.D., Sladek, V., Atluri, S.N., 2013, Applications of the MLPG Method in Engineering & Sciences: A Review, CMES-Comp Model Eng, 92, 423-475.
Sladek, J., Sladek, V., Zhang, Ch., Solek, P., Pan, E., 2007, Evaluation of Fracture Parameters in Continuously Nonhomogeneous Piezoelectric Solids, Int J Fracture, 145, 313–326.
Yang, J.S., Zhou, H.G., 2005, Amplification of Acoustic Waves in Piezoelectric Semiconductor Plates, Int J Solids Struct, 42, 3171-3183.
Yang, J.S., 2005, An Anti-Plane Crack in a Piezoelectric Semiconductor, Int J Fracture, 136, 27-32.
White, D.L., 1962, Amplification of Ultrasonic Waves in Piezoelectric Semiconductors, J Appl Phys, 33, 2547-2554.