Time-Dependent Thermo-Electro-Mechanical Creep Behavior of Radially Polarized FGPM Rotating Cylinder

Document Type: Research Paper

Authors

1 Department of Mechanical Engineering, Faculty of Engineering, University of Kashan--- Thermoelasticity Center of Excellence, Department of Mechanical Engineering, Amirkabir University of Technology

2 Department of Mechanical Engineering, Faculty of Engineering, University of Kashan

Abstract

Time-dependent creep analysis is crucial for the performance and reliability of piezoactuators used for high-precision positioning and load-bearing applications. In this study history of stresses, deformations and electric potential of hollow rotating cylinders made of functionally graded piezoelectric material (FGPM), e.g., PZT_7A have been investigated using Mendelson’s method of successive elastic solution. Loading is composed of an internal pressure, a distributed temperature field, an inertia body force and a constant electric potential difference between the inner and outer surfaces of the FGPM cylinder. All the mechanical, thermal and piezoelectric properties are assumed to be the same power functions of the radial graded direction. Using equations of equilibrium, strain displacement, stress-strain relation and the electric potential equation a differential equation containing creep strains for displacement is derived. A semi-analytical method in conjunction with the method of successive approximation has therefore been proposed for this analysis. It has been found that a major redistribution for electric potential take place throughout the thickness. Electric potentials are increasing with time in the same direction as the compressive radial stress histories. That is the electric potential histories are induced by the compressive radial stress histories during creep deformation of the FGPM cylinder.    

Keywords


[1] Jabbari M., Sohrabpour S., Eslami M.R., 2002, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, International Journal of Pressure Vessel and Piping 79: 493-497.

[2] Liew K.M., Kitipornchai S., Zhang X.Z., Lim C.W., 2003, Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders, International Journal of Solids and Structures 40: 2355-2380.

[3] You L.H., Zhang J.J., You X.Y., 2005, Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials, International Journal of Pressure Vessel and Piping 82: 347-354.

[4] Dai H.L., Fu Y.M., Dong Z.M., 2006, Exact solutions for functionally graded pressure vessels in a uniform magnetic field, International Journal of Solids and Structures 43: 5570-5580.

[5] Bahtui A., Eslami M.R., 2007, Coupled thermoelasticity of functionally graded cylindrical shells, Mechanics Research Communications 34: 1-18.

[6] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., 2011, Effect of material in-homogeneity on electro-thermo-mechanical behaviors of functionally graded piezoelectric rotating shaft, Applied Mathematical Modeling 35: 2771-2789.

[7] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., Loghman A., 2011, Electro-thermo-mechanical behaviors of FGPM spheres using analytical method and ANSYS software, Applied Mathematical Modeling 36: 139-157.

[8] Pai D.H., 1967, steady-state creep analysis of thick-walled orthotropic cylinders, International Journal of Mechanics Science 9: 335-482.

[9] Sim R.G., Penny R.K., 1971, Plane strain creep behaviour of thick-walled cylinders, International Journal of Mechanics Science 13: 987-1009.

[10] Bhatnagar N.S., Arya V.K., 1974, Large strain creep analysis of thick-walled cylinders, International Journal of Non-Linear Mechanics 9: 127-40.

[11] Simonian A.M., 1979, Calculation of thermal stresses in thick-walled cylinders taking account of non-linear creep, International Journal of Engineering Science 17: 513-522.

[12] Yang Y.Y., 2000, Time-dependent stress analysis in functionally graded materials, International Journal of Solids and Structures 37: 7593-7608.

[13] Altenbach H., Gorash Y., Naumenko K., 2008, Steady-state creep of a pressurized thick cylinder in both the linear and the power law ranges, Acta Mechanica 195: 263-274.

[14] Loghman A., Ghorbanpour Arani A., Amir S., Vajedi A., 2010, Magneto thermoelastic creep analysis of functionally graded cylinders, International Journal of Pressure Vessel and Piping 87: 389-395.

[15] Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi R., Mozdianfard M.R., Loghman A., 2011, Semi-analytical solution of time-dependent electro-thermo-mechanical creep for radially polarized piezoelectric cylinder, Computer and Structures 89: 1494-1502.

[16] Zhou D., Kamlah M., 2006, Room-temperature creep of soft PZT under static electrical and compressive stress loading, Acta Materialia 54: 1389-1396.

[17] Tiersten H.F., 1969, Linear piezoelectric plate vibrations, Plenum Press, New York.

[18] Fungn Y.C., 1965, Foundations of solid mechanics, Prentice-Hall, New York.

[19] Mendelson A., 1968, Plasticity Theory and Applications, Macmillan, New York.

[20] Kordkheili S.A.H., Naghdabadi R., 2007, Thermoelastic analysis of a functionally graded rotating disk, Computer and Structures 79: 508-516.

[21] Bayat M., Saleem M., Sahari B.B., Hamouda A.M.S., Mahdi E., 2009, Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads, International Journal of Pressure Vessel and Piping 86: 357-372.

[22] Penny R.K., Marriott D.L., 1995, Design for Creep, Chapman and Hall, London.

[23] Norton F.H., 1929, The Creep of Steel at High Temperatures, McGraw-Hill, London.

[24] Jaffe H., Berlincourt D.A., 1965, Piezoelectric transducer materials, Proceedings of IEEE 53: 1372-1386.