Journal of Computational Applied Mechanics

Elasto-plastic solution for thick-walled spherical vessels with an inner FGM layer

Document Type : Research Paper

Authors

1 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

2 Engineering Department, Urmia University, Urmia, Iran

Abstract

Purely elastic, partially and fully plastic stress states in a thick-walled spherical pressure vessel with an inner functionally graded material (FG) coating subjected to internal and external pressures are developed analytically in this paper. The modulus of elasticity and the uniaxial yield limit of the FG coating layer are considered to vary nonlinearly through the thickness. Using Tresca’s yield criterion and ideal plastic material behavior, the plastic model is established. Under pressure loading, the scenario in which the plastic deformation starts from inner surface of FG coating layer is taken into account. Having increased the pressure loading, it is assumed that the FG coating layer becomes fully plastic and the yielding commences subsequently at the inner surface of homogenous part. Essentially, the variation of FG parameters in the radial direction is properly adjusted in order to achieve the stated yielding scenario. Furthermore, axisymmetric finite element model is performed to validate the accuracy of the analytical results. It is concluded that the elastic and plastic response of the spherical pressure vessel are influenced by grading parameters and coating behavior.

Keywords

Main Subjects

[1]           S. Suresh, A. Mortensen, 1998, Fundamentals of functionally graded materials, The Institut of Materials,
[2]           J. Aboudi, M.-J. Pindera, S. M. Arnold, Higher-order theory for functionally graded materials, Composites Part B: Engineering, Vol. 30, No. 8, pp. 777-832, 1999.
[3]           D. Annaratone, 2007, Pressure vessel design, Springer,
[4]           U. Schulz, M. Peters, F.-W. Bach, G. Tegeder, Graded coatings for thermal, wear and corrosion barriers, Materials Science and Engineering: A, Vol. 362, No. 1, pp. 61-80, 2003.
[5]           H. Bufler, The arbitrarily and the periodically laminated elastic hollow sphere: exact solutions and homogenization, Archive of Applied Mechanics, Vol. 68, No. 9, pp. 579-588, 1998.
[6]           M. Eslami, M. Babaei, R. Poultangari, Thermal and mechanical stresses in a functionally graded thick sphere, International Journal of Pressure Vessels and Piping, Vol. 82, No. 7, pp. 522-527, 2005.
[7]           L. You, J. Zhang, X. You, Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials, International Journal of Pressure Vessels and Piping, Vol. 82, No. 5, pp. 347-354, 2005.
[8]           R. Poultangari, M. Jabbari, M. Eslami, Functionally graded hollow spheres under non-axisymmetric thermo-mechanical loads, International Journal of Pressure Vessels and Piping, Vol. 85, No. 5, pp. 295-305, 2008.
[9]           Y. Chen, X. Lin, Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials, Computational Materials Science, Vol. 44, No. 2, pp. 581-587, 2008.
[10]         N. Tutuncu, B. Temel, A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres, Composite Structures, Vol. 91, No. 3, pp. 385-390, 2009.
[11]         A. Saidi, S. Atashipour, E. Jomehzadeh, Exact elasticity solutions for thick-walled fg spherical pressure vessels with linearly and exponentially varying properties, Int J Eng Trans A, Vol. 22, pp. 405-416, 2009.
[12]         M. Sadeghian, H. E. Toussi, Axisymmetric yielding of functionally graded spherical vessel under thermo-mechanical loading, Computational Materials Science, Vol. 50, No. 3, pp. 975-981, 2011.
[13]         E. Carrera, M. Soave, Use of functionally graded material layers in a two-layered pressure vessel, journal of Pressure vessel Technology, Vol. 133, No. 5, pp. 051202, 2011.
[14]         A. Parvizi, R. Naghdabadi, J. Arghavani, Analysis of Al A359/SiCp functionally graded cylinder subjected to internal pressure and temperature gradient with elastic-plastic deformation, Journal of Thermal Stresses, Vol. 34, No. 10, pp. 1054-1070, 2011.
[15]         Y. Bayat, M. Ghannad, H. Torabi, Analytical and numerical analysis for the FGM thick sphere under combined pressure and temperature loading, Archive of Applied Mechanics, Vol. 82, No. 2, pp. 229-242, 2012.
[16]         M. Z. Nejad, M. Abedi, M. H. Lotfian, M. Ghannad, An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties, Journal of mechanical science and technology, Vol. 26, No. 12, pp. 4081, 2012.
[17]         M. S. Boroujerdy, M. Eslami, Thermal buckling of piezo-FGM shallow spherical shells, Meccanica, Vol. 48, No. 4, pp. 887-899, 2013.
[18]         M. Saadatfar, M. Aghaie-Khafri, Hygrothermomagnetoelectroelastic analysis of a functionally graded magnetoelectroelastic hollow sphere resting on an elastic foundation, Smart Materials and Structures, Vol. 23, No. 3, pp. 035004, 2014.
[19]         A. Parvizi, S. Alikarami, M. Asgari, Exact solution for thermoelastoplastic behavior of thick-walled functionally graded sphere under combined pressure and temperature gradient loading, Journal of Thermal Stresses, Vol. 39, No. 9, pp. 1152-1170, 2016.
[20]         S. Alikarami, A. Parvizi, Elasto-plastic analysis and finite element simulation of thick-walled functionally graded cylinder subjected to combined pressure and thermal loading, Science and Engineering of Composite Materials.
[21]         T. Akis, Elastoplastic analysis of functionally graded spherical pressure vessels, Computational Materials Science, Vol. 46, No. 2, pp. 545-554, 2009.
[22]         S. A. Atashipour, R. Sburlati, S. R. Atashipour, Elastic analysis of thick-walled pressurized spherical vessels coated with functionally graded materials, Meccanica, Vol. 49, No. 12, pp. 2965-2978, 2014.
[23]         A. Loghman, H. Parsa, Exact solution for magneto-thermo-elastic behaviour of double-walled cylinder made of an inner FGM and an outer homogeneous layer, International Journal of Mechanical Sciences, Vol. 88, pp. 93-99, 2014.
[24]         Z. Wang, Q. Zhang, L. Xia, J. Wu, P. Liu, Thermomechanical analysis of pressure vessels with functionally graded material coating, Journal of Pressure Vessel Technology, Vol. 138, No. 1, pp. 011205, 2016.
[25]         A. Afshin, M. Zamani Nejad, K. Dastani, Transient thermoelastic analysis of FGM rotating thick cylindrical pressure vessels under arbitrary boundary and initial conditions, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 15-26, 2017.
[26]         M. Gharibi, M. Zamani Nejad, A. Hadi, Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of Frobenius, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 89-98, 2017.
[27]         R. Ghajar, M. Shokrieh, A. R. Shajari, Transient thermo-visco-elastic response of a functionally graded non-axisymmetric cylinder, Journal of Computational Applied Mechanics, Vol. 46, No. 2, pp. 191-204, 2015.
[28]         S. Timoshenko, 1934, Theory of Elasticity, McGraw-Hill,
[29]         A. Mendelson, 1968, Plasticity: theory and application, Macmillan,
[30]         A. Nayebi, S. A. Sadrabadi, FGM elastoplastic analysis under thermomechanical loading, International Journal of Pressure Vessels and Piping, Vol. 111, pp. 12-20, 2013.
Journal of Computational Applied Mechanics
Volume 50, Issue 1
Spring 2019
Pages 1-13
  • Receive Date: 17 August 2017
  • Revise Date: 09 September 2017
  • Accept Date: 15 September 2017