A Semi-analytical Approach to Elastic-plastic Stress Analysis of FGM Pressure Vessels

Document Type: Research Paper

Authors

Mechanical Engineering Department, Ferdowsi University of Mashhad

Abstract

An analytical method for predicting elastic–plastic stress distribution in a cylindrical pressure vessel has been presented. The vessel material was a ceramic/metal functionally graded material, i.e. a particle–reinforcement composite. It was assumed that the material’s plastic deformation follows an isotropic strain-hardening rule based on the von-Mises yield criterion, and that the vessel was under plane-stress conditions. The mechanical properties of the graded layer were modelled by the modified rule of mixtures. By assuming small strains, Hencky’s stress–strain relation was used to obtain the governing differential equations for the plastic region. A numerical method for solving those differential equations was then proposed that enabled the prediction of stress state within the structure. Selected finite element results were also presented to establish supporting evidence for the validation of the proposed analytical modelling approach. Similar analyses were performed and solutions for spherical pressure made of FGMs were also provided.

Keywords


[1] Chakraborty A., Gopalakrishnan S., Reddy J.N., 2003, A new beam finite element for the analysis of functionally graded materials, International Journal of Mechanical Sciences 45:519–539.

[2] Jin ZH., Paulino GH., Dodds Jr RH., 2003, Cohesive fracture modeling of elastic–plastic crack growth in functionally graded materials, Engineering Fracture Mechanics 70:1885–912.

[3] Figueiredo F., Borges L., Rochinha F., 2008, Elasto-plastic stress analysis of thick-walled FGM pipes, American Institute of Physics Conference Proceedings 973:147_52.

[4] Haghpanah Jahromi B., Farrahi GH., Maleki M., Nayeb-Hashemi H., Vaziri A., 2009, Residual stresses in autofrettaged vessel made of functionally graded material, Engineering Structures 31:2930–5.

[5] Haghpanah Jahromi B., Ajdari A., Nayeb-Hashemi H., Vaziri A., 2010, Autofrettage of layered and functionally graded metal–ceramic composite vessels, Composite Structures 92:1813–22.

[6] Jahed H., Dubey RN., 1997, An axisymmetric method of elastic-plastic analysis capable of predicting residual stress field, Journal of Pressure Vessel Technology 119:264–73

[7] Jahed H., Farshi B., Karimi M., 2006, Optimum autofrettage and shrink-fit combination in multi-layer cylinders, Journal of Pressure Vessel Technology 128:196–201.

[8] Jahed H., Farshi B., Bidabadi J., 2005, Minimum weight design of inhomogeneous rotating discs, International Journal of Pressure Vessels and Piping 82:35–41.

[9] Jahed H., Shirazi R., 2001, Loading and unloading behaviour of a thermoplastic disc, International Journal of Pressure Vessels and Piping 78:637–45.

[10] You LH., Zhang JJ., You XY., 2005, Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials, International Journal of Pressure Vessels and Piping 82:374–345.

[11] Dai HL., Fu YM., Dong ZM., 2006, Exact solutions for functionally graded pressure vessels in a uniform magnetic field, International Journal of Solids and Structures 43:5570–80.

[12] Chen YZ., Lin XY., 2008, Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials, Computational Materials Science 44:581–587.

[13] Sadeghian M., Ekhteraei H., 2011, Axisymmetric yielding of functionally graded spherical vessel under thermo-mechanical loading, Computational Materials Science 50:975–81.

[14] Dunne F., Petrinic N., 2006, Introduction to Computational Plasticity, Oxford University Press.

[15] Chakrabarty J., 2006, Theory of Plasticity, UK, Elsevier Butterworth Heinemann, 3rd Edition.

[16] Mendelson A., 1968, Plasticity: Theory and Application, New York, Macmillan.

[17] Suresh S., Mortensen A., 1998, Fundamentals of Functionally Graded Materials, IOM Communications Ltd.

[18] Carpenter RD., Liang WW., Paulino GH., Gibeling JC., Munir ZA., 1999, Fracture testing and analysis of a layered functionally graded Ti/TiB beam in 3-point bending, Materials Science Forum 308–311:837–42.

[19] Jamshidi N., Abouei A., Molaei R., Rezaei R., Jamshidi M., 2011, Applied Guide on MATLAB, Tehran, Abed.

[20] Karlsson., Hibbitt., Sorensen., 2008, ABAQUS/CAE, Version 6.8-1.

[21] Setoodeh A., Kalali A., Hosseini A., 2008, Numerical analysis of FGM plate by applying virtual temperature distribution, 7 th conference of Iranian aerospace society, Tehran.