Time-Dependent Hygro-Thermal Creep Analysis of Pressurized FGM Rotating Thick Cylindrical Shells Subjected to Uniform Magnetic Field

Document Type: Research Paper

Authors

1 Mechanical Engineering Department, Yasouj University, Yasouj, Iran

2 Mechanical Engineering Department, Yasouj University,Yasouj,Iran

3 Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

Time-dependent creep analysis is presented for the calculation of stresses and displacements of axisymmetric thick-walled cylindrical pressure vessels made of functionally graded material (FGM). For the purpose of time-dependent stress analysis in an FGM pressure vessel, material creep behavior and the solutions of the stresses at a time equal to zero (i.e. the initial stress state) are needed. This corresponds to the solution of the problem considering linear elastic behavior of the material. Therefore, using equations of equilibrium, stress–strain and strain–displacement, a differential equation for displacement is obtained and subsequently the initial elastic stresses at a time equal to zero are calculated. Assuming that the Magneto-hygro-thermoelastic creep response of the material is governed by Norton’s law, using the rate form of constitutive differential equation, the displacement rate is obtained and then the stress rates are calculated. Once the stress rates are known, the stresses at any time are calculated iteratively. The analytical solution is obtained for the plane strain condition. The pressure, inner radius and outer radius are considered to be constant and the magnetic field is uniform. Material properties are considered as power law function of the radius of the cylinder and the poisson’s ratio as constant. Following this, profiles are plotted for different values of material exponent for the radial, circumferential and effective stresses as a function of radial direction and time. The in-homogeneity exponent have significant influence on the distributions of the creep stresses.

Keywords


[1] Xie H., Dai H. L., Rao Y. N., 2013, Thermoelastic dynamic behaviors of a FGM hollow cylinder under non-axisymmetric thermo-mechanical loads, Journal of Mechanics 29: 109-120.
[2] Levyakov S. V., Kuznetsov V. V., 2014, Nonlinear stability analysis of functionally graded shells using the invariant-based triangular finite element, Journal of Applied Mathematics and Mechanics 94: 101-117.
[3] Nejad, M. Z. Fatehi, P. 2015, Exact elasto-plastic analysis of rotating thick-walled cylindrical pressure vessels made of functionally graded materials, International Journal of Engineering Science 86, 26–43.
[4] Nejad, M. Z., Jabbari, M. Ghannad, M. 2015a, Elastic analysis of FGM rotating thick truncated conical shells with axially-varying properties under non-uniform pressure loading, Composite Structures 122, 561–569.
[5] Nejad, M. Z., Jabbari, M. Ghannad, M. 2015b, Elastic analysis of rotating thick cylindrical pressure vessels under non-uniform pressure: Linear and non-linear thickness, Periodica Polytechnica- Mechanical Engineering 59, 65–73.
[6] Nejad, M. Z., Jabbari, M. Ghannad, M. 2017, A general disk form formulation for thermo-elastic analysis of functionally graded thick shells of revolution with arbitrary curvature and variable thickness, Acta Mechanica 228, 215–231.
[7] Nejad, M. Z., Rastgoo, A. Hadi, A., 2014, Exact elasto-plastic analysis of rotating disks made of functionally graded materials,” International Journal of Engineering Sciences, 85, 4757.
[8] Nejad M. Z., Jabbari M., Ghannad M., 2015c, Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under non-uniform arbitrarily pressure loading, International Journal of Engineering Science 89: 86-99.
[9] Nejad M. Z., Jabbari M., Ghannad M., 2015d, Thermo-elastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading, International Journal of Engineering Science 96: 1-18.
[10] Jabbari, M., Nejad, M. Z., Ghannad, M. 2016a, Effect of thickness profile and FG function on rotating disks under thermal and mechanical loading, Journal of Mechanics 32, 35–46.
[11] Jabbari, M., Nejad, M. Z., Ghannad, M. 2016b, Thermo-elastic analysis of axially functionally graded rotating thick truncated conical shells with varying thickness, Composites Part B- Engineering 96, 20–34.
[12] Attia Y. G., Fitzgeorge D., Pope J. A., 1954, An experimental investigation of residual stresses in hollow cylinders due to the creep produced by thermal stresses, Journal of the Mechanics and Physics of Solids 2: 238-258.
[13] Weir C. D., 1957, The creep of thick walled tube under internal pressure, Journal of Applied Mechanics 24: 464-466.
[14] Wah T., 1961, Creep collapse of cylindrical shells, Journal of the Franklin Institute 272: 45-60.
[15] Bhatnagar N. S., Gupta S. K., 1969, Analysis of thick-walled orthotropic cylinder in the theory of creep, Journal of the Physical Society of Japan 27: 1655-1662.
[16] Besseling J. F., 1962, Investigation of Transient Creep in Thick-Walled Tubes Under Axially Symmetric Loading, Springer-Verlag OHG.
[17] Pai D. H., 1967, Steady-state creep analysis of thick-walled orthotropic cylinders, International Journal of Mechanical Sciences 9: 335-348.
[18] Sankaranarayanan R., 1969, Steady creep of circular cylindrical shells under combined lateral and axial pressures, International Journal of Solids and Structures 5: 17-32.
[19] Murakami S., Iwatsuki S.h., 1969, Transient creep of circular cylindrical shells, International Journal of Mechanical Sciences 11: 897-912.
[20] Murakami S., Suzuki K., 1971, On the creep analysis of pressurized circular cylindrical shells, International Journal of Non-Linear Mechanics 6: 377-392.
[21] Sim R. G., Penny R. K., 1971, Plane strain creep behaviour of thick-walled cylinders, International Journal of Mechanical Sciences 12: 987-1009.
[22] Murakami S., Iwatsuki S.h., 1971, Steady-state creep of circular cylindrical shells, Bulletin of the JSME 73: 615-623.
[23] Kashkoli M. D., Nejad M. Z., 2014, Effect of heat flux on creep stresses of thick-walled cylindrical pressure vessels, Journal of Applied Research and Technology 12: 585-597.
[24] Bhatnagar N. S., Arya V. K., 1974, Large strain creep analysis of thick-walled cylinders, International Journal of Non-Linear Mechanics 9:127-140.
[25] Murakami S., Tanaka E., 1976, On the creep buckling of circular cylindrical shells, International Journal of Mechanical Sciences 18: 185-194.
[26] Jones N., Sullivan P. F., 1976, On the creep buckling of a long cylindrical shell, International Journal of Mechanical Sciences 18: 209-213.
[27] Arya V. K., Debnath K. K., Bhatnagar N. S., 1983, Creep analysis of orthotropic circular cylindrical shells, International Journal of Pressure Vessels and Piping 11:167-190.
[28] Loghman A., Wahab M. A., 1996, Creep damage simulation of thick-walled tubes using the theta projection concept, International Journal of Pressure Vessels and Piping 67: 105-111.
[29] Yang Y. Y., 2000, Time-dependent stress analysis in functionally graded materials, International Journal of Solids and Structures 37: 7593-7608.
[30] Gupta S. K., Pathak S., 2001, Thermo creep transition in a thick walled circular cylinder under internal pressure, Indian Journal of Pure and Applied Mathematics 32: 237-253.
[31] Jahed H., Bidabadi J., 2003, An axisymmetric method of creep analysis for primary and secondary creep, International Journal of Pressure Vessels and Piping 80: 597-606.
[32] Chen J. J., Tu Sh. T., Xuan F. Z., Wang Z. D., 2007, Creep analysis for a functionally graded cylinder subjected to internal and external pressure, The Journal of Strain Analysis for Engineering Design 42: 69-77.
[33] You L. H., Ou H., Zheng Z. Y., 2007, Creep deformations and stresses in thick-walled cylindrical vessels of functionally graded materials subjected to internal pressure, Composite Structures 78: 285-291.
[34] 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.
[35] Singh T., Gupta V. K., 2009a, Creep analysis of an internally pressurized thick cylinder made of a functionally graded composite, Journal of Strain Analysis 44: 583-594.
[36] Singh T., Gupta V. K., 2009b, Effect of material parameters on steady state creep in a thick composite cylinder subjected to internal pressure, The Journal of Engineering Research 6: 20-32.
[37] Singh T., Gupta V. K., 2010a, Modeling of creep in a thick composite cylinder subjected to internal and external pressures, International Journal of Materials Research 2: 279-286.
[38] Singh T., Gupta V. K., 2010b, Modeling steady state creep in functionally graded thick cylinder subjected to internal pressure, Journal of Composite Materials 44: 1317-1333.
[39] Nejad M. Z., Kashkoli M. D., 2014, Time-dependent thermo-creep analysis of rotating FGM thick-walled cylindrical pressure vessels under heat flux, International Journal of Engineering Science 82: 222-237.
[40] Loghman A., Ghorbanpour Arani A., Amir A. S., Vajedi A., 2010, Magnetothermoelastic creep analysis of functionally graded cylinders, International Journal of Pressure Vessels and Piping 87: 389-395.
[41] Singh T., Gupta V. K., 2011, Effect of anisotropy on steady state creep in functionally graded cylinder, Composite Structures 93: 747-758.
[42] Kashkoli M. D., Nejad M. Z., 2015, Time-dependent thermo-elastic creep analysis of thick-walled spherical pressure vessels made of functionally graded materials, Journal of Theoretical and Applied Mechanics 53:1053-1065.
[43] Dai H. L., Zheng H. Y., 2012, Creep buckling and post-buckling analyses of a viscoelastic FGM cylindrical shell with initial deflection subjected to a uniform in-plane load, Journal of Mechanics 28: 391-399.
[44] Sharma S., Sahay I., Kumar R., 2012, Creep transition in non homogeneous thick-walled circular cylinder under internal and external pressure, Applied Mathematical Sciences 122: 6075-6080.
[45] Jamian S., Sato H., Tsukamoto H., Watanabe Y., 2013, Creep analysis of functionally graded material thick-walled cylinder, Applied Mechanics and Materials 315: 867-871.
[46] Singh T., Gupta V. K., 2014, Analysis of steady state creep in whisker reinforced functionally graded thick cylinder subjected to internal pressure by considering residual stress, Mechanics of Advanced Materials and Structures 21: 384-392.
[47] Nejad M. Z., Hoseini Z., Niknejad A., Ghannad M., 2015, Steady-state creep deformations and stresses in FGM rotating thick cylindrical pressure vessels, Journal of Mechanics 31: 1-6.
[48] Kashkoli M. D., Tahan K. N., Nejad M. Z., 2017, Time-dependent thermomechanical creep behavior of FGM thick hollow cylindrical shells under non-uniform internal pressure, International Journal of Applied Mechanics 9: 750086.
[49] Kashkoli M. D., Tahan K. N., Nejad M. Z., 2017, Time-dependent creep analysis for life assessment of cylindrical vessels using first order shear deformation theory, Journal of Mechanics 33: 461-474.
[50] Sharma S., Yadav S., Sharma R., 2017, Thermal creep analysis of functionally graded thick-walled cylinder subjected to torsion and internal and external pressure, Journal of Solid Mechanics 9: 302-318.
[51] Loghman A., Shayestemoghadam H., Loghman S., 2016, Creep evolution analysis of composite cylinder made of polypropylene reinforced by functionally graded MWCNTs, Journal of Solid Mechanics 8: 372-383.
[52] Loghman A., Atabakhshian V., 2012, Semi-analytical solution for time-dependent creep analysis of rotating cylinders made of anisotropic exponentially graded material (EGM), Journal of Solid Mechanics 4: 313-326.
[53] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A. A., Loghman A., 2011, Time-dependent thermo-electro-mechanical creep behavior of radially polarized FGPM rotating cylinder, Journal of Solid Mechanics 3: 142-157.
[54] Aleayoub S. M. A., Loghman A., 2010, Creep stress redistribution analysis of thick-walled FGM spheres, Journal of Solid Mechanics 2: 115-128.