Thermo-elastic creep analysis and life assessment of rotating thick pressurized cylindrical shells using third-order shear deformation theory

Document Type : Research Paper

Authors

1 Mechanical Engineering Department, Yasouj University, Yasouj, Iran.

2 Mechanical Engineering Department, Yasouj University, Yasouj, Iran

Abstract

In the present study, time-dependent thermo-elastic creep behavior and life assessment of rotating thick-walled cylindrical shells made of 304L austenitic stainless steel (304L SS) are investigated based on the third-order shear deformation theory (TSDT). Loading is composed of a uniform internal pressure, distributed temperature field, and a centrifugal body force due to rotating speed. Norton’s law is utilized as the material creep constitutive model. Using the minimum total potential energy principle, a system of differential equations in terms of displacement and boundary conditions are derived. Then, the governing equations are solved with an analytical approach, which leads to an accurate solution. Subsequently, an iterative procedure is also proposed to determine the stresses and deformations at different creep times. Larson-Miller Parameter (LMP) and Robinson's linear life fraction damage rule are employed for assessing the creep damages and the remaining life of cylindrical shells. To the best of the researcher’s knowledge, in the previous studies, there is no study carried out into third-order shear deformation theory for thermo-elastic creep analysis of cylinders. To validate the accuracy of the suggested method based on TSDT, a comparison among analytical results and those of the finite element method (FEM) is performed and very good agreement is found. The results indicate that the present analysis is accurate and computationally efficient.

Keywords

[1]           M. Z. Nejad, G. Rahimi, M. Ghannad, Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system, Mechanics, Vol. 77, No. 3, pp. 18-26, 2009.
[2]           P. Fatehi, M. Z. Nejad, Effects of material gradients on onset of yield in FGM rotating thick cylindrical shells, International Journal of Applied Mechanics, Vol. 6, No. 04, pp. 1450038, 2014.
[3]           M. Z. Nejad, M. Jabbari, M. Ghannad, A semi-analytical solution of thick truncated cones using matched asymptotic method and disk form multilayers, Archive of Mechanical Engineering, Vol. 61, No. 3, 2014.
[4]           M. Z. Nejad, P. Fatehi, Exact elasto-plastic analysis of rotating thick-walled cylindrical pressure vessels made of functionally graded materials, International Journal of Engineering Science, Vol. 86, pp. 26-43, 2015.
[5]           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.
[6]           Z. Mazarei, M. Z. Nejad, A. Hadi, Thermo-elasto-plastic analysis of thick-walled spherical pressure vessels made of functionally graded materials, International Journal of Applied Mechanics, Vol. 8, No. 04, pp. 1650054, 2016.
[7]           M. Z. Nejad, M. Jabbari, M. Ghannad, A general disk form formulation for thermo-elastic analysis of functionally graded thick shells of revolution with arbitrary curvature and variable thickness, Acta Mechanica, Vol. 228, No. 1, pp. 215-231, 2017.
[8]           M. Zamani Nejad, M. Jabbari, A. Hadi, A review of functionally graded thick cylindrical and conical shells, Journal of Computational Applied Mechanics, Vol. 48, No. 2, pp. 357-370, 2017.
[9]           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.
[10]         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.
[11]         R. Jamshidi, A. A. Jafari, Transverse sensing of simply supported truncated conical shells, Journal of Computational Applied Mechanics, Vol. 49, No. 2, pp. 212-230, 2018.
[12]         F. Ahmadi, M. Hoseini, Parametric study of nonlinear buckling capacity of short cylinders with Hemispherical heads under hydrostatic pres-sure, Journal of Computational Applied Mechanics, 2020.
[13]         M. Emadi, M. Z. Nejad, S. Ziaee, A. Hadi, Buckling analysis of arbitrary two-directional functionally graded nano-plate based on nonlocal elasticity theory using generalized differential quadrature method, Steel and Composite Structures, Vol. 39, No. 5, pp. 565-581, 2021.
[14]         T. Ebrahimi, M. Z. Nejad, H. Jahankohan, A. Hadi, Thermoelastoplastic response of FGM linearly hardening rotating thick cylindrical pressure vessels, Steel and Composite Structures, Vol. 38, No. 2, pp. 189-211, 2021.
[15]         M. M. Khoram, M. Hosseini, A. Hadi, M. Shishehsaz, Bending Analysis of Bidirectional FGM Timoshenko Nanobeam Subjected to Mechanical and Magnetic Forces and Resting on Winkler–Pasternak Foundation, International Journal of Applied Mechanics, Vol. 12, No. 08, pp. 2050093, 2020.
[16]         E. Zarezadeh, V. Hosseini, A. Hadi, Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory, Mechanics Based Design of Structures and Machines, Vol. 48, No. 4, pp. 480-495, 2020.
[17]         A. Barati, M. M. Adeli, A. Hadi, Static torsion of bi-directional functionally graded microtube based on the couple stress theory under magnetic field, International Journal of Applied Mechanics, Vol. 12, No. 02, pp. 2050021, 2020.
[18]         M. Najafzadeh, M. M. Adeli, E. Zarezadeh, A. Hadi, Torsional vibration of the porous nanotube with an arbitrary cross-section based on couple stress theory under magnetic field, Mechanics Based Design of Structures and Machines, pp. 1-15, 2020.
[19]         A. Barati, A. Hadi, M. Z. Nejad, R. Noroozi, On vibration of bi-directional functionally graded nanobeams under magnetic field, Mechanics Based Design of Structures and Machines, pp. 1-18, 2020.
[20]         K. Dehshahri, M. Z. Nejad, S. Ziaee, A. Niknejad, A. Hadi, Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates, Advances in nano research, Vol. 8, No. 2, pp. 115-134, 2020.
[21]         R. Noroozi, A. Barati, A. Kazemi, S. Norouzi, A. Hadi, Torsional vibration analysis of bi-directional FG nano-cone with arbitrary cross-section based on nonlocal strain gradient elasticity, Advances in nano research, Vol. 8, No. 1, pp. 13-24, 2020.
[22]         M. Hosseini, M. Shishesaz, A. Hadi, Thermoelastic analysis of rotating functionally graded micro/nanodisks of variable thickness, Thin-Walled Structures, Vol. 134, pp. 508-523, 2019.
[23]         M. Z. Nejad, N. Alamzadeh, A. Hadi, Thermoelastoplastic analysis of FGM rotating thick cylindrical pressure vessels in linear elastic-fully plastic condition, Composites Part B: Engineering, Vol. 154, pp. 410-422, 2018.
[24]         A. Hadi, A. Rastgoo, N. Haghighipour, A. Bolhassani, Numerical modelling of a spheroid living cell membrane under hydrostatic pressure, Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, No. 8, pp. 083501, 2018.
[25]         M. Z. Nejad, A. Hadi, A. Omidvari, A. Rastgoo, Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen's non-local elasticity theory, Structural engineering and mechanics: An international journal, Vol. 67, No. 4, pp. 417-425, 2018.
[26]         A. Hadi, M. Z. Nejad, M. Hosseini, Vibrations of three-dimensionally graded nanobeams, International Journal of Engineering Science, Vol. 128, pp. 12-23, 2018.
[27]         A. Soleimani, K. Dastani, A. Hadi, M. H. Naei, Effect of out-of-plane defects on the postbuckling behavior of graphene sheets based on nonlocal elasticity theory, Steel and Composite Structures, Vol. 30, No. 6, pp. 517-534, 2019.
[28]         M. Shishesaz, M. Hosseini, K. N. Tahan, A. Hadi, Analysis of functionally graded nanodisks under thermoelastic loading based on the strain gradient theory, Acta Mechanica, Vol. 228, No. 12, pp. 4141-4168, 2017.
[29]         A. Loghman, N. Shokouhi, Creep damage evaluation of thick-walled spheres using a long-term creep constitutive model, Journal of Mechanical Science and Technology, Vol. 23, No. 10, pp. 2577, 2009.
[30]         D. Deepak, V. Gupta, A. Dham, Creep modeling in functionally graded rotating disc of variable thickness, Journal of Mechanical science and Technology, Vol. 24, No. 11, pp. 2221-2232, 2010.
[31]         A. Loghman, A. G. Arani, A. Shajari, S. Amir, Time-dependent thermoelastic creep analysis of rotating disk made of Al–SiC composite, Archive of Applied Mechanics, Vol. 81, No. 12, pp. 1853-1864, 2011.
[32]         H. Moon, K. M. Kim, Y. H. Jeon, S. Shin, J. S. Park, H. H. Cho, Effect of thermal stress on creep lifetime for a gas turbine combustion liner, Engineering Failure Analysis, Vol. 47, pp. 34-40, 2015.
[33]         T. Bose, M. Rattan, Modeling creep behavior of thermally graded rotating disc of functionally graded material, Differential Equations and Dynamical Systems, pp. 1-14, 2017.
[34]         A. Loghman, M. Moradi, Creep damage and life assessment of thick-walled spherical reactor using Larson–Miller parameter, International Journal of Pressure Vessels and Piping, Vol. 151, pp. 11-19, 2017.
[35]         T. Bose, M. Rattan, Modeling creep analysis of thermally graded anisotropic rotating composite disc, International Journal of Applied Mechanics, Vol. 10, No. 06, pp. 1850063, 2018.
[36]         M. Bahrampour, S. Hamzeh Javaran, S. Shojaee, New insight into viscoelastic finite element modeling of time-dependent material creep problems using spherical Hankel element framework, International Journal of Applied Mechanics, Vol. 10, No. 08, pp. 1850085, 2018.
[37]         H. Mohammadi Hooyeh, A. Loghman, Creep damage and remnant life prediction of rotating hollow shaft based on the design strain and theta projection concept, Mechanics of Advanced Materials and Structures, Vol. 26, No. 11, pp. 967-974, 2019.
[38]         R. K. Desu, H. N. Krishnamurthy, A. Balu, A. K. Gupta, S. K. Singh, Mechanical properties of Austenitic Stainless Steel 304L and 316L at elevated temperatures, Journal of Materials Research and Technology, Vol. 5, No. 1, pp. 13-20, 2016.
[39]         A. Ghorbanpour Arani, R. Kolahchi, A. Mosallaie Barzoki, A. Loghman, Time-dependent thermo-electro-mechanical creep behavior of radially polarized FGPM rotating cylinder, Journal of Solid Mechanics, Vol. 3, No. 2, pp. 142-157, 2011.
[40]         H.-L. Dai, H.-J. Jiang, L. Yang, Time-dependent behaviors of a FGPM hollow sphere under the coupling of multi-fields, Solid State Sciences, Vol. 14, No. 5, pp. 587-597, 2012.
[41]         S. H. Kordkheili, M. Livani, Thermoelastic creep analysis of a functionally graded various thickness rotating disk with temperature-dependent material properties, International Journal of Pressure Vessels and Piping, Vol. 111, pp. 63-74, 2013.
[42]         M. Davoudi Kashkoli, M. Zamani Nejad, Effect of heat flux on creep stresses of thick-walled cylindrical pressure vessels, Journal of applied research and technology, Vol. 12, No. 3, pp. 585-597, 2014.
[43]         M. D. Kashkoli, M. Z. Nejad, Time-dependent thermo-elastic creep analysis of thick-walled spherical pressure vessels made of functionally graded materials, Journal of Theoretical and Applied Mechanics, Vol. 53, 2015.
[44]         H. Zharfi, H. EkhteraeiToussi, Time dependent creep analysis in thick FGM rotating disk with two-dimensional pattern of heterogeneity, International Journal of Mechanical Sciences, Vol. 140, pp. 351-360, 2018.
[45]         Y. Yang, Time-dependent stress analysis in functionally graded materials, International Journal of Solids and Structures, Vol. 37, No. 51, pp. 7593-7608, 2000.
[46]         L. You, H. Ou, Z. Zheng, Creep deformations and stresses in thick-walled cylindrical vessels of functionally graded materials subjected to internal pressure, Composite Structures, Vol. 78, No. 2, pp. 285-291, 2007.
[47]         A. Loghman, A. G. Arani, S. Amir, A. Vajedi, Magnetothermoelastic creep analysis of functionally graded cylinders, International Journal of Pressure Vessels and Piping, Vol. 87, No. 7, pp. 389-395, 2010.
[48]         T. Singh, V. Gupta, Steady-state creep analysis of a functionally graded thick cylinder subjected to internal pressure and thermal gradient, International journal of materials research, Vol. 103, No. 8, pp. 1042-1051, 2012.
[49]         T. Singh, V. Gupta, 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, Vol. 21, No. 5, pp. 384-392, 2014.
[50]         M. Nejad, Z. Hoseini, A. Niknejad, M. Ghannad, Steady-state creep deformations and stresses in FGM rotating thick cylindrical pressure vessels, Journal of Mechanics, Vol. 31, No. 1, pp. 1-6, 2015.
[51]         M. Arefi, M. Nasr, A. Loghman, Creep analysis of the FG cylinders: Time-dependent non-axisymmetric behavior, Steel and Composite Structures, Vol. 28, No. 3, pp. 331-347, 2018.
[52]         M. Moradi, A. Loghman, Non-Axisymmetric Time-Dependent Creep Analysis in a Thick-Walled Cylinder Due to the Thermo-mechanical loading, Journal of Solid Mechanics, Vol. 10, No. 4, pp. 845-863, 2018.
[53]         M. Ghannad, M. Z. Nejad, Elastic analysis of pressurized thick hollow cylindrical shells with clamped-clamped ends, Mechanics, Vol. 85, No. 5, pp. 11-18, 2010.
[54]         M. Ghannad, M. Z. Nejad, G. Rahimi, H. Sabouri, Elastic analysis of pressurized thick truncated conical shells made of functionally graded materials, Structural Engineering and Mechanics, Vol. 43, No. 1, pp. 105-126, 2012.
[55]         M. Ghannad, G. H. Rahimi, M. Z. Nejad, Determination of displacements and stresses in pressurized thick cylindrical shells with variable thickness using perturbation technique, Mechanics, Vol. 18, No. 1, pp. 14-21, 2012.
[56]         M. Ghannad, M. Z. Nejad, Elastic analysis of heterogeneous thick cylinders subjected to internal or external pressure using shear deformation theory, Acta Polytechnica Hungarica, Vol. 9, No. 6, pp. 117-136, 2012.
[57]         M. Ghannad, M. Z. Nejad, Elastic solution of pressurized clamped-clamped thick cylindrical shells made of functionally graded materials, Journal of theoretical and applied mechanics, Vol. 51, No. 4, pp. 1067-1079, 2013.
[58]         M. Ghannad, G. H. Rahimi, M. Z. Nejad, Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials, Composites Part B: Engineering, Vol. 45, No. 1, pp. 388-396, 2013.
[59]         M. Z. Nejad, M. Jabbari, M. Ghannad, Elastic analysis of FGM rotating thick truncated conical shells with axially-varying properties under non-uniform pressure loading, Composite Structures, Vol. 122, pp. 561-569, 2015.
[60]         M. Zakeri, R. Attarnejad, Numerical free vibration analysis of higher-order shear deformable beams resting on two-parameter elastic foundation, Journal of Computational Applied Mechanics, Vol. 46, No. 2, pp. 117-131, 2015.
[61]         H. Raissi, M. Shishesaz, S. Moradi, Applications of higher order shear deformation theories on stress distribution in a five layer sandwich plate, Journal of Computational Applied Mechanics, Vol. 48, No. 2, pp. 233-252, 2017.
[62]         A. Zargaripoor, A. Bahrami, M. Nikkhah Bahrami, Free vibration and buckling analysis of third-order shear deformation plate theory using exact wave propagation approach, Journal of Computational Applied Mechanics, Vol. 49, No. 1, pp. 102-124, 2018.
[63]         R. Javidi, M. Moghimi Zand, K. Dastani, Dynamics of Nonlinear rectangular plates subjected to an orbiting mass based on shear deformation plate theory, Journal of Computational Applied Mechanics, Vol. 49, No. 1, pp. 27-36, 2018.
[64]         H. Matsunaga, Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory, Composite Structures, Vol. 88, No. 4, pp. 519-531, 2009.
[65]         H.-T. Thai, S.-E. Kim, A review of theories for the modeling and analysis of functionally graded plates and shells, Composite Structures, Vol. 128, pp. 70-86, 2015.
[66]         M. Ghannad, M. Z. Nejad, G. Rahimi, Elastic solution of axisymmetric thick truncated conical shells based on first-order shear deformation theory, Mechanics, Vol. 79, No. 5, pp. 13-20, 2009.
[67]         M. Ghannad, M. Jabbari, M. Nejad, An elastic analysis for thick cylindrical pressure vessels with variable thickness, Engineering Solid Mechanics, Vol. 3, No. 2, pp. 117-130, 2015.
[68]         M. Jabbari, M. Z. Nejad, M. Ghannad, Thermo-elastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading, International journal of engineering science, Vol. 96, pp. 1-18, 2015.
[69]         M. Jabbari, M. Z. Nejad, M. Ghannad, Thermo-elastic analysis of axially functionally graded rotating thick truncated conical shells with varying thickness, Composites Part B: Engineering, Vol. 96, pp. 20-34, 2016.
[70]         M. Z. Nejad, M. Jabbari, M. Ghannad, Elastic analysis of rotating thick cylindrical pressure vessels under non-uniform pressure: linear and non-linear thickness, Periodica Polytechnica Mechanical Engineering, Vol. 59, No. 2, pp. 65-73, 2015.
[71]         A. Sofiyev, Application of the first order shear deformation theory to the solution of free vibration problem for laminated conical shells, Composite Structures, Vol. 188, pp. 340-346, 2018.
[72]         H. Gharooni, M. Ghannad, Nonlinear analysis of radially functionally graded hyperelastic cylindrical shells with axially-varying thickness and non-uniform pressure loads based on perturbation theory, Journal of Computational Applied Mechanics, Vol. 50, No. 2, pp. 324-340, 2019.
[73]         H. Gharooni, M. Ghannad, Nonlinear analytical solution of nearly incompressible hyperelastic cylinder with variable thickness under non-uniform pressure by perturbation technique, Journal of Computational Applied Mechanics, Vol. 50, No. 2, pp. 395-412, 2019.
[74]         H. R. Eipakchi, Third-order shear deformation theory for stress analysis of a thick conical shell under pressure, Journal of Mechanics of materials and structures, Vol. 5, No. 1, pp. 1-17, 2010.
[75]         M. Ghannad, H. Gharooni, Elastic analysis of pressurized thick FGM cylinders with exponential variation of material properties using TSDT, Latin American journal of solids and structures, Vol. 12, No. 6, pp. 1024-1041, 2015.
[76]         H. Gharooni, M. Ghannad, M. Z. Nejad, Thermo-elastic analysis of clamped-clamped thick FGM cylinders by using third-order shear deformation theory, Latin American Journal of Solids and Structures, Vol. 13, No. 4, pp. 750-774, 2016.
[77]         M. Jabbari, M. Zamani Nejad, M. Ghannad, Stress analysis of rotating thick truncated conical shells with variable thickness under mechanical and thermal loads, Journal of Solid Mechanics, Vol. 9, No. 1, pp. 100-114, 2017.
[78]         M. Kashkoli, K. N. Tahan, M. Nejad, Time-dependent creep analysis for life assessment of cylindrical vessels using first order shear deformation theory, Journal of Mechanics, Vol. 33, No. 4, pp. 461, 2017.
[79]         M. D. Kashkoli, M. Z. Nejad, Time-dependent creep analysis and life assessment of 304 L austenitic stainless steel thick pressurized truncated conical shells, Steel and Composite Structures, Vol. 28, No. 3, pp. 349-362, 2018.
[80]         M. D. Kashkoli, K. N. Tahan, M. Z. Nejad, Time-dependent thermomechanical creep behavior of FGM thick hollow cylindrical shells under non-uniform internal pressure, International Journal of Applied Mechanics, Vol. 9, No. 06, pp. 1750086, 2017.
[81]         M. D. Kashkoli, K. N. Tahan, M. Z. Nejad, Thermomechanical creep analysis of FGM thick cylindrical pressure vessels with variable thickness, International Journal of Applied Mechanics, Vol. 10, No. 01, pp. 1850008, 2018.
[82]         J. Jelwan, M. Chowdhry, G. Pearce, Creep life forecasting of weldment, 2011.
[83]         E. L. Robinson, Effect of temperature variation on the long-time rupture strength of steels, Trans. ASME, Vol. 77, 1952.
[84]         R. Ainsworth, P. Budden, Design and assessment of components subjected to creep, The Journal of Strain Analysis for Engineering Design, Vol. 29, No. 3, pp. 201-207, 1994.
[85]         J. Kropiwnicki, M. Hack, Improved calculation of damage due creep by more accurate time to rupture data representation, 2006.
[86]         M. Sabour, R. Bhat, Lifetime prediction in creep-fatigue environment, Materials Science-Poland, Vol. 26, No. 3, pp. 563-584, 2008.
[87]         F. V. Tahami, A. H. Daei-Sorkhabi, F. R. Biglari, Creep constitutive equations for cold-drawn 304L stainless steel, Materials Science and Engineering: A, Vol. 527, No. 18-19, pp. 4993-4999, 2010.
Volume 52, Issue 3
September 2021
Pages 366-393
  • Receive Date: 21 August 2020
  • Revise Date: 18 January 2021
  • Accept Date: 16 September 2021