Thermo-Elastic and Time-Dependent Creep Evolution Behaviour of Ferritic Steel Rotating Disks using Theta Projection Concept

Document Type: Original Article


1 Young Researchers and Elite Club, Kashan Branch, Islamic Azad University, Kashan, Iran

2 Young Researchers and Elite Club, Jasb Branch, Islamic Azad University, Jasb, Iran


In this article, thermo-elastic and creep evolution behaviour of ferritic steel rotating disks with variable thickness are investigated. Four thickness profiles of uniform, convex, concave and linear are considered for the disk geometry. The material creep constitutive model is defined by the Θ projection concept, based on the experimental results existing in the literature. Loading applied is due to the inertial body force caused by the rotation and a constant temperature field throughout the disk. To achieve history of stresses and displacements, a numerical procedure using finite difference and Prandtl-Reuss relations is used. Stress and deformation histories are calculated using successive elastic solution method. In order to verify the solution approach, both composite and aluminum rotating disks were taken into account and the thermo-elastic and time-dependent creep behaviours for composite as well as the former for aluminum were obtained. Results from the current study were found to be in very good agreement with those available from literature in the area. It was shown that convex thickness profile disks display the least creep displacement, creep effective and circumferential stresses. Additionally, constant and concave thickness profiles were positively correlated with time while for linear and convex ones, it was found to have an inverse trend.  


[1]     Loghman, A., Azami, M., “A Novel Analytical-Numerical Solution for Nonlinear Time-dependent Electro-thermo Mechanical Creep Behavior of Rotating Disk Made of Piezoelectric Polymer”, Applied Mathematical Modelling, Vol. 40, 2016, pp. 4795–4811.

[2]     Daghigh, V., Daghigh, H., Loghman, A., and Simoneau, A., “Time-dependent Creep Analysis of Rotating Ferritic Steel Disk using Taylor Series and Prandtl–Reuss Relation”, International Journal of Mechanical Sciences, Vol. 77, 2013, pp. 40–46.

[3]     Deepak, D., Gupta, V. K., and Dham, A. K., “Creep Modeling in Functionally Graded Rotating Disc of Variable Thickness”, Journal of Mechanical Science and Technology,Vol. 24, 2010, pp. 2221–2232.

[4]     Bayat, M., Saleem, M., Sahari, B. B., Hamouda, A. M., and Mahdi, E., “Analysis of Functionally Graded Rotating Disks with Variable Thickness”, Mechanics Research Communications, Vol. 35, 2008, pp. 283–309.

[5]     Loghman, A., Abdollahian, M., Jafarzadeh Jazi, A., and Chorbanpour Arani, A., “Semi-analytical Solution for Electromagnetothermoelastic Creep Response of Functionally Graded Piezoelectric Rotating Disk”, International Journal of Thermal Sciences, Vol. 65, 2013, pp. 254–266.

[6]     Hosseini Kordkheili, S. A., Naghdabadi, R., “Thermoelastic Analysis of Functionally Graded Rotating Disk”, Composite Structure, Vol. 79, 2007, pp. 508–516.

[7]     Hosseini Kordkheili, S. A., Livani, M., “Thermoelastic Creep Analysis of Functionally Graded Various Thickness Rotating Disk with Temperature-dependent Material Properties”, International Journal of Pressure Vessels and Piping, Vol. 111-112, 2013, pp. 63–74.

[8]     Garg, M., Salaria, B. S., and Gupta, V. K., “Effect of Thermal Gradient on Steady State Creep in a Rotating Disk of a Variable Thickness”, Procedia Engineering, Vol. 55, 2013, pp. 542–547.

[9]     Sharma, S., Sahai, L., and Kuma, R., “Creep Transition of a Thin Rotating Annular Disk of Exponentially Variable Thickness with Inclusion and Edge Load”, Procedia Engineering, Vol. 55, 2013, pp. 542–547.

[10]  Szuwalski, K., Ustrzycka, A., “The Influence of Boundary Conditions on Optimal Shape of Annular Disk with Respect to Ductile Creep Rupture time”, European Journal of Mechanics - A/Solids, Vol. 37, 2013, pp. 79–85.

[11]  Hassani, A., Hojjati, M. H., Farrahi, G. H., and Alashti, R. A., “Semi-exact Solution for Thermo-Mechanical Analysis of Functionally Graded Elastic-strain Hardening Rotating Disks”, Communications in Nonlinear Science and Numerical Simulation, Vol. 17, 2012, pp. 3747–3762.

[12]  Loghman, A., Moradi, M., “The Analysis of Time-Dependent Creep in FGPM Thick Walled Sphere under Electro-Magneto-Thermo-Mechanical Loadings”, Mechanics of Time-Dependent Materials, Vol. 17, 2013, pp. 315–329.

[13]  Singh, S. B., “One Parameter Model for Creep in a Whisker Reinforced Anisotropic Rotating Disk of Al-SiCw Composite”, European Journal of Mechanics - A/Solids, Vol. 27, 2008, pp. 680–690.

[14]  Ghorbanpour Arani, A., Loghman, A., and Shajari, A. R., “Semi-analytical Solution of Magneto-Thermo-elastic Stresses for Functionally Graded Variable Thickness Rotating Disksˮ, Journal of Mechanical Science and Technology, Vol. 24, 2013, pp. 2107–2117.

[15]  Loghman, A., Ghorbanpour Arani, A., Shajari, A. R., and Amir, S., “Time-dependent Thermoelastic Creep Analysis of Rotating Disk Made of Al-SiC Composite”, Archive of Applied Mechanics, Vol. 81, 2011, pp. 1853–1864.

[16]  Singh, S. B., Ray, R., “Creep Analysis in an Isotropic FGM Rotating Disk of Al-SiC Composite”, Journal of Materials Processing Technology, Vol. 143-144, 2003, pp. 616–622.

[17]  Eraslan, A. N., Argeso, H., “Limit Angular Velocities of Variable Thickness Rotating Disks”, International Journal of Solids and Structures, Vol. 39, 2002, pp. 3109–3130.

[18]  Hashiguchi, K., “Time-dependent Elastoplastic Constitutive Equation”, Archives of Mechanics, Vol. 52, 2000, pp. 609-628.

[19]  Vullo, V., Vivio, F., “Elastic Stress Analysis of Non-linear Variable Thickness Rotating Disks Subjected to Thermal Load and Having Variable Density Along the Radius”, International Journal of Solids and Structures, Vol. 45, 2008, pp. 5337–5355.

[20]  Allam, M. N. M., Badr, R. E., and Tantawy, R., “Stresses of a Rotating Circular Disk of Variable Thickness Carrying a Current and Bearing a Coaxial Viscoelastic Coating”, Applied Mathematical Modelling, Vol. 32, 2008, pp. 1643–1656.

[21]  Zafarmand, H., Hassani, B., “Analysis of Two-Dimensional Functionally Graded Rotating Thick Disks with Variable Thickness”, Acta Mechanica, Vol. 225, 2014, pp. 453–464.

[22]  Apalak, M. K., Demirbas, M. D., “Thermal Residual Stresses in In-plane Functionally Graded Clamped Hollow Circular Plates Subjected to an Edge Heat Flux”, Mechanical Engineers, Part L: Journal of Materials: Design and Applications, Vol. 229, 2015, pp. 236-260.

[23]  Das, D., Sahoo, P., and Saha, K., “Dynamic Analysis of Rotating Annular Disk of Variable Thickness under Uniform Axial Pressure”, International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 13, 2012, pp. 37-59.

[24]  Alipoura, R., Farokhi Nejad, A., “Creep Behaviour Characterisation of a Ferritic Steel Alloy Based on the Modified Theta-Projection Data at an Elevated Temperature”, International Journal of Materials Research, Vol. 107, 2016, pp. 406–412.

[25]  Loghman, A., Wahab, M. A., “Creep Damage Simulation of Thick-walled Tubes using Θ Projection Concept”, International Journal of Pressure Vessels and Piping, Vol. 67, 1996, pp. 105-111.

[26]  Loghman A., Shokouhi N., “Creep Damage Evaluation of Thick-walled Spheres using a Long-Term Creep Constitutive Model”, Journal of Mechanical Science and Technology, Vol. 23, 2009, pp. 2577-2582.

[27]  Mendelson, A., “Plasticity: Theory and Applicationˮ, Krieger, New York, 1983.

[28]  Daghigh, V., Soroush, M., Nikbin, K., and Simoneau, A., “Finite Element Modeling of Tensile and Bending on Fiber Reinforced Polymer Composites”, The 3rd International Conference on Composites: Characterization, Fabrication and Application (CCFA-3), Tehran, 2012, pp. 197–198.

[29]  Daghigh, V., Sorough, M., Daghigh, H., and Nikbin, K., “Buckling Behavior of Basalt Fiber Reinforced Epoxy Composites-Experimental and Numerical Investigation”, In: Proceeding of The Bi-Annual International Conference on Experimental Solid Mechanics, Tehran, 2014, pp. 1409-1414.