Modeling and Simulations of Multi-dimensional Thermal Behaviours of Plates during Friction Stir Additive Manufacturing

Document Type : Research Paper

Authors

1 Biomedical Engineering Dept., University of Lagos, Akoka, Lagos, +234, Nigeria

2 Mechanical Engineering Dept., University of Lagos, Akoka, Lagos, +234, Nigeria

Abstract

Friction-stir additive manufacturing is a type of solid-state additive manufacturing process that involves intense shear deformation of material during material joining process. The increasing application of the novel technology requires proper understanding of the inherent thermal process. The analysis of the transient thermal behaviour in three dimensions of the welded plates in friction-stir additive manufacturing is studied using Laplace transforms method is presented. It was established from the results that the material reduces in temperature during the simulation process as the distance of the point moving heat source increases from the centerline. Also, the time needed to attain the highest temperature increases with increasing distance between the point moving heat source and the centerline. In addition, the heating and cooling rates decrease while the distance between the point moving heat source and the centerline increases. The peak temperature is approximately 1200oC but this depends on the welding conditions, heat generation the materials. The variation of shoulder heat generation rate with welding rotational speed at different welding velocities of 100-200 mm/min depicts that increasing the tool rotational speed at constant weld speed increases the heat input, whereas the heat input decreases with an increase in the weld speed at constant tool rotational speed. It was also established that the fractional heat generation rate is between 80 to 90% heat is generated at the tool shoulder and the remaining amount at other tool surfaces. However, this depends on the welding conditions. Finally, the temperature profile typical features can be observed from the obtained results at varying monitoring points, and they provide a better analysis of the prevailing factors in the heat flow model for a point moving heat source. Hence, the model and analytical solution provide the benchmark for obtaining temperature profiles for point moving heat source during the additive manufacturing process.

Keywords

[1]          M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, Vol. 39, No. 1, pp. 23-27, 2012.
[2]          H. Mohammadi, M. Ghayour, A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version of differential quadrature method, Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, Vol. 3, No. 2, pp. 47-56, 2010.
[3]          N. GHAYOUR, A. SEDAGHAT, M. MOHAMMADI, WAVE PROPAGATION APPROACH TO FLUID FILLED SUBMERGED VISCO-ELASTIC FINITE CYLINDRICAL SHELLS, JOURNAL OF AEROSPACE SCIENCE AND TECHNOLOGY (JAST), Vol. 8, No. 1, pp. -, 2011.
[4]          H. Moosavi, M. Mohammadi, A. Farajpour, S. H. Shahidi, Vibration analysis of nanorings using nonlocal continuum mechanics and shear deformable ring theory, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 1, pp. 135-140, 2011/10/01/, 2011.
[5]          A. Farajpour, M. Danesh, M. Mohammadi, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 3, pp. 719-727, 2011.
[6]          A. Farajpour, M. Mohammadi, A. Shahidi, M. Mahzoon, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 10, pp. 1820-1825, 2011.
[7]          A. G. Arani, S. Maghamikia, M. Mohammadimehr, A. Arefmanesh, Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods, Journal of mechanical science and technology, Vol. 25, No. 3, pp. 809-820, 2011.
[8]          A. Farajpour, A. Shahidi, M. Mohammadi, M. Mahzoon, Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures, Vol. 94, No. 5, pp. 1605-1615, 2012.
[9]          M. Mohammadi, M. Goodarzi, M. Ghayour, S. Alivand, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial in-plane pre-load via nonlocal elasticity theory, 2012.
[10]        M. Mohammadi, A. Farajpour, M. Goodarzi, R. Heydarshenas, Levy Type Solution for Nonlocal Thermo-Mechanical Vibration of Orthotropic Mono-Layer Graphene Sheet Embedded in an Elastic Medium, Journal of Solid Mechanics, Vol. 5, No. 2, pp. 116-132, 2013.
[11]        M. Mohammadi, M. Goodarzi, M. Ghayour, A. Farajpour, Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory, Composites Part B: Engineering, Vol. 51, pp. 121-129, 2013.
[12]        M. Mohammadi, M. Ghayour, A. Farajpour, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B: Engineering, Vol. 45, No. 1, pp. 32-42, 2013.
[13]        M. Mohammadi, A. Farajpour, M. Goodarzi, H. Mohammadi, Temperature Effect on Vibration Analysis of Annular Graphene Sheet Embedded on Visco-Pasternak Foundation Journal of Solid Mechanics, Vol. 5, No. 3, pp. 305-323, 2013.
[14]        M. Mohammadi, A. Farajpour, M. Goodarzi, H. Shehni nezhad pour, Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Materials Science, Vol. 82, pp. 510-520, 2014/02/01/, 2014.
[15]        A. Farajpour, A. Rastgoo, M. Mohammadi, Surface effects on the mechanical characteristics of microtubule networks in living cells, Mechanics Research Communications, Vol. 57, pp. 18-26, 2014/04/01/, 2014.
[16]        M. Mohammadi, A. Farajpour, A. Moradi, M. Ghayour, Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites Part B: Engineering, Vol. 56, pp. 629-637, 2014.
[17]        S. R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, Vol. 11, No. 9, pp. 1515-1540, 2014.
[18]        M. Mohammadi, A. Farajpour, M. Goodarzi, F. Dinari, Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, pp. 659-682, 2014.
[19]        M. Mohammadi, A. Moradi, M. Ghayour, A. Farajpour, Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, No. 3, pp. 437-458, 2014.
[20]        M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco-Pasternak foundation, 2014.
[21]        S. R. Asemi, A. Farajpour, H. R. Asemi, M. Mohammadi, Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM, Physica E: Low-dimensional Systems and Nanostructures, Vol. 63, pp. 169-179, 2014.
[22]        S. R. Asemi, A. Farajpour, M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Composite Structures, Vol. 116, pp. 703-712, 2014.
[23]        M. Safarabadi, M. Mohammadi, A. Farajpour, M. Goodarzi, Effect of surface energy on the vibration analysis of rotating nanobeam, 2015.
[24]        H. Asemi, S. Asemi, A. Farajpour, M. Mohammadi, Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads, Physica E: Low-dimensional Systems and Nanostructures, Vol. 68, pp. 112-122, 2015.
[25]        M. Goodarzi, M. Mohammadi, M. Khooran, F. Saadi, Thermo-Mechanical Vibration Analysis of FG Circular and Annular Nanoplate Based on the Visco-Pasternak Foundation, Journal of Solid Mechanics, Vol. 8, No. 4, pp. 788-805, 2016.
[26]        M. Baghani, M. Mohammadi, A. Farajpour, Dynamic and Stability Analysis of the Rotating Nanobeam in a Nonuniform Magnetic Field Considering the Surface Energy, International Journal of Applied Mechanics, Vol. 08, No. 04, pp. 1650048, 2016.
[27]        M. R. Farajpour, A. Rastgoo, A. Farajpour, M. Mohammadi, Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory, Micro & Nano Letters, Vol. 11, No. 6, pp. 302-307, 2016.
[28]        A. Farajpour, M. Yazdi, A. Rastgoo, M. Mohammadi, A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment, Acta Mechanica, Vol. 227, No. 7, pp. 1849-1867, 2016.
[29]        A. Farajpour, M. H. Yazdi, A. Rastgoo, M. Loghmani, M. Mohammadi, Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates, Composite Structures, Vol. 140, pp. 323-336, 2016.
[30]        M. Mohammadi, M. Safarabadi, A. Rastgoo, A. Farajpour, Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment, Acta Mechanica, Vol. 227, No. 8, pp. 2207-2232, 2016.
[31]        A. Farajpour, A. Rastgoo, M. Mohammadi, Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment, Physica B: Condensed Matter, Vol. 509, pp. 100-114, 2017.
[32]        M. Mohammadi, M. Hosseini, M. Shishesaz, A. Hadi, A. Rastgoo, Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads, European Journal of Mechanics - A/Solids, Vol. 77, pp. 103793, 2019/09/01/, 2019.
[33]        M. Mohammadi, A. Rastgoo, Nonlinear vibration analysis of the viscoelastic composite nanoplate with three directionally imperfect porous FG core, Structural Engineering and Mechanics, An Int'l Journal, Vol. 69, No. 2, pp. 131-143, 2019.
[34]        M. Mohammadi, A. Rastgoo, Primary and secondary resonance analysis of FG/lipid nanoplate with considering porosity distribution based on a nonlinear elastic medium, Mechanics of Advanced Materials and Structures, Vol. 27, No. 20, pp. 1709-1730, 2020/10/15, 2020.
[35]        M. Mohammadi, A. Farajpour, A. Moradi, M. Hosseini, Vibration analysis of the rotating multilayer piezoelectric Timoshenko nanobeam, Engineering Analysis with Boundary Elements, Vol. 145, pp. 117-131, 2022/12/01/, 2022.
[36]        D. White, Object consolidation employing friction joining, United States Patent, Vol. 1, pp. https://patents.google, 1999.
[37]        J. J. S. Dilip, G. D. J. Ram, . Additive manufacturing with friction welding and friction deposition processes, Int J Rapid Manuf, Vol. 3, pp. 56-69, 2012.
[38]        P. H. Lequeu, R. Muzzolini, J. C. Ehrstro, Power point presentation on: high performance friction stir welded structures using advanced alloys, WA: Aeromat Conf. Seattle, 2006.
[39]        J. A. Baumann, Production of energy efficient preform structures PEEPS, 2012.
[40]        S. Palanivel, H. Sidhar, R. S. Mishra, Friction stir additive manufacturing: route to high structural performance, JOM, Vol. 67, pp. 616–621, 2015.
[41]        R. S. Mishra, Z. Ma, I. Charit, Friction stir processing: a novel technique for fabrication of surface composite, Mater Sci Eng A, Vol. 341, pp. 307-310, 2003.
[42]        M. Yuqing, K. Liming, H. Chunping, Formation characteristic, microstructure, and mechanical performances of aluminium-based components by friction stir additive manufacturing, . Int J Adv Manuf Technol, Vol. 83, pp. 1637-1647, 2016.
[43]        S. Palanivel, P. Nelaturu, B. Glass, R. S. Mishra, Friction-stir additive manufacturing for high structural performance through microstructural control in an Mg based WE43 alloy. Mater Des Vol. 65, pp. 934-952, 2015.
[44]        H. Z. Yu, M. E. Jones, G. W. Brady, R. Y. Griffiths, D. Garcia, H. A. Rauch, Non-beam-based metal additive manufacturing enabled by additive friction stir deposition, Scr Mater Vol. 153, pp. 122-130, 2018.
[45]        R. S. Srivastava, S. Maheshwari, A. N. Siddiquee, T. K. Kundra, A review on recent progress in solid state friction-based metal additive manufacturing: friction stir additive techniques, Rev Solid State Mater Sci pp. 345-347, 2018.
[46]        Z. B. Hou, R. Komanduri, General Solutions for Stationary/Moving Plane Heat Source Problems in Manufacturing and Tribology, Int. J. Heat Mass Transfer, Vol. 43, No. 10, pp. 1679-1698, 2000.
[47]        Z. Hu, Z. Liu, Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method, Advances in Mathematical Physics, Vol. ID 6067854, pp. 1-16, 2020.
[48]        C. Yang, The determination of two moving heat sources in two-dimensional inverse heat problem, Applied Mathematical Modelling, Vol. 30, pp. 278–292, 2006.
[49]        M. Akbari, D. Sinton, M. Bahrami, Moving Heat Sources In A Half Space: Effect Of Source Geometry, Proceedings of the ASME 2009 Heat Transfer Summer Conferen San Francisco, California, Vol. HT2009, pp. 1-10, 2009.
[50]        T. Sajid, M. Sagheer, S. Hussain, Impact of Temperature-Dependent Heat Source/Sink and Variable Species Diffusivity on Radiative Reiner–Philippoff Fluid, Mathematical Problems in Engineering,, Vol. ID 9701860, pp. 1-16, 2020.
[51]        C. Kim, K, An analytical solution to heat conduction with a moving heat source, Journal of Mechanical Science and Technology, Vol. 25, No. 4, 2011.
[52]        Y. Ahire, M, K. P. Ghadle, Determination Of Temperature In Thin Rectangular Plate With Internal Moving Heat Source, Journal of Applied Science and Computations, Vol. VI, No. III, 2019.
[53]        Y. Ahire, M, K. P. Ghadle, Three-Dimensional Unsteady State Temperature Distribution of Thin Rectangular Plate with Moving Point Heat Source, Indian Journal of Materials Science, Vol. ID 7563215, pp. 1-7, 2016.
Volume 53, Issue 3
September 2022
Pages 363-378
  • Receive Date: 09 June 2022
  • Revise Date: 08 July 2022
  • Accept Date: 09 July 2022
  • First Publish Date: 09 July 2022