A novel 2-D mathematical modeling to determine LHP to protect the industrial transient heat treatment quenched low carbon steels bar

Abdlmanam S.A. Elmaryami; Amal A.E. Mohamed

doi:10.5937/zasmat2303327E

Authors

Abdlmanam S.A. Elmaryami The Bright Star University [BSU], El-Brega, Libya Author
Amal A.E. Mohamed University of Tobruk,Tobruk, Libya Author

DOI:

https://doi.org/10.5937/zasmat2303327E

Keywords:

heat treatment, quenching, axisymmetric steel bar, finite element, 2-D mathematical modelling, unsteady state heat transfer

Abstract

2-dimensional mathematical model of axisymmetric transient industrial quenched low carbon steel bar, to examine the influence of process history on metallurgical and material characteristics, a water-cooled model based on the finite element technique was adopted. A 2-dimensional axisymmetric mathematical model was utilized to predict temperature history and, as a result, the hardness of the quenched steel bar at any node (point). The LHP (lowest hardness point) is evaluated. In this paper, specimen points hardness was evaluated by the transformation of determined characteristic cooling time for phase conversion t8/5 to hardness. The model can be used as a guideline to design cooling approach to attain the desired microstructure and mechanical properties, for example, hardness. The mathematical model was verified and validated by comparing its hardness results to the results of commercial finite element software. The comparison demonstrates that the proposed model is reliable.

References

Abdlmanam, S.A., Elmaryami, A., Elshayeb, M., Omar, B., Basu, P., Hasan, S.B. (2013) Development of a numerical model of quenching of steel bars for determining cooling curves.Metal Science and Heat Treatment, 55(3): 216-219

https://doi.org/10.1007/s11041-013-9608-6

Abdlmanam, S.A., Elmaryami, S., Bin, H.H., Badrul, O., Mohamed, E. (2009) Unsteady state hardness prediction of industrial quenched steel bar [one and two dimensional]. in: Materials science and technology conference and exhibition, (MS & T'09), October 25-29, 2009, Pittsburgh, USA: David L. Lawrence convention centre, ISBN: 978-161567636-1, vol.3, p. 1514-1520, Code 79396, SCOPUS indexed

Abdlmanam, S.A., Hasan, S.B., Badrul, O., Elsahbi, M. (2009) Unsteady state thermal behavior of industrial quenched steel bar. in: 18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM09, Cairns, QLD; Australia, p. 1699-1705

Ahmida, M.A., Elmaryami, A.S. (2022) Investigation of using physical optical reflectivity probes in evaluating and monitoring powder mixtures of sugar and slag.Instrumentation Mesure Métrologie, 21(2): 43-48

https://doi.org/10.18280/i2m.210202

Araz, S.Ġ., Galerkin, H.D. (2018) Method for Numerical Solution of Two Dimensional Hyperbolic Boundary Value Problem with Dirichlet Conditions.Araz&Durur/Kırklareli University Journal of Engineering and Science, 4(1): 1-11

https://doi.org/10.1155/2018/7417590

Aziz, A., et al. (2019) Comparative Study of Collocation Method and Galerkin Method for Solving Nonlinear Partial Differential Equation.International Journal of Advanced Trends in Computer Science and Engineering, 8(1): 1-4

https://doi.org/10.30534/ijatcse/2019/0181.52019

Bing, X., Xiao-Wei, G., Wei-Wu, J., Miao, C., Jun, L. (2022) Galerkin free element method and its application. in: Fracture mechanics: Engineering fracture mechanics, 218, 106575

https://doi.org/10.1016/j.engfracmech.2019.106575

Budinski, K.G. (1992) Engineering Material: Properties and Selection. Prentice Hall International, 4th ed., p.285-309

Chandler, H. (1999) Hardness testing. ASM international

Cheng, H., Xing, Z., Liu, Y. (2023) The Improved Element-Free Galerkin Method for 3D Steady Convection-Diffusion-Reaction Problems with Variable Coefficients.Mathematics, 11(3): 770-770

https://doi.org/10.3390/math11030770

Ching, H.K., Yen, S.C. (2005) Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads.Composites Part B: Engineering, 36(3): 223-240

https://doi.org/10.1016/j.compositesb.2004.09.007

Elmaryami, A., Khalid, H.M., Abdulssalam, A.M., Abdulssalam, A.A., Alssafi, M.M., Abdullateef, A.S., Mohamed, Z.A. (2021) Design of a Simple Model of S. P. P. to Study the Effect of Increasing the Boiler Pressure on the Efficiency of the Model.Engineering & Technology Review, 2(1): 1-7

https://doi.org/10.47285/etr.v2i1.60

Elmaryami, A.S., Salem, A.S., Ali, S.S., Mokhtar, H.O., Khaled, R.A. (2020) Corrosion rate calculation of carbon steel (0.4% C) after subjected to thermal cycling, sea-water cooled.Journal of Multidisciplinary Engineering Science and Technology, 1(1): 28-34

https://doi.org/10.47285/etr.v1i1.44

Elmaryami, A.S. (2008) Effect of thermal cycling on hardness of plain carbon steels. in: Materials Science and Technology Conference and Exhibition, MS&T'08, Pittsburgh, PA; United States, 1(3), 1502-1514

Elmaryami, A.S. (2007) Effect of thermal cycling on the corrosion and microstructure of plain carbon steels. in: Materials science & technology conference and exhibition: MS&T'07, 6: 3771-3784

Elmaryami, A.S., Omar, B., Ali, F.A., Mohammad, S.A., Ahmad, A.K., Wael, B.E., Moftaah, A.A. (2015) Study of LHP and effect of radius in heat-treated steel 1045 bar by 1-D FEM modeling.International Journal of Engineering and Applied Sciences, 7(5): 50-58

Elmaryami, A.S., Alsoussi, A., Gomaa, M., Abd-Allah, E. (2017) Determination the cooling time, rate of cooling, jominy distance and the hardness during heat transfer of quenched steel bar.Journal of Science-Garyounis University, 38(5): 1-11

Elmaryami, A.S.A., Khalid, H.M.B., Alamaria, A., Alashebe, O., Ali, S.S., Salem, A.S., Khaled, R.A. (2021) Determination the Corrosion Rate of Carbon Steel (0.4%C) Due to Thermal Cycling, Oil Cooled.Tecnica Italiana-Italian Journal of Engineering Science, 65(1): 74-78

https://doi.org/10.18280/ti-ijes.650111

Elmaryami, A.S.A., Badrul, O. (2011) The lowest hardness point calculation by transient computer simulation of industrial steel bar quenched in oil at different austenitizing temperatures. in: International conference on management and service science, MASS, Wuhan, China: IEEE, 1: 1-6 Article number 5999335, Indexed by Ei Compendex, SCOPUS indexed

https://doi.org/10.1109/ICMSS.2011.5999335

Elmaryami, A.S.A., Badrul, O. (2011) Projjal Basu and Suleman Bin Haji Hasan 'Unsteady State Computer Simulation of 2 Chromium Steel at 850°C as Austenitizing Temperature Quenched in Different Medium'. in: Proceedings of the ASME 2011 International Manufacturing Science and Engineering Conference, MSEC2011, Corvallis, Oregon, USA

Elmaryami, A.S.A., Omar, B. (2012) Developing 1-D MM of axisymmetric transient quenched chromium steel to determine LHP.Journal of Metallurgy, Article ID 539823

https://doi.org/10.1155/2012/539823

Elmaryami, A.S.A., Omar, B. (2013) Transient computer simulation of industrial quenched steel bar to determine LHP of molybdenum and boron steel at 850°C as austenitizing temperature quenched in different medium.International Journal of Material Science, 8(1), 13-28

Elmaryami, A.S.A., Omar, B. (2013) Modeling the effect of radius on temperaturehistory of transient quenched boron steel.Acta Metallurgica Slovaca, 19(2): 105-111

https://doi.org/10.12776/ams.v19i2.94

Elmaryami, A.S.A., Omar, B. (2013) Effect of radius on temperature history of transient industrial quenched chromium steel-8650H by developing 1-D MM.Journal of Applied Mathematical Sciences, 7(10), 471-486

https://doi.org/10.12988/ams.2013.13041

Elmaryami, A.S.A., Badrul, O. (2011) Effect of austenitizing temperatures on hardness of two chromium steel quenched in sea water by unsteady state computer simulation. in: Materials Science & Technology [MS&T'11] Conference & Exhibition, Columbus, Ohio, USA

Elmaryami, A.S.A., Omar, B. (2011) Developing 1-D mm of axisymmetrictransient quenched molybdenum steel AISI-SAE 4037H to determinelowest hardness point.Journal of Metallurgy and Materials Science, Vol. 53, No. 3, P. 289-303

Elmaryami, A.S.A., Badrul, O. (2012) Modeling LHP in carbon steel-1045 during quenching.Journal of Mathematical Theory and Modeling, 2(12): 35-47

Elmaryami, A.S.A., Badrul, O. (2012) Determination LHP of axisymmetric transient molybdenum steel-4037H quenched in sea water by developing 1-D mathematical model.Metallurgical and Materials Engineering, vol. 18, br. 3, str. 203-221

https://doi.org/10.1155/2012/539823

Elmaryami, A.S.A., Omar, B. (2012) Modeling the lowest hardness point in a steel bar during quenching.Materials Performance and Characterization, 1(1): 1-15

https://doi.org/10.1520/MPC104386

https://doi.org/10.1520/MPC-2012-0002

Elmaryami, A.S.A., Badrul, O. (2021) Unsteady state computer simulation of 2 chromiumsteel at 925°C as austenitizing temperature to determine the lowest hardness point (LHP).Metallurgical and Materials Engineering, vol. 18, br. 2, str. 79-91

Elmaryami, A.S.A., Badrul, O. (2020) A Novel (1-D) Mathematical Modeling to Determine (E-LHP) of Industrial Transient Heat Transfer Quenched Chromium Steel 5147H, Sea Water Cooled.Tecnica Italiana-Italian Journal of Engineering Science, 64(2-4): 251-258

https://doi.org/10.18280/ti-ijes.642-419

Elmaryami, A.S.A., Badrul, O. (2012) Developing 1dimensional transient heat transfer axi-symmetric MM to predict the hardness, determination LHP and to study the effect of radius on E-LHP of industrial quenched steel bar. in: Heat Transfer Phenomena and Applications, p.153-182

https://doi.org/10.5772/51947

Elmaryami, A., Sousi, A., Saleh, W., El-Mabrouk, S., El-Mawla, A., Elshayb, M. (2019) Maximum allowable thermal stresses calculation of water tube boiler during operation.International Journal of Research-Granthaalayah, 7(7): 191-199

https://doi.org/10.29121/granthaalayah.v7.i7.2019.747

Fuhrmann, J., Hömberg, D. (1999) Numerical simulation of the surface hardening of steel.International Journal of Numerical Methods for Heat & Fluid Flow, 9(6): 705-724

https://doi.org/10.1108/09615539910286042

Heng, C., Peng, M. (2022) The Improved Element-Free Galerkin Method for 3D Helmholtz Equations.Mathematics, 10(1), 14-22

https://doi.org/10.3390/math10010014

Hoq, S.M., Sulaeman, E., Okhunov, A. (2016) Error Analysis of Heat Conduction Partial Differential Equations using Galerkin's Finite Element Method.Indian Journal of Science and Technology, 9(36), 1-6

https://doi.org/10.17485/ijst/2016/v9i36/102158

Khader, M.M., Babatin, M.M., Megahed, A.M., Eid, A. (2022) Implementing the Galerkin Method Associated with the Shifted Vieta-Lucas Polynomials for Studying Numerically the Bionanofluid Flow Which Is Saturated by Gyrotactic Microorganisms over a Slippery Stretching Sheet.Journal of Mathematics, ID 5236196

https://doi.org/10.1155/2022/5236196

Li, Y., Li, J., Wen, P.H. (2019) Finite and infinite block Petrov-Galerkin method for cracks in functionally graded materials.Applied Mathematical Modelling, 68: 306-326

https://doi.org/10.1016/j.apm.2018.11.036

Moaveni, S. (2011) Finite element analysis theory and application with ANSYS. India: Pearson Education, 3/e

Moaveni, S. (2003) Finite element analysis. in: A brief history of the finite element method and ANSYS, Pearson Education, Inc, 6-8

Oguntala, G., Sobamowo, G. (2016) Galerkin's Method of Weighted Residual for a Convective Straight Fin with Temperature-Dependent Conductivity and Internal Heat Generation.International Journal of Engineering and Technology (IJET), 6(12), 432-442

Omar, B., Elshayeb, M., Elmaryami, A.S. (2009) The microstructures and corrosion of carbon steel after subjected to heat treatment then thermal cycling, water cooled.European Metallurgical Conference, 1(4): 1492-1495, 5th

Omar, B., Elmaryami, A.S.A. (2013) Developing 1-D MM of transient industrial quenched chromium steel-5147H to study the effect of radius on temperature history.Advanced Materials Research, 711: 115-127

https://doi.org/10.4028/www.scientific.net/AMR.711.115

Quenching, R.K. (2001) Tempering of welded steel tubular. Retrieved from: https://www. thefabricator.com/thefabricator/article/tubepipefabric ati n/quenching-and-tempering-of-welded-carbonsteel-tubulars

Rahel, R.G., Elmaryami, A.S.A., Ahmida, M.A., Ahmed, A.H.A.A. (2022) Computer simulation to determine LHP of 4 different types of transient industrial quenched molybdenum steel bars.European Journal of Engineering and Technology Research, 7(6): 51-55

https://doi.org/10.24018/ejeng.2022.7.6.2873

Sadek, L., Bataineh, A.S., Talibi, A.H., Hashim, I. (2023) The Novel Mittag-Leffler-Galerkin Method: Application to a Riccati Differential Equation of Fractional Order.Fractal and Fractional, 7(4): 302-302

https://doi.org/10.3390/fractalfract7040302

Sobamowo, G.M., Yinusa, A.A., Dere, Z.O., Saheed, R.O., Gbadamosi, R.O.O. (2022) Unsteady state heat transfer analysis of a convective-radiative rectangular fin using Laplace Transform-Galerkin weighted residual method.Journal of Engineering and Thermal Sciences, 2(2), 84-99

https://doi.org/10.21595/jets.2022.22807