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Applications of Crank-Nicolson method with ADI in laser transformation hardening

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Abstract

A two-dimensional numerical solution for pulsed laser transformation hardening is developed using the finite difference method (FDM). The FDM has been developed using Crank-Nicolson scheme which solved by using alternating-direction implicit method. If this present model was compared to the analytical solution, then the Crank-Nicolson scheme showed better results in terms of accuracy, consistency, stability, convergence, and performance than to the explicit scheme. The longer heating duration, higher laser beam intensity, and greater number of pulse had influences on increasing the maximum temperature. The repetitive heating had influences on extending the heat duration and increasing the initial temperature of domain. The shorter cooling duration in repetitive pulse produced higher maximum temperature. The thinner material’s thickness increased the cooling rate, which finally increased the possibility of austenite to transform into martensite phase. In addition, it was also found that the higher maximum temperature always reduced the cooling rate value when temperature cools down toward to the starting temperature of martensite formation. It reduced the possibility of martensite formation. It was also seen that the heat was conducted more effective to the axial direction than to the radial direction.

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Acknowledgments

We would like to thank the Malaysia Government for funding this research through the Fundamental Research Grant Scheme (FRGS). We also would like to thank the reviewers so that our manuscript becomes better.

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Authors and Affiliations

  1. Physical Oceanography and Modeling Group, Institute of Oceanography and Environment, Universiti Malaysia Terengganu, Mengabang Telipot, 21030, Kuala Terengganu, Terengganu, Malaysia

    Agus Kartono, Novan Tofany, Mohammad Fadhli Ahmad, Mustafa Mamat & Mohd Lokman Husain

  2. Department of Maritime Technology, Faculty of Maritime and Marine Sciences, Universiti Malaysia Terengganu, 21030, Kuala Terengganu, Terengganu, Malaysia

    Mohammad Fadhli Ahmad

  3. Department of Mathematics, Faculty of Sciences and Technology, Universiti Malaysia Terengganu, 21030, Kuala Terengganu, Terengganu, Malaysia

    Mustafa Mamat

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  1. Agus Kartono
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  2. Novan Tofany
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  3. Mohammad Fadhli Ahmad
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  4. Mustafa Mamat
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  5. Mohd Lokman Husain
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Correspondence to Agus Kartono.

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Kartono, A., Tofany, N., Ahmad, M.F. et al. Applications of Crank-Nicolson method with ADI in laser transformation hardening. Heat Mass Transfer 48, 2041–2057 (2012). https://doi.org/10.1007/s00231-012-1044-4

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  • DOI: https://doi.org/10.1007/s00231-012-1044-4

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