Grid Convergence Analysis of Grid-Characteristic Method on Chimera Meshes in Ultrasonic Nondestructive Testing of Railroad Rail

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

A three-dimensional direct problem of ultrasonic nondestructive testing of a railroad rail treated as a linear elastic medium is solved by applying a grid-characteristic method on curved structured Chimera and Cartesian background meshes. The algorithm involves mutual interpolation between Chimera and Cartesian meshes that takes into account the features of the transition from curved to Cartesian meshes in three-dimensional space. An analytical algorithm for generating Chimera meshes is proposed. The convergence of the developed numerical algorithms under mesh refinement in space is analyzed. A comparative analysis of the full-wave fields of the velocity modulus representing the propagation of a perturbation from its source is presented.

About the authors

A. A. Kozhemyachenko

Moscow Institute of Physics and Technology (National Research University); Scientific Research Institute for System Analysis, Russian Academy of Sciences

Email: anton-kozhemyachenko@yandex.ru
141701, Dolgoprudnyi, Moscow oblast, Russia; 117218, Moscow, Russia

A. V. Favorskaya

Moscow Institute of Physics and Technology (National Research University); Scientific Research Institute for System Analysis, Russian Academy of Sciences

Author for correspondence.
Email: favorskaya@phystech.edu
141701, Dolgoprudnyi, Moscow oblast, Russia; 117218, Moscow, Russia

References

  1. Rossini N.S., Dassisti M., Benyounis K.Y., Olabi A.G. Methods of measuring residual stresses in components // Materials & Design. 2012. V. 35. P. 572588.
  2. Hwang Y.I., Kim Y.I., Seo D.C., Seo M.K., Lee W.S., Kwon S., Kim K.B. Experimental Consideration of Conditions for Measuring Residual Stresses of Rails Using Magnetic Barkhausen Noise Method // Materials. 2021. V. 14. № 18. P. 5374.
  3. Palkowski H., Brück S., Pirling T., Carradò A. Investigation on the Residual Stress State of Drawn Tubes by Numerical Simulation and Neutron Diffraction Analysis // Materials. 2013. V. 6. № 11. P. 51185130.
  4. Kelleher J., Prime M.B., Buttle D., Mummery P., Webster P.J., Shackleton J., Withers P.J. // The Measurement of Residual Stress in Railway Rails by Diffraction and Other Methods // Journal of Neutron Research. 2003. V.11. № 4. P. 187–193.
  5. Huang H., Zhang K., Wu M., Li H., Wang M.J., Zhang S.M., Chen J.H., Wen M. Comparison between axial residual stresses measured by Raman spectroscopy and X-ray diffraction in SiC fiber reinforced titanium matrix composite // Acta Physica Sinica. 2018. V. 67. № 19. P. 267276
  6. Li Z., He J., Teng J., Wang Y. Internal Stress Monitoring of In-Service Structural Steel Members with Ultrasonic Method // Materials. 2016. V. 9. № 4. P. 223.
  7. Jia D.W., Bourse G., Chaki S., Lacrampe M.F., Robin C., Demouveau H. Investigation of stress and temperature effect on the longitudinal ultrasonic waves in polymers // Research in Nondestructive Evaluation. 2014. V. 25. № 1. P. 2029.
  8. Javadi Y., Azarib K., Ghalehbandi S.M., Roy M.J. Comparison between using longitudinal and shear waves in ultrasonic stress measurement to investigate the effect of post-weld heat-treatment on welding residual stresses // Research in Nondestructive Evaluation. 2017. V. 28 № 2. P. 101122.
  9. Hwang Y.I., Kim G., Kim Y.I., Park J.H., Choi M.Y., Kim K.B. Experimental Measurement of Residual Stress Distribution in Rail Specimens Using Ultrasonic LCR Waves // Applied Sciences. 2021. V. 11. № 19. P. 9306.
  10. Guo J., Fu H., Pan B., Kang R. Recent progress of residual stress measurement methods: A review // Chinese Journal of Aeronautics. 2021. V. 34. № 2. P. 5478.
  11. Alahakoon S., Sun Y.Q., Spiryagin M., Cole C. Rail flaw detection technologies for safer, reliable transportation: a review // J. of Dynamic Systems, Measurement, and Control. 2018. V. 140. № 2. P. 020801.
  12. Gao X., Liu Y., Li J., Gao X. Automatic recognition and positioning of wheel defects in ultrasonic B-scan image using artificial neural network and image processing // J. of Testing and Evaluation. 2019. V. 48. № 1. P. 20180545.
  13. Yu H., Li Q., Tan Y., Gan J., Wang J., Geng Y., Jia L. A Coarse-to-Fine Model for Rail Surface Defect Detection // IEEE Transactions on Instrumentation and Measurement. 2019. V. 68. № 3. P. 656666.
  14. Wu F.P., Li Q., Li S., Wu T. Train rail defect classification detection and its parameters learning method // Measurement. 2020. V. 151. № 2. P. 107246.
  15. Tang Z., Liu F.J., Guo S.H., Chang J., Zhang J.J. Evaluation of coupled finite element/meshfree method for a robust full-scale crashworthiness simulation of railway vehicles // Advances in Mechanical Engng. 2016. V. 8. № 4. P. 1687814016642954.
  16. Adak D., Pramod L.N.A., Ooi E.T., Natarajan S. A combined virtual element method and the scaled boundary finite element method for linear elastic fracture mechanics // Engng Analysis with Boundary Elements. 2020. V. 113. P. 916.
  17. Teng Z.H., Sun F., Wu S.C., Zhang Z.B., Chen T., Liao D.M. An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems // Comput. Mechanics. 2018. V. 62. № 5. P. 10871106.
  18. Wu S.C., Zhang S.Q., Xu Z.W. Thermal crack growth-based fatigue life prediction due to braking for a high-speed railway brake disc // Internat. Journal of Fatigue. 2016. V. 87. P. 359369 .
  19. Jiang S., Gu Y., Fan C., Qu W. Fracture mechanics analysis of bimaterial interface cracks using the generalized finite difference method // Theoretical and Applied Fracture Mechanics. 2021. V. 113. P. 102942.
  20. Nejad R.M., Liu Z., Ma W., Berto F. Reliability analysis of fatigue crack growth for rail steel under variable amplitude service loading conditions and wear // Internat. Journal of Fatigue. 2021. V. 152. P. 106450.
  21. Li S., Wu Y. Energy-preserving mixed finite element methods for the elastic wave equation // Appl. Math. and Comput.2022. V. 422. № 15. P. 126963.
  22. Cao J., Chen J.B. A parameter-modified method for implementing surface topography in elastic-wave finite-difference modeling // Geophysics. 2018. V. 83. № 6. P. 313–332.
  23. Duru K., Rannabauer L., Gabriel A.A., Igel H. A new discontinuous Galerkin method for elastic waves with physically motivated numerical fluxes // J. of Scientific Computing. 2021. V. 88. № 3. P. 1–32.
  24. Huang J., Hu T., Li Y., Song J., Liang S. Numerical dispersion and dissipation of the triangle-based discontinuous Galerkin method for acoustic and elastic velocity-stress equations // Computers & Geosciences. 2022. V. 159. № 1. P. 104979.
  25. Ladonkina M.E., Neklyudova O.A., Ostapenko V.V., Tishkin V.F. On the Accuracy of the Discontinuous Galerkin Method in Calculation of Shock Waves // Comput. Math. and Math. Phys. 2018. V. 58. № 8. P. 13441353.
  26. Sepehry N., Ehsani M., Asadi S., Shamshirsaz M., Nejad F.B. Fourier spectral element for simulation of vibro-acoustic modulation caused by contact nonlinearity in the beam // Thin-Walled Structures. 2022. V. 174. P. 109112.
  27. Trinh P.T., Brossier R., Métivier L., Tavard L., Virieux J. Efficient time-domain 3D elastic and viscoelastic full-waveform inversion using a spectral-element method on flexible Cartesian-based mesh. // Geophysics. 2019. V. 84. № 1. P. 61–83.
  28. Godunov S.K., Denisenko V.V., Klzuchinskii D.V., Fortova S.V., Shepelev V.V. Study of Entropy properties of Linearized Version of Godunov’s Method // Comput. Math. and Math. Phys. 2020. V. 60. № 4. P. 628640.
  29. Kovyrkina O., Ostapenko V.V. Monotonicity of the CABARET Scheme Approximating a Hyperbolic System of Conservation Laws // Comput. Math. and Math. Phys. 2018. V. 58. № 9. P. 14351450.
  30. Chukhno V.I., Usov E. CABARET Scheme as Applied to Numerical Approximation of Two-Fluid Flow Equations // Comput. Math. and Math. Phys. 2018. V. 58. № 9. P. 14511461.
  31. Gordon R., Turkel E., Gordon D. A compact three-dimensional fourth-order scheme for elasticity using the first-order formulation // Internat. Journal for Numerical Methods in Engng. V. 122. № 21. P. 6341–6360.
  32. Lu Z., Ma Y., Wang S., Zhang H., Guo J., Wan Y. Numerical simulation of seismic wave triggered by low-frequency sound source with 3D staggered-grid difference method in shallow water // Arabian Journal of Geosciences. 2021. V. 14. № 6. P. 1–8.
  33. Favorskaya A.V., Zhdanov M.S., Khokhlov N.I., Petrov I.B. Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid-characteristic method // Geophysical Prospecting. 2018. V. 66. № 8. P. 1485–1502.
  34. Khokhlov N., Favorskaya A., Stetsyuk V., Mitskovets I. Grid-characteristic method using Chimera meshes for simulation of elastic waves scattering on geological fractured zones // J. of Comput. Phys. 2021. V. 446. № 1. P. 110637.
  35. Kozhemyachenko A.A., Petrov I.B., Favorskaya A.V., Khokhlov N.I. Boundary conditions for modeling the impact of wheels on railway track // Comput. Math. and Math. Phys. 2020. V. 60. № 9. P. 1539–1554.
  36. Steger J.L. A Chimera grid scheme: advances in grid generation. American Society of Mechanical Engineers // Fluids Engng Division. 1983. V. 5. P. 55–70.
  37. Chesshire G., Henshaw W.D. Composite overlapping meshes for the solution of partial differential equations // J. of Comput. Phys. 1990. V.90. № 1. P. 1–64.
  38. Henshaw W.D., Schwendeman D.W. Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement // J. of Comput. Phys. 2008. V. 227. № 16. P. 7469–7502.
  39. Chang X.H., Ma R., Wang N.H., Zhao Z., Zhang L.P. A Parallel Implicit Hole-cutting Method Based on Background Mesh for Unstructured Chimera Grid // Computers & Fluids. 2020. V. 198. P. 104403.
  40. Favorskaya A.V., Khokhlov N.I., Petrov I.B. Grid-Characteristic Method on Joint Structured Regular and Curved Grids for Modeling Coupled Elastic and Acoustic Wave Phenomena in Objects of Complex Shape // Lobachevskii Journal of Mathematics. 2020. V. 41. № 4. P. 512–525.
  41. Favorskaya A., Khokhlov N. Accounting for curved boundaries in rocks by using curvilinear and Chimera grids // Procedia Computer Science. 2021. V. 192. P. 3787–3794.
  42. Favorskaya A.V. Simulation of the human head ultrasound study by grid-characteristic method on analytically generated curved meshes // Smart Innovation, Systems and Technologies. 2021. V. 214. P. 249–263.
  43. Favorskaya A., Khokhlov N., Sagan V., Podlesnykh D. Parallel computations by the grid-characteristic method on Chimera computational grids in 3D problems of railway non-destructive testing // Lecture Notes in Computer Science. 2022. V. 13708. P. 199–213.

Supplementary files


Copyright (c) 2023 А.А. Кожемяченко, А.В. Фаворская

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies