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XFEM analysis of cracked orthotropic media under non-classic thermal shock

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Abstract

This paper presents a study about cracked finite orthotropic media under a non-classic thermal shock. The fully coupled generalized thermoelasticity according to the Lord–Shulman theory is considered. The eXtended finite element method in conjunction with the Newmark scheme is used to solve the problem numerically. The thermal stress intensity factors (TSIFs) are determined using the interaction integral method. In several examples, the relevant aspects of the transmission of the thermal wave in a cracked orthotropic medium and its reflected wave are studied. The effect of the material orientation in addition to the crack direction and an insulated hole on the time history of TSIFs and temperature distribution is discussed in detail.

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References

  1. Babaei M, Chen Z. Hyperbolic heat conduction in a functionally graded hollow sphere. Int J Thermophys. 2008;29(4):1457–69.

    CAS  Google Scholar 

  2. Huberman S, Duncan RA, Chen K, et al. Observation of second sound in graphite at temperatures above 100 k. Science. 2019;364(6438):375–9.

    CAS  PubMed  Google Scholar 

  3. Bodineau T, Gallagher I, Saint-Raymond L. A microscopic view of the Fourier law. C R Phys. 2019;20(5):402–18.

    CAS  Google Scholar 

  4. Lord HW, Shulman Y. A generalized dynamical theory of thermoelasticity. J Mech Phys Solids. 1967;15(5):299–309.

    Google Scholar 

  5. Bowie O, Freese C. Central crack in plane orthotropic rectangular sheet. Int J Fract Mech. 1972;8(1):49–57.

    Google Scholar 

  6. Hoenig A. Near-tip behavior of a crack in a plane anisotropic elastic body. Eng Fract Mech. 1982;16(3):393–403.

    Google Scholar 

  7. Sih GC, Paris PC, Irwin GR. On cracks in rectilinearly anisotropic bodies. Int J Fract Mech. 1965;1(3):189–203.

    CAS  Google Scholar 

  8. Wawrzynek PA, Ingraffea A. Interactive finite element analysis of fracture processes: an integrated approach. Theor Appl Fract Mech. 1987;8(2):137–50.

    Google Scholar 

  9. Saouma VE, Ayari ML, Leavell DA. Mixed mode crack propagation in homogeneous anisotropic solids. Eng Fract Mech. 1987;27(2):171–84.

    Google Scholar 

  10. Saouma VE, Sikiotis ES. Stress intensity factors in anisotropic bodies using singular isoparametric elements. Eng Fract Mech. 1986;25(1):115–21.

    Google Scholar 

  11. Boone TJ, Wawrzynek PA, Ingraffea AR. Finite element modelling of fracture propagation in orthotropic materials. Eng Fract Mech. 1987;26(2):185–201.

    Google Scholar 

  12. Foschi RO, Barrett J. Stress intensity factors in anisotropic plates using singular isoparametric elements. Int J Numer Methods Eng. 1976;10(6):1281–7.

    Google Scholar 

  13. Heppler G, Hansen JS. Mixed mode fracture analysis of rectilinear anisotropic plates by high order finite elements. Int J Numer Methods Eng. 1981;17(3):445–64.

    Google Scholar 

  14. Doblare M, Espiga F, Gracia L, et al. Study of crack propagation in orthotropic materials by using the boundary element method. Eng Fract Mech. 1990;37(5):953–67.

    Google Scholar 

  15. Sollero P, Aliabadi M. Anisotropic analysis of cracks in composite laminates using the dual boundary element method. Compos Struct. 1995;31(3):229–33.

    Google Scholar 

  16. Pan E, Amadei B. Fracture mechanics analysis of cracked 2-d anisotropic media with a new formulation of the boundary element method. Int J Fract. 1996;77(2):161–74.

    Google Scholar 

  17. Garcıa F, Sáez A, Domınguez J. Traction boundary elements for cracks in anisotropic solids. Eng Anal Bound Elem. 2004;28(6):667–76.

    Google Scholar 

  18. Ke CC, Chen CS, Tu CH. Determination of fracture toughness of anisotropic rocks by boundary element method. Rock Mech Rock Eng. 2006;41(4):509–38.

    Google Scholar 

  19. García-Sánchez F, Zhang C, Sáez A. A two-dimensional time-domain boundary element method for dynamic crack problems in anisotropic solids. Eng Fract Mech. 2008;75(6):1412–30.

    Google Scholar 

  20. Ke C-C, Chen C-S, Ku C-Y, et al. Modeling crack propagation path of anisotropic rocks using boundary element method. Int J Numer Anal Methods Geomech. 2009;33(9):1227–53.

    Google Scholar 

  21. Rajesh KN, Rao BN. Two-dimensional analysis of anisotropic crack problems using coupled meshless and fractal finite element method. Int J Fract. 2010;164(2):285–318.

    Google Scholar 

  22. Ghorashi SS, Mohammadi S, Sabbagh-Yazdi S-R. Orthotropic enriched element free galerkin method for fracture analysis of composites. Eng Fract Mech. 2011;78(9):1906–27.

    Google Scholar 

  23. Bui TQ, Nguyen NT, Lich LV, et al. Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods. Theor Appl Fract Mech. 2018;96:642–57.

    Google Scholar 

  24. Ghorashi SS, Valizadeh N, Mohammadi S, et al. T-spline based Xiga for fracture analysis of orthotropic media. Comput Struct. 2015;147:138–46.

    Google Scholar 

  25. Gu J, Yu T, Lich LV, et al. Adaptive orthotropic xiga for fracture analysis of composites. Compos B Eng. 2019;66:176.

    Google Scholar 

  26. Fang W, Chen X, Yu T, et al. Effects of arbitrary holes/voids on crack growth using local mesh refinement adaptive xiga. Theor Appl Fract Mech. 2020;109: 102724.

    Google Scholar 

  27. Gu J, Yu T, Lich LV, et al. Crack growth adaptive Xiga simulation in isotropic and orthotropic materials. Comput Methods Appl Mech Eng. 2020;66:365.

    Google Scholar 

  28. Asadpoure A, Mohammadi S. Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method. Int J Numer Methods Eng. 2007;69(10):2150–72.

    Google Scholar 

  29. Motamedi D, Mohammadi S. Dynamic crack propagation analysis of orthotropic media by the extended finite element method. Int J Fract. 2009;161(1):21–39.

    Google Scholar 

  30. Bui TQ, Zhang C. Extended finite element simulation of stationary dynamic cracks in piezoelectric solids under impact loading. Comput Mater Sci. 2012;62:243–57.

    Google Scholar 

  31. Hattori G, Rojas-Díaz R, Sáez A, et al. New anisotropic crack-tip enrichment functions for the extended finite element method. Comput Mech. 2012;50(5):591–601.

    Google Scholar 

  32. Bouhala L, Makradi A, Belouettar S. Thermo-anisotropic crack propagation by xfem. Int J Mech Sci. 2015;103:235–46.

    Google Scholar 

  33. Huynh HD, Nguyen MN, Cusatis G, et al. A polygonal xfem with new numerical integration for linear elastic fracture mechanics. Eng Fract Mech. 2019;213:241–63.

    Google Scholar 

  34. Nguyen NT, Bui TQ, Nguyen MN, et al. Meshfree thermomechanical crack growth simulations with new numerical integration scheme. Eng Fract Mech. 2020;235: 107121.

    Google Scholar 

  35. Yu T, Bui TQ. Numerical simulation of 2-d weak and strong discontinuities by a novel approach based on xfem with local mesh refinement. Comput Struct. 2018;196:112–33.

    Google Scholar 

  36. Zamani A, Hetnarski RB, Eslami MR. Second sound in a cracked layer based on lord–shulman theory. J Therm Stress. 2011;34(3):181–200.

    Google Scholar 

  37. Zarmehri NR, Nazari MB, Rokhi MM. Xfem analysis of a 2d cracked finite domain under thermal shock based on green-lindsay theory. Eng Fract Mech. 2018;191:286–99.

    Google Scholar 

  38. Esmati V, Nazari MB, Rokhi MM. Implementation of xfem for dynamic thermoelastic crack analysis under non-classic thermal shock. Theor Appl Fract Mech. 2018;95:42–58.

    Google Scholar 

  39. Liu P, Yu T, Bui TQ, et al. Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method. Int J Solids Struct. 2014;51(11–12):2167–82.

    Google Scholar 

  40. Burlayenko VN, Altenbach H, Sadowski T, et al. Computational simulations of thermal shock cracking by the virtual crack closure technique in a functionally graded plate. Comput Mater Sci. 2016;116:11–21.

    Google Scholar 

  41. Memari A, Azar MRK. Thermo-mechanical shock fracture analysis by meshless method. Theor Appl Fract Mech. 2019;102:171–92.

    Google Scholar 

  42. Shahsavan M, Nazari MB, Mahdizadeh RM. Dynamic analysis of cracks under thermal shock considering thermoelasticity without energy dissipation. J Therm Stress. 2019;42(5):607–28.

    Google Scholar 

  43. Nazari MB, Rokhi MM. Evaluation of sifs for cracks under thermal impact based on Green–Naghdi theory. Theor Appl Fract Mech. 2020;66:102557.

    Google Scholar 

  44. Asadpoure A, Mohammadi S, Vafai A. Crack analysis in orthotropic media using the extended finite element method. Thin-Walled Struct. 2006;44(9):1031–8.

    Google Scholar 

  45. Motamedi D, Mohammadi S. Dynamic crack propagation analysis of orthotropic media by the extended finite element method. Int J Fract. 2010;161(1):21.

    Google Scholar 

  46. Motamedi D, Mohammadi S. Fracture analysis of composites by time independent moving-crack orthotropic xfem. Int J Mech Sci. 2012;54(1):20–37.

    Google Scholar 

  47. Bayesteh H, Mohammadi S. Xfem fracture analysis of orthotropic functionally graded materials. Compos B Eng. 2013;44(1):8–25.

    Google Scholar 

  48. Nguyen MN, Bui TQ, Nguyen NT, et al. Simulation of dynamic and static thermoelastic fracture problems by extended nodal gradient finite elements. Int J Mech Sci. 2017;134:370–86.

    Google Scholar 

  49. Nguyen MN, Nguyen NT, Truong TT, et al. Thermal-mechanical crack propagation in orthotropic composite materials by the extended four-node consecutive-interpolation element (xcq4). Eng Fract Mech. 2019;206:89–113.

    Google Scholar 

  50. Toolabi M, Fallah A, Baiz P, et al. Dynamic analysis of a viscoelastic orthotropic cracked body using the extended finite element method. Eng Fract Mech. 2013;109:17–32.

    Google Scholar 

  51. Shojaee S, Asgharzadeh M, Haeri A. Crack analysis in orthotropic media using combination of isogeometric analysis and extended finite element. Int J Appl Mech. 2014;6(06):1450068.

    Google Scholar 

  52. Zarrinzadeh H, Kabir MZ, Varvani-Farahani A. Static and dynamic fracture analysis of 3d cracked orthotropic shells using xfem method. Theor Appl Fract Mech. 2020;108: 102648.

    Google Scholar 

  53. Bayat SH, Nazari MB. Thermal fracture analysis in orthotropic materials by xfem. Theor Appl Fract Mech. 2020;66:102843.

    Google Scholar 

  54. Hetnarski RB, Eslami MR. Thermal stresses: advanced theory and applications. Springer; 2009.

  55. Chen T-C, Weng C-I. Generalized coupled transient thermoelastic plane problems by laplace transform/finite element method. J Appl Mech. 1988;55(2):377–82.

    Google Scholar 

  56. Tamma KK, Railkar SB. Evaluation of thermally induced non-fourier stress wave disturbances via tailored hybrid transfinite element formulations. Comput Struct. 1990;34(1):5–16.

    Google Scholar 

  57. Tehrani PH, Eslami MR. Boundary element analysis of coupled thermoelasticity with relaxation times in finite domain. AIAA J. 2000;38(3):534–41.

    Google Scholar 

  58. Bargmann S, Steinmann P. Theoretical and computational aspects of non-classical thermoelasticity. Comput Methods Appl Mech Eng. 2006;196(1–3):516–27.

    Google Scholar 

  59. Hosseini SM, Sladek J, Sladek V. Two dimensional transient analysis of coupled non-fick diffusion–thermoelasticity based on Green–Naghdi theory using the meshless local Petrov–Galerkin (mlpg) method. Int J Mech Sci. 2014;82:74–80.

    Google Scholar 

  60. Tamma KK, Namburu RR. An effective finite element modeling/analysis approach for dynamic thermoelasticity due to second sound effects. Comput Mech. 1992;9(2):73–84.

    Google Scholar 

  61. Li C, Guo H, Tian X. Time-domain finite element analysis to nonlinear transient responses of generalized diffusion-thermoelasticity with variable thermal conductivity and diffusivity. Int J Mech Sci. 2017;131:234–44.

    Google Scholar 

  62. Kiani Y, Eslami MR. A gdq approach to thermally nonlinear generalized thermoelasticity of disks. J Therm Stress. 2017;40(1):121–33.

    Google Scholar 

  63. Hughes TJ. The finite element method: linear static and dynamic finite element analysis. Courier Corporation; 2012.

  64. Newmark NM. A method of computation for structural dynamics. J Eng Mech Div. 1959;85(3):67–94.

    Google Scholar 

  65. Kim J-H, Paulino GH. The interaction integral for fracture of orthotropic functionally graded materials: evaluation of stress intensity factors. Int J Solids Struct. 2003;40(15):3967–4001.

    Google Scholar 

  66. Pasternak I. Boundary integral equations and the boundary element method for fracture mechanics analysis in 2d anisotropic thermoelasticity. Eng Anal Bound Elem. 2012;36(12):1931–41.

    Google Scholar 

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  1. Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    Seyed Hadi Bayat & Mohammad Bagher Nazari

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  1. Seyed Hadi Bayat
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  2. Mohammad Bagher Nazari
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Correspondence to Mohammad Bagher Nazari.

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Bayat, S.H., Nazari, M.B. XFEM analysis of cracked orthotropic media under non-classic thermal shock. J Therm Anal Calorim 147, 13161–13175 (2022). https://doi.org/10.1007/s10973-022-11549-4

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