Numerical Simulation of Fracture in Coatings Subjected to Sudden Temperature Change Using Element-Free Galerkin Method

  • Sahil GargEmail author
  • Mohit Pant
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The article presented broadens the dexterity of element-free Galerkin method (EFGM) for analysis of thermal fracture in case of materials with coatings under plane stress conditions. A conjugated modeling approach developed and employed in this work by amalgamation of jump function approach and enrichment criterion. This approach allows the successful modeling of multiple weak and strong discontinuities in one domain. To distinguish the interface of two materials, jump function methodology is used, while for capturing the stress field oscillations around the crack tip are intrinsic enrichment criterion is put to use. The interaction integral scheme for thermal fracture has been modified to compensate thermal strains for generating mode-I stress intensity factors (SIFs). The effect of mechanical properties on crack under sudden temperature change is compared using three cases in which Zinc and Steel substrates are used (Steel/Zinc/Steel configuration and Zinc/Steel/Zinc configuration) and compared with results of mono-material configuration.


EFGM SIF Thermal fracture Coatings 


  1. 1.
    Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Meth Eng 37:229–256CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Lu YY, Belytschko T, Gu L (1994) A new implementation of the element element-free Galerkin method. Comput Methods Appl Mech Eng 113:397–414CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Math Comput 37:141–158CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Belytschko T, Lu YY, Gu L (1995) Crack propagation by element-free Galerkin methods. Eng Fract Mech. 51:295–315Google Scholar
  5. 5.
    Belytschko T, Krongauz Y, Fleming M, Organ D (1996) Smoothing and accelerated computations in element-free Galerkin method. J Comput Appl Math 74:111–126CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Liu GR (2003) Mesh free methods—moving beyond the finite element method. CRC Press, USAzbMATHGoogle Scholar
  7. 7.
    Cordes LW, Moran B (1996) Treatment of material discontinuity in the element free Galerkin method. Comput Methods Appl Mech Eng 139:75–89CrossRefzbMATHGoogle Scholar
  8. 8.
    Belytschko T, Gracie R (2007) On XFEM applications to dislocations and interfaces. Int J Plast 23:1721–1738CrossRefzbMATHGoogle Scholar
  9. 9.
    Krongauz Y, Belytschko T (1998) EFG approximation with discontinuous derivatives. Int J Numer Meth Eng 41:1215–1233CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Arai M, Okajima Y, Kishimoto K (2007) Mixed-mode interfacial fracture toughness for thermal barrier coating. Eng Fract Mech 74:2055–2069CrossRefGoogle Scholar
  11. 11.
    Nasri K, Abbadi M, Zenasni M, Ghammouri M, Azari Z (2014) Double crack growth analysis in the presence of a bi-material interface using XFEM and FEM modelling. Eng Fract Mech 132:189–199CrossRefGoogle Scholar
  12. 12.
    Pant M, Singh IV, Mishra BK (2010) Numerical simulation of thermo-elastic fracture problems using element free Galerkin method. Int J Mech Sci 52:1745–1755CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.National Institute of TechnologyHamirpurIndia

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